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THE AMERICAN PRACTICAL NAVIGATOR - NATHANIEL BOWDITCH

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Pub. No. 9
THE
AMERICAN
PRACTICAL NAVIGATOR
AN EPITOME OF NAVIGATION
ORIGINALLY BY
NATHANIEL BOWDITCH, LL.D.
2002 BICENTENNIAL EDITION
Prepared and published by the
NATIONAL IMAGERY AND MAPPING AGENCY
Bethesda, Maryland
© COPYRIGHT 2002 BY THE NATIONAL IMAGERY AND MAPPING AGENCY, U. S. GOVERNMENT.
NO DOMESTIC COPYRIGHT CLAIMED UNDER TITLE 17 U.S.C. ALL RIGHTS RESERVED.
*7642014014652*
NSN 7642014014652
NIMA REF. NO.
NVPUB
9
V
1
For sale by the Superintendant of Documents, U.S. Government Printing Office
Internet: bookstore.gpo.gov Phone: toll free (866) 512-1800; DC area (202) 512-1800
Fax: (202) 512-2250 Mail Stop: SSOP, Washington, DC 20402-0001
Last painting by Gilbert Stuart (1828). Considered by the family of Bowditch to be the best of
various paintings made, although it was unfinished when the artist died.
iii
NATHANIEL BOWDITCH
(1773-1838)
NathanielBowditchwasbornonMarch26,1773,in
Salem,Mass.,fourthofthesevenchildrenofshipmaster
Habakkuk Bowditch and his wife, Mary.
SincethemigrationofWilliamBowditchfrom
EnglandtotheColoniesinthe17thcentury,thefamilyhad
residedatSalem.Mostofitssons,likethoseofother
familiesinthisNewEnglandseaport,hadgonetosea,and
manyofthembecameshipmasters.NathanielBowditch
himselfsailedasmasteronhislastvoyage,andtwoofhis
brothersmetuntimelydeathswhilepursuingcareersatsea.
NathanielBowditch’sfatherissaidtohavelosttwo
shipsatsea,andbylateRevolutionarydayshereturnedto
thetradeofcooper,whichhehadlearnedinhisyouth.This
providedinsufficientincometoproperlysupplytheneeds
ofhisgrowingfamily,whowereoftenhungryandcold.For
manyyearsthenearlydestitutefamilyreceivedanannual
grantof15to20dollarsfromtheSalemMarineSociety.By
thetimeNathanielhadreachedtheageof10,thefamily’s
povertyforcedhimtoleaveschoolandjoinhisfatherinthe
cooper’s trade to help support the family.
Nathanielwasunsuccessfulasacooper,andwhenhe
wasabout12yearsofage,heenteredthefirstoftwoship-
chandleryfirmsbywhichhewasemployed.Itwasduring
thenearly10yearshewassoemployedthathisgreatmind
firstattractedpublicattention.Fromthetimehebegan
schoolBowditchhadanall-consuminginterestinlearning,
particularlymathematics.Byhismiddleteenshewasrecog-
nizedinSalemasanauthorityonthatsubject.Salembeing
primarilyashippingtown,mostoftheinhabitantssooneror
laterfoundtheirwaytotheshipchandler,andnewsofthe
brilliantyoungclerkspreaduntileventuallyitcametothe
attentionofthelearnedmenofhisday.Impressedbyhisde-
siretoeducatehimself,theysuppliedhimwithbooksthathe
mightlearnofthediscoveriesofothermen.Sincemanyof
thebestbookswerewrittenbyEuropeans,Bowditchfirst
taughthimselftheirlanguages.French,Spanish,Latin,
GreekandGermanwereamongthetwodozenormorelan-
guagesanddialectshestudiedduringhislife.Attheageof
16hebeganthestudyofNewton’sPrincipia,translating
partsofitfromtheLatin.Heevenfoundanerrorinthatclas-
sictext,andthoughlackingtheconfidencetoannounceitat
thetime,helaterpublishedhisfindingsandhadthemac-
cepted by the scientific community.
DuringtheRevolutionaryWaraprivateeroutofBeverly,
aneighboringtowntoSalem,hadtakenasoneofitsprizesan
Englishvesselwhichwascarryingthephilosophicallibraryof
afamedIrishscholar,Dr.RichardKirwan.Thebookswere
broughttotheColoniesandthereboughtbyagroupof
educatedSalemmenwhousedthemtofoundthe
PhilosophicalLibraryCompany,reputedtohavebeenthebest
librarynorthofPhiladelphiaatthetime.In1791,when
Bowditchwas18,twoHarvard-educatedministers,Rev.John
PrinceandRev.WilliamBentley,persuadedtheCompanyto
allowBowditchtheuseofitslibrary.Encouragedbythesetwo
menandathird,NathanRead,anapothecaryandalsoa
Harvardman,Bowditchstudiedtheworksofthegreatmen
whohadprecededhim,especiallythemathematiciansandthe
astronomers.Bythetimehebecameofage,thisknowledge,
acquiredwhennotworkinglonghoursatthechandlery,had
madeyoungNathanieltheoutstandingmathematicianinthe
Commonwealth, and perhaps in the country.
IntheseafaringtownofSalem,Bowditchwasdrawn
tonavigationearly,learningthesubjectattheageof13
fromanoldBritishsailor.Ayearlaterhebeganstudying
surveying,andin1794heassistedinasurveyofthetown.
At15hedevisedanalmanacreputedtohavebeenofgreat
accuracy.Hisotheryouthfulaccomplishmentsincludedthe
construction of a crude barometer and a sundial.
WhenBowditchwenttoseaattheageof21,itwasas
captain’swriterandnominalsecondmate,theofficer’sberth
beingofferedhimbecauseofhisreputationasascholar.Under
CaptainHenryPrince,theshipHenrysailedfromSaleminthe
winterof1795onwhatwastobeayear-longvoyagetotheIle
de Bourbon (now called Reunion) in the Indian Ocean.
Bowditchbeganhisseagoingcareerwhenaccuratetime
wasnotavailabletotheaveragenavalormerchantship.A
reliablemarinechronometerhadbeeninventedsome60
yearsbefore,buttheprohibitivecost,plusthelongvoyages
withoutopportunitytochecktheerrorofthetimepiece,made
thelargeinvestmentanimpracticalone.Asystemof
determininglongitudeby“lunardistance,”amethodwhich
didnotrequireanaccuratetimepiece,wasknown,butthis
productofthemindsofmathematiciansandastronomerswas
soinvolvedastobebeyondthecapabilitiesofthe
uneducatedseamenofthatday.Consequently,shipswere
navigatedbyacombinationofdeadreckoningandparallel
sailing(asystemofsailingnorthorsouthtothelatitudeofthe
destinationandtheneastorwesttothedestination).The
navigationalroutineofthetimewas“lead,log,andlookout.”
ToBowditch,themathematicalgenius,computationof
lunardistanceswasnomystery,ofcourse,buthe
recognizedtheneedforaneasiermethodofworkingthem
inordertonavigateshipsmoresafelyandefficiently.
Throughanalysisandobservation,hederivedanewand
simplified formula during his first trip.
JohnHamiltonMoore’sThePracticalNavigatorwas
theleadingnavigationaltextwhenBowditchfirstwentto
sea,andhadbeenformanyyears.Earlyinhisfirstvoyage,
iv
however,thecaptain’swriter-secondmatebeganturning
uperrorsinMoore’sbook,andbeforelonghefoundit
necessarytorecomputesomeofthetableshemostoften
usedinworkinghissights.Bowditchrecordedtheerrorshe
found,andbytheendofhissecondvoyage,madeinthe
highercapacityofsupercargo,thenewsofhisfindingsin
TheNewPracticalNavigatorhadreachedEdmundBlunt,
aprinteratNewburyport,Mass.AtBlunt’srequest,
Bowditchagreedtoparticipatewithotherlearnedmenin
thepreparationofanAmericaneditionofthethirteenth
(1798)editionofMoore’swork.ThefirstAmericanedition
waspublishedatNewburyportbyBluntin1799.This
editioncorrectedmanyoftheerrorsthatMoorehad
included.
Althoughmostoftheerrorswereoflittlesignificance
topracticalnavigationbecausetheywereerrorsinthefifth
andsixthplacesoflogarithmtables,someerrorswere
significant.Themostsignificantmistakewaslistingthe
year1800asaleapyearinthetableofthesun’sdeclination.
TheconsequencewasthatMooregavethedeclinationfor
March1,1800,as7°11'.Sincetheactualvaluewas7°33',
thecalculationofameridianaltitudewouldbeinerrorby
22 minutes of latitude, or 22 nautical miles.
Bowditch’sprincipalcontributiontothefirstAmerican
editionwashischapter“TheMethodofFindingthe
LongitudeatSea,”whichdiscussedhisnewmethodfor
computinglunardistances.Followingpublicationofthefirst
Americanedition,BluntobtainedBowditch’sservicesin
checkingtheAmericanandEnglisheditionsforfurther
errors.BluntthenpublishedasecondAmericaneditionof
Moore’sthirteentheditionin1800.Whenpreparingathird
Americaneditionforthepress,BluntdecidedthatBowditch
hadrevisedMoore’sworktosuchanextentthatBowditch
shouldbenamedasauthor.ThetitlewaschangedtoThe
NewAmericanPracticalNavigatorandthebookwas
publishedin1802asafirstedition.Bowditchvowedwhile
writingthiseditionto“putdowninthebooknothingIcan’t
teachthecrew,”anditissaidthateverymemberofhiscrew
includingthecookcouldtakealunarobservationandplot
the ship’s position.
Bowditchmadeatotaloffivetripstosea,overaperiod
ofaboutnineyears,hislastasmasterandpartownerofthe
three-mastedPutnam.Homewardboundfroma13-month
voyagetoSumatraandtheIledeFrance(nowcalled
Mauritius)thePutnamapproachedSalemharboron
December25,1803,duringathickfogwithouthavinghad
acelestialobservationsincenoononthe24th.Relying
uponhisdeadreckoning,Bowditchconnedhiswooden-
hulledshiptotheentranceoftherockyharbor,wherehe
hadthegoodfortunetogetamomentaryglimpseofEastern
Point,CapeAnn,enoughtoconfirmhisposition.The
Putnamproceededin,pastsuchhazardsas“Bowditch’s
Ledge”(namedafteragreat-grandfatherwhohadwrecked
hisshipontherockmorethanacenturybefore)and
anchoredsafelyat1900thatevening.Wordofthedaring
feat,performedwhenothermasterswerehove-tooutside
theharbor,spreadalongthecoastandaddedgreatlyto
Bowditch’sreputation.Hewas,indeed,the“practical
navigator.”
Hisstandingasamathematicianandsuccessful
shipmasterearnedhimawell-paidpositionashorewithina
matterofweeksafterhislastvoyage.Hewasinstalledas
presidentofaSalemfireandmarineinsurancecompanyat
theageof30,andduringthe20yearsheheldthatposition
thecompanyprospered.In1823heleftSalemtotakea
similarpositionwithaBostoninsurancefirm,servingthat
company with equal success until his death.
Fromthetimehefinishedthe“Navigator”until1814,
Bowditch’smathematicalandscientificpursuitsconsistedof
studiesandpapersontheorbitsofcomets,applicationsof
Napier’srules,magneticvariation,eclipses,calculationson
tides,andthechartingofSalemharbor.Inthatyear,however,he
turnedtowhatheconsideredthegreatestworkofhislife,the
translationintoEnglishofMecaniqueCeleste,byPierre
Laplace.MecaniqueCelestewasasummaryofallthethen
knownfactsabouttheworkingsoftheheavens.Bowditch
translatedfourofthefivevolumesbeforehisdeath,and
publishedthemathisownexpense.Hegavemanyformula
derivationswhichLaplacehadnotshown,andalsoincluded
furtherdiscoveriesfollowingthetimeofpublication.Hiswork
madethisinformationavailabletoAmericanastronomersand
enabledthemtopursuetheirstudiesonthebasisofthatwhich
wasalreadyknown.Continuinghisstyleofwritingforthe
learner,BowditchpresentedhisEnglishversionofMecanique
Celesteinsuchamannerthatthestudentofmathematicscould
easilytracethestepsinvolvedinreachingthemostcomplicated
conclusions.
ShortlyafterthepublicationofTheNewAmerican
PracticalNavigator,HarvardCollegehonoreditsauthor
withthepresentationofthehonorarydegreeofMasterof
Arts,andin1816thecollegemadehimanhonoraryDoctor
ofLaws.FromthetimetheHarvardgraduatesofSalemfirst
assistedhiminhisstudies,Bowditchhadagreatinterestin
thatcollege,andin1810hewaselectedoneofitsOverseers,
apositionhehelduntil1826,whenhewaselectedtothe
Corporation.During1826-27hewastheleaderofasmall
groupofmenwhosavedtheschoolfromfinancialdisasterby
forcingnecessaryeconomiesonthecollege’sreluctant
president.AtonetimeBowditchwasofferedaProfessorship
inMathematicsatHarvardbutthis,aswellassimilaroffers
fromWestPointandtheUniversityofVirginia,hedeclined.
Inallhislifehewasneverknowntohavemadeapublic
speech or to have addressed any large group of people.
ManyotherhonorscametoBowditchinrecognitionof
hisastronomical,mathematical,andmarine
accomplishments.HebecameamemberoftheAmerican
AcademyofArtsandSciences,theEastIndiaMarine
Society,theRoyalAcademyofEdinburgh,theRoyal
SocietyofLondon,theRoyalIrishAcademy,theAmerican
PhilosophicalSociety,theConnecticutAcademyofArts
v
andSciences,theBostonMarineSociety,theRoyal
AstronomicalSociety,thePalermoAcademyofScience,
and the Royal Academy of Berlin.
NathanielBowditchoutlivedallofhisbrothersand
sistersbynearly30years.HediedonMarch16,1838,in
hissixty-fifthyear.ThefollowingeulogybytheSalem
MarineSocietyindicatestheregardinwhichthisdistin-
guished American was held by his contemporaries:
“Inhisdeathapublic,anational,ahumanbenefactorhas
departed.Notthiscommunity,norourcountryonly,butthe
wholeworld,hasreasontodohonortohismemory.Whenthe
voiceofEulogyshallbestill,whenthetearofSorrowshall
ceasetoflow,nomonumentwillbeneededtokeepalivehis
memoryamongmen;butaslongasshipsshallsail,theneedle
pointtothenorth,andthestarsgothroughtheirwonted
coursesintheheavens,thenameofDr.Bowditchwillbe
reveredasofonewhohelpedhisfellow-meninatimeofneed,
whowasandisaguidetothemoverthepathlessocean,andof
one who forwarded the great interests of mankind.”
vi
Original title page ofThe New American Practical Navigator, First Edition, published in 1802.
vii
PREFACE
TheNavalObservatorylibraryinWashington,D.C.,is
unnaturallyquiet.Itisalargecircularroom,filledwith
thousandsofbooks.Itsacousticsareperfect;amere
whisperfromtheroom’sopencircularbalconycanbe
easilyheardbythosestandingonthegroundfloor.A
fountaininthecenterofthegroundfloorsoftlybreaksthe
room’ssilenceasitswaterstreamgentlysplashesintoa
smallpool.Fromthissereneroom,alibraryclerkwilllead
youintoanantechamber,beyondwhichisavault
containingtheObservatory’smostrarebooks.Inthisvault,
onecanfindanoriginal1802firsteditionoftheNew
American Practical Navigator.
Onecannotholdthissmall,delicate,slipcoveredbook
withoutbeingimpressedbythenearly200-yearunbroken
chainofpublicationthatithasenjoyed.ItsailedonU.S.
merchantmenandNavyshipsshortlyafterthequasi-war
withFranceandduringBritishimpressmentofmerchant
seamenthatledtotheWarof1812.ItsailedonU.S.Naval
vesselsduringoperationsagainstMexicointhe1840’s,on
shipsofboththeUnionandConfederatefleetsduringthe
CivilWar,andwiththeU.S.NavyinCubain1898.Itwent
aroundtheworldwiththeGreatWhiteFleet,acrossthe
NorthAtlantictoEuropeduringbothWorldWars,toAsia
duringtheKoreanandVietnamWars,andtotheMiddle
EastduringOperationDesertStorm.Ithascircledtheglobe
with countless thousands of merchant ships for 200 years.
Asnavigationalrequirementsandprocedureshave
changedthroughouttheyears,Bowditchhaschangedwith
them.Originallydevotedalmostexclusivelytocelestial
navigation,itnowalsocoversahostofmoderntopics.Itis
aspracticaltodayasitwaswhenNathanielBowditch,
masterofthePutnam,gatheredthecrewondeckandtaught
themthemathematicsinvolvedincalculatinglunar
distances.Itisthatpracticalitythathasbeenthe
publication’sgreateststrength,andthatmakesthe
publication as useful today as it was in the age of sail.
Seafarershavelongmemories.Innootherprofession
istraditionmorecloselyguarded.Eventheoldestandmost
cynicalacknowledgethespecialbondthatconnectsthose
whohavemadetheirlivelihoodplyingthesea.Thisbondis
notcomprisedofasinglestrand;rather,itisarichand
variedtapestrythatstretchesfromthepresentbacktothe
birthofournationanditsseafaringculture.Asthisbookis
apartofthattapestry,itshouldnotbelightlyregarded;
rather,itshouldbepreserved,asmuchforitshistorical
importance as for its practical utility.
Sinceantiquity,marinershavegatheredavailable
navigationinformationandputitintoatextforothersto
follow.Oneofthefirstattemptsatthisinvolvedvolumesof
SpanishandPortuguesenavigationalmanualstranslated
intoEnglishbetweenabout1550to1750.Writersand
translatorsofthetime“borrowed”freelyincompiling
navigationaltexts,apracticewhichcontinuestodaywith
works such as Sailing Directions and Pilots.
ColonialandearlyAmericannavigatorsdepended
exclusivelyonEnglishnavigationtextsbecausetherewere
noAmericaneditions.ThefirstAmericannavigationaltext,
OrthodoxalNavigation,wascompletedbyBenjamin
Hubbardin1656.ThefirstAmericannavigationtext
publishedinAmericawasCaptainThomasTruxton’s
Remarks,Instructions,andExamplesRelatingtothe
LatitudeandLongitude;alsotheVariationoftheCompass,
Etc., Etc., published in 1794.
Themostpopularnavigationaltextofthelate18th
centurywasJohnHamiltonMoore’sTheNewPractical
Navigator.EdmundM.Blunt,aNewburyportpublisher,
decidedtoissuearevisedcopyofthisworkforAmerican
navigators.BluntconvincedNathanielBowditch,alocally
famousmarinerandmathematician,toreviseandupdate
TheNewPracticalNavigator.Severalotherlearnedmen
assistedinthisrevision.Blunt’sTheNewPractical
Navigatorwaspublishedin1799.Bluntalsopublisheda
second American edition of Moore’s book in 1800.
By1802,whenBluntwasreadytopublishathird
edition,NathanielBowditchandothershadcorrectedso
manyerrorsinMoore’sworkthatBluntdecidedtoissuethe
workasafirsteditionoftheNewAmericanPractical
Navigator.Itistothat1802workthatthecurrenteditionof
theAmerican Practical Navigator traces its pedigree.
TheNewAmericanPracticalNavigatorstayedinthe
BowditchandBluntfamilyuntilthegovernmentboughtthe
copyrightin1867.EdmundM.Bluntpublishedthebook
until1833;uponhisretirement,hissons,Edmundand
George,tookoverpublication.TheelderBluntdiedin
1862;hissonEdmundfollowedin1866.Thenextyear,
1867,GeorgeBluntsoldthecopyrighttothegovernment
for$25,000.ThegovernmenthaspublishedBowditchever
since. George Blunt died in 1878.
NathanielBowditchcontinuedtocorrectandrevisethe
bookuntilhisdeathin1838.Uponhisdeath,theeditorial
responsibilityfortheAmericanPracticalNavigatorpassed
tohisson,J.IngersollBowditch.IngersollBowditch
continuededitingtheNavigatoruntilGeorgeBluntsoldthe
copyrighttothegovernment.Heoutlivedalloftheprincipals
involvedinpublishingandeditingtheNavigator,dyingin
1889.
TheU.S.governmenthaspublishedsome52editions
sinceacquiringthecopyrighttothebookthathascometo
viii
beknownsimplybyitsoriginalauthor’sname,
“Bowditch.”Sincethegovernmentbeganproduction,the
bookhasbeenknownbyitsyearofpublishing,insteadof
bytheeditionnumber.Duringarevisionin1880by
CommanderPhillipH.Cooper,USN,thenamewas
changedtoAmericanPracticalNavigator.Bowditch’s
originalmethodoftaking“lunars”wasfinallydropped
fromthebookjustaftertheturnofthe20thcentury.After
severalmorerevisionsandprintingsthroughWorldWarsI
andII,Bowditchwasextensivelyrevisedforthe1958
edition and again in 1995.
Recognizingthelimitationsoftheprintedword,andthat
computersandelectronicmediapermitustothinkaboutthe
processesofbothnavigationandpublishingincompletely
newways,NIMAhas,forthe2002edition,producedthefirst
officialCompactDisk-ReadOnlyMemory(CD-ROM)
versionofthiswork.ThisCDcontains,inadditiontothefull
textoftheprintedbook,electronicenhancementsand
additionsnotpossibleinbookform.Ourgoalistoputas
muchusefulnavigationalinformationbeforethenavigatoras
possibleinthemostunderstandableandreadableformat.We
areonlybeginningtoexplorethepossibilitiesofnew
technology in this area.
Asmuchasitisapartofhistory,Bowditchisnota
historybook.Asinpasteditions,datedmaterialhasbeen
droppedandnewmethods,technologiesandtechniquesadded
tokeeppacewiththerapidlychangingworldofnavigation.
Thechangestothiseditionareintendedtoensurethatit
remainsthepremierreferenceworkformodern,practical
marinenavigation.Thiseditionreplacesbutdoesnotcancel
formereditions,whichmayberetainedandconsultedasto
historical navigation methods not discussed herein.
PART1,FUNDAMENTALS,includesanoverviewof
thetypesandphasesofmarinenavigationandtheorgani-
zationswhichdevelop,supportandregulateit.Itincludes
chaptersrelatingtothetypes,structure,useandlimitationsof
nauticalcharts;aconciseexplanationofgeodesyandchart
datums;andasummaryofvariousnecessarynavigational
publications.
PART2,PILOTING,emphasizesthepracticalaspects
ofnavigatingavesselinrestrictedwaters,usingboth
traditional and electronic methods.
PART3,ELECTRONICNAVIGATION,explainsthe
natureofradiowavesandelectronicnavigationsystems.
Chaptersdealwitheachoftheseveralelectronicmethods
ofnavigation--satellite,LoranC,andradar,withspecial
emphasisonsatellitenavigationsystemsandelectronic
charts.
PART4,CELESTIALNAVIGATION,updatesthe
formereditionwithmoremodernterminology,anddiscusses
theuseofcalculatorsandcomputersforthesolutionofcelestial
navigation problems.
PART5,NAVIGATIONALMATHEMATICS,
remains unchanged from the former edition.
PART6,NAVIGATIONALSAFETY,discussesrecent
developmentsinmanagementofnavigationalresources,the
changingroleofthenavigator,distressandsafetycommuni-
cations,proceduresforemergencynavigation,andthe
increasingly complex web of navigation regulations.
PART7,OCEANOGRAPHY,hasbeenupdatedto
reflect the latest science and terminology.
PART8,MARINEWEATHERincorporates
updatedweatherroutinginformationandnewcloud
graphics.
Thepronoun“he,”usedthroughoutthisbookasareference
to the navigator, refers to both genders.
Theprintedversionofthisvolumemaybecorrected
usingtheNoticetoMarinersandSummaryofCorrections.
Suggestionsandcommentsforchangesandadditionsmay
be sent to:
NATIONALIMAGERYANDMAPPINGAGENCY
MARITIME SAFETY INFORMATION DIVISION
MAIL STOP D-44
4600 SANGAMORE RD.
BETHESDA, MARYLAND, 20816-5003
UNITED STATES OF AMERICA
Thisbookcouldnothavebeenproducedwithoutthe
expertiseofdedicatedpersonnelfrommanygovernment
organizations,amongthem:U.S.CoastGuard,U.S.Naval
Academy,U.S.NavalOceanographicOffice,USNavy
FleetTrainingCenter,theU.S.NavalObservatory,Office
oftheNavigatoroftheNavy,U.S.MerchantMarine
Academy,U.S.CoastandGeodeticSurvey,theNational
OceanService,andtheNationalWeatherService.In
additiontoofficialgovernmentexpertise,wemustnotethe
contributionsofprivateorganizationsandindividualsfar
toonumeroustomention.Marinersworldwidecanbe
gratefulfortheexperience,dedication,andprofessionalism
ofthemanypeoplewhogenerouslygavetheirtimeinthis
effort.Acompletelistofcontributorscanbefoundinthe
“Contributor’sCorner”oftheCD-ROMversionofthis
book.
THE EDITORS
ix
TABLE OF CONTENTS
NATHANIEL BOWDITCH...........................................................................................................................................iii
PREFACE...................................................................................................................................................................vii
PART 1 — FUNDAMENTALS
CHAPTER 1.INTRODUCTION TO MARINE NAVIGATION...........................................................................1
CHAPTER 2.GEODESY AND DATUMS IN NAVIGATION...........................................................................15
CHAPTER 3.NAUTICAL CHARTS...................................................................................................................23
CHAPTER 4.NAUTICAL PUBLICATIONS......................................................................................................51
PART 2 — PILOTING
CHAPTER 5.SHORT RANGE AIDS TO NAVIGATION..................................................................................63
CHAPTER 6.COMPASSES.................................................................................................................................81
CHAPTER 7.DEAD RECKONING.....................................................................................................................99
CHAPTER 8.PILOTING....................................................................................................................................105
CHAPTER 9.TIDES AND TIDAL CURRENTS...............................................................................................129
PART 3 — ELECTRONIC NAVIGATION
CHAPTER 10.RADIO WAVES...........................................................................................................................151
CHAPTER 11.SATELLITE NAVIGATION.......................................................................................................163
CHAPTER 12.LORAN NAVIGATION...............................................................................................................173
CHAPTER 13.RADAR NAVIGATION..............................................................................................................187
CHAPTER 14.ELECTRONIC CHARTS.............................................................................................................199
PART 4 — CELESTIAL NAVIGATION
CHAPTER 15.NAVIGATIONAL ASTRONOMY..............................................................................................217
CHAPTER 16.INSTRUMENTS FOR CELESTIAL NAVIGATION.................................................................261
CHAPTER 17.AZIMUTHS AND AMPLITUDES..............................................................................................271
CHAPTER 18.TIME.............................................................................................................................................275
CHAPTER 19.THE ALMANACS.......................................................................................................................287
CHAPTER 20.SIGHT REDUCTION...................................................................................................................295
PART 5 — NAVIGATIONAL MATHEMATICS
CHAPTER 21.NAVIGATIONAL MATHEMATICS..........................................................................................317
CHAPTER 22.CALCULATIONS AND CONVERSIONS.................................................................................329
CHAPTER 23.NAVIGATIONAL ERRORS.......................................................................................................341
CHAPTER 24.THE SAILINGS............................................................................................................................345
PART 6 — NAVIGATIONAL SAFETY
CHAPTER 25.NAVIGATION PROCESSES......................................................................................................363
CHAPTER 26.EMERGENCY NAVIGATION...................................................................................................373
CHAPTER 27.NAVIGATION REGULATIONS................................................................................................383
CHAPTER 28.MARITIME SAFETY SYSTEMS...............................................................................................393
CHAPTER 29.HYDROGRAPHY........................................................................................................................409
x
PART 7 — OCEANOGRAPHY
CHAPTER 30.THE OCEANS...........................................................................................................................425
CHAPTER 31.OCEAN CURRENTS................................................................................................................433
CHAPTER 32.WAVES, BREAKERS AND SURF..........................................................................................441
CHAPTER 33.ICE NAVIGATION...................................................................................................................453
PART 8 — MARINE METEOROLOGY
CHAPTER 34.WEATHER ELEMENTS..........................................................................................................481
CHAPTER 35.TROPICAL CYCLONES..........................................................................................................503
CHAPTER 36.WEATHER OBSERVATIONS.................................................................................................519
CHAPTER 37.WEATHER ROUTING.............................................................................................................545
NAVIGATION TABLES
EXPLANATION OF NAVIGATION TABLES.......................................................................................................557
MATHEMATICAL TABLES
TABLE 1.LOGARITHMS OF NUMBERS...............................................................................................565
TABLE 2.NATURAL TRIGONOMETRIC FUNCTIONS.......................................................................575
TABLE 3.COMMON LOGARITHMS OF TRIGONOMETRIC FUNCTIONS......................................598
TABLE 4.TRAVERSE TABLES...............................................................................................................621
CARTOGRAPHIC TABLES
TABLE 5.NATURAL AND NUMERICAL CHART SCALES...............................................................666
TABLE 6.MERIDIONAL PARTS.............................................................................................................667
TABLE 7.LENGTH OF A DEGREE OF LATITUDE AND LONGITUDE............................................672
PILOTING TABLES
TABLE 8.CONVERSION TABLE FOR METERS, FEET, AND FATHOMS........................................673
TABLE 9.CONVERSION TABLE FOR NAUTICAL AND STATUTE MILES.....................................674
TABLE 10.SPEED TABLE FOR MEASURED MILE...............................................................................675
TABLE 11.SPEED, TIME, AND DISTANCE............................................................................................676
TABLE 12.DISTANCE OF THE HORIZON..............................................................................................679
TABLE 13.GEOGRAPHIC RANGE...........................................................................................................680
TABLE 14.DIP OF THE SEA SHORT OF THE HORIZON......................................................................682
TABLE 15.DISTANCE BY VERTICAL ANGLE MEASURED BETWEEN SEA HORIZON
AND TOP OF OBJECT BEYOND SEA HORIZON................................................................683
TABLE 16.DISTANCEBYVERTICALANGLE MEASURED BETWEEN WATERLINE
AT OBJECT AND TOP OF OBJECT.......................................................................................685
TABLE 17.DISTANCE BY VERTICAL ANGLE MEASURED BETWEEN WATERLINE
AT OBJECT AND SEA HORIZON BEYOND OBJECT........................................................687
TABLE 18.DISTANCE OF AN OBJECT BY TWO BEARINGS..............................................................688
xi
CELESTIAL NAVIGATION TABLES
TABLE 19.TABLE OF OFFSETS..................................................................................................................691
TABLE 20.MERIDIAN ANGLE AND ALTITUDE OF A BODY ON THE PRIME
VERTICAL CIRCLE....................................................................................................................692
TABLE 21.LATITUDE AND LONGITUDE FACTORS..............................................................................694
TABLE 22.AMPLITUDES.............................................................................................................................698
TABLE 23.CORRECTION OF AMPLITUDE AS OBSERVED ON THE
VISIBLE HORIZON....................................................................................................................700
TABLE 24.ALTITUDE FACTORS................................................................................................................701
TABLE 25.CHANGE OF ALTITUDE IN GIVEN TIME FROM MERIDIAN TRANSIT..........................706
TABLE 26.TIME ZONES, ZONE DESCRIPTIONS, AND SUFFIXES.......................................................708
TABLE 27.ALTITUDE CORRECTION FOR AIR TEMPERATURE..........................................................709
TABLE 28.ALTITUDE CORRECTION FOR ATMOSPHERIC PRESSURE..............................................709
METEOROLOGICAL TABLES
TABLE 29.CONVERSION TABLE FOR THERMOMETER SCALES.......................................................710
TABLE 30.DIRECTION AND SPEED OF TRUE WIND IN UNITS OF SHIP'S SPEED...........................711
TABLE 31.CORRECTION OF BAROMETER READING FOR HEIGHT ABOVE SEA LEVEL.............712
TABLE 32.CORRECTION OF BAROMETER READING FOR GRAVITY...............................................712
TABLE 33.CORRECTION OF BAROMETER READING FOR TEMPERATURE...................................712
TABLE 34.CONVERSION TABLE FOR MILLIBARS, INCHES, AND MILLIMETERS
OF MERCURY.............................................................................................................................713
TABLE 35.RELATIVE HUMIDITY..............................................................................................................714
TABLE 36.DEW POINT.................................................................................................................................715
GLOSSARIES
GLOSSARY OF MARINE NAVIGATION.............................................................................................................717
GLOSSARY OF ABBREVIATIONS AND ACRONYMS......................................................................................855
INDEX
863-879
1
CHAPTER 1
INTRODUCTION TO MARINE NAVIGATION
DEFINITIONS
100. The Art And Science Of Navigation
Marinenavigationblendsbothscienceandart.Agood
navigatorconstantlythinksstrategically,operationally,and
tactically.Heplanseachvoyagecarefully.Asitproceeds,
hegathersnavigationalinformationfromavarietyof
sources,evaluatesthisinformation,anddetermineshis
ship’sposition.Hethencomparesthatpositionwithhis
voyageplan,hisoperationalcommitments,andhispre-
determined“deadreckoning”position.Agoodnavigator
anticipatesdangeroussituationswellbeforetheyarise,and
alwaysstays“aheadofthevessel.”Heisreadyfornaviga-
tionalemergenciesatanytime.Heisincreasinglya
managerofavarietyofresources--electronic,mechanical,
andhuman.Navigationmethodsandtechniquesvarywith
thetypeofvessel,theconditions,andthenavigator’s
experience.Thenavigatorusesthemethodsandtechniques
bestsuitedtothevessel,itsequipment,andconditionsat
hand.
Someimportantelementsofsuccessfulnavigation
cannotbeacquiredfromanybookorinstructor.Thescience
ofnavigationcanbetaught,buttheartofnavigationmust
be developed from experience.
101. Types of Navigation
Methodsofnavigationhavechangedthroughout
history.Newmethodsoftenenhancethemariner’sabilityto
completehisvoyagesafelyandexpeditiously,andmakehis
jobeasier.Oneofthemostimportantjudgmentsthe
navigatormustmakeinvolveschoosingthebestmethodsto
use.Eachmethodortypehasadvantagesand
disadvantages,whilenoneiseffectiveinallsituations.
Commonlyrecognizedtypesofnavigationarelistedbelow.
•Deadreckoning(DR)determinespositionby
advancingaknownpositionforcoursesand
distances.Apositionsodeterminediscalledadead
reckoning(DR)position.Itisgenerallyacceptedthat
onlycourseandspeeddeterminetheDRposition.
CorrectingtheDRpositionforleeway,current
effects,andsteeringerrorresultinanestimated
position (EP).
•Pilotinginvolvesnavigatinginrestrictedwaters
withfrequentorconstantdeterminationofposition
relativetonearbygeographicandhydrographic
features.
•Celestialnavigationinvolvesreducingcelestial
measurementstakenwithasextanttolinesof
positionusingcalculatorsorcomputerprograms,or
byhandwithalmanacsandtablesorusingspherical
trigonometry.
•Radionavigationusesradiowavestodetermine
position through a variety of electronic devices.
•Radarnavigationusesradartodeterminethe
distancefromorbearingofobjectswhosepositionis
known.Thisprocessisseparatefromradar’susein
collision avoidance.
•Satellitenavigationusesradiosignalsfrom
satellites for determining position.
Electronicsystemsandintegratedbridgeconceptsare
drivingnavigationsystemplanning.Integratedsystems
takeinputsfromvariousshipsensors,electronicallyand
automaticallycharttheposition,andprovidecontrol
signalsrequiredtomaintainavesselonapresetcourse.The
navigatorbecomesasystemmanager,choosingsystem
presets,interpretingsystemoutput,andmonitoringvessel
response.
Inpractice,anavigatorsynthesizesdifferentmethod-
ologiesintoasingleintegratedsystem.Heshouldnever
feelcomfortableutilizingonlyonemethodwhenothersare
alsoavailable.Eachmethodhasadvantagesand
disadvantages.Thenavigatormustchoosemethods
appropriatetoeachsituation,andneverrelycompletelyon
only one system.
Withtheadventofautomatedpositionfixingand
electroniccharts,modernnavigationisalmostcompletely
anelectronicprocess.Themarinerisconstantlytemptedto
relysolelyonelectronicsystems.Butelectronicnavigation
systemsarealwayssubjecttofailure,andtheprofessional
marinermustneverforgetthatthesafetyofhisshipand
crewmaydependonskillsthatdifferlittlefromthose
practicedgenerationsago.Proficiencyinconventional
piloting and celestial navigation remains essential.
2INTRODUCTION TO MARINE NAVIGATION
102. Phases of Navigation
Fourdistinctphasesdefinethenavigationprocess.The
marinershouldchoosethesystemmixthatmeetsthe
accuracy requirements of each phase.
•InlandWaterwayPhase:Pilotinginnarrowcanals,
channels, rivers, and estuaries.
•Harbor/HarborApproachPhase:Navigatingtoa
harborentrancethroughbaysandsounds,and
negotiating harbor approach channels.
•CoastalPhase:Navigatingwithin50milesofthe
coast or inshore of the 200 meter depth contour.
•OceanPhase:Navigatingoutsidethecoastalareain
the open sea.
Thenavigator’spositionaccuracyrequirements,hisfix
interval,andhissystemsrequirementsdifferineachphase.
Thefollowingtablecanbeusedasageneralguidefor
selecting the proper system(s).
NAVIGATION TERMS AND CONVENTIONS
103. Important Conventions and Concepts
Throughoutthehistoryofnavigation,numerousterms
andconventionshavebeenestablishedwhichenjoy
worldwiderecognition.Theprofessionalnavigator,togain
afullunderstandingofhisfield,shouldunderstandthe
originofcertainterms,techniques,andconventions.The
following section discusses some of the important ones.
Definingaprimemeridianisacomparativelyrecent
development.Untilthebeginningofthe19thcentury,there
waslittleuniformityamongcartographersastothe
meridianfromwhichtomeasurelongitude.Butitmattered
littlebecausethereexistednomethodfordetermining
longitude accurately.
Ptolemy,inthe2ndcenturyAD,measuredlongitude
eastwardfromareferencemeridian2degreeswestofthe
CanaryIslands.In1493,PopeAlexanderVIestablisheda
lineintheAtlanticwestoftheAzorestodividethe
territoriesofSpainandPortugal.Formanyyears,cartog-
raphersofthesetwocountriesusedthisdividinglineasthe
primemeridian.In1570theDutchcartographerOrtelius
usedtheeasternmostoftheCapeVerdeIslands.John
Davis,inhis1594TheSeaman’sSecrets,usedtheIsleof
FezintheCanariesbecausetherethevariationwaszero.
Mostmarinerspaidlittleattentiontotheseconventionsand
oftenreckonedtheirlongitudefromseveraldifferentcapes
and ports during a voyage.
ThemeridianofLondonwasusedasearlyas1676,and
overtheyearsitspopularitygrewasEngland’smaritime
interestsincreased.Thesystemofmeasuringlongitudeboth
eastandwestthrough180°mayhavefirstappearedinthe
middleofthe18thcentury.Towardtheendofthatcentury,
astheGreenwichObservatoryincreasedinprominence,
Englishcartographersbeganusingthemeridianofthat
observatoryasareference.Thepublicationbythe
ObservatoryofthefirstBritishNauticalAlmanacin1767
furtherentrenchedGreenwichastheprimemeridian.An
unsuccessfulattemptwasmadein1810toestablish
Washington,D.C.astheprimemeridianforAmerican
navigatorsandcartographers.In1884,themeridianof
Greenwichwasofficiallyestablishedastheprimemeridian.
Today,allmaritimenationshavedesignatedtheGreenwich
meridiantheprimemeridian,exceptinafewcaseswhere
local references are used for certain harbor charts.
Chartsaregraphicrepresentationsofareasofthe
Earth,indigitalorgraphicform,foruseinmarineorair
navigation.Nauticalcharts,whetherindigitalorpaper
form,depictfeaturesofparticularinteresttothemarine
navigator.Chartshaveprobablyexistedsinceatleast600
B.C.Stereographicandorthographicprojectionsdatefrom
the2ndcenturyB.C.In1569GerardusMercatorpublished
achartusingthemathematicalprinciplewhichnowbears
hisname.Some30yearslater,EdwardWrightpublished
correctedmathematicaltablesforthisprojection,enabling
othercartographerstoproducechartsontheMercator
projection. This projection is still the most widely used.
SailingDirectionsorpilotshaveexistedsinceatleast
the6thcenturyB.C.Continuousaccumulationofnaviga-
tionaldata,alongwithincreasedexplorationandtrade,led
toincreasedproductionofvolumesthroughtheMiddle
Ages.“Routiers”wereproducedinFranceabout1500;the
Englishreferredtothemas“rutters.”In1584Lucas
WaghenaerpublishedtheSpieghelderZeevaerdt(The
Mariner’sMirror),whichbecamethemodelforsuch
publicationsforseveralgenerationsofnavigators.They
were known as “Waggoners” by most sailors.
Thecompasswasdevelopedabout1000yearsago.
Theoriginofthemagneticcompassisuncertain,but
InlandHarbor/
Approach
CoastalOcean
DRXXXX
PilotingXXX
CelestialXX
RadioXXX
RadarXXX
SatelliteX*XXX
Table 102. The relationship of the types and phases of
navigation. * With SA off and/or using DGPS
INTRODUCTION TO MARINE NAVIGATION3
Norsemenuseditinthe11thcentury,andChinese
navigatorsusedthemagneticcompassatleastthatearlyand
probablymuchearlier.Itwasnotuntilthe1870sthatLord
Kelvindevelopedareliabledrycardmarinecompass.The
fluid-filled compass became standard in 1906.
Variationwasnotunderstooduntilthe18thcentury,
whenEdmondHalleyledanexpeditiontomaplinesof
variationintheSouthAtlantic.Deviationwasunderstood
atleastasearlyastheearly1600s,butadequatecorrection
ofcompasserrorwasnotpossibleuntilMatthewFlinders
discoveredthataverticalironbarcouldreducecertain
typesoferrors.After1840,BritishAstronomerRoyalSir
GeorgeAiryandlaterLordKelvindeveloped
combinationsofironmassesandsmallmagnetsto
eliminate most magnetic compass error.
Thegyrocompasswasmadenecessarybyironand
steelships.LeonFoucaultdevelopedthebasicgyroscopein
1852.AnAmerican(ElmerSperry)andaGerman(Anshutz
Kampfe)bothdevelopedelectricalgyrocompassesinthe
earlyyearsofthe20thcentury.Ringlasergyrocompasses
anddigitalfluxgatecompassesaregraduallyreplacing
traditionalgyrocompasses,whilethemagneticcompass
remains an important backup device.
Thelogisthemariner’sspeedometer.Mariners
originallymeasuredspeedbyobservingachipofwood
passingdownthesideofthevessel.Laterdevelopments
includedawoodenboardattachedtoareelofline.Mariners
measuredspeedbynotinghowmanyknotsintheline
unreeledastheshipmovedameasuredamountoftime;
hencethetermknot.Mechanicallogsusingeitherasmall
paddlewheelorarotatingspinnerarrivedaboutthemiddle
ofthe17thcentury.Thetaffraillogstillinlimitedusetoday
wasdevelopedin1878.Modernlogsuseelectronicsensors
orspinningdevicesthatinducesmallelectricfieldspropor-
tionaltoavessel’sspeed.Anenginerevolutioncounteror
shaftlogoftenmeasuresspeedaboardlargeships.Doppler
speedlogsareusedonsomevesselsforveryaccuratespeed
readings.Inertialandsatellitesystemsalsoprovidehighly
accurate speed readings.
TheMetricConversionActof1975andtheOmnibus
TradeandCompetitivenessActof1988establishedthe
metricsystemofweightsandmeasuresintheUnited
States.Asaresult,thegovernmentisconvertingchartsto
themetricformat.Notwithstandingtheconversiontothe
metricsystem,thecommonmeasureofdistanceatseaisthe
nautical mile.
ThecurrentpolicyoftheNationalImageryand
MappingAgency(NIMA)andtheNationalOcean
Service(NOS)istoconvertnewcompilationsof
nautical,specialpurposecharts,andpublicationstothe
metricsystem.Alldigitalchartsusethemetricsystem.
ThisconversionbeganonJanuary2,1970.Mostmodern
maritimenationshavealsoadoptedthemeterasthe
standardmeasureofdepthsandheights.However,older
chartsstillonissueandthechartsofsomeforeign
countries may not conform to this standard.
Thefathomasaunitoflengthordepthisofobscure
origin.Posidoniusreportedasoundingofmorethan1,000
fathomsinthe2ndcenturyB.C.Howoldtheunitwasthen
isunknown.Manymodernchartsarestillbasedonthe
fathom, as conversion to the metric system continues.
Thesailingsrefertovariousmethodsofmathemat-
icallydeterminingcourse,distance,andposition.They
haveahistoryalmostasoldasmathematicsitself.Thales,
Hipparchus,Napier,Wright,andotherscontributedthe
formulasthatpermitcomputationofcourseanddistanceby
plane,traverse,parallel,middlelatitude,Mercator,and
great circle sailings.
104. The Earth
TheEarthisanirregularoblatespheroid(asphere
flattenedatthepoles).Measurementsofitsdimensionsand
theamountofitsflatteningaresubjectsofgeodesy.
However,formostnavigationalpurposes,assuminga
sphericalEarthintroducesinsignificanterror.TheEarth’s
axisofrotationisthelineconnectingthenorthandsouth
geographic poles.
Agreatcircleisthelineofintersectionofasphereand
aplanethroughitscenter.Thisisthelargestcirclethatcan
bedrawnonasphere.Theshortestlineonthesurfaceofa
spherebetweentwopointsonthesurfaceispartofagreat
circle.OnthespheroidalEarththeshortestlineiscalleda
geodesic.Agreatcircleisanearenoughapproximationto
Figure104a.Theplanesofthemeridiansatthepolaraxis.
4INTRODUCTION TO MARINE NAVIGATION
ageodesicformostproblemsofnavigation.Asmallcircle
isthelineofintersectionofasphereandaplanewhichdoes
not pass through the center. See Figure 104a.
Thetermmeridianisusuallyappliedtotheupper
branchofthehalf-circlefrompoletopolewhichpasses
throughagivenpoint.Theoppositehalfiscalledthelower
branch.
Aparallelorparalleloflatitudeisacircleonthe
surfaceoftheEarthparalleltotheplaneoftheequator.
Itconnectsallpointsofequallatitude.Theequatorisa
greatcircleatlatitude0°.SeeFigure104b.Thepolesare
singlepointsatlatitude90°.Allotherparallelsaresmall
circles.
105. Coordinates
Coordinatesoflatitudeandlongitudecandefineany
positiononEarth.Latitude(L,lat.)istheangulardistance
fromtheequator,measurednorthwardorsouthwardalong
ameridianfrom0°attheequatorto90°atthepoles.Itis
designatednorth(N)orsouth(S)toindicatethedirectionof
measurement.
Thedifferenceoflatitude(l,DLat.)betweentwo
placesistheangularlengthofarcofanymeridianbetween
theirparallels.Itisthenumericaldifferenceofthelatitudes
iftheplacesareonthesamesideoftheequator;itisthesum
ofthelatitudesiftheplacesareonoppositesidesofthe
equator.Itmaybedesignatednorth(N)orsouth(S)when
appropriate.Themiddleormid-latitude(Lm)between
twoplacesonthesamesideoftheequatorishalfthesum
oftheirlatitudes.Mid-latitudeislabeledNorStoindicate
whether it is north or south of the equator.
Theexpressionmayrefertothemid-latitudeoftwo
placesonoppositesidesoftheequator.Inthiscase,itis
equaltohalfthedifferencebetweenthetwolatitudesand
takes the name of the place farthest from the equator.
Longitude(l,long.)istheangulardistancebetween
theprimemeridianandthemeridianofapointontheEarth,
measuredeastwardorwestwardfromtheprimemeridian
through180°.Itisdesignatedeast(E)orwest(W)to
indicate the direction of measurement.
Thedifferenceoflongitude(DLo)betweentwo
placesistheshorterarcoftheparallelorthesmallerangle
atthepolebetweenthemeridiansofthetwoplaces.Ifboth
placesareonthesameside(eastorwest)ofGreenwich,
DLoisthenumericaldifferenceofthelongitudesofthetwo
places;ifonoppositesides,DLoisthenumericalsum
unless this exceeds 180°, when it is 360° minus the sum.
Thedistancebetweentwomeridiansatanyparallelof
latitude,expressedindistanceunits,usuallynauticalmiles,
iscalleddeparture(p,Dep.).Itrepresentsdistancemade
goodeastorwestasacraftproceedsfromonepointto
another.Itsnumericalvaluebetweenanytwomeridians
decreaseswithincreasedlatitude,whileDLoisnumerically
thesameatanylatitude.EitherDLoorpmaybedesignated
east (E) or west (W) when appropriate.
106. Distance on the Earth
Distance,asusedbythenavigator,isthelengthofthe
rhumblineconnectingtwoplaces.Thisisalinemaking
thesameanglewithallmeridians.Meridiansandparallels
whichalsomaintainconstanttruedirectionsmaybecon-
sideredspecialcasesoftherhumbline.Anyotherrhumb
linespiralstowardthepole,formingaloxodromiccurve
orloxodrome.SeeFigure106.Distancealongthegreat
Figure 104b. The equator is a great circle midway
between the poles.
Figure 106. A loxodrome.
INTRODUCTION TO MARINE NAVIGATION5
circleconnectingtwopointsiscustomarilydesignated
great-circledistance.Formostpurposes,consideringthe
nauticalmilethelengthofoneminuteoflatitudeintroduces
no significant error
Speed(S)israteofmotion,ordistanceperunitoftime.
Aknot(kn.),theunitofspeedcommonlyusedin
navigation,isarateof1nauticalmileperhour.The
expressionspeedofadvance(SOA)isusedtoindicatethe
speedtobemadealongtheintendedtrack.Speedoverthe
ground(SOG)istheactualspeedofthevesseloverthe
surfaceoftheEarthatanygiventime.Tocalculatespeed
madegood(SMG)betweentwopositions,dividethe
distancebetweenthetwopositionsbythetimeelapsed
between the two positions.
107. Direction on the Earth
Directionisthepositionofonepointrelativeto
another.Navigatorsexpressdirectionastheangular
differenceindegreesfromareferencedirection,usually
northortheship’shead.Course(C,Cn)isthehorizontal
directioninwhichavesselisintendedtobesteered,
expressedasangulardistancefromnorthclockwisethrough
360°.Strictlyused,thetermappliestodirectionthroughthe
water,notthedirectionintendedtobemadegoodoverthe
ground.Thecourseisoftendesignatedastrue,magnetic,
compass, or grid according to the reference direction.
Trackmadegood(TMG)isthesingleresultant
directionfromthepointofdeparturetopointofarrivalat
anygiventime.Courseofadvance(COA)isthedirection
intendedtobemadegoodovertheground,andcourseover
ground(COG)isthedirectionbetweenavessel’slastfix
andanEP.Acourselineisalinedrawnonachart
extendinginthedirectionofacourse.Itissometimes
convenienttoexpressacourseasananglefromeithernorth
orsouth,through90°or180°.Inthiscaseitisdesignated
courseangle(C)andshouldbeproperlylabeledtoindicate
theorigin(prefix)anddirectionofmeasurement(suffix).
Thus,CN35°E=Cn035°(000°+35°),CN155°W=Cn
205°(360°-155°),CS47°E=Cn133°(180°-47°).ButCn
260°maybeeitherCN100°WorCS80°W,depending
upon the conditions of the problem.
Track(TR)istheintendedhorizontaldirectionoftravel
withrespecttotheEarth.Thetermsintendedtrackand
tracklineareusedtoindicatethepathofintendedtravel.See
Figure107a.Thetrackconsistsofoneoraseriesofcourse
lines,fromthepointofdeparturetothedestination,along
whichoneintendstoproceed.Agreatcirclewhichavessel
intendstofollowiscalledagreat-circletrack,thoughit
consistsofaseriesofstraightlinesapproximatingagreatcircle
Heading(Hdg.,SH)isthedirectioninwhichavessel
ispointedatanygivenmoment,expressedasangular
distancefrom000°clockwisethrough360°.Itiseasyto
confuseheadingandcourse.Headingconstantlychangesas
avesselyawsbackandforthacrossthecourseduetosea,
wind, and steering error.
Bearing(B,Brg.)isthedirectionofoneterrestrial
pointfromanother,expressedasangulardistancefrom
000°(North)clockwisethrough360°.Whenmeasured
through90°or180°fromeithernorthorsouth,itiscalled
bearingangle(B).Bearingandazimutharesometimesused
interchangeably,butthelattermoreaccuratelyreferstothe
horizontaldirectionofapointonthecelestialspherefrom
apointontheEarth.Arelativebearingismeasuredrelative
totheship’sheadingfrom000°(deadahead)clockwise
through360°.However,itissometimesconvenientlymea-
suredrightorleftfrom000°attheship’sheadthrough
180°.ThisisparticularlytruewhenusingthetableforDis-
tance of an Object by Two Bearings.
Figure 107a. Course line, track, track made good, and heading.
6INTRODUCTION TO MARINE NAVIGATION
To convert a relative bearing to a true bearing, add the
true heading. See Figure 107b
True Bearing = Relative Bearing + True Heading.
Relative Bearing = True Bearing - True Heading.
108. Finding Latitude and Longitude
Navigatorshavemadelatitudeobservationsfor
thousandsofyears.AccuratedeclinationtablesfortheSun
havebeenpublishedforcenturies,enablingancientseamen
tocomputelatitudetowithin1or2degrees.Thosewho
todaydeterminetheirlatitudebymeasuringtheSunattheir
meridianandthealtitudeofPolarisareusingmethodswell
known to 15th century navigators.
Amethodoffindinglongitudeeludedmarinersfor
centuries.Severalsolutionsindependentoftimeprovedtoo
cumbersome.Findinglongitudebymagneticvariationwas
tried,butfoundtooinaccurate.Thelunardistancemethod,
whichdeterminesGMTbyobservingtheMoon’sposition
amongthestars,becamepopularinthe1800s.However,
themathematicsrequiredbymostoftheseprocesseswere
farabovetheabilitiesoftheaverageseaman.Itwas
apparentthatthesolutionlayinkeepingaccuratetimeat
sea.
In1714,theBritishBoardofLongitudewasformed,
offeringasmallfortuneinrewardtoanyonewhocould
provide a solution to the problem.
AnEnglishman,JohnHarrison,respondedtothe
challenge,developingfourchronometersbetween1735and
1760.Themostaccurateofthesetimepieceslostonly15
secondsona156dayroundtripbetweenLondonand
Barbados.TheBoard,however,paidhimonlyhalfthe
promisedreward.TheKingfinallyintervenedon
Harrison’sbehalf,andattheageof80yearsHarrison
received his full reward of £20,000.
Rapidchronometerdevelopmentledtotheproblemof
determiningchronometererroraboardship.Timeballs,
largeblackspheresmountedinportinprominentlocations,
weredroppedatthestrokeofnoon,enablinganyshipin
harborwhichcouldseetheballtodeterminechronometer
error.BytheendoftheU.S.CivilWar,telegraphsignals
werebeingusedtokeytimeballs.Useofradiosignalsto
sendtimetickstoshipswelloffshorebeganin1904,and
soon worldwide signals were available.
109. The Navigational Triangle
Moderncelestialnavigatorsreducetheircelestial
observationsbysolvinganavigationaltrianglewhose
pointsaretheelevatedpole,thecelestialbody,andthe
zenithoftheobserver.Thesidesofthistrianglearethepolar
distanceofthebody(codeclination),itszenithdistance
(coaltitude),andthepolardistanceofthezenith(colatitude
of the observer).
Asphericaltrianglewasfirstusedatseainsolving
lunardistanceproblems.Simultaneousobservationswere
madeofthealtitudesoftheMoonandtheSunorastarnear
theeclipticandtheangulardistancebetweentheMoonand
theotherbody.Thezenithoftheobserverandthetwo
celestialbodiesformedtheverticesofatrianglewhose
sideswerethetwocoaltitudesandtheangulardistance
betweenthebodies.Usingamathematicalcalculationthe
navigator“cleared”thisdistanceoftheeffectsofrefraction
andparallaxapplicabletoeachaltitude.Thiscorrected
valuewasthenusedasanargumentforenteringthe
almanac.Thealmanacgavethetruelunardistancefromthe
Sunandseveralstarsat3hourintervals.Previously,the
Figure 107b. Relative Bearing
INTRODUCTION TO MARINE NAVIGATION7
navigatorhadsethiswatchorcheckeditserrorandrate
withthelocalmeantimedeterminedbycelestial
observations.Thelocalmeantimeofthewatch,properly
corrected,appliedtotheGreenwichmeantimeobtained
from the lunar distance observation, gave the longitude.
Thecalculationsinvolvedweretedious.Fewmariners
couldsolvethetriangleuntilNathanielBowditchpublished
hissimplifiedmethodin1802inTheNewAmerican
Practical Navigator.
Reliablechronometerswereavailableby1800,buttheir
highcostprecludedtheirgeneraluseaboardmostships.
However,mostnavigatorscoulddeterminetheirlongitude
usingBowditch’smethod.Thiseliminatedtheneedfor
parallelsailingandthelosttimeassociatedwithit.Tablesfor
thelunardistancesolutionwerecarriedintheAmerican
nautical almanac into the 20th century.
110. The Time Sight
Thetheoryofthetimesighthadbeenknowntomath-
ematicianssincethedevelopmentofsphericaltrigonometry,
butnotuntilthechronometerwasdevelopedcoulditbeused
by mariners.
Thetimesightusedthemodernnavigationaltriangle.
Thecodeclination,orpolardistance,ofthebodycouldbe
determinedfromthealmanac.Thezenithdistance
(coaltitude)wasdeterminedbyobservation.Ifthe
colatitudewereknown,threesidesofthetrianglewere
available.Fromthesethemeridiananglewascomputed.
ThecomparisonofthiswiththeGreenwichhouranglefrom
the almanac yielded the longitude.
Thetimesightwasmathematicallysound,butthenavigator
wasnotalwaysawarethatthelongitudedeterminedwasonlyas
accurateasthelatitude,andtogethertheymerelyformedapoint
onwhatisknowntodayasalineofposition.Iftheobserved
bodywasontheprimevertical,thelineofpositionrannorthand
southandasmallerrorinlatitudegenerallyhadlittleeffecton
thelongitude.Butwhenthebodywasclosetothemeridian,a
small error in latitude produced a large error in longitude.
Figure 110.The first celestial line of position, obtained by Captain Thomas Sumner in 1837.
8INTRODUCTION TO MARINE NAVIGATION
Thelineofpositionbycelestialobservationwasun-
knownuntildiscoveredin1837by30-year-oldCaptain
ThomasH.Sumner,aHarvardgraduateandsonofaUnited
StatescongressmanfromMassachusetts.Thediscoveryof
the“Sumnerline,”asitissometimescalled,wasconsid-
eredbyMaury“thecommencementofanewerainpractical
navigation.”Thiswastheturningpointinthedevelopment
ofmoderncelestialnavigationtechnique.InSumner’sown
words, the discovery took place in this manner:
HavingsailedfromCharleston,S.C.,25thNovem-
ber,1837,boundtoGreenock,aseriesofheavygales
fromtheWestwardpromisedaquickpassage;afterpass-
ingtheAzores,thewindprevailedfromtheSouthward,
withthickweather;afterpassingLongitude21°W,noob-
servationwashaduntilneartheland;butsoundingswere
hadnotfar,aswassupposed,fromtheedgeoftheBank.
Theweatherwasnowmoreboisterous,andverythick;
andthewindstillSoutherly;arrivingaboutmidnight,
17thDecember,within40miles,bydeadreckoning,of
Tuskerlight;thewindhauledSE,true,makingtheIrish
coastaleeshore;theshipwasthenkeptclosetothewind,
andseveraltacksmadetopreserveherpositionasnearly
aspossibleuntildaylight;whennothingbeinginsight,
shewaskeptonENEundershortsail,withheavygales;
atabout10AManaltitudeoftheSunwasobserved,and
theChronometertimenoted;but,havingrunsofarwith-
outanyobservation,itwasplaintheLatitudebydead
reckoningwasliabletoerror,andcouldnotbeentirely
reliedon.Using,however,thisLatitude,infindingthe
LongitudebyChronometer,itwasfoundtoputtheship
15'ofLongitudeEfromherpositionbydeadreckoning;
whichinLatitude52°Nis9nauticalmiles;thisseemedto
agreetolerablywellwiththedeadreckoning;butfeeling
doubtfuloftheLatitude,theobservationwastriedwitha
Latitude10'furtherN,findingthisplacedtheshipENE
27nauticalmiles,oftheformerposition,itwastried
againwithaLatitude20'Nofthedeadreckoning;this
alsoplacedtheshipstillfurtherENE,andstill27nautical
milesfurther;thesethreepositionswerethenseentolie
inthedirectionofSmall’slight.Itthenatonceappeared
thattheobservedaltitudemusthavehappenedatall
thethreepoints,andatSmall’slight,andattheship,
atthesameinstantoftime;anditfollowed,that
Small’slightmustbearENE,iftheChronometer
wasright.Havingbeenconvincedofthistruth,the
shipwaskeptonhercourse,ENE,thewindbeingstill
SE.,andinlessthananhour,Small’slightwasmade
bearing ENE 1/2 E, and close aboard.
In1843Sumnerpublishedabook,ANewandAccurate
MethodofFindingaShip’sPositionatSeabyProjection
onMercator’sChart.Heproposedsolvingasingletime
sighttwice,usinglatitudessomewhatgreaterandsomewhat
lessthanthatarrivedatbydeadreckoning,andjoiningthe
two positions obtained to form the line of position.
TheSumnermethodrequiredthesolutionoftwotime
sightstoobtaineachlineofposition.Manyoldernavigators
preferrednottodrawthelinesontheircharts,buttofix
theirpositionmathematicallybyamethodwhichSumner
hadalsodevisedandincludedinhisbook.Thiswasate-
dious but popular procedure.
111. Navigational Tables
Sphericaltrigonometryisthebasisforsolvingevery
navigationaltriangle,anduntilabout80yearsagothe
navigatorhadnochoicebuttosolveeachtriangleby
tedious, manual computations.
LordKelvin,generallyconsideredthefatherofmodern
navigationalmethods,expressedinterestinabookoftableswith
whichanavigatorcouldavoidtedioustrigonometricsolutions.
However,solvingthemanythousandsoftrianglesinvolved
wouldhavemadetheprojecttoocostly.Computersfinally
providedapracticalmeansofpreparingtables.In1936thefirst
volumeofPub.No.214wasmadeavailable;later,Pub.No.249
wasprovidedforairnavigators.Pub.No.229,SightReduction
Tables for Marine Navigation, has replacedPub. No. 214.
Electroniccalculatorsaregraduallyreplacingthe
tables.Scientificcalculatorswithtrigonometricfunctions
caneasilysolvethenavigationaltriangle.Navigational
calculatorsreadilysolvecelestialsightsandperforma
varietyofvoyageplanningfunctions.Usingacalculator
generallygivesmoreaccuratelinesofpositionbecauseit
eliminatestheroundingerrorsinherentintabularinspection
and interpolation.
112. Development of Electronic Navigation
Perhapsthefirstapplicationofelectronicsto
navigationinvolvedsendingtelegraphictimesignalsin
1865tocheckchronometererror.Transmittingradiotime
signalsforchronometerchecksdatesto1904.Radio
broadcastsprovidingnavigationalwarnings,begunin1907
bytheU.S.NavyHydrographicOffice,helpedincreasethe
safety of navigation at sea.
BythelatterpartofWorldWarIthedirectional
propertiesofaloopantennaweresuccessfullyusedinthe
radiodirectionfinder.Thefirstradiobeaconwasinstalledin
1921.Early20thcenturyexperimentsbyBehmand
LangevinledtotheU.S.Navy’sdevelopmentofthefirst
practicalechosounderin1922.Radarandhyperbolic
systems grew out of WWII.
Today,electronicstouchesalmosteveryaspectof
navigation.Hyperbolicsystems,satellitesystems,and
electronicchartsallrequireanincreasinglysophisticated
electronicssuiteandtheexpertisetomanagethem.These
systems’accuracyandeaseofusemaketheminvaluable
assetstothenavigator,butthereisfarmoretousingthem
than knowing which buttons to push.
INTRODUCTION TO MARINE NAVIGATION9
113. Development of Radar
Asearlyas1904,Germanengineerswereexperimenting
withreflectedradiowaves.In1922twoAmericanscientists,
Dr.A.HoytTaylorandLeoC.Young,testingacommuni-
cationsystemattheNavalAircraftRadioLaboratory,noted
fluctuationsinthesignalswhenshipspassedbetweenstations
onoppositesidesofthePotomacRiver.In1935theBritish
beganworkonradar.In1937theUSSLearytestedthefirst
sea-goingradar,andin1940UnitedStatesandBritish
scientistscombinedtheirefforts.WhentheBritishrevealedthe
principleofthemulticavitymagnetrondevelopedbyJ.T.
RandallandH.A.H.BootattheUniversityofBirminghamin
1939,microwaveradarbecamepractical.In1945,attheclose
of World War II, radar became available for commercial use.
114. Development of Hyperbolic Radio Aids
Varioushyperbolicsystemsweredevelopedbeginning
inWorldWarII.ThesewereoutgrowthsoftheBritishGEE
system,developedtohelpbombersnavigatetoandfrom
theirmissionsoverEurope.LoranAwasdevelopedasa
long-rangemarinenavigationsystem.Thiswasreplacedby
themoreaccurateLoranCsystem,deployedthroughout
muchoftheworld.Variousshortrangeandregional
hyperbolicsystemshavebeendevelopedbyprivate
industryforhydrographicsurveying,offshorefacilities
positioning, and general navigation.
115. Other Electronic Systems
Theunderlyingconceptthatledtodevelopmentof
satellitenavigationdatesto1957andthefirstlaunchofan
artificialsatelliteintoorbit.Thefirstsystem,NAVSAT,has
beenreplacedbythefarmoreaccurateandwidelyavailable
GlobalPositioningSystem(GPS),whichhasrevolu-
tionized all aspects of navigation
Thefirstinertialnavigationsystemwasdevelopedin
1942foruseintheV2missilebythePeenemundegroupunder
theleadershipofDr.WernhervonBraun.Thissystemusedtwo
2-degree-of-freedomgyroscopesandanintegratingacceler-
ometertodeterminethemissilevelocity.BytheendofWorld
WarII,thePeenemundegrouphaddevelopedastableplatform
withthreesingle-degree-of-freedomgyroscopesandan
integratingaccelerometer.In1958aninertialnavigationsystem
wasusedtonavigatetheUSSNautilusundertheicetothe
North Pole.
NAVIGATION ORGANIZATIONS
116. Governmental Role
Navigationonlyagenerationagowasanindependent
process,carriedoutbythemarinerwithoutoutside
assistance.Withcompassandcharts,sextantand
chronometer,hecouldindependentlytravelanywherein
theworld.Theincreasinguseofelectronicnavigation
systemshasmadethenavigatordependentonmanyfactors
outsidehiscontrol.Governmentorganizationsfund,
operate,andregulatesatellites,Loran,andotherelectronic
systems.Governmentsareincreasinglyinvolvedin
regulationofvesselmovementsthroughtrafficcontrol
systemsandregulatedareas.Understandingthegovern-
mentalroleinsupportingandregulatingnavigationis
vitallyimportanttothemariner.IntheUnitedStates,there
areanumberofofficialorganizationswhichsupportthe
interestsofnavigators.Somehaveapolicy-makingrole;
othersbuildandoperatenavigationsystems.Many
maritimenationshavesimilarorganizationsperforming
similarfunctions.Internationalorganizationsalsoplaya
significant role.
117. The Coast and Geodetic Survey
TheU.S.CoastandGeodeticSurveywasfoundedin
1807whenCongresspassedaresolutionauthorizinga
surveyofthecoast,harbors,outlyingislands,andfishing
banksoftheUnitedStates.PresidentThomasJefferson
appointedFerdinandHassler,aSwissimmigrantand
professorofmathematicsatWestPoint,thefirstDirectorof
the“SurveyoftheCoast.”Thesurveybecamethe“Coast
Survey” in 1836.
TheapproachestoNewYorkwerethefirstsectionsof
thecoastcharted,andfromtheretheworkspreadnorthward
andsouthwardalongtheeasternseaboard.In1844thework
wasexpandedandarrangementsmadetosimultaneously
chartthegulfandeastcoasts.Investigationoftidal
conditionsbegan,andin1855thefirsttablesoftide
predictionswerepublished.TheCaliforniagoldrush
necessitatedasurveyofthewestcoast,whichbeganin
1850,theyearCaliforniabecameastate.CoastPilots,or
SailingDirections,fortheAtlanticcoastoftheUnited
Stateswereprivatelypublishedinthefirsthalfofthe19th
century.In1850theSurveybeganaccumulatingdatathat
ledtofederallyproducedCoastPilots.The1889Pacific
CoastPilotwasanoutstandingcontributiontothesafetyof
west coast shipping.
In1878thesurveywasrenamed“CoastandGeodetic
Survey.”In1970thesurveybecamethe“NationalOcean
Survey,”andin1983itbecamethe“NationalOcean
Service.”TheOfficeofChartingandGeodeticServices
accomplishedallchartingandgeodeticfunctions.In1991
thenamewaschangedbacktotheoriginal“Coastand
GeodeticSurvey,”organizedundertheNationalOcean
Servicealongwithseveralotherenvironmentaloffices.
Todayitprovidesthemarinerwiththechartsandcoast
pilotsofallwatersoftheUnitedStatesanditspossessions,
andtideandtidalcurrenttablesformuchoftheworld.Its
10INTRODUCTION TO MARINE NAVIGATION
administrativeorderrequirestheCoastandGeodetic
Surveytoplananddirectprogramstoproducechartsand
relatedinformationforsafenavigationofU.S.waterways,
territorialseas,andairspace.Thisworkincludesall
activitiesrelatedtotheNationalGeodeticReference
System;surveying,charting,anddatacollection;
productionanddistributionofcharts;andresearchand
developmentofnewtechnologiestoenhancethese
missions.
118. The National Imagery and Mapping Agency
InthefirstyearsofthenewlyformedUnitedStatesof
America,chartsandinstrumentsusedbytheNavyand
merchantmarinerswereleftoverfromcolonialdaysor
wereobtainedfromEuropeansources.In1830theU.S.
Navyestablisheda“DepotofChartsandInstruments”in
Washington,D.C.,asastorehousefromwhichavailable
charts,pilotsandsailingdirections,andnavigational
instrumentswereissuedtoNavalships.LieutenantL.M.
Goldsboroughandoneassistant,PassedMidshipmanR.B.
Hitchcock, constituted the entire staff.
ThefirstchartpublishedbytheDepotwasproduced
fromdataobtainedinasurveymadebyLieutenantCharles
Wilkes,whohadsucceededGoldsboroughin1834.Wilkes
laterearnedfameastheleaderofaUnitedStatesexpedition
toAntarctica.From1842until1861LieutenantMatthew
FontaineMauryservedasOfficerinCharge.Underhis
command the Depot rose to international prominence.
Maurydecideduponanambitiousplantoincreasethe
mariner’sknowledgeofexistingwinds,weather,and
currents.Hebeganbymakingadetailedrecordofpertinent
matterincludedinoldlogbooksstoredattheDepot.He
theninauguratedahydrographicreportingprogramamong
shipmasters,andthethousandsofreportsreceived,along
withthelogbookdata,werecompiledintothe“Windand
CurrentChartoftheNorthAtlantic”in1847.Thisisthe
ancestor of today’sPilot Chart.
TheUnitedStatesinstigatedaninternational
conferencein1853tointerestothernationsinasystemof
exchangingnauticalinformation.Theplan,whichwas
Maury’s,wasenthusiasticallyadoptedbyothermaritime
nations.In1854theDepotwasredesignatedthe“U.S.
NavalObservatoryandHydrographicalOffice.”Atthe
outbreakoftheAmericanCivilWarin1861,Maury,a
nativeofVirginia,resignedfromtheU.S.Navyand
acceptedacommissionintheConfederateNavy.This
effectivelyendedhiscareerasanavigator,author,and
oceanographer.Atwar’send,hefledthecountry,his
reputationsufferingfromhisembraceoftheConfederate
cause.
AfterMaury’sreturntotheUnitedStatesin1868,he
servedasaninstructorattheVirginiaMilitaryInstitute.He
continuedatthispositionuntilhisdeathin1873.Sincehis
death,hisreputationasoneofAmerica’sgreatesthydrog-
raphers has been restored.
In1866CongressseparatedtheObservatoryandthe
HydrographicOffice,broadlyincreasingthefunctionsof
thelatter.TheHydrographicOfficewasauthorizedtocarry
outsurveys,collectinformation,andprinteverykindof
nauticalchartandpublication“forthebenefitanduseof
navigators generally.”
TheHydrographicOfficepurchasedthecopyrightof
TheNewAmericanPracticalNavigatorin1867.Thefirst
NoticetoMarinersappearedin1869.Dailybroadcastof
navigationalwarningswasinauguratedin1907.In1912,
followingthesinkingoftheTitanic,theInternationalIce
Patrol was established.
In1962theU.S.NavyHydrographicOfficewas
redesignatedtheU.S.NavalOceanographicOffice.In1972
certainhydrographicfunctionsofthelatterofficewere
transferredtotheDefenseMappingAgency
HydrographicCenter.In1978theDefenseMapping
AgencyHydrographic/TopographicCenter
(DMAHTC)assumedhydrographicandtopographicchart
productionfunctions.In1996theNationalImageryand
MappingAgency(NIMA)wasformedfromDMAand
certainotherelementsoftheDepartmentofDefense.
NIMAcontinuestoproducechartsandpublicationsandto
disseminatemaritimesafetyinformationinsupportofthe
U.S. military and navigators generally.
119. The United States Coast Guard
AlexanderHamiltonestablishedtheU.S.Coast
GuardastheRevenueMarine,latertheRevenueCutter
Service,onAugust4,1790.Itwaschargedwithenforcing
thecustomslawsofthenewnation.Arevenuecutter,the
HarrietLane,firedthefirstshotfromanavalunitinthe
CivilWaratFortSumter.TheRevenueCutterService
becametheU.S.CoastGuardwhencombinedwiththe
LifesavingServicein1915.TheLighthouseServicewas
addedin1939,andtheBureauofMarineInspectionand
Navigationwasaddedin1942.TheCoastGuardwas
transferredfromtheTreasuryDepartmenttothe
Department of Transportation in 1967.
TheprimaryfunctionsoftheCoastGuardinclude
maritimesearchandrescue,lawenforcement,and
operationofthenation’saidstonavigationsystem.In
addition,theCoastGuardisresponsibleforportsafetyand
security,merchantmarineinspection,andmarinepollution
control.TheCoastGuardoperatesalargeandvariedfleet
ofships,boats,andaircraftinperformingitswidelyranging
duties
NavigationsystemsoperatedbytheCoastGuard
includethesystemofsome40,000lightedandunlighted
beacons,buoys,andrangesinU.S.andterritorialwaters;
theU.S.stationsoftheLoranCsystem;differentialGPS
(DGPS)servicesintheU.S.;andVesselTrafficServices
(VTS) in major ports and harbors of the U.S.
INTRODUCTION TO MARINE NAVIGATION11
120. The United States Navy
TheU.S.Navywasofficiallyestablishedin1798.Its
roleinthedevelopmentofnavigationaltechnologyhasbeen
singular.FromthefoundingoftheNavalObservatorytothe
developmentofthemostadvancedelectronics,theU.S.
Navyhasbeenaleaderindevelopingdevicesandtechniques
designed to make the navigator’s job safer and easier.
Thedevelopmentofalmosteverydeviceknownto
navigationsciencehasbeendeeplyinfluencedbyNaval
policy.Somesystemsaredirectoutgrowthsofspecific
Navalneeds;somearetheresultoftechnological
improvementssharedwithotherservicesandwith
commercial maritime industry.
121. The United States Naval Observatory
OneofthefirstobservatoriesintheUnitedStateswas
builtin1831-1832atChapelHill,N.C.TheDepotofCharts
andInstruments,establishedin1830,wastheagencyfrom
whichtheU.S.NavyHydrographicOfficeandtheU.S.
NavalObservatoryevolved36yearslater.Inabout1835,
underLieutenantCharlesWilkes,thesecondOfficerin
Charge,theDepotinstalledasmalltransitinstrumentfor
rating chronometers.
TheMalloryActof1842providedforthe
establishmentofapermanentobservatory.Thedirectorwas
authorizedtopurchaseeverythingnecessarytocontinue
astronomicalstudy.Theobservatorywascompletedin
1844andtheresultsofitsfirstobservationswerepublished
twoyearslater.CongressestablishedtheNaval
Observatoryasaseparateagencyin1866.In1873a
refractingtelescopewitha26inchaperture,thenthe
world’slargest,wasinstalled.Theobservatory,locatedin
Washington,D.C.,hasoccupieditspresentsitesince1893.
122. The Royal Greenwich Observatory
Englandhadnoearlyprivatelysupportedobservatories
suchasthoseonthecontinent.Theneedfornavigational
advancementwasignoredbyHenryVIIIandElizabethI,
butin1675CharlesII,attheurgingofJohnFlamsteed,
JonasMoore,LeSieurdeSaintPierre,andChristopher
Wren,establishedtheGreenwichRoyalObservatory.
Charleslimitedconstructioncoststo£500,andappointed
FlamsteedthefirstAstronomerRoyal,atanannualsalary
of£100.Theequipmentavailableintheearlyyearsofthe
observatoryconsistedoftwoclocks,a“sextant”of7foot
radius,aquadrantof3footradius,twotelescopes,andthe
starcatalogpublishedalmostacenturybeforebyTycho
Brahe.ThirteenyearspassedbeforeFlamsteedhadan
instrumentwithwhichhecoulddeterminehislatitude
accurately.
In1690atransitinstrumentequippedwithatelescope
andvernierwasinventedbyRomer;helateraddedavertical
circletothedevice.Thisenabledtheastronomerto
determinedeclinationandrightascensionatthesametime.
Oneoftheseinstrumentswasaddedtotheequipmentat
Greenwichin1721,replacingthehugequadrantpreviously
used.Thedevelopmentandperfectionofthechronometerin
thenexthundredyearsaddedtotheaccuracyofobservations.
Othernationalobservatorieswereconstructedinthe
yearsthatfollowed:atBerlinin1705,St.Petersburgin
1725,Palermoin1790,CapeofGoodHopein1820,
ParramattainNewSouthWalesin1822,andSydneyin
1855.
123. The International Hydrographic Organization
TheInternationalHydrographicOrganization
(IHO)wasoriginallyestablishedin1921astheInterna-
tionalHydrographicBureau(IHB).Thepresentnamewas
adoptedin1970asaresultofarevisedinternational
agreementamongmembernations.However,theformer
name,InternationalHydrographicBureau,wasretainedfor
theIHO’sadministrativebodyofthreeDirectorsandtheir
staff at the organization’s headquarters in Monaco.
TheIHOsetsforthhydrographicstandardstobe
agreeduponbythemembernations.Allmemberstatesare
urgedandencouragedtofollowthesestandardsintheir
surveys,nauticalcharts,andpublications.Asthese
standardsareuniformlyadopted,theproductsofthe
world’shydrographicandoceanographicofficesbecome
moreuniform.Muchhasbeendoneinthefieldofstandard-
ization since the Bureau was founded.
The principal work undertaken by the IHO is:
•Tobringaboutacloseandpermanentassociation
between national hydrographic offices.
•Tostudymattersrelatingtohydrographyandallied
sciences and techniques.
•Tofurthertheexchangeofnauticalchartsand
documentsbetweenhydrographicofficesofmember
governments.
•To circulate the appropriate documents.
•Totenderguidanceandadviceuponrequest,in
particulartocountriesengagedinsettingupor
expanding their hydrographic service.
•Toencouragecoordinationofhydrographicsurveys
with relevant oceanographic activities.
•Toextendandfacilitatetheapplicationofoceano-
graphic knowledge for the benefit of navigators.
•Tocooperatewithinternationalorganizationsand
scientific institutions which have related objectives.
Duringthe19thcentury,manymaritimenations
establishedhydrographicofficestoprovidemeansfor
improvingthenavigationofnavalandmerchantvesselsby
providingnauticalpublications,nauticalcharts,andother
navigationalservices.Thereweresubstantialdifferencesin
hydrographicprocedures,charts,andpublications.In1889,
anInternationalMarineConferencewasheldat
12INTRODUCTION TO MARINE NAVIGATION
Washington,D.C.,anditwasproposedtoestablisha
“permanentinternationalcommission.”Similarproposals
weremadeatthesessionsoftheInternationalCongressof
NavigationheldatSt.Petersburgin1908andagainin1912.
In1919thehydrographersofGreatBritainandFrance
cooperatedintakingthenecessarystepstoconvenean
internationalconferenceofhydrographers.Londonwas
selectedasthemostsuitableplaceforthisconference,and
onJuly24,1919,theFirstInternationalConference
opened,attendedbythehydrographersof24nations.The
objectoftheconferencewas“Toconsidertheadvisability
ofallmaritimenationsadoptingsimilarmethodsinthe
preparation,construction,andproductionoftheircharts
andallhydrographicpublications;ofrenderingtheresults
inthemostconvenientformtoenablethemtobereadily
used;ofinstitutingapromptsystemofmutualexchangeof
hydrographicinformationbetweenallcountries;andof
providinganopportunitytoconsultationsanddiscussions
tobecarriedoutonhydrographicsubjectsgenerallybythe
hydrographicexpertsoftheworld.”Thisisstillthemajor
purpose of the International Hydrographic Organization.
Asaresultoftheconference,apermanentorganization
wasformedandstatutesforitsoperationswereprepared.The
InternationalHydrographicBureau,nowtheInternational
HydrographicOrganization,beganitsactivitiesin1921with
18nationsasmembers.ThePrincipalityofMonacowas
selectedbecauseofitseasycommunicationwiththerestofthe
worldandalsobecauseofthegenerousofferofPrinceAlbert
IofMonacotoprovidesuitableaccommodationsforthe
BureauinthePrincipality.Therearecurrently59member
governments.Technicalassistancewithhydrographicmatters
is available through the IHO to member states requiring it.
ManyIHOpublicationsareavailabletothegeneral
public,suchastheInternationalHydrographicReview,
InternationalHydrographicBulletin,ChartSpecifications
oftheIHO,HydrographicDictionary,andothers.Inquiries
shouldbemadetotheInternationalHydrographicBureau,
7AvenuePresidentJ.F.Kennedy,B.P.445,MC98011,
Monaco, CEDEX.
124. The International Maritime Organization
TheInternationalMaritimeOrganization(IMO)
wasestablishedbyUnitedNationsConventionin1948.The
Conventionactuallyenteredintoforcein1959,althoughan
internationalconventiononmarinepollutionwasadoptedin
1954.(Until1982theofficialnameoftheorganizationwas
theInter-GovernmentalMaritimeConsultativeOrgani-
zation.)ItistheonlypermanentbodyoftheU.N.devoted
tomaritimematters,andtheonlyspecialU.N.agencyto
have its headquarters in the UK.
ThegoverningbodyoftheIMOistheAssemblyof
137memberstates,whichmeetseverytwoyears.Between
AssemblysessionsaCouncil,consistingof32member
governmentselectedbytheAssembly,governstheorgani-
zation.ItsworkiscarriedoutbytheMaritimeSafety
Committee, with subcommittees for:
•Safety of Navigation
•Radiocommunications
•Life-saving
•Search and Rescue
•Training and Watchkeeping
•Carriage of Dangerous Goods
•Ship Design and Equipment
•Fire Protection
•Stability and Load Lines/Fishing Vessel Safety
•Containers and Cargoes
•Bulk Chemicals
•Marine Environment Protection Committee
•Legal Committee
•Technical Cooperation Committee
•Facilitation Committee
IMOisheadedbytheSecretaryGeneral,appointedby
thecouncilandapprovedbytheAssembly.Heisassisted
by some 300 civil servants.
Toachieveitsobjectivesofcoordinatinginternational
policyonmarinematters,theIMOhasadoptedsome30
conventionsandprotocols,andadoptedover700codesand
recommendations.Anissuetobeadoptedfirstisbroughtbefore
acommitteeorsubcommittee,whichsubmitsadrafttoa
conference.Whentheconferenceadoptsthefinaltext,itis
submittedtomembergovernmentsforratification.Ratification
byaspecifiednumberofcountriesisnecessaryforadoption;the
moreimportanttheissue,themorecountriesmustratify.
Adopted conventions are binding on member governments.
Codesandrecommendationsarenotbinding,butin
mostcasesaresupportedbydomesticlegislationbythe
governments involved.
Thefirstandmostfar-reachingconventionadoptedby
theIMOwastheConventionofSafetyofLifeatSea
(SOLAS)in1960.Thisconventionactuallycameinto
forcein1965,replacingaversionfirstadoptedin1948.
Becauseofthedifficultprocessofbringingamendments
intoforceinternationally,noneofsubsequentamendments
becamebinding.Toremedythissituation,anew
conventionwasadoptedin1974andbecamebindingin
1980.AmongtheregulationsisV-20,requiringthecarriage
ofup-to-datechartsandpublicationssufficientforthe
intended voyage.
Otherconventionsandamendmentswerealsoadopted,
suchastheInternationalConventiononLoadLines
(adopted1966,cameintoforce1968),aconventiononthe
tonnagemeasurementofships(adopted1969,cameinto
force1982),TheInternationalConventiononSafe
Containers(adopted1972,cameintoforce1977),andthe
conventiononInternationalRegulationsforPreventing
CollisionsatSea(COLREGS)(adopted1972,cameinto
force 1977).
The1972COLREGSconventioncontained,among
otherprovisions,asectiondevotedtoTrafficSeparation
INTRODUCTION TO MARINE NAVIGATION13
Schemes,whichbecamebindingonmemberstatesafter
having been adopted as recommendations in prior years.
OneofthemostimportantconventionsistheInterna-
tionalConventionforthePreventionofPollutionfrom
Ships(MARPOL73/78),whichwasfirstadoptedin1973,
amendedbyProtocolin1978,andbecamebindingin1983.This
conventionbuiltonaseriesofpriorconventionsandagreements
datingfrom1954,highlightedbyseveralseverepollution
disastersinvolvingoiltankers.TheMARPOLconvention
reducestheamountofoildischargedintotheseabyships,and
bansdischargescompletelyincertainareas.Arelated
conventionknownastheLondonDumpingConvention
regulatesdumpingofhazardouschemicalsandotherdebrisinto
the sea.
TheIMOalsodevelopsminimumperformance
standardsforawiderangeofequipmentrelevanttosafety
atsea.AmongsuchstandardsisonefortheElectronic
ChartDisplayandInformationSystem(ECDIS),the
digitaldisplaydeemedtheoperationalandlegalequivalent
of the conventional paper chart.
Textsofthevariousconventionsandrecommendations,
aswellasacatalogandpublicationsonothersubjects,are
availablefromthePublicationsSectionoftheIMOat4
Albert Embankment, London SE1 7SR, United Kingdom.
125. The International Association of Marine Aids to
Navigation and Lighthouse Authorities
TheInternationalAssociationofMarineAidsto
NavigationandLighthouseAuthorities(formerly
IALA)bringstogetherrepresentativesoftheaidsto
navigationservicesofmorethan80membercountriesfor
technicalcoordination,informationsharing,andcoordi-
nationofimprovementstovisualaidstonavigation
throughouttheworld.Itwasestablishedin1957toprovide
apermanentorganizationtosupportthegoalsofthe
TechnicalLighthouseConferences,whichhadbeen
conveningsince1929.TheGeneralAssemblyofIALA
meetsaboutevery4years.TheCouncilof20members
meets twice a year to oversee the ongoing programs.
Fivetechnicalcommitteesmaintainthepermanent
programs:
•The Marine Marking Committee
•The Radionavigation Systems Committee
•The Vessel Traffic Services (VTS) Committee
•The Reliability Committee
•The Documentation Committee
IALAcommitteesprovideimportantdocumentationto
theIHOandotherinternationalorganizations,whilethe
IALASecretariatactsasaclearinghousefortheexchange
oftechnicalinformation,andorganizesseminarsand
technical support for developing countries.
Itsprincipleworksince1973hasbeentheimplemen-
tationoftheIALAMaritimeBuoyageSystem,describedin
Chapter5,VisualAidstoNavigation.Thissystemreplaced
some30dissimilarbuoyagesystemsinusethroughoutthe
world with 2 major systems.
IALAisbasednearParis,FranceinSaint-Germaine-
en-Laye.
126. The Radio Technical Commission for Maritime
Services
TheRadioTechnicalCommissionforMaritime
Servicesisanon-profitorganizationwhichservesasa
focalpointfortheexchangeofinformationandthe
developmentofrecommendationsandstandardsrelatedto
allaspectsofmaritimeradiocommunicationsand
radionavigation.
Specifically, RTCM:
•Promotesideasandexchangesinformationon
maritimeradiocommunicationsandradionavigation.
•Facilitatesthedevelopmentandexchangeofviews
amongandbetweengovernmentandnon-
governmentinterestsbothnationallyand
internationally.
•Conductsstudiesandpreparesreportsonmaritime
radiocommunicationsandradionavigationissuesto
improve efficiency and capabilities.
Bothgovernmentandnon-governmentorganizations
aremembers,comingfromtheU.S.andmanyother
nations.TheRTCMorganizationconsistsofaBoardof
Directors,andtheAssemblyconsistingofallmembers,
officers,staff,technicaladvisors,andworkingcommittees.
Workingcommitteesareformedasneededtodevelop
officialRTCMrecommendationsregardingtechnical
standardsandregulatorypoliciesinthemaritimefield.
Currentlycommitteesaddresssuchissuesasmaritimesafety
information,electroniccharts,emergencyposition-indicating
radiobeacons(EPIRB’s),personallocatorbeacons,ship
radars,differentialGPS,GLONASS,andmaritimesurvivor
locator devices.
The RTCM headquarters office is in Alexandria, VA.
127. The National Marine Electronic Association
TheNationalMarineElectronicAssociation
(NMEA)isaprofessionaltradeassociationfoundedin
1957whosepurposeistocoordinatetheeffortsofmarine
electronicsmanufacturers,technicians,government
agencies,shipandboatbuilders,andotherinterested
groups.Inadditiontocertifyingmarineelectronics
techniciansandprofessionallyrecognizingoutstanding
achievementsbycorporateandindividualmembers,the
NMEAsetsstandardsfortheexchangeofdigitaldatabyall
manufacturersofmarineelectronicequipment.Thisallows
theconfigurationofintegratednavigationsystemusing
equipment from different manufacturers.
14INTRODUCTION TO MARINE NAVIGATION
NMEAworkscloselywithRTCMandotherprivate
organizationsandwithgovernmentagenciestomonitorthe
statusoflawsandregulationsaffectingthemarine
electronics industry.
Italsosponsorsconferencesandseminars,and
publishesanumberofguidesandperiodicalsformembers
and the general public.
128. International Electrotechnical Commission
TheInternationalElectrotechnicalCommission
(IEC)wasfoundedin1906asanoutgrowthoftheInterna-
tionalElectricalCongressheldatSt.Louis,Missouriin
1904.Some60countriesareactivemembers.Itsmissionis
todevelopandpromotestandardizationamongallnations
inthetechnicalspecificationsofelectricalandelectronic
equipment.Thesetechnologiesincludeelectronics,
magnetics,electromagnetics,electroacoustics,multimedia,
telecommunications,electricalenergyproductionand
distribution,andassociatedfieldssuchasterminologyand
symbology,compatibility,performancestandards,safety,
and environmental factors.
Bystandardizingintheseareas,theIECseeksto
promotemoreefficientmarkets,improvethequalityof
productsandstandardsofperformance,promoteinteroper-
ability,increaseproductionefficiency,andcontributeto
human health and safety and environmental protection.
StandardsarepublishedbytheIECintheformof
officialIECdocumentsafterdebateandinputfromthe
nationalcommittees.Standardsthusrepresentaconsensus
oftheviewsofmanydifferentinterests.Adoptionofa
standardbyanycountryisentirelyvoluntary.However,
failuretoadoptastandardmayresultinatechnicalbarrier
totrade,asgoodsmanufacturedtoaproprietarystandardin
onecountrymaybeincompatiblewiththesystemsof
others.
IECstandardsarevitaltothesuccessofECDISand
otherintegratednavigationsystemsbecausetheyhelpto
ensurethatsystemsfromvariousmanufacturersindifferent
countrieswillbecompatibleandmeetrequired
specifications.
15
CHAPTER 2
GEODESY AND DATUMS IN NAVIGATION
GEODESY, THE BASIS OF CARTOGRAPHY
200. Definition
Geodesyisthescienceconcernedwiththeexact
positioningofpointsonthesurfaceoftheEarth.Italso
involvesthestudyofvariationsoftheEarth’sgravity,the
applicationofthesevariationstoexactmeasurementson
theEarth,andthestudyoftheexactsizeandshapeofthe
Earth.Thesefactorswereunimportanttoearlynavigators
becauseoftherelativeinaccuracyoftheirmethods.The
precisionoftoday’snavigationsystemsandtheglobal
natureofsatelliteandotherlong-rangepositioningmethods
demandamorecompleteunderstandingofgeodesybythe
navigator than has ever before been required.
201. The Shape of the Earth
Thetopographicsurfaceistheactualsurfaceofthe
earth,uponwhichgeodeticmeasurementsaremade.These
measurementsarethenreducedtothegeoid.Marine
navigationmeasurementsaremadeontheoceansurface
which approximates the geoid.
Thegeoidisasurfacealongwhichgravityisalways
equalandtowhichthedirectionofgravityisalwaysperpen-
dicular.Thelatterpointisparticularlysignificantbecause
opticalinstrumentscontaininglevelingdevicesare
commonlyusedtomakegeodeticmeasurements.When
properlyadjusted,theverticalaxisoftheinstrument
coincidesexactlywiththedirectionofgravityandisby
definition perpendicular to the geoid. See Figure 201.
Thegeoidisthatsurfacetowhichtheoceanswould
conformovertheentireEarthiffreetoadjusttothe
combinedeffectoftheEarth’smassattractionandthe
centrifugalforceoftheEarth’srotation.Unevendistri-
butionoftheEarth’smassmakesthegeoidalsurface
irregular.
Thegeoidreferstotheactualsizeandshapeofthe
Earth,butsuchanirregularsurfacehasseriouslimitations
as a mathematical Earth model because:
•It has no complete mathematical expression.
•Smallvariationsinsurfaceshapeovertime
introduce small errors in measurement.
•Theirregularityofthesurfacewouldnecessitatea
prohibitive amount of computations.
Figure201.Geoid,ellipsoid,andtopographicsurfaceoftheEarth,anddeflectionoftheverticalduetodifferencesinmass.
16GEODESY AND DATUMS IN NAVIGATION
Thesurfaceofthegeoid,withsomeexceptions,tends
to rise under mountains and to dip above ocean basins.
Forgeodetic,mapping,andchartingpurposes,itis
necessarytousearegularorgeometricshapewhichclosely
approximatestheshapeofthegeoideitheronalocalor
globalscaleandwhichhasaspecificmathematical
expression. This shape is called theellipsoid.
Theseparationsofthegeoidandellipsoidarecalled
geoidalheights,geoidalundulations,orgeoidal
separations.
Naturalirregularitiesindensityanddepthsofthe
materialmakinguptheuppercrustoftheEarthalsoresult
inslightalterationsofthedirectionofgravity.These
alterationsarereflectedintheirregularshapeofthegeoid,
the surface that is perpendicular to a plumb line.
SincetheEarthisinfactflattenedslightlyatthepoles
andbulgessomewhatattheequator,thegeometricfigure
usedingeodesytomostnearlyapproximatetheshapeofthe
Earthistheoblatespheroidorellipsoidofrevolution.
Thisisthethreedimensionalshapeobtainedbyrotatingan
ellipse about its minor axis.
202. Defining the Ellipsoid
Anellipsoidofrevolutionisuniquelydefinedby
specifyingtwoparameters.Geodesists,byconvention,use
thesemimajoraxisandflattening.Thesizeisrepresented
bytheradiusattheequator,thesemimajoraxis.Theshape
oftheellipsoidisgivenbytheflattening,whichindicates
howcloselyanellipsoidapproachesasphericalshape.The
flatteningistheratioofthedifferencebetweenthe
semimajorandsemiminoraxesoftheellipsoidandthe
semimajoraxis.SeeFigure202.Ifaandbrepresentthe
semimajorandsemiminoraxes,respectively,ofthe
ellipsoid, and f is the flattening,
Thisratioisabout1/300fortheEarth.Theellipsoidal
EarthmodelhasitsminoraxisparalleltotheEarth’spolar
axis.
203. Ellipsoids and the Geoid as Reference Surfaces
Sincethesurfaceofthegeoidisirregularandthe
surfaceofanellipsoidisregular,noellipsoidcanprovide
morethananapproximationofpartofthegeoidalsurface.
Figure203illustratesanexample.Avarietyofellipsoids
are necessary to cover the entire earth.
204. Coordinates
Theastronomiclatitudeistheanglebetweenaplumb
lineandtheplaneofthecelestialequator.Itisthelatitude
whichresultsdirectlyfromobservationsofcelestialbodies,
uncorrectedfordeflectionoftheverticalcomponentinthe
meridian(north-south)direction.Astronomiclatitude
appliesonlytopositionsontheEarth.Itisreckonedfrom
the astronomic equator (0°), north and south through 90°.
Theastronomiclongitudeistheanglebetweenthe
planeofthecelestialmeridianatastationandtheplaneof
thecelestialmeridianatGreenwich.Itisthelongitude
whichresultsdirectlyfromobservationsofcelestialbodies,
uncorrectedfordeflectionoftheverticalcomponentinthe
primevertical(east-west)direction.Thesearethe
Figure 202. An ellipsoid of revolution, with semimajor
axis (a), and semiminor axis (b).
Figure203.AnellipsoidwhichfitswellinNorthAmerica
may not fit well in Europe, whose ellipsoid must have a
different size, shape, and origin. Other ellipsoids are
necessary for other areas
f
ab–
a
-----------=.
GEODESY AND DATUMS IN NAVIGATION17
coordinatesobservedbythecelestialnavigatorusinga
sextantandaveryaccurateclockbasedontheEarth’s
rotation.
Celestialobservationsbygeodesistsaremadewith
opticalinstruments(theodolite,zenithcamera,prismatic
astrolabe)whichallcontainlevelingdevices.When
properlyadjusted,theverticalaxisoftheinstrument
coincideswiththedirectionofgravity,whichmaynot
coincideswiththeplaneofthemeridian.Thus,geodetically
derivedastronomicpositionsarereferencedtothegeoid.
Thedifference,fromanavigationalstandpoint,istoosmall
to be of concern.
Thegeodeticlatitudeistheanglewhichthenormalto
theellipsoidatastationmakeswiththeplaneofthe
geodeticequator.Inrecordingageodeticposition,itis
essentialthatthegeodeticdatumonwhichitisbasedalso
bestated.Ageodeticlatitudediffersfromthe
correspondingastronomiclatitudebytheamountofthe
meridian component of the local deflection of the vertical.
Thegeodeticlongitudeistheanglebetweentheplane
ofthegeodeticmeridianatastationandtheplaneofthe
geodeticmeridianatGreenwich.Ageodeticlongitude
differsfromthecorrespondingastronomiclongitudebythe
primeverticalcomponentofthelocaldeflectionofthe
verticaldividedbythecosineofthelatitude.Thegeodetic
coordinates are used for mapping.
Thegeocentriclatitudeistheangleatthecenterofthe
ellipsoid(usedtorepresenttheEarth)betweentheplaneof
theequator,andastraightline(orradiusvector)toapoint
onthesurfaceoftheellipsoid.Thisdiffersfromgeodetic
latitudebecausetheEarthisapproximatedmorecloselyby
aspheroidthanasphereandthemeridiansareellipses,not
perfect circles.
Bothgeocentricandgeodeticlatitudesrefertothe
referenceellipsoidandnottheEarth.Sincetheparallelsof
latitudeareconsideredtobecircles,geodeticlongitudeis
geocentric, and a separate expression is not used.
Becauseoftheoblateshapeoftheellipsoid,thelength
ofadegreeofgeodeticlatitudeisnoteverywherethesame,
increasingfromabout59.7nauticalmilesattheequatorto
about 60.3 nautical miles at the poles.
Ahorizontalgeodeticdatumusuallyconsistsofthe
astronomicandgeodeticlatitude,andastronomicand
geodeticlongitudeofaninitialpoint(origin);anazimuthof
aline(direction);theparameters(radiusandflattening)of
theellipsoidselectedforthecomputations;andthegeoidal
separationattheorigin.Achangeinanyofthesequantities
affects every point on the datum.
Forthisreason,whilepositionswithinagivendatumare
directlyandaccuratelyrelatable,thosefromdifferentdatums
must be transformed to a common datum for consistency.
TYPES OF GEODETIC SURVEY
205. Triangulation
Themostcommontypeofgeodeticsurveyisknownas
triangulation.Triangulationconsistsofthemeasurement
oftheanglesofaseriesoftriangles.Theprincipleof
triangulationisbasedonplanetrigonometry.Ifthedistance
alongonesideofthetriangleandtheanglesateachendare
accuratelymeasured,theothertwosidesandtheremaining
anglecanbecomputed.Inpractice,alloftheanglesof
everytrianglearemeasuredtoprovideprecise
measurements.Also,thelatitudeandlongitudeofoneend
ofthemeasuredsidealongwiththelengthanddirection
(azimuth)ofthesideprovidesufficientdatatocomputethe
latitude and longitude of the other end of the side.
Themeasuredsideofthebasetriangleiscalleda
baseline.Measurementsaremadeascarefullyand
accuratelyaspossiblewithspeciallycalibratedtapesor
wiresofInvar,analloywithaverylowcoefficientof
expansion.Thetapeorwiresarecheckedperiodically
against standard measures of length.
Toestablishanarcoftriangulationbetweentwo
widelyseparatedlocations,thebaselinemaybemeasured
andlongitudeandlatitudedeterminedfortheinitialpoints
ateachlocation.Thelinesarethenconnectedbyaseriesof
adjoiningtrianglesformingquadrilateralsextendingfrom
eachend.Allanglesofthetrianglesaremeasured
repeatedlytoreduceerrors.Withthelongitude,latitude,
andazimuthoftheinitialpoints,similardataiscomputed
foreachvertexofthetriangles,therebyestablishing
triangulationstations,orgeodeticcontrolstations.The
coordinatesofeachofthestationsaredefinedasgeodetic
coordinates.
Triangulationisextendedoverlargeareasby
connectingandextendingseriesofarcstoformanetwork
ortriangulationsystem.Thenetworkisadjustedsoasto
reduceobservationalerrorstoaminimum.Adenserdistri-
butionofgeodeticcontrolisachievedbysubdividingor
filling in with other surveys.
Therearefourgeneralclassesorordersoftriangu-
lation.First-order(primary)triangulationisthemost
preciseandexacttype.Themostaccurateinstrumentsand
rigorouscomputationmethodsareused.Itiscostlyand
time-consuming,andisusuallyusedtoprovidethebasic
frameworkofcontroldataforanarea,andthedetermi-
nationofthefigureoftheEarth.Themostaccuratefirst-
ordersurveysfurnishcontrolpointswhichcanbe
interrelatedwithanaccuracyrangingfrom1partin25,000
overshortdistancestoapproximately1partin100,000for
long distances.
Second-ordertriangulationfurnishespointscloser
togetherthanintheprimarynetwork.Whilesecond-order
surveysmaycoverquiteextensiveareas,theyareusually
18GEODESY AND DATUMS IN NAVIGATION
tiedtoaprimarysystemwherepossible.Theproceduresare
less exacting and the proportional error is 1 part in 10,000.
Third-ordertriangulationisrunbetweenpointsina
secondarysurvey.Itisusedtodensifylocalcontrolnetsand
positionthetopographicandhydrographicdetailofthe
area. Error can amount to 1 part in 5,000.
Thesoleaccuracyrequirementforfourth-ordertriangu-
lationisthatthepositionsbelocatedwithoutanyappreciable
erroronmapscompiledonthebasisofthecontrol.Fourth-
order control is done primarily as mapping control.
206. Trilateration, Traverse, And Vertical Surveying
Trilaterationinvolvesmeasuringthesidesofachainof
trianglesorotherpolygons.Fromthem,thedistanceand
directionfromAtoBcanbecomputed.Figure206showsthis
process.
Traverseinvolvesmeasuringdistancesandtheangles
betweenthemwithouttrianglesforthepurposeof
computingthedistanceanddirectionfromAtoB.See
Figure 206.
Verticalsurveyingistheprocessofdetermining
elevationsabovemeansea-level.Ingeodeticsurveysexecuted
primarilyformapping,geodeticpositionsarereferredtoan
ellipsoid,andtheelevationsofthepositionsarereferredtothe
geoid.However,forsatellitegeodesythegeoidalheightsmust
be considered to establish the correct height above the geoid.
Precisegeodeticlevelingisusedtoestablishabasic
networkofverticalcontrolpoints.Fromthese,theheightof
otherpositionsinthesurveycanbedeterminedbysupple-
mentarymethods.Themeansea-levelsurfaceusedasa
reference(verticaldatum)isdeterminedbyaveragingthe
hourlywaterheightsforaspecifiedperiodoftimeat
specified tide gauges.
Therearethreelevelingtechniques:differential,
trigonometric,andbarometric.Differentiallevelingisthe
mostaccurateofthethreemethods.Withtheinstrument
lockedinposition,readingsaremadeontwocalibrated
staffsheldinanuprightpositionaheadofandbehindthe
instrument.Thedifferencebetweenreadingsisthe
difference in elevation between the points.
Trigonometriclevelinginvolvesmeasuringavertical
anglefromaknowndistancewithatheodoliteand
computingtheelevationofthepoint.Withthismethod,
verticalmeasurementcanbemadeatthesametime
horizontalanglesaremeasuredfortriangulation.Itis,
therefore,asomewhatmoreeconomicalmethodbutless
accuratethandifferentialleveling.Itisoftentheonly
mechanicalmethodofestablishingaccurateelevationcontrol
in mountainous areas.
Inbarometricleveling,differencesinheightare
determinedbymeasuringthedifferencesinatmospheric
pressureatvariouselevations.Airpressureismeasuredby
mercurialoraneroidbarometer,oraboilingpoint
thermometer.Althoughtheaccuracyofthismethodisnot
asgreataseitheroftheothertwo,itobtainsrelativeheights
veryrapidlyatpointswhicharefairlyfarapart.Itisusedin
reconnaissanceandexploratorysurveyswheremore
accuratemeasurementswillbemadelaterorwhereahigh
degree of accuracy is not required.
Figure 206. Triangulation, trilateration, and traverse.
GEODESY AND DATUMS IN NAVIGATION19
DATUM CONNECTIONS
207. Definitions
Adatumisdefinedasanynumericalorgeometrical
quantityorsetofsuchquantitieswhichservesasa
reference point from which to measure other quantities.
Ingeodesy,cartography,andnavigation,twogeneral
typesofdatumsmustbeconsidered:horizontaldatumand
verticaldatum.Thehorizontaldatumformsthebasisfor
computationsofhorizontalposition.Theverticaldatum
providesthereferencetomeasureheightsordepths,andmay
beoneoftwotypes:Verticalgeodeticdatumisthereference
usedbysurveyorstomeasureheightsoftopographicfeatures,
andbycartographerstoportraythem.Thisshouldnotbe
confusedwiththevarioustypesoftidaldatums,whichareby
definitionverticaldatums(andhavingnohorizontal
component),usedtodefinetheheightsanddepthsof
hydrographicfeatures,suchaswaterdepthsorbridge
clearances.Theverticalgeodeticdatumisderivedfromits
mathematicalexpression,whilethetidaldatumisderived
fromactualtidaldata.Foracompletediscussionoftidal
datums, see Chapter 9.
Thischapterwilldiscussonlygeodeticdatums.For
navigationalpurposes,verticalgeodeticdatumsarequite
unimportant,whilehorizontalgeodeticdatumsandtidal
datums are vital.
Ahorizontaldatummaybedefinedatanoriginpointon
theellipsoid(localdatum)suchthatthecenteroftheellipsoid
coincideswiththeEarth’scenterofmass(geocentricdatum).
Thecoordinatesforpointsinspecificgeodeticsurveysand
triangulationnetworksarecomputedfromcertaininitial
quantities, or datums.
208. Preferred Datums
Inareasofoverlappinggeodetictriangulation
networks,eachcomputedonadifferentdatum,the
coordinatesofthepointsgivenwithrespecttoonedatum
willdifferfromthosegivenwithrespecttotheother.The
differencescanbeusedtoderivetransformationformulas.
Datumsareconnectedbydevelopingtransformation
formulasatcommonpoints,eitherbetweenoverlapping
control networks or by satellite connections.
Manycountrieshavedevelopednationaldatumswhich
differfromthoseoftheirneighbors.Accordingly,national
maps and charts often do not agree along national borders.
TheNorthAmericanDatum,1927(NAD27)has
beenusedintheUnitedStatesforabout60years,butitis
beingreplacedbydatumsbasedontheWorldGeodetic
System.NAD27coordinatesarebasedonthelatitudeand
longitudeofatriangulationstation(thereferencepoint)at
Mead’sRanchinKansas,theazimuthtoanearbytriangu-
lationstationcalledWaldo,andthemathematical
parametersoftheClarkeEllipsoidof1866.Otherdatums
throughouttheworldusedifferentassumptionsastoorigin
points and ellipsoids.
The origin of theEuropeanDatum is at Potsdam,
Germany.Numerousnationalsystemshavebeenjoined
intoalargedatumbasedupontheInternationalEllipsoidof
1924whichwasorientedbyamodifiedastrogeodetic
method.European,African,andAsiantriangulationchains
wereconnected,andAfricanmeasurementsfromCairoto
CapeTownwerecompleted.Thus,allofEurope,Africa,
andAsiaaremoldedintoonegreatsystem.Through
commonsurveystations,itwasalsopossibletoconvert
datafromtheRussianPulkova,1932systemtothe
EuropeanDatum,andasaresult,theEuropeanDatum
includestriangulationasfareastasthe84thmeridian.
AdditionaltiesacrosstheMiddleEasthavepermitted
connection of the Indian and European Datums.
TheOrdnanceSurveyofGreatBritain1936Datum
hasnopointoforigin.Thedatawasderivedasabestfit
betweenretriangulationandoriginalvaluesof11pointsof
theearlierPrincipalTriangulationofGreatBritain(1783-
1853).
TokyoDatumhasitsorigininTokyo.Itisdefinedin
termsoftheBesselEllipsoidandorientedbyasingle
astronomicstation.TriangulationtiesthroughKoreaconnect
theJapanesedatumwiththeManchuriandatum.Unfortu-
nately,Tokyoissituatedonasteepslopeonthegeoid,andthe
single-stationorientationhasresultedinlargesystematic
geoidalseparationsasthesystemisextendedfromitsinitial
point.
TheIndianDatumisthepreferreddatumforIndiaand
severaladjacentcountriesinSoutheastAsia.Itiscomputed
ontheEverestEllipsoidwithitsoriginatKalianpur,in
centralIndia.Itislargelytheresultoftheuntiringworkof
SirGeorgeEverest(1790-1866),SurveyorGeneralinIndia
from1830to1843.Heisbestknownbythemountain
namedafterhim,butbyfarhismostimportantlegacywas
the survey of the Indian subcontinent.
MODERN GEODETIC SYSTEMS
209. Development of the World Geodetic System
Bythelate1950’stheincreasingrangeandsophisti-
cationofweaponssystemshadrenderedlocalornational
datumsinadequateformilitarypurposes;thesenew
weaponsrequireddatumsatleastcontinental,ifnotglobal,
inscope.Inresponsetotheserequirements,theU.S.
DepartmentofDefensegeneratedageocentric(earth-
centered)referencesystemtowhichdifferentgeodetic
networkscouldbereferred,andestablishedcompatibility
20GEODESY AND DATUMS IN NAVIGATION
betweenthecoordinatesystems.EffortsoftheArmy,Navy,
andAirForcewerecombined,leadingtothedevelopment
of the DoDWorld Geodetic System of 1960 (WGS 60).
InJanuary1966,aWorldGeodeticSystemCommittee
waschargedwiththeresponsibilityfordevelopingan
improvedWGSneededtosatisfymapping,charting,and
geodeticrequirements.Additionalsurfacegravity
observations,resultsfromtheextensionoftriangulationand
trilaterationnetworks,andlargeamountsofDopplerand
opticalsatellitedatahadbecomeavailablesincethe
developmentofWGS60.Usingtheadditionaldataand
improvedtechniques,theCommitteeproducedWGS66
whichservedDoDneedsfollowingitsimplementationin
1967.
ThesameWorldGeodeticSystemCommitteebegan
workin1970todevelopareplacementforWGS66.Sincethe
developmentofWGS66,largequantitiesofadditionaldata
hadbecomeavailablefrombothDopplerandopticalsatellites,
surfacegravitysurveys,triangulationandtrilaterationsurveys,
high precision traverses, and astronomic surveys.
Inaddition,improvedcapabilitieshadbeendeveloped
inbothcomputersandcomputersoftware.Continued
researchincomputationalproceduresanderroranalyses
hadproducedbettermethodsandanimprovedfacilityfor
handlingandcombiningdata.Afteranextensiveeffort
extendingoveraperiodofapproximatelythreeyears,the
CommitteecompletedthedevelopmentoftheDepartment
of DefenseWorld Geodetic System 1972 (WGS 72).
FurtherrefinementofWGS72resultedinthenewWorld
GeodeticSystemof1984(WGS84),nowreferredtoas
simplyWGS.Forsurfacenavigation,WGS60,66,72andthe
newWGS84areessentiallythesame,sothatpositions
computedonanyWGScoordinatescanbeplotteddirectlyon
the others without correction.
TheWGSsystemisnotbasedonasinglepoint,but
manypoints,fixedwithextremeprecisionbysatellitefixes
andstatisticalmethods.Theresultisanellipsoidwhichfits
therealsurfaceoftheEarth,orgeoid,farmoreaccurately
thananyother.TheWGSsystemisapplicableworldwide.
AllregionaldatumscanbereferencedtoWGSoncea
survey tie has been made.
Figure 208. Major geodetic datum blocks.
GEODESY AND DATUMS IN NAVIGATION21
210. The New North American Datum Of 1983
TheCoastAndGeodeticSurveyoftheNationalOcean
Service(NOS),NOAA,isresponsibleforchartingUnited
Stateswaters.From1927to1987,U.S.chartswerebased
onNAD27,usingtheClarke1866ellipsoid.In1989,the
U.S.officiallyswitchedtoNAD83(navigationally
equivalenttoWGS)forallmappingandchartingpurposes,
andallnewNOSchartproductionisbasedonthisnew
standard.
Thegridofinterconnectedsurveyswhichcriss-crosses
theUnitedStatesconsistsofsome250,000controlpoints,
eachconsistingofthelatitudeandlongitudeofthepoint,
plusadditionaldatasuchaselevation.ConvertingtheNAD
27coordinatestoNAD83involvedrecomputingthe
positionofeachpointbasedonthenewNAD83datum.In
additiontothe250,000U.S.controlpoints,several
thousandmorewereaddedtotieinsurveysfromCanada,
Mexico, and Central America.
Conversionofneweditionchartstothenewdatums,
eitherWGS84orNAD83,involvesconvertingreference
pointsoneachchartfromtheolddatumtothenew,and
adjustingthelatitudeandlongitudegrid(knownasthe
graticule)sothatitreflectsthenewlyplottedpositions.This
adjustmentofthegraticuleistheonlydifferencebetween
chartswhichdifferonlyindatum.Allchartedfeatures
remain in exactly the same relative positions.
TheGlobalPositioningSystem(GPS)hastransformed
thescienceofsurveying,enablingtheestablishmentof
precisetiestoWGSinareaspreviouslyfoundtobetoo
remotetosurveytomodernstandards.Asaresult,new
chartsareincreasinglypreciseastopositionoffeatures.
Themorerecentachart’sdateofpublishing,themore
likelyitisthatitwillbeaccurateastopositions.Navigators
shouldalwaysrefertothetitleblockofacharttodetermine
thedateofthechart,thedateofthesurveysandsources
used to compile it, and the datum on which it is based.
DATUMS AND NAVIGATION
211. Datum Shift
Oneofthemostseriousimpactsofdifferentdatumson
navigationoccurswhenanavigationsystemprovidesafix
basedonadatumdifferentfromthatusedforthenautical
chart.Theresultingplottedpositionmaybedifferentfrom
theactuallocationonthatchart.Thisdifferenceisknown
as adatum shift.
Modernelectronicnavigationsystemshavesoftware
installedthatcanoutputpositionsinavarietyofdatums,
eliminatingthenecessityforapplyingcorrections.Allelec-
tronicchartsproducedbyNIMAarecompiledonWGSand
arenotsubjecttodatumshiftproblemsaslongastheGPS
receiverisoutputtingWGSpositiondatatothedisplaysys-
tem.ThesameistrueforNOAAchartsoftheU.S.,which
arecompiledonNAD83datum,verycloselyrelatedto
WGS.GPSreceivers,includingtheWRN-6,defaultto
WGS,sothatnoactionisnecessarytouseanyU.S.-pro-
duced electronic charts.
Toautomatedatumconversions,anumberofdatum
transformationsoftwareprogramshavebeenwrittenthat
willconvertfromanyknowndatumtoanyother,inanylo-
cation.MADTRANandGEOTRANS-2aretwosuch
programs.Theamountofdatumshiftbetweentwodifferent
datumsisnotlinear.Thatis,theamountofshiftisafunc-
tionofthepositionoftheobserver,whichmustbespecified
fortheshifttobecomputed.Varyingdifferencesoflatitude
andlongitudebetweentwodifferentdatumswillbenoted
as one’s location changes.
TherearestillafewNIMA-producedpapercharts,and
anumberofchartsfromothercountries,basedondatums
otherthanWGS.Ifthedatumofthesechartsisnotedinthe
titleblockofthechart,theWRN-6andmostotherGPSre-
ceiverscanbesettooutputpositiondatainthatdatum,
eliminatingthedatumshiftproblem.Ifthedatumisnotlist-
ed,extremecautionisnecessary.Anoffsetcansometimes
beestablishediftheship’sactualpositioncanbedeter-
minedwithsufficientaccuracy,andthisoffsetappliedto
GPSpositionsinthelocalarea.Butrememberthatsincea
datumshiftisnotlinear,thisoffsetisonlyapplicable
locally.
Anothereffectonnavigationoccurswhenshifting
betweenchartsthathavebeencompiledusingdifferent
datums.Ifapositionisreplottedonachartofanotherdatum
usinglatitudeandlongitude,thenewlyplottedpositionwill
notmatchwithrespecttootherchartedfeatures.Thedatum
shiftmaybeavoidedbytransferringpositionsusing
bearingsandrangestocommonpoints.Ifdatumshift
conversionnotesfortheapplicabledatumsaregivenonthe
charts,positionsdefinedbylatitudeandlongitudemaybe
replotted after applying the noted correction.
ThepositionsgivenforchartcorrectionsintheNoticeto
Marinersreflecttheproperdatumforeachspecificchartand
editionnumber.Duetoconversionofchartsbasedonold
datumstomoremodernones,andtheuseofmanydifferent
datumsthroughouttheworld,chartcorrectionsintendedfor
oneeditionofachartmaynotbesafelyplottedonanyother.
Asnoted,datumshiftsarenotconstantthroughouta
givenregion,butvaryaccordingtohowthediffering
datumsfittogether.Forexample,theNAD27toNAD83
conversionresultedinchangesinlatitudeof40metersin
Miami,11metersinNewYork,and20metersinSeattle.
Longitudechangesforthisconversionamountedto22
metersinMiami,35metersinNewYork,and93metersin
Seattle.
MostchartsproducedbyNIMAandNOSshowa
22GEODESY AND DATUMS IN NAVIGATION
“datumnote.”Thisnoteisusuallyfoundinthetitleblock
orintheupperleftmarginofthechart.Accordingtothe
yearofthechartedition,thescale,andpolicyatthetimeof
production,thenotemaysay“WorldGeodeticSystem
1972(WGS-72)”,“WorldGeodeticSystem1984(WGS-
84)”,or“WorldGeodeticSystem(WGS).”Adatumnote
forachartforwhichsatellitepositionscanbeplotted
withoutcorrectionwillread:“Positionsobtainedfrom
satellitenavigationsystemsreferredto(ReferenceDatum)
can be plotted directly on this chart.”
NIMAreproductionsofforeignchartswillusuallybe
inthedatumorreferencesystemoftheproducingcountry.
Inthesecasesaconversionfactorisgiveninthefollowing
format:“Positionsobtainedfromsatellitenavigation
systemsreferredtothe(ReferenceDatum)mustbemoved
X.XXminutes(Northward/Southward)andX.XXminutes
(Eastward/ Westward) to agree with this chart.”
SomechartscannotbetiedintoWGSbecauseoflack
ofrecentsurveys.Currentlyissuedchartsofsomeareasare
basedonsurveysorusedataobtainedintheageofsailing
ships.Thelackofsurveyedcontrolpointsmeansthatthey
cannotbeproperlyreferencedtomoderngeodeticsystems.
Inthiscasetheremaybeanotethatsays:“Adjustmentsto
WGS cannot be determined for this chart.”
Afewchartsmayhavenodatumnoteatall,butmay
carryanotewhichsays:“Fromvarioussourcesto(year).”
Inthesecasesthereisnowayforthenavigatortodetermine
themathematicaldifferencebetweenthelocaldatumand
WGSpositions.However,ifaradarorvisualfixcanbe
accuratelydetermined,andanoffsetestablishedasnoted
above.ThisoffsetcanthenbeprogrammedintotheGPS
receiver.
To minimize problems caused by differing datums:
•Plotchartcorrectionsonlyonthespecificchartsandedi-
tionsforwhichtheyareintended.Eachchartcorrection
isspecifictoonlyoneeditionofachart.Whenthesame
correctionismadeontwochartsbasedondifferentda-
tums,thepositionsforthesamefeaturemaydiffer
slightly.Thisdifferenceisequaltothedatumshiftbe-
tween the two datums for that area.
•Trytodeterminethesourceanddatumofpositionsof
temporaryfeatures,suchasdrillrigs.Ingeneraltheyare
giveninthedatumusedintheareainquestion.Since
thesearepreciselypositionedusingsatellites,WGSis
thenormaldatum.Adatumcorrection,ifneeded,might
be found on a chart of the area.
•Rememberthatifthedatumofaplottedfeatureisnot
known,positioninaccuraciesmayresult.Itiswiseto
allowamarginoferrorifthereisanydoubtaboutthe
datum.
•Knowhowthedatumofthepositioningsystemyou
areusing(Loran,GPS,etc.)relatestoyourchart.
GPSandothermodernpositioningsystemsuse
WGSdatum.Ifyourchartisonanyotherdatum,you
mustprogramthesystemtousethechart’sdatum,or
applyadatumcorrectionwhenplottingGPS
positions on the chart.
23
CHAPTER 3
NAUTICAL CHARTS
CHART FUNDAMENTALS
300. Definitions
Anauticalchartrepresentspartofthesphericalearth
onaplanesurface.Itshowswaterdepth,theshorelineof
adjacentland,prominenttopographicfeatures,aidstonav-
igation,andothernavigationalinformation.Itisawork
areaonwhichthenavigatorplotscourses,ascertainsposi-
tions,andviewstherelationshipoftheshiptothe
surroundingarea.Itassiststhenavigatorinavoidingdan-
gers and arriving safely at his destination.
Originallyhand-drawnonsheepskin,traditionalnauti-
calchartshaveforgenerationsbeenprintedonpaper.
Electronicchartsconsistingofadigitaldatabaseanda
displaysystemareinuseandarereplacingpapercharts
aboardmanyvessels.Anelectronicchartisnotsimplya
digitalversionofapaperchart;itintroducesanewnaviga-
tionmethodologywithcapabilitiesandlimitationsvery
differentfrompapercharts.Theelectronicchartisthelegal
equivalentofthepaperchartifitmeetscertainInternational
MaritimeOrganizationspecifications.SeeChapter14fora
complete discussion of electronic charts.
Shouldamarineaccidentoccur,thenauticalchartin
useatthetimetakesonlegalsignificance.Incasesof
grounding,collision,andotheraccidents,chartsbecome
criticalrecordsforreconstructingtheeventandassigning
liability.Chartsusedinreconstructingtheincidentcanalso
have tremendous training value.
301. Projections
Becauseacartographercannottransferaspheretoa
flatsurfacewithoutdistortion,hemustprojectthesurface
ofasphereontoadevelopablesurface.Adevelopablesur-
faceisonethatcanbeflattenedtoformaplane.This
processisknownaschartprojection.Ifpointsonthesur-
faceofthesphereareprojectedfromasinglepoint,the
projection is said to beperspective orgeometric.
Astheuseofelectronicchartsbecomesincreasingly
widespread,itisimportanttorememberthatthesamecar-
tographicprinciplesthatapplytopaperchartsapplytotheir
depiction on video screens.
302. Selecting a Projection
Eachprojectionhascertainpreferablefeatures.How-
ever,astheareacoveredbythechartbecomessmaller,the
differencesbetweenvariousprojectionsbecomelessno-
ticeable.Onthelargestscalechart,suchasofaharbor,all
projectionsarepracticallyidentical.Somedesirableproper-
ties of a projection are:
1.True shape of physical features
2.Correct angular relationships
3.Equalarea(Representsareasinproperproportions)
4.Constant scale values
5.Great circles represented as straight lines
6.Rhumb lines represented as straight lines
Someofthesepropertiesaremutuallyexclusive.For
example,asingleprojectioncannotbebothconformaland
equalarea.Similarly,bothgreatcirclesandrhumblinescan-
not be represented on a single projection as straight lines.
303. Types of Projections
Thetypeofdevelopablesurfacetowhichthespherical
surfaceistransferreddeterminestheprojection’sclassifica-
tion.Furtherclassificationdependsonwhetherthe
projectioniscenteredontheequator(equatorial),apole
(polar),orsomepointorlinebetween(oblique).Thename
of a projection indicates its type and its principal features.
MarinersmostfrequentlyuseaMercatorprojection,
classifiedasacylindricalprojectionuponaplane,thecyl-
indertangentalongtheequator.Similarly,aprojection
baseduponacylindertangentalongameridianiscalled
transverse(orinverse)Mercatorortransverse(orin-
verse)orthomorphic.TheMercatoristhemostcommon
projectionusedinmaritimenavigation,primarilybecause
rhumb lines plot as straight lines.
Inasimpleconicprojection,pointsonthesurfaceof
theeartharetransferredtoatangentcone.IntheLambert
conformalprojection,theconeintersectstheearth(ase-
cantcone)attwosmallcircles.Inapolyconicprojection,
a series of tangent cones is used.
Inanazimuthalorzenithalprojection,pointsonthe
eartharetransferreddirectlytoaplane.Iftheoriginofthe
24NAUTICAL CHARTS
projectingraysisthecenteroftheearth,agnomonicpro-
jectionresults;ifitisthepointoppositetheplane’spointof
tangency,astereographicprojection;andifatinfinity
(theprojectinglinesbeingparalleltoeachother),anortho-
graphicprojection.Thegnomonic,stereographic,and
orthographicareperspectiveprojections.Inanazimuthal
equidistantprojection,whichisnotperspective,thescale
ofdistancesisconstantalonganyradiallinefromthepoint
of tangency. See Figure 303.
Cylindricalandplaneprojectionsarespecialconical
projections, using heights infinity and zero, respectively.
Agraticuleisthenetworkoflatitudeandlongitude
lineslaidoutinaccordancewiththeprinciplesofany
projection.
304. Cylindrical Projections
Ifacylinderisplacedaroundtheearth,tangentalong
theequator,andtheplanesofthemeridiansareextended,
theyintersectthecylinderinanumberofverticallines.See
Figure304.Theseparallellinesofprojectionareequidis-
tantfromeachother,unliketheterrestrialmeridiansfrom
whichtheyarederivedwhichconvergeasthelatitudein-
creases.Ontheearth,parallelsoflatitudeareperpendicular
tothemeridians,formingcirclesofprogressivelysmaller
diameterasthelatitudeincreases.Onthecylindertheyare
shownperpendiculartotheprojectedmeridians,butbe-
causeacylinderiseverywhereofthesamediameter,the
projected parallels are all the same size.
Ifthecylinderiscutalongaverticalline(ameridian)
andspreadoutflat,themeridiansappearasequallyspaced
verticallines;andtheparallelsappearashorizontallines.
Theparallels’relativespacingdiffersinthevarioustypesof
cylindrical projections.
Ifthecylinderistangentalongsomegreatcircleother
thantheequator,theprojectedpatternoflatitudeandlongi-
tudelinesappearsquitedifferentfromthatdescribedabove,
sincethelineoftangencyandtheequatornolongercoin-
cide.Theseprojectionsareclassifiedasobliqueor
transverse projections.
305. Mercator Projection
Navigatorsmostoftenusetheplaneconformalprojection
knownastheMercatorprojection.TheMercatorprojectionis
notperspective,anditsparallelscanbederivedmathematically
aswellasprojectedgeometrically.Itsdistinguishingfeatureis
thatboththemeridiansandparallelsareexpandedatthesame
ratiowithincreasedlatitude.Theexpansionisequaltothesecant
ofthelatitude,withasmallcorrectionfortheellipticityofthe
earth.Sincethesecantof90°isinfinity,theprojectioncannotin-
cludethepoles.Sincetheprojectionisconformal,expansionis
thesameinalldirectionsandanglesarecorrectlyshown.
Rhumblinesappearasstraightlines,thedirectionsofwhichcan
bemeasureddirectlyonthechart.Distancescanalsobemea-
sureddirectlyifthespreadoflatitudeissmall.Greatcircles,
exceptmeridiansandtheequator,appearascurvedlinescon-
cavetotheequator.Smallareasappearintheircorrectshapebut
of increased size unless they are near the equator.
306. Meridional Parts
Attheequatoradegreeoflongitudeisapproximately
equalinlengthtoadegreeoflatitude.Asthedistancefrom
theequatorincreases,degreesoflatituderemainapproxi-
matelythesame,whiledegreesoflongitudebecome
Figure 303. Azimuthal projections: A, gnomonic; B,
stereographic; C, (at infinity) orthographic.
Figure 304. A cylindrical projection.
NAUTICAL CHARTS25
progressivelyshorter.Sincedegreesoflongitudeappear
everywherethesamelengthintheMercatorprojection,itis
necessarytoincreasethelengthofthemeridiansiftheex-
pansionistobeequalinalldirections.Thus,tomaintainthe
correctproportionsbetweendegreesoflatitudeanddegrees
oflongitude,thedegreesoflatitudemustbeprogressively
longerasthedistancefromtheequatorincreases.Thisisil-
lustrated in Figure 306.
Thelengthofameridian,increasedbetweentheequa-
torandanygivenlatitude,expressedinminutesofarcatthe
equatorasaunit,constitutesthenumberofmeridionalparts
(M)correspondingtothatlatitude.Meridionalparts,given
inTable6foreveryminuteoflatitudefromtheequatorto
thepole,makeitpossibletoconstructaMercatorchartand
tosolveproblemsinMercatorsailing.Thesevaluesarefor
the WGS ellipsoid of 1984.
307. Transverse Mercator Projections
ConstructingachartusingMercatorprinciples,but
withthecylindertangentalongameridian,resultsina
transverseMercatorortransverseorthomorphicpro-
jection.Theword“inverse”isusedinterchangeablywith
“transverse.”Theseprojectionsuseafictitiousgraticule
similarto,butoffsetfrom,thefamiliarnetworkofmeridi-
ansandparallels.Thetangentgreatcircleisthefictitious
equator.Ninetydegreesfromitaretwofictitiouspoles.A
groupofgreatcirclesthroughthesepolesandperpendicular
tothetangentgreatcirclearethefictitiousmeridians,while
aseriesofcirclesparalleltotheplaneofthetangentgreat
circleformthefictitiousparallels.Theactualmeridiansand
parallels appear as curved lines.
AstraightlineonthetransverseorobliqueMercator
projectionmakesthesameanglewithallfictitiousmerid-
ians,butnotwiththeterrestrialmeridians.Itistherefore
afictitiousrhumbline.Nearthetangentgreatcircle,a
straightlinecloselyapproximatesagreatcircle.Thepro-
jectionismostusefulinthisarea.Sincetheareaof
minimumdistortionisnearameridian,thisprojectionis
usefulforchartscoveringalargebandoflatitudeandex-
tendingarelativelyshortdistanceoneachsideofthe
tangentmeridian.Itissometimesusedforstarcharts
showingtheeveningskyatvariousseasonsoftheyear.
See Figure 307.
Figure 306. A Mercator map of the world.
26NAUTICAL CHARTS
308. Universal Transverse Mercator (UTM) Grid
TheUniversalTransverseMercator(UTM)gridisa
militarygridsuperimposeduponatransverseMercatorgrati-
cule,ortherepresentationofthesegridlinesuponany
graticule.Thisgridsystemandtheseprojectionsareoftenused
for large-scale (harbor) nautical charts and military charts.
309. Oblique Mercator Projections
AMercatorprojectioninwhichthecylinderistangent
alongagreatcircleotherthantheequatororameridianis
calledanobliqueMercatororobliqueorthomorphic
projection.SeeFigure309aandFigure309b.Thisprojec-
tionisusedprincipallytodepictanareainthenearvicinity
ofanobliquegreatcircle.Figure309c,forexample,shows
thegreatcirclejoiningWashingtonandMoscow.Figure
309dshowsanobliqueMercatormapwiththegreatcircle
betweenthesetwocentersasthetangentgreatcircleorfic-
titiousequator.ThelimitsofthechartofFigure309care
indicatedinFigure309d.Notethelargevariationinscale
as the latitude changes.
Figure 307. A transverse Mercator map of the Western
Hemisphere.
Figure 309a. An oblique Mercator projection.
Figure 309b. The fictitious graticule of an oblique
Mercator projection.
NAUTICAL CHARTS27
310. Rectangular Projection
AcylindricalprojectionsimilartotheMercator,but
withuniformspacingoftheparallels,iscalledarectangu-
larprojection.Itisconvenientforgraphicallydepicting
informationwheredistortionisnotimportant.Theprincipal
navigationaluseofthisprojectionisforthestarchartofthe
AirAlmanac,wherepositionsofstarsareplottedbyrectan-
gularcoordinatesrepresentingdeclination(ordinate)and
siderealhourangle(abscissa).Sincethemeridiansarepar-
allel,theparallelsoflatitude(includingtheequatorandthe
poles) are all represented by lines of equal length.
311. Conic Projections
Aconicprojectionisproducedbytransferringpoints
fromthesurfaceoftheearthtoaconeorseriesofcones.
Thisconeisthencutalonganelementandspreadoutflatto
formthechart.Whentheaxisoftheconecoincideswiththe
axisoftheearth,thentheparallelsappearasarcsofcircles,
andthemeridiansappearaseitherstraightorcurvedlines
convergingtowardthenearerpole.Limitingtheareacov-
eredtothatpartoftheconenearthesurfaceoftheearth
limitsdistortion.Aparallelalongwhichthereisnodistor-
tioniscalledastandardparallel.Neitherthetransverse
conicprojection,inwhichtheaxisoftheconeisinthe
equatorialplane,northeobliqueconicprojection,inwhich
theaxisoftheconeisobliquetotheplaneoftheequator,is
ordinarilyusedfornavigation.Theyaretypicallyusedfor
illustrative maps.
Usingconestangentatvariousparallels,asecant(in-
tersecting)cone,oraseriesofconesvariestheappearance
and features of a conic projection.
312. Simple Conic Projection
Aconicprojectionusingasingletangentconeisasim-
pleconicprojection(Figure312a).Theheightofthecone
increasesasthelatitudeofthetangentparalleldecreases.At
theequator,theheightreachesinfinityandtheconebe-
Figure 309c. The great circle between Washington and Moscow as it appears on a Mercator map.
Figure 309d. An oblique Mercator map based upon a cylinder tangent along the great circle through Washington and
Moscow.Themapincludesanarea500milesoneachsideofthegreatcircle.Thelimitsofthismapareindicatedonthe
Mercator map ofFigure 309c.
28NAUTICAL CHARTS
comesacylinder.Atthepole,itsheightiszero,andthe
conebecomesaplane.SimilartotheMercatorprojection,
thesimpleconicprojectionisnotperspectivesinceonlythe
meridiansareprojectedgeometrically,eachbecomingan
elementofthecone.Whenthisprojectionisspreadoutflat
toformamap,themeridiansappearasstraightlinescon-
vergingattheapexofthecone.Thestandardparallel,
wheretheconeistangenttotheearth,appearsasthearcof
a circle with its center at the apex of the cone. The other
parallelsareconcentriccircles.Thedistancealonganyme-
ridianbetweenconsecutiveparallelsisincorrectrelationto
thedistanceontheearth,and,therefore,canbederived
mathematically.Thepoleisrepresentedbyacircle(Figure
312b).Thescaleiscorrectalonganymeridianandalong
thestandardparallel.Allotherparallelsaretoogreatin
length,withtheerrorincreasingwithincreaseddistance
fromthestandardparallel.Sincethescaleisnotthesamein
alldirectionsabouteverypoint,theprojectionisneithera
conformalnorequal-areaprojection.Itsnon-conformalna-
ture is its principal disadvantage for navigation.
Sincethescaleiscorrectalongthestandardparallel
andvariesuniformlyoneachside,withcomparativelylittle
distortionnearthestandardparallel,thisprojectionisuseful
formappinganareacoveringalargespreadoflongitude
andacomparativelynarrowbandoflatitude.Itwasdevel-
opedbyClaudiusPtolemyinthesecondcenturyA.D.to
map just such an area: the Mediterranean Sea.
Figure 312a. A simple conic projection.
Figure 312b. A simple conic map of the Northern Hemisphere.
NAUTICAL CHARTS29
313. Lambert Conformal Projection
Theusefullatituderangeofthesimpleconicprojection
canbeincreasedbyusingasecantconeintersectingtheearth
attwostandardparallels.SeeFigure313.Theareabetweenthe
twostandardparallelsiscompressed,andthatbeyondisex-
panded.Suchaprojectioniscalledeitherasecantconicor
conic projection with two standard parallels.
Ifinsuchaprojectionthespacingoftheparallelsisal-
tered,suchthatthedistortionisthesamealongthemas
alongthemeridians,theprojectionbecomesconformal.
ThismodificationproducestheLambertconformalpro-
jection.Ifthechartisnotcarriedfarbeyondthestandard
parallels,andifthesearenotagreatdistanceapart,thedis-
tortion over the entire chart is small.
Astraightlineonthisprojectionsonearlyapproximatesa
greatcirclethatthetwoarenearlyidentical.Radiobeaconsig-
nalstravelgreatcircles;thus,theycanbeplottedonthis
projectionwithoutcorrection.Thisfeature,gainedwithoutsac-
rificingconformality,hasmadethisprojectionpopularfor
aeronauticalchartsbecauseaircraftmakewideuseofradioaids
tonavigation.Exceptinhighlatitudes,whereaslightlymodified
formofthisprojectionhasbeenusedforpolarcharts,ithasnot
replaced the Mercator projection for marine navigation.
314. Polyconic Projection
Thelatitudelimitationsofthesecantconicprojectioncan
beminimizedbyusingaseriesofcones.Thisresultsinapoly-
conicprojection.Inthisprojection,eachparallelisthebaseof
atangentcone.Attheedgesofthechart,theareabetweenpar-
allelsisexpandedtoeliminategaps.Thescaleiscorrectalong
anyparallelandalongthecentralmeridianoftheprojection.
Alongothermeridiansthescaleincreaseswithincreaseddiffer-
enceoflongitudefromthecentralmeridian.Parallelsappearas
nonconcentriccircles;meridiansappearascurvedlinescon-
verging toward the pole and concave to the central meridian.
Thepolyconicprojectioniswidelyusedinatlases,par-
ticularlyforareasoflargerangeinlatitudeandreasonably
largerangeinlongitude,suchascontinents.However,since
itisnotconformal,thisprojectionisnotcustomarilyused
in navigation.
315. Azimuthal Projections
Ifpointsontheearthareprojecteddirectlytoaplanesur-
face,amapisformedatonce,withoutcuttingandflattening,or
“developing.”Thiscanbeconsideredaspecialcaseofaconic
projection in which the cone has zero height.
Thesimplestcaseoftheazimuthalprojectionisonein
whichtheplaneistangentatoneofthepoles.Themeridiansare
straightlinesintersectingatthepole,andtheparallelsarecon-
centriccircleswiththeircommoncenteratthepole.Their
spacingdependsuponthemethodusedtotransferpointsfrom
the earth to the plane.
Iftheplaneistangentatsomepointotherthanapole,
straightlinesthroughthepointoftangencyaregreatcircles,
andconcentriccircleswiththeircommoncenteratthepoint
oftangencyconnectpointsofequaldistancefromthat
point.Distortion,whichiszeroatthepointoftangency,in-
creasesalonganygreatcirclethroughthispoint.Alongany
circlewhosecenteristhepointoftangency,thedistortion
isconstant.Thebearingofanypointfromthepointoftan-
gencyiscorrectlyrepresented.Itisforthisreasonthatthese
projectionsarecalledazimuthal.Theyarealsocalledze-
nithal.Severalofthecommonazimuthalprojectionsare
perspective.
316. Gnomonic Projection
Ifaplaneistangenttotheearth,andpointsareprojected
geometricallyfromthecenteroftheearth,theresultisa
gnomonicprojection.SeeFigure316a.Sincetheprojec-
tionisperspective,itcanbedemonstratedbyplacingalight
atthecenterofatransparentterrestrialglobeandholding
a flat surface tangent to the sphere.
Inanobliquegnomonicprojectionthemeridiansap-
pearasstraightlinesconvergingtowardthenearerpole.The
parallels,excepttheequator,appearascurves(Figure
316b).Asinallazimuthalprojections,bearingsfromthe
pointoftangencyarecorrectlyrepresented.Thedistance
scale,however,changesrapidly.Theprojectionisneither
conformalnorequalarea.Distortionissogreatthatshapes,
aswellasdistancesandareas,areverypoorlyrepresented,
except near the point of tangency.
Figure313.Asecantconeforaconicprojectionwith
two standard parallels.
30NAUTICAL CHARTS
The usefulness of this projection rests upon the fact
that any great circle appears on the map as a straight line,
giving charts made on this projection the common name
great-circle charts.
Gnomonicchartsaremostoftenusedforplanningthe
great-circletrackbetweenpoints.Pointsalongthedeter-
minedtrackarethentransferredtoaMercatorprojection.
Thegreatcircleisthenfollowedbyfollowingtherhumb
linesfromonepointtothenext.Computerprogramswhich
automaticallycalculategreatcircleroutesbetweenpoints
andprovidelatitudeandlongitudeofcorrespondingrhumb
lineendpointsarequicklymakingthisuseofthegnomonic
chart obsolete.
317. Stereographic Projection
Astereographicprojectionresultsfromprojecting
pointsonthesurfaceoftheearthontoatangentplane,from
apointonthesurfaceoftheearthoppositethepointoftan-
gency(Figure317a).Thisprojectionisalsocalledan
azimuthal orthomorphic projection.
Thescaleofthestereographicprojectionincreases
withdistancefromthepointoftangency,butitincreases
moreslowlythaninthegnomonicprojection.Thestereo-
graphicprojectioncanshowanentirehemispherewithout
excessivedistortion(Figure317b).Asinotherazimuthal
Figure 316a. An oblique gnomonic projection.
Figure 316b. An oblique gnomonic map with point of
tangency at latitude 30°N, longitude 90°W.
Figure 317a. An equatorial stereographic projection.
Figure 317b. A stereographic map of the Western
Hemisphere.
NAUTICAL CHARTS31
projections,greatcirclesthroughthepointoftangencyap-
pearasstraightlines.Othercirclessuchasmeridiansand
parallels appear as either circles or arcs of circles.
Theprincipalnavigationaluseofthestereographic
projectionisforchartsofthepolarregionsanddevicesfor
mechanicalorgraphicalsolutionofthenavigationaltrian-
gle.AUniversalPolarStereographic(UPS)grid,
mathematicallyadjustedtothegraticule,isusedasarefer-
ence system.
318. Orthographic Projection
Ifterrestrialpointsareprojectedgeometricallyfrom
infinitytoatangentplane,anorthographicprojectionre-
sults(Figure318a).Thisprojectionisnotconformal;nor
doesitresultinanequalarearepresentation.Itsprincipal
useisinnavigationalastronomybecauseitisusefulforil-
lustratingandsolvingthenavigationaltriangle.Itisalso
usefulforillustratingcelestialcoordinates.Iftheplaneis
tangentatapointontheequator,theparallels(includingthe
equator)appearasstraightlines.Themeridianswouldap-
pearasellipses,exceptthatthemeridianthroughthepoint
oftangencywouldappearasastraightlineandtheone90°
away would appear as a circle (Figure 318b).
319. Azimuthal Equidistant Projection
Anazimuthalequidistantprojectionisanazimuthal
projectioninwhichthedistancescalealonganygreatcircle
throughthepointoftangencyisconstant.Ifapoleisthe
pointoftangency,themeridiansappearasstraightradial
linesandtheparallelsasequallyspacedconcentriccircles.
Iftheplaneistangentatsomepointotherthanapole,the
concentriccirclesrepresentdistancesfromthepointoftan-
gency.Inthiscase,meridiansandparallelsappearascurves.
Theprojectioncanbeusedtoportraytheentireearth,the
point180°fromthepointoftangencyappearingasthelargest
oftheconcentriccircles.Theprojectionisnotconformal,
equalarea,orperspective.Nearthepointoftangencydistor-
tionissmall,increasingwithdistanceuntilshapesnearthe
opposite side of the earth are unrecognizable (Figure 319).
Theprojectionisusefulbecauseitcombinesthethree
featuresofbeingazimuthal,havingaconstantdistancescale
fromthepointoftangency,andpermittingtheentireearthto
beshownononemap.Thus,ifanimportantharbororairport
isselectedasthepointoftangency,thegreat-circlecourse,
distance,andtrackfromthatpointtoanyotherpointonthe
eartharequicklyandaccuratelydetermined.Forcommuni-
cationworkwiththestationatthepointoftangency,thepath
ofanincomingsignalisatonceapparentifthedirectionof
arrivalhasbeendeterminedandthedirectiontotrainadirec-
tionalantennacanbedeterminedeasily.Theprojectionis
also used for polar charts and for the star finder, No. 2102D.
Figure 318a. An equatorial orthographic projection.Figure 318b. An orthographic map of the Western Hemisphere.
32NAUTICAL CHARTS
POLAR CHARTS
320. Polar Projections
Specialconsiderationisgiventotheselectionofpro-
jectionsforpolarchartsbecausethefamiliarprojections
become special cases with unique features.
Inthecaseofcylindricalprojectionsinwhichtheaxisofthe
cylinderisparalleltothepolaraxisoftheearth,distortionbe-
comesexcessiveandthescalechangesrapidly.Suchprojections
cannotbecarriedtothepoles.However,boththetransverseand
oblique Mercator projections are used.
Conicprojectionswiththeiraxesparalleltotheearth’spo-
laraxisarelimitedintheirusefulnessforpolarchartsbecause
parallelsoflatitudeextendingthroughafull360°oflongitude
appearasarcsofcirclesratherthanfullcircles.Thisisbecausea
cone,whencutalonganelementandflattened,doesnotextend
throughafull360°withoutstretchingorresumingitsformer
conicalshape.Theusefulnessofsuchprojectionsisalsolimited
bythefactthatthepoleappearsasanarcofacircleinsteadofa
point.However,byusingaparallelverynearthepoleasthe
higherstandardparallel,aconicprojectionwithtwostandard
parallelscanbemade.Thisrequireslittlestretchingtocomplete
thecirclesoftheparallelsandeliminatethatofthepole.Sucha
projection,calledamodifiedLambertconformalorNey’s
projection,isusefulforpolarcharts.Itisparticularlyfamiliarto
thoseaccustomedtousingtheordinaryLambertconformal
charts in lower latitudes.
Azimuthalprojectionsareintheirsimplestformwhen
tangentatapole.Thisisbecausethemeridiansarestraight
linesintersectingatthepole,andparallelsareconcentric
circleswiththeircommoncenteratthepole.Withinafew
Figure 319. An azimuthal equidistant map of the world with the point of tangency latitude 40°N, longitude 100°W.
NAUTICAL CHARTS33
degreesoflatitudeofthepoletheyalllooksimilar;howev-
er,asthedistancebecomesgreater,thespacingofthe
parallelsbecomesdistinctiveineachprojection.Inthepo-
larazimuthalequidistantitisuniform;inthepolar
stereographicitincreaseswithdistancefromthepoleuntil
theequatorisshownatadistancefromthepoleequalto
twicethelengthoftheradiusoftheearth;inthepolargno-
monictheincreaseisconsiderablygreater,becoming
infinityattheequator;inthepolarorthographicitdecreases
withdistancefromthepole(Figure320).Allofthesebut
the last are used for polar charts.
321. Selection of a Polar Projection
Theprincipalconsiderationsinthechoiceofasuitable
projection for polar navigation are:
1.Conformality:Whentheprojectionrepresentsan-
glescorrectly,thenavigatorcanplotdirectlyonthe
chart.
2.Greatcirclerepresentation:Becausegreatcirclesare
moreusefulthanrhumblinesathighaltitudes,thepro-
jection should represent great circles as straight lines.
3.Scalevariation:Theprojectionshouldhaveacon-
stant scale over the entire chart.
4.Meridianrepresentation:Theprojectionshouldshow
straightmeridianstofacilitateplottingandgrid
navigation
5.Limits:Widelimitsreducethenumberofprojec-
tions needed to a minimum.
Theprojectionscommonlyusedforpolarchartsarethe
modifiedLambertconformal,gnomonic,stereographic,
andazimuthalequidistant.Alloftheseprojectionsaresim-
ilarnearthepole.Allareessentiallyconformal,andagreat
circle on each is nearly a straight line.
Asthedistancefromthepoleincreases,however,the
distinctivefeaturesofeachprojectionbecomeimportant.
ThemodifiedLambertconformalprojectionisvirtually
conformaloveritsentireextent.Theamountofitsscaledis-
tortioniscomparativelylittleifitiscarriedonlytoabout
25°or30°fromthepole.Beyondthis,thedistortionin-
creasesrapidly.Agreatcircleisverynearlyastraightline
anywhereonthechart.Distancesanddirectionscanbe
measureddirectlyonthechartinthesamemannerasona
Lambertconformalchart.However,becausethisprojection
isnotstrictlyconformal,andonitgreatcirclesarenotex-
actlyrepresentedbystraightlines,itisnotsuitedforhighly
accurate work.
Thepolargnomonicprojectionistheonepolarprojec-
tiononwhichgreatcirclesareexactlystraightlines.
However,acompletehemispherecannotberepresented
uponaplanebecausetheradiusof90°fromthecenter
would become infinity.
Thepolarstereographicprojectionisconformaloverits
entireextent,andastraightlinecloselyapproximatesagreat
circle.SeeFigure321.Thescaledistortionisnotexcessive
foraconsiderabledistancefromthepole,butitisgreater
than that of the modified Lambert conformal projection.
Thepolarazimuthalequidistantprojectionisusefulfor
showingalargeareasuchasahemispherebecausethereis
Figure 320. Expansion of polar azimuthal projections.
Figure 321. Polar stereographic projection.
34NAUTICAL CHARTS
noexpansionalongthemeridians.However,theprojection
isnotconformalanddistancescannotbemeasuredaccu-
ratelyinanybutanorth-southdirection.Greatcirclesother
thanthemeridiansdiffersomewhatfromstraightlines.The
equator is a circle centered at the pole.
Thetwoprojectionsmostcommonlyusedforpolar
chartsarethemodifiedLambertconformalandthepolarste-
reographic.Whenadirectionalgyroisusedasadirectional
reference,thetrackofthecraftisapproximatelyagreatcir-
cle.Adesirablechartisoneonwhichagreatcircleis
representedasastraightlinewithaconstantscaleandwith
anglescorrectlyrepresented.Theserequirementsarenotmet
entirelybyanysingleprojection,buttheyareapproximated
byboththemodifiedLambertconformalandthepolarste-
reographic.Thescaleismorenearlyconstantontheformer,
buttheprojectionisnotstrictlyconformal.Thepolarstereo-
graphicisconformal,anditsmaximumscalevariationcanbe
reducedbyusingaplanewhichintersectstheearthatsome
parallelintermediatebetweenthepoleandthelowestparal-
lel.Theportionwithinthisstandardparalleliscompressed,
and that portion outside is expanded.
Theselectionofasuitableprojectionforuseinpolar
regionsdependsuponmissionrequirements.Theserequire-
mentsestablishtherelativeimportanceofvariousfeatures.
Forarelativelysmallarea,anyofseveralprojectionsis
suitable.Foralargearea,however,thechoiceismoredif-
ficult.Ifgriddirectionsaretobeused,itisimportantthat
allunitsinrelatedoperationsusechartsonthesameprojec-
tion,withthesamestandardparallels,sothatasinglegrid
direction exists between any two points.
SPECIAL CHARTS
322. Plotting Sheets
Positionplottingsheetsare“charts”designedprimarily
foropenoceannavigation,whereland,visualaidstonaviga-
tion,anddepthofwaterarenotfactorsinnavigation.They
havealatitudeandlongitudegraticule,andtheymayhaveone
ormorecompassroses.Themeridiansareusuallyunlabeled,
soaplottingsheetcanbeusedforanylongitude.Plotting
sheetsonMercatorprojectionarespecifictolatitude,andthe
navigatorshouldhaveenoughaboardforalllatitudesforhis
voyage. Plotting sheets are less expensive than charts.
Aplottingsheetmaybeusedinanemergencywhen
chartshavebeenlostordestroyed.Directionsonhowto
constructplottingsheetssuitableforemergencypurposes
are given in Chapter 26, Emergency Navigation.
323. Grids
Nosystemexistsforshowingthesurfaceoftheearth
onaplanewithoutdistortion.Moreover,theappearanceof
thesurfacevarieswiththeprojectionandwiththerelation
ofthatsurfaceareatothepointoftangency.Onemaywant
toidentifyalocationorareasimplybyalpha-numericrect-
angularcoordinates.Thisisaccomplishedwithagrid.Inits
usualformthisconsistsoftwoseriesoflinesdrawnperpen-
dicularlyonthechart,markedbysuitablealpha-numeric
designations.
AgridmayusetherectangulargraticuleoftheMerca-
torprojectionorasetofarbitrarylinesonaparticular
projection.TheWorldGeodeticReferenceSystem
(GEOREF)isamethodofdesignatinglatitudeandlongi-
tudebyasystemoflettersandnumbersinsteadofby
angularmeasure.Itisnot,therefore,strictlyagrid.Itisuse-
fulforoperationsextendingoverawidearea.Examplesof
thesecondtypeofgridaretheUniversalTransverseMer-
cator(UTM)grid,theUniversalPolarStereographic
(UPS)grid,andtheTemporaryGeographicGrid(TGG).
Sincethesesystemsareusedprimarilybymilitaryforces,
they are sometimes called military grids.
CHART SCALES
324. Types Of Scales
Thescaleofachartistheratioofagivendistanceonthe
charttotheactualdistancewhichitrepresentsontheearth.It
may be expressed in various ways. The most common are:
1.Asimpleratioorfraction,knownastherepresenta-
tivefraction.Forexample,1:80,000or1/80,000
meansthatoneunit(suchasameter)onthechart
represents80,000ofthesameunitonthesurfaceof
theearth.Thisscaleissometimescalledthenatural
orfractional scale.
2.Astatementthatagivendistanceontheearthequals
agivenmeasureonthechart,orviceversa.Forexam-
ple,“30milestotheinch”meansthat1inchonthe
chartrepresents30milesoftheearth’ssurface.Simi-
larly,“2inchestoamile”indicatesthat2incheson
thechartrepresent1mileontheearth.Thisissome-
times called thenumerical scale.
3.Alineorbarcalledagraphicscalemaybedrawnat
aconvenientplaceonthechartandsubdividedinto
nauticalmiles,meters,etc.Allchartsvarysomewhat
inscalefrompointtopoint,andinsomeprojections
thescaleisnotthesameinalldirectionsaboutasingle
NAUTICAL CHARTS35
point.Asinglesubdividedlineorbarforuseoveran
entirechartisshownonlywhenthechartisofsuch
scaleandprojectionthatthescalevariesanegligible
amountoverthechart,usuallyoneofabout1:75,000
orlarger.Since1minuteoflatitudeisverynearly
equalto1nauticalmile,thelatitudescaleservesasan
approximategraphicscale.Onmostnauticalcharts
theeastandwestbordersaresubdividedtofacilitate
distance measurements.
OnaMercatorchartthescalevarieswiththelatitude.
Thisisnoticeableonachartcoveringarelativelylargedis-
tanceinanorth-southdirection.Onsuchacharttheborder
scalenearthelatitudeinquestionshouldbeusedformea-
suring distances.
Ofthevariousmethodsofindicatingscale,thegraphi-
calmethodisnormallyavailableinsomeformonthechart.
Inaddition,thescaleiscustomarilystatedonchartson
whichthescaledoesnotchangeappreciablyoverthechart.
Thewaysofexpressingthescaleofachartarereadily
interchangeable.Forinstance,inanauticalmilethereare
about72,913.39inches.Ifthenaturalscaleofachartis
1:80,000,oneinchofthechartrepresents80,000inchesof
theearth,oralittlemorethanamile.Tofindtheexact
amount,dividethescalebythenumberofinchesinamile,
or80,000/72,913.39=1.097.Thus,ascaleof1:80,000is
thesameasascaleof1.097(orapproximately1.1)milesto
aninch.Statedanotherway,thereare:72,913.39/80,000=
0.911(approximately0.9)inchtoamile.Similarly,ifthe
scaleis60nauticalmilestoaninch,therepresentativefrac-
tion is 1:(60 x 72,913.39) = 1:4,374,803.
Achartcoveringarelativelylargeareaiscalleda
small-scalechartandonecoveringarelativelysmallarea
iscalledalarge-scalechart.Sincethetermsarerelative,
thereisnosharpdivisionbetweenthetwo.Thus,achartof
scale1:100,000islargescalewhencomparedwithachartof
1:1,000,000butsmallscalewhencomparedwithoneof
1:25,000.
Asscaledecreases,theamountofdetailwhichcanbe
showndecreasesalso.Cartographersselectivelydecrease
thedetailinaprocesscalledgeneralizationwhenproduc-
ingsmallscalechartsusinglargescalechartsassources.
Theamountofdetailshowndependsonseveralfactors,
amongthemthecoverageoftheareaatlargerscalesandthe
intended use of the chart.
325. Chart Classification by Scale
Chartsareconstructedonmanydifferentscales,rang-
ingfromabout1:2,500to1:14,000,000.Small-scalecharts
coveringlargeareasareusedforrouteplanningandforoff-
shorenavigation.Chartsoflargerscale,coveringsmaller
areas,areusedasthevesselapproachesland.Severalmeth-
odsofclassifyingchartsaccordingtoscaleareusedin
variousnations.Thefollowingclassificationsofnautical
charts are used by the National Ocean Service.
Sailingchartsarethesmallestscalechartsusedfor
planning,fixingpositionatsea,andforplottingthedead
reckoningwhileproceedingonalongvoyage.Thescaleis
generallysmallerthan1:600,000.Theshorelineandtopog-
raphyaregeneralizedandonlyoffshoresoundings,the
principalnavigationallights,outerbuoys,andlandmarks
visible at considerable distances are shown.
Generalchartsareintendedforcoastwisenavigation
outsideofoutlyingreefsandshoals.Thescalesrangefrom
about 1:150,000 to 1:600,000.
Coastalchartsareintendedforinshorecoastwisenav-
igation,forenteringorleavingbaysandharborsof
considerablewidth,andfornavigatinglargeinlandwater-
ways. The scales range from about 1:50,000 to 1:150,000.
Harborchartsareintendedfornavigationandan-
chorageinharborsandsmallwaterways.Thescaleis
generally larger than 1:50,000.
IntheclassificationsystemusedbyNIMA,thesailing
chartsareincorporatedinthegeneralchartsclassification
(smallerthanabout1:150,000);thosecoastchartsespecially
usefulforapproachingmoreconfinedwaters(bays,harbors)
areclassifiedasapproachcharts.Thereisconsiderableover-
lapinthesedesignations,andtheclassificationofachartis
bestdeterminedbyitsuseandbyitsrelationshiptoother
chartsofthearea.Theuseofinsetscomplicatestheplace-
ment of charts into rigid classifications.
CHART ACCURACY
326. Factors Relating to Accuracy
Theaccuracyofachartdependsupontheaccuracyof
thehydrographicsurveysandotherdatasourcesusedto
compileitandthesuitabilityofitsscaleforitsintendeduse.
Onecansometimesestimatetheaccuracyofachart’s
surveysfromthesourcenotesgiveninthetitleofthechart.
Ifthechartisbaseduponveryoldsurveys,useitwithcau-
tion.Manyearlysurveyswereinaccuratebecauseofthe
technological limitations of the surveyor.
Thenumberofsoundingsandtheirspacingindicates
thecompletenessofthesurvey.Onlyasmallfractionofthe
soundingstakeninathoroughsurveyareshownonthe
chart,butsparseorunevenlydistributedsoundingsindicate
thatthesurveywasprobablynotmadeindetail.SeeFigure
326aandFigure326b.Largeblankareasorabsenceof
depthcontoursgenerallyindicatelackofsoundingsinthe
area.Operateinanareawithsparsesoundingdataonlyif
requiredandthenonlywithextremecaution.Runtheecho
soundercontinuouslyandoperateatareducedspeed.
36NAUTICAL CHARTS
Figure 326a. Part of a “boat sheet,” showing the soundings obtained in a survey.
Figure 326b. Part of a nautical chart made from the boat sheet ofFigure 326a. Compare the number of soundings in the
two figures.
NAUTICAL CHARTS37
Sparsesoundinginformationdoesnotnecessarilyindicate
anincompletesurvey.Relativelyfewsoundingsareshown
whenthereisalargenumberofdepthcontours,orwhere
thebottomisflat,orgentlyandevenlysloping.Additional
soundingsareshownwhentheyarehelpfulinindicatingthe
uneven character of a rough bottom.
Evenadetailedsurveymayfailtolocateeveryrockor
pinnacle.Inwaterswheretheymightbelocated,thebest
methodforfindingthemisawiredragsurvey.Areasthat
havebeendraggedmaybeindicatedonthechartbylimit-
inglinesandgreenorpurpletintandanoteaddedtoshow
the effective depth at which the drag was operated.
Changesinbottomcontoursarerelativelyrapidinar-
eassuchasentrancestoharborswheretherearestrong
currentsorheavysurf.Similarly,thereissometimesaten-
dencyfordredgedchannelstoshoal,especiallyiftheyare
surroundedbysandormud,andcrosscurrentsexist.Charts
oftencontainnotesindicatingthebottomcontoursare
known to change rapidly.
Thesamedetailcannotbeshownonasmall-scale
chartasonalargescalechart.Onsmall-scalecharts,de-
tailedinformationisomittedor“generalized”inthe
areascoveredbylargerscalecharts.Thenavigator
shouldusethelargestscalechartavailablefortheareain
whichheisoperating,especiallywhenoperatinginthe
vicinity of hazards.
Chartingagenciescontinuallyevaluateboththedetail
andthepresentationofdataappearingonachart.Develop-
mentofanewnavigationalaidmayrenderpreviouscharts
inadequate.Thedevelopmentofradar,forexample,re-
quiredupgradingchartswhichlackedthedetailrequiredfor
reliable identification of radar targets.
Afterreceivingachart,theuserisresponsibleforkeep-
ingitupdated.Mariner’sreportsoferrors,changes,and
suggestionsareusefultochartingagencies.Evenwithmod-
ernautomateddatacollectiontechniques,thereisno
substituteforon-sightobservationofhydrographiccondi-
tionsbyexperiencedmariners.Thisholdstrueespeciallyin
less frequently traveled areas of the world.
CHART READING
327. Chart Dates
NOSchartshavetwodates.Atthetopcenterofthe
chartisthedateofthefirsteditionofthechart.Inthelower
leftcornerofthechartisthecurrenteditionnumberand
date.ThisdateshowsthelatestdatethroughwhichNotice
toMarinerswereappliedtothechart.Anysubsequent
changewillbeprintedintheNoticetoMariners.Anynotic-
eswhichaccumulatebetweenthechartdateandthe
announcementdateintheNoticetoMarinerswillbegiven
withtheannouncement.Comparingthedatesofthefirst
andcurrenteditionsgivesanindicationofhowoftenthe
chartisupdated.Chartsofbusyareasareupdatedmorefre-
quentlythanthoseoflesstraveledareas.Thisintervalmay
varyfrom6monthstomorethantenyearsforNOScharts.
ThisupdateintervalmaybemuchlongerforcertainNIMA
charts in remote areas.
Neweditionsofchartsarebothdemandandsource
driven.Receivingsignificantnewinformationmayormay
notinitiateaneweditionofachart,dependingonthede-
mandforthatchart.Ifitisinasparsely-traveledarea,other
prioritiesmaydelayaneweditionforseveralyears.Con-
versely,aneweditionmaybeprintedwithoutthereceiptof
significantnewdataifdemandforthechartishighand
stocklevelsarelow.NoticetoMarinerscorrectionsareal-
ways included on new editions.
NIMAchartshavethesametwodatesastheNOS
charts;thecurrentcharteditionnumberanddateisgivenin
thelowerleftcorner.CertainNIMAchartsarereproduc-
tionsofforeignchartsproducedunderjointagreements
withanumberofothercountries.Thesecharts,eventhough
ofrecentdate,maybebasedonforeignchartsofconsider-
ablyearlierdate.Further,neweditionsoftheforeignchart
willnotnecessarilyresultinaneweditionoftheNIMAre-
production.Inthesecases,theforeignchartisthebetter
chart to use.
328. Title Block
Thecharttitleblockshouldbethefirstthinganaviga-
torlooksatwhenreceivinganeweditionchart.Referto
Figure328.Thetitleitselftellswhatareathechartcovers.
Thechart’sscaleandprojectionappearbelowthetitle.The
chartwillgivebothverticalandhorizontaldatumsand,if
necessary,adatumconversionnote.Sourcenotesordia-
grams will list the date of surveys and other charts used in
compilation.
329. Shoreline
Theshorelineshownonnauticalchartsrepresentsthe
lineofcontactbetweenthelandandwaterataselectedver-
ticaldatum.Inareasaffectedbytidalfluctuations,thisis
usuallythemeanhigh-waterline.Inconfinedcoastalwa-
tersofdiminishedtidalinfluence,ameanwaterlevelline
maybeused.Theshorelineofinteriorwaters(rivers,lakes)
isusuallyalinerepresentingaspecifiedelevationabovea
38NAUTICAL CHARTS
selecteddatum.Ashorelineissymbolizedbyaheavyline.
Abrokenlineindicatesthatthechartedpositionisapprox-
imate only. The nature of the shore may be indicated.
Ifthelowwaterlinediffersconsiderablyfromthehigh
waterline,thenadottedlinerepresentsthelowwaterline.
Ifthebottominthisareaiscomposedofmud,sand,gravel
orstones,thetypeofmaterialwillbeindicated.Ifthebot-
tomiscomposedofcoralorrock,thentheappropriate
symbolwillbeused.Theareaalternatelycoveredandun-
coveredmaybeshownbyatintwhichisusuallya
combination of the land and water tint.
Theapparentshorelineshowstheouteredgeofma-
rinevegetationwherethatlimitwouldappearas
shorelinetothemariner.Itisalsousedtoindicatewhere
marinevegetationpreventsthemarinerfromdefining
theshoreline.Alightlinesymbolizesthisshoreline.A
brokenlinemarkstheinneredgewhennoothersymbol
(suchasaclifforlevee)furnishessuchalimit.Thecom-
binedland-watertintorthelandtintmarksthearea
between inner and outer limits.
330. Chart Symbols
Muchoftheinformationcontainedonchartsis
shownbysymbols.Thesesymbolsarenotshownto
scale,buttheyindicatethecorrectpositionofthefeature
towhichtheyrefer.Thestandardsymbolsandabbrevia-
tionsusedonchartspublishedbytheUnitedStatesof
AmericaareshowninChartNo.1,NauticalChartSym-
bols and Abbreviations. See Figure 330.
Electronicchartsymbolsare,withinprogrammingand
displaylimits,muchthesameasprintedones.Thelessex-
pensiveelectronicchartshavelessextensivesymbol
libraries,andthescreen’sresolutionmayaffectthepresen-
tation detail.
MostofthesymbolsandabbreviationsshowninU.S.
ChartNo.1agreewithrecommendationsoftheInterna-
tionalHydrographicOrganization(IHO).Thelayoutis
explained in the general remarks section ofChart No. 1.
Thesymbolsandabbreviationsonanygivenchart
maydiffersomewhatfromthoseshowninChartNo.1.In
addition,foreignchartsmayusedifferentsymbology.
Whenusingaforeignchart,thenavigatorshouldhave
availabletheChartNo.1fromthecountrywhichpro-
duced the chart.
ChartNo.1isorganizedaccordingtosubjectmatter,
witheachspecificsubjectgivenaletterdesignator.The
generalsubjectareasareGeneral,Topography,Hydrogra-
phy,AidsandServices,andIndexes.Undereachheading,
letterdesignatorsfurtherdefinesubjectareas,andindivid-
ual numbers refer to specific symbols.
InformationinChartNo.1isarrangedincolumns.The
firstcolumncontainstheIHOnumbercodeforthesymbol
inquestion.Thenexttwocolumnsshowthesymbolitself,
inNOSandNIMAformats.Iftheformatsarethesame,the
twocolumnsarecombinedintoone.Thenextcolumnisa
textdescriptionofthesymbol,term,orabbreviation.The
nextcolumncontainstheIHOstandardsymbol.Thelast
columnshowscertainsymbolsusedonforeignreproduc-
tion charts produced by NIMA.
331. Lettering
Exceptonsomemodifiedreproductionsofforeign
charts,cartographershaveadoptedcertainletteringstan-
BALTIC SEA
GERMANY—NORTH COAST
DAHMESHÖVED TO WISMAR
From German Surveys
SOUNDINGS IN METERS
reduced to the approximate level of Mean Sea Level
HEIGHTS IN METERS ABOVE MEAN SEA LEVEL
MERCATOR PROJECTION
EUROPEAN DATUM
SCALE 1:50,000
Figure 328. A chart title block.
NAUTICAL CHARTS39
Figure 330. Contents of U.S. Chart No. 1.
40NAUTICAL CHARTS
dards.Verticaltypeisusedforfeatureswhicharedryathigh
waterandnotaffectedbymovementofthewater;slanting
type is used for underwater and floating features.
Therearetwoimportantexceptionstothetwogeneral
ruleslistedabove.Verticaltypeisnotusedtorepresent
heightsabovethewaterline,andslantingtypeisnotusedto
indicatesoundings,exceptonmetriccharts.Section332be-
low discusses the conventions for indicating soundings.
Evaluatingthetypeofletteringusedtodenoteafeature,
onecandeterminewhetherafeatureisvisibleathightide.
Forinstance,arockmightbearthetitle“Rock”whetheror
notitextendsabovethesurface.Ifthenameisgiveninver-
ticalletters,therockconstitutesasmallislet;ifinslanting
type, the rock constitutes a reef, covered at high water.
332. Soundings
Chartsshowsoundingsinseveralways.Numbersdenote
individualsoundings.Thesenumbersmaybeeitherverticalor
slanting;bothmaybeusedonthesamechart,distinguishingbe-
tweendatabasedupondifferentU.S.andforeignsurveys,
different datums, or smaller scale charts.
Largeblocklettersatthetopandbottomofthechart
indicatetheunitofmeasurementusedforsoundings.
SOUNDINGSINFATHOMSindicatessoundingsarein
fathomsorfathomsandfractions.SOUNDINGSIN
FATHOMSANDFEETindicatesthesoundingsarein
fathomsandfeet.Asimilarconventionisfollowedwhen
the soundings are in meters or meters and tenths.
Adepthconversionscaleisplacedoutsidetheneat-
lineonthechartforuseinconvertingcharteddepthstofeet,
meters,orfathoms.“Nobottom”soundingsareindicated
byanumberwithalineoverthetopandadotovertheline.
Thisindicatesthatthespotwassoundedtothedepthindi-
catedwithoutreachingthebottom.Areaswhichhavebeen
wiredraggedareshownbyabrokenlimitingline,andthe
cleareffectivedepthisindicated,withacharacteristicsym-
bolunderthenumbers.OnNIMAchartsapurpleorgreen
tint is shown within the swept area.
Soundingsaresupplementedbydepthcontours,lines
connectingpointsofequaldepth.Theselinespresentapicture
ofthebottom.Thetypesoflinesusedforvariousdepthsare
showninSectionIofChartNo.1.Onsomechartsdepthcon-
toursareshowninsolidlines;thedepthrepresentedbyeach
lineisshownbynumbersplacedinbreaksinthelines,aswith
landcontours.Solidlinedepthcontoursarederivedfromin-
tensivelydevelopedhydrographicsurveys.Abrokenor
indefinitecontourissubstitutedforasoliddepthcontour
whenever the reliability of the contour is questionable.
Depthcontoursarelabeledwithnumeralsintheunitof
measurementofthesoundings.Achartpresentingamore
detailedindicationofthebottomconfigurationwithfewer
numericalsoundingsisusefulwhenbottomcontournavi-
gating.Suchachartcanbemadeonlyforareaswhichhave
undergone a detailed survey
Shoalareasoftenaregivenabluetint.Chartsdesigned
togivemaximumemphasistotheconfigurationofthebot-
tomshowdepthsbeyondthe100-fathomcurveoverthe
entirechartbydepthcontourssimilartothecontoursshown
onlandareastoindicategraduationsinheight.Theseare
calledbottom contour orbathymetric charts.
Onelectroniccharts,avarietyofothercolorschemesmay
beused,accordingtothemanufacturerofthesystem.Colorper-
ceptionstudiesarebeingusedtodeterminethebestpresentation.
Thesidelimitsofdredgedchannelsareindicatedbybro-
kenlines.Theprojectdepthandthedateofdredging,if
known,areshownbyastatementinoralongthechannel.The
possibilityofsiltingisalwayspresent.Localauthorities
shouldbeconsultedforthecontrollingdepth.NOSCharts
frequentlyshowcontrollingdepthsinatable,whichiskept
current by theNotice to Mariners.
Thechartscaleisgenerallytoosmalltopermitallsound-
ingstobeshown.Intheselectionofsoundings,leastdepthsare
shownfirst.Thisconservativesoundingpatternprovidessafe-
tyandensuresanunclutteredchartappearance.Steepchanges
indepthmaybeindicatedbymoredensesoundingsinthearea.
Thelimitsofshoalwaterindicatedonthechartmaybeinerror,
andnearbyareasofundetectedshallowwatermaynotbein-
cludedonthechart.Giventhispossibility,areaswhereshoal
waterisknowntoexistshouldbeavoided.Ifthenavigator
mustenteranareacontainingshoals,hemustexerciseextreme
cautioninavoidingshallowareaswhichmayhaveescapedde-
tection.Byconstructinga“safetyrange”aroundknownshoals
andensuringhisvesseldoesnotapproachtheshoalanycloser
thanthesafetyrange,thenavigatorcanincreasehischancesof
successfullynavigatingthroughshoalwater.Constantuseof
the echo sounder is also important.
AbbreviationslistedinSectionJofChartNo.1are
usedtoindicatewhatsubstanceformsthebottom.The
meaningofthesetermscanbefoundintheGlossaryofthis
volume.Whileinagespastnavigatorsmightactuallynavi-
gatebyknowingthebottomcharacteristicsofcertainlocal
areas,todayknowingthecharacteristicofthebottomis
most important when anchoring.
333. Depths and Datums
Depthsareindicatedbysoundingsorexplanatory
notes.Onlyasmallpercentageofthesoundingsobtainedin
ahydrographicsurveycanbeshownonanauticalchart.
Theleastdepthsaregenerallyselectedfirst,andapattern
builtaroundthemtoprovidearepresentativeindicationof
bottomrelief.Inshallowwater,soundingsmaybespaced
0.2to0.4inchapart.Thespacingisgraduallyincreasedas
waterdeepens,untilaspacingof0.8to1.0inchisreached
indeeperwatersoffshore.Whereasufficientnumberof
soundingsareavailabletopermitadequateinterpretation,
depth curves are drawn in at selected intervals.
Alldepthsindicatedonchartsarereckonedfromase-
lectedlevelofthewater,calledthesoundingdatum,
(sometimesreferredtoasthereferenceplanetodistin-
guishthistermfromthegeodeticdatum).Thevarious
NAUTICAL CHARTS41
soundingdatumsareexplainedinChapter9,TidesandTid-
alCurrents.OnchartsproducedfromU.S.surveys,the
soundingdatumisselectedwithregardtothetidesofthere-
gion.Depthsshownaretheleastdepthstobeexpected
underaverageconditions.Onchartscompiledfromforeign
chartsandsurveysthesoundingdatumisthatoftheoriginal
authority.Whenitisknown,thesoundingdatumusedis
statedonthechart.Insomecaseswherethechartisbased
uponoldsurveys,particularlyinareaswheretherangeof
tide is not great, the sounding datum may not be known.
FormostNationalOceanServicechartsoftheUnited
StatesandPuertoRico,thesoundingdatumismeanlower
lowwater.MostNIMAchartsarebaseduponmeanlowwa-
ter,meanlowerlowwater,ormeanlowwatersprings.The
soundingdatumforchartspublishedbyothercountriesvar-
iesgreatly,butisusuallylowerthanmeanlowwater.On
chartsoftheBalticSea,BlackSea,theGreatLakes,andoth-
erareaswheretidaleffectsaresmallorwithoutsignificance,
thesoundingdatumadoptedisanarbitraryheightapproxi-
mating the mean water level.
Thesoundingdatumofthelargestscalechartofan
areaisgenerallythesameasthereferencelevelfromwhich
height of tide is tabulated in the tide tables.
Thechartdatumisusuallyonlyanapproximationof
theactualmeanvalue,becausedeterminationoftheactual
meanheightusuallyrequiresalongerseriesoftidalobser-
vationsthanisusuallyavailabletothecartographer.In
addition, the heights of the tide vary over time.
Sincethechartdatumisgenerallyacomputedmeanor
averageheightatsomestateofthetide,thedepthofwater
atanyparticularmomentmaybelessthanshownonthe
chart.Forexample,ifthechartdatumismeanlowerlow
water,thedepthofwateratlowerlowwaterwillbeless
thanthecharteddepthaboutasoftenasitisgreater.Alow-
er depth is indicated in the tide tables by a minus sign (–).
334. Heights
Theshorelineshownonchartsisgenerallymeanhigh
water.Alight’sheightisusuallyreckonedfrommeansea
level.Theheightsofoverhangingobstructions(bridges,
powercables,etc.)areusuallyreckonedfrommeanhigh
water.Ahighwaterreferencegivesthemarinerthemini-
mum clearance expected.
Sinceheightsareusuallyreckonedfromhighwater
anddepthsfromsomeformoflowwater,thereferencelev-
elsareseldomthesame.Exceptwheretherangeoftideis
very large, this is of little practical significance.
335. Dangers
Dangersareshownbyappropriatesymbols,asindicat-
ed in Section K ofChart No. 1.
Arockuncoveredatmeanhighwatermaybeshownas
anislet.Ifanisolated,offlyingrockisknowntouncoverat
thesoundingdatumbuttobecoveredathighwater,the
chartshowstheappropriatesymbolforarockandgivesthe
heightabovethesoundingdatum.Thechartcangivethis
heightoneoftwoways.Itcanuseastatementsuchas
“Uncov2ft.,”oritcanindicatethenumberoffeettherock
protrudesabovethesoundingdatum,underlinethisvalue,
andencloseitinparentheses(i.e.(
2)).Arockwhichdoes
notuncoverisshownbyanenclosedfigureapproximating
itsdimensionsandfilledwithlandtint.Itmaybeenclosed
by a dotted depth curve for emphasis.
Atinted,irregular-linefigureofapproximatelytruedi-
mensionsisusedtoshowadetachedcoralreefwhich
uncoversatthechartdatum.Foracoralorrockyreefwhich
issubmergedatchartdatum,thesunkenrocksymboloran
appropriatestatementisused,enclosedbyadottedorbro-
ken line if the limits have been determined.
Severaldifferentsymbolsmarkwrecks.Thenatureofthe
wreckorscaleofthechartdeterminesthecorrectsymbol.A
sunkenwreckwithlessthan11fathomsofwateroveritiscon-
sidereddangerousanditssymbolissurroundedbyadotted
curve.Thecurveisomittedifthewreckisdeeperthan11fath-
oms.Thesafeclearanceoverawreck,ifknown,isindicated
byastandardsoundingnumberplacedatthewreck.Ifthis
depthwasdeterminedbyawiredrag,thesoundingisunder-
scoredbythewiredragsymbol.Anunsurveyedwreckover
whichtheexactdepthisunknownbutasafeclearancedepthis
known is depicted with a solid line above the symbol.
Tiderips,eddies,andkelpareshownbysymbolorleg-
end.Piles,dolphins(clustersofpiles),snags,andstumps
areshownbysmallcirclesandalabelidentifyingthetype
ofobstruction.Ifsuchdangersaresubmerged,theletters
“Subm”precedethelabel.Fishstakesandtrapsareshown
when known to be permanent or hazardous to navigation.
336. Aids to Navigation
AidstonavigationareshownbysymbolslistedinSections
PthroughSofChartNo.1.Abbreviationsandadditionalde-
scriptivetextsupplementthesesymbols.Inordertomakethe
symbolsconspicuous,thechartshowstheminsizegreatlyexag-
geratedrelativetothescaleofthechart.“Positionapproximate”
circlesareusedonfloatingaidstoindicatethattheyhavenoex-
actpositionbecausetheymovearoundtheirmoorings.Formost
floatingaids,thepositioncircleinthesymbolmarkstheapprox-
imatelocationoftheanchororsinker.Theactualaidmaybe
displaced from this location by the scope of its mooring.
Thetypeandnumberofaidstonavigationshownona
chartandtheamountofinformationgivenintheirlegends
varieswiththescaleofthechart.Smallerscalechartsmay
havefeweraidsindicatedandlessinformationthanlarger
scale charts of the same area.
Lighthousesandothernavigationlightsareshownas
blackdotswithpurpledisksorasblackdotswithpurple
flaresymbols.Thecenterofthedotisthepositionofthe
light.Somemodifiedfacsimileforeignchartsuseasmall
42NAUTICAL CHARTS
star instead of a dot.
Onlarge-scalechartsthelegendelementsoflightsare
shown in the following order:
The legend for this light would appear on the chart:
Fl(2) R 10s 80m 19M “6”
Aschartscaledecreases,informationinthelegendis
selectivelydeletedtoavoidclutter.Theorderofdeletionis
usuallyheightfirst,followedbyperiod,grouprepetitionin-
terval(e.g.(2)),designation,andrange.Characteristicand
color will almost always be shown.
Smalltrianglesmarkreddaybeacons;smallsquares
markallothers.OnNIMAcharts,pictorialbeaconsare
usedwhentheIALAbuoyagesystemhasbeenimplement-
ed.Thecenterofthetrianglemarksthepositionoftheaid.
ExceptonIntracoastalWaterwaychartsandchartsofstate
waterways,theabbreviation“Bn”isshownbesidethesym-
bol,alongwiththeappropriateabbreviationforcolorif
known.Forblackbeaconsthetriangleissolidblackand
thereisnocolorabbreviation.Allbeaconabbreviationsare
in vertical lettering.
Radiobeaconsareindicatedonthechartbyapurple
circleaccompaniedbytheappropriateabbreviationindicat-
inganordinaryradiobeacon(RBn)oraradarbeacon
(Ramark or Racon, for example).
Avarietyofsymbols,determinedbyboththecharting
agencyandthetypesofbuoys,indicatenavigationbuoys.
IALAbuoys(seeChapter5,ShortRangeAidstoNaviga-
tion)inforeignareasaredepictedbyvariousstylesof
symbolswithpropertopmarksandcolors;thepositioncir-
clewhichshowstheapproximatelocationofthesinkerisat
the base of the symbol.
Amooringbuoyisshownbyoneofseveralsymbolsas
indicatedinChartNo.1.Itmaybelabeledwithaberth
number or other information.
Abuoysymbolwithahorizontallineindicatesthe
buoyhashorizontalbands.Averticallineindicatesvertical
stripes;crossedlinesindicateacheckedpattern.Thereisno
significancetotheangleatwhichthebuoysymbolappears
onthechart.Thesymbolisplacedsoastoavoidinterfer-
ence with other features.
Lightedbuoysareindicatedbyapurpleflarefromthe
buoysymbolorbyasmallpurplediskcenteredonthepo-
sition circle.
Abbreviationsforlightlegends,typeandcolorof
buoy,designation,andanyotherpertinentinformationgiv-
ennearthesymbolareinslantedtype.TheletterC,N,orS
indicatesacan,nun,orspar,respectively.Otherbuoysare
assumedtobepillarbuoys,exceptforspecialbuoyssuchas
spherical,barrel,etc.Thenumberorletterdesignationof
thebuoyisgiveninquotationmarksonNOScharts.On
otherchartstheymaybegivenwithoutquotationmarksor
other punctuation.
Aeronauticallightsincludedinthelightlistsareshown
bythelighthousesymbol,accompaniedbytheabbreviation
“AERO.”Thecharacteristicsshowndependprincipallyupon
theeffectiverangeofothernavigationallightsinthevicinity
and the usefulness of the light for marine navigation.
Directionalrangesareindicatedbyabrokenorsolid
line.Thesolidline,indicatingthatpartoftherangein-
tendedfornavigation,maybebrokenatirregularintervals
toavoidbeingdrawnthroughsoundings.Thatpartofthe
rangelinedrawnonlytoguidetheeyetotheobjectstobe
keptinrangeisbrokenatregularintervals.Thedirection,
ifgiven,isexpressedindegrees,clockwisefromtrue
north.
Soundsignalsareindicatedbytheappropriatewordin
capitalletters(HORN,BELL,GONG,orWHIS)oranab-
breviationindicatingthetypeofsound.Soundsignalsof
anytypeexceptsubmarinesoundsignalsmayberepresent-
edbythreepurple45°arcsofconcentriccirclesnearthetop
oftheaid.Thesearenotshownifthetypeofsignalislisted.
Thelocationofasoundsignalwhichdoesnotaccompanya
visualaid,eitherlightedorunlighted,isshownbyasmall
circle and the appropriate word in vertical block letters.
Privateaids,whenshown,aremarked“Priv”onNOS
charts.Someprivatelymaintainedunlightedfixedaidsare
indicatedbyasmallcircleaccompaniedbytheword
“Marker,”oralargercirclewithadotinthecenterandthe
word“MARKER.”Aprivatelymaintainedlightedaidhas
alightsymbolandisaccompaniedbythecharacteristics
andtheusualindicationofitsprivatenature.Privateaids
should be used with caution.
Alightsectoristhesectororareaboundedbytworadii
andthearcofacircleinwhichalightisvisibleorinwhichit
hasadistinctivecolordifferentfromthatofadjoiningsec-
tors.Thelimitingradiiareindicatedonthechartbydottedor
dashedlines.Sectorcolorsareindicatedbywordsspelledout
ifspacepermits,orbyabbreviations(W,R,etc.)ifitdoes
not.Limitsoflightsectorsandarcsofvisibilityasobserved
from a vessel are given in the light lists, in clockwise order.
337. Land Areas
Theamountofdetailshownonthelandareasofnautical
chartsdependsuponthescaleandtheintendedpurposeofthe
LegendExampleMeaning
CharacteristicF1(2)group flashing; 2 flashes
ColorRred
Period10s2 flashes in 10 seconds
Height80m80 meters
Range19M19 nautical miles
Designation“6” light number 6
NAUTICAL CHARTS43
chart. Contours, form lines, and shading indicate relief.
Contoursarelinesconnectingpointsofequaleleva-
tion.Heightsareusuallyexpressedinfeet(orinmeterswith
meansforconversiontofeet).Theintervalbetweencon-
toursisuniformoveranyonechart,exceptthatcertain
intermediatecontoursaresometimesshownbybrokenline.
Whencontoursarebroken,theirlocationsareapproximate.
Formlinesareapproximationsofcontoursusedforthe
purposeofindicatingrelativeelevations.Theyareusedin
areaswhereaccurateinformationisnotavailableinsuffi-
cientdetailtopermitexactlocationofcontours.Elevations
of individual form lines are not indicated on the chart.
Spotelevationsaregenerallygivenonlyforsummitsor
fortopsofconspicuouslandmarks.Theheightsofspotele-
vationsandcontoursaregivenwithreferencetomeanhigh
water when this information is available.
Whenthereisinsufficientspacetoshowtheheightsof
isletsorrocks,theyareindicatedbyslantingfiguresen-
closed in parentheses in the water area nearby.
338. Cities and Roads
Citiesareshowninageneralizedpatternthatapproxi-
matestheirextentandshape.Streetnamesaregenerallynot
chartedexceptthosealongthewaterfrontonthelargest
scalecharts.Ingeneral,onlythemainarteriesandthor-
oughfaresormajorcoastalhighwaysareshownonsmaller
scalecharts.Occasionally,highwaynumbersaregiven.
Whenshown,trailsareindicatedbyalightbrokenline.
Buildingsalongthewaterfrontorindividualonesback
fromthewaterfrontbutofspecialinteresttothemarinerare
shownonlarge-scalecharts.SpecialsymbolsfromChart
No.1areusedforcertainkindsofbuildings.Asingleline
withcrossmarksindicatesbothsingleanddoubletrackrail-
roads.Cityelectricrailwaysareusuallynotcharted.
Airportsareshownonsmall-scalechartsbysymbolandon
large-scalechartsbytheshapeofrunways.Thescaleofthe
chartdeterminesifsingleordoublelinesshowbreakwaters
andjetties;brokenlinesshowthesubmergedportionof
these features.
339. Landmarks
Landmarks are shown by symbols in Chart No. 1.
Alargecirclewithadotatitscenterisusedtoindicate
thatthepositionispreciseandmaybeusedwithoutreserva-
tionforplottingbearings.Asmallcirclewithoutadotis
usedforlandmarksnotaccuratelylocated.Capitalandlower
caselettersareusedtoidentifyanapproximatelandmark:
“Mon,”“Cup,”or“Dome.”Theabbreviation“PA”(posi-
tionapproximate)mayalsoappear.Anaccuratelandmarkis
identified by all capital type (“MON,” “CUP,” “DOME”).
Whenonlyoneobjectofagroupischarted,itsnameis
followedbyadescriptivelegendinparenthesis,including
thenumberofobjectsinthegroup,forexample“(TALL-
EST OF FOUR)” or “(NORTHEAST OF THREE).”
340. Miscellaneous Chart Features
Ameasurednauticalmileindicatedonachartisaccu-
ratetowithin6feetofthecorrectlength.Mostmeasured
milesintheUnitedStatesweremadebefore1959,whenthe
UnitedStatesadoptedtheInternationalNauticalMile.The
newvalueiswithin6feetofthepreviousstandardlengthof
6,080.20feet.Ifthemeasureddistancediffersfromthe
standardvaluebymorethan6feet,theactualmeasureddis-
tance is stated and the words “measured mile” are omitted.
Periodsafterabbreviationsinwaterareasareomitted
becausethesemightbemistakenforrocks.However,a
lower case i or j is dotted.
Commercialradiobroadcastingstationsareshownon
chartswhentheyareofvaluetothemarinereitherasland-
marks or sources of direction-finding bearings.
Linesofdemarcationbetweentheareasinwhichinter-
nationalandinlandnavigationrulesapplyareshownonly
whentheycannotbeadequatelydescribedinnotesonthe
chart.
Compassrosesareplacedatconvenientlocationson
Mercatorchartstofacilitatetheplottingofbearingsand
courses.Theoutercircleisgraduatedindegreeswithzero
at true north. The inner circle indicates magnetic north.
OnmanyNIMAchartsmagneticvariationisgivento
thenearest1'bynotesinthecentersofcompassroses.the
annualchangeisgiventothenearest1'topermitcorrection
ofthegivenvalueatalaterdate.OnNOScharts,variation
istothenearest15',updatedateachneweditionifover
threeyearsold.ThecurrentpracticeofNIMAistogivethe
magneticvariationtothenearest1',butthemagneticinfor-
mationonneweditionsisonlyupdatedtoconformwiththe
latestfiveyearepoch.Wheneverachartisreprinted,the
magneticinformationisupdatedtothelatestepoch.On
somesmallerscalecharts,thevariationisgivenbyisogonic
linesconnectingpointsofequalvariation;usuallyasepa-
ratelinerepresentseachdegreeofvariation.Thelineof
zerovariationiscalledtheagonicline.Manyplansandin-
setsshowneithercompassrosesnorisogoniclines,but
indicatemagneticinformationbynote.Alocalmagnetic
disturbanceofsufficientforcetocausenoticeabledeflec-
tionofthemagneticcompass,calledlocalattraction,is
indicated by a note on the chart.
Currentsaresometimesshownonchartswitharrows
givingthedirectionsandfiguresshowingspeeds.Thein-
formationreferstotheusualoraverageconditions.
Accordingtotidesandweather,conditionsatanygiven
time may differ considerably from those shown.
Reviewchartnotescarefullybecausetheyprovideim-
portantinformation.Severaltypesofnotesareused.Those
inthemargingivesuchinformationaschartnumber,pub-
licationnotes,andidentificationofadjoiningcharts.Notes
inconnectionwiththecharttitleincludeinformationon
scale,sourcesofdata,tidalinformation,soundings,and
cautions.Anotherclassofnotescoverssuchtopicsaslocal
magneticdisturbance,controllingdepthsofchannels,haz-
44NAUTICAL CHARTS
ards to navigation, and anchorages.
Adatumnotewillshowthegeodeticdatumofthechart
(Donotconfusewiththesoundingdatum.SeeChapter2,
GeodesyandDatumsinNavigation.)Itmayalsocontain
instructionsonplottingpositionsfromtheWGS84orNAD
83 datums on the chart if such a conversion is needed.
Anchorageareasarelabeledwithavarietyofmagenta,
black,orgreenlinesdependingonthestatusofthearea.
Anchorageberthsareshownaspurplecircles,withthe
numberorletterassignedtotheberthinscribedwithinthe
circle.Cautionnotesaresometimesshownwhenthereare
specific anchoring regulations.
Spoilareasareshownwithinshortbrokenblacklines.
SpoilareasaretintedblueonNOSchartsandlabeled.
These areas contain no soundings and should be avoided.
FiringandbombingpracticeareasintheUnitedStates
territorialandadjacentwatersareshownonNOSandNIMA
charts of the same area and comparable scale.
Dangerareasestablishedforshortperiodsoftimeare
notchartedbutareannouncedlocally.Mostmilitarycom-
mandschargedwithsupervisionofgunneryandmissile
firingareaspromulgateaweeklyschedulelistingactivated
dangerareas.Thisscheduleissubjectedtofrequentchange;
themarinershouldalwaysensurehehasthelatestschedule
priortoproceedingintoagunneryormissilefiringarea.
Dangerareasineffectforlongerperiodsarepublishedinthe
NoticetoMariners.Anyaidtonavigationestablishedto
markadangerareaorafixedorfloatingtargetisshownon
charts.
Trafficseparationschemesareshownonstandardnautical
charts of scale 1:600,000 and larger and are printed in magenta.
Alogarithmictime-speed-distancenomogramwithan
explanation of its application is shown on harbor charts.
Tidalinformationboxesareshownonchartsofscales
1:200,000andlargerforNOScharts,andvariousscaleson
DMA charts, according to the source. See Figure 340a.
Tabulationsofcontrollingdepthsareshownonsome
NationalOceanServiceharborandcoastalcharts.SeeFig-
ure 340b.
StudyChartNo.1thoroughlytobecomefamiliarwith
allthesymbolsusedtodepictthewidevarietyoffeatures
on nautical charts.
TIDAL INFORMATION
Place
Position
Height above datum of soundings
Mean High Water
Mean Low Water
N. Lat.
E. Long.
Higher
Lower
Lower
Higher
meters
meters
meters
meters
Olongapo......
14˚49'
120˚17'
...0.9...
...0.4...
...0.0...
...0.3...
Figure 340a. Tidal box.
NANTUCKET HARBOR
Tabulated from surveys by the Corps of Engineers - report of June 1972
and surveys of Nov. 1971
Controlling depths in channels entering from
seaward in feet at Mean Low Water
Project Dimensions
Name of Channel
Left
outside
quarter
Middle
half of
channel
Right
outside
quarter
Date of
Survey
Width (feet)
Length
(naut.
miles)
Depth
M. L. W.
(feet)
Entrance Channel
11.1
15.0
15.0
11 - 71
300
1.2
15
Note.-The Corps of Engineers should be consulted for changing conditions subsequent to the above.
Figure 340b.Tabulations of controlling depths.
NAUTICAL CHARTS45
REPRODUCTIONS OF FOREIGN CHARTS
341. Modified Facsimiles
Modifiedfacsimilechartsaremodifiedreproductions
offoreignchartsproducedinaccordancewithbilateralin-
ternationalagreements.Thesereproductionsprovidethe
marinerwithup-to-datechartsofforeignwaters.Modified
facsimilechartspublishedbyNIMAare,ingeneral,repro-
duced with minimal changes, as listed below:
1.Theoriginalnameofthechartmayberemovedand
replaced by an anglicized version.
2.Englishlanguageequivalentsofnamesandterms
ontheoriginalchartareprintedinasuitableglos-
sary on the reproduction, as appropriate.
3.Allhydrographicinformation,exceptbottomchar-
acteristics,isshownasdepictedontheoriginalchart.
4.BottomcharacteristicsareasdepictedinChartNo.
1, or as on the original with a glossary.
5.Theunitofmeasurementusedforsoundingsis
showninblocklettersoutsidetheupperandlower
neatlines.
6.Ascaleforconvertingcharteddepthtofeet,meters,
or fathoms is added.
7.Bluetintisshownfromasignificantdepthcurveto
the shoreline.
8.Bluetintisaddedtoalldangersenclosedbyadot-
teddangercurve,dangerouswrecks,foulareas,
obstructions,rocksawash,sunkenrocks,andswept
wrecks.
9.Cautionnotesareshowninpurpleandenclosedin
a box.
10.Restricted,danger,andprohibitedareasareusually
outlined in purple and labeled appropriately.
11.Traffic separation schemes are shown in purple.
12.Anoteontrafficseparationschemes,printedin
black, is added to the chart.
13.Wiredragged(swept)areasareshowninpurpleor
green.
14.Correctionsareprovidedtoshiftthehorizontalda-
tum to the World Geodetic System (1984).
INTERNATIONAL CHARTS
342. International Chart Standards
Theneedformarinersandchartmakerstounderstand
andusenauticalchartsofdifferentnationsbecameincreas-
inglyapparentasthemaritimenationsoftheworld
developedtheirownestablishmentsforthecompilationand
publicationofnauticalchartsfromhydrographicsurveys.
Representativesoftwenty-twonationsformedaHydro-
graphicConferenceinLondonin1919.Thatconference
resultedintheestablishmentoftheInternationalHydro-
graphicBureau(IHB)inMonacoin1921.Today,the
IHB’ssuccessor,theInternationalHydrographicOrga-
nization(IHO)continuestoprovideinternational
standardsforthecartographersofitsmembernations.(See
Chapter1,IntroductiontoMarineNavigation,forade-
scription of the IHO.)
Recognizingtheconsiderableduplicationofeffortby
memberstates,theIHOin1967movedtointroducethefirst
internationalchart.Itformedacommitteeofsixmember
statestoformulatespecificationsfortwoseriesofinterna-
tionalcharts.Eighty-threesmall-scalechartswere
approved;responsibilityforcompilingthesechartshassub-
sequentlybeenacceptedbythememberstates’
Hydrographic Offices.
OnceaMemberStatepublishesaninternationalchart,
reproductionmaterialismadeavailabletoanyotherMem-
berStatewhichmaywishtoprintthechartforitsown
purposes.
InternationalchartscanbeidentifiedbythelettersINT
beforethechartnumberandtheInternationalHydrographic
Organizationsealinadditiontoothernationalsealswhich
may appear.
CHART NUMBERING
343. The Chart Numbering System
NIMAandNOSuseasysteminwhichnumbersare
assignedinaccordancewithboththescaleandgeo-
graphicalareaofcoverageofachart.Withtheexception
ofcertainchartsproducedformilitaryuseonly,one-to
five-digitnumbersareused.Withtheexceptionofone-
digitnumbers,thefirstdigitidentifiesthearea;thenum-
berofdigitsestablishesthescalerange.Theone-digit
numbersareusedforcertainproductsinthechartsystem
which are not actually charts.
Number of DigitsScale
1No Scale
21:9 million and smaller
31:2 million to 1:9 million
4Special Purpose
51:2 million and larger
46NAUTICAL CHARTS
Two-andthree-digitnumbersareassignedtothose
small-scalechartswhichdepictamajorportionofan
oceanbasinoralargearea.Thefirstdigitidentifiesthe
applicableoceanbasin.SeeFigure343a.Two-digit
numbersareusedforchartsofscale1:9,000,000and
smaller.Three-digitnumbersareusedforchartsof
scale 1:2,000,000 to 1:9,000,000.
Duetothelimitedsizesofcertainoceanbasins,no
chartsfornavigationaluseatscalesof1:9,000,000and
smallerarepublishedtocoverthesebasins.Theother-
wiseunusedtwo-digitnumbers(30to49and70to79)
are assigned to special world charts.
Oneexceptiontothescalerangecriteriaforthree-
digitnumbersistheuseofthree-digitnumbersforase-
riesofpositionplottingsheets.Theyareoflargerscale
than1:2,000,000becausetheyhaveapplicationin
ocean basins and can be used in all longitudes.
Four-digitnumbersareusedfornon-navigational
andspecialpurposecharts,suchaschart5090,Maneu-
vering Board.
Five-digitnumbersareassignedtothosechartsof
scale1:2,000,000andlargerthatcoverportionsofthe
coastlineratherthansignificantportionsofoceanba-
sins.Thesechartsarebasedontheregionsofthe
nautical chart index. See Figure 343b.
Thefirstofthefivedigitsindicatestheregion;the
seconddigitindicatesthesubregion;thelastthreedig-
itsindicatethegeographicalsequenceofthechart
withinthesubregion.Manynumbershavebeenleftun-
usedsothatanyfuturechartsmaybeplacedintheir
proper geographical sequence.
Inordertoestablishalogicalnumberingsystem
withinthegeographicalsubregions(forthe1:2,000,000
andlarger-scalecharts),aworldwideskeletonframe-
workofcoastalchartswaslaidoutatascale1:250,000.
Thisserieswasusedasbasiccoverageexceptinareas
whereacoordinatedseriesataboutthisscalealready
existed(suchasthecoastofNorwaywhereacoordinat-
ed series of 1:200,000 charts was available).
Withineachregion,thegeographicalsubregions
arenumberedcounterclockwisearoundthecontinents,
andwithineachsubregionthebasicseriesalsoisnum-
beredcounterclockwisearoundthecontinents.The
basiccoverageisassignedgenerallyevery20thdigit,
exceptthatthefirst40numbersineachsubregionare
reservedforsmaller-scalecoverage.Chartswithscales
largerthanthebasiccoverageareassignedoneofthe
19numbersfollowingthenumberassignedtothesheet
withinwhichitfalls.Figure343cshowsthenumbering
sequenceinIceland.Notethesequenceofnumbers
aroundthecoast,thedirectionofnumbering,andthe
numberingoflargerscalechartswithinthelimitsof
smaller scales.
Five-digitnumbersarealsoassignedtothecharts
producedbyotherhydrographicoffices.Thisnumber-
ingsystemisappliedtoforeignchartssothattheycan
befiledinlogicalsequencewiththechartsproducedby
theNationalImageryandMappingAgencyandtheNa-
tional Ocean Service.
Certainexceptionstothestandardnumberingsystem
havebeenmadeforchartsintendedforthemilitary.Bottom
contourchartsdepictpartsofoceanbasins.Theyareidentified
withaletterplusfourdigitsaccordingtoaschemebestshown
inthecatalog,andarenotavailabletociviliannavigators.
Figure 343a. Ocean basins with region numbers.
NAUTICAL CHARTS47
Figure 343b. Regions and subregions of the nautical chart index.
48NAUTICAL CHARTS
Figure 343c. Chart coverage of Iceland, illustrating the sequence and direction of the U.S. chart numbering system.
NAUTICAL CHARTS49
Combatchartshave6-digitnumbersbeginningwithan“8.”
Neither is available to civilian navigators.
344. Catalogs and Stock Numbers
Chartcatalogsprovideinformationregardingnotonly
chartcoverage,butalsoavarietyofspecialpurposecharts
andpublicationsofinterest.Keepacorrectedchartcatalog
aboardshipforreviewbythenavigator.TheNIMAcatalog
containsoperatingareachartsandotherspecialproductsnot
availableforcivilianuse,butdoesnotcontainanyclassified
listings.TheNOScatalogscontainallunclassifiedcivilian-
useNOSandNIMAcharts.Militarynavigatorsreceivetheir
nauticalchartsandpublicationsautomatically;civiliannavi-
gators purchase them from chart sales agents.
Thestocknumberandbarcodearegenerallyfoundin
thelowerleftcornerofaNIMAchart,andinthelowerright
cornerofanNOSchart.Thefirsttwodigitsofthestock
numberrefertotheregionandsubregion.Thesearefol-
lowedbythreeletters,thefirstofwhichreferstothe
portfoliotowhichthechartbelongs;thesecondtwodenote
thetypeofchart:COforcoastal,HAforharborandap-
proach,andOAformilitaryoperatingareacharts.Thelast
five digits are the actual chart number.
USING CHARTS
345. Preliminary Steps
Beforeusinganeweditionofachart,verifyitsan-
nouncementintheNoticetoMarinersandcorrectitwithall
applicablecorrections.Readallthechart’snotes;there
shouldbenoquestionaboutthemeaningsofsymbolsorthe
unitsinwhichdepthsaregiven.Sincethelatitudeandlon-
gitudescalesdifferconsiderablyonvariouscharts,
carefully note those on the chart to be used.
Placeadditionalinformationonthechartasrequired.
Arcsofcirclesmightbedrawnaroundnavigationallights
toindicatethelimitofvisibilityattheheightofeyeofan
observeronthebridge.Notesregardingotherinformation
fromthelightlists,tidetables,tidalcurrenttables,andsail-
ing directions might prove helpful.
346. Maintaining Charts
Amarinernavigatingonanuncorrectedchartiscourting
disaster.Thechart’sprintdatereflectsthelatestNoticeto
Marinersusedtoupdatethechart;responsibilityformain-
tainingitafterthisdatelieswiththeuser.TheweeklyNotice
toMarinerscontainsinformationneededformaintaining
charts.Radiobroadcastsgiveadvancenoticeofurgentcor-
rections.LocalNoticetoMarinersshouldbeconsultedfor
inshoreareas.Thenavigatormustdevelopasystemtokeep
trackofchartcorrectionsandtoensurethatthechartheisus-
ingisupdatedwiththelatestcorrection.Aconvenientwayof
keepingthisrecordiswithaChart/PublicationCorrection
RecordCardsystem.Usingthissystem,thenavigatordoes
notimmediatelyupdateeverychartinhisportfoliowhenhe
receivestheNoticetoMariners.Instead,heconstructsacard
foreverychartinhisportfolioandnotesthecorrectionon
thiscard.Whenthetimecomestousethechart,hepullsthe
chartandchart’scard,andhemakestheindicatedcorrections
onthechart.Thissystemensuresthateverychartisproperly
corrected prior to use.
ASummaryofCorrections,containingacumulative
listingofpreviouslypublishedNoticetoMarinerscorrec-
tions,ispublishedannuallyin5volumesbyNIMA.Thus,
tofullycorrectachartwhoseeditiondateisseveralyears
old,thenavigatorneedsonlytheSummaryofCorrections
forthatregionandthenoticesfromthatSummaryforward;
hedoesnotneedtoobtainnoticesallthewaybacktothe
editiondate.SeeChapter4,NauticalPublications,forade-
scription of theSummaries andNotice to Mariners.
Whenaneweditionofachartispublished,itisnor-
mallyfurnishedautomaticallytoU.S.Governmentvessels.
Itshouldnotbeuseduntilitisannouncedasreadyforuse
intheNoticetoMariners.Untilthattime,correctionsinthe
Noticeapplytotheoldeditionandshouldnotbeappliedto
thenewone.Whenitisannounced,aneweditionofachart
replaces an older one.
Commercialusersandotherswhodon’tautomatically
receiveneweditionsshouldobtainneweditionsfromtheir
salesagent.Occasionally,chartsmaybereceivedorpur-
chasedseveralweeksinadvanceoftheirannouncementin
theNoticetoMariners.Thisisusuallyduetoextensivere-
schemingofachartregionandtheneedtoannouncegroups
ofchartstogethertoavoidlapsesincoverage.Themariner
bearstheresponsibilityforensuringthathischartsarethe
currentedition.Thefactthataneweditionhasbeencom-
piledandpublishedoftenindicatesthattherehavebeen
extensivechangesthatcannotbemadebyhandcorrections.
347. Using and Stowing Charts
Useandstowchartscarefully.Thisisespeciallytrue
withdigitalchartscontainedonelectronicmedia.Keepop-
ticalandmagneticmediacontainingchartdataoutofthe
sun,insidedustcovers,andawayfrommagneticinfluenc-
es.Placingadiskinaninhospitableenvironmentmay
destroy the data.
Makepermanentcorrectionstopaperchartsininkso
thattheywillnotbeinadvertentlyerased.Pencilinallother
markingssothattheycanbeeasilyerasedwithoutdamag-
ingthechart.Layoutandlabeltracksonchartsof
frequently-traveledportsinink.Drawlinesandlabelsno
largerthannecessary.Donotobscuresoundingdataoroth-
erinformationwhenlabelingachart.Whenavoyageis
completed,carefullyerasethechartsunlesstherehasbeen
agroundingorcollision.Inthiscase,preservethecharts
50NAUTICAL CHARTS
withoutchangebecausetheywillplayacriticalroleinthe
investigation.
Whennotinuse,stowchartsflatintheirproperportfo-
lio.Minimizetheirfoldingandproperlyindexthemfor
easy retrieval.
348. Chart Lighting
Marinersoftenworkinaredlightenvironmentbe-
causeredlightisleastdisturbingtonightadaptedvision.
Suchlightingseriouslyaffectstheappearanceofachart.
Beforeusingachartinredlight,testtheeffectredlighthas
onitsmarkings.Donotoutlineorotherwiseindicatenavi-
gationalhazardsinredpencilbecauseredmarkings
disappear under red light.
349. Small-Craft Charts
NOSpublishesaseriesofsmallcraftchartssometimes
called“stripcharts.”Thesechartsdepictsegmentsofthe
AtlanticIntracoastalWaterway,theGulfIntracoastalWa-
terway,andotherinlandroutesusedbyyachtsmen,
fishermen,andsmallcommercialvesselsforcoastaltravel.
Theyarenot“north-up”inpresentation,butarealigned
withthewaterwaytheydepict,whateveritsorientationis.
Mostoftentheyareusedasapilotingaidfor“eyeball”nav-
igationandplaced“course-up”infrontofthehelmsman,
becausetheroutestheyshowaretooconfinedfortaking
and plotting fixes.
AlthoughNOSsmall-craftchartsaredesignedprima-
rilyforuseaboardyachts,fishingvesselsandothersmall
craft,thesecharts,atscalesof1:80,000andlarger,arein
somecasestheonlychartsavailabledepictinginlandwa-
terstransitedbylargevessels.Inothercasesthesmall-craft
chartsmayprovideabetterpresentationofnavigational
hazardsthanthestandardnauticalchartbecauseofbetter
scaleandmoredetail.Therefore,navigatorsshoulduse
thesechartsinareaswheretheyprovidethebestcoverage.
51
CHAPTER 4
NAUTICAL PUBLICATIONS
INTRODUCTION
400. Hardcopy vs. Softcopy Publications
Thenavigatorusesmanytextualinformationsources
whenplanningandconductingavoyage.Thesesources
includenoticestomariners,summaryofcorrections,sailing
directions,lightlists,tidetables,sightreductiontables,and
almanacs.Historically,thisinformationhasbeencontained
inpaperorso-called“hardcopy”publications.But
electronicmethodsofproductionanddistributionoftextual
materialarenowcommonplace,andwillsoonreplace
manyofthenavigator’sfamiliarbooks.Thisvolume’sCD-
ROMversionisonlyoneofmany.Regardlessofhow
technologicallyadvancedwebecome,theprintedwordwill
alwaysbeanimportantmethodofcommunication.Only
the means of access will change.
Whileitisstillpossibletoobtainhard-copyprinted
publications,increasinglythesetextsarefoundon-lineorin
theformofCompactDisc-ReadOnlyMemory(CD-
ROM’s).CD-ROM’saremuchlessexpensivethanprinted
publicationstoreproduceanddistribute,andon-linepubli-
cationshavenoreproductioncostsatallfortheproducer,
andonlyminorcoststotheuser,ifhechoosestoprintthem
atall.Also,afewCD-ROM’scanholdentirelibrariesofin-
formation,makingbothdistributionandon-boardstorage
much easier.
Theadvantagesofelectronicpublicationsgobeyond
theircostsavings.Theycanbeupdatedeasierandmoreof-
ten,makingitpossibleformarinerstohavefrequentor
evencontinuousaccesstoamaintainedpublicationsdata-
baseinsteadofreceivingneweditionsatinfrequent
intervalsandenteringhandcorrectionsperiodically.Gener-
ally,digitalpublicationsalsoprovidelinksandsearch
engines to quickly access related information.
Navigationalpublicationsareavailablefrommany
sources.Militarycustomersautomaticallyreceiveor
requisitionmostpublications.Theciviliannavigator
obtainshispublicationsfromapublisher’sagent.
Largeragentsrepresentingmanypublisherscan
completelysupplyaship’schartandpublication
library.On-linepublicationsproducedbytheU.S.
government are available on the Web.
Thischapterwillrefergenerallytoprinted
publications.Ifthenavigatorhasaccesstothisdata
electronically,hismethodsofaccessandusewilldiffer
somewhat,butthediscussionhereinappliesequallytoboth
electronic and hard-copy documents.
NAUTICAL TEXTS
401.Sailing Directions
NationalImageryandMappingAgencySailing
Directionsconsistof37Enroutesand5PlanningGuides.
PlanningGuidesdescribegeneralfeaturesofoceanbasins;
Enroutesdescribefeaturesofcoastlines,ports,andharbors.
SailingDirectionsareupdatedwhennewdatarequires
extensiverevisionofanexistingvolume.Thesedataare
obtainedfromseveralsources,includingpilotsandforeign
Sailing Directions.
OnebookcomprisesthePlanningGuideandEnroute
forAntarctica.Thisconsolidationallowsforamore
effective presentation of material on this unique area.
ThePlanningGuidesarerelativelypermanent;by
contrast,SailingDirections(Enroute)arefrequently
updated.Betweenupdates,botharecorrectedbytheNotice
to Mariners.
402.Sailing Directions (Planning Guide)
PlanningGuidesassistthenavigatorinplanninganex-
tensiveoceanicvoyage.EachoftheGuidesprovidesuseful
informationaboutallthecountriesadjacenttoaparticular
oceanbasin.ThelimitsoftheSailingDirectionsinrelation
to the major ocean basins are shown in Figure 402.
PlanningGuidesarestructuredinthealphabeticalor-
derofcountriescontainedwithintheregion.Information
pertainingtoeachcountryincludesBuoyageSystems,Cur-
rency,Government,Industries,Holidays,Languages,
Regulations,FiringDangerAreas,MinedAreas,Pilotage,
SearchandRescue,ReportingSystems,SubmarineOperat-
ingAreas,TimeZone,andthelocationoftheU.S.
Embassy.
403.Sailing Directions (Enroute)
EachvolumeoftheSailingDirections(Enroute)
52NAUTICAL PUBLICATIONS
containsnumberedsectionsalongacoastorthrougha
strait.Figure403aillustratesthisdivision.Eachsectoris
sub-dividedintoparagraphsanddiscussedinturn.A
prefacewithinformationaboutauthorities,references,
andconventionsusedineachbookprecedesthesector
discussions.Eachbookalsoprovidesconversions
betweenfeet,fathoms,andmeters,andanInformation
and Suggestion Sheet.
TheChartInformationGraphic,thefirstitemineach
sector,isagraphickeyforchartspertainingtothatarea.See
Figure403b.Thegraduationoftheborderscaleofthe
chartletenablesnavigatorstoidentifythelargestscalechart
foralocationandtofindafeaturelistedintheIndex-
Gazetteer.ThesegraphicsarenotmaintainedbyNoticeto
Mariners;oneshouldrefertothechartcatalogforupdated
chartlistings.Othergraphicsmaycontainspecial
informationonanchorages,significantcoastalfeatures,and
navigation dangers.
AforeigntermsglossaryandacomprehensiveIndex-
Gazetteerfollowthesectordiscussions.TheIndex-Gazet-
teerisanalphabeticallistingofdescribedandcharted
features.TheIndexlistseachfeaturebygeographiccoordi-
nates and sector paragraph number.
U.S.militaryvesselshaveaccesstospecialfilesofdata
reportedviaofficialmessagesknownasPortVisitAfter
ActionReports.Thesereports,writtenintextformaccord-
ingtoastandardizedreportingformat,givecomplete
detailsofrecentvisitsbyU.S.militaryvesselstoallforeign
portsvisited.Virtuallyeverydetailregardingnavigation,
services,supplies,officialandunofficialcontacts,andoth-
ermattersisdiscussedindetail,makingthesereportsan
extremelyusefuladjuncttotheSailingDirections.These
filesareavailableto“.mil”usersonly,andmaybeaccessed
ontheWebat:http://cnsl.spear.navy.mil,underthe“Force
Navigator”link.TheyarealsoavailableviaDoD’sclassi-
fied Web.
404.Coast Pilots
TheNationalOceanServicepublishesnineUnited
StatesCoastPilotstosupplementnauticalchartsofU.S.
waters.Informationcomesfromfieldinspections,survey
vessels,andvariousharborauthorities.Maritimeofficials
andpilotageassociationsprovideadditionalinformation.
CoastPilotsprovidemoredetailedinformationthanSailing
DirectionsbecauseSailingDirectionsareintended
exclusivelyfortheoceangoingmariner.TheNoticeto
Mariners updatesCoast Pilots.
Eachvolumecontainscomprehensivesectionsonlocal
operationalconsiderationsandnavigationregulations.
Followingchapterscontaindetaileddiscussionsofcoastal
navigation.Anappendixprovidesinformationonobtaining
additionalweatherinformation,communicationsservices,and
otherdata.Anindexandadditionaltablescompletethe
volume.
Figure 402. Sailing Directions limits in relation to the major ocean basins.
NAUTICAL PUBLICATIONS53
Figure 403a. Sector Limits graphic.
Additional chart coverage may be found in CATP2 Catalog of Nautical Charts.
Figure 403b. Chart Information graphic.
54NAUTICAL PUBLICATIONS
405. Other Nautical Texts
Thegovernmentpublishesseveralothernauticaltexts.
NIMA,forexample,publishesPub.1310,Radar
NavigationandManeuveringBoardManualandPub.9,
American Practical Navigator.
TheU.S.CoastGuardpublishesNavigationRulesfor
internationalandinlandwaters.Thispublication,officially
known as Commandant Instruction M16672.2d, contains
theInlandNavigationRulesenactedinDecember1980
andeffectiveonallinlandwatersoftheUnitedStatesin-
cludingtheGreatLakes,aswellastheInternational
RegulationsforthePreventionofCollisionsatSea,enact-
edin1972(1972COLREGS).Marinersshouldensure
thattheyhavetheupdatedissue.TheCoastGuardalso
publishescomprehensiveuser’smanualsfortheLoran
andGPSnavigationsystems;NavigationandVesselIn-
spectionCirculars;andtheChemicalDataGuideforBulk
Shipment by Water.
TheGovernmentPrintingOfficeprovidesseveral
publicationsonnavigation,safetyatsea,communications,
weather,andrelatedtopics.Additionally,itpublishes
provisionsoftheCodeofFederalRegulations(CFR)
relatingtomaritimematters.Anumberofprivate
publishers also provide maritime publications.
TheInternationalMaritimeOrganization,International
HydrographicOrganization,andothergoverninginterna-
tionalorganizationsprovideinformationoninternational
navigationregulations.Chapter1givestheseorganiza-
tions’addresses.RegulationsforvariousVesselTraffic
Services(VTS),canals,locksystems,andotherregulated
waterwaysarepublishedbytheauthoritieswhichoperate
them.Nauticalchartandpublicationsalesagentsareagood
sourceofinformationaboutpublicationsrequiredforany
voyage.Increasingly,manyregulations,whetherinstituted
byinternationalornationalgovernments,canbefoundon-
line.ThisincludesregulationsforVesselTrafficServices,
TrafficSeparationSchemes,specialregulationsforpassage
throughmajorcanalandlocksystems,portandharborreg-
ulations,andotherinformation.AWebsearchcanoften
find the textual information the navigator needs.
USING THE LIGHT LISTS
406. Light Lists
TheUnitedStatespublishestwodifferentlightlists.
TheU.S.CoastGuardpublishestheLightListforlightsin
U.S.territorialwaters;NIMApublishestheListofLights
for lights in foreign waters.
Lightlistsfurnishdetailedinformationabout
navigationlightsandothernavigationaids,supplementing
thecharts,CoastPilots,andSailingDirections.Consultthe
chartforthelocationandlightcharacteristicsofall
navigationaids;consultthelightliststodeterminetheir
detailed description.
TheNoticetoMarinerscorrectsbothlists.Corrections
whichhaveaccumulatedsincetheprintdateareincludedin
theNoticetoMarinersasaSummaryofCorrections.Allof
thesesummarycorrections,andanycorrectionspublished
subsequently,shouldbenotedinthe“RecordofCorrections.”
Anavigatorneedstoknowboththeidentityofalight
andwhenhecanexpecttoseeit;heoftenplanstheship’s
tracktopasswithinalight’srange.Iflightsarenotsighted
whenpredicted,thevesselmaybesignificantlyoffcourse
and standing into danger.
Acirclewitharadiusequaltothevisiblerangeofthe
lightusuallydefinestheareainwhichalightcanbeseen.
Onsomebearings,however,obstructionsmayreducethe
range.Inthiscase,theobstructedarcmightdifferwith
heightofeyeanddistance.Also,lightsofdifferentcolors
maybeseenatdifferentdistances.Considerthesefactsboth
whenidentifyingalightandpredictingtherangeatwhich
it can be seen.
Atmosphericconditionshaveamajoreffectona
light’srange.Fog,haze,dust,smoke,orprecipitationcan
obscurealight.Additionally,alightcanbeextinguished.
Alwaysreportanextinguishedlightsomaritimeauthorities
can issue a warning and make repairs.
Onadark,clearnight,thevisualrangeislimitedby
either:(1)luminousintensity,or(2)curvatureoftheEarth.
Regardlessoftheheightofeye,onecannotseeaweaklight
beyondacertainluminousrange.Assuminglighttravels
linearly,anobserverlocatedbelowthelight’svisible
horizoncannotseeit.TheDistancetotheHorizontable
givesthedistancetothehorizonforvariousheightsofeye.
Thelightlistscontainacondensedversionofthistable.
Abnormalrefractionpatternsmightchangethisrange;
therefore,onecannotexactlypredicttherangeatwhicha
light will be seen.
407. Finding Range and Bearing of a Light at Sighting
Alight’sluminousrangeisthemaximumrangeat
whichanobservercanseealightunderexistingvisibility
conditions.Thisluminousrangeignorestheelevationofthe
light,theobserver’sheightofeye,thecurvatureofthe
Earth,andinterferencefrombackgroundlighting.Itisde-
terminedfromtheknownnominalrangeandtheexisting
visibilityconditions.Thenominalrangeisthemaximum
distanceatwhichalightcanbeseeninweatherconditions
where visibility is 10 nautical miles.
TheU.S.CoastGuardLightListusuallylistsalight’s
nominalrange.UsetheLuminousRangeDiagramshownin
theLightListandFigure407atoconvertthisnominalrange
toluminousrange.Rememberthattheluminousrangesob-
tainedareapproximatebecauseofatmosphericor
backgroundlightingconditions.TousetheLuminousRange
NAUTICAL PUBLICATIONS55
Diagram,firstestimatethemeteorologicalvisibilitybythe
MeteorologicalOpticalRangeTable,Figure407b.Next,en-
tertheLuminousRangeDiagramwiththenominalrangeon
thehorizontalnominalrangescale.Followaverticallineun-
tilitintersectsthecurveorreachestheregiononthediagram
representingthemeteorologicalvisibility.Finally,followa
horizontallinefromthispointorregionuntilitintersectsthe
vertical luminous range scale.
Example1:Thenominalrangeofalightasextracted
from the Light List is 15 nautical miles.
Required:Theluminousrangewhenthemeteorologi-
calvisibilityis(1)11nauticalmilesand(2)1
nautical mile.
Solution:Tofindtheluminousrangewhenthemeteo-
rologicalvisibilityis11nauticalmiles,enterthe
LuminousRangeDiagramwithnominalrange15
nauticalmilesonthehorizontalnominalrange
scale;followaverticallineupwarduntilitinter-
sectsthecurveonthediagramrepresentinga
meteorologicalvisibilityof11nauticalmiles;
fromthispointfollowahorizontallinetotheright
untilitintersectstheverticalluminousrangescale
at16nauticalmiles.Asimilarprocedureisfol-
lowedtofindtheluminousrangewhenthe
meteorological visibility is 1 nautical mile.
Answers:(1) 16 nautical miles; (2) 3 nautical miles.
Alight’sgeographicrangedependsupontheheightof
boththelightandtheobserver.Thesumoftheobserver’sdis-
Figure 407a. Luminous Range Diagram.
56NAUTICAL PUBLICATIONS
tancetothevisiblehorizon(basedonhisheightofeye)plus
thelight’sdistancetothehorizon(basedonitsheight)isits
geographicrange.SeeFigure407c.Thisillustrationusesa
light150feetabovethewater.Table12,DistanceoftheHo-
rizon,yieldsavalueof14.3nauticalmilesforaheightof150
feet.Withinthisrange,thelight,ifpowerfulenoughandat-
mosphericconditionspermit,isvisibleregardlessofthe
heightofeyeoftheobserver.Beyond14.3nauticalmiles,the
geographicrangedependsupontheobserver’sheightofeye.
Thus,bytheDistanceoftheHorizontablementionedabove,
anobserverwithheightofeyeof5feetcanseethelightonhis
horizonifheis2.6milesbeyondthehorizonofthelight.The
geographicrangeofthelightistherefore16.9miles.Fora
heightof30feetthedistanceis14.3+6.4=20.7miles.Ifthe
heightofeyeis70feet,thegeographicrangeis14.3+9.8=
24.1miles.Aheightofeyeof15feetisoftenassumedwhen
tabulating lights’ geographic ranges.
Topredictthebearingandrangeatwhichavesselwillini-
tiallysightalightfirstdeterminethelight’sgeographicrange.
Comparethegeographicrangewiththelight’sluminous
range.Thelesserofthetworangesistherangeatwhichthe
lightwillfirstbesighted.Plotavisibilityarccenteredonthe
lightandwitharadiusequaltothelesserofthegeographicor
luminousranges.Extendthevessel’strackuntilitintersects
thevisibilityarc.Thebearingfromtheintersectionpointtothe
light is the light’s predicted bearing at first sighting.
Iftheextendedtrackcrossesthevisibilityarcata
smallangle,asmalllateraltrackerrormayresultinlarge
bearingandtimepredictionerrors.Thisisparticularly
apparentifthevesselisfartherfromthelightthan
predicted;thevesselmaypassthelightwithoutsightingit.
However,notsightingalightwhenpredicteddoesnot
alwaysindicatethevesselisfartherfromthelightthan
expected.Itcouldalsomeanthatatmosphericconditions
are affecting visibility.
Example2:Thenominalrangeofanavigationallight
120feetabovethechartdatumis20nautical
miles.Themeteorologicalvisibilityis27nautical
miles.
Required:Thedistanceatwhichanobserverata
height of eye of 50 feet can expect to see the light.
Solution:Themaximumrangeatwhichthelight
maybeseenisthelesseroftheluminousor
geographicranges.At120feetthedistanceto
thehorizon,bytableorformula,is12.8miles.
Add8.3miles,thedistancetothehorizonfora
heightofeyeof50feettodeterminethe
geographicrange.Thegeographicrange,21.1
miles,islessthantheluminousrange,40miles.
Answer:21nauticalmiles.Becauseofvarious
uncertainties,therangeisroundedofftothe
nearest whole mile.
Whenfirstsightingalight,anobservercandetermine
ifitisonthehorizonbyimmediatelyreducinghisheightof
eye.Ifthelightdisappearsandthenreappearswhentheob-
serverreturnstohisoriginalheight,thelightisonthe
horizon. This process is calledbobbing a light.
Ifavesselhasconsiderableverticalmotiondueto
roughseas,alightsightedonthehorizonmayalternately
appearanddisappear.Wavetopsmayalsoobstructthelight
periodically.Thismaycausethecharacteristictoappear
differentthanexpected.Thelight’struecharacteristicscan
beascertainedeitherbyclosingtherangetothelightorby
increasing the observer’s height of eye.
Ifalight’srangegiveninaforeignpublication
approximatesthelight’sgeographicrangefora15-foot
observer’sheightofeye,onecanassumethattheprinted
rangeisthelight’sgeographicrange.Alsoassumethat
publicationhaslistedthelesserofthegeographicand
nominalranges.Therefore,ifthelight’slistedrange
approximatesthegeographicrangeforanobserverwitha
heightofeyeof15feet,thenassumethatthelight’s
limitingrangeisthegeographicrange.Then,calculatethe
light’struegeographicrangeusingtheactualobserver’s
heightofeye,nottheassumedheightofeyeof15feet.
Thiscalculatedtruegeographicrangeistherangeat
which the light will first be sighted.
Example3:Therangeofalightasprintedonaforeign
chartis17miles.Thelightis120feetabovechart
datum.Themeteorologicalvisibilityis10nautical
miles.
Required:Thedistanceatwhichanobserverata
height of eye of 50 feet can expect to see the light.
Solution:Calculatethegeographicrangeofthelight
assuminga15footobserver’sheightofeye.At
120feetthedistancetothehorizonis12.8miles.
Add4.5miles(thedistancetothehorizonata
heightof15feet)to12.8miles;thisrangeis17.3
miles.Thisapproximatestherangelistedonthe
chart.Thenassumingthatthechartedrangeisthe
Code
No.
Yards
Weather
0Dense fog . . . . . . . . . . . . . . . . . . .Less than 50
1Thick fog . . . . . . . . . . . . . . . . . . .50-200
2Moderate fog . . . . . . . . . . . . . . . .200-500
3Light fog. . . . . . . . . . . . . . . . . . . .500-1000
Nautical Miles
4Thin fog . . . . . . . . . . . . . . . . . . . .1/2-1
5Haze . . . . . . . . . . . . . . . . . . . . . . .1-2
6Light Haze . . . . . . . . . . . . . . . . . .2-5 1/2
7Clear. . . . . . . . . . . . . . . . . . . . . . .5 1/2-11
8Very Clear . . . . . . . . . . . . . . . . . .11.0-27.0.
9Exceptionally Clear . . . . . . . . . . .Over 27.0
From the International Visibility Code.
Figure 407b. Meteorological Optical Range Table.
NAUTICAL PUBLICATIONS57
geographicrangefora15-footobserverheightof
eyeandthatthenominalrangeisthegreaterthan
thischartedrange,thepredictedrangeisfoundby
calculatingthetruegeographicrangewitha50
foot height of eye for the observer.
Answer:Thepredictedrange=12.8mi.+8.3mi.=
21.1mi.Thedistanceinexcessofthecharted
rangedependsontheluminousintensityofthe
light and the meteorological visibility.
408. USCGLight Lists
TheU.S.CoastGuardLightList(7volumes)gives
informationonlightednavigationaids,unlightedbuoys,
radiobeacons,radiodirectionfindercalibrationstations,
daybeacons, racons, and Loran stations.
EachvolumeoftheLightListcontainsaidsto
navigationingeographicorderfromnorthtosouthalong
theAtlanticcoast,fromeasttowestalongtheGulfcoast,
andfromsouthtonorthalongthePacificcoast.Itlists
seacoastaidsfirst,followedbyentranceandharboraids
listedfromseaward.IntracoastalWaterwayaidsarelisted
lastingeographicorderinthedirectionfromNewJerseyto
Florida to the Texas/Mexico border.
Thelistingsareprecededbyadescriptionoftheaidsto
navigationsystemintheUnitedStates,luminousrange
diagram, geographic range tables, and other information.
409. NIMAList of Lights, Radio Aids, and Fog
Signals
TheNationalImageryandMappingAgencypublishes
theListofLights,RadioAids,andFogSignals(usually
referredtoastheListofLights,nottobeconfusedwiththe
CoastGuard’sLightList).Inadditiontoinformationon
lightedaidstonavigationandsoundsignalsinforeign
waters,theNIMAListofLightsprovidesinformationon
stormsignals,signalstations,racons,radiobeacons,radio
directionfindercalibrationstationslocatedatornearlights,
andDGPSstations.Formoredetailsonradionavigational
aids, consultPub. 117, Radio Navigational Aids.
TheNIMAListofLightsgenerallydoesnotinclude
informationonbuoys,althoughincertaininstances,a
largeoffshorebuoywitharadionavigationalaidmaybe
listed.Itdoesincludecertainaeronauticallightssituated
nearthecoast.However,theselightsarenotdesignedfor
marinenavigationandaresubjecttounreportedchanges.
Foreignnoticestomarinersarethemaincorrec-
tionalinformationsourcefortheNIMAListsofLights;
othersources,suchasshipreports,arealsoused.Many
aidstonavigationinlessdevelopedcountriesmaynotbe
wellmaintained.Theyaresubjecttodamagebystorms
andvandalism,andrepairsmaybedelayedforlong
periods.
MISCELLANEOUS NAUTICAL PUBLICATIONS
410. NIMARadio Navigational Aids (Pub. 117)
Thispublicationisaselectedlistofworldwide
radiostationswhichperformservicestothemariner.
Topicscoveredincluderadiodirectionfinderandradar
stations,radiotimesignals,radionavigationwarnings,
distressandsafetycommunications,medicaladvicevia
radio,long-rangenavigationaids,theAMVERsystem,
andinterimproceduresforU.S.vesselsintheeventof
anoutbreakofhostilities.Pub.117iscorrectedviathe
Figure 407c. Geographic Range of a light.
58NAUTICAL PUBLICATIONS
NoticetoMarinersandisupdatedperiodicallywitha
new edition.
ThoughPub.117isessentiallyalistofradio
stationsprovidingvitalmaritimecommunicationand
navigationservices,italsocontainsinformationwhich
explainsthecapabilitiesandlimitationsofthevarious
systems.
411.Chart No. 1
ChartNo.1isnotactuallyachartbutabook
containingakeytochartsymbols.Mostcountrieswhich
producechartsalsoproducesuchalist.TheU.S.ChartNo.
1 contains a listing of chart symbols in four categories:
•Chart symbols used by the National Ocean Service
•Chart symbols used by NIMA
•ChartsymbolsrecommendedbytheInternational
Hydrographic Organization
•Chartsymbolsusedonforeignchartsreproducedby
NIMA
Subjectscoveredincludegeneralfeaturesofcharts,
topography,hydrography,andaidstonavigation.Thereis
alsoacompleteindexofabbreviationsandanexplanation
of the IALA buoyage system.
412. NIMAWorld Port Index (Pub. 150)
TheWorldPortIndexcontainsatabularlistingof
thousandsofportsthroughouttheworld,describingtheir
locations,characteristics,facilities,andservicesavailable.
Informationisarrangedgeographically;theindexis
arranged alphabetically.
Codedinformationispresentedincolumnsand
rows.Thisinformationsupplementsinformationinthe
SailingDirections.TheapplicablevolumeofSailing
Directionsandthenumberoftheharborchartaregiven
intheWorldPortIndex.TheNoticetoMarinerscorrects
this book.
413. NIMADistances Between Ports (Pub. 151)
Thispublicationliststhedistancesbetweenmajor
ports.Reciprocaldistancesbetweentwoportsmaydiffer
duetodifferentrouteschosenbecauseofcurrentsand
climaticconditions.Toreducethenumberoflistings
needed,junctionpointsalongmajorroutesareusedto
consolidate routes converging from different directions.
Thisbookcanbemosteffectivelyusedforvoyage
planninginconjunctionwiththepropervolume(s)ofthe
SailingDirections(PlanningGuide).Itiscorrectedviathe
Notice to Mariners.
414. NIMAInternational Code of Signals (Pub. 102)
Thisbookliststhesignalstobeemployedbyvesselsat
seatocommunicateavarietyofinformationrelatingto
safety,distress,medical,andoperationalinformation.This
publication became effective in 1969.
Accordingtothiscode,eachsignalhasauniqueand
completemeaning.Thesignalscanbetransmittedvia
Morsecodelightandsound,flag,radiotelegraphand
telephone,andsemaphore.Sincethesemethodsof
signalingareinternationallyrecognized,differencesin
languagebetweensenderandreceiverareimmaterial;the
messagewillbeunderstoodwhendecodedinthelanguage
ofthereceiver,regardlessofthelanguageofthesender.
TheNotice to Mariners correctsPub. 102.
415. Almanacs
Forcelestialsightreduction,thenavigatorneedsan
almanacforephemerisdata.TheNauticalAlmanac,
producedjointlybyH.M.NauticalAlmanacOfficeandthe
U.S.NavalObservatory,isthemostcommonalmanacused
forcelestialnavigation.Italsocontainsinformationon
sunrise,sunset,moonrise,andmoonset,aswellascompact
sightreductiontables.TheNauticalAlmanacispublished
annually.
TheAirAlmanaccontainsslightlylessaccurate
ephemerisdataforairnavigation.Itcanbeusedformarine
navigation if slightly reduced accuracy is acceptable.
Chapter19providesmoredetailedinformationon
using theNautical Almanac.
416.Sight Reduction Tables
Withoutacalculatororcomputerprogrammedfor
sightreduction,thenavigatorneedssightreductiontables
tosolvethecelestialtriangle.Twodifferentsetsoftables
are commonly used at sea.
NIMAPub.229,SightReductionTablesforMarine
Navigation,consistsofsixvolumesoftablesdesignedfor
usewiththeNauticalAlmanacforsolutionofthecelestial
trianglebytheMarcqSaintHilaireorinterceptmethod.
Thetabulardataarethesolutionsofthenavigational
triangleofwhichtwosidesandtheincludedangleare
knownanditisnecessarytofindthethirdsideandadjacent
angle.
EachvolumeofPub.229includestwo8degreezones,
comprising15degreebandsfrom0to90degrees,witha1°
degreeoverlapbetweenvolumes.Pub.229isajoint
publicationproducedbytheNationalImageryand
MappingAgency,theU.S.NavalObservatory,andthe
Royal Greenwich Observatory.
SightReductionTablesforAirNavigation,Pub.249,is
alsoajointproductionofthethreeorganizationsabove.Itis
issuedinthreevolumes.Volume1containsthevaluesofthe
altitudeandtrueazimuthofsevenselectedstarschosento
NAUTICAL PUBLICATIONS59
provide,foranygivenpositionandtime,thebestcelestial
observations.Aneweditionisissuedevery5yearsforthe
upcomingastronomicalepoch.Volumes2(0°to40°)and3
(39°to89°)provideforsightsoftheSun,Moon,and
planets.
417. Catalogs
Achartcatalogisavaluablereferencetothenavigator
forvoyageplanning,inventorycontrol,andordering.The
catalog is used by military and civilian customers.
ThenavigatorwillseetheNIMAnauticalchart
catalogaspartofalargersuiteofcatalogsincluding
aeronautical(Part1),hydrographic(Part2),and
topographic(Part3)products.EachPartconsistsofone
ormorevolumes.UnclassifiedNIMAnauticalchartsare
listed in Part 2, Volume 1.
Thiscatalogcontainscomprehensiveordering
instructionsandinformationabouttheproductslisted.Also
listedareaddressesofallMapSupportOffices,information
oncrisissupport,andotherspecialsituations.Thecatalogis
organizedbygeographicregioncorrespondingtothechart
regions1through9.Aspecialsectionofmiscellaneous
chartsandpublicationsisincluded.Thissectionalsolists
productsproducedbyNOS,theU.S.ArmyCorpsof
Engineers,U.S.CoastGuard,U.S.NavalOceanographic
Office,andsomeforeignpublicationsfromtheUnited
Kingdom and Canada.
Theciviliannavigatorshouldalsorefertocatalogs
producedbytheNationalOceanService.ForU.S.waters,
NOSchartsarelistedinaseriesoflargesheet“charts”
showingamajorregionoftheU.S.withindividualchart
graphicsdepicted.Thesecatalogsalsolistchartsshowing
titlesandscales.Theyalsolistsalesagentsfromwhomthe
charts may be purchased.
NIMAproductsfortheciviliannavigatorarelistedby
NOSinaseriesofregionalizedcatalogssimilartoPart2
Volume1.Thesecatalogsarealsoavailablethrough
authorized NOS chart agents.
MARITIME SAFETY INFORMATION
418.Notice to Mariners
TheNoticetoMarinersispublishedweeklybythe
NationalImageryandMappingAgency(NIMA),
preparedjointlywiththeNationalOceanService(NOS)
andtheU.S.CoastGuard.Itadvisesmarinersofimportant
mattersaffectingnavigationalsafety,includingnew
hydrographicinformation,changesinchannelsandaidsto
navigation,andotherimportantdata.Theinformationin
theNoticetoMarinersisformattedtosimplifythe
correctionofpapercharts,sailingdirections,lightlists,
andotherpublicationsproducedbyNIMA,NOS,andthe
U.S. Coast Guard.
Itistheresponsibilityofuserstodecidewhichoftheir
chartsandpublicationsrequirecorrection.Suitablerecords
ofNoticetoMarinersshouldbemaintainedtofacilitatethe
updating of charts and publications prior to use.
InformationfortheNoticetoMarinersiscontributed
by:NIMA(DepartmentofDefense)forwatersoutsidethe
territoriallimitsoftheUnitedStates;NationalOcean
Service(NationalOceanicandAtmosphericAdminis-
tration,DepartmentofCommerce),whichischargedwith
surveyingandchartingthecoastsandharborsofthe
UnitedStatesanditsterritories;theU.S.CoastGuard
(DepartmentofTransportation)whichisresponsiblefor,
amongotherthings,thesafetyoflifeatseaandthe
establishmentandoperationofaidstonavigation;andthe
ArmyCorpsofEngineers(DepartmentofDefense),
whichischargedwiththeimprovementofriversand
harborsoftheUnitedStates.Inaddition,importantcontri-
butionsaremadebyforeignhydrographicofficesand
cooperating observers of all nationalities.
Over60countrieswhichproducenauticalchartsalso
produceanoticetomariners.Aboutonethirdoftheseare
weekly,anotherthirdarebi-monthlyormonthly,andthe
restirregularlyissuedaccordingtoneed.Muchofthedata
intheU.S.NoticetoMarinersisobtainedfromthese
foreign notices.
U.S.chartsmustbecorrectedonlywithaU.S.Notice
toMariners.Similarly,correctforeignchartsusingthe
foreignnoticebecausechartdatumsoftenvaryaccording
toregionandgeographicpositionsarenotthesamefor
different datums.
TheNoticetoMarinersconsistsofapageof
Hydrogramslistingimportantitemsinthenotice,a
chartcorrectionsectionorganizedbyascendingchart
number,apublicationscorrectionsection,anda
summaryofbroadcastnavigationwarningsandmiscel-
laneous information.
Marinersarerequestedtocooperateinthecorrectionof
chartsandpublicationsbyreportingalldiscrepancies
betweenpublishedinformationandconditionsactually
observedandbyrecommendingappropriateimprovements.
Aconvenientreportingformisprovidedinthebackofeach
Notice to Mariners.
NoticetoMarinersNo.1ofeachyearcontains
importantinformationonavarietyofsubjectswhich
supplementsinformationnotusuallyfoundonchartsandin
navigationalpublications.Thisinformationispublishedas
SpecialNoticetoMarinersParagraphs.Additionalitems
consideredofinteresttothemarinerarealsoincludedinthis
Notice.
419.Summary of Corrections
AclosecompaniontotheNoticetoMarinersisthe
60NAUTICAL PUBLICATIONS
SummaryofCorrections.TheSummaryispublishedin
fivevolumes.Eachvolumecoversamajorportionofthe
Earthincludingseveralchartregionsandtheirsubregions.
Volume5alsoincludesspecialchartsandpublications
correctedbytheNoticetoMariners.SincetheSummaries
containcumulativecorrections,anychart,regardlessofits
printdate,canbecorrectedwiththepropervolumeofthe
Summary and all subsequentNotice to Mariners.
420. The Maritime Safety Information Website
TheNIMAMaritimeSafetyInformationWebsite
providesworldwideremotequeryaccesstoextensive
menusofmaritimesafetyinformation24hoursaday.The
MaritimeSafetyInformationWebsitecanbeaccessedvia
theNIMAHomepage(www.nima.mil)undertheSafetyof
Navigation icon or directly at http://pollux.nss.nima.mil.
Databasesmadeavailableforaccess,queryand
downloadincludeChartCorrections,Publication
Corrections,NIMAHydrographicCatalogCorrections,
ChartandPublicationReferenceData(currentedition
number,dates,title,scale),NIMAListofLights,U.S.Coast
GuardLightLists,WorldWideNavigationalWarning
Service(WWNWS)BroadcastWarnings,Maritime
Administration(MARAD)Advisories,DepartmentofState
SpecialWarnings,MobileOffshoreDrillingUnits
(MODUs),Anti-ShippingActivityMessages(ASAMs),
WorldPortIndex,andRadioNavigationalAids.
PublicationsthatarealsomadeavailableasPortable
DocumentFormat(PDF)filesincludetheU.S.Noticeto
Mariners,U.S.ChartNo.1,TheAmericanPractical
Navigator,InternationalCodeofSignals,RadioNaviga-
tionalAids,WorldPortIndex,DistancesBetweenPorts,
SightReductionTablesforMarineNavigation,Sight
ReductionTablesforAirNavigation,andtheRadar
Navigation and Maneuvering Board Manual.
Navigatorshaveonlineaccessto,andcandownload,
alltheinformationcontainedintheprintedNoticeto
Marinersincludingchartlets.Informationonthiswebsiteis
updateddailyorweeklyaccordingtotheNoticeto
Marinersproductionschedule.BroadcastWarnings,
MARADAdvisories,ASAMsandMODUsareupdatedon
adailybasis;theremainingdataisupdatedonaweekly
basis.
Certainfiles,forexampleU.S.CoastGuardLightList
data,areentereddirectlyintothedatabasewithouteditingand
theaccuracyofthisinformationcannotbeverifiedbyNIMA
staff.Also,drillriglocationsarefurnishedbythecompanies
whichoperatethem.Theyarenotrequiredtoprovidethese
positions,andtheycannotbeverified.However,withinthese
limitations,theWebsitecanprovideinformation2weeks
soonerthantheprintedNoticetoMariners,becausethepaper
Noticemustbeprintedandmailedafterthedigitalversionis
completed and posted on the Web.
Userscanprovidesuggestions,changes,correctionsor
commentsonanyoftheMaritimeSafetyInformation
Divisionproductsandservicesbysubmittinganonline
versionoftheMarineInformationReportandSuggestion
Sheet.
AccesstotheMaritimeSafetyInformationWebsiteis
free,buttheusermustpaytheapplicablechargesfor
internetservice.AnyquestionsconcerningtheMaritime
SafetyInformationWebsiteshouldbedirectedtothe
MaritimeSafetyInformationDivision,Attn.:NSSSTAFF,
MailStopD-44,NIMA,4600SangamoreRd.,Bethesda,
MD,20816-5003;telephone(1)301-227-3296;fax(1)
301-227-4211; e-mail webmaster_nss@nima.mil.
421.Local Notice to Mariners
TheLocalNoticetoMarinersisissuedbyeachU.S.
CoastGuardDistricttodisseminateimportantinformation
affectingnavigationalsafetywithinthatDistrict.This
Noticereportschangesanddeficienciesinaidsto
navigationmaintainedbytheCoastGuard.Othermarine
informationsuchasnewcharts,channeldepths,naval
operations,andregattasisincluded.Sincetemporary
informationofshortdurationisnotincludedintheNIMA
NoticetoMariners,theLocalNoticetoMarinersmaybe
theonlysourceforit.SincecorrectinginformationforU.S.
chartsintheNIMANoticeisobtainedfromtheCoast
Guardlocalnotices,thereisalagof1or2weeksforNIMA
Noticeto publish a correction from this source.
TheLocalNoticetoMarinersmaybeobtainedfreeof
chargebycontactingtheappropriateCoastGuardDistrict
Commander.Vesselsoperatinginportsandwaterwaysin
severaldistrictsmustobtaintheLocalNoticetoMariners
fromeachdistrict.SeeFigure421foracompletelistofU.S.
Coast Guard Districts.
422. Electronic Notice to Mariners
Onemajorimpedimenttofullimplementationof
electronicchartsystemshasbeentheissueofhowtokeep
themuptodate.TheIMO,afterreviewingtherange
standardswhichmightbeemployedintheprovisionof
updatestoECDIScharts,decidedthatthecorrectionsystem
mustbe“handsoff”fromthemariner’spointofview.That
is,thecorrectionsystemcouldnotrelyontheabilityofthe
marinertoenterindividualcorrectiondatahimself,ashe
woulddoonapaperchart.Theprocessmustbeautomated
tomaintaintheintegrityofthedataandpreventerrorsin
data entry by navigators.
Nationalhydrographicofficeswhichpublish
electronicchartsmustalsopublishcorrectionsforthem.
Themannerofdoingsovariesamongthedifferenttypesof
systems.Thecorrectionsareappliedtothedataasthechart
tobedisplayediscreated,leavingthedatabaseunchanged.
Anotherpossibilityexists,andthatistosimplyreload
theentirechartdatafilewithupdatedinformation.Thisis
notascrazyasitsoundswhenoneconsiderstheamountof
datathatcanbestoredonasingleCD-ROMandtheease
NAUTICAL PUBLICATIONS61
COMMANDER, FIRST COAST GUARD DISTRICT
408 ATLANTIC AVENUE
BOSTON, MA 02110-3350
PHONE: DAY 617-223-8338, NIGHT 617-223-8558
COMMANDER, NINTH COAST GUARD DISTRICT
1240 EAST 9TH STREET
CLEVELAND, OH 44199-2060
PHONE: DAY 216-522-3991, NIGHT 216-522-3984
COMMANDER, SECOND COAST GUARD DISTRICT
1222 SPRUCE STREET
ST. LOUIS, MO 63103-2832
PHONE: DAY 314-539-3714, NIGHT 314-539-3709
COMMANDER, ELEVENTH COAST GUARD DISTRICT
FEDERAL BUILDING
501 W. OCEAN BLVD.
LONG BEACH, CA 90822-5399
PHONE: DAY 310-980-4300, NIGHT 310-980-4400
COMMANDER, FIFTH COAST GUARD DISTRICT
FEDERAL BUILDING
431 CRAWFORD STREET
PORTSMOUTH, VA 23704-5004
PHONE: DAY 804-398-6486, NIGHT 804-398-6231
COMMANDER, THIRTEENTH COAST GUARD DISTRICT
FEDERAL BUILDING
915 SECOND AVENUE
SEATTLE, WA 98174-1067
PHONE: DAY 206-220-7280, NIGHT 206-220-7004
COMMANDER, SEVENTH COAST GUARD DISTRICT
BRICKELL PLAZA FEDERAL BUILDING
909 SE 1ST AVENUE, RM: 406
MIAMI, FL 33131-3050
PHONE: DAY 305-536-5621, NIGHT 305-536-5611
COMMANDER, FOURTEENTH COAST GUARD DISTRICT
PRINCE KALANIANAOLE FEDERAL BLDG.
9TH FLOOR, ROOM 9139
300 ALA MOANA BLVD.
HONOLULU, HI 96850-4982
PHONE: DAY 808-541-2317, NIGHT 808-541-2500
COMMANDER GREATER ANTILLES SECTION
U.S. COAST GUARD
P.O. BOX S-2029
SAN JUAN, PR 00903-2029
PHONE: 809-729-6870
COMMANDER, SEVENTEENTH COAST GUARD DISTRICT
P.O. BOX 25517
JUNEAU, AK 99802-5517
PHONE: DAY 907-463-2245, NIGHT 907-463-2000
COMMANDER, EIGHTH COAST GUARD DISTRICT
HALE BOGGS FEDERAL BUILDING
501 MAGAZINE STREET
NEW ORLEANS, LA 70130-3396
PHONE: DAY 504-589-6234, NIGHT 504-589-6225
Figure 421. U.S. Coast Guard Districts.
62NAUTICAL PUBLICATIONS
withwhichitcanbereproduced.Atpresent,thesefilesare
toolargetobebroadcasteffectively,butwiththeproper
bandwidththeconceptoftransferringentirechartportfolios
worldwideviasatelliteorfiber-opticcableisentirely
feasible.
CorrectionstotheDNCpublishedbyNIMAarebeing
madebyVectorProductFormatDatabaseUpdate(VDU).
ThesearepatchcorrectionsandareavailableviatheWeb
andbyclassifieddatalinksusedbytheDepartmentof
Defense.
CorrectionstorasterchartsissuedbyNOAAarealso
availableviatheinternet.Toproducethepatch,eachchart
iscorrectedandthencompared,pixelbypixel,withthe
previous,uncorrectedversion.Anydifferencesbetweenthe
twomusthavebeentheresultofacorrection,sothosefiles
aresavedandpostedtoasiteforaccessbysubscription
users.Theuseraccessesthesite,downloadsthe
compressedfiles,uncompressesthemonhisownterminal,
andwritesthepatchesontohisrastercharts.Hecanthen
togglebetweenoldandnewversionstoseeexactlywhat
has changed, and can view the patch by itself.
NOAAdevelopedthisprocessunderanagreement
withacommercialpartner,whichproducestheCD-ROM
containingchartdata.TheCD-ROMalsocontainsCoast
Pilots,LightLists,TideTables,andTidalCurrentTables,
thuscomprisingononeCD-ROMtheentiresuiteof
publicationsrequiredbyUSCGregulationsforcertain
classesofvessels.Additionalinformationcanbefoundat
the NOAA Web site at: http://chartmaker.ncd.noaa.gov.
SeeChapter14foracompletediscussiononelectronic
charts and the means of correcting them.
63
CHAPTER 5
SHORT RANGE AIDS TO NAVIGATION
DEFINING SHORT RANGE AIDS TO NAVIGATION
500. Terms and Definitions
Shortrangeaidstonavigationarethoseintendedtobe
usedvisuallyorbyradarwhileininland,harborand
approach,andcoastalnavigation.Thetermencompasses
lightedandunlightedbeacons,ranges,leadinglights,
buoys,andtheirassociatedsoundsignals.Eachshortrange
aidtonavigation,commonlyreferredtoasaNAVAID,fits
withinasystemdesignedtowarnthemarinerofdangers
anddirecthimtowardsafewater.Anaid’sfunction
determinesitscolor,shape,lightcharacteristic,andsound.
ThischapterexplainstheU.S.AidstoNavigationSystem
as well as the IALA Maritime Buoyage System.
Theplacementandmaintenanceofmarineaidsto
navigationinU.S.watersistheresponsibilityoftheUnited
StatesCoastGuard.TheCoastGuardmaintains
lighthouses,radiobeacons,racons,soundsignals,buoys,
anddaybeaconsonthenavigablewatersoftheUnited
States,itsterritories,andpossessions.Additionally,the
CoastGuardexercisescontroloverprivatelyowned
navigation aid systems.
Abeaconisastationary,visualnavigationaid.Large
lighthousesandsmallsingle-pilestructuresareboth
beacons.Lightedbeaconsarecalledlights;unlighted
beaconsaredaybeacons.Allbeaconsexhibitadaymark
ofsomesort.Inthecaseofalighthouse,thecolorandtype
ofstructurearethedaymarks.Onsmallstructures,these
daymarks,consistingofcoloredgeometricshapescalled
dayboards,oftenhavelateralsignificance.Themarkings
on lighthouses and towers convey no lateral significance.
FIXED LIGHTS
501. Major and Minor Lights
Lightsvaryfromtall,highintensitycoastallightsto
battery-poweredlanternsonsinglewoodenpiles.
Immovable,highlyvisible,andaccuratelycharted,fixed
lightsprovidenavigatorswithanexcellentsourcefor
bearings.Thestructuresareoftendistinctivelycoloredto
aid in identification. See Figure 501a.
Amajorlightisahigh-intensitylightexhibitedfrom
afixedstructureoramarinesite.Majorlightsinclude
primaryseacoastlightsandsecondarylights.Primary
seacoastlightsaremajorlightsestablishedformaking
landfallfromseaandcoastwisepassagesfromheadlandto
headland.Secondarylightsaremajorlightsestablishedat
harborentrancesandotherlocationswherehighintensity
and reliability are required.
Aminorlightusuallydisplaysalightoflowto
moderateintensity.Minorlightsareestablishedinharbors,
alongchannels,rivers,andinisolatedlocations.They
usuallyhavenumbering,coloring,andlightandsound
characteristicsthatarepartofthelateralsystemofbuoyage.
Lighthousesareplacedwheretheywillbeofmostuse:
onprominentheadlands,atharborandportentrances,on
isolateddangers,oratotherpointswheremarinerscanbest
usethemtofixtheirposition.Thelighthouse’sprincipal
purposeistosupportalightataconsiderableheightabove
thewater,therebyincreasingitsgeographicrange.Support
equipment is often housed near the tower.
Withfewexceptions,allmajorlightsoperateautomat-
ically.Therearealsomanyautomaticlightsonsmaller
structuresmaintainedbytheCoastGuardorother
attendants.Unmannedmajorlightsmayhaveemergency
generatorsandautomaticmonitoringequipmenttoincrease
the light’s reliability.
Lightstructures’appearancesvary.Lightsinlow-lying
areasusuallyaresupportedbytalltowers;conversely,light
structuresonhighcliffsmayberelativelyshort.However
itssupporttowerisconstructed,almostalllightsare
similarly generated, focused, colored, and characterized.
Somemajorlightsusemodernrotatingorflashing
lights,butmanyolderlightsuseFresnellenses.These
lensesconsistofintricatelypatternedpiecesofglassina
heavybrassframework.ModernFresnel-typelensesare
castfromhigh-gradeplastic;theyaremuchsmallerand
lighter than their glass counterparts.
Abuoyantbeaconprovidesnearlythepositionalac-
curacyofalightinaplacewhereabuoywouldnormallybe
used.SeeFigure501b.Thebuoyantbeaconconsistsofa
heavysinkertowhichapipestructureistightlymoored.A
buoyancychambernearthesurfacesupportsthepipe.The
light,radarreflector,andotherdevicesarelocatedatopthe
pipeabovethesurfaceofthewater.Thepipewithitsbuoy-
ancychambertendstoremainuprighteveninsevere
weatherandheavycurrents,providingasmallerwatchcir-
64SHORT RANGE AIDS TO NAVIGATION
clethanabuoy.Thebuoyantbeaconismostusefulalong
narrow ship channels in relatively sheltered water.
502. Range Lights
Rangelightsarelightpairsthatindicateaspecificline
ofpositionwhentheyareinline.Thehigherrearlightis
placedbehindthefrontlight.Whenthemarinerseesthe
lightsverticallyinline,heisontherangeline.Ifthefront
lightappearsleftoftherearlight,theobserveristotheright
oftherangeline;ifthefrontappearstotherightoftherear,
theobserverisleftoftherangeline.Rangelightsare
sometimesequippedwithhighintensitylightsfordaylight
use.Theseareeffectiveforlongchannelsinhazy
conditionswhendayboardsmightnotbeseen.Therange
lightstructuresareusuallyalsoequippedwithdayboards
forordinarydaytimeuse.Somesmallerranges,primarilyin
theIntercoastalWaterway,rivers,andotherinlandwaters,
have just the dayboards with no lights.See Figure 502.
Toenhancethevisibilityofrangelights,theCoast
Guardhasdeveloped15-footlonglightedtubescalledlight
pipes.Theyaremountedvertically,andthemarinersees
themasverticalbarsoflightdistinctfrombackground
lighting.Installationoflightpipesisproceedingonseveral
rangemarkersthroughoutthecountry.TheCoastGuardis
alsoexperimentingwithlongrangesodiumlightsforareas
requiringvisibilitygreaterthanthelightpipescanprovide.
Theoutputfromalowpressuresodiumlightisalmost
entirelyatonewavelength.Thisallowstheuseofan
inexpensiveband-passfiltertomakethelightvisibleeven
duringthedaytime.Thisarrangementeliminatestheneed
forhighintensitylightswiththeirlargepowerrequirements.
Rangelightsareusuallywhite,red,orgreen.They
displayvariouscharacteristicsdifferentiatingthemfrom
surrounding lights.
Adirectionallightisasinglelightthatprojectsahigh
intensity,specialcharacteristicbeaminagivendirection.It
isusedincaseswhereatwo-lightrangemaynotbepracti-
cable.Adirectionalsectorlightisadirectionallightthat
emitstwoormorecoloredbeams.Thebeamshaveapre-
Figure 501a. Typical offshore light station.
Figure 501b. Typical design for a buoyant beacon.
SHORT RANGE AIDS TO NAVIGATION65
ciselyorientedboundarybetweenthem.Anormal
applicationofasectorlightwouldshowthreecoloredsec-
tions:red,white,andgreen.Thewhitesectorwould
indicate that thevesselisonthechannelcenterline; the
greensectorwouldindicatethatthevesselisoffthechannel
centerlineinthedirectionofdeepwater;andtheredsector
wouldindicatethatthevesselisoffthecenterlineinthe
direction of shoal water.
503. Aeronautical Lights
Aeronauticallightsmaybethefirstlightsobservedat
nightwhenapproachingthecoast.Thosesituatednearthe
coastandvisiblefromseaarelistedintheListofLights.
TheselightsarenotlistedintheCoastGuardLightList.
They usually flash alternating white and green.
Aeronauticallightsaresequencedgeographicallyinthe
ListofLightsalongwithmarinenavigationlights.However,
sincetheyarenotmaintainedformarinenavigation,theyare
subjecttochangesofwhichmaritimeauthoritiesmaynotbe
informed.ThesechangeswillbepublishedinNoticeto
Airmen but perhaps not inNotice to Mariners.
504. Bridge Lights
NavigationallightsonbridgesintheU.S.areprescribed
byCoastGuardregulations.Red,green,andwhitelights
markbridgesacrossnavigablewaters.Redlightsmarkpiers
andotherpartsofthebridge.Redlightsarealsousedon
drawbridgestoshowwhentheyareintheclosedposition.
Greenlightsmarkopendrawbridgesandmarkthecenterline
ofnavigablechannelsthroughfixedbridges.Thepositionwill
vary according to the type of structure.
Infrequently-usedbridgesmaybeunlighted.Inforeign
waters,thetypeandmethodoflightingmaybedifferentfrom
thosenormallyfoundintheUnitedStates.Drawbridgeswhich
mustbeopenedtoallowpassageoperateuponsoundandlight
signalsgivenbythevesselandacknowledgedbythebridge.
TheserequiredsignalsaredetailedintheCodeofFederal
RegulationsandtheapplicableCoastPilot.Certainbridges
may also be equipped with sound signals and radar reflectors.
505. Shore Lights
Shorelightsusuallyhaveashore-basedpowersupply.
Lightsonpilings,suchasthosefoundintheIntracoastal
Waterway,arebatterypowered.Solarpanelsmaybeinstalled
toenhancethelight’spowersupply.Thelightsconsistofa
powersource,aflashertodeterminethecharacteristic,alamp
changer to replace burned-out lamps, and a focusing lens.
Varioustypesofrotatinglightsareinuse.Theydonot
haveflashersbutremaincontinuouslylitwhilealensor
reflector rotates around the horizon.
Theaidstonavigationsystemiscarefullyengineered
Figure 502. Range lights.
66SHORT RANGE AIDS TO NAVIGATION
toprovidethemaximumamountofdirectiontothemariner
fortheleastexpense.Speciallydesignedfilamentsand
specialgradesofmaterialsareusedinthelighttowithstand
the harsh marine environment.
Theflasherelectronicallydeterminesthecharac-
teristicbyselectivelyinterruptingthelight’spowersupply
according to the chosen cycle.
Thelampchangerconsistsofseveralsockets
arrangedaroundacentralhub.Whenthecircuitisbroken
byaburned-outfilament,anewlampisrotatedinto
position.Almostalllightshavedaylightswitcheswhich
turn the light off at sunrise and on at dusk.
Thelensforsmalllightsmaybeoneofseveraltypes.
Thecommononesinuseareomni-directionallensesof
155mm,250mm,and300mmdiameter.Inaddition,lights
usingparabolicmirrorsorfocused-beamlensesareusedin
leadinglightsandranges.Thelampfilamentsmustbe
carefullyalignedwiththeplaneofthelensormirrorto
providethemaximumoutputoflight.Thelens’sizeis
chosenaccordingtothetypeofplatform,powersource,and
lampcharacteristics.Additionally,environmentalcharac-
teristicsofthelocationareconsidered.Varioustypesof
light-condensingpanels,reflexreflectors,orcoloredsector
panelsmaybeinstalledinsidethelenstoprovidetheproper
characteristic.Aspeciallyreinforced200mmlanternis
usedinlocationswhereiceandbreakingwaterareahazard.
LIGHT CHARACTERISTICS
506. Characteristics
Alighthasdistinctivecharacteristicswhich
distinguishitfromotherlightsorconveyspecific
informationbyshowingadistinctivesequenceoflightand
darkintervals.Additionally,alightmaydisplaya
distinctivecolororcolorsequence.IntheLightLists,the
dark intervals are referred to aseclipses.
Anoccultinglightisalighttotallyeclipsedatregular
intervals,thedurationoflightalwaysbeinggreaterthanthe
durationofdarkness.Aflashinglightflashesonandoffat
regularintervals,thedurationoflightalwaysbeingless
thanthedurationofdarkness.Anisophaselightflashesat
regularintervals,thedurationoflightbeingequaltothe
duration of darkness.
Lightphasecharacteristics(SeeTable506)arethe
distinctivesequencesoflightanddarkintervalsor
sequencesinthevariationsoftheluminousintensityofa
light.Thelightphasecharacteristicsoflightswhichchange
colordonotdifferfromthoseoflightswhichdonotchange
color.Alightshowingdifferentcolorsalternatelyis
describedasanalternatinglight.Thealternatingcharac-
teristic may be used with other light phase characteristics.
TYPE
ABBREVIATION
GENERAL DESCRIPTIONILLUSTRATION*
FixedF.A continuous and steady light.
OccultingOc.Thetotaldurationoflightinaperiodis
longerthanthetotaldurationofdarkness
andtheintervalsofdarkness(eclipses)
areusuallyofequalduration.Eclipse
regularly repeated.
Group occultingOc.(2)Anoccultinglightforwhichagroupof
eclipses,specifiedinnumber,isregularly
repeated.
Composite group
occulting
Oc.(2+1)Alightsimilartoagroupoccultinglight
exceptthatsuccessivegroupsinaperiod
have different numbers of eclipses.
IsophaseIsoAlightforwhichalldurationsoflightand
darkness are clearly equal.
Table 506. Light phase characteristics.
SHORT RANGE AIDS TO NAVIGATION67
FlashingFl.Alightforwhichthetotaldurationof
lightinaperiodisshorterthanthetotal
durationofdarknessandtheappearances
oflight(flashes)areusuallyofequal
duration(atarateoflessthan50flashes
per minute).
Long flashingL.Fl.Asingleflashinglightforwhichan
appearanceoflightofnotlessthan2sec.
duration(longflash)isregularlyrepeated.
Group flashingFl.(3)Aflashinglightforwhichagroupof
flashes,specifiedinnumber,isregularly
repeated.
Composite group
flashing
Fl.(2+1)Alightsimilartoagroupflashinglight
exceptthatsuccessivegroupsinaperiod
have different numbers of flashes.
Quick flashingQ.Alightforwhichaflashisregularly
repeatedatarateofnotlessthan50
flashesperminutebutlessthan80flashes
per minute.
Group quick
flashing
Q.(3)Alightforwhichaspecifiedgroupof
flashesisregularlyrepeated;flashesare
repeatedatarateofnotlessthan50
flashesperminutebutlessthan80flashes
per minute.
Q.(9)
Q.(6)+L.Fl.
Interrupted quick
flashing
I.Q.Alightforwhichthesequenceofquick
flashesisinterruptedbyregularly
repeatedeclipsesofconstantandlong
duration.
Very quick
flashing
V.Q.Alightforwhichaflashisregularly
repeatedatarateofnotlessthan80
flashesperminutebutlessthan160
flashes per minute.
TYPE
ABBREVIATION
GENERAL DESCRIPTIONILLUSTRATION*
Table 506. Light phase characteristics.
68SHORT RANGE AIDS TO NAVIGATION
Groupveryquick
flashing
V.Q.(3)Alightforwhichaspecifiedgroupofvery
quick flashes is regularly repeated.
V.Q.(9)
V.Q.(6)+L.Fl.
Interrupted very
quick flashing
I.V.Q.Alightforwhichthesequenceofvery
quickflashesisinterruptedbyregularly
repeatedeclipsesofconstantandlong
duration.
Ultra quick
flashing
U.Q.A light for which a flash is regularly
repeated at a rate of not less than 160
flashes per minute.
Interrupted ultra
quick flashing
I.U.Q.Alightforwhichthesequenceofultra
quickflashesisinterruptedbyregularly
repeatedeclipsesofconstantandlong
duration.
Morse codeMo.(U)A light for which appearances of light of
two clearly different durations are
grouped to represent a character or
characters in Morse Code.
Fixed and flashingF.Fl.Alightforwhichafixedlightiscombined
withaflashinglightofgreaterluminous
intensity
.
Alternate lightAl.Alightshowingdifferentcolors
alternately
* Periods shown are examples
only.
NOTE: Alternating lights may be used in combined
form with most of the previous types of lights
TYPE
ABBREVIATION
GENERAL DESCRIPTIONILLUSTRATION*
Table 506. Light phase characteristics.
SHORT RANGE AIDS TO NAVIGATION69
Light-sensitiveswitchesextinguishmostlighted
navigationaidsduringdaylighthours.However,owingto
thevarioussensitivitiesofthelightswitches,alllightsdo
notturnonoroffatthesametime.Marinersshouldaccount
forthiswhenidentifyingaidstonavigationduringtwilight
periodswhensomelightedaidsareonwhileothersarenot.
507. Light Sectors
Sectorsofcoloredglassorplasticaresometimes
placedinthelanternsofcertainlightstoindicatedangerous
waters.Lightssoequippedshowdifferentcolorswhen
observedfromdifferentbearings.Asectorchangesthe
colorofalight,butnotitscharacteristic,whenviewedfrom
certaindirections.Forexample,afoursecondflashing
whitelighthavingaredsectorwillappearasafoursecond
flashing red light when viewed from within the red sector.
Sectorsmaybeonlyafewdegreesinwidthorextend
inawidearcfromdeepwatertowardshore.Bearings
referringtosectorsareexpressedindegreestrueas
observedfromavessel.Inmostcases,areascoveredbyred
sectorsshouldbeavoided.Thenatureofthedangercanbe
determinedfromthechart.Insomecasesanarrowsector
maymarkthebestwateracrossashoal,oraturningpoint
in a channel.
Thetransitionfromonecolortoanotherisnotabrupt.
Thecolorschangethroughanarcofuncertaintyof2°or
greater,dependingontheopticaldesignofthelight.
Thereforedeterminingbearingsbyobservingthecolor
changeislessaccuratethanobtainingabearingwithan
azimuth circle.
508. Factors Affecting Range and Characteristics
Theconditionoftheatmospherehasaconsiderableeffect
uponalight’srange.Lightsaresometimesobscuredbyfog,
haze,dust,smoke,orprecipitation.Ontheotherhand,
refractionmaycausealighttobeseenfartherthanunder
ordinarycircumstances.Alightoflowintensitywillbeeasily
obscuredbyunfavorableconditionsoftheatmosphere.For
thisreason,theintensityofalightshouldalwaysbeconsidered
whenlookingforitinthickweather.Hazeanddistancemay
reducetheapparentdurationofalight’sflash.Insome
conditionsoftheatmosphere,whitelightsmayhaveareddish
hue.Inclearweathergreenlightsmayhaveamorewhitish
hue.
Lightsplacedathigherelevationsaremorefrequently
obscuredbyclouds,mist,andfogthanthosenearsealevel.
Inregionswhereiceconditionsprevail,anunattended
light’slanternpanesmaybecomecoveredwithiceorsnow
Thismayreducethelight’sluminousrangeandchangethe
light’s observed color.
Thedistancefromalightcannotbeestimatedbyits
apparentbrightness.Therearetoomanyfactorswhichcan
changetheperceivedintensity.Also,apowerful,distant
lightmaysometimesbeconfusedwithasmaller,closerone
withsimilarcharacteristics.Everylightsightedshouldbe
carefully evaluated to determine if it is the one expected.
Thepresenceofbrightshorelightsmaymakeit
difficulttodistinguishnavigationallightsfrombackground
lighting.Lightsmayalsobeobscuredbyvariousshore
obstructions,naturalandman-made.TheCoastGuard
requestsmarinerstoreportthesecasestothenearestCoast
Guard station.
Alight’sloomissometimesseenthroughhazeorthe
reflectionfromlow-lyingcloudswhenthelightisbeyond
itsgeographicrange.Onlythemostpowerfullightscan
generatealoom.Theloommaybesufficientlydefinedto
obtainabearing.Ifnot,anaccuratebearingonalight
beyondgeographicrangemaysometimesbeobtainedby
ascendingtoahigherlevelwherethelightcanbeseen,and
notingastardirectlyoverthelight.Thebearingofthestar
canthenbeobtainedfromthenavigatingbridgeandthe
bearing to the light plotted indirectly.
Atshortdistances,someofthebrighterflashinglights
mayshowafaintcontinuouslight,orfaintflashes,between
regularflashes.Thisisduetoreflectionsofarotatinglens
on panes of glass in the lighthouse.
Ifalightisnotsightedwithinareasonabletimeafter
prediction,adangeroussituationmayexist.Conversely,the
lightmaysimplybeobscuredorextinguished.Theship’s
positionshouldimmediatelybefixedbyothermeansto
determine any possibility of danger.
Theapparentcharacteristicofacomplexlightmay
changewiththedistanceoftheobserver.Forexample,a
lightwithacharacteristicoffixedwhiteandalternating
flashingwhiteandredmayinitiallyshowasasimple
flashingwhitelight.Asthevesseldrawsnearer,thered
flashwillbecomevisibleandthecharacteristicwill
apparentlybealternatingflashingwhiteandred.Later,the
fainterfixedwhitelightwillbeseenbetweentheflashes
andthetruecharacteristicofthelightfinallyrecognizedas
fixedwhite,alternatingflashingwhiteandred(FWAlW
R).Thisisbecauseforagivencandlepower,whiteisthe
mostvisiblecolor,greenlessso,andredleastofthethree.
Thisfactalsoaccountsforthedifferentrangesgiveninthe
LightListsforsomemulti-colorsectorlights.Thesame
lamphasdifferentrangesaccordingtothecolorimparted
by the sector glass.
Alightmaybeextinguishedduetoweather,battery
failure,vandalism,orothercauses.Inthecaseof
unattendedlights,thisconditionmightnotbeimmediately
corrected.Themarinershouldreportthisconditiontothe
nearestCoastGuardstation.Duringperiodsofarmed
conflict,certainlightsmaybedeliberatelyextinguished
withoutnotice.Offshorelightstationsshouldalwaysbeleft
well off the course whenever searoom permits.
70SHORT RANGE AIDS TO NAVIGATION
BUOYS
509. Definitions and Types
Buoysarefloatingaidstonavigation.Theymark
channels,indicateshoalsandobstructions,andwarnthe
marinerofdangers.Buoysareusedwherefixedaidswould
beuneconomicalorimpracticalduetothedepthofwater.
Bytheircolor,shape,topmark,number,andlightcharacter-
istics,buoysindicatetothemarinerhowtoavoidhazards
andstayinsafewater.Thefederalbuoyagesysteminthe
U.S. is maintained by the Coast Guard.
Therearemanydifferentsizesandtypesofbuoys
designedtomeetawiderangeofenvironmentalconditions
anduserrequirements.Thesizeofabuoyisdetermined
primarilybyitslocation.Ingeneral,thesmallestbuoy
whichwillstanduptolocalweatherandcurrentconditions
is chosen.
TherearefivetypesofbuoysmaintainedbytheCoast
Guard. They are:
1.Lateral marks
2.Isolated danger marks
3.Safe water marks
4.Special marks
5.Information/regulatory marks
Theseconformingeneraltothespecificationsofthe
InternationalAssociationofLighthouseAuthorities
(IALA) buoyage system.
Alightedbuoyisafloatinghullwithatoweronwhich
alightismounted.Batteriesforthelightareinwatertight
pocketsinthebuoyhullorinwatertightboxesmountedon
thebuoyhull.Tokeepthebuoyinanuprightposition,a
counterweightisattachedtothehullbelowthewater’s
surface. A radar reflector is built into the buoy tower.
ThelargestofthetypicalU.S.CoastGuardbuoyscan
bemooredinupto190feetofwater,limitedbytheweight
ofchainthehullcansupport.Thefocalplaneofthelightis
15to20feethigh.Thedesignednominalvisualrangeis3.8
miles, and the radar range 4 miles. Actual conditions will
cause these range figures to vary considerably.
Thesmallestbuoysaredesignedforprotectedwater.
Somearemadeofplasticandweighonly40pounds.
Speciallydesignedbuoysareusedforfastcurrent,ice,and
other environmental conditions.
Avarietyofspecialpurposebuoysareownedbyother
governmentalorganizations.Examplesoftheseorgani-
zationsincludetheSt.LawrenceSeawayDevelopment
Corporation,NOAA,andtheDepartmentofDefense.
Thesebuoysareusuallynavigationalmarksordata
collectionbuoyswithtraditionalround,boat-shaped,or
discus-shaped hulls.
Aspecialclassofbuoy,theOceanDataAcquisition
System(ODAS)buoy,ismooredorfloatsfreeinoffshore
waters.Positionsarepromulgatedthroughradiowarnings.
Thesebuoysaregenerallynotlargeenoughtocause
damagetoalargevesselinacollision,butshouldbegiven
awideberthregardless,asanylosswouldalmostcertainly
resultintheinterruptionofvaluablescientificexperiments.
Theyaregenerallybrightorangeoryellowincolor,with
verticalstripesonmooredbuoysandhorizontalbandson
free-floatingones,andhaveastrobelightfornight
visibility.
Eveninclearweather,thedangerofcollisionwitha
buoyexists.Ifstruckhead-on,alargebuoycaninflict
severedamagetoalargeship;itcansinkasmallerone.
Reducedvisibilityorheavybackgroundlightingcan
contributetotheproblemofvisibility.TheCoastGuard
sometimesreceivesreportsofbuoysmissingfromstation
thatwereactuallyrundownandsunk.Tugboatsand
towboatstowingorpushingbargesareparticularly
dangeroustobuoysbecauseofpoorover-the-bowvisibility
whenpushingoryawingduringtowing.Theprofessional
marinermustreportanycollisionwithabuoytothenearest
CoastGuardunit.Failuretodosomaycausethenextvessel
tomissthechannelorhittheobstructionmarkedbythe
buoy; it can also lead to fines and legal liability.
Routineon-stationbuoymaintenanceconsistsof
inspectingthemooring,cleaningthehulland
superstructure,replacingthebatteries,flasher,andlamps,
checkingwiringandventingsystems,andverifyingthe
buoy’sexactposition.Everyfewyears,eachbuoyis
replacedbyasimilaraidandreturnedtoaCoastGuard
maintenance facility for complete refurbishment.
Theplacementofabuoydependsonitspurposeandits
positiononthechart.Mostbuoysareplacedontheircharted
positionsasaccuratelyasconditionsallow.However,ifa
Figure 509. Buoy showing counterweight.
SHORT RANGE AIDS TO NAVIGATION71
buoy’spurposeistomarkashoalandtheshoalisfoundtobe
inadifferentpositionthanthechartshows,thebuoywillbe
placedtoproperlymarktheshoal,andnotonitscharted
position.
510. Lights on Buoys
Buoylightsystemsconsistofabatterypack,aflasher
whichdeterminesthecharacteristic,alampchangerwhich
automaticallyreplacesburned-outbulbs,alenstofocusthe
light,andahousingwhichsupportsthelensandprotects
the electrical equipment.
Thebatteriesconsistof12-voltlead/acidtype
batterieselectricallyconnectedtoprovidesufficientpower
toruntheproperflashcharacteristicandlampsize.These
batterypacksarecontainedinpocketsinthebuoyhull,
accessiblethroughwater-tightboltedhatchesorexternally
mountedboxes.Carefulcalculationsbasedonlightcharac-
teristics determine how much battery power to install.
Theflasherdeterminesthecharacteristicofthelamp.
It is installed in the housing supporting the lens.
Thelampchangerconsistsofseveralsockets
arrangedaroundacentralhub.Anewlamprotatesinto
position if the active one burns out.
Undernormalconditions,thelensesusedonbuoysare
155mmindiameteratthebase.200mmlensesareused
wherebreakingwavesorswellscallforthelargerlens.
Theyarecoloredaccordingtothechartedcharacteristicof
thebuoy.Asinshorelights,thelampmustbecarefully
focusedsothatthefilamentisdirectlyinlinewiththefocal
planeofthelens.Thisensuresthatthemajorityofthelight
producedisfocusedina360°horizontalfanbeam.Abuoy
lighthasarelativelynarrowverticalprofile.Becausethe
buoyrocksinthesea,thefocalplanemayonlybevisible
forfractionsofasecondatgreatranges.Arealisticrange
forsightingbuoylightsis4-6milesingoodvisibilityand
calm weather.
511. Sound Signals on Buoys
Lightedsoundbuoyshavethesamegeneralconfigu-
rationaslightedbuoysbutareequippedwitheitherabell,
gong,whistle,orhorn.Bellsandgongsaresoundedby
tappershangingfromthetowerthatswingasthebuoyrocks
inthesea.Bellbuoysproduceonlyonetone;gongbuoys
produceseveraltones.Thetone-producingdeviceis
mounted between the legs of the pillar or tower.
Whistlebuoysmakealoudmoaningsoundcausedby
therisingandfallingmotionsofthebuoyinthesea.A
soundbuoyequippedwithanelectronichornwillproduce
apuretoneatregularintervalsregardlessoftheseastate.
Unlightedsoundbuoyshavethesamegeneralappearance
aslightedbuoys,buttheirunderwatershapeisdesignedto
make them lively in all sea states.
512. Buoy Moorings
Buoysrequiremooringstoholdtheminposition.
Typicallythemooringconsistsofchainandalarge
concreteorcastironsinker.SeeFigure512.Becausebuoys
aresubjectedtowaves,wind,andtides,themooringsmust
bedeployedwithchainlengthsmuchgreaterthanthewater
depth.Thescopeofchainwillnormallybeabout3times
thewaterdepth.Thelengthofthemooringchaindefinesa
watchcirclewithinwhichthebuoycanbeexpectedto
swing.Itisforthisreasonthatthechartedbuoysymbolhas
a“positionapproximate”circletoindicateitscharted
position,whereasalightpositionisshownbyadotatthe
exactlocation.Actualwatchcirclesdonotnecessarily
coincidewiththe“positionapproximate”circleswhich
represent them.
Overseveralyears,thechaingraduallywearsoutand
mustbereplaced.Thewornchainisoftencastintothe
concrete of new sinkers.
513. Large Navigational Buoys
Largenavigationalbuoysaremooredinopenwater
atapproachestocertainmajorseacoastportsandmonitored
fromshorestationsbyradiosignals.These40-foot
diameterbuoys(Figure513)showlightsfromheightsof
about36feetabovethewater.Emergencylightsautomat-
icallyenergizeifthemainlightisextinguished.These
buoys may also have a radiobeacon and sound signals.
514. Wreck Buoys
Awreckbuoyusuallycannotbeplaceddirectlyover
thewreckitisintendedtomarkbecausethebuoytender
maynotwanttopassoverashallowwreckorriskfouling
thebuoymooring.Forthisreason,awreckbuoyisusually
Figure 512. A sinker used to anchor a buoy.
72SHORT RANGE AIDS TO NAVIGATION
placedascloselyaspossibleontheseawardorchannelward
sideofawreck.Insomesituations,twobuoysmaybeused
tomarkthewreck,onelyingoffeachend.Thewreckmay
liedirectlybetweenthemorinshoreofalinebetweenthem,
dependingonthelocalsituation.TheLocalNoticeto
Marinersshouldbeconsultedconcerningdetailsofthe
placementofwreckbuoysonindividualwrecks.Oftenit
willalsogiveparticularsofthewreckandwhatactivities
may be in progress to clear it.
Thechartedpositionofawreckbuoywillusuallybe
offsetfromtheactualgeographicpositionsothatthewreck
andbuoysymbolsdonotcoincide.Onlyonthelargestscale
chartwilltheactualandchartedpositionsofbothwreckand
buoybethesame.Wheretheymightoverlap,itisthewreck
symbolwhichoccupiestheexactchartedpositionandthe
buoy symbol which is offset.
Wreckbuoysarerequiredtobeplacedbytheownerof
thewreck,buttheymaybeplacedbytheCoastGuardifthe
ownerisunabletocomplywiththisrequirement.Ingeneral,
privately placed aids are not as reliable as Coast Guard aids.
Sunkenwrecksaresometimesmovedawayfromtheir
buoysbystorms,currents,freshets,orothercauses.Justas
shoalsmayshiftawayfromthebuoysplacedtomarkthem,
wrecks may shift away from wreck buoys.
515. Fallibility of Buoys
Buoyscannotbereliedontomaintaintheircharted
positionsconsistently.Theyaresubjecttoavarietyof
hazardsincludingsevereweather,collision,mooring
casualties,andelectricalfailure.Marinersshouldreport
discrepanciestotheauthorityresponsibleformaintaining
the aid.
Thebuoysymbolshownonchartsindicatesthe
approximatepositionofthesinkerwhichsecuresthebuoy
totheseabed.Theapproximatepositionisusedbecauseof
practicallimitationsinkeepingbuoysinprecise
geographicallocations.Theselimitationsinclude
prevailingatmosphericandseaconditions,theslopeand
typeofmaterialmakinguptheseabed,thescopeofthe
Figure 513. Large navigational buoy.
SHORT RANGE AIDS TO NAVIGATION73
mooringchain,andthefactthatthepositionsofthebuoys
andthesinkersarenotundercontinuoussurveillance.The
positionofthebuoyshiftsaroundtheareashownbythe
chart symbol due to the forces of wind and current.
Abuoymaynotbeinitschartedpositionbecauseof
changesinthefeatureitmarks.Forexample,abuoymeantto
markashoalwhoseboundariesareshiftingmightfrequentlybe
movedtomarktheshoalaccurately.ALocalNoticetoMariners
willreportthechange,andaNoticetoMarinerschartcorrection
mayalsobewritten.Insomesmallchannelswhichchange
often,buoysarenotchartedevenwhenconsideredpermanent;
local knowledge is advised in such areas.
Forthesereasons,amarinermustnotrelycompletely
uponthepositionoroperationofbuoys,butshould
navigateusingbearingsofchartedfeatures,structures,and
aidstonavigationonshore.Further,avesselattemptingto
passtoocloseaboardabuoyrisksacollisionwiththebuoy
or the obstruction it marks.
BUOYAGE SYSTEMS
516. Lateral and Cardinal Systems
Therearetwomajortypesofbuoyagesystems:the
lateralsystemandthecardinalsystem.Thelateral
systemisbestsuitedforwell-definedchannels.The
descriptionofeachbuoyindicatesthedirectionofdanger
relativetothecoursewhichisnormallyfollowed.In
principle,thepositionsofmarksinthelateralsystemare
determinedbythegeneraldirectiontakenbythemariner
whenapproachingportfromseaward.Thesepositions
mayalsobedeterminedwithreferencetothemainstream
offloodcurrent.TheUnitedStatesAidstoNavigation
System is a lateral system.
Thecardinalsystemisbestsuitedforcoastswith
numerousisolatedrocks,shoals,andislands,andfor
dangersintheopensea.Thecharacteristicofeachbuoy
indicatestheapproximatetruebearingofthedangerit
marks.Thus,aneasternquadrantbuoymarksadanger
whichliestothewestofthebuoy.Thefollowingpages
diagramthecardinalandlateralbuoyagesystemsasfound
outside the United States.
517. The IALA Maritime Buoyage System
Althoughmostofthemajormaritimenationshave
usedeitherthelateralorthecardinalsystemformanyyears,
detailssuchasthebuoyshapesandcolorshavevariedfrom
countrytocountry.Withtheincreaseinmaritime
commercebetweencountries,theneedforauniform
system of buoyage became apparent.
In1889,anInternationalMarineConferenceheldin
Washington,D.C.,recommendedthatinthelateralsystem,
starboardhandbuoysbepaintedredandporthandbuoys
black.Unfortunately,whenlightsforbuoyswere
introducedsomeyearslater,someEuropeancountries
placedredlightsontheblackporthandbuoystoconform
withtheredlightsmarkingtheportsideofharbor
entrances,whileinNorthAmericaredlightswereplacedon
redstarboardhandbuoys.In1936,aLeagueofNations
subcommitteerecommendedacoloringsystemoppositeto
the 1889 proposal.
TheInternationalAssociationofLighthouse
Authorities(IALA)isanon-governmentalorganization
whichconsistsofrepresentativesoftheworldwide
communityofaidstonavigationservices.Itpromotes
informationexchangeandrecommendsimprovements
basedonnewtechnologies.In1980,withtheassistanceof
IMOandtheIHO,thelighthouseauthoritiesfrom50
countriesandrepresentativesof9internationalorgani-
zationsconcernedwithaidstonavigationmetandadopted
theIALAMaritimeBuoyageSystem.Theyestablished
tworegions,RegionAandRegionB,fortheentireworld.
RegionAroughlycorrespondstothe1936Leagueof
Nations system, and Region B to the older 1889 system.
LateralmarksdifferbetweenRegionsAandB.Lateral
marksinRegionAuseredandgreencolorsbydayandnight
toindicateportandstarboardsidesofchannels,respectively.
InRegionB,thesecolorsarereversedwithredtostarboard
andgreentoport.Inbothsystems,theconventionaldirection
ofbuoyageisconsideredtobereturningfromsea,hencethe
phrase “red right returning” in IALA region B.
518. Types of Marks
TheIALAMaritimeBuoyageSystemappliestoall
fixedandfloatingmarks,otherthanlighthouses,sector
lights,rangelights,daymarks,lightshipsandlargenaviga-
tional buoys, which indicate:
1.The side and center-lines of navigable channels
2.Natural dangers, wrecks, and other obstructions
3.Regulated navigation areas
4.Other important features
Mostlightedandunlightedbeaconsotherthanrange
marksareincludedinthesystem.Ingeneral,beacon
topmarkswillhavethesameshapeandcolorsasthoseused
onbuoys.Thesystemprovidesfivetypesofmarkswhich
may be used in any combination:
1.Lateralmarksindicateportandstarboardsidesof
channels.
2.Cardinalmarks,namedaccordingtothefourpoints
ofthecompass,indicatethatthenavigablewater
lies to the named side of the mark.
3.Isolateddangermarkserectedon,ormoored
directly on or over, dangers of limited extent.
4.Safe water marks, such as midchannel buoys.
74SHORT RANGE AIDS TO NAVIGATION
5.Specialmarks,thepurposeofwhichisapparent
fromreferencetothechartorothernautical
documents.
Characteristics of Marks
Thesignificanceofamarkdependsononeormore
features:
1.By day—color, shape, and topmark
2.By night—light color and phase characteristics
Colors of Marks
Thecolorsredandgreenarereservedforlateralmarks,
andyellowforspecialmarks.Theothertypesofmarks
haveblackandyelloworblackandredhorizontalbands,or
red and white vertical stripes.
Shapes of Marks
There are five basic buoy shapes:
1.Can
2.Cone
3.Sphere
4.Pillar
5.Spar
Inthecaseofcan,conical,andspherical,theshapes
havelateralsignificancebecausetheshapeindicatesthe
correctsidetopass.Withpillarandsparbuoys,theshape
has no special significance.
Theterm“pillar”isusedtodescribeanybuoywhichis
smallerthanalargenavigationbuoy(LNB)andwhichhasa
tall,centralstructureonabroadbase;itincludesbeacon
buoys,highfocalplanebuoys,andothers(exceptsparbuoys)
whose body shape does not indicate the correct side to pass.
Topmarks
TheIALASystemmakesuseofcan,conical,
spherical,andX-shapedtopmarksonly.Topmarkson
pillarandsparbuoysareparticularlyimportantandwillbe
usedwhereverpracticable,buticeorothersevere
conditions may occasionally prevent their use.
Colors of Lights
Wheremarksarelighted,redandgreenlightsare
reservedforlateralmarks,andyellowforspecialmarks.
Theothertypesofmarkshaveawhitelight,distinguished
one from another by phase characteristic.
Phase Characteristics of Lights
Redandgreenlightsmayhaveanyphasecharac-
teristic,asthecoloraloneissufficienttoshowonwhich
sidetheyshouldbepassed.Specialmarks,whenlighted,
haveayellowlightwithanyphasecharacteristicnot
reservedforwhitelightsofthesystem.Theothertypesof
markshaveclearlyspecifiedphasecharacteristicsofwhite
light:variousquick-flashingphasecharacteristicsfor
cardinalmarks,groupflashing(2)forisolateddanger
marks,andrelativelylongperiodsoflightforsafewater
marks.
SomeshorelightsspecificallyexcludedfromtheIALA
Systemmaycoincidentallyhavecharacteristics
correspondingtothoseapprovedforusewiththenew
marks.Careisneededtoensurethatsuchlightsarenot
misinterpreted.
519. IALA Lateral Marks
Lateralmarksaregenerallyusedforwell-defined
channels;theyindicatetheportandstarboardhandsidesof
theroutetobefollowed,andareusedinconjunctionwitha
conventional direction of buoyage.
This direction is defined in one of two ways:
1.Localdirectionofbuoyageisthedirectiontaken
bythemarinerwhenapproachingaharbor,river
estuary, or other waterway from seaward.
2.Generaldirectionofbuoyageisdeterminedby
thebuoyageauthorities,followingaclockwise
directionaroundcontinentalland-masses,givenin
sailingdirections,and,ifnecessary,indicatedon
charts by a large open arrow symbol.
Insomeplaces,particularlystraitsopenatbothends,
thelocaldirectionofbuoyagemaybeoverriddenbythe
general direction.
AlongthecoastsoftheUnitedStates,thecharacter-
isticsassumethatproceeding“fromseaward”constitutesa
clockwisedirection:asoutherlydirectionalongtheAtlantic
coast,awesterlydirectionalongtheGulfofMexicocoast,
andanortherlydirectionalongthePacificcoast.Onthe
GreatLakes,awesterlyandnortherlydirectionistakenas
being“fromseaward”(exceptonLakeMichigan,wherea
southerlydirectionisused).OntheMississippiandOhio
Riversandtheirtributaries,thecharacteristicsofaidsto
navigationaredeterminedasproceedingfromseatoward
theheadofnavigation.OntheIntracoastalWaterway,
proceedinginagenerallysoutherlydirectionalongthe
Atlanticcoast,andinagenerallywesterlydirectionalong
thegulfcoast,isconsideredasproceeding“fromseaward.”
520. IALA Cardinal Marks
Acardinalmarkisusedinconjunctionwiththe
compasstoindicatewherethemarinermayfindthebest
navigablewater.Itisplacedinoneofthefourquadrants
(north,east,south,andwest),boundedbythetruebearings
SHORT RANGE AIDS TO NAVIGATION75
NW-NE,NE-SE,SE-SW,andSW-NW,takenfromthe
pointofinterest.Acardinalmarktakesitsnamefromthe
quadrantin which it is placed.
Themarinerissafeifhepassesnorthofanorthmark,east
ofaneastmark,southofasouthmark,andwestofawestmark.
A cardinal mark may be used to:
1.Indicatethatthedeepestwaterinanareaisonthe
named side of the mark.
2.Indicate the safe side on which to pass a danger.
3.Emphasizeafeatureinachannel,suchasabend,
junction, bifurcation, or end of a shoal.
Topmarks
Blackdouble-conetopmarksarethemostimportant
feature,byday,ofcardinalmarks.Theconesarevertically
placed,oneovertheother.Thearrangementoftheconesis
verylogical:Northistwoconeswiththeirpointsup(asin
“north-up”).Southistwocones,pointsdown.Eastistwo
coneswithbasestogether,andwestistwoconeswith
pointstogether,whichgivesawineglassshape.“
Westisa
Wineglass” is a memory aid.
Cardinalmarkscarrytopmarkswheneverpracticable,
with the cones as large as possible and clearly separated.
Colors
Blackandyellowhorizontalbandsareusedtocolora
cardinalmark.Thepositionoftheblackband,orbands,is
related to the points of the black topmarks.
Shape
Theshapeofacardinalmarkisnotsignificant,but
buoys must be pillars or spars.
Lights
Whenlighted,acardinalmarkexhibitsawhitelight;its
characteristicsarebasedonagroupofquickorveryquick
flasheswhichdistinguishitasacardinalmarkandindicateits
quadrant.Thedistinguishingquickorveryquickflashesare:
North—Uninterrupted
East—three flashes in a group
South—sixflashesinagroupfollowedbyalongflash
West—nine flashes in a group
Asamemoryaid,thenumberofflashesineachgroup
canbeassociatedwithaclockface:3o’clock—E,6
o’clock—S, and 9 o’clock—W.
Thelongflash(ofnotlessthan2secondsduration),
immediatelyfollowingthegroupofflashesofasouthcar-
dinalmark,istoensurethatitssixflashescannotbe
mistaken for three or nine.
Theperiodsoftheeast,south,andwestlightsare,re-
spectively,10,15,and15secondsifquickflashing;and5,
10, and 10 seconds if very quick flashing.
Quickflashinglightsflashataratebetween50and79
flashesperminute,usuallyeither50or60.Veryquick
flashinglightsflashataratebetween80and159flashesper
minute, usually either 100 or 120.
Itisnecessarytohaveachoiceofquickflashingor
veryquickflashinglightsinordertoavoidconfusionif,for
example,twonorthbuoysareplacednearenoughtoeach
other for one to be mistaken for the other.
521. IALA Isolated Danger Marks
Anisolateddangermarkiserectedon,ormooredon
orabove,anisolateddangeroflimitedextentwhichhas
navigablewaterallaroundit.Theextentofthesurrounding
navigablewaterisimmaterial;suchamarkcan,for
example,indicateeitherashoalwhichiswelloffshoreoran
islet separated by a narrow channel from the coast.
Position
Onachart,thepositionofadangeristhecenterofthe
symbolorsoundingindicatingthatdanger;anisolated
dangerbuoymaythereforebeslightlydisplacedfromits
geographicpositiontoavoidoverprintingthetwosymbols.
Thesmallerthescale,thegreaterthisoffsetwillbe.Atvery
large scales the symbol may be correctly charted.
Topmark
Ablackdouble-spheretopmarkis,byday,themost
importantfeatureofanisolateddangermark.Whenever
practicable,thistopmarkwillbecarriedwiththespheresas
large as possible, disposed vertically, and clearly separated.
Color
Blackwithoneormoreredhorizontalbandsarethe
colors used for isolated danger marks.
Shape
Theshapeofanisolateddangermarkisnotsignificant,
but a buoy will be a pillar or a spar.
NPoints upBlack above yellow
SPoints downBlack below yellow
WPoints togetherBlack, yellow above and below
EPoints apartYellow, black above and below
76SHORT RANGE AIDS TO NAVIGATION
Light
Whenlighted,awhiteflashinglightshowingagroup
oftwoflashesisusedtodenoteanisolateddangermark.As
amemoryaid,associatetwoflasheswithtwoballsinthe
topmark.
522. IALA Safe Water Marks
Asafewatermarkisusedtoindicatethatthereis
navigablewaterallaroundthemark.Suchamarkmaybe
used as a center line, mid-channel, or landfall buoy.
Color
Redandwhiteverticalstripesareusedforsafewater
marks,anddistinguishthemfromtheblack-banded,
danger-marking marks.
Shape
Spherical,pillar,orsparbuoysmaybeusedassafewater
marks.
Topmark
Asingleredsphericaltopmarkwillbecarried,
wheneverpracticable,byapillarorsparbuoyusedasasafe
water mark.
Lights
Whenlighted,safewatermarksexhibitawhitelight.
Thislightcanbeocculting,isophase,asinglelongflash,or
Morse“A.”Ifalongflash(i.e.aflashofnotlessthan2
seconds)isused,theperiodofthelightwillbe10seconds.
Asamemoryaid,rememberasingleflashandasingle
sphere topmark.
523. IALA Special Marks
Aspecialmarkmaybeusedtoindicateaspecialarea
orfeaturewhichisapparentbyreferringtoachart,sailing
directions, or notices to mariners. Uses include:
1.Ocean Data Acquisition System (ODAS) buoys
2.Traffic separation marks
3.Spoil ground marks
4.Military exercise zone marks
5.Cable or pipeline marks, including outfall pipes
6.Recreation zone marks
Anotherfunctionofaspecialmarkistodefineachannel
withinachannel.Forexample,achannelfordeepdraftvessels
inawideestuary,wherethelimitsofthechannelfornormal
navigationaremarkedbyredandgreenlateralbuoys,may
haveitsboundariesorcenterlinemarkedbyyellowbuoysof
the appropriate lateral shapes.
Color
Yellow is the color used for special marks.
Shape
Theshapeofaspecialmarkisoptional,butmustnot
conflictwiththatusedforalateralorasafewatermark.For
example,anoutfallbuoyontheporthandsideofachannel
could be can-shaped but not conical.
Topmark
Whenatopmarkiscarriedittakestheformofasingle
yellow X.
Lights
Whenalightisexhibiteditisyellow.Itmayshowany
phasecharacteristicexceptthoseusedforthewhitelightsof
cardinal,isolateddanger,andsafewatermarks.Inthecase
ofODASbuoys,thephasecharacteristicusedisgroup-
flashing with a group of five flashes every 20 seconds.
524. IALA New Dangers
Anewlydiscoveredhazardtonavigationnotyetshown
oncharts,includedinsailingdirections,orannouncedbya
NoticetoMarinersistermedanewdanger.Thetermcovers
naturally occurring and man-made obstructions.
Marking
Anewdangerismarkedbyoneormorecardinalor
lateralmarksinaccordancewiththeIALAsystemrules.If
thedangerisespeciallygrave,atleastoneofthemarkswill
beduplicatedassoonaspracticablebyanidenticalmark
until the danger has been sufficiently identified.
Lights
Ifalightedmarkisusedforanewdanger,itmust
exhibitaquickflashingorveryquickflashinglight.Ifa
cardinalmarkisused,itmustexhibitawhitelight;ifa
lateral mark, a red or green light.
Racons
TheduplicatemarkmaycarryaRacon,MorsecodedD,
showing a signal length of 1 nautical mile on a radar display.
SHORT RANGE AIDS TO NAVIGATION77
525. Chart Symbols and Abbreviations
Sparbuoysandspindlebuoysarerepresentedbythesame
symbol;itisslantedtodistinguishthemfromuprightbeacon
symbols.Theabbreviateddescriptionofthecolorofabuoyis
givenunderthesymbol.Whereabuoyiscoloredinbands,the
colorsareindicatedinsequencefromthetop.Ifthesequenceof
thebandsisnotknown,orifthebuoyisstriped,thecolorsare
indicated with the darker color first.
Topmarks
Topmarksymbolsaresolidblackexceptifthetopmark
is red.
Lights
Theperiodofthelightofacardinalmarkisdetermined
byitsquadrantanditsflashcharacteristic(eitherquick-
flashingoraveryquick-flashing).Thelight’speriodisless
importantthanitsphasecharacteristic.Wherespaceon
charts is limited, the period may be omitted.
Light Flares
Magentalight-flaresarenormallyslantedandinsertedwith
theirpointsadjacenttothepositioncirclesatthebaseofthe
symbolssotheflaresymbolsdonotobscurethetopmark
symbols.
Radar Reflectors
AccordingtoIALArules,radarreflectorsarenot
charted,forseveralreasons.First,allimportantbuoysare
fittedwithradarreflectors.Itisalsonecessarytoreducethe
sizeandcomplexityofbuoysymbolsandassociated
legends.Finally,itisunderstoodthat,inthecaseofcardinal
buoys,buoyageauthoritiesplacethereflectorsothatit
cannot be mistaken for a topmark.
ThesymbolsandabbreviationsoftheIALAMaritime
BuoyageSystemmaybefoundinU.S.ChartNo.1andin
foreign equivalents.
526. Description of the U.S. Aids to Navigation System
IntheUnitedStates,theU.S.CoastGuardhas
incorporatedthemajorfeaturesoftheIALAsystemwiththe
existinginfrastructureofbuoysandlightsasexplained
below.
Colors
Underthissystem,greenbuoysmarkachannel’sport
sideandobstructionswhichmustbepassedbykeepingthe
buoyontheporthand.Redbuoysmarkachannel’s
starboardsideandobstructionswhichmustbepassedby
keeping the buoy on the starboard hand.
Redandgreenhorizontallybandedpreferredchannel
buoysmarkjunctionsorbifurcationsinachannelor
obstructionswhichmaybepassedoneitherside.Ifthe
topmostbandisgreen,thepreferredchannelwillbe
followedbykeepingthebuoyontheporthand.Ifthe
topmostbandisred,thepreferredchannelwillbefollowed
by keeping the buoy on the starboard hand.
Redandwhiteverticallystripedsafewaterbuoysmark
a fairway or mid-channel.
Reflectivematerialisplacedonbuoystoassistintheir
detectionatnightwithasearchlight.Thecolorofthereflective
materialagreeswiththebuoycolor.Redorgreenreflective
materialmaybeplacedonpreferredchannel(junction)buoys;
rediftopmostbandisred,orgreenifthetopmostbandisgreen.
Whitereflectivematerialisusedonsafewaterbuoys.Special
purposebuoysdisplayyellowreflectivematerial.Warningor
regulatorybuoysdisplayorangereflectivehorizontalbandsand
awarningsymbol.IntracoastalWaterwaybuoysdisplaya
yellowreflectivesquare,triangle,orhorizontalstripalongwith
the reflective material coincident with the buoy’s function.
Shapes
Certainunlightedbuoysaredifferentiatedbyshape.Red
buoysandredandgreenhorizontallybandedbuoyswiththe
topmostbandredarecone-shapedbuoyscallednuns.Green
buoysandgreenandredhorizontallybandedbuoyswiththe
topmost band green are cylinder-shaped buoys calledcans.
Unlightedredandwhiteverticallystripedbuoysmaybe
pillarshapedorspherical.Lightedbuoys,soundbuoys,andspar
buoysarenotdifferentiatedbyshapetoindicatethesideon
whichtheyshouldbepassed.Theirpurposeisindicatednotby
shape but by the color, number, or light characteristics.
Numbers
Allsolidcoloredbuoysarenumbered,redbuoys
bearingevennumbersandgreenbuoysbearingodd
numbers.(NotethatthissameruleappliesinIALASystem
Aalso.)Thenumbersincreasefromseawardupstreamor
towardland.Noothercoloredbuoysarenumbered;
however, any buoy may have a letter for identification.
Light Colors
Redlightsareusedonlyonredbuoysorredandgreen
horizontallybandedbuoyswiththetopmostbandred.Green
lightsareusedonlyonthegreenbuoysorgreenandred
horizontallybandedbuoyswiththetopmostbandgreen.White
lightsareusedonboth“safewater”aidsshowingaMorseCode
“A” characteristic and on Information and Regulatory aids.
Light Characteristics
Lightsonredbuoysorgreenbuoys,ifnotocculting
78SHORT RANGE AIDS TO NAVIGATION
orisophase,willgenerallyberegularlyflashing(Fl).For
ordinarypurposes,thefrequencyofflasheswillbenot
morethan50flashesperminute.Lightswithadistinct
cautionarysignificance,suchasatsharpturnsor
markingdangerousobstructions,willflashnotlessthan
50flashesbutnotmorethan80flashesperminute(quick
flashing,Q).Lightsonpreferredchannelbuoyswill
showaseriesofgroupflasheswithsuccessivegroupsin
aperiodhavingadifferentnumberofflashes-composite
groupflashing(oraquicklightinwhichthesequenceof
flashesisinterruptedbyregularlyrepeatedeclipsesof
constantandlongduration).Lightsonsafewaterbuoys
willalwaysshowawhiteMorseCode“A”(Short-Long)
flashrecurringattherateofapproximatelyeighttimes
per minute.
Daylight Controls
Lightedbuoyshaveaspecialdevicetoenergizethe
lightwhendarknessfallsandtode-energizethelightwhen
daybreaks.Thesedevicesarenotofequalsensitivity;
thereforealllightsdonotcomeonorgooffatthesame
time.Marinersshouldensurecorrectidentificationofaids
duringtwilightperiodswhensomelightaidstonavigation
are on while others are not.
Special Purpose Buoys
Buoysforspecialpurposesarecoloredyellow.White
buoyswithorangebandsareforinformationalorregulatory
purposes.Theshapeofspecialpurposebuoyshasnosignif-
icance.Theyarenotnumbered,buttheymaybelettered.If
lighted,specialpurposebuoysdisplayayellowlight
usuallywithfixedorslowflashcharacteristics.Information
and regulatory buoys, if lighted, display white lights.
BEACONS
527. Definition and Description
Beaconsarefixedaidstonavigationplacedonshore
oronpilingsinrelativelyshallowwater.Ifunlighted,the
beaconisreferredtoasadaybeacon.Adaybeaconis
identifiedbythecolor,shape,andnumberofits
dayboard.Thesimplestformofdaybeaconconsistsofa
singlepilewithadayboardaffixedatornearitstop.See
Figure527.Daybeaconsmaybeusedtoformanunlighted
range.
.Dayboardsidentifyaidstonavigationagainstdaylight
backgrounds.Thesizeofthedayboardrequiredtomakethe
aid conspicuous depends upon the aid’s intended range.
Mostdayboardsalsodisplaynumbersorlettersforidenti-
fication.Thenumbers,letters,andbordersofmostdayboards
have reflective tape to make them visible at night.
Thedetection,recognition,andidentificationdistances
varywidelyforanyparticulardayboard.Theydependupon
theluminanceofthedayboard,theSun’sposition,andthe
local visibility conditions.
SOUND SIGNALS
528. Types of Sound Signals
Mostlighthousesandoffshorelightplatforms,aswell
assomeminorlightstructuresandbuoys,areequippedwith
sound-producingdevicestohelpthemarinerinperiodsof
lowvisibility.ChartsandLightListscontainthe
informationrequiredforpositiveidentification.Buoys
fittedwithbells,gongs,orwhistlesactuatedbywave
motionmayproducenosoundwhentheseaiscalm.Sound
signalsarenotdesignedtoidentifythebuoyorbeaconfor
navigationpurposes.Rather,theyallowthemarinertopass
clear of the buoy or beacon during low visibility.
Soundsignalsvary.Thenavigatormustusethe
LightListtodeterminetheexactlengthofeachblastand
silentinterval.Thevarioustypesofsoundsignalsalso
differintone,facilitatingrecognitionoftherespective
stations.
Diaphonesproducesoundwithaslottedpistonmoved
backandforthbycompressedair.Blastsmayconsistofa
highandlowtone.Thesealternate-pitchsignalsarecalled
“two-tone.”DiaphonesarenotusedbytheCoastGuard,but
themarinermayfindthemonsomeprivatenavigationaids.
Hornsproducesoundbymeansofadiscdiaphragm
operatedpneumaticallyorelectrically.Duplexortriplex
horn units of differing pitch produce a chime signal.
Sirensproducesoundwitheitheradiscoracup-
Figure 527. Daybeacon.
SHORT RANGE AIDS TO NAVIGATION79
shapedrotoractuatedelectricallyorpneumatically.Sirens
are not used on U.S. navigation aids.
Whistlesusecompressedairemittedthrougha
circumferential slot into a cylindrical bell chamber.
Bellsandgongsaresoundedwithamechanically
operated hammer.
529. Limitations of Sound Signals
Asaidstonavigation,soundsignalshaveserious
limitationsbecausesoundtravelsthroughtheairinan
unpredictable manner.
It has been clearly established that:
1.Soundsignalsareheardatgreatlyvarying
distancesandthatthedistanceatwhichasound
signalcanbeheardmayvarywiththebearingand
timing of the signal.
2.Undercertainatmosphericconditions,whena
soundsignalhasacombinationhighandlowtone,
itisnotunusualforoneofthetonestobeinaudible.
Inthecaseofsirens,whichproduceavaryingtone,
portions of the signal may not be heard.
3.Whenthesoundisscreenedbyanobstruction,
there are areas where it is inaudible.
4.Operatorsmaynotactivatearemotelycontrolled
soundaidforaconditionunobservedfromthe
controlling station.
5.Somesoundsignalscannotbeimmediatelystarted.
6.Thestatusofthevessel’senginesandthelocation
oftheobserverbothaffecttheeffectiverangeofthe
aid.
Theseconsiderationsjustifytheutmostcautionwhen
navigatingnearlandinafog.Anavigatorcanneverrely
onsoundsignalsalone;heshouldcontinuouslymanboth
theradarandfathometer.Heshouldplacelookoutsin
positionswherethenoisesintheshipareleastlikelyto
interferewithhearingasoundsignal.Theaiduponwhich
asoundsignalrestsisusuallyagoodradartarget,but
collisionwiththeaidorthedangeritmarksisalwaysa
possibility.
Emergencysignalsaresoundedatsomeofthelightand
fogsignalstationswhenthemainandstand-bysound
signalsareinoperative.Someoftheseemergencysound
signalsareofadifferenttypeandcharacteristicthanthe
mainsoundsignal.Thecharacteristicsoftheemergency
sound signals are listed in theLight List.
The mariner should never assume:
1.Thatheisoutofordinaryhearingdistancebecause
he fails to hear the sound signal.
2.Thatbecausehehearsasoundsignalfaintly,heis
far from it.
3.That because he hears it clearly, he is near it.
4.Thatthedistancefromandtheintensityofasound
onanyoneoccasionisaguideforanyfuture
occasion.
5.Thatthesoundsignalisnotsoundingbecausehe
does not hear it, even when in close proximity.
6.Thatthesoundsignalisinthedirectionthesound
appears to come from.
MISCELLANEOUS U.S. SYSTEMS
530. Intracoastal Waterway Aids to Navigation
TheIntracoastalWaterway(ICW)runsparalleltothe
AtlanticandGulfofMexicocoastsfromManasquanInleton
theNewJerseyshoretotheTexas/Mexicanborder.Itfollows
rivers,sloughs,estuaries,tidalchannels,andothernatural
waterways,connectedwithdredgedchannelswhere
necessary.Someoftheaidsmarkingthesewatersaremarked
withyellow;otherwise,themarkingofbuoysandbeacons
follows the same system as that in other U.S. waterways.
YellowsymbolsindicatethatanaidmarkstheIntrac-
oastalWaterway.Yellowtrianglesindicatestarboardhand
aids,andyellowsquaresindicateporthandaidswhen
followingtheICW’sconventionaldirectionofbuoyage.
Non-lateralaidssuchassafewater,isolateddanger,and
frontrangeboardsaremarkedwithahorizontalyellow
band.Rearrangeboardsdonotdisplaytheyellowband.At
ajunctionwithafederally-maintainedwaterway,the
preferredchannelmarkwilldisplayayellowtriangleor
squareasappropriate.JunctionsbetweentheICWand
privatelymaintainedwaterwaysarenotmarkedwith
preferred channel buoys.
531. Western Rivers System
AidstonavigationontheMississippiRiverandits
tributariesaboveBatonRougegenerallyconformtothe
lateralsystemofbuoyageinuseintherestoftheU.S.The
following differences are significant:
1.Buoys are not numbered.
2.Thenumbersonlightsanddaybeaconsdonothave
lateralsignificance;theyindicatethemileagefrom
a designated point, normally the river mouth.
3.Flashinglightsontheleftsideproceedingupstream
showsinglegreenorwhiteflasheswhilethoseon
therightsideshowgroupflashingredorwhite
flashes.
4.Diamondshapedcrossingdaymarksareusedto
indicatewherethechannelcrossesfromonesideof
the river to the other.
80SHORT RANGE AIDS TO NAVIGATION
532. The Uniform State Waterway Marking System
(USWMS)
ThissystemwasdevelopedjointlybytheU.S.Coast
Guardandstateboatingadministratorstoassistthesmall
craftoperatorinthosestatewatersmarkedbyparticipating
states.TheUSWMSconsistsoftwocategoriesofaidsto
navigation.Thefirstisasystemofaidstonavigation,
generallycompatiblewiththeFederallateralsystemof
buoyage,supplementingthefederalsysteminstatewaters.
Theotherisasystemofregulatorymarkerstowarnsmall
craftoperatorsofdangersortoprovidegeneral
information.
Onawell-definedchannel,redandblackbuoysare
establishedinpairscalledgates;thechannelliesbetweenthe
buoys.Thebuoywhichmarkstheleftsideofthechannel
viewedlookingupstreamortowardtheheadofnavigationis
black;thebuoywhichmarkstherightsideofthechannelis
red.
Inanirregularly-definedchannel,buoysmaybe
staggeredonalternatesidesofthechannel,buttheyare
spacedatsufficientlycloseintervalstomarkclearlythe
channel lying between them.
Wherethereisnowell-definedchannelorwherea
bodyofwaterisobstructedbyobjectswhosenatureor
locationissuchthattheobstructioncanbeapproachedbya
vesselfrommorethanonedirection,aidstonavigation
havingcardinalsignificancemaybeused.Theaids
conformingtothecardinalsystemconsistofthreedistinctly
colored buoys as follows:
1.Awhitebuoywitharedtopmustbepassedtothe
south or west of the buoy.
2.Awhitebuoywithablacktopmustbepassedtothe
north or east of the buoy.
3.Abuoyshowingalternateverticalredandwhite
stripesindicatesthatanobstructiontonavigation
extendsfromthenearestshoretothebuoyandthat
thevesselmustnotpassbetweenthebuoyandthe
nearest shore.
Theshapeofbuoyshasnosignificanceunderthe
USWMS.
Regulatorybuoysarecoloredwhitewithorange
horizontalbandscompletelyaroundthem.Onebandisat
thetopofthebuoyandasecondbandjustabovethe
waterlineofthebuoysothatbothorangebandsare
clearly visible.
Geometricshapescoloredorangeareplacedonthe
whiteportionofthebuoybody.Theauthorizedgeometric
shapes and meanings associated with them are as follows:
1.Averticalopenfaceddiamondshapemeans
danger.
2.Averticalopenfaceddiamondshapewithacross
centeredinthediamondmeansthatvesselsare
excluded from the marked area.
3.Acircularshapemeansthatvesselsinthemarked
area are subject to certain operating restrictions.
4.Asquareorrectangularshapeindicatesthat
directionsorinformationiswritteninsidethe
shape.
Regulatorymarkersconsistofsquareandrectangular
shapedsignsdisplayedfromfixedstructures.Eachsignis
whitewithanorangeborder.Geometricshapeswiththe
samemeaningsasthosedisplayedonbuoysarecenteredon
thesignboards.Thegeometricshapedisplayedona
regulatorymarkertellsthemarinerifheshouldstaywell
clearofthemarkerorifhemayapproachthemarkerin
order to read directions.
533. Private Aids to Navigation
Aprivatenavigationaidisanyaidestablishedand
maintained by entities other than the Coast Guard.
TheCoastGuardmustapprovetheplacementof
privatenavigationaids.Inaddition,theDistrictEngineer,
U.S.ArmyCorpsofEngineers,mustapprovethe
placementofanystructure,includingaidstonavigation,in
the navigable waters of the U.S.
Privateaidstonavigationaresimilartotheaids
establishedandmaintainedbytheU.S.CoastGuard;they
arespeciallydesignatedonthechartandintheLightList.
Insomecases,particularlyonlargecommercialstructures,
theaidsarethesametypeofequipmentusedbytheCoast
Guard.AlthoughtheCoastGuardperiodicallyinspects
someprivatenavigationaids,themarinershouldexercise
special caution when using them.
Inadditiontoprivateaidstonavigation,numerous
typesofconstructionandanchorbuoysareusedinvarious
oildrillingoperationsandmarineconstruction.These
buoysarenotcharted,astheyaretemporary,andmaynot
belightedwelloratall.Marinersshouldgiveawideberth
todrillingandconstructionsitestoavoidthepossibilityof
foulingmoorings.Thisisaparticulardangerinoffshore
oilfields,wherelargeanchorsareoftenusedtostabilize
thepositionsofdrillrigsindeepwater.Uptoeight
anchorsmaybeplacedatvariouspositionsasmuchasa
milefromthedrillship.Thesepositionsmayormaynot
bemarkedbybuoys.SuchoperationsintheU.S.are
announced in theLocal Notice to Mariners.
534. Protection by Law
Itisunlawfultoimpairtheusefulnessofany
navigationaidestablishedandmaintainedbytheUnited
States.Ifanyvesselcollideswithanavigationaid,itisthe
legaldutyofthepersoninchargeofthevesseltoreportthe
accident to the nearest U.S. Coast Guard station.
81
CHAPTER 6
COMPASSES
INTRODUCTION
600. Changes in Compass Technologies
Thischapterdiscussesthemajortypesofcompasses
availabletothenavigator,theiroperatingprinciples,
theircapabilities,andlimitationsoftheiruse.Aswith
otheraspectsofnavigation,technologyisrapidly
revolutionizingthefieldofcompasses.Amazingly,afterat
leastamillenniaofconstantuse,itisnowpossible
(howeveradvisableitmayormaynotbeaboardanygiven
vessel) to dispense with the traditional magnetic compass.
Formuchofmaritimehistorytheonlyheading
referencefornavigatorshasbeenthemagneticcompass.A
greatdealofeffortandexpensehasgoneinto
understandingthemagneticcompassscientificallyand
makingitasaccurateaspossiblethroughelaborate
compensation techniques.
Theintroductionoftheelectro-mechanical
gyrocompassrelegatedthemagneticcompasstobackup
statusformanylargevessels.Latercamethedevelopment
ofinertialnavigationsystemsbasedongyroscopic
principles.Theinterruptionofelectricalpowertothe
gyrocompassorinertialnavigator,mechanicalfailure,orits
physicaldestructionwouldinstantlyelevatethemagnetic
compass to primary status for most vessels.
Newtechnologiesarebothrefiningandreplacingthe
magneticcompassasaheadingreferenceandnavigational
tool.Althoughamagneticcompassforbackupiscertainly
advisable,today’snavigatorcansafelyavoidnearlyallof
theeffortandexpenseassociatedwiththebinnacle-
mountedmagneticcompass,itscompensation,adjustment,
and maintenance.
Similarly,electro-mechanicalgyrocompassesare
beingsupplantedbyfarlighter,cheaper,andmore
dependableringlasergyrocompasses.Thesedevicesdonot
operateontheprincipleofthegyroscope(whichisbasedon
Newton’slawsofmotion),butinsteadrelyontheprinciples
of electromagnetic energy and wave theory.
Magneticfluxgatecompasses,whilerelyingonthe
earth’smagneticfieldforreference,havenomoving
partsandcancompensatethemselves,adjustingforboth
deviationandvariationtoprovidetrueheading,thus
completelyeliminatingtheprocessofcompass
correction.
Totheextentthatonedependsonthemagnetic
compassfornavigation,itshouldbecheckedregularlyand
adjustedwhenobservederrorsexceedcertainminimal
limits,usuallyafewdegreesformostvessels.
Compensationofamagneticcompassaboardvessels
expectedtorelyonitoffshoreduringlongvoyagesisbest
lefttoprofessionals.However,thischapterwillpresent
enoughmaterialforthecompetentnavigatortodoa
passable job.
Whatevertypeofcompassisused,itisadvisabletocheck
itperiodicallyagainstanerrorfreereferencetodetermineits
error.Thismaybedonewhensteeringalonganyrangeduring
harborandapproachnavigation,orbyaligninganytwo
chartedobjectsandfindingthedifferencebetweentheir
observedandchartedbearings.Whennavigatingoffshore,the
useofazimuthsandamplitudesofcelestialbodieswillalso
suffice, a subjectcovered inChapter 17.
MAGNETIC COMPASSES
601. The Magnetic Compass and Magnetism
Theprincipleofthepresentdaymagneticcompassis
nodifferentfromthatofthecompassesusedbyancient
mariners.Themagneticcompassconsistsofamagnetized
needle,oranarrayofneedles,allowedtorotateinthe
horizontalplane.Thesuperiorityofpresentdaymagnetic
compassesoverancientonesresultsfromabetter
knowledgeofthelawsofmagnetismwhichgovernthe
behaviorofthecompassandfromgreaterprecisionin
design and construction.
Anymagnetizedpieceofmetalwillhaveregionsof
concentratedmagnetismcalledpoles.Anysuchmagnet
willhaveatleasttwopolesofoppositepolarity.Magnetic
force(flux)linesconnectonepoleofsuchamagnetwith
theotherpole.Thenumberofsuchlinesperunitarea
represents the intensity of the magnetic field in that area.
Iftwomagnetsareplacedclosetoeachother,thelike
poleswillrepeleachotherandtheunlikepoleswillattract
each other.
Magnetismcanbeeitherpermanentorinduced.A
barhavingpermanentmagnetismwillretainitsmagnetism
whenitisremovedfromamagnetizingfield.Abarhaving
inducedmagnetismwillloseitsmagnetismwhenremoved
82COMPASSES
fromthemagnetizingfield.Whetherornotabarwillretain
itsmagnetismonremovalfromthemagnetizingfieldwill
dependonthestrengthofthatfield,thedegreeofhardness
oftheiron(retentivity),andupontheamountofphysical
stressappliedtothebarwhileinthemagnetizingfield.The
hardertheiron,themorepermanentwillbethemagnetism
acquired.
602. Terrestrial Magnetism
ConsidertheEarthasahugemagnetsurroundedby
linesofmagneticfluxconnectingitstwomagneticpoles.
Thesemagneticpolesarenear,butnotcoincidentalwith,
theEarth’sgeographicpoles.Sincethenorthseekingendof
acompassneedleisconventionallycalledthenorthpole,
orpositivepole,itmustthereforebeattractedtoasouth
pole, ornegative pole.
Figure602aillustratestheEarthanditssurrounding
magneticfield.ThefluxlinesenterthesurfaceoftheEarth
atdifferentanglestothehorizontalatdifferentmagnetic
latitudes.Thisangleiscalledtheangleofmagneticdip,
θ,andincreasesfrom0°atthemagneticequatorto90°at
themagneticpoles.Thetotalmagneticfieldisgenerally
consideredashavingtwocomponents:H,thehorizontal
component;andZ,theverticalcomponent.These
componentschangeastheangleθchanges,suchthatHis
atitsmaximumatthemagneticequatoranddecreasesinthe
directionofeitherpole,whileZiszeroatthemagnetic
equator and increases in the direction of either pole.
SincethemagneticpolesoftheEarthdonotcoincide
withthegeographicpoles,acompassneedleinlinewiththe
Earth’smagneticfieldwillnotindicatetruenorth,but
magneticnorth.Theangulardifferencebetweenthetrue
meridian(greatcircleconnectingthegeographicpoles)and
themagneticmeridian(directionofthelinesofmagnetic
flux)iscalledvariation.Thisvariationhasdifferentvalues
atdifferentlocationsontheEarth.Thesevaluesofmagnetic
variationmaybefoundonpilotchartsandonthecompass
rose of navigational charts.
Thepolesarenotgeographicallystatic.Theyareknown
tomigrateslowly,sothatvariationformostareasundergoes
asmallannualchange,theamountofwhichisalsonotedon
charts.Figure602bandFigure602cshowmagneticdipand
variationfortheworld.Up-to-dateinformationongeomag-
netics is available at http://geomag.usgs.gov/dod.html.
603. Ship’s Magnetism
Ashipunderconstructionorrepairwillacquire
permanentmagnetismduetohammeringandvibration
whilesittingstationaryintheEarth’smagneticfield.After
launching,theshipwilllosesomeofthisoriginal
magnetismasaresultofvibrationandpoundinginvarying
magneticfields,andwilleventuallyreachamoreorless
stablemagneticcondition.Themagnetismwhichremains
is thepermanent magnetism of the ship.
Inadditiontoitspermanentmagnetism,ashipacquires
inducedmagnetismwhenplacedintheEarth’smagnetic
field.Themagnetisminducedinanygivenpieceofsoft
ironisafunctionofthefieldintensity,thealignmentofthe
softironinthatfield,andthephysicalpropertiesand
dimensionsoftheiron.Thisinducedmagnetismmayadd
to,orsubtractfrom,thepermanentmagnetismalready
presentintheship,dependingonhowtheshipisalignedin
themagneticfield.Thesoftertheiron,themorereadilyit
willbemagnetizedbytheEarth’smagneticfield,andthe
morereadilyitwillgiveupitsmagnetismwhenremoved
from that field.
Themagnetisminthevariousstructuresofaship,which
tendstochangeasaresultofcruising,vibration,oraging,but
whichdoesnotalterimmediatelysoastobeproperlytermed
inducedmagnetism,iscalledsubpermanentmagnetism.
Thismagnetism,atanyinstant,ispartoftheship’spermanent
magnetism,andconsequentlymustbecorrectedby
permanentmagnetcorrectors.Itistheprincipalcauseof
deviationchangesonamagneticcompass.Subsequent
referencetopermanentmagnetismwillrefertotheapparent
permanentmagnetismwhichincludestheexistingpermanent
and subpermanent magnetism.
Aship,then,hasacombinationofpermanent,
subpermanent,andinducedmagnetism.Therefore,theship’s
Figure 602a. Terrestrial magnetism.
COMPASSES83
Figure 602b. Magnetic dip for the world.
Figure 602c. Magnetic variation for the world.
84COMPASSES
apparentpermanentmagneticconditionissubjecttochange
fromdeperming,shocks,welding,andvibration.Theship’s
inducedmagnetismwillvarywiththeEarth’smagneticfield
strength and with the alignment of the ship in that field.
604. Magnetic Adjustment
Anarrowrodofsoftiron,placedparalleltotheEarth’s
horizontalmagneticfield,H,willhaveanorthpoleinducedin
theendtowardthenorthgeographicpoleandasouthpole
inducedintheendtowardthesouthgeographicpole.Thissame
rodinahorizontalplane,butatrightanglestothehorizontal
Earth’sfield,wouldhavenomagnetisminducedinit,because
itsalignmentinthemagneticfieldprecludeslinear
magnetization,iftherodisofnegligiblecrosssection.Should
therodbealignedinsomehorizontaldirectionbetweenthose
headingswhichcreatemaximumandzeroinduction,itwould
beinducedbyanamountwhichisafunctionoftheangleof
alignment.However,ifasimilarrodisplacedinavertical
positioninnorthernlatitudessoastobealignedwiththevertical
Earth’sfieldZ,itwillhaveasouthpoleinducedattheupperend
andanorthpoleinducedatthelowerend.Thesepolaritiesof
verticalinducedmagnetizationwillbereversedinsouthern
latitudes.
Theamountofhorizontalorverticalinductioninsuch
rods,orinshipswhoseconstructionisequivalentto
combinationsofsuchrods,willvarywiththeintensityofH
and Z, heading, and heel of the ship.
Themagneticcompassmustbecorrectedforthe
vessel’spermanentandinducedmagnetismsothatits
operationapproximatesthatofacompletelynonmagnetic
vessel.Ship’smagneticconditionscreatemagnetic
compassdeviationsandsectorsofsluggishnessand
unsteadiness.Deviationisdefinedasdeflectionrightorleft
ofthemagneticmeridiancausedbymagneticpropertiesof
thevessel.Adjustingthecompassconsistsofarranging
magneticandsoftironcorrectorsnearthecompasssothat
theireffectsareequalandoppositetotheeffectsofthe
magnetic material in the ship.
The total permanent magnetic field effect at the compass
maybebrokenintothreecomponents,mutually90°toeach
other, as shown in Figure 604a.
Theverticalpermanentcomponenttiltsthecompass
card,and,whentheshiprollsorpitches,causesoscillating
deflectionsofthecard.Oscillationeffectswhichaccompa-
nyrollaremaximumonnorthandsouthcompassheadings,
andthosewhichaccompanypitcharemaximumoneastand
west compass headings.
ThehorizontalBandCcomponentsofpermanentmag-
netismcausevaryingdeviationsofthecompassastheship
swingsinheadingonanevenkeel.Plottingthesedeviations
againstcompassheadingyieldsthesineandcosinecurves
showninFigure604b.Thesedeviationcurvesarecalled
semicircular curves because they reverse direction by 180°.
Avectoranalysisishelpfulindeterminingdeviations
orthestrengthofdeviatingfields.Forexample,ashipas
showninFigure604conaneastmagneticheadingwill
subjectitscompasstoacombinationofmagneticeffects;
namely,theEarth’shorizontalfieldH,andthedeviating
fieldB,atrightanglestothefieldH.Thecompassneedle
willalignitselfintheresultantfieldwhichisrepresentedby
thevectorsumofHandB,asshown.Asimilaranalysiswill
revealthattheresultingdirectiveforceonthecompass
wouldbemaximumonanorthheadingandminimumona
southheadingbecausethedeviationsforbothconditions
arezero.Themagnitudeofthedeviationcausedbythe
permanentBmagneticfieldwillvarywithdifferentvaluesof
H;hence,deviationsresultingfrompermanentmagneticfields
will vary with the magnetic latitude of the ship.
Figure 604a. Components of permanent magnetic field.
Figure 604b. Permanent magnetic deviation effects.
COMPASSES85
605. Effects of Induced Magnetism
Inducedmagnetismvarieswiththestrengthofthe
surroundingfield,themassofmetal,andthealignmentofthe
metalinthefield.SincetheintensityoftheEarth’smagnetic
fieldvariesovertheEarth’ssurface,theinducedmagnetismina
ship will vary with latitude, heading, and heeling angle.
Withtheshiponanevenkeel,theresultantverticalinduced
magnetism,ifnotdirectedthroughthecompassitself,willcreate
deviationswhichplotasasemicirculardeviationcurve.Thisis
truebecausetheverticalinductionchangesmagnitudeand
polarityonlywithmagneticlatitudeandheel,andnotwith
headingoftheship.Therefore,aslongastheshipisinthesame
magneticlatitude,itsverticalinducedpoleswingingaboutthe
compasswillproducethesameeffectonthecompassasa
permanent pole swinging about the compass.
TheEarth’sfieldinductionincertainotherunsymmetrical
arrangementsofhorizontalsoftironcreateaconstantAdevia-
tioncurve.InadditiontothismagneticAerror,thereare
constantAdeviationsresultingfrom:(1)physicalmisalign-
mentsofthecompass,pelorus,orgyro;(2)errorsincalculating
the Sun’s azimuth, observing time, or taking bearings.
Thenature,magnitude,andpolarityoftheseinduced
effectsaredependentuponthedispositionofmetal,the
symmetryorasymmetryoftheship,thelocationofthebin-
nacle,thestrengthoftheEarth’smagneticfield,andthe
angle of dip.
Certainheelingerrors,inadditiontothoseresulting
frompermanentmagnetism,arecreatedbythepresenceof
bothhorizontalandverticalsoftironwhichexperience
changinginductionastheshiprollsintheEarth’smagnetic
field.Thispartoftheheelingerrorwillchangeinmagni-
tudeproportionaltochangesofmagneticlatitudeofthe
ship.Oscillationeffectsassociatedwithrollingaremaxi-
mumonnorthandsouthheadings,justaswiththe
permanent magnetic heeling errors.
606. Adjustments and Correctors
Sincesomemagneticeffectsarefunctionsoftheves-
sel’smagneticlatitudeandothersarenot,eachindividual
effectshouldbecorrectedindependently.Furthermore,to
makethecorrections,weuse(1)permanentmagnetcorrec-
torstocompensateforpermanentmagneticfieldsatthe
compass,and(2)softironcorrectorstocompensateforin-
ducedmagnetism.Thecompassbinnacleprovidessupport
forboththecompassanditscorrectors.Typicallargeship
binnacles hold the following correctors:
1.Verticalpermanentheelingmagnetinthecentral
vertical tube
2.Fore-and-aftB permanent magnets in their trays
3.AthwartshipC permanent magnets in their trays
4.Vertical soft ironFlinders bar in its external tube
5.Soft ironquadrantal spheres
Theheelingmagnetistheonlycorrectorwhichcor-
rectsforbothpermanentandinducedeffects.Therefore,it
mayneedtobeadjustedforchangesinlatitudeifavessel
permanentlychangesitsnormaloperatingarea.However,
anymovementoftheheelingmagnetwillrequirereadjust-
ment of other correctors.
Fairlysophisticatedmagneticcompassesusedon
smallercommercialcraft,largeryachts,andfishingvessels,
maynothavesoftironcorrectorsorBandCpermanent
magnets.Thesecompassesareadjustedbyrotatingmag-
netslocatedinsidethebaseoftheunit,adjustablebysmall
screwsontheoutside.Anon-magneticscrewdriverisnec-
essarytoadjustthesecompasses.Occasionallyonemay
findapermanentmagnetcorrectormountednearthecom-
pass,placedduringtheinitialinstallationsoastoremovea
large,constantdeviationbeforefinaladjustmentsaremade.
Normally, this remains in place for the life of the vessel.
Figure606summarizesallthevariousmagneticcondi-
tionsinaship,thetypesofdeviationcurvestheycreate,the
correctorsforeacheffect,andheadingsonwhicheachcor-
rectorisadjusted.Whenadjustingthecompass,always
applythecorrectorssymmetricallyandasfarawayfromthe
compassaspossible.Thispreservestheuniformityofmag-
netic fields about the compass needle.
Occasionally,thepermanentmagneticeffectsatthelo-
cationofthecompassaresolargethattheyovercomethe
Earth’sdirectiveforce,H.Thisconditionwillnotonlycreate
sluggishandunsteadysectors,butmayevenfreezethecom-
passtoonereadingortoonequadrant,regardlessofthe
headingoftheship.Shouldthecompassbecomesofrozen,
thepolarityofthemagnetismwhichmustbeattractingthe
compassneedlesisindicated;hence,correctionmaybeef-
fectedsimplybytheapplicationofpermanentmagnet
Figure 604c. General force diagram.
86COMPASSES
correctorstoneutralizethismagnetism.Wheneversuchad-
justmentsaremade,theshipshouldbesteeredonaheading
suchthattheunfreezingofthecompassneedleswillbeim-
mediatelyevident.Forexample,ashipwhosecompassis
frozentoanorthreadingwouldrequirefore-and-aftBcor-
rectormagnetswiththepositiveendsforwardinorderto
neutralizetheexistingnegativepolewhichattractedthecom-
pass.Ifmadeonaneastheading,suchanadjustmentwould
beevidentwhenthecompasscardwasfreedtoindicatean
east heading.
607. Reasons for Correcting Compass
Thereareseveralreasonsforcorrectingtheerrorsofa
magneticcompass,evenifitisnottheprimarydirectional
reference:
1.Itiseasiertouseamagneticcompassifthe
deviations are small.
2.Evenknownandfullycompensateddeviation
introduceserrorbecausethecompassoperates
sluggishlyandunsteadilywhendeviationis
present.
3.Eventhoughthedeviationsarecompensatedfor,
theywillbesubjecttoappreciablechangeasa
function of heel and magnetic latitude.
Theoretically,itdoesn’tmatterwhatthecompasserror
isaslongasitisknown.Butaproperlyadjustedmagnetic
compassismoreaccurateinallseaconditions,easiertosteer
by,andlesssubjecttotransientdeviationswhichcould
result in deviations from the ship’s chosen course.
Therefore,ifamagneticcompassisinstalledandmeant
tobereliedupon,itbehoovesthenavigatortoattend
carefullytoitsadjustment.Doingsoisknownas“swinging
ship.”
608. Adjustment Check-off List
Whileaprofessionalcompassadjusterwillbeableto
obtainthesmallestpossibleerrorcurveintheshortesttime,
manyship’snavigatorsadjustthecompassthemselveswith
satisfactoryresults.Whetherornota“perfect”adjustment
isnecessarydependsonthedegreetowhichthemagnetic
compasswillberelieduponinday-to-daynavigation.Ifthe
magneticcompassisonlyusedasabackupcompass,
removalofeverylastpossibledegreeoferrormaynotbe
worthwhile.Ifthemagneticcompassistheonlysteering
referenceaboard,asisthecasewithmanysmaller
commercialcraftandfishingvessels,itshouldbeadjusted
as accurately as possible.
Priortogettingunderwaytoswingship,thenavigator
CoefficientType deviation curve
Compass
headings of
maximum
deviation
Causes of such errorsCorrectors for such errors
Magnetic or compass
headings on which to
apply correctors
AConstant.Same on all.
Human-error in calculations_ _ _ _ _ _ _ _ _ _ _ _ _ _ _
Physical-compass, gyro, pelorus alignment _ _ _ _ _ _ _ _ _
Magnetic-unsymmetrical arrangements of horiz. soft iron.
Check methods and calculations
Check alignments
Rare arrangement of soft iron rods.
Any.
B
Semicircular
090˚
270˚
Fore-and-aft component of permanent magnetic field _ _ _ _ _
Induced magnetism in unsymmetrical vertical iron forward oraft
of compass.
Fore-and-aftB magnets
Flinders bar (forward or aft)
090˚ or 270˚.
C
Semicircular
000˚
180˚
Athwartship component of permanent magnetic field- - - - - - -
Induced magnetism in unsymmetrical vertical iron port or
starboard of compass.
AthwartshipC magnets
Flinders bar (port or starboard)
000˚ or 180˚.
D
Quadrantral
045˚
135˚
225˚
315˚
Induced magnetism in all symmetrical arrangements of
horizontal soft iron.
Spheres on appropriate axis.
(athwartship for +D)
(fore and aft for -D)
See sketch a
045˚, 135˚, 225˚, or 315˚.
E
Quadrantral
000˚
090˚
180˚
270˚
Induced magnetism in all unsymmetrical arrangements of
horizontal soft iron.
Spheres on appropriate axis.
(port fwd.-stb’d for +E)
(stb’d fwd.-port aft for -E)
See sketch b
000˚, 090˚, 180˚, or 270˚.
Heeling
Oscillations with roll
or pitch.
Deviations with
constant list.
000˚
180˚
090˚
270˚
}
roll
}
pitch
Changeinthehorizontalcomponentoftheinducedorpermanent
magneticfieldsatthecompassduetorollingorpitchingofthe
ship.
Heelingmagnet(mustbereadjustedfor
latitude changes).
090˚ or 270˚ with dip needle.
000˚ or 180˚ while rolling.
Figure 606. Summary of compass errors and adjustments.
φ
s
i
n.
φcos.
2φ.sin
2φ.cos
DeviationABφCφD+cos+sin+=2φE2φφcompass heading
=()
cos+sin
COMPASSES87
mustensurethattheprocesswillproceedasexpeditiously
aspossiblebypreparingthevesselandcompass.The
followingtestsandadjustmentcanbedoneatdockside,
assumingthatthecompasshasbeeninstalledand
maintainedproperly.Initialinstallationandadjustment
shouldbedonebyaprofessionalcompasstechnician
during commissioning.
1.Checkforbubblesinthecompassbowl.Fluidmay
beaddedthroughthefillingplugifnecessary.
Largebubblesindicateseriousleakage,indicating
thatthecompassshouldbetakentoaprofessional
compass repair facility for new gaskets.
2.Checkforfreemovementofgimbals.Cleanany
dustordirtfromgimbalbearingsandlubricate
them as recommended by the maker.
3.Checkformagnetizationofthequadrantalspheres
bymovingthemclosetothecompassandrotating
them.Ifthecompassneedlemovesmorethan2
degrees,thespheresmustbeannealedtoremove
their magnetism. Annealing consists of heating the
spherestoadullredcolorinanon-magneticarea
andallowingthemtocoolslowlytoambient
temperature.
4.CheckformagnetizationoftheFlindersbarby
invertingit,preferablywiththeshiponanE/W
heading.Ifthecompassneedlemovesmorethan2
degrees the Flinders bar must be annealed.
5.Synchronizethegyrorepeaterswiththemaster
gyro so courses can be steered accurately.
6.Assemblepastdocumentationrelatingtothe
compassanditsadjustment.Havetheship’s
degaussing folder ready.
7.Ensurethateverypossiblemetallicobjectisstowed
forsea.Allguns,doors,booms,andothermovable
gearshouldbeinitsnormalseagoingposition.All
gearnormallyturnedonsuchasradios,radars,
loudspeakers,etc.shouldbeonwhileswinging
ship.
8.HavetheInternationalCodeflagsOscar-Quebec
ready to fly.
Onceunderwaytoswingship,thefollowing
procedureswillexpeditetheprocess.Choosethebest
helmsmanaboardandinstructhimtosteereachcourseas
steadilyandpreciselyaspossible.Eachcourseshouldbe
steeredsteadilyforatleasttwominutesbeforeany
adjustmentsaremadetoremoveGaussinerror.Besurethe
gyro is set for the mean speed and latitude of the ship.
Thenavigator(orcompassadjusterifoneisemployed)
shouldhaveapelorusandatableofazimuthspreparedfor
checkingthegyro,butthegyrocompasswillbetheprimary
steeringreference.Normallytheadjusterwillrequest
coursesandmovethemagnetsashefeelsnecessary,a
processmuchmoreanartthanascience.Ifaprofessional
adjuster is not available, use the following sequence:
1.Ifthereisasearunning,steercourse000°and
adjusttheheelingmagnettodecreaseoscillations
to a minimum.
2.Cometocourse090°.Whensteadyoncourse090°,
foratleasttwominutes,insert,remove,ormove
fore-and-aft B magnets to remove ALL deviation.
3.Cometoaheadingof180°.Insert,remove,ormove
athwartshipsCmagnetstoremoveALLdeviation.
4.Cometo270°andmovetheBmagnetstoremove
one half of the deviation.
5.Cometo000°andmovetheCmagnetstoremove
one half of the deviation.
6.Cometo045°(oranyintercardinalheading)and
movethequadrantalspherestowardorawayfrom
the compass to minimize any error.
7.Cometo135°(oranyintercardinalheading90°
fromthepreviouscourse)andmovethespheresin
or out to remove one half of the observed error.
8.Steertheshipinturnoneachcardinaland
intercardinalheadingaroundthecompass,
recordingtheerrorateachheadingcalledforonthe
deviationcard.Ifplotted,theerrorsshouldplot
roughly as a sine curve about the 0° line.
Ifnecessary,repeatsteps1-8.Thereisnoaverage
error,foreachshipisdifferent,butgenerallyspeaking,
errorsofmorethanafewdegrees,orerrorswhichseriously
distortthesinecurve,indicateamagneticproblemwhich
should be addressed.
Oncethecompasshasbeenswung,tightenallfittings
andcarefullyrecordtheplacementofallmagnetsand
correctors.Finally,swingforresidualdegausseddeviations
withthedegaussingcircuitsenergizedandrecordthe
deviationsonthedeviationcard.Postthiscardnearthe
chart table for ready reference by the navigation team.
Onceproperlyadjusted,themagneticcompass
deviationsshouldremainconstantuntilthereissomechange
inthemagneticconditionofthevesselresultingfrom
magnetictreatment,shock,vibration,repair,orstructural
changes. Transient deviations are discussed below.
88COMPASSES
609. Sources of Transient Error
Theshipmustbeinseagoingtrimandconditionto
properlycompensateamagneticcompass.Anymovement
oflargemetalobjectsortheenergizingofanyelectrical
equipmentinthevicinityofthecompasscancauseerrors.
Ifindoubtabouttheeffectofanysuchchanges,
temporarilymovethegearorcyclepowertotheequipment
whileobservingthecompasscardwhileonasteady
heading.Preferablythisshouldbedoneontwodifferent
headings90°apart,sincethecompassmightbeaffectedon
one heading and not on another.
Somemagneticitemswhichcausedeviationsifplaced
too close to the compass are as follows:
1.Movable guns or weapon loads
2.Magnetic cargo
3.Hoisting booms
4.Cable reels
5.Metal doors in wheelhouse
6.Chart table drawers
7.Movable gyro repeater
8.Windows and ports
9.Signal pistols racked near compass
10.Sound powered telephones
11.Magnetic wheel or rudder mechanism
12.Knives or tools near binnacle
13.Watches, wrist bands, spectacle frames
14.Hat grommets, belt buckles, metal pencils
15.Heating of smoke stack or exhaust pipes
16.Landing craft
Someelectricalitemswhichcausevariabledeviations
if placed too close to the compass are:
1.Electric motors
2.Magnetic controllers
3.Gyro repeaters
4.Nonmarried conductors
5.Loudspeakers
6.Electric indicators
7.Electric welding
8.Large power circuits
9.Searchlights or flashlights
10.Electrical control panels or switches
11.Telephone headsets
12.Windshield wipers
13.Rudder position indicators, solenoid type
14.Minesweeping power circuits
15.Engine order telegraphs
16.Radar equipment
17.Magnetically controlled switches
18.Radio transmitters
19.Radio receivers
20.Voltage regulators
Anothersourceoftransientdeviationistheretentive
error.Thiserrorresultsfromthetendencyofaship’s
structuretoretaininducedmagneticeffectsforshortperiods
oftime.Forexample,ashiptravelingnorthforseveraldays,
especiallyifpoundinginheavyseas,willtendtoretainsome
fore-and-aftmagnetisminducedundertheseconditions.
Althoughthiseffectistransient,itmaycauseslightly
incorrectobservationsoradjustments.Thissametypeof
erroroccurswhenshipsaredockedononeheadingforlong
periodsoftime.Ashortshakedown,withtheshiponother
headings,willtendtoremovesucherrors.Asimilarsortof
residualmagnetismisleftinmanyshipsifthedegaussing
circuits are not secured by the correct reversal sequence.
Asourceoftransientdeviationsomewhatshorterin
durationthanretentiveerrorisknownasGaussinerror.
Thiserroriscausedbyeddycurrentssetupbyachanging
numberofmagneticlinesofforcethroughsoftironasthe
shipchangesheading.Duetotheseeddycurrents,the
inducedmagnetismonagivenheadingdoesnotarriveat
itsnormalvalueuntilabout2minutesafterchanging
course.
Depermingandothermagnetictreatmentwillchange
themagneticconditionofthevesselandthereforerequire
compassreadjustment.Thedecayingeffectsofdeperming
canvary.Therefore,itisbesttodelayreadjustmentforsev-
eraldaysaftersuchtreatment.Sincethemagneticfields
usedforsuchtreatmentsaresometimesratherlargeatthe
compasslocations,theFlindersbar,compass,andrelated
equipmentshouldberemovedfromtheshipduringthese
operations.
DEGAUSSING (MAGNETIC SILENCING) COMPENSATION
610. Degaussing
Asteelvesselhasacertainamountofpermanent
magnetisminits“hard”ironandinducedmagnetismin
its“soft”iron.Whenevertwoormoremagneticfields
occupythesamespace,thetotalfieldisthevectorsumof
theindividualfields.Thus,nearthemagneticfieldofa
vessel,thetotalfieldisthecombinedtotaloftheEarth’s
fieldandthevessel’sfield.NotonlydoestheEarth’sfield
affectthevessel’s,thevessel’sfieldaffectstheEarth’sfield
in its immediate vicinity.
Sincecertaintypesofexplosiveminesaretriggeredby
themagneticinfluenceofavesselpassingnearthem,a
vesselmayuseadegaussingsystemtominimizeits
magneticfield.Onemethodofdoingthisistoneutralize
eachcomponentofthefieldwithanoppositefieldproduced
byelectricalcablescoiledaroundthevessel.Thesecables,
whenenergized,counteractthepermanentmagnetismof
thevessel,renderingitmagneticallyneutral.Thishas
severe effects on magnetic compasses.
COMPASSES89
Aunitsometimesusedformeasuringthestrengthofa
magneticfieldisthegauss.Reducingofthestrengthofa
magneticfielddecreasesthenumberofgaussinthatfield.
Hence, the process is calleddegaussing.
Themagneticfieldofthevesseliscompletelyaltered
whenthedegaussingcoilsareenergized,introducinglarge
deviationsinthemagneticcompass.Thisdeviationcanbe
removedbyintroducinganequalandoppositeforcewith
energizedcoilsnearthecompass.Thisiscalledcompass
compensation.Whenthereisapossibilityofconfusionwith
compassadjustmenttoneutralizetheeffectsofthenatural
magnetismofthevessel,theexpressiondegaussing
compensationisused.Sincecompensationmaynotbe
perfect,asmallamountofdeviationduetodegaussingmay
remainoncertainheadings.Thisisthereasonforswinging
theshipwithdegaussingoffandagainwithiton,andwhy
there are two separate columns in the deviation table.
611. A Vessel’s Magnetic Signature
AsimplifieddiagramofthedistortionoftheEarth’s
magneticfieldinthevicinityofasteelvesselisshownin
Figure611a.Thefieldstrengthisdirectlyproportionalto
thelinespacingdensity.Ifavesselpassesoveradevicefor
detectingandrecordingthestrengthofthemagneticfield,a
certainpatternistraced.Figure611bshowsthispattern.
Sincethemagneticfieldofeachvesselisdifferent,each
producesadistinctivetrace.Thisdistinctivetraceis
referred to as the vessel’smagnetic signature.
Severaldegaussingstationshavebeenestablishedin
majorportstodeterminemagneticsignaturesand
recommendthecurrentsneededinthevariousdegaussing
coilstorenderitmagneticallyneutral.Sinceavessel’s
inducedmagnetismvarieswithheadingandmagnetic
latitude,thecurrentsettingsofthecoilsmaysometimes
needtobechanged.Adegaussingfolderisprovidedtothe
vesseltoindicatethesechangesandtodocumentother
pertinent information.
Avessel’spermanentmagnetismchangessomewhat
withtimeandthemagnetichistoryofthevessel.Therefore,
thedatainthedegaussingfoldershouldbecheckedperiod-
ically at the magnetic station.
612. Degaussing Coils
Fordegaussingpurposes,thetotalfieldofthevesselis
dividedintothreecomponents:(1)vertical,(2)horizontal
fore-and-aft,and(3)horizontalathwartships.Thepositive
(+)directionsareconsidereddownward,forward,andto
port,respectively.Thesearethenormaldirectionsfora
vessel headed north or east in north latitude.
Eachcomponentisopposedbyaseparatedegaussing
fieldjuststrongenoughtoneutralizeit.Ideally,whenthis
hasbeendone,theEarth’sfieldpassesthroughthevessel
smoothlyandwithoutdistortion.Theopposingdegaussing
fieldsareproducedbydirectcurrentflowingincoilsof
wire.Eachofthedegaussingcoilsisplacedsothatthefield
itproducesisdirectedtoopposeonecomponentofthe
ship’s field.
Thenumberofcoilsinstalleddependsuponthe
magneticcharacteristicsofthevessel,andthedegreeof
safetydesired.Theship’spermanentandinduced
magnetismmaybeneutralizedseparatelysothatcontrolof
inducedmagnetismcanbevariedasheadingandlatitude
change,withoutdisturbingthefieldsopposingthevessel’s
permanentfield.Theprincipalcoilsemployedarethe
following:
Main(M)coil.TheMcoilishorizontaland
completelyencirclesthevessel,usuallyatornearthe
waterline.Itsfunctionistoopposetheverticalcomponent
ofthevessel’scombinedpermanentandinducedfields.
Generallytheinducedfieldpredominates.Currentinthe
M-coilisvariedorreversedaccordingtothechangeofthe
induced component of the vertical field with latitude.
Forecastle(F)andquarterdeck(Q)coils.TheFand
Qcoilsareplacedhorizontallyjustbelowtheforwardand
afterthirds(orquarters),respectively,oftheweatherdeck.
Thesecoils,inwhichcurrentcanbeindividuallyadjusted,
removemuchofthefore-and-aftcomponentoftheship’s
permanentandinducedfields.Morecommonly,the
combinedFandQcoilsconsistoftwoparts;oneparttheFP
andQPcoils,totakecareofthepermanentfore-and-aft
field,andtheotherpart,theFIandQIcoils,toneutralize
theinducedfore-and-aftfield.Generally,theforwardand
aftercoilsofeachtypeareconnectedinseries,forminga
split-coilinstallationanddesignatedFP-QPcoilsandFI-QI
coils.CurrentintheFP-QPcoilsisgenerallyconstant,but
intheFI-QIcoilsisvariedaccordingtotheheadingand
magneticlatitudeofthevessel.Insplit-coilinstallations,
thecoildesignationsareoftencalledsimplytheP-coiland
I-coil.
Longitudinal(L)coil.Bettercontrolofthefore-and-
aftcomponents,butatgreaterinstallationexpense,is
providedbyplacingaseriesofvertical,athwartshipcoils
alongthelengthoftheship.Itisthefield,notthecoils,
whichislongitudinal.CurrentinanLcoilisvariedaswith
theFI-QIcoils.Itismaximumonnorthandsouthheadings,
and zero on east and west headings.
Athwartship(A)coil.TheAcoilisinaverticalfore-
and-aftplane,thusproducingahorizontalathwartship
fieldwhichneutralizestheathwartshipcomponentofthe
vessel’sfield.Inmostvessels,thiscomponentofthe
permanentfieldissmallandcanbeignored.SincetheA-
coilneutralizestheinducedfield,primarily,thecurrentis
changedwithmagneticlatitudeandwithheading,
maximumoneastorwestheadings,andzeroonnorthor
south headings.
Thestrengthanddirectionofthecurrentineachcoilis
indicatedandadjustedatacontrolpanelaccessibletothe
navigator.Currentmaybecontrolleddirectlybyrheostats
atthecontrolpanelorremotelybypushbuttonswhich
operate rheostats in the engine room.
90COMPASSES
Figure 611a. Simplified diagram of distortion of Earth’s magnetic field in the vicinity of a steel vessel.
Figure 611b. A simplified signature of a vessel ofFigure 611a.
COMPASSES91
Appropriatevaluesofthecurrentineachcoilare
determinedatadegaussingstation,wherethevarious
currentsareadjusteduntilthevessel’smagneticsignatureis
madeasflataspossible.Recommendedcurrentvaluesand
directionsforallheadingsandmagneticlatitudesareset
forthinthevessel’sdegaussingfolder.Thisdocumentis
normallykeptbythenavigator,whomustseethatthe
recommendedsettingsaremaintainedwheneverthe
degaussing system is energized.
613. Securing The Degaussing System
Unlessthedegaussingsystemisproperlysecured,
residualmagnetismmayremaininthevessel.During
degaussingcompensationandatothertimes,as
recommendedinthedegaussingfolder,the“reversal”
methodisused.Thestepsinthereversalprocessareas
follows:
1.Startwithmaximumdegaussingcurrentusedsince
the system was last energized.
2.Decreasecurrenttozeroandincreaseitinthe
opposite direction to the same value as in step 1.
3.Decreasethecurrenttozeroandincreaseittothree-
fourths maximum value in the original direction.
4.Decreasethecurrenttozeroandincreaseittoone-
half maximum value in the opposite direction.
5.Decreasethecurrenttozeroandincreaseittoone-
fourth maximum value in the original direction.
6.Decreasethecurrenttozeroandincreaseittoone-
eighth maximum value in the opposite direction.
7.Decrease the current to zero and open switch.
614. Magnetic Treatment Of Vessels
Insomeinstances,degaussingcanbemademore
effectivebychangingthemagneticcharacteristicsofthe
vesselbyaprocessknownasdeperming.Heavycablesare
woundaroundthevesselinanathwartshipdirection,
formingverticalloopsaroundthelongitudinalaxisofthe
vessel.Theloopsarerunbeneaththekeel,upthesides,and
overthetopoftheweatherdeckatcloselyspacedequal
intervalsalongtheentirelengthofthevessel.
Predeterminedvaluesofdirectcurrentarethenpassed
throughthecoils.Whenthedesiredmagnetic
characteristicshavebeenacquired,thecablesareremoved.
Avesselwhichdoesnothavedegaussingcoils,or
whichhasadegaussingsystemwhichisinoperative,canbe
givensometemporaryprotectionbyaprocessknownas
flashing.Ahorizontalcoilisplacedaroundtheoutsideof
thevesselandenergizedwithlargepredeterminedvaluesof
directcurrent.Whenthevesselhasacquiredaverticalfield
ofpermanentmagnetismofthecorrectmagnitudeand
polaritytoreducetoaminimumtheresultantfieldbelow
thevesselfortheparticularmagneticlatitudeinvolved,the
cableisremoved.Thistypeprotectionisnotassatisfactory
asthatprovidedbydegaussingcoilsbecauseitisnot
adjustableforvariousheadingsandmagneticlatitudes,and
alsobecausethevessel’smagnetismslowlyreadjusts
following treatment.
Duringmagnetictreatmentallmagneticcompasses
andFlindersbarsshouldberemovedfromtheship.
Permanentadjustingmagnetsandquadrantalcorrectorsare
notmateriallyaffected,andneednotberemoved.Ifitis
impracticaltoremoveacompass,thecablesusedfor
magnetictreatmentshouldbekeptasfaraspracticalfrom
it.
615. Degaussing Effects
Thedegaussingofshipsforprotectionagainst
magneticminescreatesadditionaleffectsuponmagnetic
compasses,whicharesomewhatdifferentfromthe
permanentandinducedmagneticeffects.Thedegaussing
effects are electromagnetic, and depend on:
1.Number and type of degaussing coils installed.
2.Magneticstrengthandpolarityofthedegaussing
coils.
3.Relativelocationofthedifferentdegaussingcoils
with respect to the binnacle.
4.Presenceofmassesofsteel,whichwouldtendto
concentrateordistortmagneticfieldsinthevicinity
of the binnacle.
5.Thefactthatdegaussingcoilsareoperated
intermittently,withvariablecurrentvalues,and
withdifferentpolarities,asdictatedbynecessary
degaussing conditions.
616. Degaussing Compensation
Themagneticfieldscreatedbythedegaussingcoils
wouldrenderthevessel’smagneticcompassesuseless
unlesscompensated.Thisisaccomplishedbysubjecting
thecompasstocompensatingfieldsalongthreemutually
perpendicularaxes.Thesefieldsareprovidedbysmall
compensatingcoilsadjacenttothecompass.Innearlyall
installations,oneofthesecoils,theheelingcoil,is
horizontalandonthesameplaneasthecompasscard,
providingaverticalcompensatingfield.Currentinthe
heelingcoilisadjusteduntiltheverticalcomponentofthe
totaldegaussingfieldisneutralized.Theother
compensatingcoilsprovidehorizontalfieldsperpendicular
toeachother.Currentisvariedinthesecoilsuntiltheir
resultantfieldisequalandoppositetothehorizontal
componentofthedegaussingfield.Inearlyinstallations,
thesehorizontalfieldsweredirectedfore-and-aftand
athwartshipsbyplacingthecoilsaroundtheFlindersbar
andthequadrantalspheres.Compactnessandother
advantagesaregainedbyplacingthecoilsonperpendicular
axesextending045°-225°and315°-135°relativetothe
heading.Afrequentlyusedcompensatinginstallation,
92COMPASSES
calledthetypeK,isshowninFigure616.Itconsistsofa
heelingcoilextendingcompletelyaroundthetopofthe
binnacle,fourintercardinalcoils,andthreecontrolboxes.
Theintercardinalcoilsarenamedfortheirpositionsrelative
tothecompasswhenthevesselisonaheadingofnorth,and
alsoforthecompassheadingsonwhichthecurrentinthe
coilsisadjustedtothecorrectamountforcompensation.
TheNE-SWcoilsoperatetogetherasoneset,andtheNW-
SEcoilsoperateasanother.Onecontrolboxisprovidedfor
each set, and one for the heeling coil.
Thecompasscompensatingcoilsareconnectedtothe
powersupplyofthedegaussingcoils,andthecurrentspass-
ingthroughthecompensatingcoilsareadjustedbyseries
resistancessothatthecompensatingfieldisequaltothede-
gaussingfield.Thus,achangeinthedegaussingcurrentsis
accompaniedbyaproportionalchangeinthecompensating
currents.Eachcoilhasaseparatewindingforeachdegauss-
ing circuit it compensates.
Degaussingcompensationiscarriedoutwhiletheves-
selismooredattheshipyardwherethedegaussingcoilsare
installed.Thisprocessisusuallycarriedoutbycivilianpro-
fessionals, using the following procedure:
Step1.Thecompassisremovedfromitsbinnacleand
adipneedleisinstalledinitsplace.TheMcoilandheeling
coilarethenenergized,andthecurrentintheheelingcoilis
adjusteduntilthedipneedleindicatesthecorrectvaluefor
themagneticlatitudeofthevessel.Thesystemisthense-
cured by the reversing process.
Step2.Thecompassisreplacedinthebinnacle.With
auxiliarymagnets,thecompasscardisdeflecteduntilthe
compassmagnetsareparalleltooneofthecompensating
coilsorsetofcoilsusedtoproduceahorizontalfield.The
compassmagnetsarethenperpendiculartothefield
producedbythatcoil.Oneofthedegaussingcircuits
producingahorizontalfield,anditscompensatingwinding,
arethenenergized,andthecurrentinthecompensating
windingisadjusteduntilthecompassreadingreturnstothe
valueithadbeforethedegaussingcircuitwasenergized.
Thesystemisthensecuredbythereversingprocess.The
processisrepeatedwitheachadditionalcircuitusedto
createahorizontalfield.Theauxiliarymagnetsarethen
removed.
Step3.Theauxiliarymagnetsareplacedsothatthe
compassmagnetsareparalleltotheothercompensating
coilsorsetofcoilsusedtoproduceahorizontalfield.The
procedureofstep2isthenrepeatedforeachcircuitproduc-
ing a horizontal field.
Whenthevesselgetsunderway,itproceedstoasuit-
ablemaneuveringarea.Thevesselisthensteeredsothatthe
compassmagnetsareparallelfirsttoonecompensatingcoil
orsetofcoils,andthentheother.Anyneededadjustmentis
madeinthecompensatingcircuitstoreducetheerrortoa
minimum.Thevesselisthenswungforresidualdeviation,
firstwithdegaussingoffandthenwithdegaussingon,and
thecorrectcurrentsettingsdeterminedforeachheadingat
themagneticlatitudeofthevessel.Fromthevaluesthusob-
tained,the“DGOFF”and“DGON”columnsofthe
deviationtablearefilledin.Iftheresultsindicatesatisfac-
torycompensation,arecordismadeofthedegaussingcoil
settingsandtheresistance,voltages,andcurrentsinthe
compensatingcoilcircuits.Thecontrolboxesarethen
secured.
Undernormaloperatingconditions,thesettingsdonot
needtobechangedunlesschangesaremadeinthe
degaussingsystem,orunlessanalterationismadeinthe
lengthoftheFlindersbarorthesettingofthequadrantal
spheres.However,itispossibleforagroundtooccurinthe
coilsorcontrolboxifthecircuitsarenotadequately
protectedfrommoisture.Ifthisoccurs,itshouldbe
reflectedbyachangeindeviationwithdegaussingon,orby
adecreasedinstallationresistance.Undertheseconditions,
compensationshouldbedoneagain.Ifthecompasswillbe
usedwithdegaussingonbeforetheshipcanbereturnedto
ashipyardwherethecompensationcanbemadeby
experiencedpersonnel,thecompensationshouldbemade
atseaontheactualheadingsneeded,ratherthanby
Figure 616. Type K degaussing compensation installation.
COMPASSES93
deflectionofthecompassneedlesbymagnets.More
completeinformationrelatedtothisprocessisgiveninthe
degaussing folder.
Ifavesselhasbeengivenmagnetictreatment,its
magneticpropertieshavechanged,necessitating
readjustmentofeachmagneticcompass.Thisisbest
delayedforseveraldaystopermitthemagnetic
characteristicsofthevesseltosettle.Ifcompensation
cannotbedelayed,thevesselshouldbeswungagainfor
residualdeviationafterafewdays.Degaussing
compensationshouldnotbemadeuntilaftercompass
adjustment has been completed.
GYROCOMPASSES
617. Principles of the Gyroscope
Agyroscopeconsistsofaspinningwheelorrotor
containedwithingimbalswhichpermitmovementabout
threemutuallyperpendicularaxes,knownasthe
horizontalaxis,theverticalaxis,andthespinaxis.When
spunrapidly,assumingthatfrictionisnotconsidered,the
gyroscopedevelopsgyroscopicinertia,tendingtoremain
spinninginthesameplaneindefinitely.Theamountof
gyroscopicinertiadependsontheangularvelocity,mass,
and radius of the wheel or rotor.
Whenaforceisappliedtochangealignmentofthespin
axisofagyroscope,theresultantmotionisperpendicularto
thedirectionoftheforce.Thistendencyisknownas
precession.Aforceappliedtothecenterofgravityofthe
gyroscopewillmovetheentiresysteminthedirectionof
theforce.Onlyaforcethattendstochangetheaxisof
rotation produces precession.
Ifagyroscopeisplacedattheequatorwithitsspinaxis
pointingeast-west,astheearthturnsonitsaxis,gyroscopic
inertiawilltendtokeeptheplaneofrotationconstant.To
theobserver,itisthegyroscopewhichisseentorotate,not
theearth.Thiseffectiscalledthehorizontalearthrate,and
ismaximumattheequatorandzeroatthepoles.Atpoints
between, it is equal to the cosine of the latitude.
Ifthegyroisplacedatageographicpolewithitsspin
axishorizontal,itwillappeartorotateaboutitsvertical
axis.Thisistheverticalearthrate.Atallpointsbetweenthe
equatorandthepoles,thegyroappearstoturnpartlyabout
itshorizontalandpartlyaboutitsverticalaxis,being
affectedbybothhorizontalandverticalearthrates.Inorder
tovisualizetheseeffects,rememberthatthegyro,at
whateverlatitudeitisplaced,isremainingalignedinspace
while the earth moves beneath it.
618. Gyrocompass Operation
Thegyrocompassdependsuponfournatural
phenomena:gyroscopicinertia,precession,earth’s
rotation,andgravity.Tomakeagyroscopeintoa
gyrocompass,thewheelorrotorismountedinasphere,
calledthegyrosphere,andthesphereisthensupportedina
verticalring.Thewholeismountedonabasecalledthe
phantom.Thegyroscopeinagyrocompasscanbe
pendulousornon-pendulous,accordingtodesign.Therotor
may weigh as little as half a kilogram to over 25 kg.
Tomakeitseekandmaintaintruenorth,threethings
arenecessary.First,thegyromustbemadetostayonthe
planeofthemeridian.Second,itmustbemadetoremain
horizontal.Third,itmuststayinthispositiononceit
reachesitregardlessofwhatthevesselonwhichitis
mounteddoesorwhereitgoesontheearth.Tomakeitseek
themeridian,aweightisaddedtothebottomofthevertical
ring,causingittoswingonitsverticalaxis,andthusseek
toalignitselfhorizontally.Itwilltendtooscillate,soa
secondweightisaddedtothesideofthesphereinwhichthe
rotoriscontained,whichdampenstheoscillationsuntilthe
gyrostaysonthemeridian.Withthesetwoweights,the
onlypossiblepositionofequilibriumisonthemeridian
with its spin axis horizontal.
Tomakethegyroseeknorth,asystemofreservoirs
filledwithmercury,knownasmercuryballistics,isusedto
applyaforceagainstthespinaxis.Theballistics,usually
fourinnumber,areplacedsothattheircentersofgravity
exactlycoincidewiththeCGofthegyroscope.Precession
thencausesthespinaxistotraceanellipse,oneellipsetak-
ingabout84minutestocomplete.(Thisistheperiodof
oscillationofapendulumwithanarmequaltotheradiusof
theearth.)Todampenthisoscillation,theforceisapplied,
notintheverticalplane,butslightlytotheeastoftheverti-
calplane.Thiscausesthespinaxistotraceaspiralinstead
ofanellipseandeventuallysettleonthemeridianpointing
north.
619. Gyrocompass Errors
Thetotaloftheallthecombinederrorsofthe
gyrocompassiscalledgyroerrorandisexpressedin
degreesEorW,justlikevariationanddeviation.Butgyro
error,unlikemagneticcompasserror,andbeing
independentofEarth’smagneticfield,willbeconstantin
onedirection;thatis,anerrorofonedegreeeastwillapply
to all bearings all around the compass.
Theerrorstowhichagyrocompassissubjectarespeed
error,latitudeerror,ballisticdeflectionerror,ballistic
dampingerror,quadrantalerror,andgimballingerror.
Additionalerrorsmaybeintroducedbyamalfunctionor
incorrect alignment with the centerline of the vessel.
Speederroriscausedbythefactthatagyrocompass
onlymovesdirectlyeastorwestwhenitisstationary(on
therotatingearth)orplacedonavesselmovingexactlyeast
orwest.Anymovementtothenorthorsouthwillcausethe
compasstotraceapathwhichisactuallyafunctionofthe
speedofadvanceandtheamountofnortherlyorsoutherly
94COMPASSES
heading.Thiscausesthecompasstotendtosettleabitoff
truenorth.Thiserroriswesterlyifthevessel’scourseis
northerly,andeasterlyifthecourseissoutherly.Its
magnitudedependsonthevessel’sspeed,course,and
latitude.Thiserrorcanbecorrectedinternallybymeansof
acosinecammountedontheundersideoftheazimuthgear,
whichremovesmostoftheerror.Anyremainingerroris
minor in amount and can be disregarded.
Tangentlatitudeerrorisapropertyonlyofgyros
withmercuryballistics,andiseasterlyinnorthlatitudes
andwesterlyinsouthlatitudes.Thiserrorisalsocorrected
internally,byoffsettingthelubber’slineorwithasmall
movable weight attached to the casing.
Ballisticdeflectionerroroccurswhenthereisa
markedchangeinthenorth-southcomponentofthespeed.
East-westaccelerationshavenoeffect.Achangeofcourse
orspeedalsoresultsinspeederrorintheoppositedirection,
andthetwotendtocanceleachotherifthecompassis
properlydesigned.Thisaspectofdesigninvolvesslightly
offsettingtheballisticsaccordingtotheoperatinglatitude,
uponwhichthecorrectionisdependent.Aslatitude
changes,theerrorbecomesapparent,butcanbeminimized
by adjusting the offset.
Ballisticdampingerrorisatemporaryoscillation
introducedbychangesincourseorspeed.Duringachange
incourseorspeed,themercuryintheballisticissubjected
tocentrifugalandacceleration/decelerationforces.This
causesatorquingofthespinaxisandsubsequenterrorin
thecompassreading.Slowchangesdonotintroduce
enougherrortobeaproblem,butrapidchangeswill.This
erroriscounteractedbychangingthepositionofthe
ballisticssothatthetrueverticalaxisiscentered,thusnot
subjecttoerror,butonlywhencertainratesofturnor
acceleration are exceeded.
Quadrantalerrorhastwocauses.Thefirstoccursif
thecenterofgravityofthegyroisnotexactlycenteredin
thephantom.Thiscausesthegyrototendtoswingalongits
heavyaxisasthevesselrollsinthesea.Itisminimizedby
addingweightsothatthemassisthesameinalldirections
fromthecenter.Withoutalongaxisofweight,thereisno
tendencytoswinginoneparticulardirection.Thesecond
sourceofquadrantalerrorismoredifficulttoeliminate.As
avesselrollsinthesea,theapparentverticalaxisis
displaced,firsttoonesideandthentheother.Thevertical
axisofthegyrotendstoalignitselfwiththeapparent
vertical.Onnortherlyorsoutherlycourses,andoneasterly
orwesterlycourses,thecompassprecessesequallytoboth
sidesandtheresultingerroriszero.Onintercardinal
courses,theN-SandE-Wprecessionsareadditive,anda
persistenterrorisintroduced,whichchangesdirectionin
differentquadrants.Thiserroriscorrectedbyuseofa
secondgyroscopecalledafloatingballistic,which
stabilizesthemercuryballisticasthevesselrolls,
eliminatingtheerror.Anothermethodistousetwogyros
forthedirectiveelement,whichtendtoprecessinopposite
directions, neutralizing the error.
Gimballingerroriscausedbytakingreadingsfrom
thecompasscardwhenitistiltedfromthehorizontalplane.
Itappliestothecompassitselfandtoallrepeaters.To
minimizethiserror,theouterringofthegimbalofeach
repeatershouldbeinstalledinalignmentwiththefore-and-
aftlineofthevessel.Ofcourse,thelubber’slinemustbe
exactly centered as well.
620. Using the Gyrocompass
Sinceagyrocompassisnotinfluencedbymagnetism,
itisnotsubjecttovariationordeviation.Anyerroris
constantandequalaroundthehorizon,andcanoftenbe
reducedtolessthanonedegree,thuseffectivelyeliminating
italtogether.Unlikeamagneticcompass,itcanoutputa
signaltorepeatersspacedaroundthevesselatcritical
positions.
Butitalsorequiresaconstantsourceofstableelectrical
power,andifpowerislost,itrequiresseveralhourstosettle
onthemeridianagainbeforeitcanbeused.Thisperiodcan
bereducedbyaligningthecompasswiththemeridian
before turning on the power.
Thedirectiveforceofagyrocompassdependsonthe
amountofprecessiontowhichitissubject,whichinturnis
dependentonlatitude.Thusthedirectiveforceismaximum
attheequatoranddecreasestozeroatthepoles.Vessels
operatinginhighlatitudesmustconstructerrorcurves
basedonlatitudesbecausetheerrorsathighlatitudes
eventuallyovercometheabilityofthecompasstocorrect
them.
Thegyrocompassistypicallylocatedbelowdecksas
closeaspossibletothecenterofroll,pitchandyawofthe
ship,thusminimizingerrorscausedbytheship’smotion.
Repeatersarelocatedatconvenientplacesthroughoutthe
ship,suchasatthehelmforsteering,onthebridgewings
fortakingbearings,inaftersteeringforemergency
steering,andotherplaces.Theoutputcanalsobeusedto
drivecourserecorders,autopilotsystems,plotters,fire
controlsystems,andstabilizedradars.Therepeatersshould
becheckedregularlyagainstthemastertoensuretheyare
allinalignment.Therepeatersonthebridgewingusedfor
takingbearingswilllikelybeequippedwithremovable
bearingcircles,azimuthcircles,andtelescopicalidades,
whichallowonetosightadistantobjectandseeitsexact
gyrocompass bearing.
COMPASSES95
ELECTRONIC COMPASSES
621. New Direction Sensing Technologies
Themagneticcompasshasseriouslimitations,chiefly
thatofbeingunabletoisolatetheearth’smagneticfield
fromallotherscloseenoughtoinfluenceit.Italsoindicates
magneticnorth,whereasthemarinerismostinterestedin
truenorth.Mostoftheworkinvolvedwithcompensatinga
traditionalmagneticcompassinvolvesneutralizing
magneticinfluencesotherthantheearth’s,acomplicated
andinexactprocessofteninvolvingmoreartthanscience.
Residualerrorisalmostalwayspresentevenafter
compensation.Degaussingcomplicatesthesituation
immensely.
Theelectro-mechanicalgyrocompasshasbeenthe
standardsteeringandnavigationalcompasssincetheearly
20thcentury,andhasprovidedseveralgenerationsof
marinersastableandreliableheadingandbearing
reference.However,ittoohaslimitations:Itisalarge,
expensive,heavy,sensitivedevicethatmustbemounted
accordingtoratherstrictlimitations.Itrequiresastableand
uninterruptedsupplyofelectricalpower;itissensitiveto
shock,vibration,andenvironmentalchanges;anditneeds
several hours to settle after being turned on.
Fortunately,severalnewtechnologieshavebeen
developedwhichpromisetogreatlyreduceoreliminatethe
limitationsofboththemechanicalgyroscopeand
traditionalmagneticcompasses.Sometimesreferredtoas
“electroniccompasses,”thedigitalfluxgatemagnetic
compassandtheringlasergyrocompassaretwosuch
devices. They have the following advantages:
1.Solid state electronics, no moving parts
2.Operation at very low power
3.Easy backup power from independent sources
4.Standardized digital output
5.Zero friction, drift, or wear
6.Compact, lightweight, and inexpensive
7.Rapid start-up and self-alignment
8.Lowsensitivitytovibration,shock,and
temperature changes
9.Self-correcting
Bothtypesarebeinginstalledonmanyvesselsasthe
primarydirectionalreference,enablingthe
decommissioningofthetraditionalmagneticcompasses
andtheavoidanceofperiodiccompensationand
maintenance.
622. The Flux Gate Compass
Themostwidelyusedsensorfordigitalcompassesis
theflux-gatemagnetometer,developedaround1928.
Initiallyitwasusedfordetectingsubmarines,for
geophysicalprospecting,andairbornemappingofearth’s
magnetic fields.
Themostcommontype,calledthesecondharmonic
device,incorporatestwocoils,aprimaryandasecondary,
bothwrappedaroundasinglehighlypermeable
ferromagneticcore.Inthepresenceofanexternalmagnetic
field,thecore’smagneticinductionchanges.Asignal
appliedtotheprimarywindingcausesthecoretooscillate.
Thesecondarywindingemitsasignalthatisinduced
throughthecorefromtheprimarywinding.Thisinduced
signalisaffectedbychangesinthepermeabilityofthecore
andappearsasanamplitudevariationintheoutputofthe
sensingcoil.Thesignalisthendemodulatedwithaphase-
sensitivedetectorandfilteredtoretrievethemagneticfield
value.Afterbeingconvertedtoastandardizeddigital
format,thedatacanbeoutputtonumerousremotedevices,
includingsteeringcompasses,bearingcompasses,
emergency steering stations, and autopilots.
Sincetheinfluenceofaship’sinherentmagnetismis
inverselyproportionaltothesquareofthedistancetothe
compass,itislogicalthatifthecompasscouldbelocatedat
somedistancefromtheship,theinfluenceoftheship’s
magneticfieldcouldbegreatlyreduced.Oneadvantageof
thefluxgatecompassisthatthesensorcanbelocated
remotelyfromthereadoutdevice,allowingittobeplaced
atapositionasfaraspossiblefromthehullanditscontents,
suchashighuponamast,theidealplaceonmostvessels.
Afurtheradvantageisthatthedigitalsignalcanbe
processedmathematically,andalgorithmswrittenwhich
cancorrectforobserveddeviationoncethedeviationtable
hasbeendetermined.Further,the“table,”indigitalformat,
canbefoundbymerelysteeringthevesselinafullcircle.
Algorithmsthendetermineandapplycorrectionsthat
effectivelyflattentheusualsinewavepatternofdeviation.
The theoretical result is zero observed compass deviation.
Shouldtherebeanindexerror(whichhastheeffectof
skewingtheentiresinewavebeloworabovethezero
degreeaxisofthedeviationcurve)thiscanbecorrected
withanindexcorrectionappliedtoallthereadings.This
problemislargelyconfinedtoasymmetricinstallations
suchasaircraftcarriers.Similarly,acorrectionforvariation
canbeapplied,andwithGPSinput(sothesystemknows
whereitiswithrespecttotheisogonicmap)thevariation
correctioncanbeappliedautomatically,thusrenderingthe
outputintruedegrees,correctedforbothdeviationand
variation.
Itisimportanttorememberthatafluxgatecompassis
stillamagneticcompass,andthatitwillbeinfluencedby
largechangestotheship’smagneticfield.Compensation
shouldbeaccomplishedaftereverysuchchange.
Fortunately,asnoted,compensationinvolvesmerely
steeringthevesselinacircleinaccordancewiththe
manufacturer’s recommendations.
Flux-gatecompassesfromdifferentmanufacturers
sharesomesimilaroperationalmodes.Mostofthemwill
96COMPASSES
have the following:
SETCOURSEMODE:Acoursecanbesetand
“remembered”bythesystem,whichthenprovidesthe
helmsmanagraphicsteeringaid,enablinghimtoseeifthe
ship’sheadisrightorleftofthesetcourse,asifonadigital
“highway.”Normalcompassoperationcontinuesinthe
background.
DISPLAYRESPONSEDAMPING:Inthismode,a
switchisusedtochangetherateofdampingandupdateof
thedisplayinresponsetochangesinseaconditionand
vessel speed.
AUTO-COMPENSATION:Thismodeisusedto
determinethedeviationcurveforthevesselasitsteamsin
acompletecircle.Thesystemwillthenautomatically
computecorrectionfactorstoapplyaroundtheentire
compass,resultinginzerodeviationatanygivenheading.
Thisshouldbedoneaftereverysignificantchangeinthe
magneticsignatureoftheship,andwithin24hoursof
entering restricted waters.
CONTINUOUSAUTO-COMPENSATION:This
mode,whichshouldnormallybeturnedOFFinrestricted
watersandONatsea,runsthecompensationalgorithm
eachtimetheshipcompletesa360degreeturnintwo
minutes.AwarningwillflashonthedisplayintheOFF
mode.
PRE-SETVARIATION:Ineffectanindexcorrection,
pre-setvariationallowstheapplicationofmagnetic
variationtotheheading,resultinginatrueoutput
(assumingtheunithasbeenproperlycompensatedand
aligned).Sincevariationchangesaccordingtoone’s
locationontheearth,itmustbechangedperiodicallyto
agreewiththechartedvariationunlessGPSinputis
provided.TheGPSpositioninputisusedinanalgorithm
whichcomputesthevariationfortheareaandautomatically
corrects the readout.
U.S.Navalpolicyapprovestheuseoffluxgate
compassesandthedecommissioning,butnotremoval,of
thetraditionalbinnaclemountedcompass,whichshouldbe
clearlymarkedas“OutofCommission”onceanapproved
flux gate compass is properly installed and tested.
623. The Ring Laser Gyrocompass
TheringlaserhaditsbeginningsinEngland,wherein
the1890’stwoscientists,JosephLarmorandSirOliver
Lodge(alsooneofthepioneersofradio),debatedthe
possibilityofmeasuringrotationbyaringinterferometer.
Some15yearslater,aFrenchphysicist,GeorgesSagnac,
fullydescribedthephenomenonwhichtodaybearshis
name,theSagnacEffect.Thisprinciplestatesthatiftwo
beamsoflightaresentinoppositedirectionsarounda
“ring”orpolyhedronandsteeredsoastomeetand
combine,astandingwavewillformaroundthering.Ifthe
waveisobservedfromanypoint,andthatpointisthen
movedalongtheperimeterofthering,thewaveformwill
changeindirectrelationshiptothedirectionandvelocityof
movement.
Itwasn’tuntil1963thatW.MacekofSperry-Rand
Corporationtestedandrefinedtheconceptintoauseful
researchdevice.Initially,mirrorswereusedtodirectlight
aroundasquareorrectangularpattern.Butsuchmirrors
mustbemadeandadjustedtoexceptionallyclose
tolerancestoallowusefuloutput,andmustoperateina
vacuumforbesteffect.Multilayerdielectricmirrorswitha
reflectivityof99.9999percentweredeveloped.The
inventionoflaserlightsourcesandfiber-opticshasenabled
theproductionofsmall,light,anddependableringlaser
gyros.Mirror-baseddevicescontinuetobeusedinphysics
research.
Theringlasergyrocompass(RLG)operatesby
measuringlaser-generatedlightwavestravelingarounda
fiber-opticring.Abeamsplitterdividesabeamoflightinto
twocounter-rotatingwaves,whichthentravelaroundthe
fiber-opticringinoppositedirections.Thebeamsarethen
recombinedandsenttoanoutputdetector.Intheabsenceof
rotation,thepathlengthswillbethesameandthebeams
willrecombineinphase.Ifthedevicehasrotated,therewill
beadifferenceinthelengthofthepathsofthetwobeams,
resultinginadetectablephasedifferenceinthecombined
signal.Thesignalwillvaryinamplitudedependingonthe
amountofthephaseshift.Theamplitudeisthusa
measurementofthephaseshift,andconsequently,the
rotationrate.Thissignalisprocessedintoadigitalreadout
indegrees.Thisreadout,beingdigital,canthenbesenttoa
varietyofdeviceswhichneedheadinginformation,suchas
helm, autopilot, and electronic chart systems.
Asingleringlasergyroscopecanbeusedtoprovidea
one-dimensionalrotationalreference,exactlywhata
compassneeds.Theusefulnessofringlasergyrocompasses
stemsfromthatfactthattheysharemanyofthesame
characteristicsoffluxgatecompasses.Theyarecompact,
light,inexpensive,accurate,dependable,androbust.The
ringlaserdeviceisalsoquiteimmunetomagnetic
influenceswhichwouldsendatraditionalcompass
spinninghopelessly,andmightadverselyaffecteventhe
remotely mounted flux gate compass.
Ringlasergyroscopescanalsoserveasthestable
elementsinaninertialguidancesystem,usingthreegyros
torepresentthethreedegreesoffreedom,thusproviding
bothdirectionalandpositioninformation.Theprincipleof
operationisthesameasformechanicalinertialnavigation
devices,inthatasinglegyrocanmeasureanyrotation
aboutitsownaxis.Thisimpliesthatitsorientationinspace
aboutitsownaxiswillbeknownatalltimes.Threegyros
arrangedalongthreeaxeseachat90degreestotheothers
canmeasureaccelerationsinthreedimensionalspace,and
COMPASSES97
thus track movement over time.
Inertialnavigationsystemsbasedonringlasershave
beenusedinaircraftforanumberofyears,andare
becomingincreasinglycommoninmaritimeapplications.
Usesincludenavigation,radarandfirecontrolsystems,
preciseweaponsstabilization,andstabilizationof
directional sensors such as satellite antennas.
CORRECTING AND UNCORRECTING THE COMPASS
624. Ship’s Heading
Ship’sheadingistheangle,expressedindegrees
clockwisefromnorth,oftheship’sfore-and-aftlinewith
respecttothetruemeridianorthemagneticmeridian.When
thisangleisreferredtothetruemeridian,itiscalledatrue
heading.Whenthisangleisreferredtothemagnetic
meridian,itiscalledamagneticheading.Heading,as
indicatedonaparticularcompass,istermedtheship’s
compassheadingbythatcompass.Itisessentialtospecify
everyheadingastrue(T),magnetic(M),orcompass.Two
abbreviationssimplifyrecordingofcompassdirections.
TheabbreviationPGCrefersto“pergyrocompass,”and
PSCrefersto“persteeringcompass.”Thesteeringcompass
istheonebeingusedbythehelmsmanorautopilot,
regardless of type.
625. Variation And Deviation
Variationistheanglebetweenthemagneticmeridian
andthetruemeridianatagivenlocation.Ifthenortherly
partofthemagneticmeridianliestotherightofthetrue
meridian,thevariationiseasterly.Conversely,ifthispartis
totheleftofthetruemeridian,thevariationiswesterly.The
localvariationanditssmallannualchangearenotedonthe
compassroseofallnavigationalcharts.Thusthetrueand
magnetic headings of a ship differ by the local variation.
Aspreviouslyexplained,aship’smagneticinfluence
willgenerallycausethecompassneedletodeflectfromthe
magneticmeridian.Thisangleofdeflectioniscalled
deviation.Ifthenorthendoftheneedlepointseastofthe
magneticmeridian,thedeviationiseasterly;ifitpoints
west of the magnetic meridian, the deviation is westerly.
626. Heading Relationships
A summary of heading relationships follows:
1.Deviationisthedifferencebetweenthecompass
heading and the magnetic heading.
2.Variationisthedifferencebetweenthemagnetic
heading and the true heading.
3.Thealgebraicsumofdeviationandvariationisthe
compass error.
Thefollowingsimpleruleswillassistincorrectingand
uncorrecting the compass:
1.Compassleast,erroreast;compassbest,errorwest.
2.Whencorrecting,addeasterlyerrors,subtract
westerlyerrors(Remember:“CorrectingAdd
East”).
3.Whenuncorrecting,subtracteasterlyerrors,add
westerly errors.
Some typical correction operations follow:
Usethememoryaid“CanDeadMenVoteTwice,At
Elections”toremembertheconversionprocess(Compass,
Deviation,Magnetic,Variation,True;AddEast).When
convertingcompassheadingtotrueheading,addeasterly
deviationsandvariationsandsubtractwesterlydeviations
and variations.
Thesamerulesapplytocorrectinggyrocompass
errors,althoughgyroerrorsalwaysapplyinthesame
direction.Thatis,theyareEorWallaroundthecompass.
Completefamiliaritywiththecorrectingofcompasses
isessentialfornavigationbymagneticorgyrocompass.
Theprofessionalnavigatorwhodealswiththem
continuallycandotheminhisheadquicklyandaccurately.
Compass
Deviation
Magnetic
Variation
True
-> +E, -W
358°5°E003°6°E009°
120°1°W119°3°E122°
180°6°E186°8°W178°
240°5°W235°7°W228°
+W, -E <-
Figure 626. Examples of compass correcting.
99
CHAPTER 7
DEAD RECKONING
DEFINITION AND PURPOSE
700. Definition and Use
Deadreckoningistheprocessofdeterminingone’s
presentpositionbyprojectingcourse(s)andspeed(s)from
aknownpastposition,andpredictingafuturepositionby
projectingcourse(s)andspeed(s)fromaknownpresent
position.TheDRpositionisonlyanapproximateposition
becauseitdoesnotallowfortheeffectofleeway,current,
helmsman error, or compass error.
Deadreckoninghelpsindeterminingsunriseand
sunset;inpredictinglandfall,sightinglightsand
predictingarrivaltimes;andinevaluatingtheaccuracy
ofelectronicpositioninginformation.Italsohelpsin
predictingwhichcelestialbodieswillbeavailablefor
futureobservation.Butitsmostimportantuseisin
projectingthepositionoftheshipintotheimmediate
future and avoiding hazards to navigation.
ThenavigatorshouldcarefullytendhisDRplot,
updateitwhenrequired,useittoevaluateexternalforces
actingonhisship,andconsultittoavoidpotential
navigationhazards.AfixtakenateachDRpositionwill
revealtheeffectsofcurrent,wind,andsteeringerror,and
allowthenavigatortostayontrackbycorrectingforthem.
TheuseofDRwhenanElectronicChartsDisplayand
InformationSystem(ECDIS)istheprimaryplotting
methodwillvarywiththetypeofsystem.AnECDISallows
thedisplayoftheship’sheadingprojectedouttosome
futurepositionasafunctionoftime,thedisplayof
waypointinformation,andprogresstowardeachwaypoint
in turn.
UntilECDISisproventoprovidethelevelofsafety
andaccuracyrequired,theuseofatraditionalDRploton
paperchartsisaprudentbackup,especiallyinrestricted
waters.ThefollowingproceduresapplytoDRplottingon
the traditional paper chart.
CONSTRUCTING THE DEAD RECKONING PLOT
MaintaintheDRplotdirectlyonthechartinuse.DRat
leasttwofixintervalsaheadwhilepiloting.Iftransitinginthe
openocean,maintaintheDRatleastfourhoursaheadofthelast
fixposition.MaintainingtheDRplotdirectlyonthechartallows
thenavigatortoevaluateavessel’sfuturepositioninrelationto
chartednavigationhazards.Italsoallowstheconningofficer
andcaptaintoplancourseandspeedchangesrequiredtomeet
any operational commitments.
ThissectionwilldiscusshowtoconstructtheDRplot.
701. Measuring Courses and Distances
Tomeasurecourses,usethechart’scompassrose
nearesttothechartareacurrentlyinuse.Transfercourse
linestoandfromthecompassroseusingparallelrulers,
rollingrulers,ortriangles.Ifusingaparallelmotionplotter
(PMP),simplysettheplotteratthedesiredcourseandplot
thatcoursedirectlyonthechart.Transparentplastic
navigationplottersthatalignwiththelatitude/longitudegrid
may also be used.
Thenavigatorcanmeasuredirectionatanyconvenient
placeonaMercatorchartbecausethemeridiansareparallel
toeachotherandalinemakingananglewithanyonemakes
thesameanglewithallothers.Onemustmeasuredirection
onaconformalcharthavingnonparallelmeridiansatthe
meridianclosesttotheareaofthechartinuse.Theonly
commonnonconformalprojectionusedisthegnomonic;a
gnomonicchartusuallycontainsinstructionsformeasuring
direction.
Compassrosesmaygivebothtrueandmagnetic
directions.Truedirectionsareontheoutsideoftherose;
magneticdirectionsareontheinside.Formostpurposes,
use true directions.
Measuredistancesusingthechart’slatitudescale.
Althoughnottechnicallytrue,assumingthatoneminuteof
latitudeequalsonenauticalmileintroducesnosignificant
error.SincetheMercatorchart’slatitudescaleexpandsas
latitudeincreases,onsmallscalechartsonemustmeasure
distancesonthelatitudescaleclosesttotheareaofinterest,
thatis,atthesamelatitude,ordirectlytotheside.Onlarge
scalecharts,suchasharborcharts,onecanuseeitherthe
latitudescaleorthedistancescaleprovided.Tomeasurelong
distancesonsmall-scalecharts,breakthedistanceintoa
numberofsegmentsandmeasureeachsegmentatitsmid-
latitude.
100DEAD RECKONING
702. Plotting and Labeling the Course Line and
Positions
DrawanewcourselinewheneverrestartingtheDR.
Extendthecourselinefromafixinthedirectionoftheordered
course.AbovethecourselineplaceacapitalCfollowedbythe
orderedcourseindegreestrue.Belowthecourseline,placea
capitalSfollowedbythespeedinknots.Labelallcourselines
andfixesimmediatelyafterplottingthembecauseaconning
officerornavigatorcaneasilymisinterpretanunlabeledlineor
position.
EncloseafixfromtwoormoreLinesofPosition
(LOP’s)byasmallcircleandlabelitwiththetimetothe
nearestminute,writtenhorizontally.MarkaDRposition
withasemicircleandthetime,writtendiagonally.Markan
estimatedposition(EP)byasmallsquareandthetime,
writtenhorizontally.DetermininganEPiscoveredlaterin
this chapter.
Expressthetimeusingfourdigitswithoutpunctuation,
usingeitherzonetimeorGreenwichMeanTime(GMT),
accordingtoprocedure.Labeltheplotneatly,succinctly,
and clearly.
Figure702illustratesthisprocess.Thenavigatorplots
andlabelsthe0800fix.Theconningofficerordersacourse
of095°Tandaspeedof15knots.Thenavigatorextendsthe
courselinefromthe0800fixinadirectionof095°T.He
calculatesthatinonehourat15knotshewilltravel15nau-
ticalmiles.Hemeasures15nauticalmilesfromthe0800fix
positionalongthecourselineandmarksthatpointonthe
courselinewithasemicircle.HelabelsthisDRwiththe
time.Notethat,byconvention,helabelsthefixtimehori-
zontally and the DR time diagonally.
THE RULES OF DEAD RECKONING
703. Plotting the DR
Plot the vessel’s DR position:
1. At least every hour on the hour.
2. After every change of course or speed.
3. After every fix or running fix.
4. After plotting a single line of position.
Figure703illustratesapplyingtheserules.Clearingthe
harborat0900,thenavigatorobtainsalastvisualfix.This
iscalledtakingdeparture,andthepositiondeterminedis
calledthedeparture.Atthe0900departure,theconning
officerordersacourseof090°Tandaspeedof10knots.
Thenavigatorlaysoutthe090°Tcourselinefromthe
departure.
At1000,thenavigatorplotsaDRpositionaccordingto
therulerequiringplottingaDRpositionatleasteveryhour
onthehour.At1030,theconningofficerordersacourse
changeto060°T.Thenavigatorplotsthe1030DRposition
inaccordancewiththerulerequiringplottingaDRposition
ateverycourseandspeedchange.Notethatthecourseline
changesat1030to060°Ttoconformtothenewcourse.At
1100,theconningofficerchangescoursebackto090°T.
Thenavigatorplotsan1100DRduetothecoursechange.
Notethat,regardlessofthecoursechange,an1100DR
wouldhavebeenrequiredbecauseofthe“everyhouronthe
hour” rule.
Figure 702. A course line with labels.
Figure 703. A typical dead reckoning plot.
DEAD RECKONING101
At1200,theconningofficerchangescourseto180°T
andspeedto5knots.Thenavigatorplotsthe1200DR.At
1300,thenavigatorobtainsafix.Notethatthefixposition
isoffsettotheeastfromtheDRposition.Thenavigatorde-
terminessetanddriftfromthisoffsetandappliesthisset
anddrifttoanyDRpositionfrom1300untilthenextfixto
determineanestimatedposition.HealsoresetstheDRto
thefix;thatis,hedrawsthe180°Tcourselinefromthe
1300 fix, not the 1300 DR.
704. Resetting the DR
ResettheDRplottoeachfixorrunningfixinturn.In
addition,considerresettingtheDRtoaninertialestimated
position, if an inertial system is installed.
Ifanavigatorhasnottakenafixforanextendedperiod
oftime,theDRplot,nothavingbeenresettoafix,will
accumulatetime-dependenterrors.Overtimethaterror
maybecomesosignificantthattheDRwillnolongershow
theship’spositionwithacceptableaccuracy.Ifthevesselis
equippedwithaninertialnavigator,thenavigatorshould
considerresettingtheDRtotheinertialestimatedposition.
Somefactorstoconsiderwhenmakingthisdetermination
are:
(1)Timesincethelastfixandavailabilityoffix
information.Ifithasbeenashorttimesincethelastfixand
fixinformationmaysoonbecomeavailable,itmaybe
advisable to wait for the next fix to reset the DR.
(2)Dynamicsofthenavigationsituation.If,for
example,asubmergedsubmarineisoperatingintheGulf
Stream,fixinformationisavailablebutoperationalconsid-
erationsmayprecludethesubmarinefromgoingto
periscopedepthtoobtainafix.Similarly,asurfaceship
withaninertialnavigatormaybeinadynamiccurrentand
sufferatemporarylossofelectronicfixequipment.In
eithercase,thefixinformationwillbeavailableshortlybut
thedynamicsofthesituationcallforamoreaccurate
assessmentofthevessel’sposition.PlottinganinertialEP
andresettingtheDRtothatEPmayprovidethenavigator
withamoreaccurateassessmentofthenavigationsituation.
(3)Reliabilityandaccuracyofthefixsource.Ifa
submarineisoperatingundertheice,forexample,onlythe
inertialEPfixesmaybeavailableforweeksatatime.
GivenahighpriorcorrelationbetweentheinertialEPand
highlyaccuratefixsystemssuchasGPS,andthecontinued
properoperationoftheinertialnavigator,thenavigatormay
decide to reset the DR to the inertial EP.
DEAD RECKONING AND SHIP SAFETY
ProperlymaintainingaDRplotisimportantforship
safety.TheDRallowsthenavigatortoexamineafuture
positioninrelationtoaplannedtrack.Itallowshimto
anticipatechartedhazardsandplanappropriateactionto
avoidthem.RecallthattheDRpositionisonly
approximate.Usingaconceptcalledfixexpansion
compensatesfortheDR’sinaccuracyandallowsthe
navigatortousetheDRmoreeffectivelytoanticipateand
avoid danger.
705. Fix Expansion
Oftenashipsteamsintheopenoceanforextended
periodswithoutafix.Thiscanresultfromanynumberof
factorsrangingfromtheinabilitytoobtaincelestialfixesto
malfunctioningelectronicnavigationsystems.Infrequent
fixesareparticularlycommononsubmarines.Whateverthe
reason,insomeinstancesanavigatormayfindhimselfin
the position of having to steam many hours on DR alone.
Thenavigatormusttakeprecautionstoensurethatall
hazardstonavigationalonghispathareaccountedforby
theapproximatenatureofaDRposition.Onemethod
which can be used isfix expansion.
Fixexpansiontakesintoaccountpossibleerrorsinthe
DRcalculationcausedbyfactorswhichtendtoaffectthe
vessel’sactualcourseandspeedovertheground.The
navigatorconsidersallsuchfactorsanddevelopsan
expanding“errorcircle”aroundtheDRplot.Oneofthe
basicassumptionsoffixexpansionisthatthevarious
individualeffectsofcurrent,leeway,andsteeringerror
combinetocauseacumulativeerrorwhichincreasesover
time,hence,theconceptofexpansion.Whiletheerrorsmay
infactcanceleachotherout,theworstcaseisthattheywill
allbeadditive,andthisiswhatthenavigatormust
anticipate.
Errorsconsideredinthecalculationoffixexpansion
encompassallerrorsthatcanleadtoDRinaccuracy.Some
ofthemostimportantfactorsarecurrentandwind,compass
orgyroerror,andsteeringerror.Anymethodwhich
attemptstodetermineanerrorcirclemusttakethesefactors
intoaccount.Thenavigatorcanusethemagnitudeofset
anddriftcalculatedfromhisDRplot.SeeArticle707.He
canobtainthecurrent’sestimatedmagnitudefrompilot
chartsorweatherreports.Hecandeterminewindspeed
fromweatherinstruments.Hecandeterminecompasserror
bycomparisonwithanaccuratestandardorbyobtainingan
azimuthoftheSun.Thenavigatordeterminestheeffect
eachoftheseerrorshasonhiscourseandspeedover
ground,andappliesthaterrortothefixexpansion
calculation.
Asnotedpreviously,errorisafunctionoftime;it
growsastheshipproceedsalongthetrackwithout
obtainingafix.Therefore,thenavigatormustincorporate
hiscalculatederrorsintoanerrorcirclewhoseradius
growswithtime.Forexample,assumethenavigator
calculatesthatallthevarioussourcesoferrorcancreatea
cumulativepositionerrorofnomorethan2nm.Thenhis
fixexpansionerrorcirclewouldgrowatthatrate;itwould
102DEAD RECKONING
be2nmafterthefirsthour,4nmafterthesecond,andsoon.
Atwhatvalueshouldthenavigatorstartthiserror
circle?RecallthataDRislaidoutfromeveryfix.Allfix
sourceshaveafiniteabsoluteaccuracy,andtheinitialerror
circleshouldreflectthataccuracy.Assume,forexample,
thatasatellitenavigationsystemhasanaccuracyof0.5nm.
Thentheinitialerrorcirclearoundthatfixshouldbesetat
0.5nm.
First,enclosethefixpositioninacircle,theradiusof
whichisequaltotheaccuracyofthesystemusedtoobtain
thefix.Next,layouttheorderedcourseandspeedfromthe
fixposition.Thenapplythefixexpansioncircletothehourly
DR’s,increasingtheradiusofthecirclebytheerrorfactor
eachtime.Intheexamplegivenabove,theDRafteronehour
wouldbeenclosedbyacircleofradius2.5nm,aftertwo
hours4.5nm,andsoon.HavingencircledthefourhourDR
positionswiththeerrorcircles,thenavigatorthendrawstwo
linesoriginatingtangenttotheoriginalerrorcircleand
simultaneouslytangenttotheothererrorcircles.The
navigatorthencloselyexaminestheareabetweenthetwo
tangentlinesforhazardstonavigation.Thistechniqueis
illustrated in Figure 705.
Thefixexpansionencompassesthetotalareainwhichthe
vesselcouldbelocated(aslongasallsourcesoferrorare
considered).Ifanyhazardsareindicatedwithinthecone,the
navigatorshouldbeespeciallyalertforthosedangers.If,for
example,thefixexpansionindicatesthatthevesselmaybe
standingintoshoalwater,continuouslymonitorthefathometer.
Similarly,ifthefixexpansionindicatesthatthevesselmightbe
approaching a charted obstruction, post extra lookouts.
Thefixexpansionmaygrowatsucharatethatit
becomesunwieldy.Obviously,ifthefixexpansiongrows
tocovertoolargeanarea,ithaslostitsusefulnessasatool
forthenavigator,andheshouldobtainanewfixbyany
available means.
DETERMINING AN ESTIMATED POSITION
Anestimatedposition(EP)isaDRpositioncorrected
fortheeffectsofleeway,steeringerror,andcurrent.This
sectionwillbrieflydiscussthefactorsthatcausetheDR
positiontodivergefromthevessel’sactualposition.Itwill
thendiscusscalculatingsetanddriftandapplyingthese
valuestotheDRtoobtainanestimatedposition.Itwillalso
discussdeterminingtheestimatedcourseandspeedmade
good.
706. Factors Affecting DR Position Accuracy
Tidalcurrentistheperiodichorizontalmovementof
thewater’ssurfacecausedbythetide-affectinggravita-
tionalforcesoftheMoonandSun.Currentisthe
horizontalmovementoftheseasurfacecausedbymeteoro-
logical,oceanographic,ortopographicaleffects.From
whateveritssource,thehorizontalmotionofthesea’s
surface is an important dynamic force acting on a vessel.
Setreferstothecurrent’sdirection,anddriftrefersto
thecurrent’sspeed.Leewayistheleewardmotionofa
vesselduetothatcomponentofthewindvectorperpen-
diculartothevessel’strack.Leewayandcurrentcombine
toproducethemostpronouncednaturaldynamiceffectson
atransitingvessel.Leewayespeciallyaffectssailing
vessels and high-sided vessels.
Inadditiontothesenaturalforces,relativelysmall
helmsmanandsteeringcompasserrormaycombineto
cause additional error in the DR.
Figure 705. Fix expansion. All possible positions of the ship lie between the lines tangent to the expanding circles.
Examine this area for dangers.
DEAD RECKONING103
707. Calculating Set and Drift and Plotting an
Estimated Position
Itisdifficulttoquantifytheerrorsdiscussedabove
individually.However,thenavigatorcaneasilyquantify
theircumulativeeffectbycomparingsimultaneousfix
andDRpositions.Iftherearenodynamicforcesacting
onthevesselandnosteeringerror,theDRpositionand
thefixpositionwillcoincide.However,theyseldomdo
so.ThefixisoffsetfromtheDRbythevectorsumofall
the errors.
Noteagainthatthismethodologyprovidesnomeans
todeterminethemagnitudeoftheindividualerrors.It
simplyprovidesthenavigatorwithameasurablerepresen-
tation of their combined effect.
Whenthenavigatormeasuresthiscombinedeffect,heof-
tenreferstoitasthe“setanddrift.”Recallfromabovethatthese
termstechnicallywererestrictedtodescribingcurrenteffects.
However,eventhoughthefix-to-DRoffsetiscausedbyeffects
inadditiontothecurrent,thistextwillfollowtheconventionof
referring to the offset as the set and drift.
ThesetisthedirectionfromtheDRtothefix.Thedrift
isthedistanceinmilesbetweentheDRandthefixdivided
bythenumberofhourssincetheDRwaslastreset.Thisis
trueregardlessofthenumberofchangesofcourseorspeed
sincethelastfix.Theprudentnavigatorcalculatessetand
drift at every fix.
TocalculateanEP,drawavectorfromtheDRposition
inthedirectionoftheset,withthelengthequaltotheprod-
uctofthedriftandthenumberofhourssincethelastreset.
SeeFigure707.Fromthe0900DRpositionthenavigator
drawsasetanddriftvector.Theendofthatvectormarks
the0900EP.NotethattheEPisenclosedinasquareand
labeledhorizontallywiththetime.PlotandevaluateanEP
with every DR position.
708. Estimated Course and Speed Made Good
Thedirectionofastraightlinefromthelastfixtothe
EPistheestimatedtrackmadegood.Thelengthofthis
linedividedbythetimebetweenthefixandtheEPisthe
estimated speed made good.
Solvefortheestimatedtrackandspeedbyusinga
vectordiagram.Seetheexampleproblemsbelowandrefer
to Figure 708a.
Example1:Ashiponcourse080°,speed10knots,is
steamingthroughacurrenthavinganestimatedsetof140°
and drift of 2 knots.
Required:Estimated track and speed made good.
Solution:SeeFigure708a.FromA,anyconvenient
point,drawAB,thecourseandspeedoftheship,in
direction 080°, for a distance of 10 miles.
FromBdrawBC,thesetanddriftofthecurrent,indi-
rection 140°, for a distance of 2 miles.
ThedirectionandlengthofACaretheestimatedtrack
and speed made good.
Answers:Estimatedtrackmadegood089°,estimated
speed made good 11.2 knots.
Tofindthecoursetosteeratagivenspeedtomake
goodadesiredcourse,plotthecurrentvectorfromthe
origin, A, instead of from B. See Figure 708b.
Example2:Thecaptaindesirestomakegoodacourse
of095°throughacurrenthavingasetof170°andadriftof
2.5 knots, using a speed of 12 knots.
Required:The course to steer and the speed made good.
Solution:SeeFigure708b.FromA,anyconvenient
point,drawlineABextendinginthedirectionofthecourse
to be made good, 095°.
From A draw AC, the set and drift of the current.
UsingCasacenter,swinganarcofradiusCD,the
speedthroughthewater(12knots),intersectinglineABat
D.
MeasurethedirectionoflineCD,083.5°.Thisisthe
course to steer.
MeasurethelengthAD,12.4knots.Thisisthespeed
made good.
Answers:Coursetosteer083.5°,speedmadegood
12.4 knots.Figure 707. Determining an estimated position.
Figure 708a. Finding track and speed made good through a current.
104DEAD RECKONING
Tofindthecoursetosteerandthespeedtousetomake
good a desired course and speed, proceed as follows:
See Figure 708c.
Example3:Thecaptaindesirestomakegoodacourse
of265°andaspeedof15knotsthroughacurrenthavinga
set of 185° and a drift of 3 knots.
Required:The course to steer and the speed to use.
Solution:SeeFigure708c.FromA,anyconvenient
point,drawABinthedirectionofthecoursetobemade
good,265°andforlengthequaltothespeedtobemade
good, 15 knots.
From A draw AC, the set and drift of the current.
DrawastraightlinefromCtoB.Thedirectionofthis
line,276°,istherequiredcoursetosteer;andthelength,
14.8 knots, is the required speed.
Answers:Course to steer 276°, speed to use 14.8 kn.
Figure 708b. Finding the course to steer at a given speed to make good a given course through a current.
Figure 708c. Finding course to steer and speed to use to make good a given course and speed through the current.
105
CHAPTER 8
PILOTING
DEFINITION AND PURPOSE
800. Introduction
Pilotinginvolvesnavigatingavesselinrestrictedwaters
andfixingitspositionaspreciselyaspossibleatfrequent
intervals.Moresothaninotherphasesofnavigation,proper
preparationandattentiontodetailareimportant.Thischapter
willdiscussapilotingmethodologydesignedtoensurethat
proceduresarecarriedoutsafelyandefficiently.These
procedureswillvaryfromvesseltovesselaccordingtotheskills
andcompositionofthepilotingteam.Itistheresponsibilityof
thenavigatortochoosetheproceduresapplicabletohisown
situation,totrainthepilotingteamintheirexecution,andto
ensure that duties are carried out properly.
Theseproceduresarewrittenprimarilyfromthe
perspectiveofthemilitarynavigator,withsomenotesincluded
wherecivilianproceduresmightdiffer.Thissetofproceduresis
designedtominimizethechanceoferrorandmaximizesafety
of the ship.
Themilitarynavigationteamwillnearlyalwaysconsistof
severalmorepeoplethanareavailabletotheciviliannavigator.
Therefore,theciviliannavigatormuststreamlinethese
procedures,eliminatingcertainsteps,doingonlywhatis
essential to keep his ship in safe water.
Thenavigationofcivilianvesselswillthereforeproceed
differentlythanformilitaryvessels.Forexample,whilethe
militarynavigatormighthavebearingtakersstationedatthe
gyrorepeatersonthebridgewingsfortakingsimultaneous
bearings,theciviliannavigatormustoftentakeandplotthem
himself.Whilethemilitarynavigatorwillhaveabearingbook
andsomeonetorecordentriesforeachfix,theciviliannavigator
willsimplyplotthebearingsonthechartastheyaretakenand
not record them at all.
IftheshipisequippedwithanECDIS,itisreasonablefor
thenavigatortosimplymonitortheprogressoftheshipalong
thechosentrack,visuallyensuringthattheshipisproceedingas
desired,checkingthecompass,sounderandotherindicators
onlyoccasionally.Ifapilotisaboard,asisoftenthecaseinthe
mostrestrictedofwaters,hisjudgementcangenerallyberelied
uponexplicitly,furthereasingtheworkload.Butshouldthe
ECDISfail,thenavigatorwillhavetorelyonhisskillinthe
manual and time-tested procedures discussed in this chapter.
WhileanECDISisthelegalequivalentofapaperchartand
canbeusedastheprimaryplot,anECS,(non-ECDIScompliant
electronicchartsystem)cannotbesoused.AnECSmaybe
consideredasanadditionalresourceusedtoensuresafe
navigation,butcannotberelieduponforperformingallthe
routinetasksassociatedwithpiloting.Theindividualnavigator,
withknowledgeofhisvessel,hiscrew,andthecapabilitiesthey
possess,mustmakeaprofessionaljudgementastohowtheECS
cansupporthiseffortstokeephisshipinsafewater.The
navigatorshouldalwaysrememberthatrelianceonanysingle
navigationsystemcourtsdisaster.AnECSdoesnotrelievethe
navigatorofmaintainingaproperandlegalplotonapaperchart.
PREPARATION
801. Plot Setup
Thenavigator’sjobbeginswellbeforegettingunder-
way.Muchadvancepreparationisnecessarytoensurea
safeandefficientvoyage.Thefollowingstepsare
representative:
Ensuretheplottingstation(s)havethefollowing
instruments:
•Dividers:Dividersareusedtomeasuredistances
between points on the chart.
•Compasses:Compassesareusedtoplotrangearcs
forradarLOP’s.Beamcompassesareusedwhen
therangearcexceedsthespreadofaconventional
compass. Both should be available at both plots.
•Plotters:Severaltypesofplottersareavailable.The
preferreddeviceforlargevesselsistheparallel
motionplotter(PMP)usedinconjunctionwitha
draftingtable.Otherwise,useatransparent
protractorplotter,ortriangles,parallelrulersor
rollingrulersinconjunctionwiththechart’s
compassrose.Finally,theplottercanuseaonearm
protractor.Theplottershouldusethedevicewith
which he can work the most quickly and accurately.
•SharpenedPencilsandErasers:Ensurean
adequate supply of pencils is available.
106PILOTING
•FischerRadarPlottingTemplates:Fischer
plottingiscoveredinChapter13.Theplotting
templatesforthistechniqueshouldbestackednear
the radar repeater.
•Time-Speed-DistanceCalculator:Giventwoof
thethreeunknowns(betweentime,speed,and
distance),thiscalculatorallowsforrapid
computation of the third.
•TideandCurrentGraphs:Postthetideandcurrent
graphsneartheprimaryplotforeasyreference
duringthetransit.Giveacopyofthegraphstothe
conning officer and the captain.
Oncethenavigatorverifiestheaboveequipmentisinplace,
hetapesdownthechartsonthecharttable.Ifmorethanone
chartisrequiredforthetransit,tapethechartsinastacksuchthat
theplotterworksfromthetoptothebottomofthestack.This
minimizesthetimerequiredtoshiftthechartduringthetransit.
IftheplotterisusingaPMP,alignthearmofthePMPwithany
meridianoflongitudeonthechart.WhileholdingthePMParm
stationary,adjustthePMPtoread000.0°T.Thisprocedure
calibratesthePMPtothechartinuse.Performthisalignment
every time the piloting team shifts charts.
Becarefulnottofoldunderanyimportantinformation
whenfoldingthechartonthecharttable.Ensurethechart’s
distancescale,theentiretrack,andallimportantwarning
information are visible.
Energizeandtestallelectronicnavigationequipment,
ifnotalreadyinoperation.Thisincludestheradarandthe
GPSreceiver.Energizeandtestthefathometer.Ensurethe
entireelectronicnavigationsuiteisoperatingproperlyprior
to entering restricted waters.
802. Preparing Charts and Publications
•AssembleRequiredPublications.Thesepublications
shouldincludeCoastPilots,SailingDirections,USCG
LightLists,NIMAListsofLights,TideTables,Tidal
CurrentTables,NoticetoMariners,andLocalNotice
toMariners.Often,formilitaryvessels,aportwillbe
undertheoperationaldirectionofaparticularsquad-
ron;obtainthatsquadron’sportOperationOrder.
Civilianvesselsshouldobtaintheport’sharborregula-
tions.Thesepublicationswillcoverlocalregulations
suchasspeedlimitsandbridge-to-bridgeradiofre-
quencymonitoringrequirements.Assembleand
review the Broadcast Notice to Mariners file.
•SelectandCorrectCharts.Choosethelargestscale
chartavailablefortheharborapproachordeparture.
Often,theharborapproachwillbetoolongtobe
representedononlyonechart.Forexample,three
chartsarerequiredtocoverthewatersfromtheNaval
StationinNorfolktotheentranceoftheChesapeake
Bay.Therefore,obtainallthechartsrequiredtocover
theentirepassage.UsingtheNoticetoMariners,verify
thatthesechartshavebeencorrectedthroughthelatest
NoticetoMariners.ChecktheLocalNoticeto
MarinersandtheBroadcastNoticetoMarinersfileto
ensurethechartisfullycorrected.Annotateonthe
chartorachartcorrectioncardallthecorrectionsthat
havebeenmade;thiswillmakeiteasiertoverifythe
chart’scorrectionstatuspriortoitsnextuse.Naval
shipsmayneedtopreparethreesetsofcharts.Oneset
isfortheprimaryplot,thesecondsetisforthe
secondaryplot,andthethirdsetisfortheconning
officerandcaptain.Civilianvesselswillprepareone
set.
•MarktheMinimumDepthContour:Determinethe
minimumdepthofwaterinwhichthevesselcansafely
operateandoutlinethatdepthcontouronthechart.Do
thisstepbeforedoinganyotherharbornavigation
planning.Highlightthisoutlineinabrightcolorsothat
itclearlystandsout.Carefullyexaminetheareainside
thecontourandmarktheisolatedshoalslessthanthe
minimumdepthwhichfallinsidethemarkedcontour.
Determinetheminimumdepthinwhichthevesselcan
operate as follows:
Minimum Depth = Ship’s Draft – Height of Tide +
SafetyMargin+Squat.(SeeArticle804andArticle818.)
Rememberthatoftenthefathometer’stransducerisnot
locatedatthesectionofthehullthatextendsthefurthest
belowthewaterline.Therefore,theindicateddepthof
wateristhatbelowthefathometertransducer,notthe
depth of water below the vessel’s deepest draft.
•HighlightSelectedVisualNavigationAids
(NAVAIDS).Circle,highlightandlabelthemain
navigationalaidsonthechart.Consulttheapplicable
CoastPilotorSailingDirectionstodetermineaport’s
bestNAVAIDSifthepilotingteamhasnotvisitedthe
portpreviously.Theseaidscanbelighthouses,piers,
shorefeatures,ortanks;anyprominentfeaturethatis
displayedonthechartcanbeusedasaNAVAID.
Labelcriticalbuoys,suchasthosemarkingaharbor
entranceoratrafficseparationscheme.Verifycharted
lightsagainsttheLightListortheListofLightsto
confirmthechartedinformationiscorrect.This
becomesmostcriticalwhenattemptingtoidentifya
lightatnight.LabelNAVAIDSsuccinctlyandclearly.
Ensureeveryoneinthenavigationteamreferstoa
NAVAIDusingthesameterminology.Thiswill
reduceconfusionbetweenthebearingtaker,the
bearing recorder, and plotter.
•HighlightSelectedRadarNAVAIDS.Highlight
radarNAVAIDSwithatriangleinsteadofacircle.If
PILOTING107
theNAVAIDissuitableforeithervisualorradar
piloting,itcanbehighlightedwitheitheracircleora
triangle.
•PlottheDeparture/ApproachTrack.Thisprocessis
criticalforensuringsafepilotage.ConsulttheFleet
GuideandSailingDirectionsforrecommendationson
thebesttracktouse.Lookforanyinformationor
regulationspublishedbythelocalharborauthority.
Lackinganyofthisinformation,locateachannelor
saferouteonthechartandplotthevessel’strack.Most
U.S.portshavewell-definedchannelsmarkedwith
buoys.Carefullychecktheintendedtracktoensurea
sufficientdepthofwaterunderthekeelwillexistfor
theentirepassage.Ifthescaleofthechartpermits,lay
thetrackouttothestarboardsideofthechannelto
allowforanyvesseltrafficproceedingintheopposite
direction.Manychannelsaremarkedbynaturalor
man-maderanges.Thebearingsoftheserangesshould
bemeasuredtothenearest0.1°ornotedfromtheLight
List,andthisvalueshouldbemarkedonthechart.Not
onlyarerangesusefulinkeepingavesselontrack,they
areinvaluablefordetermininggyroerror.SeeArticle
807.
•LabeltheDeparture/ApproachTrack.Labelthe
trackcoursetothenearest0.5°.Similarly,labelthe
distanceofeachtrackleg.Highlightthetrackcourses
foreasyreferencewhilepiloting.Oftenanavigator
mightplantwoseparatetracks.Onetrackwouldbefor
useduringgoodvisibilityandtheotherforpoor
visibility.Considerationsmightincludeconcernfor
thenumberofturns(fewerturnsforpoorvisibility)or
proximitytoshoalwater(smallermarginforerror
mightbeacceptableingoodvisibility).Inthiscase,
labelbothtracksasaboveandappropriatelymark
when to use each track.
•UseAdvanceandTransfertoFindTurningPoints.
Thedistancethevesselmovesalongitsoriginalcourse
fromthetimetherudderisputoveruntilthenewcourse
isreachediscalledadvance.Thedistancethevessel
movesperpendiculartotheoriginalcourseduringtheturn
iscalledtransfer.Thetrackdeterminedabovedoesnot
accountforthese.SeeFigure802a.Usetheadvanceand
transfercharacteristicsofthevesseltodeterminewhen
thevesselmustputitsrudderovertogainthenextcourse.
Fromthatpoint,fairinacurvebetweentheoriginal
courseandthenewcourse.Markthepointontheoriginal
coursewherethevesselmustputitsrudderoverasthe
turning point.See Figure 802b.
•PlotTurnBearingsandRanges.Aturnbearingisa
predeterminedbearingtoachartedobjectfromthe
trackpointatwhichtheruddermustbeputoverin
ordertomakeadesiredturn.InselectingaNAVAID
foraturnbearing,findoneasclosetoabeamas
possibleattheturningpoint,andifpossibleonthe
insideelbowoftheturn.Accountforadvanceand
transferandlabelthebearingtothenearest0.1°.A
turnrangeissimilar,buttakenasaradarrangetoa
prominentobjectaheadorastern.Ideally,bothcanbe
used, one as a check against the other.
Example:Figure802billustratesusingadvanceand
transfertodetermineaturnbearing.Aship
proceedingoncourse100°istoturn60°totheleft
tocomeonarangewhichwillguideitupa
channel.Fora60°turnandtheamountofrudder
used,theadvanceis920yardsandthetransferis
350 yards.
Required:Thebearingofflagpole“FP.”whenthe
rudder is put over.
Solution:
1.Extend the original course line, AB.
2.Ataperpendiculardistanceof350yards,the
transfer,drawalineA'B'paralleltotheoriginal
courselineAB.Thepointofintersection,C,ofA'B'
withthenewcourselineistheplaceatwhichthe
turn is to be completed.
3.FromCdrawaperpendicular,CD,totheoriginal
course line, intersecting at D.
4.FromDmeasuretheadvance,920yards,back
alongtheoriginalcourseline.ThislocatesE,the
point at which the turn should be started.
5.Thedirectionof“FP.”fromE,058°,isthebearing
when the turn should be started.
Answer:Bearing 058°.
Figure 802a. Advance and transfer.
108PILOTING
•PlotaSlideBarforEveryTurnBearing:Iftheship
isofftrackimmediatelypriortoaturn,aplotting
techniqueknownastheslidebarcanquicklyrevisea
turnbearing.SeeFigure802c.Aslidebarisaline
drawnparalleltothenewcoursethroughtheturning
pointontheoriginalcourse.Thenavigatorcanquickly
determineanewturnbearingbydeadreckoningahead
fromthevessel’slastfixpositiontowheretheDR
intersectstheslidebar.Therevisedturnbearingis
simplythebearingfromthatintersectionpointtothe
turn bearing NAVAID.Drawtheslidebarwitha
differentcolorfromthatusedforthetrackinorderto
see the slide bar clearly.
•LabelDistancetoGofromEachTurnPoint:At
eachturningpoint,labelthedistancetogountileither
theshipmoors(inbound)ortheshipclearstheharbor
(outbound).Foraninboundtransit,avessel’scaptainis
usuallymoreconcernedabouttimeofarrival,so
assumeaspeedofadvanceandlabeleachturnpoint
with time to go until mooring.
•PlotDangerBearings:Dangerbearingswarna
navigatorhemaybeapproachinganavigationalhazard
tooclosely.SeeFigure802d.VectorABindicatesa
vessel’sintendedtrack.Thistrackpassesclosetothe
indicatedshoal.DrawalinefromtheNAVAIDH
tangenttotheshoal.Thebearingofthattangentline
measuredfromtheship’strackis074.0°T.Inother
words,aslongasNAVAIDHbearslessthan074°Tas
thevesselproceedsdownitstrack,thevesselwillnot
groundontheshoal.Hatchthesideofthebearinglineonthe
sideofthehazardandlabelthedangerbearingNMT(no
morethan)074.0°T.Foranaddedmarginofsafety,theline
doesnothavetobedrawnexactlytangenttotheshoal.
Perhaps,inthiscase,thenavigatormightwanttosetanerror
marginanddrawthedangerbearingat065°Tfrom
NAVAIDH.Laydownadangerbearingfromany
appropriateNAVAIDinthevicinityofanyhazardto
navigation.Ensurethetrackdoesnotcrossanydanger
bearing.
•PlotDangerRanges:Thedangerrangeisanalogous
tothedangerbearing.Itisastandoffrangefromanob-
jecttopreventthevesselfromapproachingahazard
too closely.
•LabelWarningandDangerSoundings:To
determinethedangersounding,examinethevessel’s
proposedtrackandnotetheminimumexpected
sounding.Theminimumexpectedsoundingisthe
differencebetweentheshallowestwaterexpectedon
thetransitandthevessel’smaximumdraft.Set90%of
thisdifferenceasthewarningsoundingand80%ofthis
differenceasthedangersounding.Theremaybe
peculiaritiesaboutlocalconditionsthatwillcausethe
navigatortochooseanothermethodofsettingwarning
anddangersoundings.Usetheabovemethodifno
Figure 802b. Allowing for advance and transfer.
PILOTING109
othermeansismoresuitable.Forexample:Avessel
drawsamaximumof20feet,anditisenteringa
channeldredgedtoaminimumdepthof50feet.Setthe
warninganddangersoundingsat0.9(50ft.-20ft)=
27ftand0.8(50ft.-20ft.)=24ft.,respectively.Re-
evaluatethesesoundingsatdifferentintervalsalong
thetrack,whentheminimumexpectedsoundingmay
change.Carefullylabelthepointsalongthetrack
betweenwhichthesewarninganddangersoundings
apply.
•LabelDemarcationLine:Clearlylabelthepointon
theship’strackwheretheInlandandInternational
RulesoftheRoadapply.Thisisapplicableonlywhen
piloting in U.S. ports.
•MarkSpeedLimitsWhereApplicable:Oftena
harborwillhavealocalspeedlimitinthevicinityof
piers,othervessels,orshorefacilities.Markthese
speedlimitsandthepointsbetweenwhichtheyare
applicable on the chart.
•MarkthePointofPilotEmbarkation:Someports
requirevesselsoveracertainsizetoembarkapilot.If
thisisthecase,markthepointonthechartwherethe
pilot is to embark.
•MarktheTugboatRendezvousPoint:Ifthevessel
requiresatugtomoor,markthetugrendezvouspoint
on the chart.
•MarktheChartShiftPoint:Ifmorethanonechart
Figure 802c. The slide bar technique.
Figure 802d. A danger bearing, hatched on the dangerous side, labeled with the appropriate bearing.
110PILOTING
willberequiredtocompletethepassage,markthe
pointwherethenavigatorshouldshifttothenextchart.
•HarborCommunications:Markthepointonthe
chartwherethevesselmustcontactharborcontrol.
Alsomarkthepointwhereavesselmustcontactits
parentsquadrontomakeanarrivalreport(military
vessels only).
•TidesandCurrents:Markthepointsonthechartfor
which the tides and currents were calculated.
803. Records
Ensurethefollowingrecordsareassembledand
personnel assigned to maintain them:
•BearingRecordBook:Thebearingrecordersfor
theprimaryandsecondaryplotsshouldrecordallthe
bearingsusedontheirplotduringtheentiretransit.
ThebooksshouldclearlylistwhatNAVAIDSare
beingusedandwhatmethodofnavigationwasbeing
usedontheirplot.Inpractice,theprimarybearing
bookwillcontainmostlyvisualbearingsandthe
secondarybearingbookwillcontainmostlyradar
ranges and bearings.
•FathometerLog:Inrestrictedwaters,monitor
soundingscontinuouslyandrecordsoundingseveryfive
minutesinthefathometerlog.Recordallfathometer
settings that could affect the sounding display.
•DeckLog:Thislogisthelegalrecordofthepassage.
Recordallorderedcourseandspeedchanges.Recordall
thenavigator’srecommendationsandwhetherthe
navigatorconcurswiththeactionsoftheconningofficer.
Recordallbuoyspassed,andtheshiftbetweendifferent
RulesoftheRoad.Recordthenameandembarkationof
anypilot.Recordwhohastheconnatalltimes.Record
anycasualtyorimportantevent.Thedecklogcombined
withthebearinglogshouldconstituteacompleterecord
of the passage.
804. Tides and Currents
Determiningthetidalandcurrentconditionsoftheport
iscrucial.ThisprocessiscoveredindepthinChapter9.In
ordertoanticipateearlyorlatetransit,plotagraphofthe
tidalrangeforthe24-hourperiodcenteredonthescheduled
timeofarrivalordeparture.Dependingonavessel’sdraft
andtheharbor’sdepth,somevesselsmaybeabletotransit
onlyathightide.Ifthisisthiscase,itiscriticallyimportant
to determine the time and range of the tide correctly.
Themagnitudeanddirectionofthecurrentwillgive
thenavigatorsomeideaofthesetanddriftthevesselwill
experienceduringthetransit.Thiswillallowhimtoplanin
advanceforanypotentialcurrenteffectsinthevicinityof
navigational hazards.
Whileprintedtidetablescanbeusedforpredictingand
plottingtides,itisfarmoreefficienttouseacomputerwith
appropriatesoftware,ortheinternet,tocomputetidesand
printoutthegraphs.Thesegraphscanbepostedonthe
bridgeatthecharttableforreadyreference,andcopies
madeforothersinvolvedinthepilotingprocess.NOAA
tidetablesfortheU.S.areavailableatthefollowingsite:
http://co-ops.nos.noaa.gov/tp4days.html.Always
rememberthattidetablesgivepredicteddata,butthat
actualconditionsmaybequitedifferentduetoweatheror
other natural phenomena.
805. Weather
Thenavigatorshouldobtainaweatherreportcovering
theroutewhichheintendstotransit.Thiswillallowhimto
prepareforanyadverseweatherbystationingextra
lookouts,adjustingspeedforpoorvisibility,andpreparing
forradarnavigation.Iftheweatheristhick,consider
standing off the harbor until it clears.
Thenavigatorcanreceiveweatherinformationany
numberofways.Militaryvesselsmayreceiveweather
reportsfromtheirparentsquadronspriortocominginto
port.Marinebandradiocarriescontinuousweatherreports.
Manyvesselsareequippedwithweatherfacsimile
machines.Somenavigatorscarrycellularphonestoreach
shoresidepersonnelandharborcontrol;thesecanalsobe
usedtogetweatherreportsfromNOAAweatherstations.If
theshipisusingaweatherroutingserviceforthevoyage,it
shouldprovideforecastswhenasked.Finally,ifthevessel
hasaninternetconnection,thisisanidealsourceofweather
data.NOAAweatherdatacanbeobtainedat:
http://www.nws.noaa.gov.Howeverheobtainsthe
information,thenavigatorshouldhaveagoodideaofthe
weather before entering piloting waters.
806. The Piloting Brief
Assembletheentirenavigationteamforapilotingbrief
priortoenteringorleavingport.Thevessel’scaptainand
navigatorshouldconductthebriefing.Allnavigationand
bridgepersonnelshouldattend.Thepilot,ifheisalreadyon
board,shouldalsoattend.Ifthepilotisnotonboardwhen
theship’scompanyisbriefed,thenavigatorshould
immediatelybriefhimwhenheembarks.Thepilotmust
knowtheship’smaneuveringcharacteristicsbefore
enteringrestrictedwaters.Thebriefingshouldcover,asa
minimum, the following:
•DetailedCoverageoftheTrackPlan:Gooverthe
plannedrouteindetail.Usethepreparedandapproved
chartaspartofthisbrief.Concentrateespeciallyonall
theNAVAIDSandsoundingswhicharebeingusedto
indicatedanger.Coverthebuoyagesysteminuseand
PILOTING111
theport’smajorNAVAIDS.Pointouttheradar
NAVAIDSfortheradaroperator.Often,aFleetGuide
orSailingDirectionswillhavepicturesofaport’s
NAVAIDS.Thisisespeciallyimportantforthe
pilotingpartythathasnevertransitedaparticularport
before.Ifnopicturesareavailable,considerstationing
a photographer to take some for submission to NIMA.
•HarborCommunications:Discussthebridge-to
bridgeradiofrequenciesusedtoraiseharborcontrol.
Discusswhatchannelthevesselissupposedtomonitor
onitspassageintoportandtheport’scommunication
protocol.
•DutiesandResponsibilities:Eachmemberofthe
pilotingteammusthaveathoroughunderstandingof
hisdutiesandresponsibilities.Hemustalsounderstand
howhispartfitsintothewhole.Theradarplotter,for
example,mustknowifradarwillbetheprimaryor
secondarysourceoffixinformation.Thebearing
recordermustknowwhatfixintervalthenavigatoris
planningtouse.Eachpersonmustbethoroughly
briefedonhisjob;thereislittletimeforquestionsonce
the vessel enters the channel.
807. Evolutions Prior to Piloting
Thenavigatorshouldalwaysaccomplishthefollowing
evolutions prior to piloting:
•TestingtheShaftontheMainEnginesinthe
AsternDirection:Thisensuresthattheshipcan
answerabackingbell.Iftheshipisenteringport,no
specialprecautionsarerequiredpriortothistest.Ifthe
shipistiedupatthepierpreparingtogetunderway,
exerciseextremecautiontoensurenowayisplaced
on the ship while testing the main engines.
•MakingtheAnchorReadyforLettingGo:Make
theanchorreadyforlettinggoandstationa
watchstanderindirectcommunicationswiththe
bridgeattheanchorwindlass.Bepreparedtodrop
anchorimmediatelywhenpilotingifrequiredtokeep
from drifting too close to a navigational hazard.
•CalculateGyroError:Anerrorofgreaterthan1.0°
Tindicatesagyroproblemwhichshouldbe
investigatedpriortopiloting.Thereareseveralways
to determine gyro error:
1.Comparethegyroreadingwithaknown
accurateheadingreferencesuchasaninertial
navigator.Thedifferenceinthereadingsisthe
gyro error.
2.Markthebearingofachartedrangeastherange
NAVAID’scomeintolineandcomparethegyro
bearingwiththechartedbearing.Thedifference
is the gyro error.
3.Priortogettingunderway,plotadocksidefixusing
atleastthreelinesofposition.ThethreeLOP’s
shouldintersectatapoint.Theirintersectingina
“cockedhat”indicatesagyroerror.Incrementally
adjusteachvisualbearingbythesameamountand
directionuntilthefixplotsasapinpoint.Thetotal
correctionrequiredtoeliminatethecockedhatisthe
gyro error.
4.Measureacelestialbody’sazimuthor
amplitude,orPolaris’azimuthwiththegyro,
andthencomparethemeasuredvaluewitha
valuecomputedfromtheSightReductionTables
ortheNauticalAlmanac.Thesemethodsare
covered in detail in Chapter 17.
Reportthemagnitudeanddirectionofthegyroerrorto
thenavigatorandcaptain.Thedirectionoftheerroris
determinedbytherelativemagnitudeofthegyroreading
andthevalueagainstwhichitiscompared.Whenthe
compassisleast,theerroriseast.Conversely,whenthe
compass is best, the error is west. See Chapter 6.
808. Inbound Voyage Planning
Thevessel’splannedestimatedtimeofarrival(ETA)at
itsmooringdeterminesthevessel’scourseandspeedtothe
harborentrance.Arrivingatthemooringsiteontimemaybe
importantinabusyportwhichoperatesitsportservicesona
tightschedule.Therefore,itisimportanttoplanthearrival
accurately.Takethedesiredtimeofarrivalatthemooringand
subtractfromthatthetimeitwilltaketonavigatetoitfromthe
entrance.Theresultingtimeiswhenyoumustarriveatthe
harborentrance.Next,measurethedistancebetweenthe
vessel’spresentlocationandtheharborentrance.Determine
thespeedofadvance(SOA)thevesselwillusetomakethe
transittotheharbor.Usethedistancetotheharborandthe
SOAtocalculatewhattimetoleavethepresentpositionto
makethemooringETA,orwhatspeedmustbemadegoodto
arrive on time.
Considerthesefactorswhichmightaffectthisdecision:
•Weather:Thisisthesinglemostimportantfactorin
harborapproachplanningbecauseitdirectlyaffectsthe
vessel’sSOA.Thethickertheweather,themoreslowly
thevesselmustproceed.Therefore,ifheavyfogorrain
isintheforecast,thenavigatormustallowmoretime
for the transit.
•MooringProcedures:Thenavigatormusttakemore
thandistanceintoaccountwhencalculatinghowlongit
willtakehimtopilottohismooring.Ifthevesselneedsa
112PILOTING
tug,thatwillincreasethetimeneeded.Similarly,picking
upordroppingoffapilotaddstimetothetransit.Itis
bettertoallowamarginforerrorwhentryingtoaddupall
thetimedelayscausedbytheseprocedures.Itisalways
easiertoavoidarrivingearlybyslowingdownthanitisto
make up lost time by speeding up.
•ShippingDensity:Generally,thehighertheshipping
densityenteringandexitingtheharbor,thelongerit
will take to proceed into the harbor entrance safely.
TRANSITION TO PILOTING
809. Stationing the Piloting Team
Attheappropriatetime,stationthepilotingteam.Allow
plentyoftimetoacclimatetothenavigationalsituationand
ifatnight,tothedarkness.Thenumberandtypeofpersonnel
availableforthepilotingteamdependonthevessel.ANavy
warship,forexample,hasmorepeopleavailableforpiloting
thanamerchantship.Therefore,morethanoneofthejobs
listedbelowmayhavetobefilledbyasingleperson.The
piloting team should consist of:
•TheCaptain:Thecaptainisultimatelyresponsiblefor
thesafenavigationofhisvessel.Hisjudgmentregarding
navigationisfinal.Thepilotingteamactstosupportthe
captain,advisinghimsohecanmakeinformed
decisions on handling his vessel.
•ThePilot:Thepilotisusuallytheonlymemberofthe
pilotingteamnotamemberoftheship’scompany.The
pilotingteammustunderstandtherelationshipbetween
thepilotandthecaptain.Thepilotisperhapsthe
captain’smostimportantnavigationaladvisor.
Generally,thecaptainwillfollowhisrecommendations
whennavigatinganunfamiliarharbor.Thepilot,too,
bearssomeresponsibilityforthesafepassageofthe
vessel;hecanbecensuredforerrorsofjudgmentwhich
causeaccidents.However,thepresenceofapilotinno
wayrelievesthecaptainofhisultimateresponsibility
forsafenavigation.Thepilotingteamworkstosupport
and advise the captain.
•TheOfficeroftheDeck(ConningOfficer):InNavy
pilotingteams,neitherthepilotorthecaptainusually
hastheconn.Theofficerhavingtheconndirectsthe
ship’smovementsbyrudderandengineorders.
Anotherofficeroftheship’scompanyusuallyfulfills
thisfunction.Thecaptaincantaketheconn
immediatelysimplybyissuinganordertothehelm
shouldanemergencyarise.Theconningofficerofa
merchantvesselcanbeeitherthepilot,thecaptain,or
anotherwatchofficer.Inanyevent,theofficerhaving
theconnmustbeclearlyindicatedintheship’sdeck
logatalltimes.Oftenasingleofficerwillhavethe
deckandtheconn.However,sometimesajunior
officerwilltaketheconnfortraining.Inthiscase,
differentofficerswillhavethedeckandtheconn.The
officerwhoretainsthedeckretainstheresponsibility
for the vessel’s safe navigation.
•TheNavigator:Thevessel’snavigatoristheofficer
directlyresponsibletotheship’scaptainforthesafe
navigationoftheship.Heisthecaptain’sprincipal
navigationaladvisor.Thepilotingteamworksforhim.
Hechannelstherequiredinformationdevelopedbythe
pilotingteamtotheship’sconningofficeron
recommendedcourses,speeds,andturns.Healso
carefullylooksaheadforpotentialnavigational
hazardsandmakesappropriaterecommendations.He
isthemostseniorofficerwhodevoteshiseffort
exclusivelytomonitoringthenavigationpicture.The
captainandtheconningofficerareconcernedwithall
aspectsofthepassage,includingcontactavoidance
andothernecessaryshipevolutions(makinguptugs,
maneuveringalongsideasmallboatforpersonnel
transfers,engineeringevolutions,andcoordinating
withharborcontrolviaradio,forexample).The
navigator,ontheotherhand,focusessolelyonsafe
navigation.Itishisjobtoanticipatedangers,keep
himselfappraisedofthenavigationsituationatall
times, and manage the team.
•BearingPlottingTeam:Thisteamconsists,ideally,
ofthreepersons.Thefirstpersonmeasuresthe
bearings.Thesecondpersonrecordsthebearingsinan
officialrecordbook.Thethirdpersonplotsthe
bearings.Themorequicklyandaccuratelythisprocess
iscompleted,thesoonerthenavigatorhasanaccurate
pictureoftheship’sposition.Thebearingtakershould
beanexperiencedindividualwhohastraversedthe
portbeforeandwhoisfamiliarwiththeNAVAIDS.
Heshouldtakehisroundofbearingsasquicklyas
possible,beambearingsfirst,minimizinganytime
delayerrorsintheresultingfix.Theplottershouldalso
beanexperiencedindividualwhocanquicklyand
accuratelylaydowntherequiredbearings.Thebearing
recordercanbeoneofthejuniormembersofthe
piloting team.
•TheRadarOperator:Theradaroperatorhasoneof
themoredifficultjobsoftheteam.Theradarisas
importantforcollisionavoidanceasitisfor
navigation.Therefore,thisoperatormustoften“time
share”theradarbetweenthesetwofunctions.
Determiningtheamountoftimespentonthese
functionsfallswithinthejudgmentofthecaptainand
thenavigator.Ifthedayisclearandthetrafficheavy,
thecaptainmaywanttousetheradarmostlyfor
PILOTING113
collisionavoidance.Astheweatherworsens,
obscuringvisualNAVAIDS,theimportanceofradar
forsafenavigationincreases.Theradaroperatormust
begivenclearguidanceonhowthecaptainand
navigator want the radar to be operated.
•PlotSupervisors:Onmanymilitaryships,thepiloting
teamwillconsistoftwoplots:theprimaryplotandthe
secondaryplot.Thenavigatorshoulddesignatethetype
ofnavigationthatwillbeemployedontheprimaryplot.
Allotherfixsourcesshouldbeplottedonthesecondary
plot.Thenavigatorcanfunctionastheprimaryplot
supervisor.Asenior,experiencedindividualshouldbe
employedasasecondaryplotsupervisor.Thenavigator
shouldfrequentlycomparethepositionsplottedonboth
plots as a check on the primary plot.
Therearethreemajorreasonsformaintaininga
primaryandsecondaryplot.First,asmentionedabove,the
secondaryfixsourcesprovideagoodcheckonthe
accuracyofvisualpiloting.Largediscrepanciesbetween
visualandradarpositionsmaypointoutaproblemwith
thevisualfixesthatthenavigatormightnototherwise
suspect.Secondly,thenavigatoroftenmustchangethe
primarymeansofnavigationduringthetransit.Hemay
initiallydesignatevisualbearingsastheprimaryfix
methodonlytohaveasuddenstormorfogobscurethe
visualNAVAIDS.Ifheshiftstheprimaryfixmeansto
radar,hehasatrackhistoryofthecorrelationbetween
radarandvisualfixes.Finally,thepilotingteamoftenmust
shiftchartsseveraltimesduringthetransit.Whentheold
chartistakenofftheplottingtableandbeforethenewchart
issecured,thereisaperiodoftimewhennochartisinuse.
Maintainingasecondaryploteliminatesthiscomplication.
Ensurethesecondaryplotisnotshiftedpriortogettingthe
newprimaryplotchartdownonthecharttable.Inthis
case,therewillalwaysbeachartavailableonwhichto
pilot.Donotconsidertheprimarychartshifteduntilthe
newchartisproperlysecuredandtheplotterhas
transferredthelastfixfromtheoriginalchartontothenew
chart.
•SatelliteNavigationOperator:Thisoperator
normallyworksforthesecondaryplotsupervisor.GPS
accuracywithSelectiveAvailability(SA)onisnot
sufficientfornavigatingrestrictedwaters;butwithSA
off,GPScansupportharbornavigation,inwhichcase
itshouldbeconsideredasonlyoneaidtonavigation,
notasasubstitutefortheentireprocess.Iftheteam
losesvisualbearingsinthechannelandnoradar
NAVAIDSareavailable,GPSmaybethemost
accuratefixsourceavailable.Thenavigatormusthave
somedataonthecomparisonbetweensatellite
positionsandvisualpositionsoverthehistoryofthe
passagetousesatellitepositionseffectively.Theonly
waytoobtainthisdataistoplotsatellitepositionsand
comparethesepositionstovisualpositionsthroughout
the harbor passage.
•FathometerOperator:Runthefathometercontin-
uouslyandstationanoperatortomonitorit.Donotrely
onaudiblealarmstokeyyourattentiontothiscritically
importantpilotingtool.Thefathometeroperatormust
knowthewarninganddangersoundingsforthearea
thevesselistransiting.Mostfathometerscandisplay
eithertotaldepthofwaterordepthunderthekeel.Set
thefathometertodisplaydepthunderthekeel.The
navigatormustcheckthesoundingateachfixand
comparethatvaluetothechartedsounding.A
discrepancybetweenthesevaluesiscausefor
immediateactiontotakeanotherfixandcheckthe
ship’s position.
810. Harbor Approach (Inbound Vessels Only)
Thepilotingteammustmakethetransitionfromcoastal
navigationtopilotingsmoothlyasthevesselapproaches
restrictedwaters.Thereisnorigiddemarcationbetween
coastalnavigationandpiloting.OftenvisualNAVAIDSare
visiblemilesfromshorewhereLoranandGPSareeasierto
use.Thenavigatorshouldtakeadvantageofthisoverlap
whenapproachingtheharbor.PlottingLoran,GPS,and
visualfixesconcurrentlyensuresthatthepilotingteamhas
correctlyidentifiedNAVAIDSandthatthedifferenttypesof
systemsareinagreement.Oncethevesseliscloseenoughto
theshoresuchthatsufficientNAVAIDS(atleastthreewith
sufficientbearingspread)becomevisible,thenavigator
shouldordervisualbearingsonlyfortheprimaryplotand
shiftallotherfixestothesecondaryplot,unlessthedecision
hasbeenmadetoproceedwithECDISastheprimary
system.
Takeadvantageofthecoastalnavigationandpiloting
overlaptoshortenthefixintervalgradually.Thenavigator
mustusehisjudgmentinadjustingfixintervals.Iftheship
issteaminginbounddirectlytowardstheshore,setafix
intervalsuchthattwofixintervalsliebetweenthevessel
andthenearestdanger.Uponenteringrestrictedwaters,the
pilotingteamshouldbeplottingvisualfixesatthreeminute
intervals.
CommercialvesselswithGPSand/orLoranC,
planningtheharbortransitwithapilot,willapproacha
coastdifferently.Thetransitionfromoceantocoastalto
harborapproachnavigationwillproceedasvisualaidsand
radartargetsappearandareplotted.WithGPSorECDIS
operatingandawaypointsetatthepilotstation,onlyafew
fixesarenecessarytoverifythattheGPSpositionis
correct.Oncethepilotisaboard,thecaptain/pilotteammay
elect to navigate visually, depending on the situation.
114PILOTING
TAKING FIXES WHILE PILOTING
Safenavigationwhilepilotingrequiresfrequentfixing
oftheship’sposition.IfECDISistheprimarynavigation
systeminuse,thisprocessisautomatic,andtheroleofthe
navigatoristomonitortheprogressofthevessel,cross-
checkthepositionoccasionally,andbealertforany
indication that the system is not operating optimally.
IfanECSisinuse,itshouldbeconsideredonlya
supplementtothepapernavigationplot,whichlegallymust
stillbemaintained.AslongasthemanualplotandtheECS
plotareinagreement,theECSisavaluabletoolwhich
showsthenavigatorwheretheshipisatanyinstant,nottwo
orthreeminutesagowhenthelastfixwastaken.Itcannot
legallytaketheplaceofthepaperchartandthemanualplot,
butitcanprovideanadditionalmeasureofassurancethat
theshipisinsafewaterandalertthenavigatortoa
developingdangeroussituationbeforethenextroundof
bearings or ranges.
Thenextseveralarticleswilldiscussthethreemajor
manualmethodsusedtofixaship’spositionwhenpiloting:
crossinglinesofposition,copyingsatelliteorLorandata,or
advancingasinglelineofposition.Usingonemethoddoes
notexcludeusingothermethods.Thenavigatormustobtain
asmuchinformationaspossibleandemployasmanyof
these methods as necessary.
811. Types of Fixes
WhiletheintersectionoftwoLOP’sconstitutesafix
underonedefinition,andonlyanestimatedpositionby
another,theprudentnavigatorwillalwaysuseatleastthree
LOP’siftheyareavailable,sothatanerrorisapparentif
theydon’tmeetinapoint.Someofthemostcommonly
used methods of obtaining LOP’s are discussed below:
•FixbyBearings:Thenavigatorcantakeandplotbear-
ingsfromtwoormorechartedobjects.Thisisthemost
commonandoftenthemostaccuratewaytofixaves-
sel’sposition.Bearingsmaybetakendirectlytocharted
objects,ortangentsofpointsofland.SeeFigure811a.
Theintersectionoftheselinesconstitutesafix.Aposi-
tiontakenbybearingstobuoysshouldnotbeconsidered
afix,butanestimatedposition(EP),becausebuoys
swingabouttheirwatchcircleandmaybeoutof
position.
Figure 811a. A fix by two bearing lines.
Figure 811b. A fix by two radar ranges.Figure 811c. Principle of stadimeter operation.
PILOTING115
•FixbyRanges:Thenavigatorcanplotafixconsisting
oftheintersectionoftwoormorerangearcsfromchart-
edobjects.Hecanobtainanobject’srangeinseveral
ways:
1.RadarRanges:SeeFigure811b.Thenavigatormay
takerangestotwofixedobjects.Theintersectionof
therangearcsconstitutesafix.Hecanplotranges
fromanypointontheradarscopewhichhecancor-
relateonhischart.Rememberthattheshorelineof
low-lyinglandmaymovemanyyardsinanareaof
largetidalrange,andswampyareasmaybe
indistinct.
2.StadimeterRanges:Givenaknownheightofa
NAVAID,onecanuseastadimetertodetermineits
range.SeeFigure811cforarepresentationofthe
geometryinvolved.Generally,stadimeterscontaina
heightscaleonwhichissettheheightoftheobject.
Theobserverthendirectshislineofsightthroughthe
stadimetertothebaseoftheobjectbeingobserved.
Finally,headjuststhestadimeter’srangeindexuntil
theobject’stopreflectionis“broughtdown”tothe
visiblehorizon.Readtheobject’srangeofftherange
index.
3.SextantVerticalAngles:Measurethevertical
anglefromthetopoftheNAVAIDtothe
waterlinebelowtheNAVAID.EnterTable16to
determinethedistanceoftheNAVAID.The
navigatormustknowtheheightoftheNAVAID
abovesealeveltousethistable;itcanbefoundin
theLight List.
4.SonarRanges:Ifthevesselisequippedwithasonar
suite,thenavigatorcanusesonarechoesto
determinerangestochartedunderwaterobjects.It
maytakesometrialanderrortosettheactive
signalstrengthatavaluethatwillgiveastrong
returnandstillnotcauseexcessivereverberation.
Checklocalharborrestrictionsonenergizing
activesonar.Avoidactivesonartransmissionsin
the vicinity of divers.
•FixbyBearingandRange:Thisisahybridfixof
LOP’sfromabearingandrangetoasingleobject.The
radaristheonlyinstrumentthatcangivesimultaneous
rangeandbearinginformationtothesameobject.(A
sonarsystemcanalsoprovidebearingandrangeinfor-
mation,butsonarbearingsarefartooinaccuratetouse
inpiloting.)Therefore,withtheradar,thenavigator
canobtainaninstantaneousfixfromonlyoneNA-
VAID.ThisuniquefixisshowninFigure811d.This
makestheradaranextremelyusefultoolforthepilot-
ingteam.Theradar’scharacteristicsmakeitmuch
moreaccuratedeterminingrangethandetermining
bearing;therefore,tworadarrangesarepreferabletoa
radar range and bearing.
•FixbyRangeLineandDistance:Whenthevessel
comesinlinewitharange,plotthebearingtotherange
(whilecheckingcompasserrorinthebargain)andcross
thisLOPwithadistancefromanotherNAVAID.Figure
811e shows this fix.
812. The Running Fix
WhenonlyoneNAVAIDisavailablefromwhichto
obtainbearings,useatechniqueknownastherunningfix.
Use the following method:
1.Plot a bearing to a NAVAID (LOP 1).
2.PlotasecondbearingtoaNAVAID(eitherthesame
NAVAIDoradifferentone)atalatertime(LOP2).
3.AdvanceLOP1tothetimewhenLOP2wastaken.
4.TheintersectionofLOP2andtheadvancedLOP1
constitute the running fix.
Figure 811d. A fix by range and bearing of a single
object.
Figure 811e. A fix by a range and distance.
116PILOTING
Figure812arepresentsashipproceedingoncourse
020°,speed15knots.At1505,theplotterplotsanLOP
toalighthousebearing310°.Theshipcanbeatanypoint
on this 1505 LOP. Some possible points are represented
aspointsA,B,C,D,andEinFigure812a.Tenminuteslater
theshipwillhavetraveled2.5milesindirection020°.Ifthe
shipwasatAat1505,itwillbeatA'at1515.However,ifthe
positionat1505wasB,thepositionat1515willbeB'.A
similarrelationshipexistsbetweenCandC',DandD',Eand
E'.Thus,ifanypointontheoriginalLOPismovedadistance
equaltothedistanceruninthedirectionofthemotion,aline
throughthispointparalleltotheoriginallineofposition
representsallpossiblepositionsoftheshipatthelatertime.
Thisprocessiscalledadvancingalineofposition.Movinga
linebacktoanearliertimeiscalledretiringalineofposition.
Whenadvancingalineofposition,accountforcourse
changes,speedchanges,andsetanddriftbetweenthetwo
bearinglines.ThreemethodsofadvancinganLOParedis-
cussed below:
Method1:SeeFigure812b.Toadvancethe1924LOPto
1942,firstapplythebestestimateofsetanddrifttothe1942
DRpositionandlabeltheresultingpositionpointB.Then,
measurethedistancebetweenthedeadreckoningpositionat
1924(pointA)andpointB.AdvancetheLOPadistanceequal
tothedistancebetweenpointsAandB.NotethatLOPA'B'is
in the same direction as line AB.
Method2:SeeFigure812c.AdvancetheNAVAIDS
positiononthechartforthecourseanddistancetraveledbythe
vesselanddrawthelineofpositionfromtheNAVAIDS
advancedposition.Thisisthemostsatisfactorymethodfor
advancing a circle of position.
Figure 812a. Advancing a line of position.
Figure812b.Advancingalineofpositionwithachangein
course and speed, allowing for set and drift.
Figure 812c. Advancing a circle of position.
PILOTING117
Method3:SeeFigure812d.Toadvancethe1505LOP
to1527,firstdrawacorrectionlinefromthe1505DR
positiontothe1505LOP.Next,applyasetanddrift
correctiontothe1527DRposition.Thisresultsina1527
estimatedposition(EP).Then,drawfromthe1527EPa
correctionlineofthesamelengthanddirectionastheone
drawnfromthe1505DRtothe1505LOP.Finally,parallel
the1505bearingtotheendofthecorrectionlineasshown.
Labelanadvancedlineofpositionwithboththetime
of observation and the time to which the line is adjusted.
Figure812ethroughFigure812gdemonstratethree
runningfixes.Figure812eillustratesthecaseofobtain-
ingarunningfixwithnochangeincourseorspeed
betweentakingtwobearingsonthesameNAVAID.Fig-
ure812fillustratesarunningfixwithchangesina
vessel’scourseandspeedbetweentakingtwobearings
ontwodifferentobjects.Finally,Figure812gillustrates
arunningfixobtainedbyadvancingrangecirclesofpo-
sition using the second method discussed above.
PILOTING PROCEDURES
Theprevioussectiondiscussedthemethodsforfixing
theship’sposition.Thissectiondiscussesintegratingthe
manualfixmethodsdiscussedabove,andtheuseofthe
fathometer,intoapilotingprocedure.Thenavigatormust
develophispilotingproceduretomeetseveral
requirements.Hemustobtainenoughinformationtofixthe
positionofthevesselwithoutquestion.Hemustalsoplot
andevaluatethisinformation.Finally,hemustrelayhis
evaluationsandrecommendationstothevessel’sconning
officer.Thissectionexaminessomeconsiderationsto
ensurethenavigatoraccomplishesalltheserequirements
quicklyandeffectively.Ofcourse,ifECDISistheprimary
plot,manualmethodsasdiscussedhereareforbackupuse.
813. Fix Type and Fix Interval
Thepreferredpilotingfixistakenfromvisualbearings
fromchartedfixedNAVAIDS.Plotvisualbearingsonthe
primaryplotandplotallotherfixesonthesecondaryplot.If
poorvisibilityobscuresvisualNAVAIDS,shifttoradar
pilotingontheprimaryplot.Ifneithervisualorradarpiloting
isavailable,considerstandingoffuntilthevisibilityimproves.
Theintervalbetweenfixesinrestrictedwatersshould
usuallynotexceedthreeminutes.Settingthefixintervalat
threeminutesoptimizesthenavigator’sabilitytoassimilate
andevaluateallavailableinformation.Hemustrelateitto
chartednavigationalhazardsandtohisvessel’sintendedtrack.
Itshouldtakeawelltrainedplottingteamnomorethan30
secondstomeasure,record,andplotthreebearingstothree
separateNAVAIDS.Thenavigatorshouldspendthemajority
ofthefixintervaltimeinterpretingtheinformation,evaluating
thenavigationalsituation,andmakingrecommendationstothe
conning officer.
Ifthreeminutesgoesbywithoutafix,informthe
captainandtrytoplotafixassoonaspossible.Ifthedelay
wascausedbyalossofvisibility,shifttoradarpiloting.If
thedelaywascausedbyplottingerror,takeanotherfix.If
thenavigatorcannotgetafixdownontheplotforseveral
moreminutes,considerslowingorstoppingtheshipuntil
itspositioncanbefixed.Nevercontinueapassagethrough
Figure812d.Advancingalineofpositionbyitsrelationto
the dead reckoning.
Figure 812e. A running fix by two bearings on the same
object.
118PILOTING
restricted waters if the vessel’s position is uncertain.
Thesecondaryplotsupervisorshouldmaintainthe
samefixintervalastheprimaryplot.Usually,thismeanshe
shouldplotaradarfixeverythreeminutes.Heshouldplot
otherfixsources(LoranandGPSfixes,forexample)atan
intervalsufficientformakingmeaningfulcomparisons
betweenfixsources.Everythirdfixinterval,heshouldpass
aradarfixtotheprimaryplotforcomparisonwiththevisual
fix.Heshouldinformthenavigatorhowwellallthefix
sources plotted on the secondary plot are tracking.
814. The Piloting Routine
Followingacyclicroutineensuresthetimelyand
efficientprocessingofdataandformsasmoothly
functioningpilotingteam.Itquicklyyieldstheinformation
whichthenavigatorneedstomakeinformedrecommen-
dations to the conning officer and captain.
Repeatthisroutineateachfixintervalbeginningwhen
theshipgetsunderwayuntilitclearstheharbor(outbound)
orwhentheshipenterstheharboruntilitismoored
(inbound).
The routine consists of the following steps:
1.Take, plot and label a fix.
2.Calculate set and drift from the DR position.
3.ResettheDRfromthefixandDRtwofixesahead.
•PlottingtheFix:Thisinvolvescoordinationbetween
thenavigator,bearingtaker(s),recorder,andplotter.
Figure 812f. A running fix with a change of course and speed between observations on separate landmarks.
Figure 812g. A running fix by two circles of position.
PILOTING119
ThenavigatorwillcallforeachfixattheDRtime.
Thebearingtakermustmeasurehisbearingsas
quicklyaspossible,beambearingsfirst,foreandaft
last,onthenavigator’smark.Therecorderwillwrite
thebearingsinthebook,andtheplotterwillplotthem
immediately.
•LabelingtheFix:Theplottershouldclearlymarka
visualfixwithacircleoranelectronicfixwitha
triangle.Clearlylabelthetimeofeachfix.Avisual
runningfixshouldbecircled,marked“RFix”and
labeledwiththetimeofthesecondLOP.Keepthe
chart neat and uncluttered when labeling fixes.
•DeadReckoningTwoFixIntervalsAhead:After
labelingthefix,theplottershoulddeadreckonthefix
positionaheadtwofixintervals.Thenavigatorshould
carefullychecktheareamarkedbythisDRforany
navigationalhazards.Iftheshipisapproachingaturn,
update the turn bearing as discussed in Article 802.
•CalculateSetandDriftatEveryFix:Calculatingset
anddriftiscoveredinChapter7.Calculatethesevalues
ateveryfixandinformthecaptainandconningofficer.
Comparetheactualvaluesofsetanddriftwiththe
predictedvaluesfromthecurrentgraphdiscussedin
Article804.Evaluatehowthecurrentisaffectingthe
vessel’spositioninrelationtothetrackandrecommend
coursesandspeedstoregaintheplannedtrack.Because
thenavigatorcandeterminesetanddriftonlywhen
comparingfixesandDR’splottedforthesametime,
takefixesexactlyatthetimesforwhichaDRhasbeen
plotted.Repeatthisroutineateachfixinterval
beginningwhentheshipgetsunderwayuntilitclears
theharbor(outbound)orwhentheshipentersthe
harbor until she is moored (inbound).
•PilotingRoutineWhenTurning:Modifythecyclic
routineslightlywhenapproachingaturn.Adjustthe
fixintervalsothattheplottingteamhasafixplotted
approximatelyoneminutebeforeascheduledturn.
Thisgivesthenavigatorsufficienttimetoevaluate
thepositioninrelationtotheplannedtrack,DRahead
totheslidebartodetermineanewturnbearing,relay
thenewturnbearingtotheconningofficer,andthen
monitor the turn bearing to mark the turn.
Approximately30secondsbeforethetimetoturn,
trainthealidadeontheturnbearingNAVAID.Watchthe
bearingoftheNAVAIDapproachtheturnbearing.About
1°awayfromtheturnbearing,announcetotheconning
officer:“Standbytoturn.”Slightlybeforetheturnbearing
isindicated,reporttotheconningofficer:“Marktheturn.”
Makethisreportslightlybeforethebearingisreached
becauseittakestheconningofficerafiniteamountoftime
toacknowledgethereportandorderthehelmsmantoput
overtherudder.Additionally,ittakesafiniteamountof
timeforthehelmsmantoturntherudderandfortheshipto
starttoturn.Ifthenavigatorwaitsuntiltheturnbearingis
indicated to report the turn, the ship will turn too late.
Oncetheshipissteadyonthenewcourse,immediately
takeanotherfixtoevaluatethevessel’spositioninrelation
tothetrack.Iftheshipisnotonthetrackaftertheturn,
calculateandrecommendacoursetotheconningofficerto
regain the track.
815. Using the Fathometer
Usethefathometertodeterminewhetherthedepthof
waterunderthekeelissufficienttopreventtheshipfrom
groundingandtochecktheactualwaterdepthwiththe
chartedwaterdepthatthefixposition.Thenavigatormust
comparethechartedsoundingateveryfixpositionwiththe
fathometerreadingandreporttothecaptainanydiscrep-
ancies.Takingcontinuoussoundingsinrestrictedwatersis
mandatory.
Seethediscussionofcalculatingthewarninganddanger
soundingsinArticle802.Ifthewarningsoundingisreceived,
thenslowtheship,fixtheship’spositionmorefrequently,and
proceedwithextremecaution.Ascertainimmediatelywhere
theshipisinthechannel;iftheminimumexpectedsounding
wasnotedcorrectly,thewarningsoundingindicatesthevessel
maybeleavingthechannelandstandingintoshoalwater.
Notify the vessel’s captain and conning officer immediately.
Ifthedangersoundingisreceived,takeimmediateaction
togetthevesselbacktodeepwater.Reversetheenginesand
stopthevessel’sforwardmovement.Turninthedirectionof
thedeepestwaterbeforethevessellosessteerageway.
Considerdroppingtheanchortopreventtheshipfromdrifting
aground.Thedangersoundingindicatesthattheshiphasleft
thechannelandisstandingintoimmediatedanger.Itrequires
immediatecorrectiveactionbytheship’sconningofficer,
navigator, and captain to avoid disaster.
Manyunderwaterfeaturesarepoorlysurveyed.Ifa
fathometertraceofadistinctunderwaterfeaturecanbe
obtainedalongwithaccuratepositioninformation,sendthe
fathometertraceandrelatednavigationaldatatoNIMAfor
entry into the Digital Bathymetric Data Base.
PILOTING TO AN ANCHORAGE
816. Choosing an Anchorage
MostU.S.Navyvesselsreceiveinstructionsintheir
movementordersregardingthechoiceofanchorage.
Merchantshipsareoftendirectedtospecificanchoragesby
harborauthorities.However,lackingspecificguidance,the
marinershouldchoosehisanchoringpositionsusingthe
following criteria:
120PILOTING
•DepthofWater:Chooseanareathatwillprovide
sufficientdepthofwaterthroughanentirerangeof
tides.Watertooshallowwillcausetheshiptogo
aground,andwatertoodeepwillallowtheanchorto
drag.
•TypeofBottom:Choosethebottomthatwillbest
holdtheanchor.Avoidrockybottomsandselect
sandy or muddy bottoms if they are available.
•ProximitytonavigationalHazards:Choosean
anchorageasfarawayaspossiblefromknown
navigational hazards.
•ProximitytoAdjacentShips:Anchorwellaway
fromadjacentvessels;ensurethatanothervesselwill
notswingoveryourownanchoronacurrentorwind
shift.
•ProximitytoHarborTrafficLanes:Anchorclear
oftrafficlanesandensurethatthevesselwillnot
swing into the channel on a current or wind shift.
•Weather:Chooseanareawiththeweakestwinds
and currents.
•AvailabilityofNAVAIDS:Chooseananchorage
withseveralNAVAIDSavailableformonitoringthe
ship’s position when anchored.
817. Navigational Preparations for Anchoring
Itisusuallybesttofollowanestablishedprocedureto
ensureanaccuratepositioningoftheanchor,evenwhen
anchoringinanopenroadstead.Thefollowingprocedureis
representative. See Figure 817.
Locatetheselectedanchoringpositiononthechart.
Considerlimitationsofland,current,shoals,andotherves-
selswhendeterminingthedirectionofapproach.Where
conditionspermit,maketheapproachheadingintothecur-
rent.Closeobservationofanyotheranchoredvesselswill
providecluesastowhichwaytheshipwilllietoheran-
chor.Ifwindandcurrentarestrongandfromdifferent
directions,shipswilllietotheiranchorsaccordingtothe
balancebetweenthesetwoforcesandthedraftandtrimof
eachship.Differentshipsmaylieatdifferentheadingsin
thesameanchoragedependingonthebalanceofforcesaf-
fecting them.
Figure 817. Anchoring.
PILOTING121
ApproachfromadirectionwithaprominentNAVAID,
preferablyarange,availabledeadaheadtoserveasasteer-
ingguide.Ifpracticable,useastraightapproachofatleast
1200yardstopermitthevesseltosteadyontherequired
course.Drawintheapproachtrack,allowingforadvance
andtransferduringanyturns.InFigure817,thechimney
wasselectedasthissteeringbearing.Aturnrangemayalso
beusedifaradar-prominentobjectcanbefounddirectly
ahead or astern.
Next,drawacirclewiththeselectedpositionofthe
anchorasthecenter,andwitharadiusequaltothe
distancebetweenthehawsepipeandpelorus,alidade,or
periscopeusedformeasuringbearings.Thiscircleis
marked“A”inFigure817.Theintersectionofthiscircle
andtheapproachtrackisthepositionofthevessel’s
bearing-measuringinstrumentatthemomentoflettingthe
anchorgo.SelectaNAVAIDwhichwillbeonthebeam
whenthevesselisatthepointoflettinggotheanchor.This
NAVAIDismarked“FS”inFigure817.Determinewhat
thebearingtothatobjectwillbewhentheshipisatthedrop
pointandmeasurethisbearingtothenearest0.1°T.Label
this bearing as the letting go bearing.
Duringtheapproachtotheanchorage,plotfixesatfre-
quentintervals.Thenavigatormustadvisetheconning
officerofanytendencyofthevesseltodriftfromthede-
siredtrack.Thenavigatormustfrequentlyreporttothe
conningofficerthedistancetogo,permittingadjustmentof
thespeedsothatthevesselwillbedeadinthewaterorhave
veryslightsternwaywhentheanchorisletgo.Toaidinde-
terminingthedistancetothedroppoint,drawandlabela
numberofrangearcsasshowninFigure817representing
distances to go to the drop point.
Atthemomentoflettingtheanchorgo,takeafixand
plotthevessel’sexactpositiononthechart.Thisis
importantintheconstructionoftheswinganddragcircles
discussedbelow.Todrawthesecirclesaccurately,
determinethepositionofthevesselatthetimeoflettinggo
the anchor as accurately as possible.
Veertheanchorchaintoalengthequaltofivetoseven
timesthedepthofwaterattheanchorage.Theexactamount
toveerisafunctionofbothvesseltypeandseverityof
weatherexpectedattheanchorage.Whencalculatingthe
scopeofanchorchaintoveer,takeintoaccountthe
maximum height of tide.
Oncetheshipisanchored,constructtwoseparate
circlesaroundtheship’spositionwhentheanchorwas
dropped.Thesecirclesarecalledtheswingcircleandthe
dragcircle.Usetheswingcircletocheckfornavigational
hazardsandusethedragcircletoensuretheanchoris
holding.
Theswingcircle’sradiusisequaltothesumofthe
ship’slengthandthescopeoftheanchorchainreleased.
Thisrepresentsthemaximumarcthroughwhichashipcan
swingwhileridingatanchoriftheanchorholds.Examine
thisswingcirclecarefullyfornavigationalhazards,
interferingcontacts,andotheranchoredshipping.Usethe
lowestheightoftideexpectedduringtheanchoringperiod
when checking inside the swing circle for shoal water.
Thedragcircle’sradiusequalsthesumofthehawsepipe
topelorusdistanceandthescopeofthechainreleased.Any
bearingtakentocheckonthepositionoftheshipshould,if
theanchorisholding,fallwithinthedragcircle.Ifafixfalls
outsideofthatcircle,thentheanchorisdragging.Ifthe
vesselhasaGPSorLoransystemwithanoff-stationalarm,
set the alarm at the drag circle radius, or slightly more.
Insomecases,thedifferencebetweentheradiiofthe
swinganddragcircleswillbesosmallthat,foragiven
chartscale,therewillbenodifferencebetweenthecircles
whenplotted.Ifthatisthecase,plotonlytheswingcircle
andtreatthatcircleasbothaswingandadragcircle.Onthe
otherhand,ifthereisanappreciabledifferenceinradii
betweenthecircleswhenplotted,plotbothonthechart.
Whichmethodtousefallswithinthesoundjudgmentofthe
navigator.
Whendeterminingiftheanchorisholdingordragging,
themostcrucialperiodisimmediatelyafteranchoring.
Fixesshouldbetakenfrequently,atleasteverythree
minutes,forthefirstthirtyminutesafteranchoring.The
navigatorshouldcarefullyevaluateeachfixtodetermineif
theanchorisholding.Iftheanchorisholding,thenavigator
canthenincreasethefixinterval.Whatintervaltosetfalls
withinthejudgmentofthenavigator,buttheinterval
shouldnotexceed30minutes.IfanECDIS,Loran,orGPS
isavailable,useitsoff-stationalarmfeatureforan
additional safety factor.
NAVIGATIONAL ASPECTS OF SHIP HANDLING
818. Effects Of Banks, Channels, and Shallow Water
Ashipmovingthroughshallowwaterexperiences
pronouncedeffectsfromtheproximityofthenearby
bottom.Similarly,ashipinachannelwillbeaffectedbythe
proximityofthesidesofthechannel.Theseeffectscan
easilycauseerrorsinpilotingwhichleadtogrounding.The
effectsareknownassquat,bankcushion,andbank
suction.Theyaremorefullyexplainedintextson
shiphandling,butcertainnavigationalaspectsarediscussed
below.
Squatiscausedbytheinteractionofthehullofthe
ship,thebottom,andthewaterbetween.Asashipmoves
throughshallowwater,someofthewateritdisplaces
rushesunderthevesseltoriseagainatthestern.Thiscauses
aventurieffect,decreasingupwardpressureonthehull.
Squatmakestheshipsinkdeeperinthewaterthannormal
andslowsthevessel.Thefastertheshipmovesthrough
shallowwater,thegreateristhiseffect;groundingsonboth
chartedandunchartedshoalsandrockshaveoccurred
122PILOTING
becauseofthisphenomenon,whenatreducedspeedthe
shipcouldhavesafelyclearedthedangers.When
navigatinginshallowwater,thenavigatormustreduce
speedtoavoidsquat.Ifbowandsternwavesnearlyperpen-
dicularthedirectionoftravelarenoticed,andthevessel
slowswithnochangeinshaftspeed,squatisoccurring.
Immediatelyslowtheshiptocounterit.Squattingoccursin
deepwateralso,butismorepronouncedanddangerousin
shoalwater.Thelargewavesgeneratedbyasquattingship
also endanger shore facilities and other craft.
Bankcushionistheeffectonashipapproachinga
steepunderwaterbankatanobliqueangle.Aswateris
forcedintothenarrowinggapbetweentheship’sbowand
theshore,ittendstoriseorpileuponthelandwardside,
causing the ship to sheer away from the bank.
Banksuctionoccursatthesternofashipinanarrow
channel.Waterrushingpasttheshiponthelandwardside
exertslessforcethanwaterontheoppositeoropenwater
side.Thiseffectcanactuallybeseenasadifferenceindraft
readingsfromonesideofthevesseltotheother,andis
similartotheventurieffectseeninsquat.Thesternofthe
shipisforcedtowardthebank.Iftheshipgetstooclosetothe
bank,itcanbeforcedsidewaysintoit.Thesameeffect
occurs between two vessels passing close to each other.
Theseeffectsincreaseasspeedincreases.Therefore,in
shallowwaterandnarrowchannels,navigatorsshould
decreasespeedtominimizetheseeffects.Skilledpilotsmay
usetheseeffectstoadvantageinparticularsituations,but
theaveragemariner’sbestchoiceisslowspeedandcareful
attention to piloting.
ADVANCED PILOTING TECHNIQUES
819. Assuming Current Values to Set Safety Margins
for Running Fixes
Currentaffectstheaccuracyofarunningfix.Con-
sider,forexample,thesituationofanunknownhead
current.InFigure819a,ashipisproceedingalonga
coast,oncourse250°speed12knots.At0920lightA
bears190°,andat0930itbears143°.Iftheearlierbear-
inglineisadvancedadistanceof2miles(10minutes
at12knots)inthedirectionofthecourse,therunning
fixisasshownbythesolidlines.However,ifthereisa
headcurrentof2knots,theshipismakinggoodaspeed
ofonly10knots,andin10minuteswilltraveladis-
tanceofonly1
2
/
3
miles.Ifthefirstbearinglineis
advancedthisdistance,asshownbythebrokenline,the
actualpositionoftheshipisatB.Thisactualposition
isnearertheshorethantherunningfixactuallyplotted.
Afollowingcurrent,conversely,wouldshowaposition
toofarfromtheshorefromwhichthebearingwas
measured.
Ifthenavigatorassumesafollowingcurrentwhen
advancinghisLOP,theresultingrunningfixwillplot
furtherfromtheNAVAIDthanthevessel’sactualpo-
sition.Conversely,ifheassumesaheadcurrent,the
runningfixwillplotclosertotheNAVAIDthanthe
vessel’sactualposition.Toensureamarginofsafety
whenplottingrunningfixbearingstoaNAVAIDon
shore,alwaysassumethecurrentslowsavessel’sspeed
overground.Thiswillcausetherunningfixtoplot
closer to the shore than the ship’s actual position.
Whentakingthesecondrunningfixbearingfroma
differentobject,maximizethespeedestimateifthesec-
ondobjectisonthesamesideandfartherforward,or
ontheoppositesideandfartheraft,thanthefirstobject
was when observed.
Allofthesesituationsassumethatdangerisonthe
samesideastheobjectobservedfirst.Ifthereiseithera
headorfollowingcurrent,aseriesofrunningfixesbased
uponanumberofbearingsofthesameobjectwillplotina
straightlineparalleltothecourseline,asshowninFigure
819b.Theplottedlinewillbetooclosetotheobjectob-
servedifthereisaheadcurrentandtoofaroutifthereisa
followingcurrent.Theexistenceofthecurrentwillnotbe
apparentunlesstheactualspeedoverthegroundisknown.
Thepositionoftheplottedlinerelativetothedeadreckon-
ing course line is not a reliable guide.
820. Determining Track Made Good by Plotting
Running Fixes
Acurrentobliquetoavessel’scoursewillalsoresultinan
incorrectrunningfixposition.Anobliquecurrentcanbe
detectedbyobservingandplottingseveralbearingsofthe
sameobject.Therunningfixobtainedbyadvancingone
Figure 819a. Effect of a head current on a running fix.
PILOTING123
Figure 819b.A number of running fixes with a following current.
Figure 820a. Detecting the existence of an oblique current, by a series of running fixes.
124PILOTING
bearinglinetothetimeofthenextonewillnotagreewiththe
runningfixobtainedbyadvancinganearlierline.SeeFigure
820a.IfbearingsA,B,andCareobservedatfive-minute
intervals,therunningfixobtainedbyadvancingBtothetime
ofCwillnotbethesameasthatobtainedbyadvancingAto
the time of C, as shown in Figure 820a.
Whateverthecurrent,thenavigatorcandeterminethe
directionofthetrackmadegood(assumingconstant
currentandconstantcourseandspeed).Observeandplot
threebearingsofachartedobjectO.SeeFigure820b.
ThroughOdrawXYinanydirection.Usingaconvenient
scale,determinepointsAandBsothatOAandOBare
proportionaltothetimeintervalsbetweenthefirstand
secondbearingsandthesecondandthirdbearings,respec-
tively.FromAandBdrawlinesparalleltothesecond
bearingline,intersectingthefirstandthirdbearinglinesat
CandD,respectively.ThedirectionofthelinefromCand
D is the track made good.
ThedistanceofthelineCDinFigure820bfromthe
trackisinerrorbyanamountproportionaltotheratioofthe
speedmadegoodtothespeedassumedforthesolution.Ifa
goodfix(notarunningfix)isobtainedatsometimebefore
thefirstbearingfortherunningfix,andthecurrenthasnot
changed,thetrackcanbedeterminedbydrawingaline
fromthefix,inthedirectionofthetrackmadegood.The
intersectionofthetrackwithanyofthebearinglinesisan
actual position.
821. Fix by Distance of an Object by Two Bearings
(Table 18)
Geometricalrelationshipscandefinearunningfix.In
Figure821,thenavigatortakesabearingonNAVAIDD.The
bearingisexpressedasdegreesrightorleftofcourse.Later,at
B,hetakesasecondbearingtoD;similarly,hetakesabearing
atC,whenthelandmarkisbroadonthebeam.Thenavigator
knowstheanglesatA,B,andCandthedistancerunbetween
points.ThevarioustrianglescanbesolvedusingTable18.
Fromthistable,thenavigatorcancalculatethelengthsof
segmentsAD,BD,andCD.Heknowstherangeandbearing;
hecanthenplotanLOP.HecanthenadvancetheseLOP’sto
the time of taking the CD bearing to plot a running fix.
Enterthetablewiththedifferencebetweenthecourse
andfirstbearing(angleBADinFigure821)alongthetop
ofthetableandthedifferencebetweenthecourseandsec-
ondbearing(angleCBD)attheleftofthetable.Foreach
pairofangleslisted,twonumbersaregiven.Tofindthedis-
tancefromthelandmarkatthetimeofthesecondbearing
(BD),multiplythedistancerunbetweenbearings(innauti-
calmiles)bythefirstnumberfromTable18.Tofindthe
distancewhentheobjectisabeam(CD),multiplythedis-
tancerunbetweenAandBbythesecondnumberfromthe
table.Iftherunbetweenbearingsisexactly1mile,thetab-
ulated values are the distances sought.
Example:Ashipissteamingoncourse050°,speed15knots.At
1130 a lighthouse bears 024°, and at 1140 it bears 359°.
Required:
(1)Distance from the light at 1140.
(2)Distance form the light when it is broad on the port beam.
Solution:
(1)Thedifferencebetweenthecourseandthefirstbearing
(050°–24°)is26°,andthedifferencebetweenthecourse
and the second bearing (050° + 360° - 359°) is 51°.
(2)FromTable18,thetwonumbers(factorsare1.04and
0.81, found by interpolation.
(3)Thedistancerunbetweenbearingsis2.5miles(10
minutes at 15 knots).
(4)Thedistancefromthelighthouseatthetimeofthe
second bearing is 2.5× 1.04 = 2.6 miles.
Figure 820b. Determining the track made good.
Figure 821. Triangles involved in aTable 18 running fix.
PILOTING125
(5)Thedistancefromthelighthousewhenitisbroadon
the beam is 2.5× 0.81 = 2.0 miles.
Answer:(1) D 2.6 mi., (2) D 2.0 mi.
Thismethodyieldsaccurateresultsonlyifthehelms-
manhassteeredasteadycourseandthenavigatorusesthe
vessel’s speed over ground.
MINIMIZING ERRORS IN PILOTING
822. Common Errors
Pilotingrequiresathoroughfamiliaritywithprinciples
involved,constantalertness,andjudgment.Astudyof
groundingsrevealsthatthecauseofmostisafailuretouse
orinterpretavailableinformation.Amongthemore
common errors are:
1.Failure to obtain or evaluate soundings
2.Mis-identification of aids to navigation
3.Failure to use available navigational aids effectively
4.Failure to correct charts
5.Failuretoadjustamagneticcompassorkeepa
table of corrections
6.Failure to apply deviation
7.Failure to apply variation
8.Failuretocheckgyroandmagneticcompass
readings regularly
9.Failure to keep a dead reckoning plot
10.Failure to plot new information
11.Failure to properly evaluate information
12.Poor judgment
13.Failuretouseinformationinchartsandnaviga-
tional publications
14.Poor navigation team organization
15.Failure to “keep ahead of the vessel”
16.Failuretohavebackupnavigationalmethodsin
place
17.Failuretorecognizedegradationofelectronically
obtained LOP’s or lat./long. positions
Someoftheerrorslistedabovearemechanicaland
somearemattersofjudgment.Conscientiouslyapplying
theprinciplesandproceduresofthischapterwillgoalong
waytowardseliminatingmanyofthemechanicalerrors.
However,thenavigatormustguardagainstthefeelingthat
infollowingachecklisthehaseliminatedallsourcesof
error.Anavigator’sjudgmentisjustasimportantashis
checklists.
823. Minimizing Errors with a Two Bearing Plot
WhenmeasuringbearingsfromtwoNAVAIDS,the
fixerrorresultingfromanerrorheldconstantforbothob-
servationsisminimizediftheangleofintersectionofthe
bearingsis90°.IftheobserverinFigure823aislocatedat
pointTandthebearingsofabeaconandcupolaareob-
servedandplottedwithouterror,theintersectionofthe
bearinglinesliesonthecircumferenceofacirclepassing
throughthebeacon,cupola,andtheobserver.Withconstant
error,theangulardifferencebetweenthebearingsofthe
beaconandthecupolaisnotaffected.Thus,theangle
formedatpointFbythebearinglinesplottedwithconstant
errorisequaltotheangleformedatpointTbythebearing
linesplottedwithouterror.Fromgeometryitisknownthat
angleshavingtheirapexesonthecircumferenceofacircle
andthataresubtendedbythesamechordareequal.Since
theanglesatpointsTandFareequalandtheanglesaresub-
tendedbythesamechord,theintersectionatpointFlieson
thecircumferenceofacirclepassingthroughthebeacon,
cupola, and the observer.
Assumingonlyconstanterrorintheplot,thedirection
ofdisplacementofthetwo-bearingfixfromthepositionof
theobserverisinaccordancewiththesign(ordirection)of
theconstanterror.However,athirdbearingisrequiredto
determine the direction of the constant error.
Assumingonlyconstanterrorintheplot,thetwo-bear-
ingfixliesonthecircumferenceofthecirclepassing
throughthetwochartedobjectsobservedandtheobserver.
Thefixerror,thelengthofthechordFTinFigure823b,de-
pendsonthemagnitudeoftheconstanterror∈,thedistance
betweenthechartedobjects,andthecosecantoftheangle
of cut, angleθ. In Figure 823b,
where∈isthemagnitudeoftheconstanterror,BCis
thelengthofthechordBC,andθistheangleoftheLOP’s
intersection.
Figure 823a. Two-bearing plot.
The fix errorFT
BCθcsc
2
--------------------==
126PILOTING
Sincethefixerrorisafunctionofthecosecantofthe
angleofintersection,itisleastwhentheangleofintersec-
tionis90°.AsillustratedinFigure823c,theerrorincreases
inaccordancewiththecosecantfunctionastheangleofin-
tersectiondecreases.Theincreaseintheerrorbecomes
quiterapidaftertheangleofintersectionhasdecreasedto
belowabout30°.Withanangleofintersectionof30°,the
fix error is about twice that at 90°.
824. Finding Compass Error by Trial and Error
Ifseveralfixesobtainedbybearingsonthreeobjects
producetrianglesoferrorofaboutthesamesize,there
mightbeaconstanterrorinobservingorplottingthe
bearings.Ifapplyingofaconstanterrortoallbearings
resultsinapinpointfix,applysuchacorrectiontoall
subsequentfixes.Figure824illustratesthistechnique.
Thesolidlinesindicatetheoriginalplot,andthebroken
linesindicateeachlineofpositionmoved3°ina
clockwise direction.
Employthisprocedurecarefully.Attempttofindand
eliminatetheerrorsource.Theerrormaybeinthegyro-
compass,therepeater,orthebearingtransmissionsystem.
Comparetheresultingfixpositionswithasatelliteposition,
aradarposition,orthechartedsounding.Ahighdegreeof
correlationbetweenthesethreeindependentpositioning
systemsandan“adjusted”visualfixisfurtherconfirmation
of a constant bearing error.
TRAINING
825. Piloting Simulators
Civilianpilotingtraininghastraditionallybeena
functionofbothmaritimeacademiesandon-the-job
experience.Thelatterisusuallymorevaluable,because
thereisnosubstituteforexperienceindevelopingjudgment.
Militarypilotingtrainingconsistsofadvanced
correspondencecoursesandformalclassroominstruction
combinedwithdutiesonthebridge.U.S.NavyQuarter-
mastersfrequentlyattendShip’sPilotingandNavigation
(SPAN)trainersasaroutinesegmentofshoresidetraining.
Militaryvesselsingeneralhaveamuchclearerdefinitionof
responsibilities,aswellasmorepeopletocarrythemout,
thancivilianships,sotrainingisgenerallymorethorough
and targeted to specific skills.
Computertechnologyhasmadepossiblethe
developmentofcomputerizedshipsimulators,which
allowpilotingexperiencetobegainedwithoutrisking
accidentsatseaandwithoutincurringunderwayexpenses.
Simulatorsrangefromsimplemicro-computer-based
softwaretoacompletelyequippedship’sbridgewithradar,
enginecontrols,360°horizonviews,programmablesea
motions,andthecapabilitytosimulatealmostanynaviga-
tional situation.
Adifferenttypeofsimulatorconsistsofscalemodels
ofships.Themodels,actuallysmallcraftofabout20-30
feet,havehullformsandpower-to-weightratiossimilarto
varioustypesofships,primarilysupertankers,andthe
operatorpilotsthevesselfromapositionsuchthathisview
isfromthecraft’s“bridge.”Theseareprimarilyusedin
trainingpilotsandmastersindockingmaneuverswith
exceptionally large vessels.
Figure 823b. Two-bearing plot with constant error.
Figure 823c. Error of two-bearing plot.
PILOTING127
Thefirstcomputershipsimulatorscameintouseinthe
late1970s.SeveralyearslatertheU.S.CoastGuardbegan
acceptingalimitedamountofsimulatortimeas“seatime”
forlicensingpurposes.Theycansimulatevirtuallyany
conditionsencounteredatseaorinpilotingwaters,
includingland,aidstonavigation,ice,wind,fog,snow,
rain,andlightning.Thesystemcanalsobeprogrammedto
simulatehydrodynamiceffectssuchasshallowwater,
passing vessels, current, and tugs.
Virtuallyanytypeofvesselcanbesimulated,
includingtankers,bulkers,containerships,tugsandbarges,
yachts,andmilitaryvessels.Similarly,anygivennaviga-
tionalsituationcanbemodeled,includingpassagethrough
anychosenharbor,river,orpassage,convoyoperations,
meeting and passing situations at sea and in harbors.
Simulatorsareusednotonlytotrainmariners,butalso
totestfeasibilityofportandharborplansandvisualaidsto
navigationsystemdesigns.Thisallowspilotsto“navigate”
simulatedshipsthroughsimulatedharborsbefore
constructionbeginstotesttheadequacyofchannels,
turning basins, aids to navigation, and other factors.
Afull-capabilitysimulatorconsistsofaship’sbridge
whichmayhavemotionandnoise/vibrationinputs,a
programmablevisualdisplaysystemwhichprojectsa
simulatedpictureoftheareasurroundingthevesselinboth
daylightandnightmodes,imagegeneratorsforthevarious
inputstothescenariosuchasvideoimagesandradar,a
centraldataprocessor,ahumanfactorsmonitoringsystem
whichmayrecordandvideotapebridgeactivitiesforlater
analysis,andacontrolstationwhereinstructorscontrolthe
entire scenario.
Somesimulatorsarepart-taskinnature,providingspe-
cifictraininginonlyoneaspectofnavigationsuchasradar
navigation, collision avoidance, or night navigation.
Whilethereisnosubstituteforon-the-jobtraining,
simulatorsareextremelycosteffectivesystemswhichcan
berunforafractionofthecostofanactualvessel.Further,
theypermittraineestolearnfrommistakeswithnopossi-
bilityofanaccident,theycanmodelaninfinitevarietyof
scenarios,andtheypermitreplayandreassessmentofeach
maneuver.
Figure 824. Adjusting a fix for constant error.
129
CHAPTER 9
TIDES AND TIDAL CURRENTS
ORIGINS OF TIDES
900. Introduction
Tidesaretheperiodicmotionofthewatersofthesea
duetochangesintheattractiveforcesoftheMoonandSun
upontherotatingEarth.Tidescaneitherhelporhindera
mariner.Ahightidemayprovideenoughdepthtocleara
bar,whilealowtidemayprevententeringorleavinga
harbor.Tidalcurrentmayhelpprogressorhinderit,mayset
theshiptowarddangersorawayfromthem.By
understandingtidesandmakingintelligentuseof
predictionspublishedintideandtidalcurrenttablesand
descriptionsinsailingdirections,thenavigatorcanplanan
expeditious and safe passage through tidal waters.
901. Tide and Current
Theriseandfalloftideisaccompaniedbyhorizontal
movementofthewatercalledtidalcurrent.Itisnecessary
todistinguishclearlybetweentideandtidalcurrent,forthe
relationbetweenthemiscomplexandvariable.Forthesake
ofclaritymarinershaveadoptedthefollowingdefinitions:
Tideistheverticalriseandfallofthewater,andtidal
currentisthehorizontalflow.Thetiderisesandfalls,the
tidalcurrentfloodsandebbs.Thenavigatorisconcerned
withtheamountandtimeofthetide,asitaffectsaccessto
shallowports.Thenavigatorisconcernedwiththetime,
speed,anddirectionofthetidalcurrent,asitwillaffecthis
ship’s position, speed, and course.
Tidesaresuperimposedonnontidalrisingand
fallingwaterlevels,causedbyweather,seismicevents,
orothernaturalforces.Similarly,tidalcurrentsare
superimposeduponnon-tidalcurrentssuchasnormal
river flows, floods, and freshets.
902. Causes of Tides
TheprincipaltidalforcesaregeneratedbytheMoon
andSun.TheMoonisthemaintide-generatingbody.Due
toitsgreaterdistance,theSun’seffectisonly46percentof
theMoon’s.Observedtideswilldifferconsiderablyfrom
thetidespredictedbyequilibriumtheorysincesize,depth,
andconfigurationofthebasinorwaterway,friction,land
masses,inertiaofwatermasses,Coriolisacceleration,and
otherfactorsareneglectedinthistheory.Nevertheless,
equilibriumtheoryissufficienttodescribethemagnitude
anddistributionofthemaintide-generatingforcesacross
the surface of the Earth.
Newton’suniversallawofgravitationgovernsboththe
orbitsofcelestialbodiesandthetide-generatingforces
whichoccuronthem.Theforceofgravitationalattraction
between any two masses, m
1
and m
2
, is given by:
wheredisthedistancebetweenthetwomasses,andGisa
constantwhichdependsupontheunitsemployed.Thislaw
assumesthatm
1
andm
2
arepointmasses.Newtonwasable
toshowthathomogeneousspherescouldbetreatedas
point masseswhendeterminingtheir orbits.
F
Gm
1
m
2
d
2
--------------------=
Figure 902a. Earth-Moon barycenter.
130TIDES AND TIDAL CURRENTS
However,whencomputingdifferentialgravitationalforces,
theactualdimensionsofthemassesmustbetakeninto
account.
Usingthelawofgravitation,itisfoundthattheorbits
oftwopointmassesareconicsectionsaboutthe
barycenterofthetwomasses.Ifeitheroneorbothofthe
massesarehomogeneousspheresinsteadofpointmasses,
theorbitsarethesameastheorbitswhichwouldresultifall
ofthemassofthespherewereconcentratedatapointatthe
centerofthesphere.InthecaseoftheEarth-Moonsystem,
boththeEarthandtheMoondescribeellipticalorbitsabout
theirbarycenterifbothbodiesareassumedtobe
homogeneousspheresandthegravitationalforcesofthe
Sunandotherplanetsareneglected.TheEarth-Moon
barycenterislocated74/100ofthedistancefromthecenter
oftheEarthtoitssurface,alongthelineconnectingthe
Earth’s and Moon’s centers. See Figure 902a.
ThusthecenterofmassoftheEarthdescribesavery
smallellipseabouttheEarth-Moonbarycenter,whilethe
centerofmassoftheMoondescribesamuchlargerellipse
aboutthesamebarycenter.Ifthegravitationalforcesofthe
otherbodiesofthesolarsystemareneglected,Newton’s
lawofgravitationalsopredictsthattheEarth-Moon
barycenterwilldescribeanorbitwhichisapproximately
ellipticalaboutthebarycenteroftheSun-Earth-Moon
system.ThisbarycentricpointliesinsidetheSun.See
Figure 902b.
903. The Earth-Moon-Sun System
Thefundamentaltide-generatingforceontheEarthhas
twointeractivebutdistinctcomponents.Thetide-generat-
ingforcesaredifferentialforcesbetweenthegravitational
attractionofthebodies(Earth-SunandEarth-Moon)and
thecentrifugalforcesontheEarthproducedbytheEarth’s
orbitaroundtheSunandtheMoon’sorbitaroundtheEarth.
Newton’sLawofGravitationandhisSecondLawofMo-
tioncanbecombinedtodevelopformulationsforthe
differentialforceatanypointontheEarth,asthedirection
andmagnitudearedependentonwhereyouareonthe
Earth’ssurface.Asaresultofthesedifferentialforces,the
tidegeneratingforcesF
dm
(Moon)andF
ds
(Sun)arein-
verselyproportionaltothecubeofthedistancebetweenthe
bodies, where:
whereM
m
isthemassoftheMoonandM
s
isthemassof
theSun,R
e
istheradiusoftheEarthanddisthedistanceto
theMoonorSun.Thisexplainswhythetide-generating
forceoftheSunisonly46/100ofthetide-generatingforce
oftheMoon.EventhoughtheSunismuchmoremassive,
it is also much farther away.
UsingNewton’ssecondlawofmotion,wecancalcu-
latethedifferentialforcesgeneratedbytheMoonandthe
SunaffectinganypointontheEarth.Theeasiestcalcula-
tionisforthepointdirectlybelowtheMoon,knownasthe
sublunarpoint,andthepointontheEarthexactlyoppo-
site,knownastheantipode.Similarcalculationsaredone
for the Sun.
IfweassumethattheentiresurfaceoftheEarthiscov-
eredwithauniformlayerofwater,thedifferentialforces
mayberesolvedintovectorsperpendicularandparallelto
thesurfaceoftheEarthtodeterminetheireffect.SeeFigure
903a.
Theperpendicularcomponentschangethemasson
whichtheyareacting,butdonotcontributetothetidalef-
fect.Thehorizontalcomponents,paralleltotheEarth’s
surface,havetheeffectofmovingthewaterinahorizontal
Figure 902b. Orbit of Earth-Moon barycenter (not to scale).
Figure 903a. Differential forces along a great circle
connecting the sublunar point and antipode.
F
dm
GM
m
R
e
d
m
3
---------------------=F
ds
GM
s
R
e
d
s
3
-------------------=;
TIDES AND TIDAL CURRENTS131
directiontowardthesublunarandantipodalpointsuntilan
equilibriumpositionisfound.Thehorizontalcomponents
ofthedifferentialforcesaretheprincipaltide-generating
forces.Thesearealsocalledtractiveforces.Tractiveforc-
esarezeroatthesublunarandantipodalpointsandalong
thegreatcirclehalfwaybetweenthesetwopoints.Tractive
forcesaremaximumalongthesmallcircleslocated45°
fromthesublunarpointandtheantipode.Figure903b
shows the tractive forces across the surface of the Earth.
Equilibriumwillbereachedwhenabulgeofwaterhas
formedatthesublunarandantipodalpointssuchthatthe
tractiveforcesduetotheMoon’sdifferentialgravitational
forcesonthemassofwatercoveringthesurfaceofthe
EartharejustbalancedbytheEarth’sgravitationalattrac-
tion (Figure 903c).
NowconsidertheeffectoftherotationoftheEarth.If
thedeclinationoftheMoonis0°,thebulgeswilllieonthe
equator.AstheEarthrotates,anobserverattheequatorwill
notethattheMoontransitsapproximatelyevery24hours
and50minutes.Sincetherearetwobulgesofwateronthe
equator,oneatthesublunarpointandtheotherattheanti-
pode,theobserverwillalsoseetwohightidesduringthis
intervalwithonehightideoccurringwhentheMoonis
overheadandanotherhightide12hours25minuteslater
whentheobserverisattheantipode.Hewillalsoexperi-
encealowtidebetweeneachhightide.Thetheoretical
rangeoftheseequilibriumtidesattheequatorwillbeless
than 1 meter.
Intheory,theheightsofthetwohightidesshouldbe
equalattheequator.Atpointsnorthorsouthoftheequator,
anobserverwouldstillexperiencetwohighandtwolow
tides,buttheheightsofthehightideswouldnotbeasgreat
astheyareattheequator.Theeffectsofthedeclinationof
theMoonareshowninFigure903d,forthreecases,A,B,
and C.
A.WhentheMoonisontheplaneoftheequator,the
forcesareequalinmagnitudeatthetwopointson
thesameparalleloflatitudeand180°apartin
longitude.
B.WhentheMoonhasnorthorsouthdeclination,the
forcesareunequalatsuchpointsandtendtocause
aninequalityinthetwohighwatersandthetwo
low waters each day.
C.ObserversatpointsX,Y,andZexperienceone
hightidewhentheMoonisontheirmeridian,then
anotherhightide12hours25minuteslaterwhenat
X',Y',andZ'.Thesecondhightideisthesameat
X'asatX.HightidesatY'andZ'arelowerthan
high tides at Y and Z.
Figure 903b. Tractive forces across the surface of the Earth.
Figure903c.TheoreticalequilibriumconfigurationduetoMoon’sdifferentialgravitationalforces.Onebulgeofthewater
envelope is located at the sublunar point, the other bulge at the antipode.
132TIDES AND TIDAL CURRENTS
Theprecedingdiscussionpertainingtotheeffectsof
theMoonisequallyvalidwhendiscussingtheeffectsof
theSun,takingintoaccountthatthemagnitudeoftheso-
lareffectissmaller.Hence,thetideswillalsovary
accordingtotheSun’sdeclinationanditsvaryingdistance
fromtheEarth.Asecondenvelopeofwaterrepresenting
theequilibriumtidesduetotheSunwouldresemblethe
envelopeshowninFigure903cexceptthattheheightsof
thehightideswouldbesmaller,andthelowtidescorre-
spondinglynotaslow.Thetheoreticaltideatanyplace
representsthecombinationoftheeffectsofboththeMoon
and Sun.
FEATURES OF TIDES
904. General Features
Atmostplacesthetidalchangeoccurstwicedaily.The
tiderisesuntilitreachesamaximumheight,calledhigh
tideorhighwater,andthenfallstoaminimumlevelcalled
low tide orlow water.
Therateofriseandfallisnotuniform.Fromlowwater,
thetidebeginstoriseslowlyatfirst,butatanincreasing
rateuntilitisabouthalfwaytohighwater.Therateofrise
thendecreasesuntilhighwaterisreached,andtherise
ceases.
Thefallingtidebehavesinasimilarmanner.Theperi-
odathighorlowwaterduringwhichthereisnoapparent
changeofleveliscalledstand.Thedifferenceinheightbe-
tween consecutive high and low waters is therange.
Figure904isagraphicalrepresentationoftheriseand
fallofthetideatNewYorkduringa24-hourperiod.The
curve has the general form of a variable sine curve.
905. Types of Tide
Abodyofwaterhasanaturalperiodofoscillation,
dependentuponitsdimensions.Noneoftheoceansisa
singleoscillatingbody;rathereachoneismadeupof
severalseparateoscillatingbasins.Assuchbasinsare
acteduponbythetide-producingforces,somerespond
morereadilytodailyordiurnalforces,otherstosemidi-
urnalforces,andothersalmostequallytoboth.Hence,
tidesareclassifiedasoneofthreetypes,semidiurnal,di-
urnal,ormixed,accordingtothecharacteristicsofthe
tidal pattern.
Figure 903d. Effects of the declination of the Moon.
Figure 904. The rise and fall of the tide at New York,
shown graphically.
TIDES AND TIDAL CURRENTS133
Inthesemidiurnaltide,therearetwohighandtwo
lowwaterseachtidalday,withrelativelysmalldifferences
intherespectivehighsandlows.TidesontheAtlanticcoast
oftheUnitedStatesareofthesemidiurnaltype,whichisil-
lustratedinFigure905abythetidecurveforBoston
Harbor.
Inthediurnaltide,onlyasinglehighandsinglelow
wateroccureachtidalday.Tidesofthediurnaltypeoccur
alongthenorthernshoreoftheGulfofMexico,intheJava
Sea,theGulfofTonkin,andinafewotherlocalities.The
tidecurveforPei-Hai,China,illustratedinFigure905b,is
an example of the diurnal type.
Inthemixedtide,thediurnalandsemidiurnaloscilla-
tionsarebothimportantfactorsandthetideischaracterized
byalargeinequalityinthehighwaterheights,lowwater
heights,orinboth.Thereareusuallytwohighandtwolow
waterseachday,butoccasionallythetidemaybecomedi-
urnal.SuchtidesareprevalentalongthePacificcoastofthe
UnitedStatesandinmanyotherpartsoftheworld.Exam-
plesofmixedtypesoftideareshowninFigure905c.At
LosAngeles,itistypicalthattheinequalitiesinthehigh
andlowwatersareaboutthesame.AtSeattlethegreaterin-
equalitiesaretypicallyinthelowwaters,whileatHonolulu
it is the high waters that have the greater inequalities.
906. Solar Tide
Thenaturalperiodofoscillationofabodyofwater
mayaccentuateeitherthesolarorthelunartidaloscilla-
tions.ThoughasageneralrulethetidesfollowtheMoon,
therelativeimportanceofthesolareffectvariesindifferent
areas.Thereareafewplaces,primarilyintheSouthPacific
andtheIndonesianareas,wherethesolaroscillationisthe
moreimportant,andatthoseplacesthehighandlowwaters
occurataboutthesametimeeachday.AtPortAdelaide,
Australiathesolarandlunarsemidiurnaloscillationsare
equal and nullify one another at neaps.
907. Special Tidal Effects
Asawaveentersshallowwater,itsspeedisdecreased.
Sincethetroughisshallowerthanthecrest,itisretarded
Figure 905a. Semidiurnal type of tide.Figure 905b. Diurnal tide.
Figure 905c. Mixed tide.
134TIDES AND TIDAL CURRENTS
more,resultinginasteepeningofthewavefront.Inafew
estuaries,theadvanceofthelowwatertroughissomuch
retardedthatthecrestoftherisingtideovertakesthelow,
andadvancesupstreamasabreakingwavecalledabore.
Boresthatarelargeanddangerousattimesoflargetidal
rangesmaybemereripplesatthosetimesofthemonth
whentherangeissmall.ExamplesoccurinthePetitcodiac
RiverintheBayofFundy,andatHaining,China,inthe
TsientangKaing.Thetidetablesindicatewherebores
occur.
Otherspecialfeaturesarethedoublelowwater(asat
HoekVanHolland)andthedoublehighwater(asat
Southampton,England).Atsuchplacesthereisoftena
slightfallorriseinthemiddleofthehighorlowwaterpe-
riod.Thepracticaleffectistocreatealongerperiodofstand
athighorlowtide.Thetidetableslisttheseandotherpecu-
liarities where they occur.
908. Variations in Range
Thoughthetideataparticularplacecanbeclassified
astotype,itexhibitsmanyvariationsduringthemonth
(Figure908a).Therangeofthetidevariesaccordingtothe
intensityofthetide-producingforces,thoughtheremaybe
alagofadayortwobetweenaparticularastronomiccause
and the tidal effect.
Thecombinedlunar-solareffectisobtainedbyadding
theMoon’stractiveforcesvectoriallytotheSun’strac-
tiveforces.Theresultanttidalbulgewillbepredominantly
lunarwithmodifyingsolareffectsuponboththeheightof
thetideandthedirectionofthetidalbulge.Specialcasesof
interestoccurduringthetimesofnewandfullMoon(Fig-
ure908b).WiththeEarth,Moon,andSunlying
approximatelyonthesameline,thetractiveforcesofthe
SunareactinginthesamedirectionastheMoon’stractive
forces(modifiedbydeclinationeffects).Theresultanttides
arecalledspringtides,whoserangesaregreaterthan
average.
Betweenthespringtides,theMoonisatfirstandthird
quarters.Atthosetimes,thetractiveforcesoftheSunare
actingatapproximatelyrightanglestotheMoon’stractive
forces.Theresultsaretidescalledneaptides,whoseranges
are less than average.
WiththeMooninpositionsbetweenquadratureand
neworfull,theeffectoftheSunistocausethetidalbulge
toeitherlagorprecedetheMoon(Figure908c).Theseef-
fects are calledpriming andlagging the tides.
Thus,whentheMoonisatthepointinitsorbitnearest
theEarth(atperigee),thelunarsemidiurnalrangeis
increasedandperigeantidesoccur.WhentheMoonis
farthestfromtheEarth(atapogee),thesmallerapogean
tidesoccur.WhentheMoonandSunareinlineandpulling
together,asatnewandfullMoon,springtidesoccur(the
termspringhasnothingtodowiththeseasonofyear);
whentheMoonandSunopposeeachother,asatthe
quadratures,thesmallerneaptidesoccur.Whencertainof
thesephenomenacoincide,perigeanspringtidesand
apogean neap tides occur.
Thesearevariationsinthesemidiurnalportionofthe
tide.VariationsinthediurnalportionoccurastheMoon
andSunchangedeclination.WhentheMoonisatits
maximumsemi-monthlydeclination(eithernorthorsouth),
tropictidesoccurinwhichthediurnaleffectisata
maximum.Whenitcrossestheequator,thediurnaleffectis
a minimum andequatorial tides occur.
Whentherangeoftideisincreased,asatspringtides,
thereismorewateravailableonlyathightide;atlowtide
thereisless,forthehighwatersrisehigherandthelowwa-
tersfallloweratthesetimes.Thereismorewateratneap
lowwaterthanatspringlowwater.Withtropictides,there
isusuallymoredepthatonelowwaterduringthedaythan
attheother.Whileitisdesirabletoknowthemeaningsof
theseterms,thebestwayofdeterminingtheheightofthe
tideatanyplaceandtimeistoexaminethetidepredictions
fortheplaceasgiveninthetidetables,whichtakeallthese
effects into account.
909. Tidal Cycles
Tidaloscillationsgothroughanumberofcycles.The
shortestcycle,completedinabout12hoursand25minutes
forasemidiurnaltide,extendsfromanyphaseofthetideto
thenextrecurrenceofthesamephase.Duringalunarday
(averaging24hoursand50minutes)therearetwohighs
andtwolows(twooftheshortercycles)forasemidiurnal
tide.TheMoonrevolvesaroundtheEarthwithrespectto
theSuninasynodicalmonthofabout291/2days,
commonlycalledthelunarmonth.Theeffectofthephase
variationiscompletedinone-halfofasynodicalmonthor
about2weeksastheMoonvariesfromnewtofullorfull
to new.
TheeffectoftheMoon’sdeclinationisalsorepeatedin
one-halfofatropicalmonthof271/3days,oraboutevery
2weeks.ThecycleinvolvingtheMoon’sdistancerequires
ananomalisticmonthofabout271/2days.TheSun’s
declinationanddistancecyclesarerespectivelyahalfyear
and a year in length.
Animportantlunarcycle,calledthenodalperiodor
Metoniccycle(afterGreekphilosopherMeton,fifth
centuryBC,whodiscoveredthephenomenon)is18.6years
(usuallyexpressedinroundfiguresas19years).Foratidal
value,particularlyarange,tobeconsideredatruemean,it
mustbeeitherbaseduponobservationsextendedoverthis
periodoftime,oradjustedtotakeaccountofvariations
known to occur during the nodal period.
ThenodalperiodistheresultofaxisoftheMoon’sro-
tationbeingtilted5degreeswithrespecttotheaxisofthe
Earth’srotation.SincetheEarth’saxisistilted23.5degrees
withrespecttotheplaneofitsrevolutionaroundthesun,
thecombinedeffectisthattheMoon’sdeclinationvaries
from28.5degreesto18.5degreesinacyclelasting18.6
years.Forpracticalpurposes,thenodalperiodcanbecon-
TIDES AND TIDAL CURRENTS135
Figure 908a. Monthly tidal variations at various places.
136TIDES AND TIDAL CURRENTS
sideredasthetimebetweentheSunandMoonappearingin
precisely the same relative positions in the sky.
910. Time of Tide
Sincethelunartide-producingforcehasthegreatest
effectinproducingtidesatmostplaces,thetides“follow
theMoon.”BecausetheEarthrotates,highwaterlags
behindbothupperandlowermeridianpassageofthe
Moon.Thetidalday,whichisalsothelunarday,isthe
timebetweenconsecutivetransitsoftheMoon,or24hours
and50minutesontheaverage.Wherethetideislargely
semidiurnalintype,thelunitidalinterval(theinterval
betweentheMoon’smeridiantransitandaparticularphase
oftide)isfairlyconstantthroughoutthemonth,varying
somewhatwiththetidalcycles.Therearemanyplaces,
however,wheresolarordiurnaloscillationsareeffectivein
upsettingthisrelationship.Theintervalgenerallygivenis
theaverageelapsedtimefromthemeridiantransit(upperor
lower)oftheMoonuntilthenexthightide.Thismaybe
calledmeanhighwaterlunitidalintervalorcorrected
(ormean)establishment.Thecommonestablishmentis
theaverageintervalondaysoffullornewMoon,and
approximates the mean high water lunitidal interval.
Intheocean,thetidemaybeinthenatureofa
progressivewavewiththecrestmovingforward,astationary
orstandingwavewhichoscillatesinaseesawfashion,ora
combinationofthetwo.Consequently,cautionshouldbe
usedininferringthetimeoftideataplacefromtidaldatafor
nearbyplaces.Inariverorestuary,thetideentersfromthe
seaandisusuallysentupstreamasaprogressivewavesothat
thetideoccursprogressivelylateratvariousplacesupstream.
TIDAL DATUMS
911. Low Water Datums
Atidaldatumisagivenaveragetidelevelfromwhich
heightsoftidesandoverheadclearancesaremeasured.Itis
averticaldatum,butisnotthesameasverticalgeodeticda-
tum,whichisamathematicalquantitydevelopedaspartof
ageodeticsystemusedforhorizontalpositioning.Thereare
anumberoftidallevelsofreferencethatareimportantto
the mariner.See Figure 911.
Themostimportantlevelofreferenceisthesounding
datumshownoncharts.Thesoundingdatumissometimes
referredtoasthereferenceplanetodistinguishitfromver-
ticalgeodeticdatum.Sincethetiderisesandfalls
continuallywhilesoundingsarebeingtakenduringahy-
Figure908b.(A)Springtidesoccurattimesofnewandfull
Moon.Rangeoftideisgreaterthanaveragesincesolar
andlunartractiveforcesactinsamedirection.(B)Neap
tiesoccurattimesoffirstandthirdquarters.Rangeoftide
islessthanaveragesincesolarandlunartractiveforces
act at right angles.
Figure 908c. Priming and lagging the tides.
TIDES AND TIDAL CURRENTS137
drographicsurvey,thetideisrecordedduringthesurveyso
thatsoundingstakenatallstagesofthetidecanbereduced
toacommonsoundingdatum.Soundingsonchartsshow
depthsbelowaselectedlowwaterdatum(occasionally
meansealevel),andtidepredictionsintidetablesshow
heightsaboveandbelowthesamelevel.Thedepthofwater
availableatanytimeisobtainedbyaddingalgebraicallythe
heightofthetideatthetimeinquestiontothecharted
depth.
Byinternationalagreement,thelevelusedaschart
datumshouldbelowenoughsothatlowwatersdonotfall
veryfarbelowit.Atmostplaces,thelevelusedisone
determinedfromameanofanumberoflowwaters(usually
overa19yearperiod);therefore,somelowwaterscanbe
expectedtofallbelowit.Thefollowingaresomeofthe
datums in general use.
Meanlowwater(MLW)istheaverageheightofall
lowwatersatagivenplace.Abouthalfofthelowwaters
fall below it, and half above.
Meanlowwatersprings(MLWS),usuallyshortened
tolowwatersprings,istheaveragelevelofthelowwaters
that occur at the times of spring tides.
Meanlowerlowwater(MLLW)istheaverageheight
of the lower low waters of each tidal day.
Tropiclowerlowwater(TcLLW)istheaverage
heightofthelowerlowwaters(orofthesingledailylow
watersifthetidebecomesdiurnal)thatoccurwhenthe
Moonisnearmaximumdeclinationandthediurnaleffectis
mostpronounced.Thisdatumisnotincommonuseasatid-
al reference.
Indianspringlowwater(ISLW),sometimescalled
Indiantideplaneorharmonictideplane,isalowwater
datumthatincludesthespringeffectofthesemi-diurnal
portionofthetideandthetropiceffectofthediurnalpor-
tion.Itisabouttheleveloflowerlowwaterofmixedtides
atthetimethattheMoon’smaximumdeclinationcoincides
with the time of new or full Moon.
Meanlowerlowwatersprings(MLLWS)istheav-
eragelevelofthelowerofthetwolowwatersonthedays
of spring tides.
Figure 911. Variations in the ranges and heights of tide where the chart sounding datum is Indian Spring Low Water.
138TIDES AND TIDAL CURRENTS
Somelowerdatumsusedonchartsaredetermined
fromtideobservationsandsomearedeterminedarbitrarily
andlaterreferredtothetide.Mostofthemfallclosetoone
or the other of the following two datums.
Lowestnormallowwaterisadatumthatapprox-
imatestheaverageheightofmonthlylowestlowwaters,
discarding any tides disturbed by storms.
Lowestlowwaterisanextremelylowdatum.It
conformsgenerallytothelowesttideobserved,oreven
somewhatlower.Onceatidaldatumisestablished,itis
sometimesretainedforanindefiniteperiod,eventhoughit
mightdifferslightlyfromabetterdeterminationfromlater
observations.Whenthisoccurs,theestablisheddatummay
becalledlowwaterdatum,lowerlowwaterdatum,etc.
Thesedatumsareusedinalimitedareaandprimarilyfor
riverandharborengineeringpurposes.Examplesare
BostonHarborLowWaterDatumandColumbiaRiver
Lower Low Water Datum.
Somesoundingdatumsarebasedonthepredictedtide
ratherthananaverageofobservations.ABritishsounding
datumthatmaybeadoptedinternationallyistheLowest
AstronomicalTide(LAT).LATistheelevationofthelow-
estwaterlevelpredictedina19-yearperiod.Canadian
coastalchartsuseadatumofLowerLowWater,LargeTide
(LLWLT)whichistheaverageofthelowestlowwaters,
one from each of the 19 years of predictions.
Figure911illustratesvariationsintherangesand
heightsoftidesinalocalitysuchastheIndianOcean,
wherepredictedandobservedwaterlevelsarereferencedto
achartsoundingdatumthatwillalwayscausethemtobe
additive relative to the charted depth.
Inareaswherethereislittleornotide,variousother
datumsareused.FortheBlackSeaforinstance,MeanSea
Level(MSL,sometimesreferredtoasMeanWaterLevelor
MWL)isused,andistheaverageofthehourlyheights
observedoveraperiodoftimeandadjustedtoa19-year
period.IntheUnitedStates,aLowWaterDatum(LWD)is
usedinthosecoastalareasthathavetransitionedfromtidal
tonon-tidal(e.g.LagunaMadre,TexasandPamlicoSound,
NorthCarolina)andissimply0.5footbelowacomputed
MLW.FortheGreatLakes,theUnitedStatesandCanada
useaseparateLWDforeachlake,whichisdesignedto
ensurethattheactualwaterlevelisabovethedatummost
ofthetimeduringthenavigationseason.Lakelevelsvary
by several feet over a period of years.
Inconsistenciesofterminologyarefoundamongcharts
ofdifferentcountriesandbetweenchartsissuedatdifferent
times.
Large-scalechartsusuallyspecifythedatumofsound-
ingsandmaycontainatidenotegivingmeanheightsofthe
tideatoneormoreplacesonthechart.Theseheightsarein-
tendedmerelyasaroughguidetothechangeindepthtobe
expectedunderthespecifiedconditions.Theyshouldnotbe
usedforthepredictionofheightsonanyparticularday,
which should be obtained from tide tables.
912. High Water Datums
Heightsofterrestrialfeaturesareusuallyreferredon
nauticalchartstoahighwaterdatum.Thisgivesthe
marineramarginoferrorwhenpassingunderbridges,
overheadcables,andotherobstructions.Theoneusedon
chartsoftheUnitedStates,itsterritoriesandpossessions,
andwidelyusedelsewhere,ismeanhighwater(MHW),
whichistheaverageheightofallhighwatersovera19year
period.Anyotherhighwaterdatuminuseonchartsis
likelytobehigherthanthis.Otherhighwaterdatumsare
meanhighwatersprings(MHWS),whichistheaverage
levelofthehighwatersthatoccuratthetimeofspring
tides;meanhigherhighwater(MHHW),whichisthe
averageheightofthehigherhighwatersofeachtidalday;
andtropichigherhighwater(TcHHW),whichisthe
averageheightofthehigherhighwaters(orthesingledaily
highwatersifthetidebecomesdiurnal)thatoccurwhenthe
Moonisnearmaximumdeclinationandthediurnaleffectis
mostpronounced.Areferencemerelyto“highwater”
leavessomedoubtastothespecificlevelreferredto,forthe
heightofhighwatervariesfromdaytoday.Wherethe
rangeislarge,thevariationduringa2weekperiodmaybe
considerable.
Becausethereareperiodicandapparentseculartrends
insealevel,aspecific19yearcycle(theNationalTidal
DatumEpoch)isissuedforallUnitedStatesdatums.The
NationalTidalDatumEpochofficiallyadoptedbythe
NationalOceanServiceispresently1960through1978.
The Epoch is reviewed for revision every 25 years.
TIDAL CURRENTS
913. Tidal and Nontidal Currents
Horizontalmovementofwateriscalledcurrent.It
maybeeither“tidal”and“nontidal.”Tidalcurrentisthe
periodichorizontalflowofwateraccompanyingtherise
andfallofthetide.Nontidalcurrentincludesallcurrents
notduetothetidalmovement.Nontidalcurrentsinclude
thepermanentcurrentsinthegeneralcirculatorysystemof
theoceansaswellastemporarycurrentsarisingfrom
meteorologicalconditions.Thecurrentexperiencedatany
timeisusuallyacombinationoftidalandnontidalcurrents.
914. General Features
Offshore,wherethedirectionofflowisnotrestricted
byanybarriers,thetidalcurrentisrotary;thatis,itflows
continuously,withthedirectionchangingthroughallpoints
ofthecompassduringthetidalperiod.Thisrotationis
causedbytheEarth’srotation,andunlessmodifiedbylocal
conditions,isclockwiseintheNorthernHemisphereand
TIDES AND TIDAL CURRENTS139
counterclockwiseintheSouthernHemisphere.Thespeed
usuallyvariesthroughoutthetidalcycle,passingthrough
twomaximumsinapproximatelyoppositedirections,and
twominimumsabouthalfwaybetweenthemaximumsin
timeanddirection.Rotarycurrentscanbedepictedasin
Figure914a,byaseriesofarrowsrepresentingthedirection
andspeedofthecurrentateachhour.Thisissometimes
calledacurrentrose.Becauseoftheellipticalpattern
formedbytheendsofthearrows,itisalsoreferredtoasa
current ellipse.
Inriversorstraits,orwherethedirectionofflowis
moreorlessrestrictedtocertainchannels,thetidalcurrent
isreversing;thatis,itflowsalternatelyinapproximately
oppositedirectionswithaninstantorshortperiodoflittle
ornocurrent,calledslackwater,ateachreversalofthe
current.Duringtheflowineachdirection,thespeedvaries
fromzeroatthetimeofslackwatertoamaximum,called
strengthoffloodorebb,aboutmidwaybetweentheslacks.
Reversingcurrentscanbeindicatedgraphically,asin
Figure914b,byarrowsthatrepresentthespeedofthe
currentateachhour.Thefloodisusuallydepictedabove
theslackwaterlineandtheebbbelowit.Thetidalcurrent
curveformedbytheendsofthearrowshasthesame
characteristicsineformasthetidecurve.Inillustrations
andforcertainotherpurposesitisconvenienttoomitthe
arrows and show only the curve.
Aslightdeparturefromthesineformisexhibitedby
thereversingcurrentinastraitthatconnectstwodifferent
tidalbasins,suchastheEastRiver,NewYork.Thetidesat
thetwoendsofastraitareseldominphaseorequalin
range,andthecurrent,calledhydrauliccurrent,is
generatedlargelybythecontinuouslychangingdifference
inheightofwateratthetwoends.Thespeedofahydraulic
currentvariesnearlyasthesquarerootofthedifferencein
height.Thespeedreachesamaximummorequicklyand
remainsatstrengthforalongerperiodthanshowninFigure
914b,andtheperiodofweakcurrentnearthetimeofslack
is considerably shortened.
Thecurrentdirection,orset,isthedirectiontoward
whichthecurrentflows.Thespeedissometimescalledthe
drift.Theterm“velocity”isoftenusedastheequivalentof
“speed”whenreferringtocurrent,althoughstrictly
speaking“velocity”impliesdirectionaswellasspeed.The
term“strength”isalsousedtorefertospeed,butmoreoften
togreatestspeedbetweenconsecutiveslackwaters.The
movementtowardshoreorupstreamistheflood,the
movementawayfromshoreordownstreamistheebb.Ina
purelysemidiurnalcurrentunaffectedbynontidalflow,the
floodandebbeachlastabout6hoursand13minutes.But
ifthereiseitherdiurnalinequalityornontidalflow,the
durations of flood and ebb may be quite unequal.
915. Types of Tidal Current
Tidalcurrents,liketides,maybeofthesemidiurnal,
diurnal,ormixedtype,correspondingtoaconsiderable
degreetothetypeoftideattheplace,butoftenwitha
stronger semidiurnal tendency.
ThetidalcurrentsintidalestuariesalongtheAtlantic
coastoftheUnitedStatesareexamplesofthesemidiurnal
typeofreversingcurrent.AlongtheGulfofMexicocoast,
suchasatMobileBayentrance,theyarealmostpurelydi-
urnal.Atmostplaces,however,thetypeismixedtoa
greaterorlesserdegree.AtTampaandGalvestonentrances
thereisonlyonefloodandoneebbeachdaywhenthe
Moonisnearitsmaximumdeclination,andtwofloodsand
twoebbseachdaywhentheMoonisneartheequator.
AlongthePacificcoastoftheUnitedStatestherearegen-
erallytwofloodsandtwoebbseveryday,butoneofthe
floodsorebbshasagreaterspeedandlongerdurationthan
theother,theinequalityvaryingwiththedeclinationofthe
Moon.
Theinequalitiesinthecurrentoftendifferconsiderably
fromplacetoplaceevenwithinlimitedareas,suchasadja-
centpassagesinPugetSoundandvariouspassagesbetween
theAleutianIslands.Figure915ashowsseveraltypesofre-
Figure914a.Rotarytidalcurrent.Timesarehoursbefore
andafterhighandlowtideatNantucketShoals.The
bearingandlengthofeacharrowrepresentsthehourly
direction and speed of the current.
Figure 914b. Reversing tidal current.
140TIDES AND TIDAL CURRENTS
versingcurrent.Figure915bshowshowtheflood
disappearsasthediurnalinequalityincreasesatonestation.
Offshorerotarycurrentsthatarepurelysemidiurnal
repeattheellipticalpatterneachtidalcycleof12hours
and25minutes.Ifthereisconsiderablediurnalinequality,
theplottedhourlycurrentarrowsdescribeasetoftwoel-
lipsesofdifferentsizesduringaperiodof24hoursand50
minutes,asshowninFigure915c,andthegreaterthedi-
urnalinequality,thegreaterthedifferencebetweenthe
sizesofthetwoellipses.Inacompletelydiurnalrotary
current,thesmallerellipsedisappearsandonlyoneellipse
is produced in 24 hours and 50 minutes.
916. Tidal Current Periods and Cycles
Tidalcurrentshaveperiodsandcyclessimilartothose
ofthetides,andaresubjecttosimilarvariations,butflood
andebbofthecurrentdonotnecessarilyoccuratthesame
times as the rise and fall of the tide.
Thespeedatstrengthincreasesanddecreasesduring
the2weekperiod,month,andyearalongwiththe
variationsintherangeoftide.Thus,thestrongerspringand
perigeancurrentsoccurnearthetimesofnewandfull
MoonandnearthetimesoftheMoon’sperigee,orattimes
ofspringandperigeantides;theweakerneapandapogean
currentsoccuratthetimesofneapandapogeantides;and
tropiccurrentswithincreaseddiurnalspeedsorwithlarger
diurnalinequalitiesinspeedoccurattimesoftropictides;
andequatorialcurrentswithaminimumdiurnaleffect
occur at times of equatorial tides.
Aswiththetide,ameanvaluerepresentsanaverage
obtainedfroma19yearseries.Sinceaseriesofcurrent
observationsisusuallylimitedtoafewdays,andseldom
coversmorethanamonthortwo,itisnecessarytoadjust
theobservedvalues,usuallybycomparisonwithtidesata
Figure915a.Severaltypesofreversingcurrent.The
patternchangesgraduallyfromdaytoday,particularlyfor
mixed types, passing through cycles.
Figure915b.Changesinacurrentofthemixedtype.Note
thateachdayastheinequalityincreases,themorning
slacksdrawtogetherintimeuntilonthe17ththemorning
flooddisappears.Onthatdaythecurrentebbsthroughout
the morning.
Figure915c.Rotarytidalcurrentwithdiurnalinequality.
Timesareinhoursreferredtotides(higherhigh,lowerlow,
lower high, and higher low) at Swiftsure Bank.
TIDES AND TIDAL CURRENTS141
nearby place, to obtain such a mean.
917. Effect of Nontidal Flow
Thecurrentexistingatanytimeisseldompurelytidal,
butusuallyincludesalsoanontidalcurrentthatisdueto
drainage,oceaniccirculation,wind,orothercauses.The
methodinwhichtidalandnontidalcurrentscombineisbest
explainedgraphically,asinFigure917aandFigure917b.
Thepatternofthetidalcurrentremainsunchanged,butthe
curveisshiftedfromthepointorlinefromwhichthecur-
rentsaremeasured,inthedirectionofthenontidalcurrent,
andbyanamountequaltoit.Itissometimesmoreconve-
nientgraphicallymerelytomovethelineorpointoforiginin
theoppositedirection.Thus,thespeedofthecurrentflowing
inthedirectionofthenontidalcurrentisincreasedbyan
amountequaltothemagnitudeofthenontidalcurrent,and
thespeedofthecurrentflowingintheoppositedirectionis
decreased by an equal amount.
InFigure917a,anontidalcurrentisrepresentedboth
indirectionandspeedbythevectorAO.Sincethisisgreat-
erthanthespeedofthetidalcurrentintheopposite
direction,thepointAisoutsidetheellipse.Thedirection
andspeedofthecombinedtidalandnontidalcurrentsatany
timeisrepresentedbyavectorfromAtothatpointonthe
curverepresentingthegiventime,andcanbescaledfrom
thegraph.Thestrongestandweakestcurrentsmaynolong-
erbeinthedirectionsofthemaximumandminimumofthe
tidalcurrent.Ifthenontidalcurrentisnorthwestat0.3knot,
itmayberepresentedbyBO,andallhourlydirectionsand
speedswillthenbemeasuredfromB.Ifitis1.0knot,itwill
berepresentedbyAOandtheactualresultanthourlydirec-
tionsandspeedswillbemeasuredfromA,asshownbythe
arrows.
Inareversingcurrent(Figure917b),theeffectisto
advancethetimeofoneslack,andtoretardthefollowing
one.Ifthespeedofthenontidalcurrentexceedsthatofthe
reversingtidalcurrent,theresultantcurrentflowscontin-
uouslyinonedirectionwithoutcomingtoaslack.Inthis
case,thespeedvariesfromamaximumtoaminimumand
backtoamaximumineachtidalcycle.InFigure917b,the
horizontallineArepresentsslackwaterifonlytidal
currentsarepresent.LineBrepresentstheeffectofa0.5
knotnontidalebb,andlineCtheeffectofa1.0knot
nontidalebb.WiththeconditionshownatCthereisonly
onefloodeachtidalday.Ifthenontidalebbweretoincrease
toapproximately2knots,therewouldbenoflood,two
maximumebbsandtwominimumebbsoccurringduringa
tidal day.
918. Time of Tidal Current and Time of Tide
Atmanyplaceswherecurrentandtideareboth
semidiurnal,thereisadefiniterelationshipbetweentimes
ofcurrentandtimesofhighandlowwaterinthelocality.
Currentatlasesandnotesonnauticalchartsoftenmakeuse
ofthisrelationshipbypresentingforparticularlocations,
thedirectionandspeedofthecurrentateachsucceeding
hourafterhighandlowwater,ataplaceforwhichtide
predictions are available.
Wherethereisconsiderablediurnalinequalityintide
orcurrent,orwherethetypeofcurrentdiffersfromthetype
oftide,therelationshipisnotconstant,anditmaybe
hazardoustotrytopredictthetimesofcurrentfromtimes
oftide.NotethecurrentcurveforUnimakPassinthe
AleutiansinFigure915a.Itshowsthecurrentaspredicted
inthetidalcurrenttables.Predictionsofhighandlow
watersinthetidetablesmighthaveledonetoexpectthe
currenttochangefromfloodtoebbinthelatemorning,
whereasactuallythecurrentcontinuedtorunfloodwith
some strength at that time.
Sincetherelationshipbetweentimesoftidalcurrent
andtideisnotthesameeverywhere,andmaybevariableat
thesameplace,oneshouldexerciseextremecautionin
usinggeneralrules.Thebeliefthatslacksoccuratlocal
highandlowtidesandthatthemaximumfloodandebb
occurwhenthetideisrisingorfallingmostrapidlymaybe
Figure917a.Effectofnontidalcurrentontherotarytidal
current ofFigure 914a.
Figure917b.Effectofnontidalcurrentonthereversing
tidal current ofFigure 914b.
142TIDES AND TIDAL CURRENTS
approximatelytrueattheseawardentranceto,andinthe
upperreachesof,aninlandtidalwaterway.Butgenerally
thisisnottrueinotherpartsofinlandwaterways.Whenan
inlandwaterwayisextensiveoritsentranceconstricted,the
slacksinsomepartsofthewaterwayoftenoccurmidway
betweenthetimesofhighandlowtide.Usuallyinsuch
waterwaystherelationshipchangesfromplacetoplaceas
oneprogressesupstream,slackwatergettingprogressively
closerintimetothelocaltidemaximumuntilattheheadof
tidewater(theinlandlimitofwateraffectedbyatide)the
slacks occur at about the times of high and low tide.
919.RelationshipBetweenSpeedofCurrentandRange
of Tide
Thespeedofthetidalcurrentisnotnecessarily
consistentwiththerangeoftide.Itmaybethereverse.For
example,currentsareweakintheGulfofMainewherethe
tidesarelarge,andstrongnearNantucketIslandandin
NantucketSoundwherethetidesaresmall.However,at
anyoneplacethespeedofthecurrentatstrengthofflood
andebbvariesduringthemonthinaboutthesame
proportionastherangeoftide,andthisrelationshipcanbe
usedtodeterminetherelativestrengthofcurrentsonany
given day.
920. Variation Across an Estuary
Ininlandtidalestuariesthetimeoftidalcurrentvaries
acrossthechannelfromshoretoshore.Ontheaverage,the
currentturnsearliernearshorethaninmidstream,where
thespeedisgreater.Differencesofhalfanhourtoanhour
arenotuncommon,butthedifferencevariesandthe
relationshipmaybenullifiedbytheeffectofnontidalflow.
Thespeedofthecurrentalsovariesacrossthechannel,
usuallybeinggreaterinmidstreamormidchannelthannear
shore,butinawindingriverorchannelthestrongest
currentsoccurneartheconcaveshore,ortheoutsidecorner
ofthecurve.Neartheopposite(convex)shorethecurrents
are weak or eddying.
921. Variation with Depth
Intidalriversthesubsurfacecurrentactingonthelower
portionofaship’shullmaydifferconsiderablyfromthe
surfacecurrent.Anappreciablesubsurfacecurrentmaybe
presentwhenthesurfacemovementappearstobepractically
slack,andthesubsurfacecurrentmayevenbeflowingwith
appreciablespeedintheoppositedirectiontothesurface
current.
Inatidalestuary,particularlyinthelowerreaches
wherethereisconsiderabledifferenceindensityfromtop
tobottom,thefloodusuallybeginsearliernearthebottom
thanatthesurface.Thedifferencemaybeanhourortwo,
oraslittleasafewminutes,dependingupontheestuary,
thelocationintheestuary,andfreshetconditions.Even
whenthefreshwaterrunoffbecomessogreatastoprevent
thesurfacecurrentfromflooding,itmaystillfloodbelow
thesurface.Thedifferenceintimeofebbfromsurfaceto
bottomisnormallysmallbutsubjecttovariationwithtime
and location.
Theebbspeedatstrengthusuallydecreasesgradually
fromtoptobottom,butthespeedoffloodatstrengthoften
is stronger at subsurface depths than at the surface.
922. Tidal Current Observations
Observationsofcurrentaremadewithsophisticated
electroniccurrentmeters.Currentmetersaresuspended
fromabuoyoranchoredtothebottomwithnosurface
markeratall.Verysensitivecurrentmetersmeasureand
recorddeepoceancurrents;thesearelaterrecoveredby
triggeringareleasemechanismwithasignalfromthe
surface.Untendedcurrentmeterseitherrecorddata
internallyorsenditbyradiotoabasestationonshipor
land.Theperiodofobservationvariesfromafewhoursto
as long as 6 months.
TIDE AND CURRENT PREDICTION
923. Tidal Height Predictions
Tomeasuretheheightoftides,hydrographersselecta
referencelevel,sometimesreferredtoasthereference
plane,orverticaldatum.Thisverticaltidaldatumisnotthe
sameastheverticalgeodeticdatum.Soundingsshownon
thelargestscalechartsaretheverticaldistancesfromthis
datumtothebottom.Atanygiventimetheactualdepthis
thischarteddepthplustheheightoftide.Inmostplacesthe
referencelevelissomeformoflowwater.Butalllow
watersatagivenplacearenotthesameheight,andthe
selectedreferencelevelisseldomthelowesttideoccurring
attheplace.Whenlowertidesoccur,theseareindicatedin
thetidetablesbyanegativesign.Thus,ataspotwherethe
charteddepthis15feet,theactualdepthis15feetplusthe
tidalheight.Whenthetideisthreefeet,thedepthis
15+3=18feet.Whenitis-1foot,thedepthis15-1=14
feet.Theactualdepthcanbelessthanthecharteddepth.In
anareawherethereisaconsiderablerangeoftide(the
differencebetweenhighwaterandlowwater),theheightof
tidemightbeanimportantconsiderationwhenusing
soundings to determine if the vessel is in safe water.
Theheightsgiveninthetidetablesarepredictions,and
whenassumedconditionsvaryconsiderably,the
predictionsshownmaybeconsiderablyinerror.Heights
lowerthanpredictedcanbeanticipatedwhenthe
atmosphericpressureishigherthannormal,orwhenthere
isapersistentstrongoffshorewind.Thegreatertherange
TIDES AND TIDAL CURRENTS143
oftide,thelessreliablearethepredictionsforbothheight
and current.
924. Tidal Heights
Thenatureofthetideatanyplacecanbestbe
determinedbyobservation.Thepredictionsintidetablesand
thetidaldataonnauticalchartsarebasedupondetailed
observationsatspecificlocations,insteadoftheoretical
predictions.
Tidalelevationsareusuallyobservedwithacontin-
uouslyrecordinggage.Ayearofobservationsisthe
minimumlengthdesirablefordeterminingtheharmonic
constantsusedinprediction.Forestablishingmeansealevel
andlong-termchangesintherelativeelevationsoflandand
sea,aswellasforotherspecialuses,observationshavebeen
madeoverperiodsof20,30,andeven120yearsatimportant
locations.Observationsforamonthorlesswillestablishthe
typeoftideandsufficeforcomparisonwithalongerseriesof
observations to determine tidal differences and constants.
Mathematically,thevariationsinthelunarandsolar
tide-producingforces,suchasthoseduetochangingphase,
distance,anddeclination,areconsideredasseparate
constituentforces,andtheharmonicanalysisof
observationsrevealstheresponseofeachconstituentofthe
tidetoitscorrespondingforce.Atanyoneplacethis
responseremainsconstantandisshownforeach
constituentbyharmonicconstantswhichareintheform
ofaphaseangleforthetimerelationandanamplitudefor
theheight.Harmonicconstantsareusedinmaking
technicalstudiesofthetideandintidalpredictionson
computers.Thetidalpredictionsinmostpublishedtide
tables are produced by computer.
925. Meteorological Effects
Theforegoingdiscussionoftidalbehaviorassumes
normalweatherconditions.However,sealevelisalso
affectedbywindandatmosphericpressure.Ingeneral,
onshorewindsraisethelevelandoffshorewindslowerit,
buttheamountofchangevariesatdifferentplaces.During
periodsoflowatmosphericpressure,thewaterleveltends
tobehigherthannormal.Forastationarylow,theincrease
in elevation can be found by the formula
R
0
=0.01(1010 - P),
inwhichR
0
istheincreaseinelevationinmetersandPis
theatmosphericpressureinhectopascals.Thisisequal
approximatelyto1centimeterperhectopascaldepression,
orabout13.6inchesperinchdepression.Foramovinglow,
the increase in elevation is given by the formula
inwhichRistheincreaseinelevationinfeet,R
0
isthe
increaseinmetersforastationarylow,Cistherateof
motionofthelowinfeetpersecond,gistheacceleration
duetogravity(32.2feetpersecondpersecond),andhisthe
depth of water in feet.
Wheretherangeoftideisverysmall,themeteoro-
logicaleffectmaysometimesbegreaterthanthenormal
tide.Whereabodyofwaterislargeinareabutshallow,
highwindscanpushthewaterfromthewindwardtothelee
shore,creatingmuchgreaterlocaldifferencesinwater
levelsthanoccursnormally,andpartiallyorcompletely
maskingthetides.Theeffectisdependentontheconfigu-
rationanddepthofthebodyofwaterrelativetothewind
direction, strength and duration.
926 Tidal Current Predictions
Tidalcurrentsaredueprimarilytotidalaction,but
othercausesareoftenpresent.TheTidalCurrentTables
givethebestpredictionoftotalcurrent.Followingheavy
rainsoradrought,ariver’scurrentpredictionmaybe
considerablyinerror.Setanddriftmayvaryconsiderably
overdifferentpartsofaharbor,becausedifferencesin
bathymetryfromplacetoplaceaffectcurrent.Sincethisis
usuallyanareawheresmallerrorsinavessel’spositionare
crucial,aknowledgeofpredictedcurrents,particularlyin
reducedvisibility,isimportant.Strongcurrentsoccur
mostlyinnarrowpassagesconnectinglargerbodiesof
water.Currentsofmorethan5knotsaresometimes
encounteredattheGoldenGateinSanFrancisco,and
currentsofmorethan13knotssometimesoccuratSeymour
Narrows, British Columbia.
Instraightportionsofriversandchannels,the
strongestcurrentsusuallyoccurinthemiddleofthe
channel.Incurvedportionstheswiftestcurrents(and
deepestwater)usuallyoccurneartheouteredgeofthe
curve.Countercurrentsandeddiesmayoccuroneitherside
ofthemaincurrentofariverornarrowpassage,especially
near obstructions and in bights.
Ingeneral,therangeoftideandthevelocityoftidal
currentareataminimumintheopenoceanoralongstraight
coasts.Thegreatesttidaleffectsareusuallyencounteredin
estuaries,bays,andothercoastalindentations.Avessel
proceedingalonganindentedcoastmayencounteraset
towardorawayfromtheshore;asimilarsetisseldom
experienced along a straight coast.
R
R
0
1
C
2
gh
------–
---------------=
144TIDES AND TIDAL CURRENTS
PUBLICATIONS FOR PREDICTING TIDES AND CURRENTS
927.Tide Tables
Usually,tidalinformationisobtainedfromtideand
tidalcurrenttables,orfromspecializedcomputersoftware
orcalculators.However,ifthesearenotavailable,orifthey
donotincludeinformationatadesiredplace,themariner
maybeabletoobtainlocallythemeanhighwater
lunitidalintervalorthehighwaterfullandchange.The
approximatetimeofhighwatercanbefoundbyadding
eitherintervaltothetimeoftransit(eitherupperorlower)
oftheMoon.Lowwateroccursapproximately1/4tidalday
(about6
h
12
m
)beforeandafterthetimeofhighwater.The
actualintervalvariessomewhatfromdaytoday,but
approximateresultscanbeobtainedinthismanner.Similar
informationfortidalcurrents(lunicurrentinterval)is
seldom available.
TheNationalOceanService(NOS)hastraditionally
publishedhardcopytidetablesandtidalcurrenttables.
TideandtidalcurrentdatacontinuetobeupdatedbyNOS,
buthardcopypublicationhasbeentransferredtoprivate
companiesworkingwithNOSdata,publishedonCD-
ROM.
Tidaldataforvariouspartsoftheworldispublished
in4volumesbytheNationalOceanService.Thesevol-
umes are:
•CentralandWesternPacificOceanandIndian
Ocean
•EastCoastofNorthandSouthAmerica(including
Greenland)
•Europe and West Coast of Africa
•WestCoastofNorthandSouthAmerica(including
the Hawaiian Islands)
Asmallseparatevolume,theAlaskanSupplement,is
also published.
Each volume has 5 common tables:
•Table1containsacompletelistofthepredictedtimes
andheightsofthetideforeachdayoftheyearata
number of places designated asreference stations.
•Table2givestidaldifferencesandratioswhichcanbe
usedtomodifythetidalinformationforthereference
stationstomakeitapplicabletoarelativelylargenumber
ofsubordinate stations.
•Table3providesinformationforfindingthe
approximateheightofthetideatanytimebetweenhigh
water and low water.
•Table4isasunrise-sunsettableatfive-dayintervalsfor
variouslatitudesfrom76°Nto60°S(40°Sinone
volume).
•Table5providesanadjustmenttoconvertthelocalmean
time of Table 4 to zone or standard time.
FortheEastCoastandWestCoastvolumes,each
containsaTable6,amoonriseandmoonsettable;Table7
forconversionfromfeettocentimeters;Table8,atableof
estimatedtidepredictionaccuracies;aglossaryofterms;
andanindextostations.Eachtableisprecededbya
completeexplanation.Sampleproblemsaregivenwhere
necessary.Theinsidebackcoverofeachvolumecontainsa
calendarofcriticalastronomicaldatatohelpexplainthe
variationsofthetideduringeachmonthandthroughoutthe
year.
928. Tide Predictions for Reference Stations
Foreachday,thedateanddayofweekaregiven,and
thetimeandheightofeachhighandlowwaterarelistedin
chronologicalorder.Althoughhighandlowwatersarenot
labeledassuch,theycanbedistinguishedbytherelative
heightsgivenimmediatelytotherightofthetimes.Iftwo
hightidesandtwolowtidesoccureachtidalday,thetideis
semidiurnal.Sincethetidaldayislongerthanthecivilday
(becauseoftherevolutionoftheMooneastwardaroundthe
Earth),anygiventideoccurslatereachday.Becauseof
latertimesofcorrespondingtidesfromdaytoday,certain
days have only one high water or only one low water.
929. Tide Predictions for Subordinate Stations
Foreachsubordinatestationlisted,thefollowing
information is given:
1.Number.Thestationsarelistedingeographicalorder
andassignedconsecutivenumbers.Eachvolume
containsanalphabeticalstationlistingcorrelatingthe
stationwithitsconsecutivenumbertoassistinfinding
the entry in Table 2.
2.Place.Thelistofplacesincludesbothsubordinateand
reference stations; the latter are in bold type.
3.Position.Theapproximatelatitudeandlongitudeare
giventoassistinlocatingthestation.Thelatitudeis
northorsouth,andthelongitudeeastorwest,
dependingupontheletters(N,S,E,W)nextabovethe
entry.Thesemaynotbethesameasthoseatthetopof
the column.
4.Differences.Thedifferencesaretobeappliedtothe
predictionsforthereferencestation,shownincapital
lettersabovetheentry.Timeandheightdifferencesare
givenseparatelyforhighandlowwaters.Where
differencesareomitted,theyareeitherunreliableor
unknown.
5.Ranges.Variousrangesaregiven,asindicatedinthe
tables.Ineachcasethisisthedifferenceinheight
betweenhighwaterandlowwaterforthetidesindicated.
6.Meantidelevel.Thisistheaveragebetweenmeanlow
and mean high water, measured from chart datum.
TIDES AND TIDAL CURRENTS145
Thetimedifferenceisthenumberofhoursand
minutestobeappliedtothereferencestationtimetofind
thetimeofthecorrespondingtideatthesubordinatestation.
Thisintervalisaddedifprecededbyaplussign(+)and
subtractedifprecededbyaminussign(-).Theresults
obtainedbytheapplicationofthetimedifferenceswillbe
inthezonetimeofthetimemeridianshowndirectlyabove
thedifferenceforthesubordinatestation.Special
conditionsoccurringatafewstationsareindicatedby
footnotesontheapplicablepages.Insomeinstances,the
correspondingtidefallsonadifferentdateatreferenceand
subordinate stations.
Heightdifferencesareshowninavarietyofways.For
mostentries,separateheightdifferencesinfeetaregiven
forhighwaterandlowwater.Theseareappliedtothe
heightgivenforthereferencestation.Inmanycasesa
ratioisgivenforeitherhighwaterorlowwater,orboth.
Theheightatthereferencestationismultipliedbythis
ratiotofindtheheightatthesubordinatestation.Forafew
stations,botharatioanddifferencearegiven.Inthiscase
theheightatthereferencestationisfirstmultipliedbythe
ratio,andthedifferenceisthenapplied.Anexampleis
givenineachvolumeoftidetables.Specialconditionsare
indicatedinthetableorbyfootnote.Forexample,a
footnoteindicatesthat“ValuesfortheHudsonRiver
aboveGeorgeWashingtonBridgearebasedupon
averagesforthesixmonthsMaytoOctober,whenthe
fresh-water discharge is a minimum.”
930. Finding Height of Tide at any Time
Table3providesmeansfordeterminingtheapproxi-
mateheightoftideatanytime.Itassumesthatplotting
heightversustimeyieldsasinecurve.Actualvaluesmay
varyfromthis.Theexplanationofthetablecontainsdirec-
tionsforbothmathematicalandgraphicalsolutions.
Thoughthemathematicalsolutionisquicker,ifthevessel’s
ETAchangessignificantly,itwillhavetobedoneforthe
newETA.Therefore,ifthereisdoubtabouttheETA,the
graphicalsolutionwillprovideaplotofpredictionsforsev-
eralhoursandallowquickreferencetothepredictedheight
foranygiventime.Thismethodwillalsoquicklyshowat
whattimeagivendepthofwaterwilloccur.Figure930a
showstheOPNAVformusedtocalculateheightsoftides.
Figure930bshowstheimportanceofcalculatingtidesin
shallow water.
931.Tidal Current Tables
TidalCurrentTablesaresomewhatsimilartoTide
Tables,butthecoverageislessextensive.NOSpublishes2
volumesonanannualbasis:AtlanticCoastofNorth
America,andPacificCoastofNorthAmericaandAsia.
Each of the two volumes is arranged as follows:
Eachvolumealsocontainscurrentdiagramsand
instructionsfortheiruse.Explanationsandexamplesare
given in each table.
•Table1containsacompletelistofpredictedtimesof
maximumcurrentsandslackwater,withthevelocityof
themaximumcurrents,foranumberofreference
stations.
•Table2givesdifferences,ratios,andotherinformation
relatedtoarelativelylargenumberofsubordinate
OPNAV 3530/40 (4-73)
HT OF TIDE
Date
Location
Time
Ref Sta
HW Time Diff
LW Time Diff
HW Ht Diff
LW Ht Diff
Ref Sta
HW/LW Time
HW/LW Time Diff
Sub Sta
HW/LW Time
Ref Sta
HW/LW Ht
HW/LW Ht Diff
Sub Sta
HW/LW Ht
Duration
Rise
Fall
Time Fm
Near
Tide
Range of Tide
Ht of Neat Tide
Corr Table 3
Ht of Tide
Charted Depth
Depth of Water
Draft
Clearance
Figure 930a. OPNAV 3530/40 Tide Form.
146TIDES AND TIDAL CURRENTS
stations.
•Table3providesinformationtodeterminethecurrent’s
velocity at any time between entries in tables 1 and 2.
•Table4givesdurationofslack,orthenumberofminutes
thecurrentdoesnotexceedstatedamounts,forvarious
maximum velocities.
•Table5(AtlanticCoastofNorthAmericaonly)gives
information on rotary tidal currents.
Thevolumesalsocontaingeneraldescriptive
informationonwind-drivencurrents,combinationcurrents,
andinformationsuchasGulfStreamcurrentsfortheeast
coast and coastal currents on the west coast.
932. Tidal Current Prediction for Reference Stations
Foreachday,thedateanddayofweekaregiven;
currentinformationfollows.Ifthecycleisrepeated
twiceeachtidalday,currentsaresemidiurnal.Onmost
daystherearefourslackwatersandfourmaximum
currents,twofloods(F)andtwoebbs(E).However,
sincethetidaldayislongerthanthecivilday,the
correspondingconditionoccurslatereachday,andon
certaindaysthereareonlythreeslackwatersorthree
maximumcurrents.Atsomeplaces,thecurrentonsome
daysrunsmaximumfloodtwice,butebbsonlyonce,a
minimumfloodoccurringinplaceofthesecondebb.The
tables show this information.
933.TidalCurrentPredictionsforSubordinateStations
ForeachsubordinatestationlistedinTable2ofthe
tidal current tables, the following information is given:
1.Number:Thestationsarelistedingeographical
orderandassignedconsecutivenumbers,asinthe
tidetables.Eachvolumecontainsanalphabetical
stationlistingcorrelatingthestationwithits
consecutivenumbertoassistinlocatingtheentryin
Table 2.
2.Place:Thelistofplacesincludesbothsubordinate
andreferencestations,thelattergiveninboldtype.
3.Position:Theapproximatelatitudeandlongitude
aregiventoassistinlocatingthestation.The
latitudeisnorthorsouthandthelongitudeeastor
westasindicatedbytheletters(N,S,E,W)next
abovetheentry.Thecurrentgivenisforthecenter
ofthechannelunlessanotherlocationisindicated
by the station name.
4.Timedifference:Twotimedifferencesare
tabulated.Oneisthenumberofhoursandminutes
tobeappliedtothetabulatedtimesofslackwater
atthereferencestationtofindthetimesofslack
watersatthesubordinatestation.Theothertime
differenceisappliedtothetimesofmaximum
currentatthereferencestationtofindthetimesof
thecorrespondingmaximumcurrentatthe
subordinatestation.Theintervals,whichareadded
orsubtractedinaccordancewiththeirsigns,
includeanydifferenceintimebetweenthetwo
stations,sothattheansweriscorrectforthe
standardtimeofthesubordinatestation.Limited
applicationandspecialconditionsareindicatedby
footnotes.
5.Velocityratios:Speedofthecurrentatthesubor-
dinatestationistheproductofthevelocityatthe
referencestationandthetabulatedratio.Separate
ratiosmaybegivenforfloodandebbcurrents.Spe-
cial conditions are indicated by footnotes.
6.AverageSpeedsandDirections:Minimumand
maximumvelocitiesbeforefloodandebbarelisted
foreachstation,alongwiththetruedirectionsof
theflow.Minimumvelocityisnotalways0.0
knots.
Figure 930b. Height of tide required to pass clear of charted obstruction.
TIDES AND TIDAL CURRENTS147
934. Finding Velocity of Tidal Current at any Time
Table3ofthetidalcurrenttablesprovidesmeansfor
determiningtheapproximatevelocityatanytime.Direc-
tionsaregiveninanexplanationprecedingthetable.Figure
934 shows the OPNAV form used for current prediction.
935. Duration of Slack Water
Thepredictedtimesofslackwaterlistedinthetidal
currenttablesindicatetheinstantofzerovelocity.Thereis
aperiodeachsideofslackwater,however,duringwhich
thecurrentissoweakthatforpracticalpurposesitmaybe
considerednegligible.Table4ofthetidalcurrenttables
gives,forvariousmaximumcurrents,theapproximate
periodoftimeduringwhichcurrentsnotexceeding0.1to
0.5knotswillbeencountered.Thisperiodincludesthelast
ofthefloodorebbandthebeginningofthefollowingflood
orebb;thatis,halfofthedurationwillbebeforeandhalf
after the time of slack water.
Whenthereisadifferencebetweenthevelocitiesofthe
maximumfloodandebbprecedingandfollowingtheslack
forwhichthedurationisdesired,itwillbesufficiently
accuratetofindaseparatedurationforeachmaximum
velocityandaveragethetwotodeterminethedurationof
the weak current.
Ofthetwosub-tablesofTable4,TableAisusedforall
placesexceptthoselistedforTableB;TableBisusedfor
justtheplaceslistedandthestationsinTable2whichare
referred to them.
936. Additional Tide Prediction Publications
NOSalsopublishesaspecialRegionalTideandTidal
CurrentTableforNewYorkHarbortoChesapeakeBay,
andaTidalCirculationandWaterLevelForecastAtlasfor
Delaware River and Bay.
937.Tidal Current Charts
TidalCurrentchartspresentacomprehensiveviewof
thehourlyvelocityofcurrentindifferentbodiesofwater.
Theyalsoprovideameansfordeterminingthecurrent’sve-
locityatvariouslocationsinthesewaters.Thearrowsshow
thedirectionofthecurrent;thefiguresgivethespeedin
knotsatthetimeofspringtides.Aweakcurrentisdefined
aslessthan0.1knot.Thesechartsdepicttheflowofthetid-
alcurrentundernormalweatherconditions.Strongwinds
andfreshets,however,maycausenontidalcurrents,consid-
erably modifying the velocity indicated on the charts.
TidalCurrentchartsareprovided(1994)forBoston
Harbor,CharlestonHarborSC,LongIslandSoundand
BlockIslandSound,NarragansettBay,NarragansettBayto
NantucketSound,PugetSound(NorthernPart),Puget
Sound(SouthernPart),UpperChesapeakeBay,andTampa
Bay.
Thetidalcurrent’svelocityvariesfromdaytodayasa
functionofthephase,distance,anddeclinationofthe
Moon.Therefore,toobtainthevelocityforanyparticular
dayandhour,thespringvelocitiesshownonthecharts
OPNAV 3530/40 (4-73)
VEL OF CURRENT
Date
Location
Time
Ref Sta
Time Diff
Stack Water
Time Diff
Max Current
Vel Ratio
Max Flood
Vel Ratio
Max Ebb
Flood Dir
Ebb Dir
Ref Sta
Stack Water Time
Time Diff
Local Sta
Stack Water Time
Ref Sta Max
Current Time
Time Diff
Local Sta Max
Current Time
Ref Sta Max
Current Vel
Vel Ratio
Local Sta Max
Current Vel
Int Between Slack and
Desired Time
Int Between Slack and
Max Current
Max Current
Factor Table 3
Velocity
Direction
Figure 934. OPNAV 3530/41 Current Form.
148TIDES AND TIDAL CURRENTS
mustbemodifiedbycorrectionfactors.Acorrectiontable
given in the charts can be used for this purpose.
AllofthechartsexceptNarragansettBayrequirethe
useoftheannualTidalCurrentTables.NarragansettBay
requires use of the annualTide Tables.
938. Current Diagrams
Acurrentdiagramisagraphshowingthevelocityof
thecurrentalongachannelatdifferentstagesofthetidal
currentcycle.Thecurrenttablesincludediagramsfor
Martha’sVineyardandNantucketSounds(onediagram);
EastRiver,NewYork;NewYorkHarbor;DelawareBay
andRiver(onediagram);andChesapeakeBay.These
diagramsarenolongerpublishedbyNOS,butareavailable
privately and remain useful as they are not ephemeral.
OnFigure938,eachverticallinerepresentsagivenin-
stantidentifiedbythenumberofhoursbeforeorafterslack
wateratTheNarrows.Eachhorizontallinerepresentsadis-
tancefromAmbroseChannelentrance,measuredalongthe
usuallytraveledroute.Thenamesalongtheleftmarginare
placedatthecorrectdistancesfromAmbroseChannelen-
trance.Thecurrentisforthecenterofthechannelopposite
thesepoints.Theintersectionofanyverticallinewithany
horizontallinerepresentsagivenmomentinthecurrentcy-
cleatagivenplaceinthechannel.Ifthisintersectionisin
ashadedarea,thecurrentisflooding;ifinanunshadedar-
ea,itisebbing.Thevelocitycanbefoundbyinterpolation
betweenthenumbersgiveninthediagram.Thegivenval-
uesareaverages.Tofindthevalueatanytime,multiplythe
velocityfoundfromthediagrambytheratioofmaximum
velocityofthecurrentinvolvedtothemaximumshownon
thediagram.Ifthediurnalinequalityislarge,theaccuracy
canbeimprovedbyalteringthewidthoftheshadedareato
fitconditions.Thediagramcovers11/2currentcycles,so
that the right 1/3 duplicates the left 1/3.
UseTable1or2todeterminethecurrentforasingle
station.Thecurrentdiagramsareintendedforuseineither
oftwoways:todetermineafavorabletimeforpassage
throughthechannelandtofindtheaveragecurrenttobeex-
pectedduringapassagethroughthechannel.Forbothof
theseuses,anumberof“velocitylines”areprovided.When
theappropriatelineistransferredtothecorrectpartofthe
diagram,thecurrenttobeencounteredduringpassageisin-
dicated along the line.
Ifthetransferredvelocitylineispartlyinafloodcur-
rentarea,allebbcurrents(thoseincreasingtheship’s
velocity)aregivenapositivesign(+),andallfloodcurrents
anegativesign(-).Aseparateratioshouldbedetermined
foreachcurrent(floodorebb),andappliedtotheentriesfor
thatcurrent.IntheChesapeakeBay,itiscommonforan
outboundvesseltoencounterthreeorevenfourseparate
currentsduringpassage.Underthelattercondition,itis
goodpracticetomultiplyeachcurrenttakenfromthedia-
gram by the ratio for the current involved.
Ifthetimeofstartingthepassageisfixed,andthe
currentduringpassageisdesired,thestartingtimeis
identifiedintermsofthereferencetidalcycle.Thevelocity
lineisthendrawnthroughtheintersectionofthisvertical
timelineandthehorizontallinethroughtheplace.The
averagecurrentisthendeterminedinthesamemanneras
when the velocity line is located as described above.
939. Computer Predictions
Untilrecently,tidalpredictionswerecompiledonlyon
mainframeorminicomputersandthenputintohardcopy
tableformforthemariner.Thereareseveraltypesof
commercialsoftwareavailablenowforpersonalcomputers
(PC’s)thatprovidedigitalversionsoftheNOStidetables
andalsographthetidalheights.Thetabularinformation
andgraphscanbeprintedforthedesiredlocationsforpre-
voyageplanning.Therearealsoseveraltypesofspecialized
hand-heldcalculatorsandtideclocksthatcanbeusedto
predict tides for local areas.
Figure 938. Current diagram for New York Harbor.
TIDES AND TIDAL CURRENTS149
NewerversionsofPCsoftwareusetheactualharmonic
constantsavailableforlocations,thepredictionequation,
anddigitalversionsofTable2intheTideTablestoproduce
evenmoreproductsforthenavigator’suse.SinceNOShas
publishedthedata,eveninexpensivenavigationelectronics
suchashandheldGPSreceiversandplottersforsmallcraft
navigation often include graphic tide tables.
Emergingapplicationsincludeintegrationoftidalpre-
dictionwithpositioningsystemsandvesseltrafficsystems
whicharenowmovingtowardsfulluseofGPS.Inaddition,
someelectronicchartsystemsarealreadyabletointegrate
tidepredictioninformation.Manyofthesenewsystems
willalsousereal-timewaterlevelandcurrentinformation.
Activeresearchalsoincludesprovidingpredictionsoftotal
waterlevelthatwillincludenotonlythetidalprediction
component, but also the weather-related component.
151
CHAPTER 10
RADIO WAVES
ELECTROMAGNETIC WAVE PROPAGATION
1000. Source of Radio Waves
Considerelectriccurrentasaflowofelectronsalonga
conductorbetweenpointsofdifferingpotential.Adirect
currentflowscontinuouslyinthesamedirection.Thiswould
occurifthepolarityoftheelectromotiveforcecausingthe
electronflowwereconstant,suchasisthecasewithabattery.
If,however,thecurrentisinducedbytherelativemotion
betweenaconductorandamagneticfield,suchasisthecase
inarotatingmachinecalledagenerator,thentheresulting
currentchangesdirectionintheconductorasthepolarityofthe
electromotiveforcechangeswiththerotationofthe
generator’s rotor. This is known asalternating current.
Theenergyofthecurrentflowingthroughthe
conductoriseitherdissipatedasheat(anenergyloss
proportionaltoboththecurrentflowingthroughthe
conductorandtheconductor’sresistance)orstoredinan
electromagneticfieldorientedsymmetricallyaboutthe
conductor.Theorientationofthisfieldisafunctionofthe
polarityofthesourceproducingthecurrent.Whenthe
currentisremovedfromthewire,thiselectromagneticfield
will, after a finite time, collapse back into the wire.
Whatwouldoccurshouldthepolarityofthecurrent
sourcesupplyingthewirebereversedataratewhich
exceedsthefiniteamountoftimerequiredfortheelectro-
magneticfieldtocollapsebackuponthewire?Inthiscase,
anothermagneticfield,proportionalinstrengthbutexactly
oppositeinmagneticorientationtotheinitialfield,willbe
formeduponthewire.Theinitialmagneticfield,itscurrent
sourcegone,cannotcollapsebackuponthewirebecauseof
theexistenceofthissecondelectromagneticfield.Instead,
itpropagatesoutintospace.Thisisthebasicprincipleofa
radioantenna,whichtransmitsawaveatafrequency
proportionaltotherateofpolereversalandataspeedequal
to the speed of light.
1001. Radio Wave Terminology
Themagneticfieldstrengthinthevicinityofa
conductorisdirectlyproportionaltothemagnitudeofthe
currentflowingthroughtheconductor.Recallthe
discussionofalternatingcurrentabove.Arotating
generatorproducescurrentintheformofasinewave.That
is,themagnitudeofthecurrentvariesasafunctionofthe
relativepositionoftherotatingconductorandthestationary
magneticfieldusedtoinducethecurrent.Thecurrentstarts
atzero,increasestoamaximumastherotorcompletesone
quarterofitsrevolution,andfallstozerowhentherotor
completesonehalfofitsrevolution.Thecurrentthen
approachesanegativemaximum;thenitonceagainreturns
to zero. This cycle can be represented by a sine function.
Therelationshipbetweenthecurrentandthemagnetic
fieldstrengthinducedintheconductorthroughwhichthe
currentisflowingisshowninFigure1001.Recallfromthe
discussionabovethatthisfieldstrengthisproportionaltothe
magnitudeofthecurrent;thatis,ifthecurrentisrepresented
byasinewavefunction,thensotoowillbethemagneticfield
strengthresultingfromthatcurrent.Thischaracteristicshape
ofthefieldstrengthcurvehasledtotheuseoftheterm
“wave”whenreferringtoelectromagneticpropagation.The
maximumdisplacementofapeakfromzeroiscalledthe
amplitude.Theforwardsideofanywaveiscalledthewave
front.Foranon-directionalantenna,eachwaveproceeds
outward as an expanding sphere (or hemisphere).
Onecycleisacompletesequenceofvalues,asfromcrest
tocrest.Thedistancetraveledbytheenergyduringonecycle
isthewavelength,usuallyexpressedinmetricunits(meters,
centimeters,etc.).Thenumberofcyclesrepeatedduringunit
time(usually1second)isthefrequency.Thisisgiveninhertz
(cyclespersecond).Akilohertz(kHz)is1,000cyclesper
second.Amegahertz(MHz)is1,000,000cyclespersecond.
Wavelength and frequency are inversely proportional.
Thephaseofawaveistheamountbywhichthecycle
Figure 1001. Radio wave terminology.
152RADIO WAVES
hasprogressedfromaspecifiedorigin.Formostpurposesit
isstatedincircularmeasure,acompletecyclebeing
considered360°.Generally,theoriginisnotimportant,
principalinterestbeingthephaserelativetothatofsome
otherwave.Thus,twowaveshavingcrests1/4cycleapart
aresaidtobe90°“outofphase.”Ifthecrestofonewave
occursatthetroughofanother,thetwoare180°outof
phase.
1002. The Electromagnetic Spectrum
Theentirerangeofelectromagneticradiationfrequen-
ciesiscalledtheelectromagneticspectrum.The
frequencyrangesuitableforradiotransmission,theradio
spectrum,extendsfrom10kilohertzto300,000mega-
hertz.Itisdividedintoanumberofbands,asshownin
Table 1002.
Belowtheradiospectrum,butoverlappingit,istheau-
diofrequencyband,extendingfrom20to20,000hertz.
Abovetheradiospectrumareheatandinfrared,thevisible
spectrum(lightinitsvariouscolors),ultraviolet,X-rays,
gammarays,andcosmicrays.TheseareincludedinTable
1002.Wavesshorterthan30centimetersareusuallycalled
microwaves.
Withinthefrequenciesfrom1-40gHz(1,000-40,000
MHz), additional bands are defined as follows:
L-band: 1-2 gHz (1,000-2,000 MHz)
S-band: 2-4 gHz (2,000-4,000 MHz
C-band: 4-8 gHz (4,000-8,000 MHz)
X-band: 8-12.5 gHz (8,000-12,500 MHz)
Lower K-band: 12.5-18 gHz (12,500-18,000 MHz)
Upper K-band: 26.5-40 gHz (26,500-40,000 MHz)
MarineradarsystemscommonlyoperateintheSand
Xbands,whilesatellitenavigationsystemsignalsarefound
in the L-band.
ThebreakoftheK-bandintolowerandupperrangesis
necessarybecausetheresonantfrequencyofwatervapor
occursinthemiddleregionofthisband,andsevereabsorp-
tion of radio waves occurs in this part of the spectrum.
BandAbbreviationRange of frequencyRange of wavelength
Audio frequencyAF20 to 20,000 Hz15,000,000 to 15,000 m
Radio frequencyRF10 kHz to 300,000 MHz30,000 m to 0.1 cm
Very low frequencyVLF10 to 30 kHz30,000 to 10,000 m
Low frequencyLF30 to 300 kHz10,000 to 1,000 m
Medium frequencyMF300 to 3,000 kHz1,000 to 100 m
High frequencyHF3 to 30 MHz100 to 10 m
Very high frequencyVHF30 to 300 MHz10 to 1 m
Ultra high frequencyUHF300 to 3,000 MHz100 to 10 cm
Super high frequencySHF3,000 to 30,000 MHz10 to 1 cm
Extremely high
frequency
EHF30,000 to 300,000 MHz1 to 0.1 cm
Heat and infrared*
10
6
to 3.9×10
8
MHz0.03 to 7.6×10
-5
cm
Visible spectrum*
3.9×10
8
to 7.9×10
8
MHz7.6×10
-5
to 3.8×10
-5
cm
Ultraviolet*
7.9×10
8
to 2.3×10
10
MHz3.8×10
-5
to 1.3×10
-6
cm
X-rays*
2.0×10
9
to 3.0×10
13
MHz1.5×10
-5
to 1.0×10
-9
cm
Gamma rays*
2.3×10
12
to 3.0×10
14
MHz1.3×10
-8
to 1.0×10
-10
cm
Cosmic rays*
>4.8×10
15
MHz<6.2×10
-12
cm
* Values approximate.
Table 1002. Electromagnetic spectrum.
RADIO WAVES153
1003. Polarization
Radiowavesproducebothelectricandmagneticfields.
Thedirectionoftheelectriccomponentofthefieldiscalled
thepolarizationoftheelectromagneticfield.Thus,ifthe
electriccomponentisvertical,thewaveissaidtobe
“verticallypolarized,”andifhorizontal,“horizontally
polarized.”
Awavetravelingthroughspacemaybepolarizedin
anydirection.OnetravelingalongthesurfaceoftheEarthis
alwaysverticallypolarizedbecausetheEarth,aconductor,
short-circuitsanyhorizontalcomponent.Themagneticfield
and the electric field are always mutually perpendicular.
1004. Reflection
Whenradiowavesstrikeasurface,thesurfacereflects
theminthesamemanneraslightwaves.Radiowavesofall
frequenciesarereflectedbythesurfaceoftheEarth.The
strengthofthereflectedwavedependsuponangleof
incidence(theanglebetweentheincidentrayandthe
horizontal),typeofpolarization,frequency,reflecting
propertiesofthesurface,anddivergenceofthereflected
ray.Lowerfrequenciespenetratetheearth’ssurfacemore
thanhigherones.Atverylowfrequencies,usableradio
signalscanbereceivedsomedistancebelowthesurfaceof
the sea.
Aphasechangeoccurswhenawaveisreflectedfrom
thesurfaceoftheEarth.Theamountofthechangevaries
withtheconductivityoftheEarthandthepolarizationof
thewave,reachingamaximumof180°forahorizontally
polarizedwavereflectedfromseawater(consideredto
have infinite conductivity).
Whendirectwaves(thosetravelingfromtransmitterto
receiverinarelativelystraightline,withoutreflection)and
reflectedwavesarriveatareceiver,thetotalsignalisthe
vectorsumofthetwo.Ifthesignalsareinphase,theyrein-
forceeachother,producingastrongersignal.Ifthereisa
phasedifference,thesignalstendtocanceleachother,the
cancellationbeingcompleteifthephasedifferenceis180°
andthetwosignalshavethesameamplitude.Thisinterac-
tion of waves is calledwave interference.
Aphasedifferencemayoccurbecauseofthechangeof
phaseofareflectedwave,orbecauseofthelongerpathit
follows.Thesecondeffectdecreaseswithgreaterdistance
betweentransmitterandreceiver,forunderthesecondi-
tions the difference in path lengths is smaller.
Atlowerfrequenciesthereisnopracticalsolutionto
interferencecausedinthisway.ForVHFandhigherfre-
quencies,theconditioncanbeimprovedbyelevatingthe
antenna,ifthewaveisverticallypolarized.Additionally,
interferenceathigherfrequenciescanbemorenearlyelim-
inatedbecauseofthegreatereaseofbeamingthesignalto
avoid reflection.
Reflectionsmayalsooccurfrommountains,trees,and
otherobstacles.Suchreflectionisnegligibleforlower
frequencies,butbecomesmoreprevalentasfrequency
increases.Inradiocommunication,itcanbereducedby
usingdirectionalantennas,butthissolutionisnotalways
available for navigational systems.
Variousreflectingsurfacesoccurintheatmosphere.At
highfrequencies,reflectionstakeplacefromrain.Atstill
higherfrequencies,reflectionsarepossiblefromclouds,
particularlyrainclouds.Reflectionsmayevenoccurata
sharplydefinedboundarysurfacebetweenairmasses,as
whenwarm,moistairflowsovercold,dryair.Whensucha
surfaceisroughlyparalleltothesurfaceoftheEarth,radio
wavesmaytravelforgreaterdistancesthannormalThe
principalsourceofreflectionintheatmosphereisthe
ionosphere.
1005. Refraction
Refractionofradiowavesissimilartothatoflight
waves.Thus,asasignalpassesfromairofonedensityto
thatofadifferentdensity,thedirectionoftravelisaltered.
Theprincipalcauseofrefractionintheatmosphereisthe
differenceintemperatureandpressureoccurringatvarious
heights and in different air masses.
Refractionoccursatallfrequencies,butbelow30MHz
theeffectissmallascomparedwithionosphericeffects,
diffraction,andabsorption.Athigherfrequencies,
refractioninthelowerlayeroftheatmosphereextendsthe
radiohorizontoadistanceabout15percentgreaterthanthe
visiblehorizon.Theeffectisthesameasiftheradiusofthe
Earthwereaboutone-thirdgreaterthanitisandtherewere
no refraction.
Sometimesthelowerportionoftheatmosphere
becomesstratified.Thisstratificationresultsinnonstandard
temperatureandmoisturechangeswithheight.Ifthereisa
markedtemperatureinversionorasharpdecreaseinwater
vaporcontentwithincreasedheight,ahorizontalradioduct
maybeformed.Highfrequencyradiowavestraveling
horizontallywithintheductarerefractedtosuchanextent
thattheyremainwithintheduct,followingthecurvatureof
theEarthforphenomenaldistances.Thisiscalledsuper-
refraction.Maximumresultsareobtainedwhenboth
transmittingandreceivingantennasarewithintheduct.
Thereisalowerlimittothefrequencyaffectedbyducts.It
varies from about 200 MHz to more than 1,000 MHz.
Atnight,surfaceductsmayoccuroverlanddueto
coolingofthesurface.Atsea,surfaceductsabout50feet
thickmayoccuratanytimeinthetradewindbelt.Surface
ducts100feetormoreinthicknessmayextendfromland
outtoseawhenwarmairfromthelandflowsoverthe
cooleroceansurface.Elevatedductsfromafewfeetto
morethan1,000feetinthicknessmayoccuratelevationsof
1,000to5,000feet,duetothesettlingofalargeairmass.
ThisisafrequentoccurrenceinSouthernCaliforniaand
certain areas of the Pacific Ocean.
Abendinginthehorizontalplaneoccurswhena
groundwavecrossesacoastatanobliqueangle.Thisisdue
154RADIO WAVES
toamarkeddifferenceintheconductingandreflecting
propertiesofthelandandwateroverwhichthewavetravels.
The effect is known ascoastal refraction orland effect.
1006. The Ionosphere
Sinceanatomnormallyhasanequalnumberof
negativelychargedelectronsandpositivelycharged
protons,itiselectricallyneutral.Anionisanatomorgroup
ofatomswhichhasbecomeelectricallycharged,either
positivelyornegatively,bythelossorgainofoneormore
electrons.
Lossofelectronsmayoccurinavarietyofways.Inthe
atmosphere,ionsareusuallyformedbycollisionofatoms
withrapidlymovingparticles,orbytheactionofcosmic
raysorultravioletlight.Inthelowerportionofthe
atmosphere,recombinationsoonoccurs,leavingasmall
percentageofions.Inthinatmospherefarabovethesurface
oftheEarth,however,atomsarewidelyseparatedanda
largenumberofionsmaybepresent.Theregionof
numerouspositiveandnegativeionsandunattached
electronsiscalledtheionosphere.Theextentofionization
dependsuponthekindsofatomspresentintheatmosphere,
thedensityoftheatmosphere,andthepositionrelativeto
theSun(timeofdayandseason).Aftersunset,ionsand
electronsrecombinefasterthantheyareseparated,
decreasing the ionization of the atmosphere.
Anelectroncanbeseparatedfromitsatomonlybythe
applicationofgreaterenergythanthatholdingtheelectron.
Sincetheenergyoftheelectrondependsprimarilyuponthe
kindofanatomofwhichitisapart,anditspositionrelative
tothenucleusofthatatom,differentkindsofradiationmay
cause ionization of different substances.
Intheoutermostregionsoftheatmosphere,thedensity
issolowthatoxygenexistslargelyasseparateatoms,rather
thancombiningasmoleculesasitdoesnearerthesurfaceof
theEarth.Atgreatheightstheenergylevelislowand
ionizationfromsolarradiationisintense.Thisisknownas
theFlayer.Abovethisleveltheionizationdecreases
becauseofthelackofatomstobeionized.Belowthislevel
itdecreasesbecausetheionizingagentofappropriate
energyhasalreadybeenabsorbed.Duringdaylight,two
levelsofmaximumFionizationcanbedetected,theF
2
layeratabout125statutemilesabovethesurfaceofthe
Earth,andtheF
1
layeratabout90statutemiles.Atnight,
these combine to form a single F layer.
Ataheightofabout60statutemiles,thesolarradiation
notabsorbedbytheFlayerencounters,forthefirsttime,large
numbersofoxygenmolecules.Anewmaximumionization
occurs,knownastheElayer.Theheightofthislayerisquite
constant,incontrastwiththefluctuatingFlayer.Atnightthe
E layer becomes weaker by two orders of magnitude.
BelowtheElayer,aweakDlayerformsataheightof
about45statutemiles,wheretheincomingradiation
encountersozoneforthefirsttime.TheDlayeristhe
principalsourceofabsorptionofHFwaves,andof
reflection of LF and VLF waves during daylight.
1007. The Ionosphere and Radio Waves
Whenaradiowaveencountersaparticlehavingan
electriccharge,itcausesthatparticletovibrate.The
vibratingparticleabsorbselectromagneticenergyfromthe
radiowaveandradiatesit.Theneteffectisachangeof
polarizationandanalterationofthepathofthewave.That
portionofthewaveinamorehighlyionizedregiontravels
faster,causingthewavefronttotiltandthewavetobe
directed toward a region of less intense ionization.
RefertoFigure1007a,inwhichasinglelayerofthe
ionosphereisconsidered.Ray1enterstheionosphereat
suchananglethatitspathisaltered,butitpassesthrough
andproceedsoutwardintospace.Astheanglewiththe
horizontaldecreases,acriticalvalueisreachedwhereray2
isbentorreflectedbacktowardtheEarth.Astheangleis
stillfurtherdecreased,suchasat3,thereturntoEarth
occurs at a greater distance from the transmitter.
Awavereachingareceiverbywayoftheionosphere
iscalledaskywave.Thisexpressionisalsoappropriately
appliedtoawavereflectedfromanairmassboundary.In
commonusage,however,itisgenerallyassociatedwiththe
ionosphere.Thewavewhichtravelsalongthesurfaceofthe
Earthiscalledagroundwave.Atanglesgreaterthanthe
criticalangle,noskywavesignalisreceived.Therefore,
thereisaminimumdistancefromthetransmitteratwhich
skywavescanbereceived.Thisiscalledtheskipdistance,
showninFigure1007a.Ifthegroundwaveextendsoutfor
lessdistancethantheskipdistance,askipzoneoccurs,in
which no signal is received.
Thecriticalradiationangledependsupontheintensity
ofionization,andthefrequencyoftheradiowave.Asthe
frequencyincreases,theanglebecomessmaller.Atfre-
quenciesgreaterthanabout30MHzvirtuallyallofthe
energypenetratesthroughorisabsorbedbytheionosphere.
Therefore,atanygivenreceiverthereisamaximumusable
frequencyifskywavesaretobeutilized.Thestrongestsig-
nalsarereceivedatorslightlybelowthisfrequency.There
isalsoalowerpracticalfrequencybeyondwhichsignalsare
tooweaktobeofvalue.Withinthisbandtheoptimumfre-
quencycanbeselectedtogivebestresults.Itcannotbetoo
nearthemaximumusablefrequencybecausethisfrequency
fluctuateswithchangesofintensitywithintheionosphere.
Duringmagneticstormstheionospheredensitydecreases.
Themaximumusablefrequencydecreases,andthelower
usablefrequencyincreases.Thebandofusablefrequencies
isthusnarrowed.Underextremeconditionsitmaybecom-
pletelyeliminated,isolatingthereceiverandcausinga
radio blackout.
Skywavesignalsreachingagivenreceivermayarrive
byanyofseveralpaths,asshowninFigure1007b.Asignal
whichundergoesasinglereflectioniscalleda“one-hop”
signal,onewhichundergoestworeflectionswithaground
reflectionbetweeniscalleda“two-hop”signal,etc.A
RADIO WAVES155
“multihop”signalundergoesseveralreflections.Thelayer
atwhichthereflectionoccursisusuallyindicated,also,as
“one-hop E,” “two-hop F,” etc.
Becauseofthedifferentpathsandphasechangesoc-
curringateachreflection,thevarioussignalsarrivingata
receiverhavedifferentphaserelationships.Sincethedensi-
tyoftheionosphereiscontinuallyfluctuating,thestrength
andphaserelationshipsofthevarioussignalsmayundergo
analmostcontinuouschange.Thus,thevarioussignalsmay
reinforceeachotheratonemomentandcanceleachother
atthenext,resultinginfluctuationsofthestrengthoftheto-
talsignalreceived.Thisiscalledfading.Thisphenomenon
mayalsobecausedbyinteractionofcomponentswithina
singlereflectedwave,orchangesinitsstrengthdueto
changesinthereflectingsurface.Ionosphericchangesare
associatedwithfluctuationsintheradiationreceivedfrom
theSun,sincethisistheprincipalcauseofionization.Sig-
nalsfromtheFlayerareparticularlyerraticbecauseofthe
rapidly fluctuating conditions within the layer itself.
Themaximumdistanceatwhichaone-hopEsignalcanbe
receivedisabout1,400miles.Atthisdistancethesignalleaves
thetransmitterinapproximatelyahorizontaldirection.Aone-
hopFsignalcanbereceivedouttoabout2,500miles.Atlow
frequencies groundwaves extend out for great distances.
Askywavemayundergoachangeofpolarization
duringreflectionfromtheionosphere,accompaniedbyan
alterationinthedirectionoftravelofthewave.Thisis
calledpolarizationerror.Nearsunriseandsunset,when
rapidchangesareoccurringintheionosphere,reception
maybecomeerraticandpolarizationerroramaximum.
This is callednight effect.
1008. Diffraction
Whenaradiowaveencountersanobstacle,itsenergyisre-
flectedorabsorbed,causingashadowbeyondtheobstacle.
However,someenergydoesentertheshadowareabecauseof
diffraction.ThisisexplainedbyHuygens’principle,which
Figure 1007a. The effect of the ionosphere on radio waves.
Figure 1007b. Various paths by which a skywave signal might be received.
156RADIO WAVES
statesthateverypointonthesurfaceofawavefrontisasource
ofradiation,transmittingenergyinalldirectionsaheadofthe
wave.Nonoticeableeffectofthisprincipleisobserveduntilthe
wavefrontencountersanobstacle,whichinterceptsaportionof
thewave.Fromtheedgeoftheobstacle,energyisradiatedinto
theshadowarea,andalsooutsideofthearea.Thelatterinteracts
withenergyfromotherpartsofthewavefront,producingalter-
natebandsinwhichthesecondaryradiationreinforcesortends
tocanceltheenergyoftheprimaryradiation.Thus,thepractical
effectofanobstacleisagreatlyreducedsignalstrengthinthe
shadowarea,andadisturbedpatternforashortdistanceoutside
the shadow area. This is illustrated in Figure 1008.
Theamountofdiffractionisinverselyproportionalto
the frequency, being greatest at very low frequencies.
1009. Absorption and Scattering
Theamplitudeofaradiowaveexpandingoutward
throughspacevariesinverselywithdistance,weakening
withincreaseddistance.Thedecreaseofstrengthwith
distanceiscalledattenuation.Undercertainconditionsthe
attenuation is greater than in free space.
AwavetravelingalongthesurfaceoftheEarthlosesa
certainamountofenergytotheEarth.Thewaveis
diffracteddownwardandabsorbedbytheEarth.Asaresult
ofthisabsorption,theremainderofthewavefronttilts
downward,resultinginfurtherabsorptionbytheEarth.
Attenuationisgreateroverasurfacewhichisapoor
conductor.Relativelylittleabsorptionoccursoversea
water,whichisanexcellentconductoratlowfrequencies,
andlowfrequencygroundwavestravelgreatdistancesover
water.
Askywavesuffersanattenuationlossinitsencounter
withtheionosphere.Theamountdependsupontheheight
andcompositionoftheionosphereaswellasthefrequency
oftheradiowave.Maximumionosphericabsorptionoccurs
at about 1,400 kHz.
Ingeneral,atmosphericabsorptionincreaseswith
frequency.ItisaproblemonlyintheSHFandEHF
frequencyrange.Atthesefrequencies,attenuationisfurther
increasedbyscatteringduetoreflectionbyoxygen,water
vapor, water droplets, and rain in the atmosphere.
1010. Noise
Unwantedsignalsinareceiverarecalledinterference.
Theintentionalproductionofsuchinterferencetoobstruct
communicationiscalledjamming.Unintentional
interference is callednoise.
Noisemayoriginatewithinthereceiver.Humis
usuallytheresultofinductionfromneighboringcircuits
carryingalternatingcurrent.Irregularcracklingorsizzling
soundsmaybecausedbypoorcontactsorfaulty
componentswithinthereceiver.Straycurrentsinnormal
componentscausesomenoise.Thissourcesetstheultimate
limitofsensitivitythatcanbeachievedinareceiver.Itis
Figure 1008. Diffraction.
RADIO WAVES157
the same at any frequency.
Noiseoriginatingoutsidethereceivermaybeeither
man-madeornatural.Man-madenoisesoriginatein
electricalappliances,motorandgeneratorbrushes,ignition
systems,andothersourcesofsparkswhichtransmitelectro-
magneticsignalsthatarepickedupbythereceivingantenna.
Naturalnoiseiscausedprincipallybydischargeof
staticelectricityintheatmosphere.Thisiscalled
atmosphericnoise,atmospherics,orstatic.Anextreme
exampleisathunderstorm.Anexposedsurfacemay
acquireaconsiderablechargeofstaticelectricity.Thismay
becausedbyfrictionofwaterorsolidparticlesblown
againstoralongsuchasurface.Itmayalsobecausedby
splittingofawaterdropletwhichstrikesthesurface,one
partofthedropletrequiringapositivechargeandtheother
anegativecharge.Thesechargesmaybetransferredtothe
surface.Thechargetendstogatheratpointsandridgesof
theconductingsurface,andwhenitaccumulatestoa
sufficientextenttoovercometheinsulatingpropertiesof
theatmosphere,itdischargesintotheatmosphere.Under
suitableconditionsthisbecomesvisibleandisknownasSt.
Elmo’sfire,whichissometimesseenatmastheads,the
ends of yardarms, etc.
Atmosphericnoiseoccurstosomeextentatall
frequenciesbutdecreaseswithhigherfrequencies.Above
about 30 MHz it is not generally a problem.
1011. Antenna Characteristics
Antennadesignandorientationhaveamarkedeffect
uponradiowavepropagation.Forasingle-wireantenna,
strongestsignalsaretransmittedalongtheperpendicularto
thewire,andvirtuallynosignalinthedirectionofthewire.
Foraverticalantenna,thesignalstrengthisthesameinall
horizontaldirections.Unlessthepolarizationundergoesa
changeduringtransit,thestrongestsignalreceivedfroma
verticaltransmittingantennaoccurswhenthereceiving
antenna is also vertical.
Forlowerfrequenciestheradiationofaradiosignal
takesplacebyinteractionbetweentheantennaandthe
ground.Foraverticalantenna,efficiencyincreaseswith
greaterlengthoftheantenna.Forahorizontalantenna,
efficiencyincreaseswithgreaterdistancebetweenantenna
andground.Near-maximumefficiencyisattainedwhen
thisdistanceisone-halfwavelength.Thisisthereasonfor
elevatinglowfrequencyantennastogreatheights.
However,atthelowestfrequencies,therequiredheight
becomesprohibitivelygreat.At10kHzitwouldbeabout8
nauticalmilesforahalf-wavelengthantenna.Therefore,
lowerfrequencyantennasareinherentlyinefficient.Thisis
partlyoffsetbythegreaterrangeofalowfrequencysignal
of the same transmitted power as one of higher frequency.
Athigherfrequencies,thegroundisnotused,both
conductingportionsbeingincludedinadipoleantenna.Not
onlycansuchanantennabemadeefficient,butitcanalso
bemadesharplydirective,thusgreatlyincreasingthe
strength of the signal transmitted in a desired direction.
Thepowerreceivedisinverselyproportionaltothe
squareofthedistancefromthetransmitter,assumingthere
is no attenuation due to absorption or scattering.
1012. Range
Therangeatwhichausablesignalisreceiveddepends
uponthepowertransmitted,thesensitivityofthereceiver,
frequency,routeoftravel,noiselevel,andperhapsother
factors.Forthesametransmittedpower,boththe
groundwaveandskywaverangesaregreatestatthelowest
frequencies,butthisissomewhatoffsetbythelesser
efficiencyofantennasforthesefrequencies.Athigher
frequencies,onlydirectwavesareuseful,andtheeffective
rangeisgreatlyreduced.Attenuation,skipdistance,ground
reflection,waveinterference,conditionoftheionosphere,
atmosphericnoiselevel,andantennadesignallaffectthe
distance at which useful signals can be received.
1013. Radio Wave Spectra
Frequencyisanimportantconsiderationinradiowave
propagation.Thefollowingsummaryindicatestheprincipal
effectsassociatedwiththevariousfrequencybands,starting
withthelowestandprogressingtothehighestusableradio
frequency.
VeryLowFrequency(VLF,10to30kHz):TheVLF
signalspropagatebetweentheboundsoftheionosphere
andtheEarthandarethusguidedaroundthecurvatureof
theEarthtogreatdistanceswithlowattenuationand
excellentstability.Diffractionismaximum.Becauseofthe
longwavelength,largeantennasareneeded,andeventhese
areinefficient,permittingradiationofrelativelysmall
amountsofpower.Magneticstormshavelittleeffectupon
transmissionbecauseoftheefficiencyofthe“Earth-
ionospherewaveguide.”Duringsuchstorms,VLFsignals
mayconstitutetheonlysourceofradiocommunication
overgreatdistances.However,interferencefrom
atmosphericnoisemaybetroublesome.Signalsmaybe
received from below the surface of the sea.
LowFrequency(LF,30to300kHz):Asfrequencyis
increasedtotheLFbandanddiffractiondecreases,thereis
greaterattenuationwithdistance,andrangeforagiven
poweroutputfallsoffrapidly.However,thisispartlyoffset
bymoreefficienttransmittingantennas.LFsignalsare
moststablewithingroundwavedistanceofthetransmitter.
Awiderbandwidthpermitspulsedsignalsat100kHz.This
allowsseparationofthestablegroundwavepulsefromthe
variableskywavepulseupto1,500km,andupto2,000km
foroverwaterpaths.ThefrequencyforLoranCisintheLF
band.Thisbandisalsousefulforradiodirectionfinding
and time dissemination.
MediumFrequency(MF,300to3,000kHz):
Groundwavesprovidedependableservice,buttherangefor
agivenpowerisreducedgreatly.Thisrangevariesfrom
158RADIO WAVES
about400milesatthelowerportionofthebandtoabout15
milesattheupperendforatransmittedsignalof1kilowatt.
Thesevaluesareinfluenced,however,bythepowerofthe
transmitter,thedirectivityandefficiencyoftheantenna,
andthenatureoftheterrainoverwhichsignalstravel.
Elevatingtheantennatoobtaindirectwavesmayimprove
thetransmission.Atthelowerfrequenciesoftheband,
skywavesareavailablebothdayandnight.Asthe
frequencyisincreased,ionosphericabsorptionincreasesto
amaximumatabout1,400kHz.Athigherfrequenciesthe
absorptiondecreases,permittingincreaseduseof
skywaves.Sincetheionospherechangeswiththehour,
season,andsunspotcycle,thereliabilityofskywavesignals
isvariable.Bycarefulselectionoffrequency,rangesofas
muchas8,000mileswith1kilowattoftransmittedpower
arepossible,usingmultihopsignals.However,the
frequencyselectioniscritical.Ifitistoohigh,thesignals
penetratetheionosphereandarelostinspace.Ifitistoo
low,signalsaretooweak.Ingeneral,skywavereceptionis
equallygoodbydayornight,butlowerfrequenciesare
neededatnight.Thestandardbroadcastbandfor
commercial stations (535 to 1,605 kHz) is in the MF band.
HighFrequency(HF,3to30MHz):Aswithhigher
mediumfrequencies,thegroundwaverangeofHFsignals
islimitedtoafewmiles,buttheelevationoftheantenna
mayincreasethedirect-wavedistanceoftransmission.
Also,theheightoftheantennadoeshaveanimportant
effectuponskywavetransmissionbecausetheantennahas
an“image”withintheconductingEarth.Thedistance
betweenantennaandimageisrelatedtotheheightofthe
antenna,andthisdistanceisascriticalasthedistance
betweenelementsofanantennasystem.Maximumusable
frequenciesfallgenerallywithintheHFband.Bydaythis
maybe10to30MHz,butduringthenightitmaydropto8
to10MHz.TheHFbandiswidelyusedforship-to-shipand
ship-to-shore communication.
VeryHighFrequency(VHF,30to300MHz):
Communicationislimitedprimarilytothedirectwave,or
thedirectwaveplusaground-reflectedwave.Elevatingthe
antennatoincreasethedistanceatwhichdirectwavescan
beusedresultsinincreaseddistanceofreception,even
thoughsomewaveinterferencebetweendirectandground-
reflectedwavesispresent.Diffractionismuchlessthan
withlowerfrequencies,butitismostevidentwhensignals
crosssharpmountainpeaksorridges.Undersuitable
conditions,reflectionsfromtheionospherearesufficiently
strongtobeuseful,butgenerallytheyareunavailable.
Thereisrelativelylittleinterferencefromatmospheric
noiseinthisband.Reasonablyefficientdirectional
antennasarepossiblewithVHF.TheVHFbandismuch
used for communication.
UltraHighFrequency(UHF,300to3,000MHz):
SkywavesarenotusedintheUHFbandbecausethe
ionosphereisnotsufficientlydensetoreflectthewaves,
whichpassthroughitintospace.Groundwavesandground-
reflectedwavesareused,althoughthereissomewave
interference.Diffractionisnegligible,buttheradiohorizon
extendsabout15percentbeyondthevisiblehorizon,due
principallytorefraction.ReceptionofUHFsignalsis
virtuallyfreefromfadingandinterferencebyatmospheric
noise.Sharplydirectiveantennascanbeproducedfor
transmissioninthisband,whichiswidelyusedforship-to-
ship and ship-to-shore communication.
SuperHighFrequency(SHF,3,000to30,000MHz):
IntheSHFband,alsoknownasthemicrowaveorasthe
centimeterwaveband,therearenoskywaves,transmission
beingentirelybydirectandground-reflectedwaves.
Diffractionandinterferencebyatmosphericnoisearevirtually
nonexistent.Highlyefficient,sharplydirectiveantennascan
beproduced.Thus,transmissioninthisbandissimilartothat
ofUHF,butwiththeeffectsofshorterwavesbeinggreater.
Reflectionbyclouds,waterdroplets,dustparticles,etc.,
increases,causinggreaterscattering,increasedwave
interference,andfading.TheSHFbandisusedformarine
navigational radar.
ExtremelyHighFrequency(EHF,30,000to300,000
MHz):Theeffectsofshorterwavesaremorepronouncedin
theEHFband,transmissionbeingfreefromwave
interference,diffraction,fading,andinterferenceby
atmosphericnoise.Onlydirectandground-reflectedwaves
areavailable.Scatteringandabsorptionintheatmosphere
arepronouncedandmayproduceanupperlimittothe
frequency useful in radio communication.
1014. Regulation of Frequency Use
Whilethecharacteristicsofvariousfrequenciesare
importanttotheselectionofthemostsuitableoneforany
givenpurpose,thesearenottheonlyconsiderations.
Confusionandextensiveinterferencewouldresultifevery
userhadcompletefreedomofselection.Someformof
regulationisneeded.Theallocationofvariousfrequency
bandstoparticularusesisamatterofinternational
agreement.WithintheUnitedStates,theFederalCommuni-
cationsCommissionhasresponsibilityforauthorizinguse
ofparticularfrequencies.Insomecasesagivenfrequencyis
allocatedtoseveralwidelyseparatedtransmitters,butonly
underconditionswhichminimizeinterference,suchas
duringdaylighthours.Interferencebetweenstationsis
furtherreducedbytheuseofchannels,eachofanarrow
bandoffrequencies.Assignedfrequenciesareseparatedby
anarbitrarybandoffrequenciesthatarenotauthorizedfor
use.Inthecaseofradioaidstonavigationandship
communicationsbandsofseveralchannelsareallocated,
permitting selection of band and channel by the user.
1015. Types of Radio Transmission
Aseriesofwavestransmittedatconstantfrequencyand
amplitudeiscalledacontinuouswave(CW).Thiscannotbe
heardexceptattheverylowestradiofrequencies,whenitmay
produce, in a receiver, an audible hum of high pitch.
RADIO WAVES159
Althoughacontinuouswavemaybeuseddirectly,asin
radiodirectionfindingorDecca,itismorecommonlymodi-
fiedinsomemanner.Thisiscalledmodulation.Whenthis
occurs,thecontinuouswaveservesasacarrierwaveforinfor-
mation. Any of several types of modulation may be used.
Inamplitudemodulation(AM)theamplitudeofthe
carrierwaveisalteredinaccordancewiththeamplitudeof
amodulatingwave,usuallyofaudiofrequency,asshownin
Figure1015a.Inthereceiverthesignalisdemodulatedby
removingthemodulatingwaveandconvertingitbacktoits
originalform.Thisformofmodulationiswidelyusedin
voiceradio,asinthestandardbroadcastbandofcommer-
cial broadcasting.
Ifthefrequencyinsteadoftheamplitudeisalteredin
accordancewiththeamplitudeoftheimpressedsignal,as
showninFigure1015a,frequencymodulation(FM)
occurs.ThisisusedforcommercialFMradiobroadcasts
and the sound portion of television broadcasts.
Pulsemodulation(PM)issomewhatdifferent,there
beingnoimpressedmodulatingwave.Inthisformoftrans-
mission,veryshortburstsofcarrierwavearetransmitted,
separatedbyrelativelylongperiodsof“silence,”during
whichthereisnotransmission.Thistypeoftransmission,
illustratedinFigure1015b,isusedinsomecommonradio
navigational aids, including radar and Loran C.
1016. Transmitters
Aradiotransmitterconsistsessentiallyof(1)apower
supplytofurnishdirectcurrent,(2)anoscillatortoconvert
directcurrentintoradio-frequencyoscillations(thecarrier
wave),(3)adevicetocontrolthegeneratedsignal,and(4)
anamplifiertoincreasetheoutputoftheoscillator.For
sometransmittersamicrophoneisneededwithamodulator
andfinalamplifiertomodulatethecarrierwave.Inaddi-
tion,anantennaandground(forlowerfrequencies)are
neededtoproduceelectromagneticradiation.Thesecom-
ponents are illustrated in Figure 1016.
1017. Receivers
Whenaradiowavepassesaconductor,acurrentis
inducedinthatconductor.Aradioreceiverisadevice
whichsensesthepowerthusgeneratedinanantenna,and
transformsitintousableform.Itisabletoselectsignalsof
asinglefrequency(actuallyanarrowbandoffrequencies)
fromamongthemanywhichmayreachthereceiving
antenna.Thereceiverisabletodemodulatethesignaland
provideadequateamplification.Theoutputofareceiver
maybepresentedaudiblybyearphonesorloudspeaker;or
visuallyonadial,cathode-raytube,counter,orother
Figure1015a.Amplitudemodulation(upperfigure)andfrequencymodulation(lowerfigure)bythesamemodulatingwave.
Figure 1015b. Pulse modulation.
160RADIO WAVES
display.Thus,theusefulreceptionofradiosignalsrequires
threecomponents:(1)anantenna,(2)areceiver,and(3)a
display unit.
Radioreceiversdiffermainlyin(1)frequencyrange,
therangeoffrequenciestowhichtheycanbetuned;(2)
selectivity,theabilitytoconfinereceptiontosignalsofthe
desiredfrequencyandavoidothersofnearlythesame
frequency;(3)sensitivity,theabilitytoamplifyaweak
signaltousablestrengthagainstabackgroundofnoise;(4)
stability,theabilitytoresistdriftfromconditionsorvalues
towhichset;and(5)fidelity,thecompletenesswithwhich
theessentialcharacteristicsoftheoriginalsignalare
reproduced.Receiversmayhaveadditionalfeaturessuchas
anautomaticfrequencycontrol,automaticnoiselimiter,
etc.
Someofthesecharacteristicsareinterrelated.For
instance,ifareceiverlacksselectivity,signalsofa
frequencydifferingslightlyfromthosetowhichthe
receiveristunedmaybereceived.Thisconditioniscalled
spillover,andtheresultinginterferenceiscalledcrosstalk.
Iftheselectivityisincreasedsufficientlytoprevent
spillover,itmaynotpermitreceiptofagreatenoughband
offrequenciestoobtainthefullrangeofthoseofthedesired
signal. Thus, the fidelity may be reduced.
Atransponderisatransmitter-receivercapableof
acceptingthechallengeofaninterrogatorandautomat-
ically transmitting an appropriate reply.
U.S. RADIO NAVIGATION POLICY
1018. The Federal Radionavigation Plan
Theidealnavigationsystemshouldprovidethree
thingstotheuser.First,itshouldbeasaccurateasnecessary
forthejobitisexpectedtodo.Second,itshouldbeavailable
100%ofthetime,inallweather,atanytimeofdayornight.
Third,itshouldhave100%integrity,warningtheuserand
shuttingitselfdownwhennotoperatingproperly.Themix
ofnavigationsystemsintheU.S.iscarefullychosento
providemaximumaccuracy,availability,andintegritytoall
users,marine,aeronautical,andterrestrial,withinthe
constraints of budget and practicality.
TheFederalRadionavigationPlan(FRP)isproduced
bytheU.S.DepartmentsofDefenseandTransportation.It
establishesgovernmentpolicyonthemixofelectronic
navigationsystems,ensuringconsiderationofnational
interestsandefficientuseofresources.Itpresentsan
integratedfederalplanforallcommon-usecivilianand
militaryradionavigationsystems,outlinesapproachesfor
consolidationofsystems,providesinformationand
schedules,definesandclarifiesneworunresolvedissues,
andprovidesafocalpointforuserinput.TheFRPisa
reviewofexistingandplannedradionavigationsystems
usedinair,space,land,andmarinenavigation.Itisavailable
fromtheNationalTechnicalInformationService,
Springfield, Virginia, 22161, http://www.ntis.gov.
ThefirsteditionoftheFRPwasreleasedin1980as
partofapresidentialreporttoCongress.Itmarkedthefirst
timethatajointDepartmentofTransportation/Department
ofDefenseplanhadbeendevelopedforsystemsusedby
bothdepartments.TheFRPhashadinternationalimpacton
navigationsystems;itisdistributedtotheInternational
MaritimeOrganization(IMO),theInternationalCivil
AviationOrganization(ICAO),theInternational
AssociationofLighthouseAuthorities(IALA),andother
international organizations.
Duringanationalemergency,anyorallofthesystems
maybetemporarilydiscontinuedbythefederal
government.Thegovernment’spolicyistocontinueto
operateradionavigationsystemsaslongastheU.S.andits
alliesderivegreaterbenefitthanadversaries.Operating
agenciesmayshutdownsystemsorchangesignalformats
and characteristics during such an emergency.
Theplanisreviewedcontinuallyandupdated
Figure 1016. Components of a radio transmitter.
RADIO WAVES161
biennially.Industry,advisorygroups,andotherinterested
partiesprovideinput.Theplanconsidersgovernmental
responsibilitiesfornationalsecurity,publicsafety,and
transportationsystemeconomy.Itistheofficialsourceof
radionavigationsystemspolicyandplanningfortheUnited
States.SystemscoveredbytheFRPincludeGPS,DGPS,
WAAS,LAAS,LoranC,TACAN,MLS,VOR/VOR-
DME/VORTAC, and ILS.
1019. System Plans
Inordertomeetbothcivilianandmilitaryneeds,the
federalgovernmenthasestablishedanumberofdifferent
navigationsystems.Eachsystemutilizesthelatest
technologyavailableatthetimeofimplementationandis
upgradedastechnologyandresourcespermit.TheFRP
addressesthelengthoftimeeachsystemshouldbepartof
thesystemmix.The2001FRPsetsforththefollowing
system policy guidelines:
RADIOBEACONS:AllU.S.marineradiobeacons
havebeendiscontinuedandmostofthestationsconverted
into DGPS sites.
LORANC:LoranCprovidesnavigation,location,
andtimingservicesforbothcivilandmilitaryair,land,and
maritimeusers.ItisslatedforreplacementbyGPS,butdue
tothelargenumberofusers,isexpectedtoremaininplace
indefinitelywhileitscontinuationisevaluated.Reasonable
notice will be given if the decision is made to terminate it.
GPS:TheGlobalPositioningSystem,orGPS,willbe
thenation’sprimaryradionavigationsystemwellintothe
next century. It is operated by the U.S. Air Force.
1020. Enhancements to GPS
DifferentialGPS(DGPS):TheU.S.CoastGuard
operatesmarineDGPSinU.S.coastalwaters.DGPSisa
systeminwhichdifferencesbetweenobservedand
calculatedGPSsignalsarebroadcasttousersusingmedium
frequencies.DGPSserviceisavailableinallU.S.coastal
watersincludingHawaii,Alaska,andtheGreatLakes.It
willprovide4-20metercontinuousaccuracy.Aterrestrial
DGPSsystemisbeinginstalledacrosstheUnitedStatesto
bring differential GPS service to land areas.
WideAreaAugmentationSystem(WAAS):WAAS
isaserviceoftheFAAsimilartoDGPS,andisintendedfor
cross-countryandlocalairnavigation,usingaseriesof
referencestationsandbroadcastingcorrectiondatathrough
geostationarysatellites.WAASisnotoptimizedformarine
use,andwhilenotcertifiedformaritimenavigation,may
provideadditionalpositionaccuracyifthesignalis
unobstructed.Accuraciesofafewmetersarepossible,
about the same as with DGPS.
LocalAreaAugmentationSystem(LAAS):LAASis
aprecisionpositioningsystemprovidedbytheFAAfor
localnavigationintheimmediatevicinityofairportsso
equipped.ThecorrectionalsignalsarebroadcastonHF
radiowitharangeofabout30miles.LAASisnotintended
orconfiguredformarineuse,butcanprovideextremely
accurate position data in a local area.
1021. Factors Affecting Navigation System Mix
Thenavigatorreliesonsimple,traditionalgear,andon
someofthemostcomplexandexpensivespace-based
electronicsystemsmanhaseverdeveloped.Thesuccessof
GPSasarobust,accurate,available,andflexiblesystemis
rapidlydrivingoldersystemsoffthescene.Severalhave
mettheirdemisealready(Transit,Omega,andmarine
radiobeaconsintheU.S.),andthedaysarenumberedfor
others, as GPS assumes primacy in navigation technology.
IntheU.S.,theDepartmentsofDefenseandTranspor-
tationcontinuallyevaluatethecomponentswhichmakeup
thefederallyprovidedandmaintainedradionavigation
system.Severalfactorsinfluencethedecisionontheproper
mixofsystems;cost,militaryutility,accuracy
requirements,anduserrequirementsalldrivetheproblem
ofallocatingscarceresourcestodevelopandmaintain
navigationsystems.Thedecreasingcostofreceiversand
increasingaccuracyoftheGlobalPositioningSystem
increaseitsattractivenessastheprimarynavigationmethod
ofthefutureforbothmilitaryandcivilianuse,although
thereareissuesofreliabilitytobeaddressedinthefaceof
threats to jam or otherwise compromise the system.
Manyfactorsinfluencethechoiceofnavigation
systems,whichmustsatisfyanextremelydiversegroupof
users.Internationalagreementsmustbehonored.The
currentinvestmentinexistingsystemsbybothgovernment
andusersmustbeconsidered.Thefulllife-cyclecostof
eachsystemmustbeconsidered.Nosystemwillbephased
outwithoutconsiderationofthesefactors.TheFRP
recognizesthatGPSmaynotmeettheneedsofallusers;
therefore,somesystemsarecurrentlybeingevaluated
independentlyofGPS.Thegoalistomeetallmilitaryand
civilian requirements in the most efficient way possible.
RADIO DIRECTION FINDING
1022. Introduction
Thesimplestuseofradiowavesinnavigationisradio
directionfinding,inwhichamediumfrequencyradiosignal
isbroadcastfromastationataknownlocation.Thissignalis
omnidirectional,butadirectionalantennaonavesselisused
162RADIO WAVES
todeterminethebearingofthestation.Thisconstitutesan
LOP,whichcanbecrossedwithanotherLOPtodeterminea
fix.
Onceusedextensivelythroughouttheworld,
radiobeaconshavebeendiscontinuedintheU.S.andmany
otherareas.Theyarenowchieflyusedashomingdevicesby
localfishermen,andverylittleoftheocean’ssurfaceis
coveredbyanyradiobeaconsignal.Becauseofitslimited
range,limitedavailability,andinherenterrors,radiodirection
finding is of limited usefulness to the professional navigator.
Inthepast,whenradiobeaconstationswerepowerfuland
commonenoughforroutineoceannavigation,correctionof
radiobearingswasnecessarytoobtainthemostaccurate
LOP’s.Thecorrectionprocessaccountedforthefactthat,
whileradiobearingstravelalonggreatcircles,theyaremost
oftenplottedonMercatorcharts.Therelativelyshortrangeof
thosestationsremaininghasmadethisprocessobsolete.Once
comprisingamajorpartofNIMAPub.117,RadioNaviga-
tionalAids,radiobeaconsarenowlistedinthebackofeach
volume of the geographically appropriateList of Lights.
ARadioDirectionFindingStationisonewhichthe
marinercancontactviaradioandrequestabearing.Mostof
thesestationsareforemergencyuseonly,andafeemaybe
involved.Thesestationsandproceduresforusearelistedin
NIMA Pub. 117, Radio Navigational Aids.
1023. Using Radio Direction Finders
DependinguponthedesignoftheRDF,thebearingsof
theradiotransmissionsaremeasuredasrelativebearings,or
asbothrelativeandtruebearings.Themostcommontypeof
marineradiobeacontransmitsradiowavesofapproximately
uniformstrengthinalldirections.Exceptduringcalibration,
radiobeaconsoperatecontinuously,regardlessofweather
conditions.Simplecombinationsofdotsanddashes
comprisingMorsecodelettersareusedforstationidentifi-
cation.Allradiobeaconssuperimposethecharacteristicona
carrierwave,whichisbroadcastcontinuouslyduringthe
periodoftransmission.A10-seconddashisincorporatedin
thecharacteristicsignaltoenableusersoftheauralnulltype
of radio direction finder to refine the bearing.
Bearingmeasurementisaccomplishedwithadirectional
antenna.Nearlyalltypesofreceivingantennashavesomedi-
rectionalproperties,buttheRDFantennaisdesignedtobeas
directionalaspossible.SimplesmallcraftRDFunitsusually
haveaferriterodantennamounteddirectlyonareceiver,with
a360degreegraduatedscale.Togetabearing,aligntheunit
tothevessel’scourseortotruenorth,androtatetheantenna
backandforthtofindtheexactnullpoint.Thebearingtothe
station,relativeortrueaccordingtothealignment,willbein-
dicatedonthedial.SomesmallcraftRDF’shaveaportable
hand-heldcombinationferriterodandcompass,withear-
phones to hear the null.
Twotypesofloopantennaareusedinlargerradio
directionfinders.Inoneofthese,thecrossedlooptype,two
loopsarerigidlymountedinsuchmannerthatoneisplacedat
90degreestotheother.Therelativeoutputofthetwo
antennasisrelatedtotheorientationofeachwithrespectto
thedirectionoftraveloftheradiowave,andismeasuredbya
device called a goniometer.
1024. Errors of Radio Direction Finders
RDFbearingsaresubjecttocertainerrors.Quadrantal
erroroccurswhenradiowavesarriveatareceiverandare
influenced by the immediate shipboard environment.
Aradiowavecrossingacoastlineatanobliqueangle
experiencesachangeofdirectionduetodifferencesin
conductingandreflectingpropertiesoflandandwaterknown
ascoastalrefraction,sometimescalledlandeffect.Itis
avoidedbynotusing,orregardingasofdoubtfulaccuracy,
bearings which cross a shoreline at an oblique angle.
Ingeneral,goodradiobearingsshouldnotbeinerrorby
morethantwoorthreedegreesfordistancesunder150
nauticalmiles.However,conditionsvaryconsiderably,and
skillisanimportantfactor.Byobservingthetechnical
instructionsfortheequipmentandpracticingfrequentlywhen
resultscanbechecked,onecandevelopskillandlearntowhat
extentradiobearingscanberelieduponundervarious
conditions.Otherfactorsaffectingaccuracyincluderange,
theconditionoftheequipment,andtheaccuracyof
calibration.
Thestrengthofthesignaldeterminestheusablerangeof
aradiobeacon.Theactualusefulrangemayvaryconsiderably
fromthepublishedrangewithdifferenttypesofradio
directionfindersandduringvaryingatmosphericconditions.
Thesensitivityofaradiodirectionfinderdeterminesthe
degreetowhichthefullrangeofaradiobeaconcanbe
utilized.Selectivityvarieswiththetypeofreceiverandits
condition.
163
CHAPTER 11
SATELLITE NAVIGATION
INTRODUCTION
1100. Development
Theideathatledtodevelopmentofthesatellite
navigationsystemsdatesbackto1957andthefirstlaunch
ofanartificialsatelliteintoorbit,Russia’sSputnikI.Dr.
WilliamH.GuierandDr.GeorgeC.Wieffenbachatthe
AppliedPhysicsLaboratoryoftheJohnsHopkins
Universityweremonitoringthefamous“beeps”
transmittedbythepassingsatellite.Theyplottedthe
receivedsignalsatpreciseintervals,andnoticedthata
characteristicDopplercurveemerged.Sincesatellites
generallyfollowfixedorbits,theyreasonedthatthiscurve
couldbeusedtodescribethesatellite’sorbit.Theythen
demonstratedthattheycoulddeterminealloftheorbital
parametersforapassingsatellitebyDopplerobservationof
asinglepassfromasinglefixedstation.TheDopplershift
apparentwhilereceivingatransmissionfromapassing
satelliteprovedtobeaneffectivemeasuringdevicefor
establishing the satellite orbit.
Dr.FrankT.McClure,alsooftheAppliedPhysics
Laboratory,reasonedinreverse:Ifthesatelliteorbitwas
known,Dopplershiftmeasurementscouldbeusedto
determineone’spositiononEarth.Hisstudiesinsupportof
thishypothesisearnedhimthefirstNationalAeronautics
andSpaceAdministrationawardforimportantcontri-
butions to space development.
In1958,theAppliedPhysicsLaboratoryproposed
exploringthepossibilityofanoperationalsatelliteDoppler
navigationsystem.TheChiefofNavalOperationsthenset
forthrequirementsforsuchasystem.Thefirstsuccessful
launchingofaprototypesystemsatelliteinApril1960
demonstrated the Doppler system’s operational feasibility.
TheNavyNavigationSatelliteSystem(NAVSAT,
alsoknownasTRANSIT)wasthefirstoperationalsatellite
navigationsystem.Thesystem’saccuracywasbetterthan
0.1nauticalmileanywhereintheworld,thoughits
availabilitywassomewhatlimited.Itwasusedprimarily
forthenavigationofsurfaceshipsandsubmarines,butit
alsohadsomeapplicationsinairnavigation.Itwasalso
usedinhydrographicsurveyingandgeodeticposition
determination.
Thetransitlaunchprogramendedin1988andthe
systemwasdisestablishedwhentheGlobalPositioning
System became operational in 1996.
THE GLOBAL POSITIONING SYSTEM
1101. System Description
TheFederalRadionavigationPlanhasdesignated
theNAVigationSystemusingTimingAndRanging
(NAVSTAR)GlobalPositioningSystem(GPS)asthe
primarynavigationsystemoftheU.S.government.GPS
isaspaced-basedradiopositioningsystemwhich
providessuitablyequippeduserswithhighlyaccurate
position,velocity,andtimedata.Itconsistsofthree
majorsegments:aspacesegment,acontrolsegment,
and auser segment.
Thespacesegmentcomprisessome24satellites.
Spacingofthesatellitesintheirorbitsisarrangedsothat
atleastfoursatellitesareinviewtoauseratanytime,
anywhereontheEarth.Eachsatellitetransmitssignals
ontworadiofrequencies,superimposedonwhichare
navigationandsystemdata.Includedinthisdataare
predictedsatelliteephemeris,atmosphericpropagation
correctiondata,satelliteclockerrorinformation,and
satellitehealthdata.Thissegmentnormallyconsistsof
21operationalsatelliteswiththreesatellitesorbitingas
activespares.Thesatellitesorbitatanaltitudeof20,200
km,insixseparateorbitalplanes,eachplaneinclined
55°relativetotheequator.Thesatellitescompletean
orbit approximately once every 12 hours.
GPSsatellitestransmitpseudorandomnoise(PRN)
sequence-modulatedradiofrequencies,designatedL1
(1575.42MHz)andL2(1227.60MHz).Thesatellite
transmitsbothaCoarseAcquisitionCode(C/Acode)and
aPrecisionCode(Pcode).BoththePandC/Acodesare
transmittedontheL1carrier;onlythePcodeistransmitted
ontheL2carrier.SuperimposedonboththeC/AandP
codesisthenavigationmessage.Thismessagecontainsthe
satelliteephemerisdata,atmosphericpropagation
correction data, and satellite clock bias.
GPSassignsauniqueC/AcodeandauniquePcodeto
eachsatellite.Thispractice,knownascodedivision
multipleaccess(CDMA),allowsallsatellitestheuseofa
commoncarrierfrequencywhilestillallowingthereceiver
todeterminewhichsatelliteistransmitting.CDMAalso
164SATELLITE NAVIGATION
allowsforeasyuseridentificationofeachGPSsatellite.
SinceeachsatellitebroadcastsusingitsownuniqueC/A
andPcodecombination,itcanbeassignedauniquePRN
sequencenumber.Thisnumberishowasatelliteis
identifiedwhentheGPScontrolsystemcommunicateswith
users about a particular GPS satellite.
Thecontrolsegmentincludesamastercontrol
station(MCS),anumberofmonitorstations,andground
antennaslocatedthroughouttheworld.Themastercontrol
station,locatedinColoradoSprings,Colorado,consistsof
equipmentandfacilitiesrequiredforsatellitemonitoring,
telemetry,tracking,commanding,control,uploading,and
navigationmessagegeneration.Themonitorstations,
locatedinHawaii,ColoradoSprings,Kwajalein,Diego
Garcia,andAscensionIsland,passivelytrackthe
satellites,accumulatingrangingdatafromthesatellites’
signalsandrelayingthemtotheMCS.TheMCS
processesthisinformationtodeterminesatelliteposition
andsignaldataaccuracy,updatesthenavigationmessage
ofeachsatelliteandrelaysthisinformationtotheground
antennas.Thegroundantennasthentransmitthis
informationtothesatellites.Thegroundantennas,located
atAscensionIsland,DiegoGarcia,andKwajalein,are
alsousedfortransmittingandreceivingsatellitecontrol
information.
Theuserequipmentisdesignedtoreceiveand
processsignalsfromfourormoreorbitingsatellites
eithersimultaneouslyorsequentially.Theprocessorin
thereceiverthenconvertsthesesignalstonavigation
information.SinceGPSisusedinawidevarietyof
applications,frommarinenavigationtolandsurveying,
these receivers can vary greatly in function and design.
1102. System Capabilities
GPSprovidesmultipleuserswithaccurate,
continuous,worldwide,all-weather,common-grid,three-
dimensional positioning and navigation information.
Toobtainanavigationsolutionofposition(latitude,
longitude,andaltitude)andtime(fourunknowns),four
satellitesmustbeused.TheGPSusermeasures
pseudorangeandpseudorangeratebysynchronizingand
trackingthenavigationsignalfromeachofthefour
selectedsatellites.Pseudorangeisthetruedistance
betweenthesatelliteandtheuserplusanoffsetduetothe
user’sclockbias.Pseudorangerateisthetrueslantrange
rateplusanoffsetduetothefrequencyerroroftheuser’s
clock.Bydecodingtheephemerisdataandsystem
timinginformationoneachsatellite’ssignal,theuser’s
receiver/processorcanconvertthepseudorangeand
pseudorangeratetothree-dimensionalpositionand
velocity.Fourmeasurementsarenecessarytosolvefor
thethreeunknowncomponentsofposition(orvelocity)
and the unknown user time (or frequency) bias.
Thenavigationaccuracythatcanbeachievedbyany
userdependsprimarilyonthevariabilityoftheerrorsin
makingpseudorangemeasurements,theinstantaneous
geometryofthesatellitesasseenfromtheuser’slocation
onEarth,andthepresenceofSelectiveAvailability(SA).
Selective Availability is discussed further below.
1103. Global Positioning System Concepts
GPSmeasuresdistancesbetweensatellitesinorbitand
areceiveronEarth,andcomputesspheresofpositionfrom
thosedistances.Theintersectionsofthosespheresof
position then determine the receiver’s position.
Thedistancemeasurementsdescribedabovearedoneby
comparingtimingsignalsgeneratedsimultaneouslybythe
satellites’andreceiver’sinternalclocks.Thesesignals,charac-
terizedbyaspecialwaveformknownasthepseudo-random
code,aregeneratedinphasewitheachother.Thesignalfrom
thesatellitearrivesatthereceiverfollowingatimedelay
proportionaltoitsdistancetraveled.Thistimedelayis
detectedbythephaseshiftbetweenthereceivedpseudo-
randomcodeandthecodegeneratedbythereceiver.Knowing
thetimerequiredforthesignaltoreachthereceiverfromthe
satelliteallowsthereceivertocalculatethedistancefromthe
satellite.Thereceiver,therefore,mustbelocatedonasphere
centeredatthesatellitewitharadiusequaltothisdistance
measurement.Theintersectionofthreespheresofposition
yieldstwopossiblepointsofreceiverposition.Oneofthese
pointscanbedisregardedsinceitishundredsofmilesfromthe
surfaceoftheEarth.Theoretically,then,onlythreetime
measurements are required to obtain a fix from GPS.
Inpractice,however,afourthmeasurementisrequiredto
obtainanaccuratepositionfromGPS.Thisisduetoreceiver
clockerror.Timingsignalstravelfromthesatellitetothe
receiveratthespeedoflight;evenextremelyslighttiming
errorsbetweentheclocksonthesatelliteandinthereceiver
willleadtotremendousrangeerrors.Thesatellite’satomic
clockisaccurateto10
-9
seconds;installingaclockthat
accurateonareceiverwouldmakethereceiverprohibitively
expensive.Therefore,receiverclockaccuracyissacrificed,
andanadditionalsatellitetimingmeasurementismade.The
fixerrorcausedbytheinaccuraciesinthereceiverclockis
reducedbysimultaneouslysubtractingaconstanttimingerror
fromfoursatellitetimingmeasurementsuntilapinpointfixis
reached.
Assumingthatthesatelliteclocksareperfectlysynchro-
nizedandthereceiverclock’serrorisconstant,the
subtractionofthatconstanterrorfromtheresultingdistance
determinationswillreducethefixerroruntila“pinpoint”po-
sitionisobtained.Itisimportanttonoteherethatthenumber
oflinesofpositionrequiredtoemploythistechniqueisa
functionofthenumberoflinesofpositionrequiredtoobtain
afix.GPSdeterminespositioninthreedimensions;thepres-
enceofreceiverclockerroraddsanadditionalunknown.
Therefore,fourtimingmeasurementsarerequiredtosolvefor
the resulting four unknowns.
SATELLITE NAVIGATION165
1104. GPS Signal Coding
Twoseparatecarrierfrequenciescarrythesignal
transmittedbyaGPSsatellite.Thefirstcarrierfrequency
(L1)transmitson1575.42MHz;thesecond(L2)transmits
on1227.60MHz.TheGPSsignalconsistsofthreeseparate
messages:theP-code,transmittedonbothL1andL2;the
C/Acode,transmittedonL1only;andanavigationdata
message.ThePcodeandC/Acodemessagesaredivided
intoindividualbitsknownaschips.Thefrequencyatwhich
bitsaresentforeachtypeofsignalisknownasthechipping
rate.ThechippingratefortheP-codeis10.23MHz(10.23
×10
6
bitspersecond);fortheC/Acode,1.023MHz(1.023
×10
6
bitspersecond);andforthedatamessage,50Hz(50
bitspersecond).ThePandC/Acodesphasemodulatethe
carriers;theC/Acodeistransmittedataphaseangleof90°
fromthePcode.TheperiodsofrepetitionfortheC/AandP
codesdiffer.TheC/Acoderepeatsonceeverymillisecond;
the P-code sequence repeats every seven days.
AsstatedabovetheGPScarrierfrequenciesarephase
modulated.Thisissimplyanotherwayofsayingthatthe
digital“1’s”and“0’s”containedinthePandC/Acodesare
indicatedalongthecarrierbyashiftinthecarrierphase.
Thisisanalogoustosendingthesamedataalongacarrier
byvaryingitsamplitude(amplitudemodulation,orAM)or
itsfrequency(frequencymodulation,orFM).SeeFigure
1104a.Inphasemodulation,thefrequencyandtheampli-
tudeofthecarrierareunchangedbythe“information
signal,”andthedigitalinformationistransmittedbyshift-
ingthecarrier’sphase.Thephasemodulationemployedby
GPS is known as bi-phase shift keying (BPSK).
Figure 1104a. Digital data transmission with amplitude, frequency and phase modulation.
Figure 1104b. Modulation of the L1 and L2 carrier frequencies with the C/A and P code signals.
166SATELLITE NAVIGATION
DuetothisBPSK,thecarrierfrequencyis“spread”
aboutitscenterfrequencybyanamountequaltotwicethe
“chippingrate”ofthemodulatingsignal.Inthecaseofthe
Pcode,thisspreadingisequalto(2×10.23MHz)=20.46
MHz.FortheC/Acode,thespreadingisequalto(2×1.023
MHz)=2.046MHz.SeeFigure1104b.NotethattheL1
carriersignal,modulatedwithboththePcodeandC/A
code,isshapeddifferentlyfromtheL2carrier,modulated
withonlythePcode.Thisspreadingofthecarriersignal
lowersthetotalsignalstrengthbelowthethermalnoise
thresholdpresentatthereceiver.Thiseffectisdemonstrat-
edinFigure1104c.Whenthesatellitesignalismultiplied
withtheC/AandPcodesgeneratedbythereceiver,thesat-
ellitesignalwillbecollapsedintotheoriginalcarrier
frequencyband.Thesignalpoweristhenraisedabovethe
thermal noise level.
ThenavigationmessageissuperimposedonboththeP
codeandC/Acodewithadatarateof50bitspersecond(50
Hz.)Thenavigationmessageconsistsof25dataframes,
eachframeconsistingof1500bits.Eachframeisdivided
intofivesubframesof300bitseach.Itwill,therefore,take
30secondstoreceiveonedataframeand12.5minutesto
receiveall25frames.Thenavigationmessagecontains
GPSsystemtimeoftransmission;ahandoverword
(HOW),allowingthetransitionbetweentrackingtheC/A
codetothePcode;ephemerisandclockdataforthe
satellitebeingtracked;andalmanacdataforthesatellitesin
orbit.Italsocontainscoefficientsforionosphericdelay
modelsusedbyC/Areceiversandcoefficientsusedto
calculate Universal Coordinated Time (UTC).
1105. The Correlation Process
Thecorrelationprocesscomparesthesignalreceived
fromthesatelliteswiththesignalgeneratedbythereceiver
bycomparingthesquarewavefunctionofthereceived
signalwiththesquarewavefunctiongeneratedbythe
receiver.Thecomputerlogicofthereceiverrecognizesthe
squarewavesignalsaseithera+1ora0dependingon
whetherthesignalis“on”or“off.”Thesignalsare
processedandmatchedbyusinganautocorrelation
function.
Thisprocessdefinesthenecessityfora“pseudo-
randomcode.”Thecodemustberepeatable(i.e.,non-
random)becauseitisincomparingthetwosignalsthatthe
receivermakesitsdistancecalculations.Atthesametime,
thecodemustberandomforthecorrelationprocessto
work;therandomnessofthesignalsmustbesuchthatthe
matchingprocessexcludesallpossiblecombinations
exceptthecombinationthatoccurswhenthegenerated
signalisshiftedadistanceproportionaltothereceived
signal’stimedelay.Thesesimultaneousrequirementstobe
bothrepeatable(non-random)andrandomgiverisetothe
descriptionof“pseudo-random”;thesignalhasenough
repeatabilitytoenablethereceivertomaketherequired
measurementwhilesimultaneouslyretainingenough
randomness to ensure incorrect calculations are excluded.
1106. Precise Positioning Service and Standard
Positioning Service
Twolevelsofnavigationalaccuracyareprovidedby
theGPS:thePrecisePositioningService(PPS)andthe
StandardPositioningService(SPS).GPSwasdesigned,
firstandforemost,bytheU.S.DepartmentofDefenseasa
UnitedStatesmilitaryasset;itsextremelyaccurate
positioningcapabilityisanassetaccesstowhichtheU.S.
militarymayneedtolimitduringtimeofwartopreventuse
byenemies.Therefore,thePPSisavailableonlyto
authorizedusers,mainlytheU.S.militaryandauthorized
allies.SPS,ontheotherhand,isavailableworldwideto
anyonepossessingaGPSreceiver.ThereforePPSprovides
Figure 1104c. GPS signal spreading and recovery from satellite to receiver.
SATELLITE NAVIGATION167
a more accurate position than does SPS.
TwocryptographicmethodsareemployedtodenyPPS
accuracytocivilianusers:selectiveavailability(SA)and
anti-spoofing(A-S).SAoperatesbyintroducingcontrolled
errorsintoboththeC/AandPcodesignals.SAcanbe
programmedtodegradethesignals’accuracyevenfurther
duringtimeofwar,denyingapotentialadversarytheability
touseGPStonominalSPSaccuracy.SAintroducestwo
errorsintothesatellitesignal:(1)Theepsilonerror:an
errorinsatelliteephemerisdatainthenavigationmessage;
and(2)clockdither:errorintroducedinthesatelliteatomic
clocks’timing.ThepresenceofSAisthelargestsourceof
errorpresentinanSPSGPSpositionmeasurement.The
statusofSA,whetherofforon,canbecheckedatthe
USCG’s NAVCEN Web site:
http://www.navcen.uscg.gov.
Anti-spoofingisdesignedtonegateanyhostileimita-
tionofGPSsignals.ThetechniquealtersthePcodeinto
anothercode,designatedtheYcode.TheC/Acoderemains
unaffected.TheU.S.employsthistechniquetothesatellite
signalsatrandomtimesandwithoutwarning;therefore,ci-
vilianusersareunawarewhenthisPcodetransformation
takesplace.Sinceanti-spoofingisappliedonlytotheP
code, the C/A code is not protected and can be spoofed.
Onlyusersemployingthepropercryptographic
devicescandefeatbothSAandanti-spoofing.Without
thesedevices,theuserwillbesubjecttotheaccuracy
degradation of SA and will be unable to track the Y code.
GPSPPSreceiverscanuseeitherthePcodeortheC/A
code,orboth,indeterminingposition.Maximumaccuracy
isobtainedbyusingthePcodeonbothL1andL2.The
differenceinpropagationdelayisthenusedtocalculate
ionosphericcorrections.TheC/Acodeisnormallyusedto
acquirethesatellitesignalanddeterminetheapproximateP
codephase.Then,thereceiverlocksonthePcodefor
precisepositioning(subjecttoSAifnotcryptographically
equipped).SomePPSreceiverspossessaclockaccurate
enoughtotrackandlockonthePcodesignalwithout
initiallytrackingtheC/Acode.SomePPSreceiverscan
trackonlytheC/AcodeanddisregardthePcodeentirely.
SincetheC/Acodeistransmittedononlyonefrequency,
thedualfrequencyionospherecorrectionmethodologyis
unavailableandanionosphericmodelingprocedureis
required to calculate the required corrections.
SPSreceivers,asmentionedabove,providepositions
withadegradedaccuracy.TheA-SfeaturedeniesSPSusers
accesstothePcodewhentransformedtotheYcode.
Therefore,theSPSusercannotrelyonaccesstothePcode
tomeasurepropagationdelaysbetweenL1andL2and
computeionosphericdelaycorrections.Consequently,the
typicalSPSreceiverusesonlytheC/Acodebecauseitis
unaffectedbyA-S.SinceC/AistransmittedonlyonL1,the
dualfrequencymethodofcalculatingionospheric
correctionsisunavailable;anionosphericmodeling
techniquemustbeused.Thisislessaccuratethanthedual
frequencymethod;thisdegradationinaccuracyisaccounted
forinthe100-meteraccuracycalculation.Figure1106
presentstheeffectonSAandA-SondifferenttypesofGPS
measurements.
1107. GPS Receiver Operations
InorderfortheGPSreceivertonavigate,ithastotrack
satellitesignals,makepseudorangemeasurements,and
collect navigation data.
Atypicalsatellitetrackingsequencebeginswiththe
receiverdeterminingwhichsatellitesareavailableforitto
track.Satellitevisibilityisdeterminedbyuser-entered
predictionsofposition,velocity,andtime,andbyalmanac
informationstoredinternaltothereceiver.Ifnostored
almanacinformationexists,thenthereceivermustattempt
tolocateandlockontothesignalfromanysatelliteinview.
Whenthereceiverislockedontoasatellite,itcan
demodulatethenavigationmessageandreadthealmanac
informationaboutalltheothersatellitesintheconstel-
lation.Acarriertrackinglooptracksthecarrierfrequency
whileacodetrackinglooptrackstheC/AandPcode
signals.Thetwotrackingloopsoperatetogetherinan
iterative process to acquire and track satellite signals.
Thereceiver’scarriertrackingloopwilllocally
generateanL1carrierfrequencywhichdiffersfromthe
satelliteproducedL1frequencyduetoaDopplershiftinthe
receivedfrequency.ThisDoppleroffsetisproportionalto
therelativevelocityalongthelineofsightbetweenthe
SA/A-S ConfigurationSIS Interface ConditionsPPS UsersSPS Users
SA Set to Zero
A-S Off
P-Code, no errors
C/A-Code, no errors
Full accuracy,
spoofable
Full accuracy,*
spoofable
SA at Non-Zero Value
A-S Off
P-Code, errors
C/A-Code, errors
Full accuracy,
spoofable
Limited accuracy,
spoofable
SA Set to Zero
A-S On
Y-Code, no errors
C/A-Code, no errors
Full accuracy,
Not spoofable**
Full accuracy,***
spoofable
SA at Non-Zero Value
A-S On
Y-Code, errors
C/A-Code, errors
Full accuracy,
Not spoofable**
Limited accuracy,
spoofable
*
**
***
“Full accuracy” defined as equivalent to a PPS-capable UE operated in a similar manner.
Certain PPS-capable UE do not have P- or Y-code tracking abilities and remain spoofable
despite A-S protection being applied
Assuming negligible accuracy degradation due to C/A-code operation (but more
susceptible to jamming).
Figure 1106. Effect of SA and A-S on GPS accuracy.
168SATELLITE NAVIGATION
satelliteandthereceiver,subjecttoareceiverfrequency
bias.Thecarriertrackingloopadjuststhefrequencyofthe
receiver-generatedfrequencyuntilitmatchestheincoming
frequency.Thisdeterminestherelativevelocitybetween
thesatelliteandthereceiver.TheGPSreceiverusesthis
relativevelocitytocalculatethevelocityofthereceiver.
This velocity is then used to aid the code tracking loop.
Thecodetrackingloopisusedtomakepseudorange
measurementsbetweentheGPSreceiverandthesatellites.
Thereceiver’strackingloopwillgenerateareplicaofthe
targetedsatellite’sC/Acodewithestimatedrangingdelay.
Inordertomatchthereceivedsignalwiththeinternally
generatedreplica,twothingsmustbedone:1)Thecenter
frequencyofthereplicamustbeadjustedtobethesameas
thecenterfrequencyofthereceivedsignal;and2)thephase
ofthereplicacodemustbelinedupwiththephaseofthe
receivedcode.Thecenterfrequencyofthereplicaissetby
usingtheDoppler-estimatedoutputofthecarriertracking
loop.Thereceiverwillthenslewthecodeloopgenerated
C/Acodethoughamillisecondsearchwindowtocorrelate
with the received C/A code and obtain C/A tracking.
Oncethecarriertrackingloopandthecodetracking
loophavelockedontothereceivedsignalandtheC/Acode
hasbeenstrippedfromthecarrier,thenavigationmessage
isdemodulatedandread.Thisgivesthereceiverother
informationcrucialtoapseudorangemeasurement.The
navigationmessagealsogivesthereceiverthehandover
word,thecodethatallowsaGPSreceivertoshiftfromC/A
code tracking to P code tracking.
Thehandoverwordisrequiredduetothelongphase
(sevendays)ofthePcodesignal.TheC/Acoderepeatsevery
millisecond,allowingforarelativelysmallsearchwindow.
ThesevendayrepeatperiodofthePcoderequiresthatthe
receiverbegiventheapproximatePcodephasetonarrowits
searchwindowtoamanageabletime.Thehandoverword
providesthisPcodephaseinformation.Thehandoverwordis
repeatedeverysubframeina30bitlongblockofdatainthe
navigationmessage.Itisrepeatedinthesecond30seconddata
blockofeachsubframe.Forsomereceivers,thishandover
wordisunnecessary;theycanacquirethePcodedirectly.This
normallyrequiresthereceivertohaveaclockwhoseaccuracy
approachesthatofanatomicclock.Sincethisgreatlyincreases
thecostofthereceiver,mostreceiversfornon-militarymarine
use do not have this capability.
Oncethereceiverhasacquiredthesatellitesignalsfrom
fourGPSsatellites,achievedcarrierandcodetracking,and
hasreadthenavigationmessage,thereceiverisreadyto
beginmakingpseudorangemeasurements.Recallthatthese
measurementsaretermedpseudorangebecauseareceiver
clockoffsetmakestheminaccurate;thatis,theydonot
representthetruerangefromthesatellite,onlyarange
biasedbyareceiverclockerror.Thisclockbiasintroduces
afourthunknownintothesystemofequationsforwhichthe
GPSreceivermustsolve(theotherthreebeingthex
coordinate,ycoordinate,andzcoordinateofthereceiver
position).RecallfromthediscussioninArticle1101thatthe
receiversolvesthisclockbiasproblembymakingafourth
pseudorangemeasurement,resultinginafourthequationto
allowsolvingforthefourthunknown.Oncethefour
equationsaresolved,thereceiverhasanestimateofthe
receiver’spositioninthreedimensionsandofGPStime.
Thereceiverthenconvertsthispositionintocoordinates
referencedtoanEarthmodelbasedontheWorldGeodetic
System (1984).
1108. User Range Errors and Geometric Dilution of
Precision
Therearetwoformalpositionaccuracyrequirements
for GPS:
1)ThePPSsphericalpositionaccuracyshallbe16
meters SEP (spherical error probable) or better.
2)TheSPSusertwodimensionalpositionaccuracy
shall be 100 meters 2 drms or better.
AssumethatauniversalsetofGPSpseudorange
measurementsresultsinasetofGPSposition
measurements.Theaccuracyofthesemeasurementswill
conformtoanormal(i.e.valuessymmetricallydistributed
aroundameanofzero)probabilityfunctionbecausethe
twomostimportantfactorsaffectingaccuracy,the
geometricdilutionofprecision(GDOP)andtheuser
equivalentrangeerror(UERE),arecontinuously
variable.
TheUEREistheerrorinthemeasurementofthe
pseudorangesfromeachsatellitetotheuser.TheUEREis
theproductofseveralfactors,includingtheclockstability,
thepredictabilityofthesatellite’sorbit,errorsinthe50Hz
navigationmessage,theprecisionofthereceiver’s
correlationprocess,errorsduetoatmosphericdistortionand
thecalculationstocompensateforit,andthequalityofthe
satellite’ssignal.TheUERE,therefore,isarandomerror
whichisthefunctionoferrorsinboththesatellitesandthe
user’s receiver.
TheGDOPdependsonthegeometryofthesatellitesin
relationtotheuser’sreceiver.Itisindependentofthequalityof
thebroadcastsignalsandtheuser’sreceiver.Generally
speaking,theGDOPmeasuresthe“spread”ofthesatellites
aroundthereceiver.Theoptimumcasewouldbetohaveone
satellitedirectlyoverheadandtheotherthreespaced120°
aroundthereceiveronthehorizon.TheworstGDOPwould
occurifthesatelliteswerespacedcloselytogetherorinaline
overhead.
TherearespecialtypesofDOP’sforeachofthe
positionandtimesolutiondimensions;theseparticular
DOP’scombinetodeterminetheGDOP.Forthevertical
dimension,theverticaldilutionofprecision(VDOP)
describestheeffectofsatellitegeometryonaltitude
calculations.Thehorizontaldilutionofprecision
(HDOP)describessatellitegeometry’seffectonposition
(latitudeandlongitude)errors.ThesetwoDOP’scombine
SATELLITE NAVIGATION169
todeterminethepositiondilutionofprecision(PDOP).
ThePDOPcombinedwiththetimedilutionofprecision
(TDOP) results in the GDOP. See Figure 1108.
1109. Ionospheric Delay Errors
Article1108coverederrorsinGPSpositionsdueto
errorsinherentinthesatellitesignal(UERE)andthe
geometryofthesatelliteconstellation(GDOP).Another
majorcauseofaccuracydegradationistheeffectofthe
ionosphereontheradiofrequencysignalsthatcomprisethe
GPS signal.
AdiscussionofamodeloftheEarth’satmospherewill
beusefulinunderstandingthisconcept.ConsidertheEarth
assurroundedbythreelayersofatmosphere.Thefirstlayer,
extendingfromthesurfaceoftheEarthtoanaltitudeof
approximately10km,isknownasthetroposphere.Above
thetroposphereandextendingtoanaltitudeofapproxi-
mately50kmisthestratosphere.Finally,abovethe
stratosphereandextendingtoanaltitudethatvariesasa
functionofthetimeofdayistheionosphere.Thoughradio
signalsaresubjectedtoeffectswhichdegradeitsaccuracy
inallthreelayersofthisatmosphericmodel,theeffectsof
the ionosphere are the most significant to GPS operation.
Theionosphere,asthenameimplies,isthatregionof
theatmospherewhichcontainsalargenumberofionized
moleculesandacorrespondinglyhighnumberoffree
electrons.Thesechargedmoleculeshavelostoneormore
electrons.Noatomwilllooseanelectronwithoutaninput
ofenergy;theenergyinputthatcausestheionstobeformed
intheionospherecomesfromtheultraviolet(U-V)
radiationoftheSun.Therefore,themoreintensetheSun’s
rays,thelargerthenumberoffreeelectronswhichwillexist
in this region of the atmosphere.
Thelargesteffectthatthisionosphericeffecthason
GPSaccuracyisaphenomenonknownasgrouptime
delay.Asthenameimplies,grouptimedelayresultsina
delayinthetimeasignaltakestotravelthroughagiven
distance.Obviously,sinceGPSreliesonextremely
accuratetimingmeasurementofthesesignalsbetween
satellitesandgroundreceivers,thisgrouptimedelaycan
haveanoticeableeffectonthemagnitudeofGPSposition
error.
Thegrouptimedelayisafunctionofseveralelements.
Itisinverselyproportionaltothesquareofthefrequencyat
whichthesatellitetransmits,anditisdirectlyproportionalto
theatmosphere’stotalelectroncontent(TEC),ameasure
ofthedegreeoftheatmosphere’sionization.Thegeneral
form of the equation describing the delay effect is:
where
SincetheSun’sU-Vradiationionizesthemoleculesin
theupperatmosphere,itstandstoreasonthatthetimedelay
valuewillbehighestwhentheSunisshiningandlowestat
night.Experimentalevidencehasbornethisout,showing
thatthevalueforTECishighestaround1500localtimeand
lowestaround0500localtime.Therefore,themagnitudeof
theaccuracydegradationcausedbythiseffectwillbe
highestduringdaylightoperations.Inadditiontothese
dailyvariations,themagnitudeofthistimedelayerroralso
Figure 1108. Position and time error computations.
Δt=group time delay
f=operating frequency
K=constant
t
Δ
K(TEC×)
f
2
---------------------------=
170SATELLITE NAVIGATION
varieswiththeseasons;itishighestatthevernalequinox.
Finally,thiseffectshowsasolarcycledependence.The
greaterthenumberofsunspots,thehighertheTECvalue
andthegreaterthegrouptimedelayeffect.Thesolarcycle
typicallyfollowsanelevenyearpattern.Thenextsolar
cyclewillbeataminimumin2006andpeakagainin2010.
Giventhatthisionosphericdelayintroducesaserious
accuracydegradationintothesystem,howdoesGPSac-
countforit?Therearetwomethodsused:(1)thedual
frequencytechnique,and(2)theionosphericdelaymethod.
1110. Dual Frequency Correction Technique
Asthetermimplies,thedualfrequencytechnique
requirestheabilitytoacquireandtrackboththeL1andL2
frequencysignals.RecallfromthediscussioninArticle
1103thattheC/AandPcodesaretransmittedoncarrier
frequencyL1,butonlythePcodeistransmittedonL2.
Recallalsothatonlyauthorizedoperatorswithaccessto
DODcryptographicmaterialareabletocopythePcode.
Itfollows,then,thatonlythoseauthorizedusersareable
tocopytheL2carrierfrequency.Therefore,onlythose
authorizedusersareabletousethedualfrequency
correctionmethod.Thedualfrequencymethodmeasures
thedistancebetweenthesatelliteandtheuserbasedon
boththeL1andL2carriersignal.Theserangeswillbe
differentbecausethegrouptimedelayforeachsignalwill
bedifferent.Thisisbecauseofthefrequencydependence
ofthetimedelayerror.Therangefromthesatellitetothe
userwillbethetruerangecombinedwiththerangeerror
causedbythetimedelay,asshownbythefollowing
equation:
whereR(f)istherangewhichdiffersfromtheactualrange
asafunctionofthecarrierfrequency.Thedualfrequency
correctionmethodtakestwosuchrangemeasurements,
R(L1)andR(L2).Recallthattheerrortermisafunctionof
aconstantdividedbythesquareofthefrequency.By
combiningthetworangeequationsderivedfromthetwo
frequencymeasurements,theconstanttermcanbe
eliminatedandoneisleftwithanequationinwhichthetrue
rangeissimplyafunctionofthetwocarrierfrequenciesand
themeasuredrangesR(L1)andR(L2).Thismethodhas
twomajoradvantagesovertheionosphericmodelmethod.
(1)Itcalculatescorrectionsfromreal-timemeasureddata;
therefore,itismoreaccurate.(2)Italleviatestheneedto
includeionosphericdataonthenavigationmessage.A
significantportionofthedatamessageisdevotedto
ionosphericcorrectiondata.Ifthereceiverisdual
frequency capable, then it does not need any of this data.
Thevastmajorityofmaritimeuserscannotcopydual
frequencysignals.Forthem,theionosphericdelaymodel
provides the correction for the group time delay.
1111. The Ionospheric Delay Model
Theionosphericdelaymodelmathematicallymodels
thediurnalionosphericvariation.Thevalueforthistime
delayisdeterminedfromacosinusoidalfunctionintowhich
coefficientsrepresentingthemaximumvalueofthetime
delay(i.e.,theamplitudeofthecosinewaverepresentingthe
delayfunction);thetimeofday;theperiodofthevariation;
andaminimumvalueofdelayareintroduced.Thismodelis
designedtobemostaccurateatthediurnalmaximum.This
isobviouslyareasonabledesignconsiderationbecauseitis
atthetimeofdaywhenthemaximumdiurnaltimedelay
occursthatthelargestmagnitudeoferrorappears.The
coefficientsforuseinthisdelaymodelaretransmittedtothe
receiverinthenavigationdatamessage.AsstatedinArticle
1110,thismethodofcorrectionisnotasaccurateasthedual
frequencymethod;however,forthenon-militaryuser,itis
the only method of correction available.
1112. Multipath Reflection Errors
Multipathreflectionerrorsoccurwhenthereceiver
detectspartsofthesamesignalattwodifferenttimes.The
firstreceptionisthedirectpathreception,thesignalthatis
receiveddirectlyfromthesatellite.Thesecondreceptionis
fromareflectionofthatsamesignalfromthegroundorany
otherreflectivesurface.Thedirectpathsignalarrivesfirst,
thereflectedsignal,havinghadtotravelalongerdistance
tothereceiver,arriveslater.TheGPSsignalisdesignedto
minimizethismultipatherror.TheL1andL2frequencies
useddemonstrateadiffusereflectionpattern,loweringthe
signalstrengthofanyreflectionthatarrivesatthereceiver.
Inaddition,thereceiver’santennacanbedesignedtoreject
asignalthatitrecognizesasareflection.Inadditiontothe
propertiesofthecarrierfrequencies,thehighdata
frequencyofboththePandC/Acodesandtheirresulting
goodcorrelationpropertiesminimizetheeffectof
multipath propagation.
Thedesignfeaturesmentionedabovecombineto
reducethemaximumerrorexpectedfrommultipath
propagation to less than 20 feet.
DIFFERENTIAL GPS
1113. Differential GPS Concept
ThediscussionsabovemakeitclearthattheGlobal
PositioningSystemprovidesthemostaccuratepositions
availabletonavigatorstoday.Theyshouldalsomakeclear
thatthemostaccuratepositioninginformationisavailable
toonlyasmallfractionoftheusingpopulation:U.S.and
alliedmilitary.Formostopenoceannavigation
Rf()R
actual
error term+=
SATELLITE NAVIGATION171
applications,thedegradedaccuracyinherentinselective
availabilityandtheinabilitytocopytheprecisioncode
presentsnoserioushazardtonavigation.Amarinerseldom
ifeverneedsgreaterthan100meteraccuracyinthemiddle
of the ocean.
Itisadifferentsituationasthemarinerapproaches
shore.Typicallyforharborapproachesandpiloting,the
marinerwillshifttovisualpiloting.Theincreasein
accuracyprovidedbythisnavigationalmethodisrequired
toensureship’ssafety.The100meteraccuracyofGPSin
thissituationisnotsufficient.Anymarinerwhohasgroped
hiswaythrougharestrictedchannelinathickfogwill
certainlyappreciatethefactthatevenadegradedGPS
positionisavailableforthemtoplot.However,100meter
accuracyisnotsufficienttoensureship’ssafetyinmost
pilotingsituations.Inthissituation,themarinerneedsP
codeaccuracy.Theproblemthenbecomeshowtoobtain
theaccuracyofthePrecisePositioningServicewithdue
regardtothelegitimatesecurityconcernsoftheU.S.
military.Theanswertothisseemingdilemmaliesinthe
concept ofDifferential GPS (DGPS).
DifferentialGPSisasysteminwhichareceiveratan
accuratelysurveyedpositionutilizesGPSsignalsto
calculatetimingerrorsandthenbroadcastsacorrection
signaltoaccountfortheseerrors.Thisisanextremely
powerfulconcept.TheerrorswhichcontributetoGPS
accuracydegradation,ionospherictimedelayandselective
availability,areexperiencedsimultaneouslybyboththe
DGPSreceiverandarelativelycloseuser’sreceiver.The
extremelyhighaltitudeoftheGPSsatellitesmeansthat,as
longastheDGPSreceiveriswithin100-200kmofthe
user’sreceiver,theuser’sreceiveriscloseenoughtotake
advantage of any DGPS correction signal.
ThetheorybehindaDGPSsystemisstraightforward.
Locatedonanaccuratelysurveyedsite,theDGPS
receiveralreadyknowsitslocation.Itreceivesdatawhich
tellitwherethesatelliteis.Knowingthetwolocations,it
thencalculatesthetheoreticaltimeitshouldtakefora
satellite’ssignaltoreachit.Itthencomparesthetimethat
itactuallytakesforthesignaltoarrive.Thisdifferencein
timebetweenthetheoreticalandtheactualisthebasisfor
theDGPSreceiver’scomputationofatimingerrorsignal;
thisdifferenceintimeiscausedbyalltheerrorstowhich
theGPSsignalissubjected;errors,exceptforreceiver
errorandmultipatherror,towhichboththeDGPSandthe
user’sreceiversaresimultaneouslysubject.TheDGPS
systemthenbroadcastsatimingcorrectionsignal,the
effectofwhichistocorrectforselectiveavailability,
ionosphericdelay,andalltheothererrorsourcesthetwo
receivers share in common.
Forsuitablyequippedusers,DGPSresultsinpositions
atleastasaccurateasthoseobtainablebythePrecise
PositioningService.Thiscapabilityisnotlimitedtosimply
displayingthecorrectpositionforthenavigatortoplot.The
DGPSpositioncanbeusedastheprimaryinputtoan
electronicchartsystem,providinganelectronicreadoutof
positionaccurateenoughtopilotsafelyinthemost
restricted channel.
WAAS AND LAAS IN MARINE NAVIGATION
1114. WAAS/LAAS for Aeronautical Use
In1994theNationalTelecommunicationsandInfor-
mationAdministration(NTIA)producedatechnicalreport
fortheDepartmentofTransportationwhichconcludedthat
theoptimummixofenhancedGPSsystemsforoverallci-
vilianusewouldconsistofDGPSformarineandterrestrial
useandacombinedWAAS/LAASsystemforair
navigation.
TheWideAreaAugmentationSystem(WAAS)
conceptissimilartotheDGPSconcept,exceptthatcorrec-
tionalsignalsaresentfromgeostationarysatellitesviaHF
signalsdirectlytotheuser’sGPSreceiver.Thiseliminates
theneedforaseparatereceiverandantenna,asisthecase
withDGPS.WAASisintendedforenrouteairnavigation,
with25referencestationswidelyspacedacrosstheUnited
States,forcoverageoftheentireU.S.andpartsofMexico
and Canada.
TheLocalAreaAugmentationSystem(LAAS)is
intendedforprecisionairportapproaches,withreference
stationslocatedatairportsandbroadcastingtheircorrection
message on VHF radio frequencies.
WhilemanymarineGPSreceiversincorporateWAAS
circuitry(butnotthemoreaccurate,shorter-rangeLAAS),
WAASisnotoptimizedforsurfacenavigationbecausethe
HFradiosignalsareline-of-sightandaretransmittedfrom
geostationarysatellites.Atlowanglestothehorizon,the
WAASsignalmaybeblockedandtheresultingGPS
positionaccuracysignificantlydegradedwithnowarning.
TheDGPSsignal,ontheotherhand,isaterrain-following
signalthatisunaffectedbyobjectsinitspath.Itsimply
flows around them and continues on unblocked.
TheaccuracyofWAASandDGPSiscomparable,on
theorderofafewmeters.WAASwasdesignedtoprovide
7meteraccuracy95%ofthetime.DGPSwasdesignedto
provide10meteraccuracy95%ofthetime,butinactual
useonecanexpectabout1-3meteraccuracywhentheuser
iswithin100milesofheDGPStransmitter.Over100
miles,DGPSaccuracywillcommonlydegradebyan
additional1meterper100milesfromthetransmittersite.
Bothsystemshavebeenfoundinactualusetoprovide
accuracies somewhat better than designed.
TheWAASsignal,whilenotcertifiedforuseinthe
marineenvironmentasisDGPS,canbeaveryuseful
navigationaltoolifitslimitationsareunderstood.Inopen
watersofthecontinentalU.S.,theWAASsignalcanbe
172SATELLITE NAVIGATION
expectedtobeavailableanduseful,providedthereceiver
hasWAAScircuitryandisprogrammedtousetheWAAS
data.OutsidetheU.S.,orinanyareawheretallbuildings,
trees,orotherobstructionsriseabovethehorizon,the
WAASsignalmaybeblocked,andtheresultingGPSfix
couldbeinerrorbymanymeters.Sincethehighest
accuracyisnecessaryinthemostconfinedwaters,WAAS
should be used with extreme caution in these areas.
WAAScanenhancethenavigator’ssituational
awarenesswhenavailable,butavailabilityisnotassured.
Further,amarinereceiverwillprovidenoindicationwhen
WAASdataisnotapartofthefix.[AircraftGPSreceivers
maycontainReceiverAutonomousIntegrityMonitoring
(RAIM)software,whichdoesprovidewarningofWAAS
satellitesignalfailure,andremovestheaffectedsignalfrom
the fix solution.]
LAASdata,broadcastonVHF,islesssubjecttoblock-
ing,butisonlyavailableinselectedareasnearairports.Its
rangeisabout30miles.Itisthereforenotsuitableforgen-
eral marine navigational use.
NON-U.S. SATELLITE NAVIGATION SYSTEMS
1115. The Galileo System
SincethedevelopmentofGPS,variousEuropean
councilsandcommissionshaveexpressedaneedforasat-
ellitenavigationsystemindependentofGPS.Economic
studieshaveemphasizedthisneed,andtechnologicalstud-
iesbytheEuropeanSpaceAgencyoverseveralyearshave
provenitsfeasibility.Inearly2002theEuropeanUnion
(EU)decidedtofundthedevelopmentofitsnewGalileo
satellitenavigationsystem.Agreatdealofpreliminarysci-
entificworkhasalreadybeenaccomplished,whichwill
enablethefulldeploymentofGalileooverthenextfew
years.
SeveralfactorsinfluencedthedecisiontodevelopGa-
lileo,theprimaryonebeingthatGPSisaU.S.militaryasset
thatcanbedegradedforcivilianuseonorderoftheU.S.
Government(asistheRussiansatellitenavigationsystem
GLONASS).DisruptionofeithersystemmightleaveEuro-
peanuserswithouttheirprimarynavigationsystemata
criticaltime.Incontrast,Galileowillbeunderciviliancon-
trolanddedicatedprimarilytocivilianuse.Itisimportant
tonotethatsinceGPShasbeenoperational,civilianuses
areproliferatingfarmorerapidlythananticipated,tothe
pointthatGPSplannersaredevelopingnewfrequencies
andenhancementstoGPSforcivilianuse(WAASand
LAAS),SAhasbeenturnedoff(asofMay1,2000),andthe
cost and size of receivers have plummeted.
PlanscallfortheGalileoconstellationtoconsistof30
satellites(27usableandthreespares)inthreeorbitalplanes,
eachinclined56degreestotheequator.Theorbitsareatan
altitudeof23,616km(about12,750nm).Galileowillbe
designedtoservehigherlatitudesthanGPS,anadditional
factorintheEUdecision,basedonScandinavian
participation.
WhileU.S.GPSsatellitesareonlylaunchedoneata
time,Galileosatellitesarebeingdesignedwithnewminia-
turizationtechniquesthatwillallowseveraltobelaunched
onthesamerocket,afarmorecost-efficientwaytoplace
them in orbit and maintain the constellation.
Galileowillalsoprovideanimportantfeatureforcivil-
ianusethatGPSdoesnot:integritymonitoring.Currently,
acivilianGPSuserreceivesnoindicationthathisunitisnot
receivingpropersatellitesignals,therebeingnoprovision
forsuchnotificationinthecode.However,Galileowillpro-
videsuchasignal,alertingtheuserthatthesystemis
operating improperly.
TheissueofcompatibilitywithGPSisbeingaddressed
duringongoingdevelopment.FrequencysharingwithGPS
isunderdiscussion,anditisreasonabletoassumethata
highdegreeofcompatibilitywillexistwhenGalileoisop-
erational.Manufacturerswillundoubtedlyofferavarietyof
systemswhichexploitthebesttechnologiesofbothGPS
andGalileo.Integrationwithexistingshipboardelectronic
systems such as ECDIS and ECS will be ensured.
ThebenefitofGalileoforthenavigatoristhatthere
willbetwoseparatesatellitenavigationsystemstorelyon,
providingnotonlyredundancy,butalsoanincreasedde-
greeofaccuracy(forsystemsthatcanintegrateboth
systems’signals).Galileoshouldbefirstavailablein2005,
and the full constellation is scheduled to be up by 2008.
1116. GLONASS
TheGlobalNavigationSatelliteSystem(GLONASS),
underthecontroloftheRussianmilitary,hasbeeninuse
since1993,andisbasedonthesameprinciplesasGPS.The
spacesegmentconsistsof24satellitesinthreeorbital
planes,theplanesseparatedby120degreesandtheindivid-
ualsatellitesby45degrees.Theorbitsareinclinedtothe
equatoratanangleof64.8degrees,andtheorbitalperiodis
about11hours,15minutesatanaltitudeof19,100km
(10,313nm).Thedesignedsystemfixaccuracyforcivilian
useis100metershorizontal(95%),150metersvertical,and
15cm/sec.invelocity.Militarycodesprovideaccuraciesof
some 10-20 meters horizontal.
ThegroundsegmentofGLONASSliesentirelywithin
theformerSovietUnion.Reliabilityhasbeenanongoing
problemfortheGLONASSsystem,butnewsatellitede-
signswithlongerlifespansareaddressingtheseconcerns.
Theusersegmentconsistsofvarioustypesofreceiversthat
provide position, time, and velocity information.
GLONASSsignalsareintheL-band,operatingin25
channelswith0.5625MHzseparationin2bands:from
1602.5625MHzto1615.5MHz,andfrom1240to1260
MHz.
173
CHAPTER 12
LORAN NAVIGATION
INTRODUCTION TO LORAN
1200. History and Role of Loran
Thetheorybehindtheoperationofhyperbolicnaviga-
tionsystemswasknowninthelate1930’s,butittookthe
urgencyofWorldWarIItospeeddevelopmentofthesys-
temintopracticaluse.Byearly1942,theBritishhadan
operatinghyperbolicsysteminusedesignedtoaidinlong-
rangebombernavigation.Thissystem,namedGee,operat-
edonfrequenciesbetween30MHzand80MHzand
employed“master”and“slave”transmittersspacedap-
proximately100milesapart.TheAmericanswerenotfar
behindtheBritishindevelopmentoftheirownsystem.By
1943,theU.S.CoastGuardwasoperatingachainofhyper-
bolicnavigationtransmittersthatbecameLoranA(The
termLoranwasoriginallyanacronymforLOngRAnge
Navigation).Bytheendofthewar,thenetworkconsisted
ofover70transmittersprovidingcoverageoverapproxi-
mately 30% of the earth’s surface.
Inthelate1940’sandearly1950’s,experimentsinlow
frequencyLoranproducedalongerrange,moreaccurate
system.Usingthe90-110kHzband,Lorandevelopedinto
a24-hour-a-day,all-weatherradionavigationsystem
namedLoranC.Fromthelate1950’s,LoranAandLoran
Csystemswereoperatedinparalleluntilthemid1970’s
whentheU.S.GovernmentbeganphasingoutLoranA.
TheUnitedStatescontinuedtooperateLoranCinanumber
ofareasaroundtheworld,includingEurope,Asia,theMed-
iterraneanSea,andpartsofthePacificOceanuntilthemid
1990’swhenitbeganclosingitsoverseasLoranCstations
ortransferringthemtothegovernmentsofthehostcoun-
tries.ThiswasaresultoftheU.S.DepartmentofDefense
adoptingtheGlobalPositioningSystem(GPS)asitsprima-
ryradionavigationservice.IntheUnitedStates,Loran
servesthe48contiguousstates,theircoastalareasandparts
ofAlaska.Itprovidesnavigation,location,andtimingser-
vicesforbothcivilandmilitaryair,land,andmarineusers.
LoransystemsarealsooperatedinCanada,China,India,
Japan,NorthwestEurope,Russia,SaudiArabia,andSouth
Korea.
ThefutureroleofLorandependsontheradionaviga-
tionpoliciesofthecountriesandinternational
organizationsthatoperatetheindividualchains.Inthe
UnitedStates,theFederalGovernmentplanstocontinue
operatingLoranintheshorttermwhileitevaluatesthe
long-termneedforthesystem.TheU.S.Governmentwill
giveusersreasonablenoticeifitconcludesthatLoranisno
longerneededorisnotcosteffective,sothatuserswillhave
theopportunitytotransitiontoalternativenavigationaids
and timing services.
CurrentinformationontheU.S.Loransystem,includ-
ingNoticestoMariners,maybeobtainedattheU.S.Coast
GuardNavigationCenterWorldWideWebsiteat
http://www.navcen.uscg.gov/.
LORAN C DESCRIPTION
1201. Summary of Operation
TheLoranC(hereafterreferredtosimplyasLoran)
systemconsistsoftransmittingstations,whichareplaced
severalhundredmilesapartandorganizedintochains.
WithinaLoranchain,onestationisdesignatedasthemas-
terstationandtheothersassecondarystations.Every
Loranchaincontainsatleastonemasterstationandtwo
secondarystationsinordertoprovidetwolinesofposition.
Themasterandsecondarystationstransmitradiopuls-
esatprecisetimeintervals.ALoranreceivermeasuresthe
timedifference(TD)betweenwhenthevesselreceivesthe
mastersignalandwhenitreceiveseachofthesecondary
signals.Whenthiselapsedtimeisconvertedtodistance,the
locusofpointshavingthesameTDbetweenthemasterand
eachsecondaryformsthehyperbolicLOP.Theintersection
oftwoormoreoftheseLOP’sproducesafixofthevessel’s
position.
Therearetwomethodsbywhichthenavigatorcancon-
vertthisinformationintoageographicposition.Thefirst
involvestheuseofachartoverprintedwithaLorantime
delaylatticeconsistingofhyperbolicTDlinesspacedat
convenientintervals.Thenavigatorplotsthedisplayed
TD’sbyinterpolatingbetweenthelatticelinesprintedon
thechart,manuallyplotsthefixwheretheyintersectand
thendetermineslatitudeandlongitude.Inthesecondmeth-
od,computeralgorithmsinthereceiver’ssoftwareconvert
the TD’s to latitude and longitude for display.
Aswithothercomputerizednavigationreceivers,a
typicalLoranreceivercanacceptandstorewaypoints.
174LORAN NAVIGATION
Waypointsaresetsofcoordinatesthatdescribeeitherloca-
tionsofnavigationalinterestorpointsalongaplanned
route.Waypointsmaybeenteredbyvisitingthespotofin-
terestandpressingtheappropriatereceivercontrolkey,or
bykeyinginthewaypointcoordinatesmanually,eitherasa
TDorlatitude-longitudepair.Ifusingwaypointstomarka
plannedroute,thenavigatorcanusethereceivertomonitor
thevessel’sprogressinrelationtothetrackbetweeneach
waypoint.Bycontinuouslyprovidingparameterssuchas
cross-trackerror,courseoverground,speedoverground,
andbearinganddistancetonextwaypoint,thereceivercon-
tinually serves as a check on the primary navigation plot.
1202. Components of the Loran System
Forthemarinenavigator,thecomponentsoftheLoran
systemconsistoftheland-basedtransmittingstations,the
Loranreceiverandantenna,theLorancharts.Inaddition
tothemasterandsecondarytransmittingstationsthem-
selves,land-basedLoranfacilitiesalsoincludetheprimary
andsecondarysystemareamonitorsites,thecontrolsta-
tionandaprecisetimereference.Thetransmittersemit
Loransignalsatpreciselytimedintervals.Themonitorsites
andcontrolstationscontinuallymeasureandanalyzethe
characteristicsoftheLoransignalsreceivedtodetectany
anomaliesorout-of-specificationconditions.Sometrans-
mittersserveonlyonefunctionwithinachain(i.e.,either
masterorsecondary).However,inmanyinstances,one
transmittertransmitssignalsforeachoftwoadjacent
chains. This practice is termeddual rating.
Loranreceiversexhibitvaryingdegreesofsophistication,
buttheirsignalprocessingissimilar.Thefirstprocessingstage
consistsofsearchandacquisition,duringwhichthereceiver
searchesforthesignalfromaparticularLoranchainandestab-
lishestheapproximatetimereferenceofthemasterand
secondarieswithsufficientaccuracytopermitsubsequentset-
tling and tracking.
Aftersearchandacquisition,thereceiverentersthesettle
phase.Inthisphase,thereceiversearchesforanddetectsthe
frontedgeoftheLoranpulse.Afterdetectingthefrontedgeof
the pulse, it selects the correct cycle of the pulse to track.
Havingselectedthecorrecttrackingcycle,thereceiver
beginsthetrackingandlockphase,inwhichthereceiver
maintainssynchronizationwiththeselectedreceivedsig-
nals.Oncethisphaseisreached,thereceiverdisplayseither
thetimedifferenceofthesignalsorthecomputedlatitude
and longitude.
1203. The Loran Signal
TheLoransignalconsistsofaseriesof100kHzpulses
sentfirstbythemasterstationandthen,inturn,bythesec-
ondarystations.Boththeshapeoftheindividualpulseand
thepatternoftheentirepulsesequenceareshowninFigure
1203a.Ascomparedtoacarriersignalofconstantampli-
tude,pulsedtransmissionallowsthesamesignalrangetobe
achievedwithaloweraverageoutputpower.Pulsedtrans-
missionalsoyieldsbettersignalidentificationproperties
and more precise timing of the signals.
TheindividualsinusoidalLoranpulseexhibitsasteep
risetoitsmaximumamplitudewithin65µsecofemission
andanexponentialdecaytozerowithin200to300µsec.
Thesignalfrequencyisnominallydefinedas100kHz;in
actuality,thesignalisdesignedsuchthat99%oftheradiat-
edpoweriscontainedina20kHzbandcenteredon100
kHz.
TheLoranreceiverisprogrammedtotrackthesignal
onthecyclecorrespondingtothecarrierfrequency’sthird
positivecrossingofthex-axis.Thisoccurrence,termedthe
standardzerocrossing,ischosenfortworeasons.First,it
islateenoughforthepulsetohavebuiltupsufficientsignal
strengthforthereceivertodetectit.Second,itisearly
enoughinthepulsetoensurethatthereceiverisdetecting
thetransmittingstation’sgroundwavepulseandnotitssky
wavepulse.Skywavepulsesareaffectedbyatmospheric
refractionandifusedunknowingly,wouldintroducelarge
errorsintopositionsdeterminedbyaLoranreceiver.The
pulsearchitecturedescribedherereducesthismajorsource
of error.
Anotherimportantparameterofthepulseistheenve-
lope-to-cycledifference(ECD).Thisparameterindicates
howpropagationofthesignalcausesthepulseshapeenve-
lope(i.e.,theimaginarylineconnectingthepeakofeach
sinusoidalcycle)toshiftintimerelativetothezerocross-
ings.TheECDisimportantbecausereceiversusethe
preciselyshapedpulseenvelopetoidentifythecorrectzero
crossing.Transmittingstationsarerequiredtokeepthe
ECDwithindefinedlimits.Manyreceiversdisplaythere-
ceived ECD as well.
Next,individualpulsesarecombinedintosequences.
Forthemastersignal,aseriesofninepulsesistransmitted,
thefirsteightspaced1000µsecapartfollowedbyaninth
transmitted2000µsecaftertheeighth.Secondarystations
transmitaseriesofeightpulses,eachspaced1000µsec
apart.SecondarystationsaregivenletterdesignationsofU,
W,X,Y,andZ;thisletterdesignationindicatestheorderin
whichtheytransmitfollowingthemaster.Ifachainhastwo
secondaries,theywillbedesignatedYandZ.Ifachainhas
threesecondaries,theyareX,YandZ,andsoon.Someex-
ceptionstothisgeneralnamingpatternexist(e.g.,W,Xand
Y for some 3-secondary chains).
Thespacingbetweenthemastersignalandeachofthe
secondarysignalsisgovernedbyseveralparametersasil-
lustratedinFigure1203b.Thegeneralideaisthateachof
thesignalsmustcleartheentirechaincoverageareabefore
thenextoneistransmitted,sothatnosignalcanbereceived
outoforder.Thetimerequiredforthemastersignaltotrav-
eltothesecondarystationisdefinedastheaveragebaseline
traveltime(BTT),orbaselinelength(BLL).Tothistime
intervalisaddedanadditionaldelaydefinedasthesecond-
arycodingdelay(SCD),orsimplycodingdelay(CD).
Thetotalofthesetwodelaysistermedtheemissiondelay
LORAN NAVIGATION175
(ED),whichistheexacttimeintervalbetweenthetransmis-
sionofthemastersignalandthetransmissionofthe
secondarysignal.EachsecondarystationhasitsownED
value.Inordertoensurethepropersequence,theEDofsec-
ondaryYislongerthanthatofX,andtheEDofZislonger
than that of Y.
Oncethelastsecondaryhastransmitted,themaster
transmitsagain,andthecycleisrepeated.Thetimetocom-
pletethiscycleoftransmissiondefinesanimportant
characteristicforthechain:thegrouprepetitioninterval
(GRI).Thegrouprepetitionintervaldividedbytenyields
thechain’snumericdesignator.Forexample,theinterval
betweensuccessivetransmissionsofthemasterpulsegroup
forthenortheastU.S.chainis99,600µsec,justlessthan
onetenthofasecond.Fromthedefinitionabove,theGRI
designatorforthischainisdefinedas9960.Asmentioned
previously,theGRImustbesufficientlylargetoallowthe
signalsfromthemasterandsecondarystationsinthechain
topropagatefullythroughouttheregioncoveredbythe
chain before the next cycle of pulses begins.
Twoadditionalcharacteristicsofthepulsegroupare
phasecodingandblinkcoding.Inphasecoding,thephase
ofthe100kHzcarriersignalisreversedfrompulsetopulse
inapresetpatternthatrepeatseverytwoGRI’s.Phasecod-
ingallowsareceivertoremoveskywavecontamination
fromthegroundwavesignal.LoranCsignalstravelaway
Figure 1203a. Pulse pattern and shape for Loran C transmission.
176LORAN NAVIGATION
fromatransmittingstationinallpossibledirections.
GroundwaveistheLoranenergythattravelsalongthesur-
faceoftheearth.SkywaveisLoranenergythattravelsup
intothesky.Theionospherereflectssomeofthesesky-
wavesbacktotheearth’ssurface.Theskywavealways
arriveslaterthanthegroundwavebecauseittravelsagreat-
erdistance.Theskywaveofonepulsecanthuscontaminate
thegroundwaveofthenextpulseinthepulsegroup.Phase
codingensuresthatthisskywavecontaminationwillalways
“cancelout”whenallthepulsesoftwoconsecutiveGRI’s
are averaged together.
BlinkcodingprovidesintegritytothereceivedLoran
signal.Whenasignalfromasecondarystationisoutoftol-
eranceandthereforetemporarilyunsuitablefornavigation,
theaffectedsecondarystationwillblink;thatis,thefirst
twopulsesoftheaffectedsecondarystationareturnedoff
andoninarepeatingcycle,3.6secondsoffand0.4seconds
on.Thereceiverdetectsthisconditionanddisplaysittothe
operator.Whentheblinkindicationisreceived,theoperator
shouldnotusetheaffectedsecondarystation.Ifastation’s
signalwillbetemporarilyshutdownformaintenance,the
CoastGuardcommunicatesthisinformationinaNoticeto
Mariners.TheU.S.CoastGuardNavigationCenterposts
theseonlineathttp://www.navcen.uscg.gov/.Ifamaster
stationisoutoftolerance,allsecondariesintheaffected
chain will blink.
TwootherconceptsimportanttotheunderstandingofLo-
ranoperationarethebaselineandbaselineextension.The
geographiclineconnectingamastertoaparticularsecondary
stationisdefinedasthestationpairbaseline.Thebaselineis,in
otherwords,thatpartofagreatcircleonwhichlieallthe
pointsconnectingthetwostations.Theextensionofthisline
beyondthestationstoencompassthepointsalongthisgreat
circlenotlyingbetweenthetwostationsdefinesthebaseline
extension.Theoptimalregionforhyperbolicnavigationoc-
cursinthevicinityofthebaseline,whilethemostcaremustbe
exercisedintheregionsnearthebaselineextension.These
concepts are further developed in the next few articles.
1204. Loran Theory of Operation
InLorannavigation,thelocusofpointshavingacon-
stantdifferenceindistancebetweenanobserverandeachof
twotransmitterstationsdefinesahyperbola,whichisaline
of position.
Assumingaconstantspeedofpropagationofelectro-
magneticradiationintheatmosphere,thetimedifferencein
thearrivalofelectromagneticradiationfromthetwotrans-
mittersitesisproportionaltothedistancebetweeneachof
thetransmittingsites,thuscreatingthehyperbolaonthe
earth’ssurface.Thefollowingequationsdemonstratethis
proportionality between distance and time:
Distance=Velocity x Time
or, using algebraic symbols
d=c x t
Figure 1203b. The time axis for Loran TD for point “A.”
LORAN NAVIGATION177
Therefore,ifthevelocity(c)isconstant,thedistance
betweenavesselandeachoftwotransmittingstationswill
bedirectlyproportionaltothetimedelaydetectedatthe
vesselbetweenpulsesofelectromagneticradiationtrans-
mitted from the two stations.
Anexampleillustratestheconcept.AsshowninFigure
1204,letusassumethattwoLorantransmittingstations,a
masterandasecondary,arelocatedalongwithanobserver
inaCartesiancoordinatesystemwhoseunitsareinnautical
miles.Weassumefurtherthatthemasterstation,designated
“M”,islocatedatcoordinates(x,y)=(-200,0)andthesec-
ondary,designated“X,”islocatedat(x,y)=(+200,0).An
observerwithareceivercapableofdetectingelectromag-
neticradiationispositionedatanypoint“A”whose
coordinates are defined as (x
a
,y
a
).
Notethatformathematicalconvenience,thesehyper-
bolalabelshavebeennormalizedsothatthehyperbola
perpendiculartothebaselineislabeledzero,withbothneg-
ativeandpositivedifferencevalues.Inactualpractice,all
Loran TD’s are positive.
ThePythagoreantheoremcanbeusedtodeterminethe
distancebetweentheobserverandthemasterstation;simi-
larly,onecanobtainthedistancebetweentheobserverand
the secondary station:
The difference between these distances (D) is:
Substituting,
Withthemasterandsecondarystationsinknowngeo-
graphicpositions,theonlyunknownsarethetwo
geographic coordinates of the observer.
EachhyperboliclineofpositioninFigure1204
representsthelocusofpointsforwhich(D)isheldconstant.
Forexample,iftheobserverabovewerelocatedatpointA
(271.9,200)thenthedistancebetweenthatobserverandthe
secondarystation(thepointdesignated“X”inFigure
1204a)wouldbe212.5NM.Inturn,theobserver’sdistance
fromthemasterstationwouldbe512.5NM.Thefunction
Dwouldsimplybethedifferenceofthetwo,or300NM.
Foreveryotherpointalongthehyperbolapassingthrough
A,distanceDhasavalueof300NM.AdjacentLOP’s
indicate where D is 250 NM or 350 NM.
Toproduceafix,theobservermustobtainasimilarhy-
perboliclineofpositiongeneratedbyanothermaster-
secondarypair.Letussayanothersecondarystation“Y”is
placedatpoint(50,500).Mathematically,theobserverwill
thenhavetwoequationscorrespondingtotheM-XandM-
Y TD pairs:
DistancesD
1
andD
2
areknownbecausethetime
differenceshavebeenmeasuredbythereceiverand
convertedtothesedistances.Thetworemainingunknowns,
x
a
and y
a
, may then be solved.
Theaboveexampleisexpressedintermsofdistancein
nauticalmiles.BecausethenavigatorusesTD’stoperform
Loranhyperbolicnavigation,letusreworktheexamplefor
theM-XTDpairintermsoftimeratherthandistance,add-
ingtimingdetailsspecifictoLoran.Letusassumethat
electromagneticradiationtravelsatthespeedoflight(one
nauticalmiletraveledin6.18µsec).Thedistancefrommas-
terstationMtopointAwas512.5NM.Fromthe
relationshipjustdefinedbetweendistanceandtime,it
wouldtakeasignal(6.18µsec/NM)×512.5NM=3,167
µsectotravelfromthemasterstationtotheobserverat
pointA.Atthearrivalofthissignal,theobserver’sLoran
receiverwouldstarttheTDmeasurement.Recallfromthe
generaldiscussionabovethatasecondarystationtransmits
afteranemissiondelayequaltothesumofthebaseline
traveltimeandthesecondarycodingdelay.Inthisexample,
Figure 1204. Depiction of Loran LOP’s.
distance
am
x
a
200+
()
2
y
a
2
+
[]
0.5
=
distance
ax
x
a
200–
()
2
y
a
2
+
[]
0.5
=
D
distance
am
distance
ax
–=
D
x
a
200+()
2
y
a
2
+[]
0.5
x
a
200–()
2
y
a
2
+[]
0.5
–=
D
1
x
a
200+()
2
y
a
2
+[]
0.5
x
a
200–()
2
y
a
2
+[]
0.5
–=
D
2
x
a
200+()
2
y
a
2
+[]
0.5
x
a
50–()
2
y
a
500)–(
2
+[]
0.5
–=
178LORAN NAVIGATION
themasterandthesecondaryare400NMapart;therefore,
thebaselinetraveltimeis(6.18µsec/NM)×400NM=
2,472µsec.Assumingasecondarycodingdelayof11,000
µsec,thesecondarystationinthisexamplewouldtransmit
(2,472+11,000)µsecor13,472µsecafterthemastersta-
tion.Thesecondarysignalthenpropagatesoveradistance
212.5NMtoreachpointA,taking(6.18µsec/NM)×212.5
NM=1,313µsectodoso.Therefore,thetotaltimefrom
transmissionofthemastersignaltothereceptionofthesec-
ondarysignalbytheobserveratpointAis(13,472+1,313)
µsec = 14,785µsec.
Recall,however,thattheLoranreceivermeasuresthe
timedelaybetweenreceptionofthemastersignalandthe
receptionofthesecondarysignal.Therefore,thetimequan-
tityabovemustbecorrectedbysubtractingtheamountof
timerequiredforthesignaltotravelfromthemastertrans-
mittertotheobserveratpointA.Thisamountoftimewas
3,167µsec.Therefore,theTDobservedatpointAinthis
hypotheticalexamplewouldbe(14,785-3,167)µsecor
11,618µsec.Onceagain,thistimedelayisafunctionofthe
simultaneousdifferencesindistancebetweentheobserver
andthetwotransmittingstations,anditgivesrisetoahy-
perboliclineofpositionwhichcanbecrossedwithanother
LOP to fix the observer’s position.
1205. Allowances for Non-Uniform Propagation Rates
Theinitialcalculationsaboveassumedthespeedof
lightinfreespace;however,theactualspeedatwhichelec-
tromagneticradiationpropagatesonearthisreducedboth
bytheatmospherethroughwhichittravelsandbythecon-
ductivesurfaces—seaandland—overwhichitpasses.The
specifiedaccuracyneededfromLoranthereforerequires
three corrections to the propagation speed of the signal.
Thereductioninpropagationspeedduetotheatmo-
sphereisrepresentedbythefirstcorrectionterm:the
PrimaryPhaseFactor(PF).Similarly,aSecondary
PhaseFactor(SF)accountsforthereducedpropagation
speedduetotravelingoverseawater.Thesetwocorrections
aretransparenttotheoperatorsincetheyareuniformlyin-
corporatedintoallcalculationsrepresentedonchartsandin
Loran receivers.
Becauselandsurfaceshavelowerconductivitythan
seawater,thepropagationspeedoftheLoransignalpassing
overlandisfurtherreducedascomparedtothesignalpass-
ingoverseawater.Athirdandfinalcorrection,the
AdditionalSecondaryPhaseFactor(ASF),accountsfor
thedelayduetothelandconductivitywhenconvertingtime
delaystodistancesandthentogeographiccoordinates.De-
pendingonthemariner’slocation,signalsfromsomeLoran
transmittersmayhavetraveledhundredsofmilesoverland
andmustbecorrectedtoaccountforthisnon-seawaterpor-
tionofthesignalpath.Ofthethreecorrectionsmentioned
inthisarticle,thisisthemostcomplexandthemostimpor-
tantonetounderstand,andisaccordinglytreatedindetail
in Article 1210.
LORAN ACCURACY
1206. Defining Accuracy
SpecificationsofLoranandotherradionavigation
systemstypicallyrefertothreetypesofaccuracy:absolute,
repeatableand relative.
Absoluteaccuracy,alsotermedpredictableorgeodet-
icaccuracy,istheaccuracyofapositionwithrespecttothe
geographiccoordinatesoftheearth.Forexample,ifthe
navigatorplotsapositionbasedontheLoranlatitudeand
longitude(orbasedonLoranTD’s)thedifferencebetween
theLoranpositionandtheactualpositionisameasureof
the system’s absolute accuracy.
Repeatableaccuracyistheaccuracywithwhichthe
navigatorcanreturntoapositionwhosecoordinateshave
beenmeasuredpreviouslywiththesamenavigationalsys-
tem.Forexample,supposeanavigatorweretotraveltoa
buoyandnotetheTD’satthatposition.Later,supposethe
navigator,wantingtoreturntothebuoy,returnstothepre-
viouslymeasuredTD’s.Theresultingpositiondifference
betweenthevesselandthebuoyisameasureofthesys-
tem’s repeatable accuracy.
Relativeaccuracyistheaccuracywithwhichauser
canmeasurepositionrelativetothatofanotheruserofthe
samenavigationsystematthesametime.Ifonevesselwere
totraveltotheTD’sdeterminedbyanothervessel,thedif-
ferenceinpositionbetweenthetwovesselswouldbea
measure of the system’s relative accuracy.
Thedistinctionbetweenabsoluteandrepeatableaccu-
racyisthemostimportantonetounderstand.Withthe
correctapplicationofASF’sandwithinthecoveragearea
definedforeachchain,theabsoluteaccuracyoftheLoran
systemvariesfrombetween0.1and0.25nauticalmiles.
However,therepeatableaccuracyofthesystemismuch
better,typicallybetween18and90meters(approximately
60to300feet)dependingonone’slocationinthecoverage
area.Ifthenavigatorhasbeentoanareapreviouslyandnot-
edtheTD’scorrespondingtodifferentnavigationalaids
(e.g.,abuoymarkingaharborentrance),thehighrepeat-
ableaccuracyofthesystemenableslocationofthebuoyin
adverseweather.Similarly,selectedTDdataforvarious
harbornavigationalaidsandotherlocationsofinteresthave
beencollectedandrecordedandisgenerallycommercially
available.Thisinformationprovidesanexcellentbackup
navigationalsourcetoconventionalharborapproach
navigation.
LORAN NAVIGATION179
1207. Limitations to Loran Accuracy
Therearelimitsontheaccuracyofanynavigational
system,andLoranisnoexception.Severalfactorsthatcon-
tributetolimitingtheaccuracyofLoranasanavigational
aidarelistedinTable1207andarebrieflydiscussedinthis
article.Eventhoughallthesefactorsexceptoperatorerror
areincludedinthepublishedaccuracyofLoran,themari-
ner’saimshouldbetohaveaworkingknowledgeofeach
oneandminimizeanythatareunderhiscontrolsoastoob-
tain the best possible accuracy.
ThegeometryofLOP’susedinaLoranfixisofprime
importancetothemariner.Becauseunderstandingofthis
factorissocriticaltoproperLoranoperation,theeffectsof
crossinganglesandgradientsarediscussedindetailinthe
Article1208.Theremainingfactorsarebrieflyexplainedas
follows.
TheageoftheCoastGuard’sLorantransmitting
equipmentvariesfromstationtostation.Whensomeolder
typesofequipmentareswitchedfromstandbytoactiveand
viceversa,aslighttimingshiftaslargeastensofnanosec-
ondsmaybeseen.Thisissosmallthatitisundetectableby
mostmarinereceivers,butsinceallerrorsaccumulate,it
should be understood as part of the Loran “error budget.”
Theeffectsofactionstocontrolchaintimingaresimi-
lar.Thetimingofeachstationinachainiscontrolledbased
ondatareceivedattheprimarysystemareamonitorsite.
Signaltimingerrorsarekeptasneartozeroaspossibleat
theprimarysite,makingtheabsoluteaccuracyofLoran
generallythebestinthevicinityoftheprimarysite.When-
ever,duetoequipmentcasualtyortoaccomplishsystem
maintenance,thecontrolstationshiftstothesecondarysys-
temareamonitorsite,slighttimingshiftsmaybe
introduced in parts of the coverage area.
Atmosphericnoise,generallycausedbylightning,re-
ducesthesignal-to-noiseratio(SNR)availableatthe
receiver.ThisinturndegradesaccuracyoftheLOP.Man-
madenoisehasasimilareffectonaccuracy.Inrarecases,a
man-madenoisesourcewhosecarriersignalfrequencyor
harmonicsarenear100kHz(suchastheconstantcarrier
controlsignalscommonlyusedonhigh-tensionpower
lines)mayalsointerferewithlock-onandtrackingofaLo-
ranreceiver.Ingeneral,Loranstationsthataretheclosest
totheuserwillhavethehighestSNRandwillproduce
LOP’swiththelowesterrors.Geometry,however,remains
akeyfactorinproducingagoodfixfromcombinedLOP’s.
Therefore,thebestLOP’sforafixmaynotallbefromthe
very nearest stations.
Theusershouldalsobeawarethatthepropagation
speedofLoranchangeswithtimeaswell.Temporalchang-
esmaybeseasonal,duetosnowcoverorchanging
groundwaterlevels,ordiurnal,duetoatmosphericandsur-
facechangesfromdaytonight.Seasonalchangesmaybe
aslargeas1µsecanddiurnalchangesaslargeas0.2µsec,
butthesevarywithlocationandchainbeingused.Passing
cold weather fronts may have temporary effects as well.
Disturbancesonthesun’ssurface,mostnotablysolar
flares,disturbtheearth’satmosphereaswell.TheseSudden
IonosphericDisturbances(SID’s)increaseattenuationof
radiowavesandthusdisturbLoransignalsandreduce
SNR.SuchadisturbancemayinterferewithLoranrecep-
tion for periods of hours or even longer.
Thefactorsaboveallrelatetothepropagatedsignalbe-
foreitreachesthemariner.Theremainingfactorsdiscussed
belowaddresstheaccuracywithwhichthemarinerre-
ceives and interprets the signal.
FactorHas effect on
Absolute AccuracyRepeatable Accuracy
Crossing angles and gradients of the Loran LOP’sYesYes
Stability of the transmitted signal (e.g., transmitter effect)YesYes
Loranchaincontrolparameters(e.g.,howcloselyactualED
ismaintainedtopublishedED,whichsystemareamonitoris
being used, etc.)
YesYes
Atmospheric and man-made ambient electronic noiseYesYes
Factorswithtemporalvariationsinsignalpropagationspeed
(e.g., weather, seasonal effects, diurnal variations, etc.)
YesYes
Sudden ionospheric disturbancesYesYes
Receiver quality and sensitivityYesYes
Shipboard electric noiseYesYes
Accuracy with which LOP’s are printed on nautical chartsYesNo
Accuracy of receiver’s computer algorithms for coordinate
conversion
YesNo
Operator errorYesYes
Table 1207. Selected Factors that Limit Loran Accuracy.
180LORAN NAVIGATION
Receiversvaryinprecision,qualityandsophistication.
SomereceiversdisplayTD’stothenearest0.1µsec;others
to0.01µsec.Internalprocessingalsovaries,whetherinthe
analog“frontend”orthedigitalcomputeralgorithmsthat
usetheprocessedanalogsignal.Byreferencingtheuser
manual,themarinermaygainanappreciationforthead-
vantagesandlimitationsoftheparticularmodelavailable,
andmayadjustoperatorsettingstomaximizeperformance.
Thebestreceiveravailablemaybehinderedbyapoor
installation.Similarly,electronicnoiseproducedbyengine
anddrivemachinery,variouselectricmotors,otherelec-
tronicequipmentorevenhouseholdappliancesmayhinder
theperformanceofaLoranreceiver.Themarinershould
consultdocumentationsuppliedwiththereceiverforproper
installation.Generally,properinstallationandplacementof
thereceiver’scomponentswillmitigatetheseproblems.In
somecases,contactingthemanufacturerorobtainingpro-
fessional installation assistance may be appropriate.
TherawTD’sobtainedbythereceivermustbecorrect-
edwithASF’sandthentranslatedtoposition.Whetherthe
receiverperformsthisentireprocessorthemarinerassists
bytranslatingTD’stopositionmanuallyusingaLoran
overprintedchart,publishedaccuraciestakeintoaccount
the small errors involved in this conversion process.
Finally,asinallendeavors,operatorerrorwhenusing
Loranisalwayspossible.Thiscanbeminimizedwithalert-
ness, knowledge and practice.
1208. The Effects of Crossing Angles and Gradients
The hyperbolic nature of Loran requires the operator
to pay special attention to the geometry of the fix, specifi-
cally to crossing angles and gradients, and to the possibil-
ity of fix ambiguity. We begin with crossing angles.
Asdiscussedabove,theTD’sfromanygivenmaster-
secondarypairformafamilyofhyperbolas.Eachhyperbo-
lainthisfamilycanbeconsideredalineofposition;the
vesselmustbesomewherealongthatlocusofpointswhich
formsthehyperbola.Atypicalfamilyofhyperbolasis
shown in Figure 1208a.
Now,supposethehyperbolicfamilyfromtheMaster-
XraystationpairshowninFigure1204weresuperimposed
uponthefamilyshowninFigure1208a.Theresultswould
be the hyperbolic lattice shown in Figure 1208b.
Ashasbeennoted,LoranLOP’sforvariouschainsand
secondariesareprintedonnauticalcharts.Eachofthesets
ofLOP’sisgivenaseparatecolorandisdenotedbyachar-
acteristicsetofsymbols.Forexample,anLOPmightbe
designated9960-X-25750.Thedesignationisreadasfol-
lows:thechainGRIdesignatoris9960,theTDisforthe
Master-Xraypair(M-X),andthetimedifferencealongthis
LOPis25750µsec.Thechartshowsonlyalimitednumber
ofLOP’storeduceclutteronthechart.Therefore,iftheob-
servedtimedelayfallsbetweentwochartedLOP’s,
interpolationbetweenthemisrequiredtoobtaintheprecise
LOP.Afterhavinginterpolated(ifnecessary)betweentwo
TDmeasurementsandplottedtheresultingLOP’sonthe
chart,thenavigatormarkstheintersectionoftheLOP’sand
labelsthatintersectionastheLoranfix.NotealsoinFigure
1208bthevariousanglesatwhichthehyperbolascrosseach
other.
Figure1208cshowsgraphicallyhowerrormagnitude
variesasafunctionofcrossingangle.AssumethatLOP1
Figure 1208a. A family of hyperbolic lines generated by
Loran signals.
Figure1208b.Ahyperboliclatticeformedbystationpairs
M-X and M-Y.
LORAN NAVIGATION181
isknowntocontainnoerror,whileLOP2hasanuncertain-
tyasshown.Asthecrossingangle(i.e.,theangleof
intersectionofthetwoLOP’s)approaches90°,rangeof
possiblepositionsalongLOP1(i.e.,thepositionuncertain-
tyorfixerror)approachesaminimum;conversely,asthe
crossingangledecreases,thepositionuncertaintyincreas-
es;thelinedefiningtherangeofuncertaintygrowslonger.
Thisillustrationdemonstratesthedesirabilityofchoosing
LOP’sforwhichthecrossingangleisascloseto90°as
possible.
Therelationshipbetweencrossingangleandfixuncer-
tainty can be expressed mathematically:
where xis the crossing angle.
Rearrangingalgebraically,
AssumingthatLOPerrorisconstant,thenpositionun-
certaintyisinverselyproportionaltothesineofthecrossing
angle.Asthecrossingangleincreasesfrom0°to90°,the
sineofthecrossingangleincreasesfrom0to1.Therefore,
theerrorisataminimumwhenthecrossingangleis90°,
and increases thereafter as the crossing angle decreases.
UnderstandingandproperuseofTDgradientsarealso
importanttothenavigator.Thegradientisdefinedasthe
rateofchangeofdistancewithrespecttoTD.Putanother
way,thisquantityistheratioofthespacingbetweenadja-
centLoranTD’s(usuallyexpressedinfeetormeters)and
thedifferenceinmicrosecondsbetweentheseadjacent
LOP’s.Forexample,ifataparticularlocationtwoprinted
TDlinesdifferby20µsecandare6NMapart,thegradient
is.
Thesmallerthegradient,thesmallerthedistanceerror
thatresultsfromanyTDerror.Thus,thebestaccuracyfrom
LoranisobtainedbyusingTD’swhosegradientisthe
smallestpossible(i.e.thehyperboliclinesareclosestto-
gether).Thisoccursalongthebaseline.Gradientsaremuch
larger (i.e. hyperbolic lines are farther apart) in the vicinity
ofthebaselineextension.Therefore,theusershouldselect
TD’s having the smallest possible gradients.
AnotherLoraneffectthatcanleadtonavigationalerror
inthevicinityofthebaselineextensionisfixambiguity.Fix
ambiguityresultswhenoneLoranLOPcrossesanother
LOPintwoseparateplaces.Nearthebaselineextension,
the“ends”ofahyperbolacanwraparoundsothatthey
crossanotherLOPtwice,oncealongthebaseline,andagain
Figure 1208c. Error in Loran LOP’s is magnified if the crossing angle is less than 90°.
sin(x)
LOP error
fix uncertainty
-----------------------------------=
fix uncertainty
LOP error
x()sin
--------------------------=
Gradient
6NM6076ft/NM×
20µsec
-----------------------------------------------
1822.8ft/µsec==
182LORAN NAVIGATION
alongthebaselineextension.AthirdLOPwouldresolve
the ambiguity.
MostLoranreceivershaveanambiguityalarmtoalert
thenavigatortothisoccurrence.However,bothfixambigu-
ityandlargegradientsnecessitatethatthenavigatoravoid
usingamaster-secondarypairwhenoperatinginthevicinity
of that pair’s baseline extension.
1209. Coverage Areas
The0.25NMabsoluteaccuracyspecifiedforLoran
isvalidwithineachchain’scoveragearea.Thisarea,
whoselimitsdefinethemaximumrangeofLoranfora
particularchain,istheregioninwhichbothaccuracy
andSNRcriteriaaremet.TheNationalOceanographic
andAtmosphericAdministration(NOAA)hasgeneral-
lyfollowedthesecoveragearealimitswhenselecting
wheretoprintparticularLoranTDlinesonLoranover-
printedcharts.Coverageareadiagramsofeachchain
arealsoavailableonlinefromtheU.S.CoastGuard’s
NavigationCenter,currentlyathttp://www.navcen.us-
cg.gov/ftp/loran/lgeninfo/h-book/loranappendixb.pdf.
OtherhelpfulinformationavailableatthisFTPsitein-
cludestheLoranCUser’sHandbookandtheLoranC
SignalSpecification,twokeysourcesofmaterialinthis
chapter.
Onecaveattorememberwhenconsideringcoverage
areasisthatthe0.25NMaccuracycriteriaismodifiedin-
sidethecoverageareainthevicinityofthecoastlinedueto
ASFeffects.Thefollowingarticledescribesthismorefully.
1210. Understanding Additional Secondary Factors
(ASF’s)
Mathematically,calculatingthereductioninpropaga-
tionspeedofanelectromagneticsignalpassingoveraland
surfaceofknownconductivityisrelativelystraightforward.
In practice, however, determining this Loran ASF correc-
tion accurately for use in the real world can be complex.
Thereareatleastfourreasonsforthiscomplexity.
First,theconductivityofgroundvariesfromregiontore-
gion,sothecorrectiontobeappliedisdifferentforevery
signalpath.Moreover,groundconductivitydatacurrently
availabledonottakeintoaccountalltheminorvariations
withineachregion.Second,methodsusedtocompute
ASF’svary.ASF’scanbedeterminedfromeitheramathe-
maticalmodelbasedonknownapproximateground
conductivities,orfromempiricaltimedelaymeasurements
invariouslocations,oracombinationofboth.Methodsin-
corporatingempiricalmeasurementstendtoyieldmore
accurateresults.Onereceivermanufacturermaynotuseex-
actlythesamecorrectionmethodasanother,andneither
mayuseexactlythesamemethodasthoseincorporatedinto
timedifferencesprintedonaparticularnauticalchart.
Whilesuchdifferencesareminor,auserunawareofthese
differencesmaynotobtainthebestaccuracypossiblefrom
Loran.Third,relativelylargelocalvariationsinASFvaria-
tionsthatcannotfullybeaccountedforincurrentASF
modelsappliedtothecoverageareaasawhole,maybeob-
servedintheregionwithin10NMofthecoast.Overthe
years,evenempiricallymeasuredASF’smaychange
slightlyintheseareaswiththeadditionofbuildings,bridg-
esandotherstructurestocoastalareas.Fourthandfinally,
ASF’svaryseasonallywithchangesingroundwaterlevels,
snow pack depths and similar factors.
DesignersoftheLoransystem,includingLoranreceiv-
ermanufacturers,haveexpendedagreatdealofeffortto
includeASF’sinerrorcalculationsandtominimizethese
effects.Indeed,inaccuraciesinASFmodelingareaccount-
edforinpublishedaccuracyspecificationsforLoran.What
thendoesthemarinenavigatorneedtoknowaboutASF’s
beyondthis?Toobtainthe0.25NMabsoluteaccuracyad-
vertisedforLoran,theanswerisclear.Onemustknow
whereinthecoverageareaASF’saffectpublishedaccura-
cies,andonemustknowwhenASF’sarebeing
incorporated, both in the receiver and on any chart in use.
WithrespecttowhereASF’saffectpublishedaccura-
cies,onemustrememberthatlocalvariationsinthevicinity
ofthecoastlinearethemostunpredictableofallASFrelat-
edeffectsbecausetheyarenotadequatelyexplainedby
currentpredictiveASFmodels.Asaresult,eventhough
fixesdeterminedbyLoranmaysatisfythe0.25NMaccu-
racyspecificationintheseareas,suchaccuracyisnot
“guaranteed”forLoranwithin10NMofthecoast.Users
shouldalsoavoidrelyingsolelyonthelatticeofLoranTD’s
in inshore areas.
WithrespecttowhenASF’sarebeingapplied,one
shouldrealizethatthedefaultmodeinmostreceiverscom-
binesASF’swithrawTDmeasurements.Thisisbecause
theinclusionofASF’sisrequiredinordertomeetthe0.25
NMaccuracycriteria.Thenavigatorshouldverifywhich
modethereceiverisin,andensurethemodeisnotchanged
unknowingly.Similarly,currentNOAALoranoverprinted
chartsoftheU.S.incorporateASF’s,andinthechart’smar-
gin the following note appears:
“LoranCcorrectiontablespublishedbytheNa-
tionalImageryandMappingAgencyorothers
shouldnotbeusedwiththischart.Thelinesof
positionshownhavebeenadjustedbasedon
surveydata.Everyefforthasbeenmadetomeet
the0.25nauticalmileaccuracycriteriaestab-
lishedbytheU.S.CoastGuard.Marinersare
cautionednottorelysolelyonthelatticesinin-
shore waters.”
Thekeypointtorememberthereisthatthe“ASFin-
cluded”and“ASFnotincluded”modesmustnotbemixed.
Inotherwords,thereceiverandanychartinusemusthan-
dleASF’sinthesamemanner.Ifthereceiverincludesthem,
anychartinusemustalsoincludethem.Ifoperatingona
chartthatdoesnotincludeASF’s—Lorancoverageareasin
anotherpartoftheworld,forexample—thereceivermust
besettothesamemode.Ifthenavigatordesirestocorrect
LORAN NAVIGATION183
ASF’smanually,tablesforU.S.Loranchainsareavailable
athttp://chartmaker.ncd.noaa.gov/mcd/loranc.htm.These
documentsalsoprovideafullerexplanationofmanualASF
corrections.WhenviewingASFtables,rememberthatal-
thoughtheASFcorrectionforasinglesignalisalways
positive(indicatingthatthesignalisalwaysslowedand
neverspeededbyitspassageoverland),theASFcorrection
foratimedifferencemaybenegativebecausetwosignalde-
lays are included in the computation.
TheU.S.Governmentdoesnotguaranteetheaccuracy
ofASFcorrectionsincorporatedintoLoranreceiversby
theirrespectivemanufacturers.Theprudentnavigatorwill
regularlycheckLoranTD’sagainstchartedLOP’swhenin
aknownposition,andwillcompareLoranlatitudeandlon-
gitudereadoutsagainstothersourcesofposition
information.Ensuringtheproperconfigurationandopera-
tionoftheLoranreceiverremainsthenavigator’s
responsibility.
Uptothispoint,ourdiscussionhaslargelyfocusedon
correctlyunderstandingandusingLoraninordertoobtain
publishedaccuracies.Insomeportionsofthecoveragear-
eas,accuracylevelsactuallyobtainablemaybe
significantlybetterthantheseminimumpublishedvalues.
Thefollowingarticlesdiscusspracticaltechniquesformax-
imizingtheabsolute,repeatableandrelativeaccuracyof
Loran.
1211. Maximizing Loran’s Absolute Accuracy
ObtainingthebestpossibleabsoluteaccuracyfromLo-
ranrestsprimarilyonthenavigator’sselectionofTD’s,
particularlytakingintoaccountgeometry,SNRandprox-
imitytothebaselineandbaselineextension.Asavessel
transitsthecoveragearea,thesefactorsgraduallychange
and,exceptforSNR,arenotvisibleonthedisplaypanelof
theLoranreceiver.Mostreceiverstrackanentirechainand
sometrackmultiplechainssimultaneously,butthemajority
ofinstalledmarinereceiversstilluseonlytwoTD’stopro-
ducealatitudeandlongitude.Somereceiversmonitorthese
factorsandmayautomaticallyselectthebestpair.Thebest
wayforthenavigator,however,tomonitorthesefactorsis
byreferringtoaLoranoverprintedchart,evenifnotactu-
allyplottingfixesonit.Thealertnavigatorwillfrequently
reevaluatetheselectionofTD’sduringatransitandmake
adjustments as necessary.
Beyondthisadvice,twoadditionalconsiderationsmay
helpthenavigatormaximizeabsoluteaccuracy.Thefirstis
therealizationthatLoranTDerrorisnotevenlydistributed
overthecoveragearea.Besidestheeffectsoftransmitter
stationlocationongeometryandfixerror,thelocationsof
theprimaryandsecondarymonitorsitesalsohaveadis-
cernibleeffectonTDerrorinthecoveragearea.AsASF’s
changedailyandseasonally,theLorancontrolstationscon-
tinuallyadjusttheemissiondelayofeachsecondarystation
tokeepitstatisticallyatitsnominalvalueasobservedatthe
primarymonitorsite.Whatthismeansisthat,onaverage,
theLoranTDismorestableandmoreaccurateintheabso-
lutesenseinthevicinityoftheprimarymonitorsite.The
primarysystemareamonitorforstations9960-M,9960-X
and9960-YwasplacedattheentrancetoNewYorkharbor
atSandyHook,NewJerseyforjustthisreason.Aswitchby
thecontrolstationtothesecondarymonitorsitewillshift
theerrordistributionslightlywithinthecoveragearea,re-
ducingitnearthesecondarysiteandslightlyincreasingit
elsewhere.Thelocationsofprimarysystemareamonitor
sites can be found at the USCG NAVCEN web site.
Thesecondconsiderationinmaximizingabsoluteac-
curacyisthatmostLoranreceiversmaybemanually
calibratedusingafeaturevariouslycalled“bias,”“offset,”
“homeport”orasimilarterm.Wheninhomeportoranother
knownlocation,theknownlatitudeandlongitude(orin
somecases,thedifferencebetweenthecurrentLorandis-
playandtheknownvalues)isenteredintothereceiver.This
forcesthereceiver’spositionerrortobezeroatthatpartic-
ular point and time.
Thelimitationofthistechniqueisthatthiscorrection
becomeslessaccuratewiththepassageoftimeandwithin-
creasingdistanceawayfromthepointused.Mostpublished
sourcesindicatethetechniquetobeofvalueouttoadis-
tanceof10to100milesofthepointwherethecalibration
wasperformed.Thiscorrectiondoesnottakeintoaccount
localdistortionsoftheLorangridduetobridges,power
linesorothersuchman-madestructures.Thenavigator
shouldevaluateexperimentallytheeffectivenessofthis
techniqueingoodweatherconditionsbeforerelyingonit
fornavigationatothertimes.Thebiasshouldalsobead-
justedregularlytoaccountforseasonalLoranvariations;
usingthesamevaluethroughouttheyearisnotthemostef-
fectiveapplicationofthistechnique.Also,enteringan
offsetintoaLoranreceiveralterstheapparentlocationof
waypoints stored prior to establishing this correction.
Finally,receiversvaryinhowthisfeatureisimple-
mented.Somereceiverssavetheoffsetwhenthereceiveris
turnedoff;otherszerothecorrectionwhenthereceiveris
turnedon.SomereceiversreplacetheinternalASFvalue
withtheoffset,whileothersaddittotheinternalASFval-
ues. Refer to the owner’s manual for the receiver in use.
1212. Maximizing Loran’s Repeatable Accuracy
Manyusersconsiderthehighrepeatableaccuracyof
Loranitsmostimportantcharacteristic.Toobtainthebest
repeatableaccuracyconsistently,thenavigatorshoulduse
measuredTD’sratherthanlatitudeandlongitudevalues
supplied by the receiver.
ThereasonforthisliesintheASFconversionprocess.
RecallthatLoranreceiversuseASF’stocorrectTD’s.Re-
callalsothattheASF’sareafunctionoftheterrainover
whichthesignalmustpasstoreachthereceiver.Therefore,
theASF’sforonestationpairaredifferentfromtheASF’s
foranotherstationpairbecausethesignalsfromthediffer-
entpairsmusttraveloverdifferentterraintoreachthe
184LORAN NAVIGATION
receiver.
ThisconsiderationmattersbecauseaLoranreceiver
maynotalwaysusethesamepairsofTD’stocalculatea
fix.Supposeanavigatormarksthepositionofachannel
buoybyrecordingitslatitudeandlongitudeusingtheTD
pairselectedautomaticallybytheLoranreceiver.If,onthe
returntrip,thereceiverisusingadifferentTDpair,thelat-
itudeandlongitudereadingsfortheexactsamebuoywould
beslightlydifferentbecausethenewTDpairwouldbeus-
ingadifferentASFvalue.Byusingpreviously-measured
TD’sandnotpreviously-measuredlatitudesandlongitudes,
thisASF-introducederrorisavoided.Thenavigatorshould
alsorecordthevaluesofallsecondaryTD’satthewaypoint
andnotjusttheonesusedbythereceiveratthetime.When
returningtothewaypoint,otherTD’swillbeavailableeven
ifthepreviouslyusedTDpairisnot.Recordingthetime
anddatethewaypointisstoredwillalsohelpevaluatethe
cyclicalseasonalanddiurnalvariationsthatmayhavesince
occurred.
1213. Maximizing Loran’s Relative Accuracy
Theclassicalapplicationofrelativeaccuracyinvolves
twousersfindingthesamepointontheearth’ssurfaceat
thesametimeusingthesamenavigationsystem.Themax-
imumrelativeLoranaccuracywouldbetheoreticallybe
achievedbyidenticalreceivers,configuredandinstalled
identicallyonidenticalvessels,trackingthesameTD’s.In
practice,thetwomostimportantfactorsaretrackingthe
sameTD’sandensuringthatASF’sarebeingtreatedcon-
sistentlybetweenthetworeceivers.Byattendingtothese,
thenavigatorshouldobtainrelativeaccuracyclosetothe
theoretical maximum.
Anotherapplicationofrelativeaccuracyisthecurrent
practiceofconvertingoldLoranTD’sintolatitudeandlon-
gitudeforusewithGPSandDGPSreceivers.Several
commercialfirmssellsoftwareapplicationsthatperform
thistedioustask.Onekeyquestionposedbythesepro-
gramsiswhetherornottheLoranTD’sincludeASF’s.The
difficultyinansweringthisquestiondependsonhowthe
LoranTD’swereobtained,andofcourseanunderstanding
ofASF’s.Ifindoubt,thenavigatorcanperformtheconver-
siononcebyspecifying“with”ASF’sandonce“without,”
andthencarefullychoosingwhichisthevalidone,assisted
by direct observation underway if needed.
ToroundoutthediscussionofLoran,thefollowingar-
ticlebrieflydescribespresentandpossiblefutureusesfor
thissystembeyondthewell-knownhyperbolicnavigation
mode.
NON-HYPERBOLIC USES OF LORAN C
1214. Precise Timing with Loran
BecauseLoranisfundamentallyaprecisetimingsys-
tem,asignificantsegmentoftheusercommunityuses
LoranforthepropagationofCoordinatedUniversalTime
(UTC).TheaccessibilityofUTCatanydesiredlocationen-
ablessuchapplicationsasthesynchronizationoftelephone
anddatanetworks.TheU.S.CoastGuardmakeseveryef-
forttoensurethateachLoranmastertransmitterstation
emitsitssignalwithin100nsofUTC.Becausethetiming
ofeachsecondarystationisrelativetothemaster,itstiming
accuracy derives from that of the master.
ThestartofeachLoranstation’sGRIperiodicallyco-
incideswiththestartoftheUTCsecond.Thisistermedthe
TimeofCoincidence(TOC).TheU.S.NavalObservatory
publishesTOC’sathttp://tycho.usno.navy.mil/loran.html
forthebenefitoftimingusers.BecauseoneLoranstationis
sufficienttoprovideanabsolutetimingreference,timing
receiversdonottypicallyrelyonthehyperbolicmodeor
use TD’s per se.
AnoteworthyfeatureofLoranisthateachtransmitter
stationhasanindependenttimingreferenceconsistingof
threemoderncesiumbeamoscillators.Timingequipment
atthetransmitterstationsconstantlycomparesthesesignals
andadjuststominimizeoscillatordrift.Theendresultisa
nationwidesystemwithalargeensembleofindependent
timingsources.ThisstrengthenstheU.S.technologyinfra-
structure.Asanothercross-checkofLorantime,daily
comparisonsaremadewithUTC,asdisseminatedviaGPS.
1215. Loran Time of Arrival (TOA) Mode
Withtheadventofthepowerfuldigitalprocessorsand
compactpreciseoscillatorsnowembeddedinuserreceiv-
ers,technicallimitationsthatdictatedLoran’shyperbolic
architecturedecadesagohavebeenovercome.Areceiver
cannowpredictinrealtimetheexactpointintimeaLoran
stationwilltransmititssignal,aswellastheexacttimethe
signal will be received at any assumed position.
Analternatereceiverarchitecturethattakesadvantage
ofthesecapabilitiesusesLoranTimeofArrival(TOA)
measurement,whicharemeasuredrelativetoUTCrather
thantoanarbitrarymasterstation’stransmission.Areceiv-
eroperatinginTOAmodecanlocateandtrackallLoran
signalsinview,promptingthedescriptor“allinview”for
thistypeofreceiver.Thisarchitecturestepsbeyondthelim-
itationsofusingonlyoneLoranchainatatime.Asaresult,
systemavailabilitycanbeimprovedacrossalltheoverlap-
pingcoverageareas.CoupledwithadvancedReceiver
AutonomousIntegrityMonitor(RAIM)algorithms,thisar-
chitecturecanalsoaddanadditionallayerofintegrityatthe
user level, independent of Loran blink.
Onetechnicalpossibilityarisingoutofthisnewcapa-
bilityistocontrolthetimeoftransmissionofeachstation
independentlywithdirectreferencetoUTC,ratherthanby
usingsystemareamonitors.Suchanarrangementcouldof-
LORAN NAVIGATION185
fertheadvantageofmoreuniformlydistributingLoranfix
errorsacrossthecoverageareas.Thiscouldinturnmore
naturallyconfigureLoranforuseinanintegratednaviga-
tion system.
1216. Loran in an Integrated Navigation System
Anexponentialworldwideincreaseinrelianceonelec-
tronicnavigationsystems,mostnotablyGPS,for
positioningandtiminghasfueledadriveformorerobust
systemsimmunefromaccidentalorintentionalinterfer-
ence.EvenashortoutageofGPS,forexample,would
likelyhaveseveresafetyandeconomicconsequencesfor
the United States and other nations.
Inthisenvironment,integratednavigationsystemsare
attractiveoptionsasrobustsourcesofpositionandtime.
Theidealintegratednavigationsystemcantoleratethedeg-
radationorfailureofanycomponentsystemwithout
degradation as a whole.
Loranoffersseveraladvantagestoanintegratedsys-
tembasedonGPSorDGPS.AlthoughLoranreliesonradio
propagationandisthussimilarlyvulnerabletolarge-scale
atmosphericeventssuchasionosphericdisturbances,at
100kHzitoccupiesaverydifferentportionofthespectrum
thanthe1.2GHzto1.6GHzbandusedbyGPS.Loranisa
high-powersystemwhoselowfrequencyrequiresavery
largeantennaforefficientpropagation.Therefore,jamming
Loranoverabroadareaismuchmoredifficultthanjam-
mingGPSoverthesamearea.Loransignalsarepresentin
urbanandnaturalcanyonsandunderfoliage,whereGPS
signalsmaybepartiallyorcompletelyblocked.Loran’sin-
dependenttimingsourcealsoprovidesanadditionaldegree
ofrobustnesstoanintegratedsystem.Inshort,thecircum-
stancesthatcausefailureordegradationofLoranarevery
differentfromthosethatcausefailureordegradationof
GPSorDGPS.WhentheabsoluteaccuracyofLoraniscon-
tinuallycalibratedbyGPS,therepeatableaccuracyof
Lorancouldensurenear-GPSperformanceofanintegrated
systeminseveralpossiblenavigationandtimingscenarios,
forperiodsofseveralhourstoafewdaysafteratotalloss
of GPS.
1217. Loran as a Data Transfer Channel
TheU.S.CoastGuardhaspracticedlowdataratetrans-
missionusingLoransignalsduringvariousperiodssince
the1970’s.Thetwoprimaryusesofthiscapabilitywere
Loranchaincontrolandbackupmilitarycommunications.
Inallcases,thedatasuperimposedontheLoransignalwere
transparenttotheusers,whowerenearlyuniversallyun-
aware of this dual use.
Inthelate1990’s,theNorthwestEuropeanLoranSys-
tem(NELS)implementedapulse-positionmodulation
patterntermedEurofixtoprovidedifferentialGPScorrec-
tionsviatheLoransignaltocertainareasinwesternand
northernEurope.Eurofixsuccessfullyincorporatedsophis-
ticateddatacommunicationstechniquestobroadcastGPS
correctionsinrealtimewhileallowingtraditionalLoranus-
ers to operate without interruption.
AnotherpossibleuseofaLorandatatransferchannel
istobroadcastGPScorrectionsprovidedbytheU.S.Wide
AreaAugmentationSystem(WAAS),whichwasdesigned
forthebenefitofaircraftintheU.S.NationalAirspaceSys-
tem(NAS).PreliminarytestshaveshownmodulatedLoran
signalscouldbesuccessfullyusedtobroadcastWAAS
data.
187
CHAPTER 13
RADAR NAVIGATION
PRINCIPLES OF RADAR OPERATION
1300. Introduction
Radardeterminesdistancetoanobjectbymeasuring
thetimerequiredforaradiosignaltotravelfroma
transmittertotheobjectandreturn.Suchmeasurementscan
beconvertedintolinesofposition(LOP’s)comprisedof
circleswithradiusequaltothedistancetotheobject.Since
marineradarsusedirectionalantennae,theycanalso
determineanobject’sbearing.However,duetoitsdesign,
aradar’sbearingmeasurementislessaccuratethanits
distancemeasurement.Understandingthisconceptis
crucialtoensuringtheoptimalemploymentoftheradarfor
safe navigation.
1301. Signal Characteristics
Inmostmarinenavigationapplications,theradar
signalispulsemodulated.Signalsaregeneratedbyatiming
circuitsothatenergyleavestheantennainveryshort
pulses.Whentransmitting,theantennaisconnectedtothe
transmitterbutnotthereceiver.Assoonasthepulseleaves,
anelectronicswitchdisconnectstheantennafromthe
transmitterandconnectsittothereceiver.Anotherpulseis
nottransmitteduntilaftertheprecedingonehashadtimeto
traveltothemostdistanttargetwithinrangeandreturn.
Sincetheintervalbetweenpulsesislongcomparedwiththe
lengthofapulse,strongsignalscanbeprovidedwithlow
averagepower.Thedurationorlengthofasinglepulseis
calledpulselength,pulseduration,orpulsewidth.This
pulseemissionsequencerepeatsagreatmanytimes,
perhaps1,000persecond.Thisratedefinesthepulse
repetitionrate(PRR).Thereturnedpulsesaredisplayed
on an indicator screen.
1302. The Display
Theradardisplayisoftenreferredtoastheplan
positionindicator(PPI).OnaPPI,thesweepappearsasa
radialline,centeredatthecenterofthescopeandrotating
insynchronizationwiththeantenna.Anyreturnedecho
causesabrighteningofthedisplayscreenatthebearingand
rangeoftheobject.Becauseofaluminescentcoatingonthe
insideofthetube,theglowcontinuesafterthetracerotates
past the target.
OnaPPI,atarget’sactualrangeisproportionaltoits
distancefromthecenterofthescope.Amoveablecursor
helpstomeasurerangesandbearings.Inthe“heading-
upward”presentation,whichindicatesrelativebearings,
thetopofthescoperepresentsthedirectionoftheship’s
head.Inthisunstabilizedpresentation,theorientation
changesastheshipchangesheading.Inthestabilized
“north-upward”presentation,gyronorthisalwaysatthe
top of the scope.
1303. The Radar Beam
Thepulsesofenergycomprisingtheradarbeamwould
formasinglelobe-shapedpatternofradiationifemittedin
freespace.Figure1303ashowsthisfreespaceradiation
pattern,includingtheundesirableminorlobesorsidelobes
associated with practical antenna design.
Althoughtheradiatedenergyisconcentratedintoa
relativelynarrowmainbeambytheantenna,thereisno
clearlydefinedenvelopeoftheenergyradiated,although
mostoftheenergyisconcentratedalongtheaxisofthe
beam.Withtherapiddecreaseintheamountofradiated
energyindirectionsawayfromthisaxis,practicalpower
limitsmaybeusedtodefinethedimensionsoftheradar
beam.
Aradarbeam’shorizontalandverticalbeamwidthsare
referencedtoarbitrarilyselectedpowerlimits.Themost
commonconventiondefinesbeamwidthastheangular
widthbetweenhalfpowerpoints.Thehalfpowerpoint
correspondstoadropin3decibelsfromthemaximum
beam strength.
Thedefinitionofthedecibelshowsthishalvingof
poweratadecreasein3dBfrommaximumpower.A
decibelissimplythelogarithmoftheratioofafinalpower
level to a reference power level:
whereP
1
isthefinalpowerlevel,andP
0
isareference
powerlevel.WhencalculatingthedBdropfora50%
reduction in power level, the equation becomes:
TheradiationdiagramshowninFigure1303bdepicts
relativevaluesofpowerinthesameplaneexistingatthe
samedistancesfromtheantennaortheoriginoftheradar
dB10
P
1
P
0
------
log=
dB10.5()
dB– 3 dB=
log=
188RADAR NAVIGATION
beam.Maximumpowerisinthedirectionoftheaxisof
thebeam.Powervaluesdiminishrapidlyindirections
awayfromtheaxis.Thebeamwidthistakenastheangle
between the half-power points.
Thebeamwidthdependsuponthefrequencyor
wavelengthofthetransmittedenergy,antennadesign,and
thedimensionsoftheantenna.Foragivenantennasize
(antennaaperture),narrowerbeamwidthsresultfromusing
shorterwavelengths.Foragivenwavelength,narrower
beam widths result from using larger antennas.
Withradarwavesbeingpropagatedinthevicinityof
thesurfaceofthesea,themainlobeoftheradarbeamis
composedofanumberofseparatelobes,asopposedtothe
singlelobe-shapedpatternofradiationasemittedinfree
space.Thisphenomenonistheresultofinterferencebe-
tweenradarwavesdirectlytransmitted,andthosewaves
whicharereflectedfromthesurfaceofthesea.Radar
wavesstrikethesurfaceofthesea,andtheindirectwaves
reflectoffthesurfaceofthesea.SeeFigure1303c.These
reflectedwaveseitherconstructivelyordestructivelyinter-
ferewiththedirectwavesdependinguponthewaves’phase
relationship.
1304. Diffraction and Attenuation
Diffractionisthebendingofawaveasitpassesan
obstruction.Becauseofdiffractionthereissomeillumi-
nationoftheregionbehindanobstructionortargetbythe
radarbeam.Diffractioneffectsaregreateratthelower
frequencies.Thus,theradarbeamofalowerfrequency
radartendstoilluminatemoreoftheshadowregionbehind
anobstructionthanthebeamofaradarofhigherfrequency
or shorter wavelength.
Attenuationisthescatteringandabsorptionofthe
energyintheradarbeamasitpassesthroughthe
atmosphere.Itcausesadecreaseinechostrength.
Attenuationisgreateratthehigherfrequenciesorshorter
wavelengths.
Whilereflectedechoesaremuchweakerthanthe
transmittedpulses,thecharacteristicsoftheirreturntothe
sourcearesimilartothecharacteristicsofpropagation.The
strengthsoftheseechoesaredependentupontheamountof
transmittedenergystrikingthetargetsandthesizeand
reflecting properties of the targets.
1305. Refraction
Iftheradarwavestraveledinstraightlines,the
distancetotheradarhorizonwouldbedependentonlyon
thepoweroutputofthetransmitterandtheheightofthe
antenna.Inotherwords,thedistancetotheradarhorizon
wouldbethesameasthatofthegeometricalhorizonforthe
antennaheight.However,atmosphericdensitygradients
bendradarraysastheytraveltoandfromatarget.This
bending is calledrefraction.
Thedistancetotheradarhorizondoesnotlimitthedis-
tancefromwhichechoesmaybereceivedfromtargets.As-
sumingthatadequatepoweristransmitted,echoesmaybe
receivedfromtargetsbeyondtheradarhorizoniftheirre-
flectingsurfacesextendaboveit.Thedistancetotheradar
horizonisthedistanceatwhichtheradarrayspasstangent
to the surface of the Earth.
Thefollowingformula,wherehistheheightofthean-
tennainfeet,givesthetheoreticaldistancetotheradar
horizon in nautical miles:
1306. Factors Affecting Radar Interpretation
Radar’svalueasanavigationalaiddependsonthe
navigator’sunderstandingitscharacteristicsand
limitations.Whethermeasuringtherangetoasingle
reflectiveobjectortryingtodiscernashorelinelostamid
severeclutter,knowledgeofthecharacteristicsofthe
individualradarusedarecrucial.Someofthefactorstobe
considered in interpretation are discussed below:
•ResolutioninRange.InpartAofFigure1306a,a
transmittedpulsehasarrivedatthesecondoftwo
targetsofinsufficientsizeordensitytoabsorbor
reflectalloftheenergyofthepulse.Whilethepulse
hastraveledfromthefirsttothesecondtarget,theecho
fromthefirsthastraveledanequaldistanceinthe
Figure 1303a. Freespace radiation pattern.
Figure 1303b. Radiation diagram.
Figure 1303c. Direct and indirect waves.
d1.22h
.
=
RADAR NAVIGATION189
oppositedirection.AtB,thetransmittedpulsehas
continuedonbeyondthesecondtarget,andthetwo
echoesarereturningtowardthetransmitter.The
distancebetweenleadingedgesofthetwoechoesis
twicethedistancebetweentargets.Thecorrect
distancewillbeshownonthescope,whichis
calibratedtoshowhalfthedistancetraveledoutand
back.AtCthetargetsareclosertogetherandthepulse
lengthhasbeenincreased.Thetwoechoesmerge,and
onthescopetheywillappearasasingle,largetarget.
AtDthepulselengthhasbeendecreased,andthetwo
echoesappearseparated.Theabilityofaradarto
separatetargetsclosetogetheronthesamebearingis
calledresolutioninrange.Itisrelatedprimarilyto
pulselength.Theminimumdistancebetweentargets
thatcanbedistinguishedasseparateishalfthepulse
length.This(halfthepulselength)istheapparent
depthorthicknessofatargetpresentingaflatperpen-
dicularsurfacetotheradarbeam.Thus,severalships
closetogethermayappearasanisland.Echoesfroma
numberofsmallboats,piles,breakers,orevenlarge
shipsclosetotheshoremayblendwithechoesfrom
theshore,resultinginanincorrectindicationofthe
position and shape of the shoreline.
•ResolutioninBearing.Echoesfromtwoormore
targetsclosetogetheratthesamerangemaymergeto
formasingle,widerecho.Theabilitytoseparatetargets
closetogetheratthesamerangeiscalledresolutionin
bearing.Bearingresolutionisafunctionoftwo
variables:beamwidthandrangetothetargets.A
narrowerbeamandashorterdistancetotheobjects
both increase bearing resolution.
•HeightofAntennaandTarget.Iftheradarhorizonis
betweenthetransmittingvesselandthetarget,the
lowerpartofthetargetwillnotbevisible.Alarge
vesselmayappearasasmallcraft,orashorelinemay
appear at some distance inland.
•ReflectingQualityandAspectofTarget.Echoes
fromseveraltargetsofthesamesizemaybequite
differentinappearance.Ametalsurfacereflectsradio
wavesmorestronglythanawoodensurface.Asurface
perpendiculartothebeamreturnsastrongerechothan
anonperpendicularone.Avesselseenbroadside
returnsastrongerechothanoneheadingdirectly
towardoraway.Somesurfacesabsorbmostradar
energy rather that reflecting it.
•Frequency.Asfrequencyincreases,reflectionsoccur
from smaller targets.
Atmosphericnoise,seareturn,andprecipitationcom-
plicateradarinterpretationbyproducingclutter.Clutteris
usuallystrongestnearthevessel.Strongechoescansome-
timesbedetectedbyreducingreceivergaintoeliminate
weakersignals.Bywatchingtherepeaterduringseveralro-
tationsoftheantenna,theoperatorcanoftendiscriminate
betweenclutterandatargetevenwhenthesignalstrengths
fromclutterandthetargetareequal.Ateachrotation,the
signalsfromtargetswillremainrelativelystationaryonthe
displaywhilethosecausedbyclutterwillappearatdiffer-
ent locations on each sweep.
Anothermajorproblemliesindeterminingwhich
featuresinthevicinityoftheshorelineareactually
representedbyechoesshownontherepeater.Particularlyin
caseswherealowlyingshoreisbeingscanned,theremaybe
considerable uncertainty.
Arelatedproblemisthatcertainfeaturesontheshore
willnotreturnechoesbecausetheyareblockedfromthe
radarbeambyotherphysicalfeaturesorobstructions.This
factorinturncausesthechart-likeimagepaintedonthe
scope to differ from the chart of the area.
Ifthenavigatoristobeabletointerpretthepresentation
onhisradarscope,hemustunderstandthecharacteristicsof
radarpropagation,thecapabilitiesofhisradarset,the
reflectingpropertiesofdifferenttypesofradartargets,and
theabilitytoanalyzehischarttodeterminewhichcharted
featuresaremostlikelytoreflectthetransmittedpulsesorto
beblocked.Experiencegainedduringclearweather
comparison between radar and visual images is invaluable.
Landmassesaregenerallyrecognizablebecauseofthe
steadybrillianceoftherelativelylargeareaspaintedonthe
PPI.Also,landshouldbeatpositionsexpectedfromtheship’s
navigationalposition.Althoughlandmassesarereadily
recognizable,theprimaryproblemistheidentificationof
specificlandfeatures.Identificationofspecificfeaturescanbe
quitedifficultbecauseofvariousfactors,includingdistortion
resultingfrombeamwidthandpulselength,anduncertaintyas
to just which charted features are reflecting the echoes.
Sandspitsandsmooth,clearbeachesnormallydonot
appearonthePPIatrangesbeyond1or2milesbecausethese
targetshavealmostnoareathatcanreflectenergybacktothe
radar.Rangesdeterminedfromthesetargetsarenotreliable.
Ifwavesarebreakingoverasandbar,echoesmaybereturned
fromthesurf.Wavesmay,however,breakwelloutfromthe
actualshoreline,sothatrangingonthesurfmaybe
misleading.
Mudflatsandmarshesnormallyreflectradarpulses
onlyalittlebetterthanasandspit.Theweakechoesreceived
atlowtidedisappearathightide.Mangrovesandotherthick
growthmayproduceastrongecho.Areasthatareindicated
asswampsonachart,therefore,mayreturneitherstrongor
weakechoes,dependingonthedensitytype,andsizeofthe
vegetation growing in the area.
Whensanddunesarecoveredwithvegetationandare
wellbackfromalow,smoothbeach,theapparentshoreline
determinedbyradarappearsasthelineofthedunesrather
thanthetrueshoreline.Undersomeconditions,sanddunes
mayreturnstrongechosignalsbecausethecombinationof
theverticalsurfaceofthevegetationandthehorizontal
190RADAR NAVIGATION
beach may form a sort of corner reflector.
Lagoonsandinlandlakesusuallyappearasblankareas
onaPPIbecausethesmoothwatersurfacereturnsno
energytotheradarantenna.Insomeinstances,thesandbar
orreefsurroundingthelagoonmaynotappearonthePPI
because it lies too low in the water.
Coralatollsandlongchainsofislandsmayproduce
longlinesofechoeswhentheradarbeamisdirected
perpendiculartothelineoftheislands.Thisindicationis
especiallytruewhentheislandsarecloselyspaced.The
reasonisthatthespreadingresultingfromthewidthofthe
radarbeamcausestheechoestoblendintocontinuous
lines.Whenthechainofislandsisviewedlengthwise,or
obliquely,however,eachislandmayproduceaseparate
return.Surfbreakingonareefaroundanatollproducesa
ragged, variable line of echoes.
Oneortworocksprojectingabovethesurfaceofthe
water,orwavesbreakingoverareef,mayappearonthe
PPI.
Ifthelandrisesinagradual,regularmannerfromthe
shoreline,nopartoftheterrainproducesanechothatis
strongerthantheechofromanyotherpart.Asaresult,a
generalhazeofechoesappearsonthePPI,anditisdifficult
to ascertain the range to any particular part of the land.
Blotchysignalsarereturnedfromhillyground,because
thecrestofeachhillreturnsagoodechoalthoughthevalley
beyondisinashadow.Ifhighreceivergainisused,thepat-
tern may become solid except for the very deep shadows.
Lowislandsordinarilyproducesmallechoes.When
thickpalmtreesorotherfoliagegrowontheisland,strong
echoesoftenareproducedbecausethehorizontalsurfaceof
thewateraroundtheislandformsasortofcornerreflector
withtheverticalsurfacesofthetrees.Asaresult,wooded
islandsgivegoodechoesandcanbedetectedatamuch
Figure 1306a. Resolution in range.
RADAR NAVIGATION191
greater range than barren islands.
Sizablelandmassesmaybemissingfromtheradardis-
playbecauseofcertainfeaturesbeingblockedfromtheradar
beambyotherfeatures.Ashorelinewhichiscontinuouson
thePPIdisplaywhentheshipisatoneposition,maynotbe
continuouswhentheshipisatanotherpositionandscanning
thesameshoreline.Theradarbeammaybeblockedfroma
segmentofthisshorelinebyanobstructionsuchasaprom-
ontory.Anindentationintheshoreline,suchasacoveorbay,
appearingonthePPIwhentheshipisatoneposition,may
notappearwhentheshipisatanotherpositionnearby.Thus,
radarshadowalonecancauseconsiderabledifferencesbe-
tweenthePPIdisplayandthechartpresentation.Thiseffect
inconjunctionwithbeamwidthandpulselengthdistortion
of the PPI display can cause even greater differences.
Thereturnsofobjectsclosetoshoremaymergewith
theshorelineimageonthePPI,becauseofdistortioneffects
ofhorizontalbeamwidthandpulselength.Targetimages
onthePPIaredistortedangularlybyanamountequaltothe
effectivehorizontalbeamwidth.Also,thetargetimagesal-
waysaredistortedradiallybyanamountatleastequalto
one-halfthepulselength(164yardspermicrosecondof
pulse length).
Figure1306billustratestheeffectsofship’sposition,
beamwidth,andpulselengthontheradarshoreline.Be-
causeofbeamwidthdistortion,astraight,ornearly
straight,shorelineoftenappearscrescent-shapedonthe
PPI.Thiseffectisgreaterwiththewiderbeamwidths.Note
thatthisdistortionincreasesastheanglebetweenthebeam
axis and the shoreline decreases.
Figure1306cillustratesthedistortioneffectsofradar
shadow,beamwidth,andpulselength.ViewAshowsthe
actualshapeoftheshorelineandthelandbehindit.Notethe
steeltoweronthelowsandbeachandthetwoshipsatan-
chorclosetoshore.TheheavylineinviewBrepresentsthe
shorelineonthePPI.Thedottedlinesrepresenttheactual
position and shape of all targets. Note in particular:
1.The low sand beach is not detected by the radar.
2.Thetoweronthelowbeachisdetected,butitlookslikea
shipinacove.Atcloserrangethelandwouldbedetected
andthecove-shapedareawouldbegintofillin;thenthe
towercouldnotbeseenwithoutreducingthereceivergain.
3.Theradarshadowbehindbothmountains.Distortion
owingtoradarshadowsisresponsibleformore
confusionthananyothercause.Thesmallislanddoes
not appear because it is in the radar shadow.
4.Thespreadingofthelandinbearingcausedbybeam
widthdistortion.Lookattheuppershoreofthe
peninsula.Theshorelinedistortionisgreatertothewest
becausetheanglebetweentheradarbeamandtheshore
issmallerasthebeamseeksoutthemorewesterlyshore.
5.ShipNo.1appearsasasmallpeninsula.Itsreturnhas
mergedwiththelandbecauseofthebeamwidth
Figure 1306b. Effects of ship’s position, beam width, and pulse length on radar shoreline.
192RADAR NAVIGATION
distortion.
6.ShipNo.2alsomergeswiththeshorelineandformsa
bump.Thisbumpiscausedbypulselengthandbeam
widthdistortion.Reducingreceivergainmightcause
theshiptoseparatefromland,providedtheshipisnot
tooclosetotheshore.TheFastTimeConstant(FTC)
controlcouldalsobeusedtoattempttoseparatetheship
from land.
1307. Recognition of Unwanted Echoes
Indirectorfalseechoesarecausedbyreflectionofthe
mainlobeoftheradarbeamoffship’sstructuressuchas
stacksandkingposts.Whensuchreflectiondoesoccur,the
echowillreturnfromalegitimateradarcontacttothe
antennabythesameindirectpath.Consequently,theecho
willappearonthePPIatthebearingofthereflecting
surface.AsshowninFigure1307a,theindirectechowill
appearonthePPIatthesamerangeasthedirectecho
received,assumingthattheadditionaldistancebythe
indirect path is negligible.
Characteristicsbywhichindirectechoesmayberecog-
nized are summarized as follows:
1.Indirect echoes will often occur in shadow sectors.
2.Theyarereceivedonsubstantiallyconstant
bearings,althoughthetruebearingoftheradar
contact may change appreciably.
3.Theyappearatthesamerangesasthe
corresponding direct echoes.
4.Whenplotted,theirmovementsareusually
abnormal.
5.Theirshapesmayindicatethattheyarenotdirect
echoes.
Side-lobeeffectsarereadilyrecognizedinthatthey
produceaseriesofechoes(Figure1307b)oneachsideof
themainlobeechoatthesamerangeasthelatter.Semicir-
cles,orevencompletecircles,maybeproduced.Becauseof
thelowenergyoftheside-lobes,theseeffectswillnormally
occuronlyattheshorterranges.Theeffectsmaybemini-
mizedoreliminated,throughuseofthegainandanti-clutter
controls.Slottedwaveguideantennashavelargelyelimi-
nated the side-lobe problem.
Multipleechoesmayoccurwhenastrongechois
receivedfromanothershipatcloserange.Asecondorthird
ormoreechoesmaybeobservedontheradarscopeat
double,triple,orothermultiplesoftheactualrangeofthe
radar contact (Figure 1307c).
Second-traceechoes(multiple-traceechoes)are
echoesreceivedfromacontactatanactualrangegreater
thantheradarrangesetting.Ifanechofromadistanttarget
isreceivedafterthefollowingpulsehasbeentransmitted,
theechowillappearontheradarscopeatthecorrectbearing
butnotatthetruerange.Second-traceechoesareunusual,
exceptunderabnormalatmosphericconditions,or
conditionsunderwhichsuper-refractionispresent.Second-
traceechoesmayberecognizedthroughchangesintheir
positionsontheradarscopeinchangingthepulserepetition
rate(PRR);theirhazy,streaky,ordistortedshape;andthe
erratic movements on plotting.
AsillustratedinFigure1307d,atargetreturnisdetect-
edonatruebearingof090°atadistanceof7.5miles.On
changingthePRRfrom2,000to1,800pulsespersecond,
thesametargetisdetectedonabearingof090°atadistance
of3miles(Figure1307e).Thechangeinthepositionofthe
returnindicatesthatthereturnisasecond-traceecho.The
actualdistanceofthetargetisthedistanceasindicatedon
thePPIplushalfthedistancetheradarwavetravelsbe-
tween pulses.
Electronicinterferenceeffects,suchasmayoccur
Figure 1306c. Distortion effects of radar shadow, beam width, and pulse length.
RADAR NAVIGATION193
whennearanotherradaroperatinginthesamefrequency
bandasthatoftheobserver’sship,isusuallyseenonthe
PPIasalargenumberofbrightdotseitherscatteredatran-
domorintheformofdottedlinesextendingfromthecenter
to the edge of the PPI.
Interferenceeffectsaregreateratthelongerradar
rangescalesettings.Theinterferenceeffectscanbedistin-
guishedeasilyfromnormalechoesbecausetheydonot
appearinthesameplacesonsuccessiverotationsofthe
antenna.
Stacks,masts,samsonposts,andotherstructures,may
causeareductionintheintensityoftheradarbeambeyondthese
obstructions,especiallyiftheyareclosetotheradarantenna.If
theangleattheantennasubtendedbytheobstructionismore
thanafewdegrees,thereductionoftheintensityoftheradar
beambeyondtheobstructionmayproduceablindsector.Less
reductionintheintensityofthebeambeyondtheobstructions
mayproduceshadowsectors.Withinashadowsector,small
targetsatcloserangemaynotbedetected,whilelargertargetsat
much greater ranges will appear.
SpokingappearsonthePPIasanumberofspokesorradial
lines.Spokingiseasilydistinguishedfrominterferenceeffects
becausethelinesarestraightonallrange-scalesettings,andare
lines rather than a series of dots.
ThespokesmayappearallaroundthePPI,ortheymay
beconfinedtoasector.Ifspokingisconfinedtoanarrow
sector,theeffectcanbedistinguishedfromaRamarksignal
ofsimilarappearancethroughobservationofthesteadyrel-
ativebearingofthespokeinasituationwherethebearing
oftheRamarksignalshouldchange.Spokingindicatesa
needformaintenanceoradjustment.ThePPIdisplaymay
appearasnormalsectorsalternatingwithdarksectors.This
isusuallyduetotheautomaticfrequencycontrolbeingout
ofadjustment.Theappearanceofserratedrangeringsindi-
cates a need for maintenance.
Aftertheradarsethasbeenturnedon,thedisplaymay
notspreadimmediatelytothewholeofthePPIbecauseof
staticelectricityinsidetheCRT.Usually,thestaticelectric-
ityeffect,whichproducesadistortedPPIdisplay,lastsno
longer than a few minutes.
Hour-glasseffectappearsaseitheraconstrictionorex-
pansionofthedisplaynearthecenterofthePPI.The
expansioneffectissimilarinappearancetotheexpanded
centerdisplay.Thiseffect,whichcanbecausedbyanon-
lineartimebaseorthesweepnotstartingontheindicatorat
thesameinstantasthetransmissionofthepulse,ismostap-
parent when in narrow rivers or close to shore.
Theechofromanoverheadpowercablecanbewrongly
identifiedastheechofromashiponasteadybearingandde-
creasingrange.Coursechangestoavoidthecontactare
ineffective;thecontactremainsonasteadybearing,decreas-
ingrange.Thisphenomenonisparticularlyapparentforthe
power cable spanning the Straits of Messina.
Figure 1307a. Indirect echo.
194RADAR NAVIGATION
1308. Aids to Radar Navigation
Radarnavigationaidshelpidentifyradartargetsand
increaseechosignalstrengthfromotherwisepoorradar
targets.
Buoysareparticularlypoorradartargets.Weak,
fluctuatingechoesreceivedfromthesetargetsareeasilylost
intheseaclutter.Toaidinthedetectionofthesetargets,
radarreflectors,designatedcornerreflectors,maybeused.
Thesereflectorsmaybemountedonthetopsofbuoysor
designed into the structure.
Eachcornerreflector,showninFigure1308a,consists
ofthreemutuallyperpendicularflatmetalsurfaces.Aradar
wavestrikinganyofthemetalsurfacesorplateswillbe
reflectedbackinthedirectionofitssource.Maximum
energywillbereflectedbacktotheantennaiftheaxisofthe
radarbeammakesequalangleswithallthemetalsurfaces.
Frequently,cornerreflectorsareassembledinclustersto
maximize the reflected signal.
Althoughradarreflectorsareusedtoobtainstronger
echoesfromradartargets,othermeansarerequiredformore
positiveidentificationofradartargets.Radarbeaconsare
transmittersoperatinginthemarineradarfrequencyband,
whichproducedistinctiveindicationsontheradarscopesof
shipswithinrangeofthesebeacons.Therearetwogeneral
classesofthesebeacons:racons,whichprovideboth
bearingandrangeinformationtothetarget,andramarks
whichprovidebearinginformationonly.However,ifthe
ramarkinstallationisdetectedasanechoontheradarscope,
the range will be available also.
Araconisaradartransponderwhichemitsacharac-
teristicsignalwhentriggeredbyaship’sradar.Thesignal
maybeemittedonthesamefrequencyasthatofthe
triggeringradar,inwhichcaseitissuperimposedonthe
ship’sradardisplayautomatically.Thesignalmaybe
emittedonaseparatefrequency,inwhichcasetoreceive
thesignaltheship’sradarreceivermustbetunedtothe
beaconfrequency,oraspecialreceivermustbeused.In
eithercase,thePPIwillbeblankexceptforthebeacon
signal.However,theonlyraconsinserviceare“inband”
Figure 1307b. Side-lobe effects.Figure 1307c. Multiple echoes.
Figure 1307d. Second-trace echo on 12-mile range scale.Figure 1307e. Position of second-trace echo on 12-mile
range scale after changing PRR.
RADAR NAVIGATION195
beaconswhichtransmitinoneofthemarineradarbands,
usually only the 3-centimeter band.
TheraconsignalappearsonthePPIasaradialline
originatingatapointjustbeyondthepositionoftheradar
beacon,orasaMorsecodesignal(Figure1308b)displayed
radially from just beyond the beacon.
Aramarkisaradarbeaconwhichtransmitseithercon-
tinuouslyoratintervals.Thelattermethodoftransmission
isusedsothatthePPIcanbeinspectedwithoutanyclutter
introducedbytheramarksignalonthescope.Theramark
signalasitappearsonthePPIisaradiallinefromthecen-
ter.Theradiallinemaybeacontinuousnarrowline,a
brokenline(Figure1308c),aseriesofdots,oraseriesof
dots and dashes.
Figure 1308a. Corner reflectors.
Figure 1308b. Coded racon signal.Figure 1308c. Ramark appears as broken radial line.
196RADAR NAVIGATION
RADAR PILOTING
1309. Introduction
Whennavigatinginrestrictedwaters,amarinermost
oftenreliesonvisualpilotingtoprovidetheaccuracy
requiredtoensureshipsafety.Visualpiloting,however,
requiresclearweather;often,marinersmustnavigate
throughfog.Whenweatherconditionsrendervisual
pilotingimpossibleonavesselnotequippedwithECDIS,
radarnavigationprovidesamethodoffixingavessel’s
positionwithsufficientaccuracytoallowsafepassage.See
Chapter8foradetaileddiscussionofintegratingradarinto
a piloting procedure.
1310. Fix by Radar Ranges
Sinceradarcanmoreaccuratelydeterminerangesthan
bearings,themostaccurateradarfixesresultfrom
measuringandplottingrangestotwoormoreobjects.
Measureobjectsdirectlyaheadorasternfirst;measure
objects closest to the beam last.
Thisprocedureistheoppositetothatrecommendedfor
takingvisualbearings,whereobjectsclosesttothebeam
aremeasuredfirst;however,bothrecommendationsreston
thesameprinciple.Whenmeasuringobjectstodeterminea
lineofposition,measurefirstthosewhichhavethegreatest
rateofchangeinthequantitybeingmeasured;measurelast
thosewhichhavetheleastrateofchange.Thisminimizes
measurementtimedelayerrors.Sincetherangeofthoseob-
jectsdirectlyaheadorasternoftheshipchangesmore
rapidlythanthoseobjectslocatedabeam,wemeasurerang-
es to objects ahead or astern first.
Recordtherangestothenavigationaidsusedandlay
theresultingrangearcsdownonthechart.Theoretically,
theselinesofpositionshouldintersectatapointcoincident
with the ship’s position at the time of the fix.
Thoughverifyingsoundingsisalwaysagoodpractice
inallnavigationscenarios,itsimportanceincreaseswhen
pilotingusingonlyradar.Assumingproperoperationofthe
fathometer,soundingsgivethenavigatorinvaluableinfor-
mation on the reliability of his fixes.
1311. Fix by Range and Bearing to One Object
Visualpilotingrequiresbearingsfromatleasttwo
objects;radar,withitsabilitytodeterminebothbearingand
rangefromoneobject,allowsthenavigatortoobtainafix
whereonlyasinglenavigationaidisavailable.Anexample
ofusingradarinthisfashionoccursinapproachingaharbor
whoseentranceismarkedwithasingle,prominentobject
suchasChesapeakeLightattheentranceoftheChesapeake
Bay.Wellbeyondtherangeofanyland-basedvisual
navigationaid,andbeyondthevisualrangeofthelight
itself,ashipboardradarcandetectthelightandprovide
bearingsandrangesfortheship’spilotingparty.Caremust
betakenthatfixesarenottakenonanynearbystationary
vessel.
Thismethodologyislimitedbytheinherentinaccuracy
associatedwithradarbearings;typically,aradarbearingis
accuratetowithinabout5°ofthetruebearing.Therefore,
thenavigatormustcarefullyevaluatetheresultingposition,
possiblycheckingitwithasounding.Ifavisualbearingis
availablefromtheobject,usethatbearinginsteadofthe
radarbearingwhenlayingdownthefix.Thisillustratesthe
basicconceptdiscussedabove:radarrangesareinherently
moreaccuratethanradarbearings.Onemustalsobeaware
thatiftheradarisgyrostabilizedandthereisagyroerror
ofmorethanadegreeorso,radarbearingswillbeinerror
by that amount.
Priortousingthismethod,thenavigatormustensure
thathehascorrectlyidentifiedtheobjectfromwhichthe
bearingandrangearetobetaken.Usingonlyone
navigationaidforbothlinesofpositioncanleadtodisaster
if the navigation aid is not properly identified.
1312. Fix Using Tangent Bearings and Range
Thismethodcombinesbearingstangenttoanobject
witharangemeasurementfromsomepointonthatobject.
Theobjectmustbelargeenoughtoprovidesufficient
bearingspreadbetweenthetangentbearings;oftenan
islandorpeninsulaworkswell.Identifysomeprominent
featureoftheobjectthatisdisplayedonboththechartand
theradardisplay.Takearangemeasurementfromthat
featureandplotitonthechart.Thendeterminethetangent
bearings to the feature and plot them on the chart.
Steep-sidedfeaturesworkthebest.Tangentstolow,
slopingshorelineswillseriouslyreduceaccuracy,aswill
tangentbearingsinareasofexcessivelyhightides,which
canchangethelocationoftheapparentshorelinebymany
meters.
1313. Fix by Radar Bearings
Theinherentinaccuracyofradarbearingsdiscussed
abovemakesthismethodlessaccuratethanfixingpositionby
radarrange.Usethismethodtoplotapositionquicklyonthe
chartwhenapproachingrestrictedwaterstoobtainan
approximateship’spositionforevaluatingradartargetstouse
forrangemeasurements.Unlessnomoreaccuratemethodis
available,thismethodisnotsuitablewhilepilotingin
restricted waters.
1314. Fischer Plotting
InFischerplotting,thenavigatoradjuststhescaleof
RADAR NAVIGATION197
theradartomatchthescaleofthechartinuse.Thenhe
placesaclearplasticdisk,sizedtotheradar,onthecenter
oftheradarscreenandquicklytracestheshapeoflandand
locationofanynavigationaidsontotheplasticoverlaywith
agreasepencil.Takingtheplasticwiththetracingsonitto
thechart,hematchesthefeaturestracedfromtheradarwith
thechart’sfeatures.Aholeinthecenteroftheplastic
allowsthenavigatortomarkthepositionoftheshipatthe
time the tracing was done.
RASTER RADARS
1315. Basic Description
ConventionalPPI-displayradarsuseacircular
CathodeRayTube(CRT)todirectanelectronbeamata
screencoatedontheinsidewithphosphorus,whichglows
whenilluminatedbythebeam.Internalcircuitryformsthe
beamsuchthata“sweep”isindicatedonthefaceofthe
PPI.Thissweepistimedtocoincidewiththesweepofthe
radar’santenna.Areturnechoisaddedtothesweepsignal
sothatthescreenismorebrightlyilluminatedatapoint
correspondingtothebearingandrangeofthetargetthat
returned the echo.
Therasterradaralsoemploysacathoderaytube;
however,theendofthetubeuponwhichthepictureis
formedisrectangular,notcircularasinthePPIdisplay.The
rasterradardoesnotproduceitspicturefromacircular
sweep;itutilizesalinerscaninwhichthepictureis
“drawn,”linebyline,horizontallyacrossthescreen.Asthe
sweepmovesacrossthescreen,theelectronbeamfromthe
CRTilluminatesthepictureelements,orpixels,onthe
screen.Apixelisthesmallestareaofadisplaythatcanbe
excited individually.
Inordertoproduceasufficientlyhighresolution,
largerrasterradarsrequireover1millionpixelsperscreen
combinedwithanupdaterateof60ormorescansper
second.Processingsuchalargenumberofpixelelements
requiresarathersophisticatedcomputer.Onewaytolower
costistoslowdowntherequiredprocessingspeed.This
speedcanbeloweredtoapproximately30framesper
secondbeforethepicturedevelopsanoticeableflicker,but
thebestradarshavescanratesofatleast60scansper
second.
Furthercostreductioncanbegainedbyusingan
interlaceddisplay.Aninterlaceddisplaydoesnotdrawthe
entirepictureinonepass.Onthefirstpass,itdrawsevery
otherline;itdrawstheremaininglinesonthesecondpass.
Thistypeofdisplayreducesthenumberofscreensthat
havetobedrawnperunitoftimebyafactoroftwo;
however,ifthetwopicturesaremisaligned,thepicturewill
appear to jitter.
199
CHAPTER 14
ELECTRONIC CHARTS
INTRODUCTION
1400. The Importance of Electronic Charts
Sincethebeginningofmaritimenavigation,thedesire
ofthenavigatorhasalwaysbeentoanswerafundamental
question:“Where,exactly,ismyvessel?”Toanswerthat
question,thenavigatorwasforcedtocontinuallytakefixes
oncelestialbodies,onfixedobjectsashore,orusingradio
signals,andplottheresultinglinesofpositionasafixona
paperchart.Onlythencouldhebegintoassessthesafetyof
theshipanditsprogresstowarditsdestination.Hespentfar
moretimetakingfixes,workingoutsolutions,andplotting
theresultsthanonmakingassessments,andthefixonly
toldhimwheretheshipwasatthetimethatfixwastaken,
notwherethevesselwassometimelaterwhentheassess-
mentwasmade.Hewasalways“behindthevessel.”Onthe
highseasthisisoflittleimport.Nearshore,itbecomes
vitally important.
Electronicchartsautomatetheprocessofintegrating
real-timepositionswiththechartdisplayandallowthe
navigatortocontinuouslyassessthepositionandsafetyof
thevessel.Further,theGPS/DGPSfixesarefarmoreaccu-
rateandtakenfarmoreoftenthananynavigatorevercould.
Agoodpilotingteamisexpectedtotakeandplotafixevery
threeminutes.Anelectronicchartsystemcandoitonceper
secondtoastandardofaccuracyatleastanorderofmagni-
tude better.
Electronicchartsalsoallowtheintegrationofother
operationaldata,suchasship’scourseandspeed,depth
soundings,andradardataintothedisplay.Further,they
allowautomationofalarmsystemstoalertthenavigatorto
potentiallydangeroussituationswellinadvanceofa
disaster.
Finally,thenavigatorhasacompletepictureofthe
instantaneoussituationofthevesselandallcharteddangers
inthearea.Witharadaroverlay,thetacticalsituationwith
respecttoothervesselsisclearaswell.Thischapterwill
discussthevarioustypesofelectroniccharts,therequire-
mentsforusingthem,theircharacteristics,capabilitiesand
limitations.
1401. Terminology
Beforeunderstandingwhatanelectronicchartisand
whatitdoes,onemustlearnanumberoftermsanddefini-
tions.Wemustfirstmakeadistinctionbetweenofficialand
unofficialcharts.Officialchartsarethose,andonlythose,
producedbyagovernmenthydrographicoffice(HO).
Unofficialchartsareproducedbyavarietyofprivate
companiesandmayormaynotmeetthesamestandards
usedbyHO’sfordataaccuracy,currency,and
completeness.
Anelectronicchartsystem(ECS)isacommercial
electronicchartsystemnotdesignedtosatisfytheregula-
toryrequirementsoftheIMOSafetyofLifeatSea
(SOLAS)convention.ECSisanaidtonavigationandwhen
usedonSOLASregulatedvesselsistobeusedinconjunc-
tions with corrected paper charts.
Anelectronicchartdisplayandinformationsystem
(ECDIS)isanelectronicchartsystemwhichsatisfiesthe
IMOSOLASconventioncarriagerequirementsforcorrect-
edpaperchartswhenusedwithanENCoritsfunctional
equivalent (e.g. NIMA Digital Nautical Chart.)
Anelectronicchart(EC)isanydigitizedchartintend-
ed for display on a computerized navigation system.
Anelectronicchartdatabase(ECDB)isthedigital
database from which electronic charts are produced.
Anelectronicnavigationalchart(ENC)isanelec-
tronicchartissuedbyanationalhydrographicauthority
designedtosatisfytheregulatoryrequirementsforchart
carriage.
Theelectronicnavigationchartdatabase(ENCDB)
isthehydrographicdatabasefromwhichtheENCis
produced.
Thesystemelectronicnavigationchart(SENC)is
the database created by an ECDIS from the ENC data.
Arasternavigationchart(RNC)isaraster-formatted
chart produced by a national hydrographic office.
Arasterchartdisplaysystem(RCDS)isasystem
whichdisplaysofficialraster-formattedchartsonan
ECDISsystem.Rasterchartscannottaketheplaceofpaper
chartsbecausetheylackkeyfeaturesrequiredbytheIMO,
sothatwhenanECDISusesrasterchartsitoperatesinthe
ECS mode.
Overscaleandunderscalerefertothedisplayofelec-
tronicchartdataattoolargeandtoosmallascale,
respectively.Inthecaseofoverscale,thedisplayis
“zoomedin”tooclose,beyondthestandardofaccuracyto
whichthedatawasdigitized.Underscaleindicatesthat
largerscaledataisavailablefortheareainquestion.ECDIS
provides a warning in either case.
Rasterchartdataisadigitized“picture”ofachart
comprisedofmillionsof“pictureelements”or“pixels.”All
200ELECTRONIC CHARTS
dataisinonelayerandoneformat.Thevideodisplaysim-
plyreproducesthepicturefromitsdigitizeddatafile.With
rasterdata,itisdifficulttochangeindividualelementsof
thechartsincetheyarenotseparatedinthedatafile.Raster
datafilestendtobelarge,sinceadatapointwithassociated
colorandintensityvaluesmustbeenteredforeverypixel
on the chart.
Vectorchartdataisdatathatisorganizedintomany
separatefilesorlayers.Itcontainsgraphicsfilesand
programstoproducecertainsymbols,points,lines,and
areaswithassociatedcolors,text,andotherchartelements.
Theprogrammercanchangeindividualelementsinthefile
andlinkelementstoadditionaldata.Vectorfilesofagiven
areaareafractionthesizeofrasterfiles,andatthesame
timemuchmoreversatile.Thenavigatorcanselectively
displayvectordata,adjustingthedisplayaccordingtohis
needs.Vectordatasupportsthecomputationofprecise
distancesbetweenfeaturesandcanprovidewarningswhen
hazardous situations arise.
1402. Components of ECS’s and ECDIS’s
ThetermsECSandECDISencompassesmany
possiblecombinationsofequipmentandsoftwaredesigned
foravarietyofnavigationalpurposes.Ingeneral,the
following components comprise an ECS or ECDIS.
•Computerprocessor,software,andnetwork:These
subsystemscontroltheprocessingofinformationfromthe
vessel’snavigationsensorsandtheflowofinformation
betweenvarioussystemcomponents.Electronicpositioning
informationfromGPSorLoranC,contactinformationfrom
radar,anddigitalcompassdata,forexample,canbeinte-
grated with the electronic chart data.
•Chartdatabase:AttheheartofanyECSliesadatabase
ofdigitalcharts,whichmaybeineitherrasterorvector
format.Itisthisdataset,oraportionofit,thatproducesthe
chart seen on the display screen.
•Systemdisplay:Thisunitdisplaystheelectronicchartand
indicatesthevessel’spositiononit,andprovidesotherinfor-
mationsuchasheading,speed,distancetothenextwaypoint
ordestination,soundings,etc.Therearetwomodesof
display,relativeandtrue.Intherelativemodetheship
remainsfixedinthecenterofthescreenandthechart
movespastit.Thisrequiresalotofcomputerpower,asall
thescreendatamustbeupdatedandre-drawnateachfix.
Intruemode,thechartremainsfixedandtheshipmoves
acrossit.Thedisplaymayalsobenorth-uporcourse-up,
accordingtotheavailabilityofdatafromaheadingsensor
such as a digital compass.
•Userinterface:Thisistheuser’slinktothesystem.Itallows
thenavigatortochangesystemparameters,enterdata,control
thedisplay,andoperatethevariousfunctionsofthesystem.
RadarmaybeintegratedwiththeECDISorECSfornavigation
orcollisionavoidance,butisnotrequiredbySOLAS
regulations.
1403. Legal Aspects of Using Electronic Charts
Requirementsforcarriageofchartsarefoundin
SOLASChapterV,whichstatesinpart:“Allshipsshall
carryadequateandup-to-datecharts...necessaryforthe
intendedvoyage.”Aselectronicchartshavedevelopedand
thesupportingtechnologyhasmatured,regulationshave
beenadoptedinternationallytosetstandardsforwhat
constitutesa“chart”intheelectronicsense,andunderwhat
conditionssuchachartwillsatisfythechartcarriage
requirement.
Anextensivebodyofrulesandregulationscontrolsthe
productionofECDISequipment,whichmustmeetcertain
highstandardsofreliabilityandperformance.Bydefini-
tion,onlyanECDIScanreplaceapaperchart.No
systemwhichisnotanECDISrelievesthenavigatorofthe
responsibilityofmaintainingaplotonacorrectedpaper
chart.Neithercanthepresenceofanelectronicchartsystem
substituteforgoodjudgement,seasense,andtakingall
reasonableprecautionstoensurethesafetyofthevesseland
crew.
Anelectronicchartsystemshouldbeconsideredasan
aidtonavigation,oneofmanythenavigatormighthaveat
hisdisposaltohelpensureasafepassage.Whilepossessing
revolutionarycapabilities,itmustbeconsideredasatool,
notaninfallibleanswertoallnavigationalproblems.The
rulefortheuseofelectronicchartsisthesameasforall
otheraidstonavigation:Theprudentnavigatorwillnever
rely completely on any single one.
CAPABILITIES AND PERFORMANCE STANDARDS
1404. ECDIS Performance Standards
ThespecificationsforECDISconsistofasetofinter-
relatedstandardsfromthreeorganizations,theInternational
MaritimeOrganization(IMO),theInternationalHydro-
graphicOrganization(IHO),andtheInternational
ElectrotechnicalCommission(IEC).TheIMOpublisheda
resolutioninNovember1995toestablishperformance
standardsforthegeneralfunctionalityofECDIS,andto
definetheconditionsforitsreplacementofpapercharts.It
consistedofa15-sectionannexand5originalappendices.
Appendix6wasadoptedin1996todefinethebackup
requirementsforECDIS.Appendix7wasadoptedin1998
todefinetheoperationofECDISinarasterchartmode.
Previous standards related only to vector data.
TheIMOperformancestandardsrefertoIHOSpecial
ELECTRONIC CHARTS201
PublicationS-52forspecificationoftechnicaldetailsper-
tainingtotheECDISdisplay.Producedin1997,the3rd
editionofS-52includesappendicesspecifyingtheissue,
updating,display,color,andsymbologyofofficialelec-
tronicnavigationalcharts(ENC),aswellasarevised
glossaryofECDIS-relatedterms.TheIMOperformance
standardsalsorefertoIECInternationalStandard61174for
therequirementsoftypeapprovalofanECDIS.Published
in1998,theIECstandarddefinesthetestingmethodsand
requiredresultsforanECDIStobecertifiedascompliant
withIMOstandards.Accordingly,thefirstECDISwasgiv-
entypeapprovalbyGermany’sclassificationsociety
(BSH)in1999.Sincethen,severalothermakesofECDIS
havegainedtypeapprovalbyvariousclassification
societies.
TheIMOperformancestandardsspecifythefollowing
generalrequirements:Displayofgovernment-authorized
vectorchartdataincludinganupdatingcapability;enable
routeplanning,routemonitoring,manualpositioning,and
continuousplottingoftheship’sposition;haveapresenta-
tionasreliableandavailableasanofficialpaperchart;
provideappropriatealarmsorindicationsregardingdis-
playedinformationormalfunctions;andpermitamodeof
operation with raster charts similar to the above standards.
Theperformancestandardsalsospecifyadditional
functions, summarized as follows:
•Display of system information in three selectable
levels of detail
•Means to ensure correct loading of ENC data and
updates
•Apply updates automatically to system display
•Protect chart data from any alteration
•Permit display of update content
•Store updates separately and keep records of appli-
cation in system
•Indicatewhenuserzoomstoofarinoroutonachart
(over-orunder-scale)orwhenalargerscalechartis
available in memory
•Permit the overlay of radar image and ARPA infor-
mation onto the display
•Requirenorth-uporientationandtruemotionmode,
but permit other combinations
•Use IHO-specified resolution, colors and symbols
•UseIEC-specifiednavigationalelementsandparam-
eters (range & bearing marker, position fix, own
ship’strackandvector,waypoint,tidalinformation,
etc.)
•Use specified size of symbols, letters and figures at
scale specified in chart data
•Permit display of ship as symbol or in true scale
•Display route planning and other tasks
•Display route monitoring
•Permitdisplaytobeclearlyviewedbymorethanone
user in day or night conditions
•Permit route planning in straight and curved
segments and adjustment of waypoints
•Displayarouteplaninadditiontotherouteselected
for monitoring
•Permittracklimitselectionanddisplayanindication
if track limit crosses a safety contour or a selected
prohibited area
•Permit display of an area away from ship while
continuing to monitor selected route
•Give an alarm at a selectable time prior to ship
crossingaselectedsafetycontourorprohibitedarea
•Plot ship’s position using a continuous positioning
systemwithanaccuracyconsistentwiththerequire-
ments of safe navigation
•Identifyselectablediscrepancybetweenprimaryand
secondary positioning system
•Provide an alarm when positioning system input is
lost
•Provideanalarmwhenpositioningsystemandchart
are based on different geodetic datums
•Storeandprovideforreplaytheelementsnecessary
toreconstructnavigationandverifychartdatainuse
during previous 12 hours
•Recordthetrackforentirevoyagewithatleastfour
hour time marks
•Permit accurate drawing of ranges and bearings not
limited by display resolution
•Require system connection to continuous position-
fixing, heading and speed information
•Neither degrade nor be degraded by connection to
other sensors
•Conduct on-board tests of major functions with
alarm or indication of malfunction
•Permitnormalfunctionsonemergencypowercircuit
•Permit power interruptions of up to 45 seconds
without system failure or need to reboot
•Enable takeover by backup unit to continue naviga-
tion if master unit fails,
BeforeanIMO-compliantECDIScanreplacepaper
chartsonvesselsgovernedbySOLASregulations,the
routeoftheintendedvoyagemustbecoveredcompletely
byENCdata,thatENCdatamustincludethelatestupdates,
theECDISinstallationmustbeIMO-compliantincluding
themaster-slavenetworkwithfullsensorfeedtobothunits,
andthenationalauthorityofthetransitedwatersmustallow
forpaperlessnavigationthroughpublishedregulations.The
202ELECTRONIC CHARTS
lattermayalsoincluderequirementsforcertifiedtrainingin
the operational use of ECDIS.
Thefirsttypeapprovalwasearnedin1999andsince
thefinalizationofthestandardsin1998,manymanufactur-
ers of ECDIS equipment have gained such certification.
Thecertifyingagencyissuesacertificatevalidfortwo
years.Forrenewal,asurveyisconductedtoensurethatsys-
tems,softwareversions,componentsandmaterialsused
complywithtype-approveddocumentsandtoreviewpos-
siblechangesindesignofsystems,softwareversions,
components,materialsperformance,andmakesurethat
such changes do not affect the type approval granted.
Manufacturershavebeenwillingtoprovidetype-ap-
provedECDIStovesseloperators,butinanon-compliant
installation.WithoutthegeographicalcoverageofENCda-
ta,theexpensivedual-networkinstallationrequiredby
ECDISwillnoteliminatetherequirementtocarryacor-
rectedportfolioofpapercharts.Thesepartialinstallations
rangefromapprovedECDISsoftwareinasinglePC,to
ECDISwithitsIEC-approvedhardware.Intheseinstances,
plottingonpaperchartscontinuestobetheprimarymeans
ofnavigation.AsmoreENCdataandupdatesbecome
available,andasgovernmentsregulatepaperlesstransits,
vesseloperatorsareupgradingtheirinstallationstomeet
fullIMOcomplianceandtomakeECDIStheprimary
means of navigation.
1405. ECS Standards
AlthoughtheIMOhasdeclinedtoissueguidelineson
ECS,theRadioTechnicalCommissionforMaritimeSer-
vices(RTCM)intheUnitedStatesdevelopedavoluntary,
industry-widestandardforECS.PublishedinDecember
1994,theRTCMStandardcalledforECStobecapableof
executingbasicnavigationalfunctions,providingcontinu-
ousplotsofownshipposition,andprovidingappropriate
indicatorswithrespecttoinformationdisplayed.The
RTCMECSStandardallowstheuseofeitherrasterorvec-
tordata,andincludestherequirementforsimpleand
reliableupdatingofinformation,oranindicationthatthe
electronic chart information has changed.
InNovember2001,RTCMpublishedVersion2.1of
the“RTCMRecommendedStandardsforElectronicChart
Systems.”Thisupdatedversionisintendedtobetterdefine
requirementsapplicabletovariousclassesofvesselsoper-
atinginavarietyofareas.Threegeneralclassesofvessels
are designated:
Large commercial vessels (oceangoing ships)
Smallcommercialvessels(tugs,researchvessels.etc.)
Smaller craft (yachts, fishing boats, etc.)
Theintentisthatusers,manufacturers,andregulatory
authoritieswillhaveameansofdifferentiatingbetweenthe
needsofvariousvesselsasrelatestoECS.Inconcept,an
ECSmeetingtheminimumrequirementsoftheRTCM
standardshouldreducetheriskofincidentsandimprove
the efficiency of navigating for many types of vessels.
However,unlikeIMO-compliantECDIS,anECSis
notintendedtocomplywiththeup-to-datechartrequire-
mentsofSOLAS.Assuch,anECSmustbeconsideredasa
singleaidtonavigation,andshouldalwaysbeusedwitha
correctedchartfromagovernment-authorizedhydro-
graphic office.
Initially,IMOregulationsrequiretheuseofvectordata
inanECDIS;rasterdatadoesnothavetheflexibility
neededtodowhattheECDISmustdo.Butitsoonbecame
clearthatthehydrographicofficesoftheworldwouldnot
beabletoproducevectordataforanysignificantpartofthe
worldforsomeyears.Meanwhile,commercialinterests
wererasterizingchartsasfastastheycouldforthe
emergingelectronicchartmarket,andnationalhydro-
graphicofficesbeganrasterizingtheirowninventoriesto
meetpublicdemand.Theresultwasarathercompletesetof
rasterdataforthemostheavilytravelledwatersofthe
world,whileproductionofman-powerintensivevector
datalaggedfarbehind.IMOregulationswerethen
amendedtoallowECDIStofunctioninanRCDSmode
usingofficialrasterdatainconjunctionwithanappropriate
portfolioofcorrectedpapercharts.Nationsmayissueregu-
lationsauthorizingtheuseofRCDSanddefinewhat
constitutesanappropriatefolioofpaperchartsforusein
their waters.
Ingeneral,anECSisnotdesignedtoreadanddisplay
theS-57format,anddoesnotmeettheperformancestan-
dardsofeitherECDISorRCDS.ButanECDIScanoperate
inECSmodewhenusingrasterchartsorwhenusingnon-
S-57vectorcharts.Whenatype-approvedECDISisin-
stalledwithoutbeingnetworkedtoabackupECDIS,or
whenitisusingnon-officialENCdata,orENCdatawith-
outupdates,itcanbesaidtobeoperatinginanECSmode,
andassuchcannotbeusedasasubstituteforofficial,cor-
rected paper charts.
1406. Display Characteristics
Whilemanufacturersofelectronicchartsystemshave
designedtheirownproprietarycolorsandsymbols,the
IMOPerformanceStandardrequiresthatallIMOapproved
ECDISfollowtheInternationalHydrographicOrganiza-
tion(IHO)Color&SymbolSpecifications.These
specificationsareembodiedintheECDISPresentation
Library.Theirdevelopmentwasajointeffortbetween
CanadaandGermanyduringthe1990s.InorderforECDIS
toenhancethesafetyofnavigation,everydetailofthe
displayshouldbeclearlyvisible,unambiguousinits
meaning,andunclutteredbysuperfluousinformation.The
unofficialECS’scontinuetobefreetodevelopindependent
ofIHOcontrol.Ingeneraltheyseektoemulatethelookof
the traditional paper chart.
Toreduceclutter,theIMOStandardlaysdowna
permanentdisplaybaseofessentialssuchasdepths,aidsto
ELECTRONIC CHARTS203
navigation,shoreline,etc.,makingtheremaininginforma-
tionselectable.Thenavigatormaythenselectonlywhatis
essentialforthenavigationaltaskathand.Ablack-back-
grounddisplayfornightuseprovidesgoodcolorcontrast
withoutcompromisingthemariner'snightvision.Simi-
larly,a“brightsun”colortableisdesignedtooutput
maximumluminanceinordertobedaylightvisible,andthe
colorsfordetailssuchasbuoysaremadeascontrastingas
possible.
ThesymbolsforECDISarebasedonthefamiliarpaper
chartsymbols,withsomeoptionalextrassuchassimplified
buoysymbolsthatshowupbetteratnight.SincetheECDIS
canbecustomizedtoeachship'srequirements,new
symbolswereaddedsuchasahighlighted,marinerselect-
able,safetycontourandaprominentisolateddanger
symbol.
ThePresentationLibraryisasetofcolorsandsymbols
togetherwithrulesrelatingthemtothedigitaldataofthe
ENC,andproceduresforhandlingspecialcases,suchas
prioritiesforthedisplayofoverlappingobjects.Every
featureintheENCisfirstpassedthroughthelook-uptable
ofthePresentationLibrarythateitherassignsasymbolor
linestyleimmediately,or,forcomplexcases,passesthe
objecttoasymbologyprocedure.Suchproceduresareused
forobjectslikelights,whichhavesomanyvariationsthata
look-uptablefortheirsymbolizationwouldbetoolong.
ThePresentationLibraryincludesaChart1,illustratingthe
symbology.GiventheIHOS-57datastandardsandS-52
displayspecifications,awaterwayshouldlookthesameno
matterwhichhydrographicofficeproducedtheENC,and
no matter which manufacturer built the ECDIS.
Theoverwhelmingadvantageofthevector-based
ECDISdisplayisitsabilitytoremoveclutteringinforma-
tionnotneededatagiventime.Bycomparison,thepaper
chartanditsrasterequivalentisanunchangeablediagram.
Asecondadvantageistheabilitytoorientthedisplay
course-upwhenthisisconvenient,whilethetextremains
screen-up.
Takingadvantageofaffordableyethigh-powered
computers,someECDIS’snowpermitasplitscreen
display,wheremodeofmotion,orientationandscaleare
individuallyselectableoneachpanel.Thispermits,for
example,anorth-upsmall-scaleoverviewintruemotion
alongsideacourse-uplarge-scaleviewinrelativemotion.
Yetanotherdisplayadvantageoccurswithzooming,inthat
symbolsandtextdescribingareascenterthemselvesauto-
maticallyinwhateverpartoftheareaappearsonthescreen.
None of these functions are possible with raster charts.
Thedisplayoperatesbyasetofrules,anddatais
arrangedhierarchically,Forexample,wherelinesoverlap,
thelessimportantlineisnotdrawn.Amorecomplexrule
alwaysplacestextatthesamepositionrelativetotheobject
itappliesto,nomatterwhatelsemaybethere.Sincealong
nameorlightdescriptionwilloftenover-writeanother
object,theonlysolutionistozoominuntiltheobjectssepa-
ratefromeachother.Notethatbecausetextcausessomuch
clutter,andisseldomvitalforsafenavigation,itiswritten
automaticallywhentheobjectitreferstoisonthedisplay,
butisanoptionunderthe“allotherinformation”display
level.
Flexibilityindisplayscalerequiressomeindicationof
distancetoobjectsseenonthedisplay.Somemanufacturers
usetheratherrestrictivebutfamiliarradarrangeringsto
providethis,whileanotherusesalinesymbolkeyedto
data’soriginalscale.TheECDISdesignalsoincludesa
one-milescalebaratthesideofthedisplay,andanoption-
allydisplayedcourseandspeedmadegoodvectorforown
ship.Theremaybeaheadinglineleadingfromthevessel’s
positionindicatingherfuturetrackforoneminute,three
minutes, or some other selectable time.
Toprovidetheoptionofcreatingmanualchartcorrec-
tions,ECDISincludesameansofdrawinglines,adding
textandinsertingstoredobjectsonthedisplay.Thesemay
besavedasuserfiles,calledupfromasubdirectory,anded-
itedonthedisplay.OnceloadedintotheSENC,theobjects
maybeselectedorde-selectedjustaswithotherobjectsof
the SENC.
DisplayoptionsforECDISincludetransferofARPA-
acquiredtargetsandradarimageoverlay.IMOstandards
forECDISrequirethattheoperatorbeabletodeselectthe
radarpicturefromthechartwithasingleoperatoractionfor
fast “uncluttering” of the chart presentation.
1407. Units, Data Layers and Calculations
ECDIS uses the following units of measure:
•Position:Latitudeandlongitudewillbeshownin
degrees,minutes,anddecimalminutes,normally
based on WGS-84 datum.
•Depth:Depthswillbeindicatedinmetersand
decimeters.
•Height: Meters
•Distance: Nautical miles and tenths, or meters
•Speed: Knots and tenths
ECDISrequiresdatalayerstoestablishapriorityof
datadisplayed.Theminimumnumberofinformationcate-
goriesrequiredandtheirrelativepriorityfromhighestto
lowest are listed below:
•ECDIS warnings and messages
•Hydrographic office data
•Notice to Mariners information
•Hydrographic office cautions
•Hydrographic office color-fill area data
•Hydrographic office on demand data
•Radar information
•User’s data
•Manufacturer’s data
•User’s color-fill area data
•Manufacturer’s color-fill area data
204ELECTRONIC CHARTS
Asaminimum,anECDISsystemmustbeableto
perform the following calculations and conversions:
•Geographicalcoordinatestodisplaycoordinates,and
display coordinates to geographical coordinates.
•Transformation from local datum to WGS-84.
•Truedistanceandazimuthbetweentwogeographical
positions.
•Geographicpositionfromaknownpositiongiven
distance and azimuth.
•Projectioncalculationssuchasgreatcircleand
rhumb line courses and distances.
1408. Warnings and Alarms
Appendix5oftheIMOPerformanceStandardspeci-
fiesthatECDISmustmonitorthestatusofitssystems
continuously,andmustprovidealarmsandindicationsfor
certainfunctionsifaconditionoccursthatrequiresimme-
diateattention.Indicationsmaybeeithervisualoraudible.
An alarm must be audible and may be visual as well.
An alarm is required for the following:
•Exceeding cross-track limits
•Crossing selected safety contour
•Deviation from route
•Position system failure
•Approaching a critical point
•Chartondifferentgeodeticdatumfrompositioning
system
An alarm or indication is required for the following:
•Largestscaleforalarm(indicatesthatpresently
loadedchartistoosmallascaletoactivateanti-
grounding feature)
•Areawithspecialconditions(meansaspecialtypeof
chart is within a time or distance setting)
•MalfunctionofECDIS(meansthemasterunitina
master-backup network has failed)
An indication is required for the following:
•Chart overscale (zoomed in too close)
•Larger scale ENC available
•Differentreferenceunits(charteddepthsnotin
meters)
•Route crosses safety contour
•Route crosses specified area activated for alarms
•System test failure
Astheselistsreveal,ECDIShasbeenprogrammedto
constantly“know”whatthenavigationteamshouldknow,
andtohelptheteamtoapplyitsexperienceandjudgment
through the adjustment of operational settings.
ThisautomationinECDIShastwoimportantconse-
quences:First,routeortrackmonitoringdoesnotreplace
situationalawareness;itonlyenhancesit.Thealarmfunc-
tions,whileuseful,arepartialandhavethepotentialtobe
in error, misinterpreted, ignored, or overlooked.
Secondly,situationalawarenessmustnowinclude,es-
peciallywhenECDISisusedastheprimarymeansof
navigation,theprocessesandstatusoftheelectroniccom-
ponentsofthesystem.Thisincludesallattachedsensors,
theserialconnectionsandcommunicationportsanddata
interfaces,thecomputerprocessorandoperatingsystem,
navigationandchartsoftware,datastoragedevices,and
powersupply.Furthermore,thesenewresponsibilitiesmust
stillbebalancedwiththetraditionalmattersofkeepinga
vigilant navigational watch.
ECDISornot,thewindowsinthepilothousearestill
thebesttoolforsituationalawareness.Paradoxically,EC-
DISmakesthenavigator’sjobbothsimplerandmore
complex.
1409. ECDIS Outputs
Duringthepast12hoursofthevoyage,ECDISmustbe
abletoreconstructthenavigationandverifytheofficialda-
tabaseused.Recordedatoneminuteintervals,the
information includes:
•Ownship’spasttrackincludingtime,position,head-
ing, and speed
•ArecordofofficialENCusedincludingsource,edi-
tion, date, cell and update history
ItisimportanttonotethatifECDISisturnedoff,such
asforchartmanagementorthroughmalfunction,voyage
recordingceases,unlessanetworkedbackupsystemtakes
overthefunctionsofthemasterECDIS.Inthatcase,the
voyagerecordingwillcontinue,includinganentryinthe
electroniclogforallthealarmsthatwereactivatedandreset
duringtheswitchover.Voyagefilesconsistoflogbook
files,trackfilesandtargetfiles.Thefilestructureisbased
onthedateandisautomaticallycreatedatmidnightforthe
timereferenceinuse.Ifthecomputersystemtimeisused
forthatpurpose,thepossibilityexistsforoverwritingvoy-
agefilesifthesystemtimeismanuallysetback.Allowing
GPS time as the system reference avoids this pitfall.
Inaddition,ECDISmustbeabletorecordthecomplete
trackfortheentirevoyagewithtimemarksatleastonceev-
eryfourhours.ECDISshouldalsohavethecapabilityto
preservetherecordoftheprevious12hoursofthevoyage.
Itisarequirementthattherecordedinformationbeinacces-
sibletoalteration.Preservingvoyagefilesshouldfollow
proceduresforarchivingdata.Unlessradaroverlaydatais
beingrecorded,voyagefilestendtoberelativelysmall,per-
mittingbackupontolow-capacitymedia,andpurgingfrom
systemmemoryatregularintervals.(Thisformofbacking
upshouldnotbeconfusedwiththenetworkmaster-slave
ELECTRONIC CHARTS205
backup system.)
Adequatebackuparrangementsmustbeprovidedto
ensuresafenavigationincaseofECDISfailure.Thisin-
cludesprovisionstotakeoverECDISfunctionssothatan
ECDISfailuredoesnotdevelopintoacriticalsituation,and
ameansofsafenavigationfortheremainingpartofthe
voyage in case of complete failure.
1410. Voyage Data Recorder (VDR)
ThepurposeofthevoyagedatarecorderVDRisto
provideaccuratehistoricalnavigationaldataintheinvesti-
gationofmaritimeincidents.Itisadditionallyusefulfor
systemperformancemonitoring.AcertifiedVDRconfigu-
rationrecordsalldatapoints,asperIMOResolution
A.861(20)&ECDirective1999/35/EC.Someofthevoy-
agedatacanberelayedthroughECDIS.AfullyIEC
compliant data capsule passes fire and immersion tests.
Theimplementationofasecure“blackbox”andcom-
prehensiveVoyageDataRecorder(VDR)isnowacarriage
requirementonpassengerandRo-Rovesselsover3000GT
(1600GRT)engagedininternationalpassages.Existing
vesselsmustberetrofittedbyJuly2004,andallvessels
builtafterJuly2002mustbefittedwithaVDR.Retrofit
regulationsforothervesselsbuiltbeforeJuly2002arestill
indevelopment.Non-RO-ROpassengervesselsbuiltbe-
foreJuly2002maybeexemptedfromcarriagewherean
operatorcanshowthatinterfacingaVDRwiththeexisting
equipmentontheshipisunreasonableandimpracticable.
TheEuropeanUnionrequiresthatallRO-ROferriesor
highspeedcraftengagedonaregularserviceinEuropean
waters(domesticorinternational)befittedwithaVDRif
builtbeforeFebruary2003,andotherwiseretrofittedby
July 2004.
VDR features include:
•Radarvideocapture:Radarvideoiscapturedand
compressedevery15secondstocomplywithIEC
performance standards.
•I/Osubsystem:Tocollectawidevarietyofdata
types,asensorinterfaceunitprovidessignalcondi-
tioningforallanalog,digitalandserialinputs.All
dataisconvertedandtransmittedtoadataacquisi-
tion unit via an ethernet LAN.
•Audiocompression:Anaudiomodulecollectsana-
logsignalsfrommicrophonepreamplifiers.Thedata
isdigitizedandcompressedtomeetLloydsofLon-
don 24-hour voice storage requirements.
•Integraluninterruptiblepowersupply(UPS)IECre-
quiresaUPSbackupforallcomponentsofthedata
acquisitionunitandforthedatacapsuletoprovide
twohourscontinuousrecordingfollowinga
blackout.
•Hardenedfixeddatacapsule:IEC61996compliant
datacapsulesfittedwithethernetconnectionspro-
videfastdownloadaswellasfastuploadtosatellite
links.
•Remotedatarecoveryandshoresideplayback:Op-
tions available in several systems.
•Annualsystemcertification:TheIMOrequiresthat
theVDRsystem,includingallsensors,besubjected
to an annual performance test for certification.
DATA FORMATS
1411. Official Vector Data
HowECDISoperatesdependsonwhattypeofchart
dataisused.ENC’s(electronicnavigationalcharts)and
RNC’s(rasternauticalcharts)areapprovedforuseinEC-
DIS.BydefinitionbothENC’sandRNC’sareissuedunder
theauthorityofnationalhydrographicoffices(HO’s).EC-
DISfunctionsasatrueECDISwhenusedwithcorrected
ENCdata,butECDISoperatesinthelessfunctionalraster
chartdisplaysystem(RCDS)modewhenusingcorrected
RNCdata.WhenECDISisusedwithnon-officialvector
chart data (corrected or not), it operates in the ECS mode.
Invectorcharts,hydrographicdataiscomprisedofa
seriesoffilesinwhichdifferentlayersofinformationare
storedordisplayed.Thisformof“intelligent”spatialdata
isobtainedbydigitizinginformationfromexistingpaper
chartsorbystoringalistofinstructionsthatdefinevarious
position-referencedfeaturesorobjects(e.g.,buoys,light-
houses,etc.).IndisplayingvectorchartdataonECDIS,the
userhasconsiderableflexibilityanddiscretionregarding
the amount of information that is displayed.
AnENCisvectordataconformingtotheIHOS-57
ENCproductspecificationintermsofcontent,structure
andformat.AnENCcontainsallthechartinformation
necessaryforsafenavigationandmaycontainsupplemen-
taryinformationinadditiontothatcontainedinthepaper
chart.Ingeneral,anS-57ENCisastructurallylayereddata
setdesignedforarangeofhydrographicapplications.As
definedinIHOS-57Edition3,thedataiscomprisedofa
seriesofpoints,lines,areas,features,andobjects.The
minimumsizeofadatasetisacell,whichisaspherical
rectangle(i.e.,borderedbymeridiansandlatitudes).Adja-
centcellsdonotoverlap.Thescaleofthedatacontainedin
thecellisdependentuponthenavigationalpurpose(e.g.,
general, coastal, approach, harbor).
UnderS-57,cellshaveastandardformatbutdonot
haveastandardcoveragesize.Instead,cellsarelimitedto
5mbofdata.S-57cellsarenormallycopyprotectedand
thereforerequireapermitbeforeuseisallowed.These
permitsaredeliveredaseitherafilecontainingthechart
206ELECTRONIC CHARTS
permitsorasacode.Inbothcasesthefirststepistoinstall
thechartpermitintotheECDIS.Somehydrographic
officesdeliverS-57cellswithoutcopyprotectionand
therefore permits are not required.
Anyregionalagencyresponsibleforcollectingand
distributingS-57data,suchasPRIMARforNorthern
Europe,willalsomaintaindataconsistency.National
hydrographicofficesareresponsibleforproducingS-57
datafortheirowncountryarea.ThroughouttheworldHO’s
havebeenslowtoproducesufficientquantitiesofENC
data.Thisisduetothefactthatthestandardsevolvedover
severalyears,andthatvectordataismuchhardertocollect
than raster data.
In1996theIHOS-57datastandardandIHOS-52
specificationsforchartcontentanddisplaywere“frozen.”
IttookthreeversionsofS-57beforetheissuewasfinally
settledastowhatactuallycomprisesanENC(i.e.,ENC
ProductSpecification)andwhatisrequiredforupdating
(ENCUpdatingProfile).TheENCTestDatasetthatthe
InternationalElectrotechnicalCommission(IEC)requires
foruseinconjunctionwithIECPublication61174(IEC
1997)wasfinalizedbyIHOin1998.Itwasnotpossibleto
conductECDIStype-approvalprocedureswithouta
complete and validated IHO ENC Test Dataset.
MajorareasofENCcoveragenowincludemostof
CanadianandJapanesewaters,theBalticandNorthSea,
andimportantwaterwayssuchastheStraitsofMalacca,
Singapore Strait, and the Straits of Magellan (Chile).
Atthesametime,manycountriesincludingtheUnited
States,aresteppinguptheirproductionofENC’swhere
issuesofportsecurityrequirethecollectionofbaselinedata
ofsubmergedhazards.IntheU.S.,NOAAplansto
completeitsportfoliooflarge-scalechartsof42portsin
ENCformatbymid-2003,withsmallerscalechartcomple-
tionby2005.Asthechartcellsarecompleted,thedatais
beingmadeavailableontheWorldWideWebatnocost.
Beginningin2003,NOAAwillpostcriticalnoticeto
marinercorrectionswithoutrestrictionsinmonthlyincre-
ments.AtthatpointthestatusofNOAA’savailableENC
data will be changed from provisional to official.
ENCdataiscurrentlyavailablefromtheHO’sofmost
NorthernEuropeancountries,Japan,Korea,HongKong,
Singapore,Canada,Chile,andtheUnitedStates,although
thecoverageandupdatingprocessisincomplete.Most
ENCisavailableonlythroughpurchase,permitsor
licensing.
1412. Vector Data Formats Other Than IHO S-57
Thelargestofthenon-S-57formatdatabasesisthe
DigitalNauticalChart(DNC).TheNationalImageryand
MappingAgency(NIMA)producesthecontentandformat
fortheDNCaccordingtoamilitaryspecification.Thisal-
lowscompatibilityamongallU.S.DefenseDepartment
assets.TheDNCisavector-baseddigitalproductthatpor-
trayssignificantmaritimefeaturesinaformatsuitablefor
computerizedmarinenavigation.TheDNCisageneral-
purposeglobaldatabasedesignedtosupportmarinenaviga-
tionandGeographicInformationSystem(GIS)
applications.DNCdataisonlyavailabletotheU.S.mili-
taryandselectedallies.Itisdesignedtoconformtothe
IMOPerformanceStandardandIHOspecificationsfor
ECDIS.
Severalcommercialmanufacturershavedeveloped
vectordatabasesbeyondthosethathavebeenissuedbyof-
ficialhydrographicoffices.Thesecompaniesaretypically
manufacturersofECDISorECSequipmentorhavedirect
relationshipswithcompaniesthatdo,andtypicallyhavede-
velopeddatainproprietaryformatinordertoprovide
optionstorasterchartsintheabsenceofENCdata.HO-is-
suedpaperchartsprovidethesourcedatafortheseformats,
althoughinsomecasesnon-officialpaperchartsareused.
Insomecases,ECSmanufacturersprovidearegularupdat-
ingandmaintenanceservicefortheirvectordata,resulting
inaddedconfidenceandsatisfactionamongusers.The
manufacturer’ssourceoftheupdatesisthroughHO’s.
Hence,thesetwoparticularnon-officialformatsallowsfor
averyhighdegreeofconfidenceandsatisfactionamong
mariners using this data.
ECSsystemssometimesapplyrulesofpresentation
similartoofficiallyspecifiedrules.Thusinformationis
displayedorremovedautomaticallyaccordingtoscale
leveltomanageclutter.Thesameindicationspertinentto
overscalingENCapplytoprivatevectordata.Sincethe
chartdataisnotENC,thesystemsmustdisplaythatnon-
official status when used in an ECDIS.
1413. Raster Data
Rasternavigationalchart(RNC)dataisstoredas
pictureelements(pixels).Eachpixelisaminutecomponent
ofthechartimagewithadefinedcolorandbrightnesslevel.
Raster-scannedimagesarederivedbyscanningpaper
chartstoproduceadigitalphotographofthechart.Raster
dataarefareasiertoproducethanvectordata,butraster
charts present many limitations to the user.
The official raster chart formats are:
ARCS (British Admiralty)
Seafarer (Australia)
BSB (U.S., NOAA/Maptech)
Thesechartsareproducedfromthesamerasterprocess
usedtoprintpapercharts.Theyareaccuraterepresentations
oftheoriginalpaperchartwitheverypixelgeographically
referenced.Whereapplicable,horizontaldatumshiftsare
includedwitheachcharttoenablereferencingtoWGS84.
Thispermitscompatibilitywithinformationoverlaidonthe
chart.Note:NotallavailablechartshaveWGS84shift
information.Extremecautionisnecessaryifthedatumshift
cannot be determined exactly.
Rasternauticalchartsrequiresignificantlylarger
ELECTRONIC CHARTS207
amountsofmemorythanvectorcharts.Whereasaworld
portfolioofmorethan7500vectorchartsmayoccupyabout
500mb,atypicalcoastalregioninrasterformatmayconsist
ofjust40chartsandoccupymorethan1000mbofmemory.
Forpracticalpurposes,mostofaportfolioofraster
chartsshouldbeleftontheCDandnotloadedintothe
ECDISharddriveunlessoneisrouteplanningoractually
sailinginagivenregion.Ofcourse,updatescanonlybe
performed on charts that are loaded onto the hard drive.
Certainnon-officialrasterchartsareproducedthat
coverEuropeanandsomeSouthAmericanwaters.These
arescannedfromlocalpapercharts.Additionally,some
ECDISandECSmanufacturersalsoproducerastercharts
in proprietary formats.
In1998theIMO’sMaritimeSafetyCommittee(MSC
70)adoptedtheRasterChartDisplaySystem(RCDS)as
Appendix7totheIMOPerformanceStandards.TheIMO-
IHOHarmonizationGrouponECDIS(HGE)considered
thisissueforoverthreeyears.WhereIHOS-57Ed.3ENC
datacoverageisnotavailable,rasterdataprovidedbyoffi-
cialHO’scanbeusedasaninterimsolution.ButthisRCDS
modedoesnothavethefullfunctionalityofanotherwise
IMO-compliantECDISusingENCdata.Therefore,RCDS
doesnotmeetSOLASrequirementsforcarriageofpaper
charts,meaningthatwhenECDISequipmentisoperatedin
theRCDSmode,itmustbeusedtogetherwithanappropri-
ate portfolio of corrected paper charts.
SomeofthelimitationsofRCDScomparedtoECDIS
include:
•Chartfeaturescannotbesimplifiedorremovedto
suit a particular navigational circumstance or task.
•OrientationoftheRCDSdisplaytocourse-upmay
affectthereadabilityofthecharttextandsymbols
sincethesearefixedtothechartimageinanorth-up
orientation.
•Dependingonthesourceoftherasterchartdata,dif-
ferentcolorsmaybeusedtoshowsimilarchart
information,andtheremaybedifferencesbetween
colors used during day and night time.
•Theaccuracyoftherasterchartdatamaybelessthan
that of the position-fixing system being used.
•Unlikevectordata,chartedobjectsonrastercharts
do not support any underlying information.
•RNCdatawillnottriggerautomaticalarms.(How-
ever,somealarmscanbegeneratedbytheRCDS
from user-inserted information.).
•Soundingsonrasterchartsmaybeinfathomsand
feet, rather than meters.
TheuseofECDISinRCDSmodecanonlybeconsid-
eredaslongasthereisabackupfolioofappropriateup-to-
date paper charts.
INTEGRATED BRIDGE SYSTEMS
1414. Description
AnIntegratedBridgeSystem(IBS)isacombinationof
equipmentandsoftwarewhichusesinterconnectedcontrols
anddisplaystopresentacomprehensivesuiteofnaviga-
tionalinformationtothemariner.Rulesfromclassification
societiessuchasDetNorskeVeritas(DNV)specifydesign
criteriaforbridgeworkstations.Theirrulesdefinetasksto
beperformed,andspecifyhowandwhereequipment
shouldbesitedtoenablethosetaskstobeperformed.
Equipmentcarriagerequirementsarespecifiedforships
accordingtotherequestedclasscertificationornotation.
PublicationIEC61029definesoperationalandperfor-
mancerequirements,methodsoftesting,andrequiredtest
results for IBS.
Classificationsocietyrulesaddressthetotalbridge
systeminfourparts:technicalsystem,humanoperator,
man/machineinterface,andoperationalprocedures.The
DNVclassifiesIBSwiththreecertifications:NAUT-Ccov-
ersbridgedesign;W1-OCcoversbridgedesign,
instrumentationandbridgeprocedures;W1augmentscer-
tain portions of W1-OC.
An IBS generally consists of at least:
•DualECDISinstallation–oneservingmasterand
the other as backup and route planning station
•Dual radar/ARPA installation
•Conningdisplaywithaconcentratedpresentationof
navigational information (the master ECDIS)
•DGPS positioning
•Ship's speed measuring system
•Auto-pilot and gyrocompass system
•Full GMDSS functionality
Somesystemsincludefullinternalcommunications,
andameansofmonitoringfirecontrol,shipboardstatus
alarms,andmachinerycontrol.Additionally,functionsfor
the loading and discharge of cargo may also be provided.
AnIBSisdesignedtocentralizethefunctionsofmon-
itoringcollisionandgroundingrisks,andtoautomate
navigationandshipcontrol.Controlanddisplayofcompo-
nentsystemsarenotsimplyinterconnected,butoftenshare
aproprietarylanguageorcode.Severalinstrumentsandin-
dicatorsareconsideredessentialforsafeandefficient
performanceoftasks,andareeasilyreadableatthenaviga-
tionworkstation,suchasheading,rudderangle,depth,
propellerspeedorpitch,thrusterazimuthandforce,and
speed and distance log.
TypeapprovalbyDetNorskeVeritasfortheDNV-
W1-ANTS(AutomaticNavigationandTrack-Keeping
208ELECTRONIC CHARTS
System)certificationisgiventoshipbridgesystemsde-
signedforone-manwatch(W1)inanunboundedseaarea.
DNValsoprovidesfortheothertwoclassnotations,
NAUT-CandW1-OC.TheW1specificationsrequirethe
integration of:
•CDIS(providingthefunctionsofsafety-contour
checksandalarmsduringvoyageplanningand
execution)
•Manualandautomaticsteeringsystem(including
softwareforcalculation,executionandadjustments
tomaintainapre-plannedroute,andincludingrate
of turn indicator)
•AutomaticNavigationandTrack-keepingSystem
(ANTS)
•Conning information display
•Differential GPS (redundant)
•Gyrocompass (redundant)
•Radar (redundant) and ARPA
•Central alarm panel
•Wind measuring system
•Internal communications systems
•GMDSS
•Speedoverground(SOG)andspeedthroughwater
(STW or Doppler log)
•Depth sounder (dual transducer >250m)
•Course alteration warnings and acknowledgment
•Provisiontodigitizepaperchartsforareasnotcov-
ered by ENC data
TheW1classificationrequiresthatmaneuveringinfor-
mationbemadeavailableonthebridgeandpresentedasa
pilotcard,wheelhouseposter,andmaneuveringbooklet.
Theinformationshouldincludecharacteristicsofspeed,
stopping,turning,coursechange,low-speedsteering,
coursestability,trialswiththeauxiliarymaneuveringde-
vice, and man-overboard rescue maneuvers.
TheW1-OCandW1classificationsspecifyresponsi-
bilitiesofshipownerandshipoperator,qualifications,
bridgeprocedures,andparticulartoW1,arequirementfor
operationalsafetystandards.TheW1operationalsafety
manualrequirescompliancewithguidelinesonbridgeor-
ganization,navigationalwatchroutines,operationand
maintenanceofnavigationalequipment,proceduresforar-
rivalanddeparture,navigationalproceduresforvarious
conditionsofconfinementandvisibility,andsystemfall-
backprocedures.Bothclassificationsalsorequirecompli-
ancewithacontingencyandemergencymanual,including
organization,accident,security,evacuation,andotherre-
lated issues.
MILITARY ECDIS
1415. ECDIS-N
In1998,theU.S.Navyissuedapolicyletterforanaval
versionofECDIS,ECDIS-N,andincludedaperformance
standardthatnotonlyconformstotheIMOPerformance
Standards,butextendsittomeetuniquerequirementsofthe
U.S. Department of Defense.
AmajordifferencefromanIMO-compliantECDISis
therequirementthattheECDIS-NSENCmustbethe
DigitalNauticalChart(DNC)issuedbytheNational
ImageryandMappingAgency(NIMA).TheDNC
conformstotheU.S.DoDstandardVectorProductFormat
(VPF),animplementationoftheNATODIGESTCVector
RelationalFormat.AllofNIMA’snautical,aeronautical,
andtopographicvectordatabasesareinVPFtoensure
interoperability between DoD forces.
IntheUnitedStates,NIMAproducestheDigitalNau-
ticalChart(DNC).Itisavectordatabaseofsignificant
maritimefeaturesthatcanbeusedwithshipboardintegrat-
ednavigationsystemssuchasECDIS,ECDIS-N,orother
typesofgeographicinformationsystems.NIMAhasbeen
workingcloselywiththeU.S.Navytohelpfacilitateatran-
sitionfromrelianceonpaperchartstoelectronicchart
navigationusingtheDNC.TheU.S.Navyplanstohaveall
ofitssurfaceandsub-surfacevesselsusingDNC’sby2004.
NIMAhasproducedtheDNCtosupportworldwidenavi-
gationrequirementsoftheU.S.NavyandU.S.Coast
Guard.
ToensurethattheDNCdatawouldnotbemanipulated
orinadvertentlyalteredwhenusedbydifferentmilitary
units,adecisionwasmadetoproduceaspecificdatasoft-
wareproductthatmustbeusedina“directread”capability.
Assuch,aDNCisreallyasystemelectronicnavigational
chart(SENC)thatcontainsspecifieddataanddisplaychar-
acteristics.ControloftheSENCprovidesthemilitarywith
interoperabilityacrossdeployedsystems,whichisparticu-
larly important when integrated with military data layers.
1416. Navigation Sensor System Interface (NAVSSI)
TheNavigationSensorSystemInterface(NAVSSI)
containstheU.S.Navy’sversionofECDIS,andalsohas
significantadditionalcapabilitiesfortheNavy’sdefense
missions.NIMA’sVectorProductFormat(VPF)DNC’s
areusedinconjunctionwithNAVSSI.NAVSSIperforms
three important functions:
•Navigation Safety: NAVSSI distributes real time
navigationdatatothenavigationteammembersto
ensure navigation safety.
•WeaponsSystemSupport:NAVSSIprovidesinitial-
ELECTRONIC CHARTS209
ization data for weapons systems.
•BattlegroupPlanning:NAVSSIprovidesaworksta-
tion for battlegroup planning.
ThenavigationalfunctionofNAVSSI,therefore,is
onlyoneofseveraltasksaccomplishedbythesystem.The
navigationalportionofNAVSSIcomplieswiththe
IMO/IHO ECDIS standards for content and function.
TheheartofNAVSSIistheRealTimeSubsystem
(RTS).TheRTSreceives,processesanddistributesnaviga-
tionaldatatothenavigationdisplay,weaponssystems,and
othernetworkedvessels.Thisensuresthatallelementsofa
battlegrouphavethesamenavigationalpicture.Inputs
comefromGPS,Loran,inertialnavigationsystems,com-
pass,andspeedlog.Thebridgedisplayconsistsofa
monitorandcontrolpanel,whiletheRTSismountedbelow
decks.DNC’sarecontainedintheDisplayandControl
Subsystem(DCS)typicallymountedinthechartroomwith
amonitoronthebridge.Thisisunlikemanycurrentcom-
mercialsystemswhichhouseallhardwareandsoftwarein
asingleunitonthebridge.AseparateNAVSSIsoftware
packagesupportsoperatorinterface,waypointcapability,
collisionandgroundingavoidancefeatures,andotheras-
pects of an ECDIS.
Figure1416illustratesabasicblockdiagramofthe
NAVSSIsystem.TheRTStakesinputsfromtheinertial
navigators,theGPSinPPSmode,thecompass,theEM
Log,andtheSRN-25.TheRTSdistributesnavigationin-
formationtothevarioustacticalapplicationsrequiring
navigationinput,anditcommunicatesviafiberopticnet-
workwiththeDCS.TheDCSexchangesinformationwith
the Navigator’s Workstation.
1417. The Digital Nautical Chart
NAVSSIusestheDigitalNauticalChart(DNC)asits
chartdatabase.TheDNCisinVectorProductFormat
(VPF)andisbasedonthecontentsofthetraditionalpaper
harbor,approach,coastalandgeneralchartsproducedby
NIMA andNOS.
HorizontaldatumisWGS84(NAD83intheU.S.is
equivalent).Therearethreeverticaldatums.Topographic
featuresarereferencedtoMeanSeaLevelandtheshore
lineisreferencedtoMeanHighWater.Hydrographyis
referencedtoalowwaterlevelsuitablefortheregion.All
measurements are metric.
TheDNCportfolioconsistsof29CD-ROM’sandpro-
videsglobalcoveragebetween84degreesNand81degrees
S.Thiscomprisessome4,820chartsgroupintofivelibrar-
ies based on scale:
General: (>1:500K)
Coastal: (1:75K - 1: 500K)
Approach (1:25K - 1:75K)
Harbor (1 <1:50K)
Browse Index (1:3,100,000)
Figure 1416. Block diagram of NAVSSI.
210ELECTRONIC CHARTS
DNCdataislayeredtogetherinto12relatedfeatureclasses:
•Cultural Landmarks
•Earth Cover
•Inland Waterways
•Relief
•Landcover
•Port Facilities
•Aids to Navigation
•Obstructions
•Hydrography
•Environment
•Limits
•Data Quality
Contentisgenerallythesameasonapaperchart.
Thedataisstoredinlibraries;eachlibraryrepresentsa
differentlevelofdetail.Thelibrariesarethenstoredon
CD-ROMandorganizedastilesaccordingtotheWorld
Geodetic Reference System (GEOREF) tiling scheme.
AsubsetoftheDNCisknownasTacticalOceanData
(TOD).TODdataisbathymetricinnatureandintendedfor
Naval operations.
There are 6 levels of TOD:
Level 0 - OPAREA charts
Level 1 - Bottom Contour
Level 2 - Bathymetric Navigation Planning Charts
Level 3 - Shallow Water
Level 4 - Hull Integrity Test Charts
Level 5 - Strategic Straits Charts
1418. Warship ECDIS (WECDIS)
AWarshipECDISisanECDISapprovedbyinter-
nationalauthoritiesforwarshipuse,which,while
meetingtheoperatingstandardsofECDIS,maynot
conform exactly to ECDIS specifications.
PerformanceStandardsfor“Warship”ECDIS
(WECDIS)wereapprovedbytheNorthAtlanticTreaty
Organization(NATO)in1999andissuedasSTANAG
4564.ThecorefunctionalityofWECDISisanIMO-
compliantECDIS.Beyondtheminimumperformance
requirementsforECDIS,WECDIShastheabilityto
useavarietyofgeospatialdatafrombothcivilianand
militarysources.Fornavigationaldata,WECDISuses
bothIHOS-57ENCdataanddataconformingto
NATODigitalGeographicInformationExchange(DI-
GEST)Standards.Thislatterincludessuchproductsas
VectorProductFormat(VPF)andDigitalNautical
Chart (DNC).
Inadditiontocorenavigationinformation(IHOS-
57ENCandVPF-DNC),WECDISwillalsouseAddi-
tionalNavigationInformation(ANI)providedby
governmenthydrographicofficesandmilitarysources.
SpecifictypesofANIdataincludeRasterNavigational
Charts(RNC’s),suchasAdmiraltyRasterChart
Service(ARCS)orNOAA’srasterchartsdistributed
andupdatedbyMaptech,Inc.Theabilitytouse
differenttypesofnavigationaldatafromavariety
sources is often referred to as “multi-fuel.”
CORRECTING ELECTRONIC CHARTS
1419. ECDIS Correction Systems
ECDISsoftwarecreatesadatabasefromtheENCdata
calledthesystemelectronicnavigationalchart(SENC)and
fromthisselectsinformationfordisplay.TheECDISsoft-
waremeanwhilereceivesandprocessesserialdatafrom
navigationalsensorsanddisplaysthattextualandgraphical
information simultaneously with the SENC information.
ItistheSENCthatisequivalenttoup-to-datecharts,as
statedbythePerformanceStandards.Asoriginallycon-
ceived,ECDISwasdesignedtouseinternationally
standardizedandofficiallyproducedvectordatacalledthe
ENC(electronicnavigationalchart).OnlywhenusingENC
datacanECDIScreateanSENC,andtherebyfunctionin
the ECDIS mode.
UpdatesforENCareinstalledintotheECDISseparate
fromtheENCdataitself.Forthemariner,thisinvolvesac-
tivatingaspecialutilityaccompanyingtheECDISand
followingtheon-screenprompts.Withinthissameutility,
updatecontentandupdatelogfilesintextualformcanbe
viewed.OncetheECDISsoftwareitselfisreactivated,the
updateinformationisaccessedinconjunctionwiththe
ENC data and the SENC database is created.
JustasENCandupdatesaretransformedintothe
SENC,sotooareotherdatatypesaccessedandcombined.
Theuserhastheoptiontoaddlines,objects,textandlinks
tootherfilessupportedbyapplication.Referredtointhe
PerformanceStandardsasdataaddedbythemariner,these
notesfunctionaslayersonthedisplayedchart.Theusercan
selectallorpartsofthelayersfordisplaytokeepclutterto
aminimum.Themariner’sownlayers,however,mustbe
calledintotheSENCfromstoredmemory.Asapractical
matter,notonlymustthemarinertakecaretoassociatefile
nameswithactualcontent,suchaswithmanuallycreated
chartcorrections,butalsomustrealizethatthefilesthem-
selvesdonothavethetamper-proofstatusthatENCand
official updates have.
WithintheSENCresidesalltheinformationavailable
forthedisplay.ThePresentationLibraryrulessuchasStan-
dardDisplayandDisplayBasedefinewhatlevelsof
information from the SENC can be shown.
AnENCupdatingprofileiscontainedwithintheIHO
S-57Edition3.0specification.Thisenablestheefficient
addition,removalorreplacementofanyline,feature,object
ELECTRONIC CHARTS211
orareacontainedwithintheENCdataset.Guidanceonthe
meansandprocessforENCupdatingisprovidedinIHOS-
52,Appendix1.IntermsofwhatiscalledforintheIMO
PerformanceStandards,anENCdatasetbeingusedinan
ECDISmustalsohaveanENCupdatingservice.Thisper-
mitstheENCandtheSENCtobecorrectedfortheintended
voyage,andthusachievesanimportantcomponentofSO-
LAS compliance.
Accordingly,ECDISmustbecapableofacceptingof-
ficialupdatestotheENCdataprovidedinconformitywith
IHOstandard.Updatedcellsarestoredinafileandtrans-
mittedbye-mail,floppydiskorCD-ROM,orsatellite.For
example,PRIMARchartsandupdatesaredeliveredontwo
CD’s:theBaseCDcontainsthePRIMARdatabaseatthe
timeindicatedonthelabelandthesecondCDcontainsthe
updatesforthosecharts.ButtheupdateCDalsocontains
newchartsissuedsincethebaseCDwasprinted.Sincethe
operatormustacquirethefilesandtheninitiatetheupdate
functionsoftheECDISsoftware,thisformofupdatingis
referred to as semi-automatic.
Generally,ECDISwillrejectupdatesiftheupdateis-
suingauthorityisdifferentfromthecellissuingauthority.
Itwillalsorejectcorruptedupdatefilesandfileswithanin-
correctextension.ECDISchecksthatupdatesareappliedin
therightsequence.Ifoneupdateismissingthenextupdate
isrejected.AnupdateCD-ROMshouldcontainallavail-
ableupdatesforallS57cells.Generally,ECDISwill
automaticallyrunallupdatesintherightorderforallcells.
ForS-57data,thecontentofupdatesintextformcan
beviewedfromwithintheutilitythatpermitsthemanage-
mentofchartdata.Generallyitcanonlyberunwhen
ECDISisterminated.ECDISisalsocapableofshowingor
hidingS-57updatesonagivenchartorcell.Theupdate
mustfirstbeinstalledviathechartutility.Afterrestarting
ECDIS,andafterloadingintothedisplaytheparticular
chartwiththecorrection,thecorrectionshouldbemanually
accepted.ThatenablesthefunctioninS-57chartoptionsto
showorhidethesymbolindicatingthelocationofthe
correction.
NIMA DNC Corrections
NIMAhasproducedtheDNCVectorProductFormat
DatabaseUpdate(VDU)tosupportworldwideDNCnavi-
gationrequirementsoftheU.S.Navy,theU.S.Coast
Guard,andcertainallies.NIMAdoesnotdistributeDNCto
otherthanU.S.governmentagenciesandforeigngovern-
mentshavingdataexchangeagreementswithNIMA.The
DNCmaintenancesystemwillbeabletoapplynewsource
materialssuchasbathymetry,imagery,NoticetoMariners,
localnotices,newforeigncharts,etc.forinclusioninthe
DNC database.
TheVDUsystemworksbyperformingabinarycom-
parisonofthecorrectedchartwiththepreviousversion.
Thedifferencesarethenwrittentoabinary“patch”file
withinstructionsastoitsexactlocation.Theuserthenap-
pliesthispatchbyspecifyingtheproperpathandfilename
onhisownship.Everynewchangeincorporatesallprevi-
ouschanges,sothenavigatorisassuredthat,having
receivedthelatestchange,hehasallchangesissuedtodate.
Filesizesaresmallenoughtosupportbandwidthlimi-
tationsofshipsatseaandrequiresonlyone-way
communication.Patchfilesarepostedeveryfourweeks.
AuthorizedcommandsmayaccessDNC’sandtheassociat-
ed VDU files through the NIMA Gateway:
OSIS http://osis.nima.mil/gidbe/index.htm
SIPRNET http://www.nima.smil.mil/products/dnc1
JWICS http://www.nima.is.gov/products/dnc1
TheVDUpatchfilesarepostedtotheWorldWide
Web monthly at:
http://www.nima.mil/dncpublic/
AseparatelayerwithinDNCprovidestheuserwith
identificationofwherechangeshavebeenmadeduringthe
updating process.
British RCS Corrections
FortheBritishRCSsystem,updatesforall2700charts
affectedbyAdmiraltyNoticetoMarinersarecompiledand
placedonaweeklyARCSUpdateCD-ROM.Applyingthe
correctionsisonlysemi-automatic(notfullyautomatic),
butitisalsoerror-free,andeachCD-ROMprovidescumu-
lativeupdates.TheCD-ROM’sareavailablethroughchart
agents.
NOAA Corrections
IntheU.S.,NOAAhascontractedwithMaptech,Inc.
toprovideupdatingofallNOSrasterchartsusinginforma-
tionfromtheUSCG,NIMAandtheCanadian
HydrographicService(CHS).Maptechusesa“patchtech-
nique”toupdateonlythosepartsofagivenchartidentified
asneedingcorrection.Themethodcomparestheexisting
chartfileanditscorrectedcounterpartonapixel-by-pixel
basis.Thesoftwarecreatesa“differencefile”thatisasso-
ciatedwiththeexistingrasterfiletowhichitapplies.This
differencefileisthencompressedsothatatypicalpatch
containsonlyafewkilobytesofdata.Ninety-ninepercent
areunder10kb.Typicaldownloadsforacharttake15sec-
onds to 5 minutes depending on modem speed.
Therasterchartisupdatedasthepatchfilealtersthe
pixelsontheoriginalchart.Updatepatchesareavailableby
download,andarecumulativefortheallthechartspacked
onagivensourcefolioCD.Furtherrefinementwillpermit
theseparatestorageoftheRNCandupdatepatches,sothat
asthepatchisapplieddynamicallyinrealtime,theuser
willbeabletoviewthecorrection.Thedynamicpatching
issimilartoENCupdatinginthattheoriginalchartdatais
212ELECTRONIC CHARTS
notaltered.Presentlytheserviceisasubscriptionservice
withweeklyupdatesatanominalcost.Informationisavail-
able at http://chartmaker.ncd.noaa.gov.
Commercial Systems
ThereareavarietyofECS’savailableforsmallcraft,
oftenfoundaboardfishingvessels,tugs,researchvessels,
yachts,andothercraftnotlargeenoughtoneedSOLAS
equipmentbutwantingthebestinnavigationtechnology.
Giventhatthesesystemscompriseasingleaidtonaviga-
tionanddonotrepresentalegalchartinanysense,itis
probablynotacriticalpointthatcorrectionsystemsfor
theseproductsarenotrobustenoughtosupportregularap-
plication of changes.
Infact,oftentheonlywaytomakechangesistopur-
chaseneweditions,althoughthemoresophisticatedones
allowtheplacementofelectronic“notes”onthechart.The
dataiscommonlystoredonRAMchipsofvarioustypes,
andcannotbechangedorwithoutre-programmingthechip
fromaCD-ROMordiskcontainingthedata.Ifthedatais
onCD-ROM,anewCD-ROMistheupdatemechanism,
andtheyare,forthemostpart,infrequentlyproduced.Us-
ersofthesesystemsarerequiredtomaintainaplotona
corrected paper chart.
USING ELECTRONIC CHARTS
1420. Digital Chart Accuracy
Asisthecasewithanyshipboardgear,theusermust
beawareofthecapabilitiesandlimitationsofdigitalcharts.
Themarinershouldunderstandthatnauticalchartdatadis-
playedpossessinherentaccuracylimitations.Because
digitalchartsarenecessarilybasedprimarilyonpaper
charts,manyoftheselimitationshavemigratedfromthe
paperchartintotheelectronicchart.Electronicchartaccu-
racyis,forthemostpart,dependentontheaccuracyofthe
featuresbeingdisplayedandmanipulated.WhilesomeEC-
DISandECShavethecapabilitytouselarge-scaledata
producedfromrecenthydrographicsurveyoperations(e.g.,
dredgedchannellimitsorpier/terminalfacilities)mostras-
terandvector-basedelectronicchartdataarederivedfrom
existing paper charts.
Twentyyearsago,marinersweretypicallyobtaining
positionfixesusingradarranges,visualbearingsorLoran.
Generally,thesepositioningmethodswereanorderofmag-
nitudelessaccuratethanthehorizontalaccuracyofthe
surveyinformationportrayedonthechart.Forexample,a
three-linefixthatresultsinanequilateraltrianglewithsides
twomillimetersinlengthatachartscaleof1:20,000repre-
sentsatrianglewith40-metersidesinreal-world
coordinates.
Apotentialsourceoferrorisrelatedtothesystemcon-
figuration,ratherthantheaccuracyofelectronicchartdata
beingused.AllECDIS’sandmostECS’senabletheuserto
inputthevessel'sdimensionsandGPSantennalocation.On
largervessels,therelativepositionoftheGPSantenna
aboardtheshipcanbeasourceoferrorwhenviewingthe
“own-ship” icon next to a pier or wharf.
InU.S.waters,theCoastGuard'sDGPSprovidesa
horizontalaccuracyof+/-10meters(95percent).However,
withselectiveavailabilityoff,eventhemostbasicGPSre-
ceiverinanon-differentialmodemaybecapableof
providingbetterthan10meterhorizontalaccuracy.Inactu-
aloperation,accuraciesof3-5metersarebeingachieved.
Asaresult,somemarinershavereportedthatwhenusingan
electronicchartwhilemooredalongsideapier,thevessel
icon plots on top of the pier or out in the channel.
Similarly,somemarinerstransitingarangethatmarks
thecenterlineofachannelreportthatthevesseliconplots
alongtheedgeorevenoutsideofthechannel.Mariners
nowexpect,justastheydid20yearsago,thatthehorizontal
accuracyoftheirchartswillbeasaccurateastheposition-
ingsystemavailabletothem.Unfortunately,anyelectronic
chartbasedonapaperchart,whetheritisrasterorvector,
is not able to meet this expectation.
Theoverallhorizontalaccuracyofdataportrayedon
paperchartsisacombinationoftheaccuracyoftheunder-
lyingsourcedataandtheaccuracyofthechartcompilation
process.Mostpaperchartsaregeneralizedcompositedoc-
umentscompiledfromsurveydatathathavebeencollected
byvarioussourcesoveralongperiodoftime.Agivenchart
mightencompassoneareathatisbasedonaleadlineand
sextanthydrographicsurveyconductedin1890,whilean-
otherareaofthesamechartmighthavebeensurveyedin
theyear2000withafull-coverageshallow-watermulti-
beamsystem.IntheU.S.,agencieshavetypicallyusedthe
mostaccuratehydrographicsurveyinstrumentationavail-
able at the time of the survey.
Whilesurveypositioningmethodshavechangedover
theyears,standardshavegenerallybeensuchthatsurveys
wereconductedwithapositioningaccuracyofbetterthan
0.75millimetersatthescaleofthechart.Therefore,ona
1:20,000-scalechart,thesurveydatawasrequiredtobeac-
curateto15meters.Featureswhosepositionsoriginatein
thelocalnoticetomariners,reportedbyunknownsource,
areusuallychartedwithqualifyingnotationslikeposition
approximate(PA)orpositiondoubtful(PD).Thecharted
positionsofthesefeatures,iftheydoexist,maybeinerror
by miles.
Asof2002,over50percentofthedepthinformation
foundonU.S.chartsisbasedonhydrographicsurveyscon-
ductedbefore1940.Surveysconductedmanyyearsago
withleadlinesorsingle-beamechosounderssampledonly
atinypercentageoftheoceanbottom.Hydrographerswere
unabletocollectdatabetweenthesoundinglines.Depend-
ingonthewaterdepth,theselinesmayhavebeenspacedat
ELECTRONIC CHARTS213
50,100,200or400meters.Asareasarere-surveyedand
full-bottomcoverageisobtained,unchartedfeatures,some
dangeroustonavigation,arediscoveredquiteoften.These
featureswereeither:1)notdetectedonpriorsurveys,2)ob-
jectssuchaswrecksthathaveappearedontheocean
bottomsincethepriorsurveyor3)theresultofnatural
changes that have occurred since the prior survey.
Inasimilarmanner,theshorelinefoundonmostU.S.
chartsisbasedonphotogrammetricorplanetablesurveys
thataremorethan20yearsold.Inmajorcommercialhar-
bors,thewaterfrontisconstantlychanging.Newpiers,
wharves,anddocksareconstructedandoldfacilitiesarede-
molished.Someoftheseman-madechangesareaddedto
thechartwhentheresponsibleauthorityprovidesas-built
drawings.However,manychangesarenotreportedand
thereforedonotappearonthechart.Naturalerosionalong
theshoreline,shiftingsandbarsandspits,andgeological
subsidenceandupliftalsotendtorenderthechartedshore-
line inaccurate over time.
Anothercomponentofhorizontalchartaccuracyin-
volvesthechartcompilationprocess.Forexample,inthe
U.S.beforeNOAA'ssuiteofchartswasscannedintoraster
formatin1994,allchartcompilationwasperformedmanu-
ally.Projectionlineswereconstructedanddrawnbyhand
andallplottingwasdonerelativetotheselines.Cartogra-
phersgraphicallyreducedlargescalesurveysor
engineeringdrawingstochartscale.Veryoftenthesedraw-
ingswerereferencedtostateplaneorotherlocalcoordinate
systems.Thedatawouldthenbeconvertedtothehorizontal
datumofthechart(e.g.,theNorthAmerican1927(NAD
27)ortheNorthAmericanDatum1983(NAD83).Inthe
late1980'sandearly1990's,NOAAconvertedallofits
chartstoNAD83.Inaccomplishingthistask,averaging
techniqueswereusedandalloftheprojectionlineswerere-
drawn.
WhenNOAAscanneditschartsandmoveditscarto-
graphicproductionintoacomputerenvironment,variations
werenotedbetweenmanuallyconstructedprojectionlines
andthosethatwerecomputergenerated.Alloftheraster
chartswereadjustedorwarpedsothatthemanualprojec-
tionlinesconformedtothecomputer-generatedprojection.
Indoingso,allinformationdisplayedonthechartwas
moved or adjusted.
SimilarprocessestakeplaceduringNIMA’sdigital
chartproduction,butinvolvingmorecomplexity,since
NIMAcartographersmustworkwithavarietyofdifferent
datumsinusethroughouttheworld,andwithhydrographic
datafromhundredsofofficialandunofficialsources.While
muchofNIMA’sincomingdatawascollectedtoIHOstan-
dardsduringhydrographicsurveys,manysourcesare
questionable at best, especially among the older data.
Today,whensurveycrewsandcontractorsobtain
DGPSpositionsonprominentshorelinefeaturesandcom-
parethosepositionstothechart,biasesmaybefoundthat
areontheorderoftwomillimetersatthescaleofthechart
(e.g.,20meterson1:10,000-scalechart).Highaccuracy
aerialphotographyrevealssimilardiscrepanciesbetween
thetrueshorelineandthechartedshoreline.Itstandstorea-
sonthatotherimportantfeaturessuchasdredgedchannel
limitsandnavigationalaidsalsoexhibitthesetypesofbias-
es.Unfortunately,onanygivenchart,themagnitudeand
thedirectionofthesediscrepancieswillvarybyunknown
amountsindifferentareasofthechart.Therefore,nosys-
tematicadjustmentcaneasilybeperformedthatwill
improvetheinherentaccuracyofthepaperorelectronic
chart.
Somemarinershavethemisconceptionthatbecause
chartscanbeviewedonacomputer,theinformationhas
somehowbecomemoreaccuratethanitappearsonpaper.
Somemarinersbelievethatvectordataismoreaccurate
thanpaperorrasterdata.Clearly,ifanelectronicchartda-
tabaseisbuiltbydigitizingapaperchart,itcanbenomore
accurate than the paper chart.
ThemostaccuratewaytocreateanENCistore-com-
pilethechartfromalloftheoriginalsourcematerial.
Unfortunately,theprocessisfartoolaborintensive.Inthe
U.S.,NOAAhasusedoriginalsourcematerialwherepos-
sibletocompilenavigationcriticalinformationsuchasaids
tonavigationandchannellimits.Theremainingdataare
being digitized from the largest scale paper charts.
OnceENC’sarecompiled,theymaybeenhancedwith
higher-accuracydataovertime.High-resolutionshoreline
datamaybeincorporatedintotheENC’sasnewphoto-
grammetricsurveysareconducted.Likewise,depthsfrom
newhydrographicsurveyswillgraduallysupersededepths
that originated from old surveys.
1421. Route Planning and Monitoring
Presumably,routeplanningtakesplacebeforethe
voyagebegins,exceptinsituationswheremajorchangesin
theroutearecalledforwhiletheshipisunderway.Ineither
case,bothECDISandECSwillallowthedisplayofthe
smallestscalechartsoftheoperatingareaandtheselection
ofwaypointsfromthosecharts.ECDISrequiresawarning
thatachosenroutecrossesasafetycontourorprohibited
area;ECSwillnotnecessarilydoso.Ifthedataisraster,
thisfunctionisnotpossible.Oncethewaypointsare
chosen,theycanbesavedasarouteinaseparatefilefor
later reference and output to the autopilot.
Itisagoodideatozoominoneachwaypointifthe
chartscalefromwhichitisselectedisverysmall,sothat
thenavigationalpictureintheareacanbeseenatareason-
ablescale.Also,ifagreatcirclerouteisinvolved,the
softwaremaybeabletoenterthewaypointsdirectlyfrom
thegreatcircleroutefile.Ifnot,theywillhavetobeentered
by hand.
Duringroutemonitoring,ECDISmustshowown
ship’spositionwheneverthedisplaycoversthatarea.Al-
thoughthenavigatormaychoseto“look-ahead”whilein
routemonitoring,itmustbepossibletoreturntoownship’s
positionwithasingleoperatoraction.Keyinformationpro-
214ELECTRONIC CHARTS
videdduringroutemonitoringincludesacontinuous
indicationofvesselposition,course,andspeed.Additional
informationthatECDISorECScanprovideincludesdis-
tanceright/leftofintendedtrack,time-to-turn,distance-to-
turn,positionandtimeof“wheel-over”,andpasttrack
history.
AsspecifiedinAppendix5oftheIMOPerformance
Standard,ECDISmustprovideanindicationofthecondi-
tionofthesystemanditscomponents.Analarmmustbe
providedifthereisaconditionthatrequiresimmediateat-
tention.Anindicationcanbevisual,whileanalarmmust
either be audible, or both audible and visual.
Theoperatorcancontrolcertainsettingsandfunctions,
someofthemostimportantofwhicharetheparametersfor
certain alarms and indications, including:
•Cross-trackerror:Setthedistancetoeithersideof
thetrackthevesselcanstraybeforeanalarmsounds.
Thiswilldependonthephaseofnavigation,weath-
er, and traffic.
•Safetycontour:Setthedepthcontourlinewhichwill
alertthenavigatorthatthevesselisapproaching
shallow water.
•Coursedeviation:Setthenumberofdegreesoff
coursethevessel’sheadingshouldbeallowedto
stray before an alarm sounds.
•Criticalpointapproach:Setthedistancebeforeap-
proachingeachwaypointorothercriticalpointthat
an alarm will sound.
•Datum:Setthedatumofthepositioningsystemto
the datum of the chart, if different.
1422. Waypoints and Routes
Intherouteplanningmode,theECSorECDISwillal-
lowtheentryofwaypointsascoordinatesoflatitudeand
longitude,ortheselectionofwaypointsbymovingacursor
aroundonthecharts.Itwillallowthecreationandstorage
ofnumerouspre-definedroutes,whichcanbecombinedin
various ways to create complex voyages.
Forexample,onemightdefinearoutefromtheinner
harbortotheouterharborofamajorport,arouteforeach
oftwoormorechannelstothesea,andseveralmorefor
opensearoutestodifferentdestinations.Thesecanthenbe
combinedindifferentwaystocreatecomprehensiveroutes
thatwillcompriseentiredock-to-dockvoyages.Theymay
also be run in reverse for the return trip.
Whenselectingwaypoints,takecaretoleaveanyaids
tonavigationmarkingtheroutewelltoonesideofthe
course.Manynavigationalsoftwareprogramscontaindata-
baseslistingthelocationoftheaidstonavigationinthe
UnitedStatesandothercountries.ThislistshouldNOTbe
usedtocreateroutes,becausetheaccuracyoftoday’snav-
igationsystemsisgoodenoughthattodosoinvitesa
collisionwithanyaidwhoseactualpositionisenteredasa
waypoint.Alwaysleaveaprudentamountofroombetween
the waypoint and the aid.
Somepublishedroutesexist,alsoafeatureofcertain
softwareprograms.Thewisenavigatorwillnotusethese
untilhehasverifiedtheexactpositionofeachwaypointus-
ingthebestscalechart.Usingpre-programmedroutesfrom
anunknownsourceisthesameaslettingsomeoneelsenav-
igatoryourvessel.Sucharoutemaypassovershoalwater,
underabridge,orthroughanareathatyourownvessel
mightfindhazardous.Alwayscheckeachwaypoint
personally.
Manyelectronicchartsystemswillalsoallowthecou-
plingofthenavigationsystemtotheautopilot.Technically,
itispossibletoturnthenavigationofthevesselovertothe
autopilotalmostassoonasthevesselisunderway,allowing
theautopilottomakethecoursechangesaccordingtoeach
waypoint.Whilethismaybepossibleforsmallcraftin
mostinland,harborandharborapproachsituations,the
largerthevessel,thelessadvisablethispracticeis,because
autopilotsdonottakeadvanceandtransferintoaccount.
Thelargeshipunderautopilotcontrolwillnotanticipatethe
turninachannel,andwillnotbegintheturnuntiltheanten-
naofthepositioningsystem,presumablyGPSandoften
locatedinthesternoftheship,isattheexactwaypoint.By
thistimeitistoolate,fortheturnshouldlikelyhavebeen
startedatleasttwoshiplengthsprevious.Itisperfectlypru-
denttoallowautopilotcontrolofcoursechangesforvessels
intheopenseaiftheproperparametersformaximumrud-
der angle have been set.
1423. Training and Simulation
In2001,theIMOissuedguidelinesfortrainingwith
ECDISsimulation.TheguidelinesstipulatethatECDIS
trainingshouldincludesimulationoflivedatastreams,as
wellasARPAandAutomatedInformationSystem(AIS)
targetinformation,andaVoyageDataRecorder(VDR)
interface.ButtheIMOhasnotspecificallyrequiredECDIS
trainingotherthanasageneralsubstitutionintheStandards
ofTraining,Certification,andWatchkeeping(STCW)95
code for navigation with paper charts.
Alsoin2001,theUSCGapprovedthecountry’sfirst
STCW-compliantfivedayECDIStrainingcourseinthe
U.S.Long-termSTCW95trainingandeducationprograms
arepresentlyindevelopment.Thetwolevelsofcompeten-
cydefinedbySTCWareoperational(OICor3rdmate/2nd
mate)andmanagement(CCMor1stofficer/Master).Itis
likelythatformarinerssailingsinceAugust1998,training
andeducationinnavigationatboththeOICandCCMlev-
elswillincludethefivedaycompetency-basedECDIS
training course.
Accordingly,certifiedtrainingintheoperationaluseof
ECDISshouldconsistofafivedaycoursemakinguseof
simulationequipmentforareal-timeoperatingenviron-
mentappropriatefortasksinnavigation,watchkeepingand
maneuvering.Theprimarygoalisthatthetraineeshouldbe
ELECTRONIC CHARTS215
abletosmoothlyoperatetheECDISequipment,useallof
itsnavigationalfunctions,selectandassessallrelevantin-
formation,respondcorrectlyinthecaseofamalfunction,
describecommonerrorsofinterpretationanddescribepo-
tentialerrorsofdisplayeddata.Thetraineeshouldfollow
structuredpracticeinthefollowing:settingupandmain-
tainingthedisplay;operationaluseofelectroniccharts
includingupdating,routemonitoring,routeplanning,han-
dlingalarms;workwithmotionparametersandposition
correction;workwithlogrecordsandvoyagefiles;andop-
erateinterfaceswithradar,ARPA,AIStransponders,and
VDR’s.
217
CHAPTER 15
NAVIGATIONAL ASTRONOMY
PRELIMINARY CONSIDERATIONS
1500. Definitions
ThescienceofAstronomystudiesthepositionsand
motionsofcelestialbodiesandseekstounderstandandex-
plaintheirphysicalproperties.Navigationalastronomy
dealswiththeircoordinates,time,andmotions.Thesym-
bolscommonlyrecognizedinnavigationalastronomyare
given in Table 1500.
Table 1500. Astronomical symbols.
218NAVIGATIONAL ASTRONOMY
1501. The Celestial Sphere
Lookingattheskyonadarknight,imaginethatce-
lestialbodiesarelocatedontheinnersurfaceofavast,
Earth-centeredsphere(Figure1501).Thismodelisuse-
fulsinceweareonlyinterestedintherelativepositions
andmotionsofcelestialbodiesonthisimaginarysur-
face.Understandingtheconceptofthecelestialsphereis
mostimportantwhendiscussingsightreductionin
Chapter 20.
1502. Relative and Apparent Motion
Celestialbodiesareinconstantmotion.Thereisno
fixedpositioninspacefromwhichonecanobserve
absolutemotion.Sinceallmotionisrelative,thepositionof
theobservermustbenotedwhendiscussingplanetary
motion.FromtheEarthweseeapparentmotionsof
celestialbodiesonthecelestialsphere.Inconsideringhow
planetsfollowtheirorbitsaroundtheSun,weassumea
hypotheticalobserveratsomedistantpointinspace.When
discussingtherisingorsettingofabodyonalocalhorizon,
wemustlocatetheobserverataparticularpointonthe
EarthbecausethesettingSunforoneobservermaybethe
rising Sun for another.
Motiononthecelestialsphereresultsfromthemotions
inspaceofboththecelestialbodyandtheEarth.Without
specialinstruments,motionstowardandawayfromthe
Earth cannot be discerned.
Figure 1501. The celestial sphere.
NAVIGATIONAL ASTRONOMY219
1503. Astronomical Distances
We can consider the celestial sphere as having an infi-
niteradiusbecausedistancesbetweencelestialbodiesare
sovast.Foranexampleinscale,iftheEarthwererepresent-
edbyaballoneinchindiameter,theMoonwouldbeaball
one-fourthinchindiameteratadistanceof30inches,the
Sunwouldbeaballninefeetindiameteratadistanceof
nearlyafifthofamile,andPlutowouldbeaballhalf
aninchindiameteratadistanceofaboutsevenmiles.
Theneareststarwouldbeone-fifthoftheactualdis-
tance to the Moon.
Becauseofthesizeofcelestialdistances,itisin-
convenienttomeasurethemincommonunitssuchas
themileorkilometer.Themeandistancetoournearest
neighbor,theMoon,is238,855miles.Forconvenience
thisdistanceissometimesexpressedinunitsofthe
equatorial radius of the Earth: 60.27 Earth radii.
Distancesbetweentheplanetsareusuallyexpressedin
termsoftheastronomicalunit(AU),themeandistance
betweentheEarthandtheSun.Thisisapproximately
92,960,000miles.ThusthemeandistanceoftheEarthfrom
theSunis1AU.ThemeandistanceofPluto,theoutermost
knownplanetinoursolarsystem,is39.5A.U.Expressedin
astronomicalunits,themeandistancefromtheEarthtothe
Moon is 0.00257 A.U.
Distancestothestarsrequireanotherleapinunits.A
commonly-usedunitisthelight-year,thedistancelight
travelsinoneyear.Sincethespeedoflightisabout1.86×
10
5
milespersecondandthereareabout3.16×10
7
seconds
peryear,thelengthofonelight-yearisabout5.88×10
12
miles.Theneareststars,AlphaCentaurianditsneighbor
Proxima,are4.3light-yearsaway.Relativelyfewstarsare
lessthan100light-yearsaway.Thenearestgalaxies,the
CloudsofMagellan,are150,000to200,000lightyears
away.Themostdistantgalaxiesobservedbyastronomers
are several billion light years away.
1504. Magnitude
Therelativebrightnessofcelestialbodiesisindicated
byascaleofstellarmagnitudes.Initially,astronomers
dividedthestarsinto6groupsaccordingtobrightness.The
20brightestwereclassifiedasofthefirstmagnitude,and
thedimmestwereofthesixthmagnitude.Inmoderntimes,
whenitbecamedesirabletodefinemorepreciselythelimits
ofmagnitude,afirstmagnitudestarwasconsidered100
timesbrighterthanoneofthesixthmagnitude.Sincethe
fifthrootof100is2.512,thisnumberisconsideredthe
magnituderatio.Afirstmagnitudestaris2.512timesas
brightasasecondmagnitudestar,whichis2.512timesas
brightasathirdmagnitudestar,.Asecondmagnitudeis
2.512×2.512=6.310timesasbrightasafourthmagnitude
star.Afirstmagnitudestaris2.512
20
timesasbrightasa
starofthe21stmagnitude,thedimmestthatcanbeseen
through a 200-inch telescope.
Brightnessisnormallytabulatedtothenearest0.1
magnitude,aboutthesmallestchangethatcanbedetected
bytheunaidedeyeofatrainedobserver.Allstarsof
magnitude1.50orbrighterarepopularlycalled“first
magnitude”stars.Thosebetween1.51and2.50arecalled
“secondmagnitude”stars,thosebetween2.51and3.50are
called“thirdmagnitude”stars,etc.Sirius,thebrighteststar,
hasamagnitudeof–1.6.Theonlyotherstarwithanegative
magnitudeisCanopus,–0.9.AtgreatestbrillianceVenus
hasamagnitudeofabout–4.4.Mars,Jupiter,andSaturnare
sometimesofnegativemagnitude.ThefullMoonhasa
magnitudeofabout–12.6,butvariessomewhat.The
magnitude of the Sun is about –26.7.
THE UNIVERSE
1505. The Solar System
TheSun,themostconspicuouscelestialobjectinthesky,
isthecentralbodyofthesolarsystem.Associatedwithitareat
leastnineprincipalplanetsandthousandsofasteroids,com-
ets, and meteors. Some planets have moons.
1506. Motions of Bodies of the Solar System
Astronomersdistinguishbetweentwoprincipalmo-
tionsofcelestialbodies.Rotationisaspinningmotion
aboutanaxiswithinthebody,whereasrevolutionisthe
motionofabodyinitsorbitaroundanotherbody.Thebody
aroundwhichacelestialobjectrevolvesisknownasthat
body’sprimary.Forthesatellites,theprimaryisaplanet.
Fortheplanetsandotherbodiesofthesolarsystem,thepri-
maryistheSun.Theentiresolarsystemisheldtogetherby
thegravitationalforceoftheSun.Thewholesystemre-
volvesaroundthecenteroftheMilkyWaygalaxy(Article
1515),andtheMilkyWayisinmotionrelativetoitsneigh-
boring galaxies.
Thehierarchiesofmotionsintheuniversearecaused
bytheforceofgravity.Asaresultofgravity,bodiesattract
eachotherinproportiontotheirmassesandtotheinverse
squareofthedistancesbetweenthem.Thisforcecausesthe
planetstogoaroundthesuninnearlycircular,elliptical
orbits.
Ineachplanet’sorbit,thepointnearesttheSunis
calledtheperihelion.ThepointfarthestfromtheSunis
calledtheaphelion.Thelinejoiningperihelionandaph-
elioniscalledthelineofapsides.IntheorbitoftheMoon,
thepointnearesttheEarthiscalledtheperigee,andthat
pointfarthestfromtheEarthiscalledtheapogee.Figure
1506showstheorbitoftheEarth(withexaggeratedeccen-
tricity), and the orbit of the Moon around the Earth.
220NAVIGATIONAL ASTRONOMY
1507. The Sun
TheSundominatesoursolarsystem.Itsmassisnearlya
thousandtimesthatofallotherbodiesofthesolarsystemcom-
bined.Itsdiameterisabout865,000miles.Sinceitisastar,it
generatesitsownenergythroughathermonuclearreaction,
thereby providing heat and light for the entire solar system.
ThedistancefromtheEarthtotheSunvariesfrom
91,300,000atperihelionto94,500,000milesataphelion.
WhentheEarthisatperihelion,whichalwaysoccursearly
inJanuary,theSunappearslargest,32.6'ofarcindiameter.
Sixmonthslaterataphelion,theSun’sapparentdiameteris
a minimum of 31.5'.
ObservationsoftheSun’ssurface(calledthephoto-
sphere)revealsmalldarkareascalledsunspots.Theseare
areasofintensemagneticfieldsinwhichrelativelycoolgas
(at7000°F.)appearsdarkincontrasttothesurroundinghot-
tergas(10,000°F.).Sunspotsvaryinsizefromperhaps
50,000milesindiametertothesmallestspotsthatcanbe
detected(afewhundredmilesindiameter).Theygenerally
appearingroups.SeeFigure1507.Largesunspotscanbe
seen without a telescope if the eyes are protected.
Surroundingthephotosphereisanoutercoronaofvery
hotbuttenuousgas.Thiscanonlybeseenduringaneclipseof
the Sun, when the Moon blocks the light of the photosphere.
TheSuniscontinuouslyemittingchargedparticles,
whichformthesolarwind.Asthesolarwindsweepspast
theEarth,theseparticlesinteractwiththeEarth’smagnetic
field.Ifthesolarwindisparticularlystrong,theinteraction
canproducemagneticstormswhichadverselyaffectradio
signalsontheEarth.Atsuchtimestheaurorasareparticu-
larly brilliant and widespread.
TheSunismovingapproximatelyinthedirectionof
Vegaatabout12milespersecond,orabouttwo-thirdsas
fast as the Earth moves in its orbit around the Sun.
Figure 1506. Orbits of the Earth and Moon.
Figure 1507. Whole solar disk and an enlargement of the
great spot group of April 7, 1947. Courtesy of Mt. Wilson
and Palomar Observatories.
NAVIGATIONAL ASTRONOMY221
1508. The Planets
TheprincipalbodiesorbitingtheSunarecalledplan-
ets.Nineprincipalplanetsareknown:Mercury,Venus,
Earth,Mars,Jupiter,Saturn,Uranus,Neptune,andPluto.
Ofthese,onlyfourarecommonlyusedforcelestialnaviga-
tion: Venus, Mars, Jupiter, and Saturn.
ExceptforPluto,theorbitsoftheplanetslieinnearly
thesameplaneastheEarth’sorbit.Therefore,asseenfrom
theEarth,theplanetsareconfinedtoastripofthecelestial
sphereneartheecliptic,whichistheintersectionofthe
meanplaneoftheEarth’sorbitaroundtheSunwiththece-
lestial sphere.
Thetwoplanetswithorbitssmallerthanthatofthe
Eartharecalledinferiorplanets,andthosewithorbits
largerthanthatoftheEartharecalledsuperiorplanets.
ThefourplanetsnearesttheSunaresometimescalledthe
innerplanets,andtheotherstheouterplanets.Jupiter,
Saturn,Uranus,andNeptunearesomuchlargerthanthe
othersthattheyaresometimesclassedasmajorplanets.
Uranusisbarelyvisibletotheunaidedeye;Neptuneand
Pluto are not visible without a telescope.
Planetscanbeidentifiedintheskybecause,unlikethe
stars,theydonottwinkle.Thestarsaresodistantthatthey
arepointsourcesoflight.Thereforethestreamoflightfrom
astariseasilyscatteredintheatmosphere,causingthe
twinklingeffect.Thenaked-eyeplanets,however,areclose
enoughtopresentperceptibledisks.Thebroaderstreamof
light from a planet is not easily disrupted.
Theorbitsofmanythousandsoftinyminorplanetsor
asteroidsliechieflybetweentheorbitsofMarsandJupiter.
These are all too faint to be seen with the naked eye.
1509. The Earth
Incommonwithotherplanets,theEarthrotatesonits
axisandrevolvesinitsorbitaroundtheSun.Thesemotions
aretheprincipalsourceofthedailyapparentmotionsof
othercelestialbodies.TheEarth’srotationalsocausesa
deflectionofwaterandaircurrentstotherightinthe
NorthernHemisphereandtotheleftintheSouthern
Hemisphere.BecauseoftheEarth’srotation,hightideson
the open sea lag behind the meridian transit of the Moon.
Formostnavigationalpurposes,theEarthcanbe
consideredasphere.However,liketheotherplanets,the
Earthisapproximatelyanoblatespheroid,orellipsoidof
revolution,flattenedatthepolesandbulgedattheequator.
SeeFigure1509.Therefore,thepolardiameterislessthan
theequatorialdiameter,andthemeridiansareslightly
elliptical,ratherthancircular.ThedimensionsoftheEarth
arerecomputedfromtimetotime,asadditionalandmore
precisemeasurementsbecomeavailable.SincetheEarthis
notexactlyanellipsoid,resultsdifferslightlywhenequally
preciseandextensivemeasurementsaremadeondifferent
parts of the surface.
1510. Inferior Planets
SinceMercuryandVenusareinsidetheEarth’sorbit,
theyalwaysappearintheneighborhoodoftheSun.Overa
periodofweeksormonths,theyappeartooscillateback
andforthfromonesideoftheSuntotheother.Theyare
seeneitherintheeasternskybeforesunriseorinthe
westernskyaftersunset.Forbriefperiodstheydisappear
intotheSun’sglare.AtthistimetheyarebetweentheEarth
andSun(knownasinferiorconjunction)oronthe
oppositesideoftheSunfromtheEarth(superior
conjunction).Onrareoccasionsatinferiorconjunction,the
planetwillcrossthefaceoftheSunasseenfromtheEarth.
This is known as atransit of the Sun.
WhenMercuryorVenusappearsmostdistantfromthe
Sunintheeveningsky,itisatgreatesteasternelongation.
(Althoughtheplanetisinthewesternsky,itisatitseast-
ernmostpointfromtheSun.)Fromnighttonighttheplanet
willapproachtheSununtilitdisappearsintotheglareof
twilight.AtthistimeitismovingbetweentheEarthand
Suntoinferiorconjunction.Afewdayslater,theplanetwill
appearinthemorningskyatdawn.Itwillgraduallymove
awayfromtheSuntowesternelongation,thenmoveback
towardtheSun.Afterdisappearinginthemorningtwilight,
itwillmovebehindtheSuntosuperiorconjunction.After
thisitwillreappearintheeveningsky,headingtowardeast-
ern elongation.
Mercuryisneverseenmorethanabout28°fromthe
Sun.Forthisreasonitisnotcommonlyusedfornavigation.
Neargreatestelongationitappearsnearthewesternhorizon
aftersunset,ortheeasternhorizonbeforesunrise.Atthese
timesitresemblesafirstmagnitudestarandissometimes
reportedasaneworstrangeobjectinthesky.Theinterval
duringwhichitappearsasamorningoreveningstarcan
Figure 1509. Oblate spheroid or ellipsoid of revolution.
222NAVIGATIONAL ASTRONOMY
varyfromabout30to50days.Aroundinferiorconjunction,
Mercurydisappearsforabout5days;nearsuperiorcon-
junction,itdisappearsforabout35days.Observedwitha
telescope,Mercuryisseentogothroughphasessimilarto
those of the Moon.
Venuscanreachadistanceof47°fromtheSun,
allowingittodominatethemorningoreveningsky.At
maximumbrilliance,aboutfiveweeksbeforeandafter
inferiorconjunction,ithasamagnitudeofabout–4.4andis
brighterthananyotherobjectintheskyexcepttheSun
andMoon.Atthesetimesitcanbeseenduringthedayand
issometimesobservedforacelestiallineofposition.It
appearsasamorningoreveningstarforapproximately263
daysinsuccession.NearinferiorconjunctionVenus
disappearsfor8days;aroundsuperiorconjunctionit
disappearsfor50days.WhenittransitstheSun,Venuscan
beseenbythenakedeyeasasmalldotaboutthesizeofa
groupofSunspots.Throughstrongbinocularsoratelescope,
Venus can be seen to go through a full set of phases.
1511. Superior Planets
AsplanetsoutsidetheEarth’sorbit,thesuperior
planetsarenotconfinedtotheproximityoftheSunasseen
fromtheEarth.TheycanpassbehindtheSun
(conjunction),buttheycannotpassbetweentheSunandthe
Earth.InsteadweseethemmoveawayfromtheSununtil
theyareoppositetheSuninthesky(opposition).Whena
superiorplanetisnearconjunction,itrisesandsetsapprox-
imatelywiththeSunandisthuslostintheSun’sglare.
Graduallyitbecomesvisibleintheearlymorningsky
beforesunrise.Fromdaytoday,itrisesandsetsearlier,
becomingincreasinglyvisiblethroughthelatenighthours
untildawn.Approachingopposition,theplanetwillrisein
thelateevening,untilatopposition,itwillrisewhenthe
Sunsets,bevisiblethroughoutthenight,andsetwhenthe
Sun rises.
Observedagainstthebackgroundstars,theplanets
normallymoveeastwardinwhatiscalleddirectmotion.
Approachingopposition,however,aplanetwillslowdown,
pause(atastationarypoint),andbeginmovingwestward
(retrogrademotion),untilitreachesthenextstationary
pointandresumesitsdirectmotion.Thisisnotbecausethe
planetismovingstrangelyinspace.Thisrelative,observed
motionresultsbecausethefastermovingEarthiscatching
up with and passing by the slower moving superior planet.
Thesuperiorplanetsarebrightestandclosesttothe
Earthatopposition.Theintervalbetweenoppositionsis
knownasthesynodicperiod.Thisperiodislongestforthe
closestplanet,Mars,andbecomesincreasinglyshorterfor
Figure 1510. Planetary configurations.
NAVIGATIONAL ASTRONOMY223
the outer planets.
UnlikeMercuryandVenus,thesuperiorplanetsdonot
gothroughafullcycleofphases.Theyarealwaysfullor
highly gibbous.
Marscanusuallybeidentifiedbyitsorangecolor.It
canbecomeasbrightasmagnitude–2.8butismoreoften
between–1.0and–2.0atopposition.Oppositionsoccurat
intervalsofabout780days.Theplanetisvisibleforabout
330daysoneithersideofopposition.Nearconjunctionitis
lostfromviewforabout120days.Itstwosatellitescanonly
be seen in a large telescope.
Jupiter,largestoftheknownplanets,normally
outshinesMars,regularlyreachingmagnitude–2.0or
brighteratopposition.Oppositionsoccuratintervalsof
about400days,withtheplanetbeingvisibleforabout180
daysbeforeandafteropposition.Theplanetdisappearsfor
about32daysatconjunction.Foursatellites(ofatotal16
currentlyknown)arebrightenoughtobeseenwith
binoculars.TheirmotionsaroundJupitercanbeobserved
over the course of several hours.
Saturn,theoutermostofthenavigationalplanets,
comestooppositionatintervalsofabout380days.Itis
visibleforabout175daysbeforeandafteropposition,and
disappearsforabout25daysnearconjunction.At
oppositionitbecomesasbrightasmagnitude+0.8to–0.2.
Throughgood,highpoweredbinoculars,Saturnappearsas
elongatedbecauseofitssystemofrings.Atelescopeis
neededtoexaminetheringsinanydetail.Saturnisnow
knowntohaveatleast18satellites,noneofwhichare
visible to the unaided eye.
Uranus,NeptuneandPlutoaretoofainttobeusedfor
navigation;Uranus,ataboutmagnitude5.5,isfaintly
visible to the unaided eye.
1512. The Moon
TheMoonistheonlysatelliteofdirectnavigationalin-
terest.ItrevolvesaroundtheEarthonceinabout27.3days,
asmeasuredwithrespecttothestars.Thisiscalledthesi-
derealmonth.BecausetheMoonrotatesonitsaxiswith
thesameperiodwithwhichitrevolvesaroundtheEarth,the
samesideoftheMoonisalwaysturnedtowardtheEarth.
ThecycleofphasesdependsontheMoon’srevolutionwith
respecttotheSun.Thissynodicmonthisapproximately
29.53days,butcanvaryfromthisaveragebyuptoaquar-
ter of a day during any given month.
Figure 1512. Phases of the Moon. The inner figures of the Moon represent its appearance from the Earth.
224NAVIGATIONAL ASTRONOMY
WhentheMoonisinconjunctionwiththeSun(new
Moon),itrisesandsetswiththeSunandislostintheSun’s
glare.TheMoonisalwaysmovingeastwardatabout12.2°
perday,sothatsometimeafterconjunction(aslittleas16
hours,oraslongastwodays),thethinlunarcrescentcanbe
observedaftersunset,lowinthewest.Forthenextcouple
ofweeks,theMoonwillwax,becomingmorefullyillumi-
nated.Fromdaytoday,theMoonwillrise(andset)later,
becomingincreasinglyvisibleintheeveningsky,until
(about7daysafternewMoon)itreachesfirstquarter,when
theMoonrisesaboutnoonandsetsaboutmidnight.Over
thenextweektheMoonwillriselaterandlaterintheafter-
noonuntilfullMoon,whenitrisesaboutsunsetand
dominatestheskythroughoutthenight.Duringthenext
coupleofweekstheMoonwillwane,risinglaterandlater
atnight.Bylastquarter(aweekafterfullMoon),theMoon
risesaboutmidnightandsetsatnoon.Asitapproachesnew
Moon,theMoonbecomesanincreasinglythincrescent,
andisseenonlyintheearlymorningsky.Sometimebefore
conjunction(16hoursto2daysbeforeconjunction)thethin
crescent will disappear in the glare of morning twilight.
AtfullMoon,theSunandMoonareonoppositesides
oftheecliptic.Therefore,inthewinterthefullMoonrises
early,crossesthecelestialmeridianhighinthesky,andsets
late;astheSundoesinthesummer.Inthesummerthefull
Moonrisesinthesoutheasternpartofthesky(Northern
Hemisphere),remainsrelativelylowinthesky,andsets
alongthesouthwesternhorizonafterashorttimeabovethe
horizon.
Atthetimeoftheautumnalequinox,thepartofthe
eclipticoppositetheSunismostnearlyparalleltothehori-
zon.SincetheeastwardmotionoftheMoonis
approximatelyalongtheecliptic,thedelayinthetimeof
risingofthefullMoonfromnighttonightislessthanat
othertimesoftheyear.ThefullMoonnearesttheautumnal
equinoxiscalledtheHarvestMoon;thefullMoonamonth
later is called theHunter’s Moon. See Figure 1512.
1513. Comets and Meteors
Althoughcometsarenotedasgreatspectaclesofna-
ture,veryfewarevisiblewithoutatelescope.Thosethat
becomewidelyvisibledosobecausetheydeveloplong,
glowingtails.Cometsareswarmsofrelativelysmallsolid
bodiesheldtogetherbygravity.Aroundthenucleus,agas-
eousheadorcomaandtailmayformasthecomet
approachestheSun.ThetailisdirectedawayfromtheSun,
sothatitfollowstheheadwhilethecometisapproaching
theSun,andprecedestheheadwhilethecometisreceding.
Thetotalmassofacometisverysmall,andthetailisso
thinthatstarscaneasilybeseenthroughit.In1910,the
EarthpassedthroughthetailofHalley’scometwithoutno-
ticeable effect.
Comparedtothewell-orderedorbitsoftheplanets,
cometsareerraticandinconsistent.Sometraveleasttowest
andsomewesttoeast,inhighlyeccentricorbitsinclinedat
anyangletotheecliptic.Periodsofrevolutionrangefrom
about3yearstothousandsofyears.Somecometsmay
speedawayfromthesolarsystemaftergainingvelocityas
they pass by Jupiter or Saturn.
Theshort-periodcometslongagolostthegasses
neededtoformatail.Longperiodcomets,suchasHalley’s
comet,aremorelikelytodeveloptails.Thevisibilityofa
cometdependsverymuchonhowcloseitapproachesthe
Earth.In1910,Halley’scometspreadacrossthesky
(Figure1513).Yetwhenitreturnedin1986,theEarthwas
notwellsituatedtogetagoodview,anditwasbarely
visible to the unaided eye.
Meteors,popularlycalledshootingstars,aretiny,
solidbodiestoosmalltobeseenuntilheatedto
incandescencebyairfrictionwhilepassingthroughthe
Earth’satmosphere.Aparticularlybrightmeteoriscalleda
fireball.Onethatexplodesiscalledabolide.Ameteorthat
survivesitstripthroughtheatmosphereandlandsasasolid
particle is called ameteorite.
Vast numbers of meteors exist. An estimated average of
some 1,000,000 meteors large enough to be seen enter the
Earth’s atmosphere each hour, and many times this number un-
doubtedly enter, but are too small to attract attention. The
cosmic dust they create falls to earth in a constant shower.
Meteorshowersoccuratcertaintimesoftheyear
whentheEarthpassesthroughmeteorswarms,the
scatteredremainsofcometsthathavebrokenup.At
thesetimesthenumberofmeteorsobservedismanytimes
the usual number.
Afaintglowsometimesobservedextendingupward
approximatelyalongtheeclipticbeforesunriseandafter
sunsethasbeenattributedtothereflectionofSunlightfrom
quantitiesofthismaterial.Thisglowiscalledzodiacal
light.Afaintglowatthatpointoftheecliptic180°fromthe
Sun is called thegegenschein orcounterglow.
1514. Stars
StarsaredistantSuns,inmanywaysresemblingour
own.LiketheSun,starsaremassiveballsofgasthatcreate
their own energy through thermonuclear reactions.
Althoughstarsdifferinsizeandtemperature,these
differencesareapparentonlythroughanalysisby
astronomers.Somedifferencesincolorarenoticeabletothe
unaidedeye.Whilemoststarsappearwhite,some(thoseof
lowertemperature)haveareddishhue.InOrion,blueRigel
andredBetelgeuse,locatedonoppositesidesofthebelt,
constitute a noticeable contrast.
Thestarsarenotdistributeduniformlyaroundthesky.
Strikingconfigurations,knownasconstellations,were
notedbyancientpeoples,whosuppliedthemwithnames
andmyths.Todayastronomersuseconstellations—88in
all—to identify areas of the sky.
Underidealviewingconditions,thedimmeststarthat
canbeseenwiththeunaidedeyeisofthesixthmagnitude.
Intheentireskythereareabout6,000starsofthis
NAVIGATIONAL ASTRONOMY225
magnitudeorbrighter.Halfofthesearebelowthehorizon
atanytime.Becauseofthegreaterabsorptionoflightnear
thehorizon,wherethepathofaraytravelsforagreater
distancethroughtheatmosphere,notmorethanperhaps
2,500starsarevisibletotheunaidedeyeatanytime.
However,theaveragenavigatorseldomusesmorethan
perhaps 20 or 30 of the brighter stars.
Starswhichexhibitanoticeablechangeofmagnitude
arecalledvariablestars.Astarwhichsuddenlybecomes
severalmagnitudesbrighterandthengraduallyfadesis
calledanova.Aparticularlybrightnovaiscalleda
supernova.
Twostarswhichappeartobeveryclosetogetherare
calledadoublestar.Ifmorethantwostarsareincludedin
thegroup,itiscalledamultiplestar.Agroupofafew
dozentoseveralhundredstarsmovingthroughspace
togetheriscalledanopencluster.ThePleiadesisan
exampleofanopencluster.Therearealsospherically
symmetricclustersofhundredsofthousandsofstarsknown
asglobularclusters.Theglobularclustersarealltoo
distant to be seen with the naked eye.
Acloudypatchofmatterintheheavensiscalleda
nebula.IfitiswithinthegalaxyofwhichtheSunisapart,
itiscalledagalacticnebula;ifoutside,itiscalledan
extragalactic nebula.
Motionofastarthroughspacecanbeclassifiedbyits
vectorcomponents.Thatcomponentinthelineofsightis
calledradialmotion,whilethatcomponentacrosstheline
ofsight,causingastartochangeitsapparentposition
relativetothebackgroundofmoredistantstars,iscalled
proper motion.
1515. Galaxies
Agalaxyisavastcollectionofclustersofstarsand
cloudsofgas.Inagalaxythestarstendtocongregate
ingroupscalledstarcloudsarrangedinlongspiral
arms.Thespiralnatureisbelievedduetorevolutionof
thestarsaboutthecenterofthegalaxy,theinnerstars
revolvingmorerapidlythantheouterones(Figure
1515).
TheEarthislocatedintheMilkyWaygalaxy,a
slowlyspinningdiskmorethan100,000lightyearsin
diameter.AllthebrightstarsintheskyareintheMilky
Way.However,themostdenseportionsofthegalaxy
areseenasthegreat,broadbandthatglowsinthesum-
mernighttimesky.Whenwelooktowardthe
constellationSagittarius,wearelookingtowardthe
Figure 1513. Halley’s Comet; fourteen views, made between April 26 and June 11, 1910.
Courtesy of Mt. Wilson and Palomar Observatories.
226NAVIGATIONAL ASTRONOMY
center of the Milky Way, 30,000 light years away.
Despitetheirsizeandluminance,almostallother
galaxiesaretoofarawaytobeseenwiththeunaided
eye.Anexceptioninthenorthernhemisphereisthe
GreatGalaxy(sometimescalledtheGreatNebula)in
Andromeda,whichappearsasafaintglow.Inthe
southernhemisphere,theLargeandSmallMagellanic
Clouds(namedafterFerdinandMagellan)arethenear-
estknownneighborsoftheMilkyWay.Theyare
approximately1,700,000lightyearsdistant.TheMa-
gellanicCloudscanbeseenassizableglowingpatches
in the southern sky.
APPARENT MOTION
1516. Apparent Motion due to Rotation of the Earth
ApparentmotioncausedbytheEarth’srotationis
muchgreaterthananyotherobservedmotionofcelestial
bodies.Itisthismotionthatcausescelestialbodiesto
appeartorisealongtheeasternhalfofthehorizon,climbto
maximumaltitudeastheycrossthemeridian,andsetalong
thewesternhorizon,ataboutthesamepointrelativetodue
westastherisingpointwastodueeast.Thisapparent
motionalongthedailypath,ordiurnalcircle,ofthebody
isapproximatelyparalleltotheplaneoftheequator.It
wouldbeexactlysoifrotationoftheEarthweretheonly
motionandtheaxisofrotationoftheEarthwerestationary
in space.
TheapparenteffectduetorotationoftheEarthvaries
withthelatitudeoftheobserver.Attheequator,wherethe
equatorialplaneisvertical(sincetheaxisofrotationofthe
Earthisparalleltotheplaneofthehorizon),bodiesappear
toriseandsetvertically.Everycelestialbodyisabovethe
horizonapproximatelyhalfthetime.Thecelestialsphereas
seenbyanobserverattheequatoriscalledtherightsphere,
shown in Figure 1516a.
Foranobserveratoneofthepoles,bodieshaving
constantdeclinationneitherrisenorset(neglecting
precessionoftheequinoxesandchangesinrefraction),but
circlethesky,alwaysatthesamealtitude,makingone
completetriparoundthehorizoneachday.AttheNorth
Polethemotionisclockwise,andattheSouthPoleitis
counterclockwise.Approximatelyhalfthestarsarealways
abovethehorizonandtheotherhalfneverare.Theparallel
sphere at the poles is illustrated in Figure 1516b.
Betweenthesetwoextremes,theapparentmotionisa
combinationofthetwo.Onthisobliquesphere,illustrated
inFigure1516c,circumpolarcelestialbodiesremainabove
thehorizonduringtheentire24hours,circlingtheelevated
celestialpoleeachday.ThestarsofUrsaMajor(theBig
Dipper)andCassiopeiaarecircumpolarformanyobservers
in the United States.
Anapproximatelyequalpartofthecelestialspherere-
mainsbelowthehorizonduringtheentireday.For
example,CruxisnotvisibletomostobserversintheUnited
States.Otherbodiesriseobliquelyalongtheeasternhori-
zon,climbtomaximumaltitudeatthecelestialmeridian,
andsetalongthewesternhorizon.Thelengthoftimeabove
thehorizonandthealtitudeatmeridiantransitvarywith
boththelatitudeoftheobserverandthedeclinationofthe
body.AtthepolarcirclesoftheEartheventheSunbe-
comescircumpolar.ThisisthelandofthemidnightSun,
wheretheSundoesnotsetduringpartofthesummerand
does not rise during part of the winter.
Theincreasedobliquityathigherlatitudesexplains
whydaysandnightsarealwaysaboutthesamelengthinthe
tropics,andthechangeoflengthofthedaybecomesgreater
aslatitudeincreases,andwhytwilightlastslongerinhigher
latitudes.Eveningtwilightstartsatsunset,andmorning
twilightendsatsunrise.Thedarkerlimitoftwilightoccurs
whenthecenteroftheSunisastatednumberofdegreesbe-
lowthecelestialhorizon.Threekindsoftwilightare
Figure 1515. Spiral nebula Messier 51, In Canes Venetici.
Satellite nebula is NGC 5195.
Courtesy of Mt. Wilson and Palomar Observatories.
NAVIGATIONAL ASTRONOMY227
Figure 1516a. The right sphere.Figure 1516b. The parallel sphere.
Figure 1516c. The oblique sphere at latitude 40°N.Figure 1516d. The various twilight at latitude 20°N and
latitude 60°N.
TwilightLighter limitDarker limitAt darker limit
civil–0°50'–6°Horizon clear; bright stars visible
nautical–0°50'–12°Horizon not visible
astronomical–0°50'–18°Full night
Table 1516. Limits of the three twilights.
228NAVIGATIONAL ASTRONOMY
defined: civil, nautical and astronomical. See Table 1516.
Theconditionsatthedarkerlimitarerelativeandvary
considerably under different atmospheric conditions.
InFigure1516d,thetwilightbandisshown,withthe
darkerlimitsofthevariouskindsindicated.Thenearlyver-
ticalcelestialequatorlineisforanobserveratlatitude
20°N.Thenearlyhorizontalcelestialequatorlineisforan
observeratlatitude60°N.Thebrokenlineineachcaseis
thediurnalcircleoftheSunwhenitsdeclinationis15°N.
Therelativedurationofanykindoftwilightatthetwolat-
itudesisindicatedbytheportionofthediurnalcircle
betweenthehorizonandthedarkerlimit,althoughitisnot
directlyproportionaltotherelativelengthoflineshown
sincetheprojectionisorthographic.Thedurationoftwi-
lightatthehigherlatitudeislonger,proportionally,than
shown.Notethatcompletedarknessdoesnotoccuratlati-
tude 60°N when the declination of the Sun is 15°N.
1517. Apparent Motion due to Revolution of the Earth
IfitwerepossibletostoptherotationoftheEarthso
thatthecelestialspherewouldappearstationary,theeffects
oftherevolutionoftheEarthwouldbecomemore
noticeable.InoneyeartheSunwouldappeartomakeone
completetriparoundtheEarth,fromwesttoeast.Hence,it
wouldseemtomoveeastwardalittlelessthan1°perday.
Thismotioncanbeobservedbywatchingthechanging
positionoftheSunamongthestars.ButsincebothSunand
starsgenerallyarenotvisibleatthesametime,abetterway
istoobservetheconstellationsatthesametimeeachnight.
Onanynightastarrisesnearlyfourminutesearlierthanon
thepreviousnight.Thus,thecelestialsphereappearsto
shiftwestwardnearly1°eachnight,sothatdifferent
constellationsareassociatedwithdifferentseasonsofthe
year.
ApparentmotionsofplanetsandtheMoonareduetoa
combinationoftheirmotionsandthoseoftheEarth.Ifthe
rotationoftheEarthwerestopped,thecombinedapparent
motionduetotherevolutionsoftheEarthandotherbodies
wouldbesimilartothatoccurringifbothrotationand
revolutionoftheEarthwerestopped.Starswouldappear
nearlystationaryintheskybutwouldundergoasmallannual
cycleofchangeduetoaberration.ThemotionoftheEarthin
itsorbitissufficientlyfasttocausethelightfromstarsto
appeartoshiftslightlyinthedirectionoftheEarth’smotion.
Thisissimilartotheeffectoneexperienceswhenwalkingin
vertically-fallingrainthatappearstocomefromaheaddueto
theobserver’sownforwardmotion.Theapparentdirectionof
thelightrayfromthestaristhevectordifferenceofthemotion
oflightandthemotionoftheEarth,similartothatofapparent
windonamovingvessel.Thiseffectismostapparentfora
bodyperpendiculartothelineoftraveloftheEarthinitsorbit,
forwhichitreachesamaximumvalueof20.5".Theeffectof
aberrationcanbenotedbycomparingthecoordinates
(declinationandsiderealhourangle)ofvariousstars
throughouttheyear.Achangeisobservedinsomebodiesas
theyearprogresses,butattheendoftheyearthevalueshave
returnedalmosttowhattheywereatthebeginning.Thereason
theydonotreturnexactlyisduetopropermotionand
precessionoftheequinoxes.Itisalsoduetonutation,an
irregularityinthemotionoftheEarthduetothedisturbing
effectofothercelestialbodies,principallytheMoon.Polar
motionisaslightwobblingoftheEarthaboutitsaxisof
rotationandsometimeswanderingofthepoles.Thismotion,
whichdoesnotexceed40feetfromthemeanposition,
producesslightvariationoflatitudeandlongitudeofplaceson
the Earth.
1518. Apparent Motion due to Movement of other
Celestial Bodies
Evenifitwerepossibletostopboththerotationand
revolutionoftheEarth,celestialbodieswouldnotappear
stationaryonthecelestialsphere.TheMoonwouldmake
onerevolutionabouttheEartheachsiderealmonth,rising
inthewestandsettingintheeast.Theinferiorplanets
wouldappeartomoveeastwardandwestwardrelativeto
theSun,stayingwithinthezodiac.Superiorplanetswould
appeartomakeonerevolutionaroundtheEarth,fromwest
to east, each sidereal period.
SincetheSun(andtheEarthwithit)andallotherstars
areinmotionrelativetoeachother,slowapparentmotions
wouldresultinslightchangesinthepositionsofthestars
relativetoeachother.Thisspacemotionis,infact,observed
bytelescope.Thecomponentofsuchmotionacrosstheline
ofsight,calledpropermotion,producesachangeinthe
apparentpositionofthestar.Themaximumwhichhasbeen
observedisthatofBarnard’sStar,whichismovingattherate
of10.3secondsperyear.Thisisatenth-magnitudestar,not
visibletotheunaidedeye.Ofthe57starslistedonthedaily
pagesofthealmanacs,RigilKentaurushasthegreatest
propermotion,about3.7secondsperyear.Arcturus,with2.3
secondsperyear,hasthegreatestpropermotionofthe
navigationalstarsintheNorthernHemisphere.Inafew
thousandyearspropermotionwillbesufficienttomaterially
altersomefamiliarconfigurationsofstars,notablyUrsa
Major.
1519. The Ecliptic
TheeclipticisthepaththeSunappearstotakeamong
thestarsduetotheannualrevolutionoftheEarthinitsor-
bit.Itisconsideredagreatcircleofthecelestialsphere,
inclinedatanangleofabout23°26'tothecelestialequator,
butundergoingacontinuousslightchange.Thisangleis
calledtheobliquityoftheecliptic.Thisinclinationisdue
tothefactthattheaxisofrotationoftheEarthisnotperpen-
diculartoitsorbit.ItisthisinclinationwhichcausestheSun
toappeartomovenorthandsouthduringtheyear,giving
theEarthitsseasonsandchanginglengthsofperiodsof
daylight.
RefertoFigure1519a.TheEarthisatperihelionearly
NAVIGATIONAL ASTRONOMY229
inJanuaryandataphelion6monthslater.OnoraboutJune
21,about10or11daysbeforereachingaphelion,the
northernpartoftheEarth’saxisistiltedtowardtheSun.
ThenorthpolarregionsarehavingcontinuousSunlight;the
NorthernHemisphereishavingitssummerwithlong,
warmdaysandshortnights;theSouthernHemisphereis
havingwinterwithshortdaysandlong,coldnights;andthe
southpolarregionisincontinuousdarkness.Thisisthe
summersolstice.Threemonthslater,aboutSeptember23,
theEarthhasmovedaquarterofthewayaroundtheSun,
butitsaxisofrotationstillpointsinaboutthesame
directioninspace.TheSunshinesequallyonboth
hemispheres,anddaysandnightsarethesamelengthover
theentireworld.TheSunissettingattheNorthPoleand
risingattheSouthPole.TheNorthernHemisphereis
havingitsautumn,andtheSouthernHemisphereitsspring.
Thisistheautumnalequinox.Inanotherthreemonths,on
oraboutDecember22,theSouthernHemisphereistilted
towardtheSunandconditionsarethereverseofthosesix
monthsearlier;theNorthernHemisphereishavingits
winter,andtheSouthernHemisphereitssummer.Thisis
thewintersolstice.Threemonthslater,whenboth
hemispheresagainreceiveequalamountsofSunshine,the
NorthernHemisphereishavingspringandtheSouthern
Hemisphereautumn,thereverseofconditionssixmonths
before. This is thevernal equinox.
Theword“equinox,”meaning“equalnights,”is
appliedbecauseitoccursatthetimewhendaysandnights
areofapproximatelyequallengthallovertheEarth.The
word“solstice,”meaning“Sunstandsstill,”isapplied
becausetheSunstopsitsapparentnorthwardorsouthward
motionandmomentarily“standsstill”beforeitstartsinthe
oppositedirection.Thisaction,somewhatanalogoustothe
“stand”ofthetide,referstothemotioninanorth-south
directiononly,andnottothedailyapparentrevolution
aroundtheEarth.NotethatitdoesnotoccurwhentheEarth
isatperihelionoraphelion.RefertoFigure1519a.Atthe
timeofthevernalequinox,theSunisdirectlyoverthe
equator,crossingfromtheSouthernHemispheretothe
NorthernHemisphere.Itrisesdueeastandsetsduewest,
remainingabovethehorizonforapproximately12hours.It
isnotexactly12hoursbecauseofrefraction,semidiameter,
andtheheightoftheeyeoftheobserver.Thesecauseitto
beabovethehorizonalittlelongerthanbelowthehorizon.
Followingthevernalequinox,thenortherlydeclination
increases,andtheSunclimbshigherintheskyeachday(at
thelatitudesoftheUnitedStates),untilthesummer
solstice,whenadeclinationofabout23°26'northofthe
celestialequatorisreached.TheSunthengraduallyretreats
southwarduntilitisagainovertheequatorattheautumnal
equinox,atabout23°26'southofthecelestialequatoratthe
wintersolstice,andbackoverthecelestialequatoragainat
the next vernal equinox.
TheEarthisnearesttheSunduringthenorthernhemi-
spherewinter.ItisnotthedistancebetweentheEarthand
Sunthatisresponsibleforthedifferenceintemperature
duringthedifferentseasons,butthealtitudeoftheSunin
theskyandthelengthoftimeitremainsabovethehorizon.
Figure 1519a. Apparent motion of the Sun in the ecliptic.
230NAVIGATIONAL ASTRONOMY
Duringthesummertheraysaremorenearlyvertical,and
hencemoreconcentrated,asshowninFigure1519b.Since
theSunisabovethehorizonmorethanhalfthetime,heat
isbeingaddedbyabsorptionduringalongerperiodthanit
isbeinglostbyradiation.Thisexplainsthelagofthesea-
sons.Followingthelongestday,theEarthcontinuesto
receivemoreheatthanitdissipates,butatadecreasingpro-
portion.Graduallytheproportiondecreasesuntilabalance
isreached,afterwhichtheEarthcools,losingmoreheat
thanitgains.Thisisanalogoustotheday,whenthehighest
temperaturesnormallyoccurseveralhoursaftertheSun
reachesmaximumaltitudeatmeridiantransit.Asimilarlag
occursatotherseasonsoftheyear.Astronomically,thesea-
sonsbeginattheequinoxesandsolstices.Meteorologically,
they differ from place to place.
SincetheEarthtravelsfasterwhennearesttheSun,the
northernhemisphere(astronomical)winterisshorterthan
its summer by about seven days.
Everywherebetweentheparallelsofabout23°26'Nand
about23°26'StheSunisdirectlyoverheadatsometime
duringtheyear.Exceptattheextremes,thisoccurstwice:
onceastheSunappearstomovenorthward,andthesecond
timeasitmovessouthward.Thisisthetorridzone.The
northernlimitistheTropicofCancer,andthesouthern
limitistheTropicofCapricorn.Thesenamescomefrom
theconstellationswhichtheSunenteredatthesolstices
whenthenameswerefirstappliedmorethan2,000years
ago.Today,theSunisinthenextconstellationtowardthe
westbecauseofprecessionoftheequinoxes.Theparallels
about23°26'fromthepoles,markingtheapproximatelimits
ofthecircumpolarSun,arecalledpolarcircles,theonein
theNorthernHemispherebeingtheArcticCircleandthe
oneintheSouthernHemispheretheAntarcticCircle.The
areasinsidethepolarcirclesarethenorthandsouthfrigid
zones.Theregionsbetweenthefrigidzonesandthetorrid
zones are the north and southtemperate zones.
Theexpression“vernalequinox”andassociated
expressionsareappliedbothtothetimesandpointsof
occurrenceofthevariousphenomena.Navigationally,the
vernalequinoxissometimescalledthefirstpointofAries
(symbol)because,whenthenamewasgiven,theSun
enteredtheconstellationAries,theram,atthistime.This
pointisofinteresttonavigatorsbecauseitistheoriginfor
measuringsiderealhourangle.TheexpressionsMarch
equinox,Junesolstice,Septemberequinox,andDecember
solsticeareoccasionallyappliedasappropriate,becausethe
morecommonnamesareassociatedwiththeseasonsinthe
NorthernHemisphereandaresixmonthsoutofstepforthe
Southern Hemisphere.
TheaxisoftheEarthisundergoingaprecessional
motionsimilartothatofatopspinningwithitsaxistilted.
Inabout25,800yearstheaxiscompletesacycleandreturns
tothepositionfromwhichitstarted.Sincethecelestial
equatoris90°fromthecelestialpoles,ittooismoving.The
resultisaslowwestwardmovementoftheequinoxesand
solstices,whichhasalreadycarriedthemabout30°,orone
constellation,alongtheeclipticfromthepositionsthey
occupiedwhennamedmorethan2,000yearsago.Since
siderealhourangleismeasuredfromthevernalequinox,
anddeclinationfromthecelestialequator,thecoordinates
ofcelestialbodieswouldbechangingevenifthebodies
themselveswerestationary.Thiswestwardmotionofthe
equinoxesalongtheeclipticiscalledprecessionofthe
equinoxes.Thetotalamount,calledgeneralprecession,is
about50secondsofarcperyear.Itmaybeconsidered
dividedintotwocomponents:precessioninrightascension
(about46.10secondsperyear)measuredalongthecelestial
equator,andprecessionindeclination(about20.04"per
year)measuredperpendiculartothecelestialequator.The
annualchangeinthecoordinatesofanygivenstar,dueto
precessionalone,dependsuponitspositiononthecelestial
sphere,sincethesecoordinatesaremeasuredrelativetothe
polaraxiswhiletheprecessionalmotionisrelativetothe
ecliptic axis.
Duetoprecessionoftheequinoxes,thecelestial
polesareslowlydescribingcirclesinthesky.Thenorth
celestialpoleismovingclosertoPolaris,whichitwill
passatadistanceofapproximately28minutesaboutthe
year2102.Followingthis,thepolardistancewill
increase,andeventuallyotherstars,intheirturn,will
become the Pole Star.
TheprecessionoftheEarth’saxisistheresultof
gravitationalforcesexertedprincipallybytheSunand
MoonontheEarth’sequatorialbulge.ThespinningEarth
respondstotheseforcesinthemannerofagyroscope.
Regressionofthenodesintroducescertainirregularities
knownasnutationintheprecessionalmotion.SeeFigure
1519c.
Figure 1519b. Sunlight in summer and winter. Winter
sunlightisdistributedoveralargerareaandshinesfewer
hours each day, causing less heat energy to reach the
Earth.
NAVIGATIONAL ASTRONOMY231
1520. The Zodiac
Thezodiacisacircularbandoftheskyextending8°
oneachsideoftheecliptic.Thenavigationalplanetsand
theMoonarewithintheselimits.Thezodiacisdividedinto
12sectionsof30°each,eachsectionbeinggiventhename
andsymbol(“sign”)ofaconstellation.Theseareshownin
Figure1520.Thenameswereassignedmorethan2,000
yearsago,whentheSunenteredAriesatthevernal
equinox,Canceratthesummersolstice,Libraatthe
autumnalequinox,andCapricornusatthewintersolstice.
Becauseofprecession,thezodiacalsignshaveshiftedwith
respecttotheconstellations.Thusatthetimeofthevernal
equinox,theSunissaidtobeatthe“firstpointofAries,”
though it is in the constellation Pisces.
Figure 1519c. Precession and nutation.
232NAVIGATIONAL ASTRONOMY
1521. Time and the Calendar
Traditionally,astronomyhasfurnishedthebasisfor
measurementoftime,asubjectofprimaryimportanceto
thenavigator.Theyearisassociatedwiththerevolutionof
theEarthinitsorbit.ThedayisonerotationoftheEarth
about its axis.
ThedurationofonerotationoftheEarthdependsupon
theexternalreferencepointused.Onerotationrelativeto
theSuniscalledasolarday.However,rotationrelativeto
theapparentSun(theactualSunthatappearsinthesky)
doesnotprovidetimeofuniformratebecauseofvariations
intherateofrevolutionandrotationoftheEarth.Theerror
duetolackofuniformrateofrevolutionisremovedby
usingafictitiousmeanSun.Thus,meansolartimeis
nearlyequaltotheaverageapparentsolartime.Becausethe
accumulateddifferencebetweenthesetimes,calledthe
equationoftime,iscontinuallychanging,theperiodof
daylightisshiftingslightly,inadditiontoitsincreaseor
decreaseinlengthduetochangingdeclination.Apparent
andmeanSunsseldomcrossthecelestialmeridianatthe
sametime.Theearliestsunset(inlatitudesoftheUnited
States)occursabouttwoweeksbeforethewintersolstice,
andthelatestsunriseoccursabouttwoweeksafterwinter
solstice.Asimilarbutsmallerapparentdiscrepancyoccurs
at the summer solstice.
UniversalTimeisaparticularcaseofthemeasure
knowningeneralasmeansolartime.UniversalTimeisthe
meansolartimeontheGreenwichmeridian,reckonedin
daysof24meansolarhoursbeginningwith0hoursat
midnight.UniversalTimeandsiderealtimearerigorously
relatedbyaformulasothatifoneisknowntheothercanbe
found.UniversalTimeisthestandardintheapplicationof
astronomy to navigation.
Ifthevernalequinoxisusedasthereference,a
siderealdayisobtained,andfromit,siderealtime.This
indicatestheapproximatepositionsofthestars,andforthis
reasonitisthebasisofstarchartsandstarfinders.Because
oftherevolutionoftheEartharoundtheSun,asiderealday
isabout3minutes56secondsshorterthanasolarday,and
thereisonemoresiderealthansolardaysinayear.One
meansolardayequals1.00273791meansiderealdays.
Becauseofprecessionoftheequinoxes,onerotationofthe
Earthwithrespecttothestarsisnotquitethesameasone
rotationwithrespecttothevernalequinox.Onemeansolar
dayaverages1.0027378118868rotationsoftheEarthwith
respect to the stars.
Intideanalysis,theMoonissometimesusedasthe
reference,producingalunardayaveraging24hours50
minutes (mean solar units) in length, and lunar time.
Sinceeachkindofdayisdividedarbitrarilyinto24
hours,eachhourhaving60minutesof60seconds,the
lengthofeachoftheseunitsdifferssomewhatinthevarious
kinds of time.
Timeisalsoclassifiedaccordingtotheterrestrial
meridianusedasareference.Localtimeresultsifone’s
Figure 1520. The zodiac.
NAVIGATIONAL ASTRONOMY233
ownmeridianisused,zonetimeifanearbyreference
meridianisusedoveraspreadoflongitudes,and
GreenwichorUniversalTimeiftheGreenwichmeridian
is used.
Theperiodfromonevernalequinoxtothenext(the
cycleoftheseasons)isknownasthetropicalyear.Itis
approximately365days,5hours,48minutes,45seconds,
thoughthelengthhasbeenslowlychangingformany
centuries.Ourcalendar,theGregoriancalendar,approx-
imatesthetropicalyearwithacombinationofcommon
yearsof365daysandleapyearsof366days.Aleapyearis
anyyeardivisiblebyfour,unlessitisacenturyyear,which
mustbedivisibleby400tobealeapyear.Thus,1700,
1800,and1900werenotleapyears,but2000was.A
criticalmistakewasmadebyJohnHamiltonMoorein
calling1800aleapyear,causinganerrorinthetablesinhis
book,ThePracticalNavigator.Thiserrorcausedthelossof
atleastoneshipandwaslaterdiscoveredbyNathaniel
BowditchwhilewritingthefirsteditionofTheNew
American Practical Navigator.
See Chapter 18 for an in-depth discussion of time.
1522. Eclipses
IftheorbitoftheMooncoincidedwiththeplaneofthe
ecliptic,theMoonwouldpassinfrontoftheSunatevery
newMoon,causingasolareclipse.AtfullMoon,theMoon
wouldpassthroughtheEarth’sshadow,causingalunar
eclipse.BecauseoftheMoon’sorbitisinclined5°with
respecttotheecliptic,theMoonusuallypassesaboveor
belowtheSunatnewMoonandaboveorbelowtheEarth’s
shadowatfullMoon.However,therearetwopointsat
whichtheplaneoftheMoon’sorbitintersectstheecliptic.
ThesearethenodesoftheMoon’sorbit.IftheMoonpasses
oneofthesepointsatthesametimeastheSun,asolar
eclipse takes place. This isshown in Figure 1522.
TheSunandMoonareofnearlythesameapparentsize
toanobserverontheEarth.IftheMoonisatperigee,the
Moon’sapparentdiameterislargerthanthatoftheSun,and
itsshadowreachestheEarthasanearlyrounddotonlya
fewmilesindiameter.Thedotmovesrapidlyacrossthe
Earth,fromwesttoeast,astheMooncontinuesinitsorbit.
Withinthedot,theSuniscompletelyhiddenfromview,
andatotaleclipseoftheSunoccurs.Foraconsiderable
distancearoundtheshadow,partofthesurfaceoftheSun
isobscured,andapartialeclipseoccurs.Inthelineof
traveloftheshadowapartialeclipseoccursastheround
diskoftheMoonappearstomoveslowlyacrossthesurface
oftheSun,hidinganever-increasingpartofit,untilthe
totaleclipseoccurs.Becauseoftheunevenedgeofthe
mountainousMoon,thelightisnotcutoffevenly.But
severallastilluminatedportionsappearthroughthevalleys
orpassesbetweenthemountainpeaks.Thesearecalled
Baily’s Beads.
Atotaleclipseisaspectacularphenomenon.Asthelast
lightfromtheSuniscutoff,thesolarcorona,orenvelope
ofthin,illuminatedgasaroundtheSunbecomesvisible.
Wispsofmoredensegasmayappearassolar
prominences.Theonlylightreachingtheobserveristhat
diffusedbytheatmospheresurroundingtheshadow.Asthe
MoonappearstocontinueonacrossthefaceoftheSun,the
Sunfinallyemergesfromtheotherside,firstasBaily’s
Beads,andthenasaneverwideningcrescentuntilnopart
of its surface is obscured by the Moon.
Thedurationofatotaleclipsedependsuponhow
nearlytheMooncrossesthecenteroftheSun,thelocation
oftheshadowontheEarth,therelativeorbitalspeedsofthe
MoonandEarth,and(principally)therelativeapparent
diametersoftheSunandMoon.Themaximumlengththat
can occur is a little more than seven minutes.
IftheMoonisnearapogee,itsapparentdiameterisless
thanthatoftheSun,anditsshadowdoesnotquitereachthe
Earth.OverasmallareaoftheEarthdirectlyinlinewiththe
MoonandSun,theMoonappearsasablackdiskalmost
coveringthesurfaceoftheSun,butwithathinringofthe
Sunarounditsedge.Thisannulareclipseoccursalittle
more often than a total eclipse.
IftheshadowoftheMoonpassesclosetotheEarth,
butnotdirectlyinlinewithit,apartialeclipsemayoccur
without a total or annular eclipse.
AneclipseoftheMoon(orlunareclipse)occurswhen
theMoonpassesthroughtheshadowoftheEarth,asshown
inFigure1522.SincethediameteroftheEarthisabout3
1
/
2
timesthatoftheMoon,theEarth’sshadowatthedistance
oftheMoonismuchlargerthanthatoftheMoon.Atotal
eclipseoftheMooncanlastnearly1
3
/
4
hours,andsome
partoftheMoonmaybeintheEarth’sshadowforalmost
4 hours.
Figure 1522. Eclipses of the Sun and Moon.
234NAVIGATIONAL ASTRONOMY
DuringatotalsolareclipsenopartoftheSunisvisible
becausetheMoonisinthelineofsight.Butduringalunar
eclipsesomelightdoesreachtheMoon,diffractedbythe
atmosphereoftheEarth,andhencetheeclipsedfullMoon
isvisibleasafaintreddishdisk.Alunareclipseisvisible
overtheentirehemisphereoftheEarthfacingtheMoon.
Anyone who can see the Moon can see the eclipse.
Duringanyoneyeartheremaybeasmanyasfive
eclipsesoftheSun,andalwaysthereareatleasttwo.There
maybeasmanyasthreeeclipsesoftheMoon,ornone.The
totalnumberofeclipsesduringasingleyeardoesnotexceed
seven,andcanbeasfewastwo.Therearemoresolarthan
lunareclipses,butthelattercanbeseenmoreoftenbecause
of the restricted areas over which solar eclipses are visible.
TheSun,Earth,andMoonarenearlyalignedonthe
lineofnodestwiceeacheclipseyearof346.6days.Thisis
lessthanacalendaryearbecauseofregressionofthe
nodes.Inalittlemorethan18yearsthelineofnodes
returnstoapproximatelythesamepositionwithrespectto
theSun,Earth,andMoon.Duringanalmostequalperiod,
calledthesaros,acycleofeclipsesoccurs.Duringthe
followingsarosthecycleisrepeatedwithonlyminor
differences.
COORDINATES
1523. Latitude And Longitude
Latitudeandlongitudearecoordinatesusedtolocate
positionsontheEarth.Thisarticlediscussesthreedifferent
definitions of these coordinates.
Astronomiclatitudeistheangle(ABQ,Figure1523)
betweenalineinthedirectionofgravity(AB)atastation
andtheplaneoftheequator(QQ').Astronomiclongitude
istheanglebetweentheplaneofthecelestialmeridianata
stationandtheplaneofthecelestialmeridianatGreenwich.
Thesecoordinatesarecustomarilyfoundbymeansofceles-
tialobservations.IftheEarthwereperfectlyhomogeneous
andround,thesepositionswouldbeconsistentandsatisfac-
tory.However,becauseofdeflectionoftheverticaldueto
unevendistributionofthemassoftheEarth,linesofequal
astronomiclatitudeandlongitudearenotcircles,although
theirregularitiesaresmall.IntheUnitedStatestheprime
verticalcomponent(affectinglongitude)maybealittle
morethan18",andthemeridionalcomponent(affecting
latitude) as much as 25".
Geodeticlatitudeistheangle(ACQ,Figure1523)be-
tweenanormaltothespheroid(AC)atastationandthe
planeofthegeodeticequator(QQ').Geodeticlongitudeis
theanglebetweentheplanedefinedbythenormaltothe
spheroidandtheaxisoftheEarthandtheplaneofthegeo-
deticmeridianatGreenwich.Thesevaluesareobtained
whenastronomicallatitudeandlongitudearecorrectedfor
deflectionofthevertical.Thesecoordinatesareusedfor
chartingandarefrequentlyreferredtoasgeographiclati-
tudeandgeographiclongitude,althoughthese
expressionsaresometimesusedtorefertoastronomical
latitude.
Geocentriclatitudeistheangle(ADQ,Figure1523)
atthecenteroftheellipsoidbetweentheplaneofitsequator
(QQ')andastraightline(AD)toapointonthesurfaceof
theEarth.Thisdiffersfromgeodeticlatitudebecausethe
Earthisaspheroidratherthanasphere,andthemeridians
areellipses.Sincetheparallelsoflatitudeareconsideredto
becircles,geodeticlongitudeisgeocentric,andaseparate
expressionisnotused.Thedifferencebetweengeocentric
andgeodeticlatitudesisamaximumofabout11.6'atlati-
tude 45°.
Becauseoftheoblateshapeoftheellipsoid,thelength
ofadegreeofgeodeticlatitudeisnoteverywherethesame,
increasingfromabout59.7nauticalmilesattheequatorto
about60.3nauticalmilesatthepoles.Thevalueof60
nauticalmilescustomarilyusedbythenavigatoriscorrect
at about latitude 45°.
MEASUREMENTS ON THE CELESTIAL SPHERE
1524. Elements of the Celestial Sphere
Thecelestialsphere(Article1501)isanimaginary
sphereofinfiniteradiuswiththeEarthatitscenter(Figure
1524a).Thenorthandsouthcelestialpolesofthissphere
arelocatedbyextensionoftheEarth’saxis.Thecelestial
equator(sometimescalledequinoctial)isformedbypro-
jectingtheplaneoftheEarth’sequatortothecelestial
sphere.Acelestialmeridianisformedbytheintersection
oftheplaneofaterrestrialmeridianandthecelestial
sphere.Itisthearcofagreatcirclethroughthepolesofthe
celestial sphere.
Figure 1523. Three kinds of latitude at point A.
NAVIGATIONAL ASTRONOMY235
Thepointonthecelestialsphereverticallyoverheadof
anobserveristhezenith,andthepointontheoppositeside
ofthesphereverticallybelowhimisthenadir.Thezenith
andnadiraretheextremitiesofadiameterofthecelestial
spherethroughtheobserverandthecommoncenterofthe
Earthandthecelestialsphere.Thearcofacelestialmerid-
ianbetweenthepolesiscalledtheupperbranchifit
containsthezenithandthelowerbranchifitcontainsthe
nadir.Theupperbranchisfrequentlyusedinnavigation,
andreferencestoacelestialmeridianareunderstoodto
meanonlyitsupperbranchunlessotherwisestated.Celes-
tialmeridianstakethenamesoftheirterrestrial
counterparts, such as 65° west.
Anhourcircleisagreatcirclethroughthecelestial
polesandapointorbodyonthecelestialsphere.Itis
similartoacelestialmeridian,butmoveswiththecelestial
sphereasitrotatesabouttheEarth,whileacelestial
meridian remains fixed with respect to the Earth.
Thelocationofabodyonitshourcircleisdefinedby
thebody’sangulardistancefromthecelestialequator.This
distance,calleddeclination,ismeasurednorthorsouthof
thecelestialequatorindegrees,from0°through90°,
similar to latitude on the Earth.
Acircleparalleltothecelestialequatoriscalledapar-
allelofdeclination,sinceitconnectsallpointsofequal
declination.ItissimilartoaparalleloflatitudeontheEarth.
Thepathofacelestialbodyduringitsdailyapparentrevo-
lutionaroundtheEarthiscalleditsdiurnalcircle.Itisnot
actuallyacircleifabodychangesitsdeclination.Sincethe
declinationofallnavigationalbodiesiscontinuallychang-
ing,thebodiesaredescribingflat,sphericalspiralsasthey
circletheEarth.However,sincethechangeisrelatively
slow,adiurnalcircleandaparallelofdeclinationareusu-
ally considered identical.
Apointonthecelestialspheremaybeidentifiedatthe
intersectionofitsparallelofdeclinationanditshourcircle.
The parallel of declination is identified by the declination.
Twobasicmethodsoflocatingthehourcirclearein
use.First,theangulardistancewestofareferencehour
circlethroughapointonthecelestialsphere,calledthe
vernalequinoxorfirstpointofAries,iscalledsidereal
hourangle(SHA)(Figure1524b).Thisangle,measured
eastwardfromthevernalequinox,iscalledrightascension
and is usually expressed in time units.
Thesecondmethodoflocatingthehourcircleisto
indicateitsangulardistancewestofacelestialmeridian
(Figure1524c).IftheGreenwichcelestialmeridianis
usedasthereference,theangulardistanceiscalled
Greenwichhourangle(GHA),andifthemeridianof
theobserver,itiscalledlocalhourangle(LHA).Itis
Figure 1524a. Elements of the celestial sphere. The celestial equator is the primary great circle.
236NAVIGATIONAL ASTRONOMY
Figure 1524b. A point on the celestial sphere can be located by its declination and sidereal hour angle.
Figure 1524c. A point on the celestial sphere can be located by its declination and hour angle.
NAVIGATIONAL ASTRONOMY237
sometimesmoreconvenienttomeasurehourangleeither
eastwardorwestward,aslongitudeismeasuredonthe
Earth,inwhichcaseitiscalledmeridianangle
(designated “t”).
Apointonthecelestialspheremayalsobelocated
usingaltitudeandazimuthcoordinatesbaseduponthe
horizonastheprimarygreatcircleinsteadofthecelestial
equator.
COORDINATE SYSTEMS
1525. The Celestial Equator System of Coordinates
Thefamiliargraticuleoflatitudeandlongitudelines,
expandeduntilitreachesthecelestialsphere,formsthebasis
ofthecelestialequatorsystemofcoordinates.Onthecelestial
spherelatitudebecomesdeclination,whilelongitude
becomessiderealhourangle,measuredfromthevernal
equinox.
Declinationisangulardistancenorthorsouthofthe
celestialequator(dinFigure1525a).Itismeasuredalong
anhourcircle,from0°atthecelestialequatorthrough90°
atthecelestialpoles.ItislabeledNorStoindicatethe
directionofmeasurement.Allpointshavingthesame
declination lie along a parallel of declination.
Polardistance(p)isangulardistancefromacelestial
pole,orthearcofanhourcirclebetweenthecelestialpole
andapointonthecelestialsphere.Itismeasuredalongan
hourcircleandmayvaryfrom0°to180°,sinceeitherpole
maybeusedastheoriginofmeasurement.Itisusually
consideredthecomplementofdeclination,thoughitmaybe
either 90° – d or 90° + d, depending upon the pole used.
Localhourangle(LHA)isangulardistancewestofthe
localcelestialmeridian,orthearcofthecelestialequatorbe-
tweentheupperbranchofthelocalcelestialmeridianandthe
hourcirclethroughapointonthecelestialsphere,measured
westwardfromthelocalcelestialmeridian,through360°.Itis
alsothesimilararcoftheparallelofdeclinationandtheangle
atthecelestialpole,similarlymeasured.IftheGreenwich(0°)
meridianisusedasthereference,insteadofthelocalmeridi-
an,theexpressionGreenwichhourangle(GHA)isapplied.
Itissometimesconvenienttomeasurethearcorangleinei-
theraneasterlyorwesterlydirectionfromthelocalmeridian,
through180°,whenitiscalledmeridianangle(t)andlabeled
EorWtoindicatethedirectionofmeasurement.Allbodies
orotherpointshavingthesamehourangleliealongthesame
hour circle.
Figure 1525a. The celestial equator system of coordinates, showing measurements of declination, polar distance, and
local hour angle.
238NAVIGATIONAL ASTRONOMY
Becauseoftheapparentdailyrotationofthecelestial
sphere,houranglecontinuallyincreases,butmeridianan-
gleincreasesfrom0°atthecelestialmeridianto180°W,
whichisalso180°E,andthendecreasesto0°again.The
rateofchangeforthemeanSunis15°perhour.Therateof
allotherbodiesexcepttheMooniswithin3'ofthisval-
ue. The average rate of the Moon is about 15.5°.
Asthecelestialsphererotates,eachbodycrosseseach
branchofthecelestialmeridianapproximatelyonceaday.
Thiscrossingiscalledmeridiantransit(sometimescalled
culmination).Itmaybecalleduppertransittoindicate
crossingoftheupperbranchofthecelestialmeridian,and
lower transit to indicate crossing of the lower branch.
ThetimediagramshowninFigure1525billustrates
therelationshipbetweenthevarioushouranglesandmerid-
ianangle.Thecircleisthecelestialequatorasseenfrom
abovetheSouthPole,withtheupperbranchoftheobserv-
er’smeridian(P
s
M)atthetop.TheradiusP
s
Gisthe
Greenwichmeridian;P
s
isthehourcircleofthevernal
equinox.TheSun’shourcircleistotheeastoftheobserv-
er’smeridian;theMoon’shourcircleistothewestofthe
observer’smeridianNotethatwhenLHAislessthan180°,
tisnumericallythesameandislabeledW,butthatwhen
LHAisgreaterthan180°,t=360°–LHAandislabeledE.
InFigure1525barcGMisthelongitude,whichinthiscase
iswest.Therelationshipsshownapplyequallytootherar-
rangementsofradii,exceptforrelativemagnitudesofthe
quantities involved.
1526. The Horizons
Thesecondsetofcelestialcoordinateswithwhichthe
navigatorisdirectlyconcernedisbaseduponthehorizonas
theprimarygreatcircle.However,sinceseveraldifferent
horizonsaredefined,theseshouldbethoroughly
understoodbeforeproceedingwithaconsiderationofthe
horizon system of coordinates.
ThelinewhereEarthandskyappeartomeetiscalled
thevisibleorapparenthorizon.Onlandthisisusuallyan
irregularlineunlesstheterrainislevel.Atseathevisible
horizonappearsveryregularandisoftenverysharp.
However,itspositionrelativetothecelestialsphere
dependsprimarilyupon(1)therefractiveindexoftheair
and (2) the height of the observer’s eye above the surface.
Figure1526showsacrosssectionoftheEarthandce-
lestialspherethroughthepositionofanobserveratA.A
straightlinethroughAandthecenteroftheEarthOisthe
verticaloftheobserverandcontainshiszenith(Z)andnadir
(Na).Aplaneperpendiculartothetrueverticalisahorizon-
talplane,anditsintersectionwiththecelestialsphereisa
horizon.Itisthecelestialhorizoniftheplanepasses
throughthecenteroftheEarth,thegeoidalhorizonifitis
tangenttotheEarth,andthesensiblehorizonifitpasses
throughtheeyeoftheobserveratA.Sincetheradiusofthe
Earthisconsiderednegligiblewithrespecttothatofthece-
lestialsphere,thesehorizonsbecomesuperimposed,and
mostmeasurementsarereferredonlytothecelestialhori-
zon. This is sometimes called therational horizon.
IftheeyeoftheobserverisatthesurfaceoftheEarth,
hisvisiblehorizoncoincideswiththeplaneofthegeoidal
horizon;butwhenelevatedabovethesurface,asatA,his
eyebecomesthevertexofaconewhichistangenttotheFigure 1525b. Time diagram.
Figure 1526. The horizons used in navigation.
NAVIGATIONAL ASTRONOMY239
EarthatthesmallcircleBB,andwhichintersectstheceles-
tialsphereinB'B',thegeometricalhorizon.This
expression is sometimes applied to the celestial horizon.
Becauseofrefraction,thevisiblehorizonC'C'appears
abovebutisactuallyslightlybelowthegeometricalhorizon
asshowninFigure1526.InFigure1525btheLocalhour
angle,Greenwichhourangle,andsiderealhourangleare
measuredwestwardthrough360°.Meridianangle(t)is
measuredeastwardorwestwardthrough180°andlabeledE
or W to indicate the direction of measurement.
Foranyelevationabovethesurface,thecelestial
horizonisusuallyabovethegeometricalandvisible
horizons,thedifferenceincreasingaselevationincreases.It
isthuspossibletoobserveabodywhichisabovethevisible
horizonbutbelowthecelestialhorizon.Thatis,thebody’s
altitudeisnegativeanditszenithdistanceisgreaterthan90°.
1527. The Horizon System of Coordinates
Thissystemisbaseduponthecelestialhorizonasthe
primarygreatcircleandaseriesofsecondaryvertical
circleswhicharegreatcirclesthroughthezenithandnadir
oftheobserverandhenceperpendiculartohishorizon
(Figure1527a).Thus,thecelestialhorizonissimilartothe
equator,andtheverticalcirclesaresimilartomeridians,but
withoneimportantdifference.Thecelestialhorizonand
verticalcirclesaredependentuponthepositionofthe
observerandhencemovewithhimashechangesposition,
whiletheprimaryandsecondarygreatcirclesofboththe
geographicalandcelestialequatorsystemsareindependent
oftheobserver.Thehorizonandcelestialequatorsystems
coincideforanobserveratthegeographicalpoleofthe
Earthandaremutuallyperpendicularforanobserveronthe
equator. At all other places the two are oblique.
Theverticalcirclethroughthenorthandsouthpoints
ofthehorizonpassesthroughthepolesofthecelestialequa-
torsystemofcoordinates.Oneofthesepoles(havingthe
samenameasthelatitude)isabovethehorizonandiscalled
theelevatedpole.Theother,calledthedepressedpole,is
belowthehorizon.Sincethisverticalcircleisagreatcircle
throughthecelestialpoles,andincludesthezenithofthe
observer,itisalsoacelestialmeridian.Inthehorizonsys-
temitiscalledtheprincipalverticalcircle.Thevertical
circlethroughtheeastandwestpointsofthehorizon,and
henceperpendiculartotheprincipalverticalcircle,iscalled
theprime vertical circle, or simply theprime vertical.
Figure 1527a. Elements of the celestial sphere. The celestial horizon is the primary great circle.
240NAVIGATIONAL ASTRONOMY
AsshowninFigure1527b,altitudeisangulardistance
abovethehorizon.Itismeasuredalongaverticalcircle,
from0°atthehorizonthrough90°atthezenith.Altitude
measuredfromthevisiblehorizonmayexceed90°because
ofthedipofthehorizon,asshowninFigure1526.Angular
distancebelowthehorizon,callednegativealtitude,ispro-
videdforbyincludingcertainnegativealtitudesinsome
tablesforuseincelestialnavigation.Allpointshavingthe
same altitude lie along a parallel of altitude.
Zenithdistance(z)isangulardistancefromthe
zenith,orthearcofaverticalcirclebetweenthezenithand
apointonthecelestialsphere.Itismeasuredalonga
verticalcirclefrom0°through180°.Itisusuallyconsidered
thecomplementofaltitude.Forabodyabovethecelestial
Figure 1527b. The horizon system of coordinates, showing measurement of altitude, zenith distance, azimuth, and
azimuth angle.
EarthCelestial EquatorHorizonEcliptic
equatorcelestial equatorhorizonecliptic
polescelestial poleszenith; nadirecliptic poles
meridianshours circle; celestial meridiansvertical circlescircles of latitude
prime meridianhour circle of Ariesprincipal or prime vertical circlecircle of latitude through Aries
parallelsparallels of declinationparallels of altitudeparallels of latitude
latitudedeclinationaltitudecelestial altitude
colatitudepolar distancezenith distancecelestial colatitude
longitudeSHA; RA; GHA; LHA; tazimuth; azimuth angle; amplitudecelestial longitude
Table 1527. The four systems of celestial coordinates and their analogous terms.
NAVIGATIONAL ASTRONOMY241
horizonitisequalto90°–handforabodybelowthe
celestial horizon it is equal to 90° – (– h) or 90° + h.
Thehorizontaldirectionofapointonthecelestial
sphere,orthebearingofthegeographicalposition,iscalled
azimuthorazimuthangledependinguponthemethodof
measurement.Inbothmethodsitisanarcofthehorizon(or
parallelofaltitude),oranangleatthezenith.Itisazimuth
(Zn)ifmeasuredclockwisethrough360°,startingatthe
northpointonthehorizon,andazimuthangle(Z)if
measuredeitherclockwiseorcounterclockwisethrough
180°,startingatthenorthpointofthehorizoninnorth
latitudeandthesouthpointofthehorizoninsouthlatitude.
Theeclipticsystemisbasedupontheeclipticasthe
primarygreatcircle,analogoustotheequator.Thepoints
90°fromtheeclipticarethenorthandsoutheclipticpoles.
Theseriesofgreatcirclesthroughthesepoles,analogousto
meridians,arecirclesoflatitude.Thecirclesparalleltothe
planeoftheecliptic,analogoustoparallelsontheEarth,are
parallelsoflatitudeorcirclesoflongitude.Angular
distancenorthorsouthoftheecliptic,analogoustolatitude,
iscelestiallatitude.Celestiallongitudeismeasured
eastwardalongtheeclipticthrough360°,startingatthe
vernalequinox.Thissystemofcoordinatesisofinterest
chiefly to astronomers.
Thefoursystemsofcelestialcoordinatesareanalogous
toeachotherandtotheterrestrialsystem,althougheachhas
distinctionssuchasdifferencesindirections,units,andlim-
itsofmeasurement.Table1527indicatestheanalogous
term or terms under each system.
1528. Diagram on the Plane of the Celestial Meridian
Fromanimaginarypointoutsidethecelestialsphere
andoverthecelestialequator,atsuchadistancethatthe
viewwouldbeorthographic,thegreatcircleappearingas
theouterlimitwouldbeacelestialmeridian.Othercelestial
meridianswouldappearasellipses.Thecelestialequator
wouldappearasadiameter90°fromthepoles,andparallels
ofdeclinationasstraightlinesparalleltotheequator.The
view would be similar to an orthographic map of the Earth.
Anumberofusefulrelationshipscanbedemonstrated
bydrawingadiagramontheplaneofthecelestialmeridian
showingthisorthographicview.Arcsofcirclescanbe
substitutedfortheellipseswithoutdestroyingthebasic
relationships.RefertoFigure1528a.Inthelowerdiagram
thecirclerepresentsthecelestialmeridian,QQ'thecelestial
equator,PnandPsthenorthandsouthcelestialpoles,
respectively.Ifastarhasadeclinationof30°N,anangleof
30°canbemeasuredfromthecelestialequator,asshown.
Itcouldbemeasuredeithertotherightorleft,andwould
havebeentowardthesouthpoleifthedeclinationhadbeen
south.Theparallelofdeclinationisalinethroughthispoint
andparalleltothecelestialequator.Thestarissomewhere
on this line (actually a circle viewed on edge).
Tolocatethehourcircle,drawtheupperdiagramso
thatPnisdirectlyabovePnofthelowerfigure(inlinewith
thepolaraxisPn-Ps),andthecircleisofthesamediameter
asthatofthelowerfigure.Thisistheplanview,looking
downonthecelestialspherefromthetop.Thecircleisthe
celestialequator.Sincetheviewisfromabovethenorth
celestialpole,westisclockwise.ThediameterQQ'isthe
celestialmeridianshownasacircleinthelowerdiagram.If
therighthalfisconsideredtheupperbranch,localhour
angleismeasuredclockwisefromthislinetothehour
circle,asshown.InthiscasetheLHAis80°.The
intersectionofthehourcircleandcelestialequator,pointA,
canbeprojecteddowntothelowerdiagram(pointA')bya
straightlineparalleltothepolaraxis.Theellipticalhour
circlecanberepresentedapproximatelybyanarcofacircle
throughA',Pn,Ps.Thecenterofthiscircleissomewhere
alongthecelestialequatorlineQQ',extendedifnecessary.
Itisusuallyfoundbytrialanderror.Theintersectionofthe
hour circle and parallel of declination locates the star.
SincetheupperdiagramservesonlytolocatepointA'in
thelowerdiagram,thetwocanbecombined.Thatis,theLHA
arccanbedrawninthelowerdiagram,asshown,andpointA
projectedupwardtoA'.Inpractice,theupperdiagramisnot
drawn, being shown here for illustrative purposes.
Inthisexamplethestarisonthathalfofthesphere
towardtheobserver,orthewesternpart.IfLHAhadbeen
greaterthan180°,thebodywouldhavebeenontheeastern
or “back” side.
Fromtheeastorwestpointoverthecelestialhorizon,
theorthographicviewofthehorizonsystemofcoordinates
wouldbesimilartothatofthecelestialequatorsystemfrom
apointoverthecelestialequator,sincethecelestialmeridian
isalsotheprincipalverticalcircle.Thehorizonwould
appearasadiameter,parallelsofaltitudeasstraightlines
paralleltothehorizon,thezenithandnadiraspoles90°from
thehorizon,andverticalcirclesasellipsesthroughthe
zenithandnadir,exceptfortheprincipalverticalcircle,
whichwouldappearasacircle,andtheprimevertical,
whichwouldappearasadiameterperpendiculartothe
horizon.
Acelestialbodycanbelocatedbyaltitudeandazimuth
inamannersimilartothatusedwiththecelestialequator
system.Ifthealtitudeis25°,thisangleismeasuredfrom
thehorizontowardthezenithandtheparallelofaltitudeis
drawnasastraightlineparalleltothehorizon,asshownat
hh'inthelowerdiagramofFigure1528b.Theplanview
fromabovethezenithisshownintheupperdiagram.If
northistakenattheleft,asshown,azimuthsaremeasured
clockwisefromthispoint.Inthefiguretheazimuthis290°
andtheazimuthangleisN70°W.Theverticalcircleis
locatedbymeasuringeitherarc.PointAthuslocatedcanbe
projectedverticallydownwardtoA'onthehorizonofthe
lowerdiagram,andtheverticalcirclerepresentedapproxi-
matelybythearcofacirclethroughA'andthezenithand
nadir.ThecenterofthiscircleisonNS,extendedif
necessary.Thebodyisattheintersectionoftheparallelof
altitudeandtheverticalcircle.Sincetheupperdiagram
servesonlytolocateA'onthelowerdiagram,thetwocan
242NAVIGATIONAL ASTRONOMY
becombined,pointAlocatedonthelowerdiagramand
projectedupwardtoA',asshown.Sincethebodyofthe
examplehasanazimuthgreaterthan180°,itisonthe
western or “front” side of the diagram.
Sincethecelestialmeridianappearsthesameinboth
thecelestialequatorandhorizonsystems,thetwodiagrams
canbecombinedand,ifproperlyoriented,abodycanbe
locatedbyonesetofcoordinates,andthecoordinatesofthe
other system can be determined by measurement.
RefertoFigure1528c,inwhichtheblacklines
representthecelestialequatorsystem,andtheredlinesthe
horizonsystem.Byconvention,thezenithisshownatthe
topandthenorthpointofthehorizonattheleft.Thewest
pointonthehorizonisatthecenter,andtheeastpoint
directlybehindit.Inthefigurethelatitudeis37°N.
Therefore,thezenithis37°northofthecelestialequator.
Sincethezenithisestablishedatthetopofthediagram,the
equatorcanbefoundbymeasuringanarcof37°towardthe
south,alongthecelestialmeridian.Ifthedeclinationis
30°NandtheLHAis80°,thebodycanbelocatedasshown
by the black lines, and described above.
Thealtitudeandazimuthcanbedeterminedbythere-
verseprocesstothatdescribedabove.Drawalinehh'
throughthebodyandparalleltothehorizon,NS.Thealti-
tude,25°,isfoundbymeasurement,asshown.Drawthearc
ofacirclethroughthebodyandthezenithandnadir.From
A',theintersectionofthisarcwiththehorizon,drawaver-
ticallineintersectingthecircleatA.Theazimuth,N70°W,
isfoundbymeasurement,asshown.TheprefixNisapplied
toagreewiththelatitude.Thebodyisleft(north)ofZNa,
theprimeverticalcircle.ThesuffixWappliesbecausethe
LHA, 80°, shows that the body is west of the meridian.
Ifaltitudeandazimutharegiven,thebodyislocatedby
meansoftheredlines.Theparallelofdeclinationisthen
drawnparalleltoQQ',thecelestialequator,andthedecli-
nationdeterminedbymeasurement.PointL'islocatedby
drawingthearcofacirclethroughPn,thestar,andPs.
FromL'alineisdrawnperpendiculartoQQ',locatingL.
Themeridianangleisthenfoundbymeasurement.Thedec-
linationisknowntobenorthbecausethebodyisbetween
Figure1528a.Measurementofcelestialequatorsystemof
coordinates.
Figure 1528b. Measurement of horizon system of
coordinates.
NAVIGATIONAL ASTRONOMY243
thecelestialequatorandthenorthcelestialpole.Themerid-
ianangleiswest,toagreewiththeazimuth,andhenceLHA
is numerically the same.
SinceQQ'andPnPsareperpendicular,andZNaand
NSarealsoperpendicular,arcNPnisequaltoarcZQ.That
is,thealtitudeoftheelevatedpoleisequaltothe
declinationofthezenith,whichisequaltothelatitude.This
relationshipisthebasisofthemethodofdetermining
latitude by an observation of Polaris.
Thediagramontheplaneofthecelestialmeridianis
usefulinapproximatinganumberofrelationships.
ConsiderFigure1528d.Thelatitudeoftheobserver(NPn
orZQ)is45°N.ThedeclinationoftheSun(Q4)is20°N.
Neglectingthechangeindeclinationforoneday,notethe
following:Atsunrise,position1,theSunisonthehorizon
(NS),atthe“back”ofthediagram.Itsaltitude,h,is0°.Its
azimuthangle,Z,isthearcNA,N63°E.ThisisprefixedN
toagreewiththelatitudeandsuffixedEtoagreewiththe
meridianangleoftheSunatsunrise.Hence,Zn=063°.The
amplitude,A,isthearcZA,E27°N.Themeridianangle,t,
isthearcQL,110°E.ThesuffixEisappliedbecausethe
Suniseastofthemeridianatrising.TheLHAis360°–
110° = 250°.
AstheSunmovesupwardalongitsparallelof
declination,itsaltitudeincreases.Itreachesposition2at
about0600,whent=90°E.Atposition3itisontheprime
vertical,ZNa.Itsazimuthangle,Z,isN90°E,andZn=
090°. The altitude is Nh' or Sh, 27°.
Movingonupitsparallelofdeclination,itarrivesat
position4onthecelestialmeridianaboutnoon-whentand
LHAareboth0°,bydefinition.Onthecelestialmeridiana
body’sazimuthis000°or180°.Inthiscaseitis180°because
thebodyissouthofthezenith.Themaximumaltitudeoccurs
atmeridiantransit.InthiscasethearcS4representsthe
maximumaltitude,65°.Thezenithdistance,z,isthearcZ4,
25°.Abodyisnotinthezenithatmeridiantransitunlessits
declination’smagnitudeandnamearethesameasthe
latitude.
Continuingon,theSunmovesdownwardalongthe
“front”orwesternsideofthediagram.Atposition3itisagain
ontheprimevertical.Thealtitudeisthesameaswhen
previouslyontheprimevertical,andtheazimuthangleis
numericallythesame,butnowmeasuredtowardthewest.
Theazimuthis270°.TheSunreachesposition2sixhours
aftermeridiantransitandsetsatposition1.Atthispoint,the
azimuthangleisnumericallythesameasatsunrise,but
westerly,andZn=360°–63°=297°.Theamplitudeis
W27°N.
AftersunsettheSuncontinuesondownward,alongits
parallelofdeclination,untilitreachesposition5,onthe
lowerbranchofthecelestialmeridian,aboutmidnight.Its
negativealtitude,arcN5,isnowgreatest,25°,anditsazi-
muthis000°.Atthispointitstartsbackupalongthe“back”
ofthediagram,arrivingatposition1atthenextsunrise,to
start another cycle.
Halfthecycleisfromthecrossingofthe90°hourcir-
cle(thePnPsline,position2)totheupperbranchofthe
celestialmeridian(position4)andbacktothePnPsline
(position2).Whenthedeclinationandlatitudehavethe
samename(bothnorthorbothsouth),morethanhalfthe
parallelofdeclination(position1to4to1)isabovetheho-
rizon,andthebodyisabovethehorizonmorethanhalfthe
Figure 1528c. Diagram on the plane of the celestial meridian.Figure 1528d. A diagram on the plane of the celestial
meridian for lat. 45°N.
244NAVIGATIONAL ASTRONOMY
time,crossingthe90°hourcircleabovethehorizon.Itrises
andsetsonthesamesideoftheprimeverticalastheelevat-
edpole.Ifthedeclinationisofthesamenamebut
numericallysmallerthanthelatitude,thebodycrossesthe
primeverticalabovethehorizon.Ifthedeclinationandlat-
itudehavethesamenameandarenumericallyequal,the
bodyisinthezenithatuppertransit.Ifthedeclinationisof
thesamenamebutnumericallygreaterthanthelatitude,the
bodycrossestheupperbranchofthecelestialmeridianbe-
tweenthezenithandelevatedpoleanddoesnotcrossthe
primevertical.Ifthedeclinationisofthesamenameasthe
latitudeandcomplementarytoit(d+L=90°),thebodyis
onthehorizonatlowertransitanddoesnotset.Ifthedec-
linationisofthesamenameasthelatitudeandnumerically
greaterthanthecolatitude,thebodyisabovethehorizon
duringitsentiredailycycleandhasmaximumandmini-
mumaltitudes.Thisisshownbytheblackdottedlinein
Figure 1528d.
Ifthedeclinationis0°atanylatitude,thebodyisabove
thehorizonhalfthetime,followingthecelestialequator
QQ',andrisesandsetsontheprimevertical.Ifthedeclina-
tionisofcontraryname(onenorthandtheothersouth),the
bodyisabovethehorizonlessthanhalfthetimeandcrosses
the90°hourcirclebelowthehorizon.Itrisesandsetsonthe
oppositesideoftheprimeverticalfromtheelevatedpole.
Ifthedeclinationisofcontrarynameandnumerically
smallerthanthelatitude,thebodycrossestheprimevertical
belowthehorizon.Ifthedeclinationisofcontraryname
andnumericallyequaltothelatitude,thebodyisinthena-
diratlowertransit.Ifthedeclinationisofcontraryname
andcomplementarytothelatitude,thebodyisonthehori-
zonatuppertransit.Ifthedeclinationisofcontraryname
andnumericallygreaterthanthecolatitude,thebodydoes
not rise.
Alloftheserelationships,andthosethatfollow,canbe
derivedbymeansofadiagramontheplaneofthecelestial
meridian.Theyaremodifiedslightlybyatmospheric
refraction,heightofeye,semidiameter,parallax,changesin
declination,andapparentspeedofthebodyalongits
diurnal circle.
Itiscustomarytokeepthesameorientationinsouth
latitude,asshowninFigure1528e.Inthisillustrationthe
latitudeis45°S,andthedeclinationofthebodyis15°N.
SincePsistheelevatedpole,itisshownabovethesouthern
horizon,withbothSPsandZQequaltothelatitude,45°.
Thebodyrisesatposition1,ontheoppositesideofthe
primeverticalfromtheelevatedpole.Itmovesupward
alongitsparallelofdeclinationtoposition2,ontheupper
branchofthecelestialmeridian,bearingnorth;andthenit
movesdownwardalongthe“front”ofthediagramtoposi-
tion1,whereitsets.Itremainsabovethehorizonforless
thanhalfthetimebecausedeclinationandlatitudeareof
contraryname.TheazimuthatrisingisarcNA,theampli-
tudeZA,andtheazimuthangleSA.Thealtitudecircleat
meridian transit is shown at hh'.
Figure 1528e. A diagram on the plane of the celestial
meridian for lat. 45°S.
Figure 1528f. Locating a point on an ellipse of a
diagram on the plane of the celestial meridian.
NAVIGATIONAL ASTRONOMY245
Adiagramontheplaneofthecelestialmeridiancanbe
usedtodemonstratetheeffectofachangeinlatitude.Asthe
latitudeincreases,thecelestialequatorbecomesmorenear-
lyparalleltothehorizon.Thecolatitudebecomessmaller
increasingthenumberofcircumpolarbodiesandthose
whichneitherrisenorset.Italsoincreasesthedifferencein
thelengthofthedaysbetweensummerandwinter.Atthe
polescelestialbodiescirclethesky,paralleltothehorizon.
Attheequatorthe90°hourcirclecoincideswiththehori-
zon.Bodiesriseandsetvertically;andareabovethe
horizonhalfthetime.Atrisingandsettingtheamplitudeis
equaltothedeclination.Atmeridiantransitthealtitudeis
equaltothecodeclination.Asthelatitudechangesname,
thesame-contrarynamerelationshipwithdeclinationre-
verses.Thisaccountsforthefactthatonehemispherehas
winter while the other is having summer.
NAVIGATIONAL COORDINATES
CoordinateSymbolMeasured fromMeasured along
Direc-
tion
Measured toUnits
Preci-
sion
Maximum
value
Labels
latitudeL, lat.equatormeridianN, Sparallel
°,′0′.190°N, S
colatitudecolat.polesmeridianS, Nparallel
°,′0′.190°—
longitudeλ, long.prime meridianparallelE, Wlocal meridian
°,′0′.1180°E, W
declinationd, dec.celestial equatorhour circleN, S
parallel of
declination
°,′0′.190°N, S
polar distancepelevated polehour circleS, N
parallel of
declination
°,′0′.1180°—
altitudehhorizonvertical circleup
parallel of
altitude
°,′0′.190°*—
zenith
distance
zzenithvertical circledown
parallel of
altitude
°,′0′.1180°—
azimuthZnnorthhorizonEvertical circle
°0°.1360°—
azimuth angleZnorth, southhorizonE, Wvertical circle
°0°.1180° or 90°N, S...E, W
amplitudeAeast, westhorizonN, Sbody
°0°.190°E, W...N, S
Greenwich
hour angle
GHA
Greenwich
celestial
meridian
parallel of
declination
Whour circle
°,′0′.1360°—
local hour
angle
LHA
local celestial
meridian
parallel of
declination
Whour circle
°,′0′.1360°—
meridian
angle
t
local celestial
meridian
parallel of
declination
E, Whour circle
°,′0′.1180°E, W
sidereal hour
angle
SHA
hour circle of
vernal equinox
parallel of
declination
Whour circle
°,′0′.1360°—
right
ascension
RA
hour circle of
vernal equinox
parallel of
declination
Ehour circle
h
,
m
,
s
1
s
24
h
—
Greenwich
mean time
GMT
lower branch
Greenwich
celestial
meridian
parallel of
declination
W
hourcirclemean
Sun
h
,
m
,
s
1
s
24
h
—
local mean
time
LMT
lower branch
local celestial
meridian
parallel of
declination
W
hourcirclemean
Sun
h
,
m
,
s
1
s
24
h
—
zone timeZT
lower branch
zone celestial
meridian
parallel of
declination
W
hourcirclemean
Sun
h
,
m
,
s
1
s
24
h
—
Greenwich
apparent time
GAT
lower branch
Greenwich
celestial
meridian
parallel of
declination
W
hour circle
apparent Sun
h
,
m
,
s
1
s
24
h
—
localapparent
time
LAT
lower branch
local celestial
meridian
parallel of
declination
W
hour circle
apparent Sun
h
,
m
,
s
1
s
24
h
—
Greenwich
sidereal time
GST
Greenwich
celestial
meridian
parallel of
declination
W
hour circle
vernal equinox
h
,
m
,
s
1
s
24
h
—
local sidereal
time
LST
local celestial
meridian
parallel of
declination
W
hour circle
vernal equinox
h
,
m
,
s
1
s
24
h
—
*When measured from celestial horizon.
Figure 1528g. Navigational Coordinates.
246NAVIGATIONAL ASTRONOMY
Theerrorarisingfromshowingthehourcirclesand
verticalcirclesasarcsofcirclesinsteadofellipsesincreases
withincreaseddeclinationoraltitude.Moreaccurateresults
canbeobtainedbymeasurementofazimuthontheparallel
ofaltitudeinsteadofthehorizon,andofhourangleonthe
parallelofdeclinationinsteadofthecelestialequator.Refer
toFigure1528f.Theverticalcircleshownisforabodyhav-
inganazimuthangleofS60°W.Thearcofacircleisshown
inblack,andtheellipseinred.Theblackarcisobtainedby
measurementaroundthehorizon,locatingA'bymeansof
A,aspreviouslydescribed.Theintersectionofthisarcwith
thealtitudecircleat60°placesthebodyatM.Ifasemicir-
cleisdrawnwiththealtitudecircleasadiameter,andthe
azimuthanglemeasuredaroundthis,toB,aperpendicular
tothehourcirclelocatesthebodyatM',ontheellipse.By
thismethodthealtitudecircle,ratherthanthehorizon,is,in
effect,rotatedthrough90°forthemeasurement.Thisre-
finementisseldomusedbecauseactualvaluesareusually
foundmathematically,thediagramontheplaneoftheme-
ridian being used primarily to indicate relationships.
Withexperience,onecanvisualizethediagramonthe
planeofthecelestialmeridianwithoutmakinganactual
drawing.Deviceswithtwosetsofsphericalcoordinates,on
eithertheorthographicorstereographicprojection,pivoted
atthecenter,havebeenproducedcommerciallytoprovide
amechanicaldiagramontheplaneofthecelestialmeridian.
However,sincethediagram’sprincipaluseistoillustrate
certainrelationships,suchadeviceisnotanecessarypart
of the navigator’s equipment.
Figure1528gsummarizesnavigationcoordinate
systems.
1529. The Navigational Triangle
Atriangleformedbyarcsofgreatcirclesofasphereis
calledasphericaltriangle.Asphericaltriangleonthe
celestialsphereiscalledacelestialtriangle.Thespherical
triangleofparticularsignificancetonavigatorsiscalledthe
navigationaltriangle,formedbyarcsofacelestial
meridian,anhourcircle,andaverticalcircle.Itsvertices
aretheelevatedpole,thezenith,andapointonthecelestial
sphere(usuallyacelestialbody).Theterrestrialcounterpart
isalsocalledanavigationaltriangle,beingformedbyarcs
oftwomeridiansandthegreatcircleconnectingtwoplaces
ontheEarth,oneoneachmeridian.Theverticesarethetwo
placesandapole.Ingreat-circlesailingtheseplacesarethe
pointofdepartureandthedestination.Incelestial
navigationtheyaretheassumedposition(AP)ofthe
observerandthegeographicalposition(GP)ofthebody
(thepointhavingthebodyinitszenith).TheGPoftheSun
issometimescalledthesubsolarpoint,thatoftheMoon
thesublunarpoint,thatofasatellite(eithernaturalor
artificial)thesubsatellitepoint,andthatofastarits
substellarorsubastralpoint.Whenusedtosolvea
celestialobservation,eitherthecelestialorterrestrial
triangle may be called theastronomical triangle.
ThenavigationaltriangleisshowninFigure1529aon
adiagramontheplaneofthecelestialmeridian.TheEarth
isatthecenter,O.ThestarisatM,dd'isitsparallelof
declination, and hh' is its altitude circle.
Inthefigure,arcQZofthecelestialmeridianisthe
latitudeoftheobserver,andPnZ,onesideofthetriangle,is
thecolatitude.ArcAMoftheverticalcircleisthealtitude
ofthebody,andsideZMofthetriangleisthezenith
distance,orcoaltitude.ArcLMofthehourcircleisthe
declinationofthebody,andsidePnMofthetriangleisthe
polar distance, or codeclination.
Theangleattheelevatedpole,ZPnM,havingthehour
circleandthecelestialmeridianassides,isthemeridian
angle,t.Theangleatthezenith,PnZM,havingthevertical
circleandthatarcofthecelestialmeridian,whichincludes
theelevatedpole,assides,istheazimuthangle.Theangle
atthecelestialbody,ZMPn,havingthehourcircleandthe
verticalcircleassides,istheparallacticangle(X)
(sometimescalledthepositionangle),whichisnot
generally used by the navigator.
Anumberofproblemsinvolvingthenavigationaltri-
angleareencounteredbythenavigator,eitherdirectlyor
indirectly. Of these, the most common are:
1.Givenlatitude,declination,andmeridianangle,tofind
altitudeandazimuthangle.Thisisusedinthereduction
of a celestial observation to establish a line of position.
2.Givenlatitude,altitude,andazimuthangle,tofind
declinationandmeridianangle.Thisisusedto
identify an unknown celestial body.
Figure 1529a. The navigational triangle.
NAVIGATIONAL ASTRONOMY247
3.Givenmeridianangle,declination,andaltitude,to
findazimuthangle.Thismaybeusedtofind
azimuth when the altitude is known.
4.GiventhelatitudeoftwoplacesontheEarthand
thedifferenceoflongitudebetweenthem,tofind
theinitialgreat-circlecourseandthegreat-circle
distance.Thisinvolvesthesamepartsofthe
triangleasin1,above,butintheterrestrialtriangle,
and hence is defined differently.
Bothcelestialandterrestrialnavigationaltrianglesare
shown in perspective in Figure 1529b.
IDENTIFICATION OF STARS AND PLANETS
1530. Introduction
Abasicrequirementofcelestialnavigationisthe
abilitytoidentifythebodiesobserved.Thisisnotdiffi-
cultbecauserelativelyfewstarsandplanetsare
commonlyusedfornavigation,andvariousaidsare
availabletoassistintheiridentification.SeeFigure
1530a and Figure 1532a.
Navigationalcalculatorsorcomputerprogramscan
identifyvirtuallyanycelestialbodyobserved,giveninputs
ofDRposition,azimuth,andaltitude.Infact,acomplete
roundofsightscanbetakenandsolvedwithoutknowing
thenamesofasingleobservedbody.Oncethedataisen-
tered,thecomputeridentifiesthebodies,solvesthesights,
Figure 1529b. The navigational triangle in perspective.
248NAVIGATIONAL ASTRONOMY
Figure 1530a. Navigational stars and the planets.
NAVIGATIONAL ASTRONOMY249
andplotstheresults.Inthisway,thenavigatorcanlearnthe
stars by observation instead of by rote memorization.
Noproblemisencounteredintheidentificationof
theSunandMoon.However,theplanetscanbemistaken
forstars.Apersonworkingcontinuallywiththenight
skyrecognizesaplanetbyitschangingpositionamong
therelativelyfixedstars.Theplanetsareidentifiedby
notingtheirpositionsrelativetoeachother,theSun,the
Moon,andthestars.Theyremainwithinthenarrow
limitsofthezodiac,butareinalmostconstantmotion
relativetothestars.Themagnitudeandcolormaybe
helpful.TheinformationneededisfoundintheNautical
Almanac.The“PlanetNotes”nearthefrontofthat
volumeareparticularlyuseful.Planetscanalsobe
identifiedbyplanetdiagram,starfinder,skydiagram,or
by computation.
1531. Stars
TheNauticalAlmanaclistsfullnavigationalinforma-
tionon19firstmagnitudestarsand38secondmagnitude
stars,plusPolaris.Abbreviatedinformationislistedfor115
more.AdditionalstarsarelistedintheAstronomicalAlma-
nacandinvariousstarcatalogs.About6,000starsofthe
sixthmagnitudeorbrighter(ontheentirecelestialsphere)
are visible to the unaided eye on a clear, dark night.
Starsaredesignatedbyoneormoreofthefollowing
naming systems:
•CommonName:Mostnamesofstars,asnowused,
weregivenbytheancientArabsandsomebythe
GreeksorRomans.OneofthestarsoftheNautical
Almanac,Nunki,wasnamedbytheBabylonians.
Onlyarelativelyfewstarshavenames.Severalof
thestarsonthedailypagesofthealmanacshadno
name prior to 1953.
•Bayer’sName:Mostbrightstars,includingthose
withnames,havebeengivenadesignation
consistingofaGreekletterfollowedbythe
possessiveformofthenameoftheconstellation,
suchasαCygni(Deneb,thebrighteststarinthe
constellationCygnus,theswan).Romanlettersare
usedwhentherearenotenoughGreekletters.
Usually,thelettersareassignedinorderof
brightnesswithintheconstellation;however,thisis
notalwaysthecase.Forexample,theletter
designationsofthestarsinUrsaMajorortheBig
Dipperareassignedinorderfromtheouterrimof
thebowltotheendofthehandle.Thissystemofstar
designationwassuggestedbyJohnBayerof
Augsburg,Germany,in1603.Allofthe173stars
includedinthelistnearthebackoftheNautical
AlmanacarelistedbyBayer’sname,and,when
applicable, their common name.
•Flamsteed’sNumber:Thissystemassignsnumbers
tostarsineachconstellation,fromwesttoeastinthe
orderinwhichtheycrossthecelestialmeridian.An
exampleis95Leonis,the95thstarintheconstel-
lationLeo.ThissystemwassuggestedbyJohn
Flamsteed (1646-1719).
•CatalogNumber:Starsaresometimesdesignated
bythenameofastarcatalogandthenumberofthe
starasgiveninthecatalog,suchasA.G.
Washington632.Inthesecatalogs,starsarelistedin
orderfromwesttoeast,withoutregardtoconstel-
lation,startingwiththehourcircleofthevernal
equinox.Thissystemisusedprimarilyforfainter
starshavingnootherdesignation.Navigators
seldom have occasion to use this system.
1532. Star Charts
Itisusefultobeabletoidentifystarsbyrelativeposition.A
starchart(Figure1532aandFigure1532b)ishelpfulinlocating
theserelationshipsandotherswhichmaybeuseful.Thismethod
islimitedtoperiodsofrelativelyclear,darkskieswithlittleorno
overcast.StarscanalsobeidentifiedbytheAirAlmanacskydi-
agrams,astarfinder,Pub.No.249,orbycomputationbyhand
or calculator.
Starchartsarebaseduponthecelestialequatorsys-
temofcoordinates,usingdeclinationandsiderealhour
angle(orrightascension).Thezenithoftheobserverisat
theintersectionoftheparallelofdeclinationequaltohis
latitude,andthehourcirclecoincidingwithhiscelestial
meridian.ThishourcirclehasanSHAequalto360°–
LHA(orRA=LHA).Thehorizoniseverywhere
90°fromthezenith.Astarglobeissimilartoaterrestrial
sphere,butwithstars(andoftenconstellations)shownin-
steadofgeographicalpositions.TheNauticalAlmanac
includesinstructionsforusingthisdevice.Onastar
globethecelestialsphereisshownasitwouldappearto
anobserveroutsidethesphere.Constellationsappearre-
versed.Starchartsmayshowasimilarview,butmore
oftentheyarebasedupontheviewfrominsidethesphere,
asseenfromtheEarth.Onthesecharts,northisatthetop,
aswithmaps,buteastistotheleftandwesttotheright.
Thedirectionsseemcorrectwhenthechartisheldover-
head,withthetoptowardthenorth,sotherelationshipis
similar to the sky.
TheNauticalAlmanachasfourstarcharts.Thetwoprinci-
palonesareonthepolarazimuthalequidistantprojection,one
centeredoneachcelestialpole.Eachchartextendsfromitspole
todeclination10°(samenameaspole).Beloweachpolarchart
isanauxiliarychartontheMercatorprojection,from30°Nto
30°S.Onanyofthesecharts,thezenithcanbelocatedasindicat-
ed,todeterminewhichstarsareoverhead.Thehorizonis90°
fromthezenith.Thechartscanalsobeusedtodeterminethelo-
cation of a star relative to surrounding stars.
250NAVIGATIONAL ASTRONOMY
Figure 1532a. Star chart from Nautical Almanac.
NAVIGATIONAL ASTRONOMY251
Figure 1532b. Star chart from Nautical Almanac.
252NAVIGATIONAL ASTRONOMY
The star charts shown in Figure 1533 through Figure
1536, on the transverse Mercator projection, are designed
toassistinlearningPolarisandthestarslistedonthedaily
pages of theNautical Almanac. Each chart extends about
20°beyondeachcelestialpole,andabout60°(fourhours)
eachsideofthecentralhourcircle(atthecelestialequator).
Therefore,theydonotcoincideexactlywiththathalfofthe
celestialsphereabovethehorizonatanyonetimeorplace.
Thezenith,andhencethehorizon,varieswiththeposition
oftheobserverontheEarth.Italsovarieswiththerotation
oftheEarth(apparentrotationofthecelestialsphere).The
chartsshowallstarsoffifthmagnitudeandbrighterasthey
appearinthesky,butwithsomedistortiontowardtheright
and left edges.
Theoverprintedlinesaddcertaininformationofusein
locatingthestars.OnlyPolarisandthe57starslistedonthe
dailypagesoftheNauticalAlmanacarenamedonthe
charts.Thealmanacstarchartscanbeusedtolocatethead-
ditionalstarsgivennearthebackoftheNauticalAlmanac
andtheAirAlmanac.Dashedlinesconnectstarsofsomeof
themoreprominentconstellations.Solidlinesindicatethe
celestialequatorandusefulrelationshipsamongstarsin
differentconstellations.Thecelestialpolesaremarkedby
crosses,andlabeled.Bymeansofthecelestialequatorand
thepoles,onecanlocatehiszenithapproximatelyalongthe
midhourcircle,whenthiscoincideswithhiscelestialme-
ridian,asshowninTable1532.Atanytimeearlierthan
thoseshowninTable1532thezenithistotherightofcen-
ter,andatalatertimeitistotheleft,approximatelyone-
quarterofthedistancefromthecentertotheouteredge(at
thecelestialequator)foreachhourthatthetimediffers
fromthatshown.ThestarsinthevicinityoftheNorthPole
canbeseeninproperperspectivebyinvertingthechart,so
thatthezenithofanobserverintheNorthernHemisphereis
up from the pole.
1533. Stars in the Vicinity of Pegasus
Inautumntheeveningskyhasfewfirstmagnitude
stars.Mostarenearthesouthernhorizonofanobserverin
thelatitudesoftheUnitedStates.Arelativelylargenumber
ofsecondandthirdmagnitudestarsseemconspicuous,per-
hapsbecauseofthesmallnumberofbrighterstars.Highin
thesouthernskythreethirdmagnitudestarsandonesecond
magnitudestarformasquarewithsidesnearly15°ofarc
in length. This is Pegasus, the winged horse.
OnlyMarkabatthesouthwesterncornerandAlpheratz
atthenortheasterncornerarelistedonthedailypagesofthe
NauticalAlmanac.Alpheratzispartoftheconstellation
Andromeda,theprincess,extendinginanarctowardthe
northeastandterminatingatMirfakinPerseus,legendary
rescuer of Andromeda.
Alineextendingnorthwardthroughtheeasternsideof
thesquareofPegasuspassesthroughtheleading(western)
starofM-shaped(orW-shaped)Cassiopeia,thelegendary
motheroftheprincessAndromeda.Theonlystarofthis
constellationlistedonthedailypagesoftheNauticalAlma-
nacisSchedar,thesecondstarfromtheleadingoneasthe
configurationcirclesthepoleinacounterclockwisedirec-
tion.Ifthelinethroughtheeasternsideofthesquareof
Pegasusiscontinuedontowardthenorth,itleadstosecond
magnitudePolaris,theNorthStar(lessthan1°fromthe
northcelestialpole)andbrighteststarofUrsaMinor,the
LittleDipper.Kochab,asecondmagnitudestarattheother
endofUrsaMinor,isalsolistedinthealmanacs.Atthis
seasonUrsaMajorislowinthenorthernsky,belowthece-
lestialpole.AlineextendingfromKochabthroughPolaris
leadstoMirfak,assistinginitsidentificationwhenPegasus
and Andromeda are near or below the horizon.
Deneb,inCygnus,theswan,andVegaarebright,first
magnitudestarsinthenorthwesternsky.Thelinethrough
theeasternsideofthesquareofPegasusapproximatesthe
hourcircleofthevernalequinox,shownatAriesonthece-
lestialequatortothesouth.TheSunisatAriesonorabout
March21,whenitcrossesthecelestialequatorfromsouth
tonorth.IfthelinethroughtheeasternsideofPegasusis
extendedsouthwardandcurvedslightlytowardtheeast,it
leadstosecondmagnitudeDiphda.Alongerandstraighter
linesouthwardthroughthewesternsideofPegasusleadsto
firstmagnitudeFomalhaut.Alineextendingnortheasterly
fromFomalhautthroughDiphdaleadstoMenkar,athird
magnitudestar,butthebrightestinitsvicinity.Ankaa,
Diphda,andFomalhautformanisoscelestriangle,withthe
apexatDiphda.Ankaaisnearorbelowthesouthernhori-
zonofobserversinlatitudesoftheUnitedStates.Fourstars
farthersouththanAnkaamaybevisiblewhenontheceles-
Fig. 1534Fig.1535Fig. 1536Fig. 1537
Local sidereal time0000060012001800
LMT 1800Dec. 21Mar. 22June 22Sept. 21
LMT 2000Nov. 21Feb. 20May 22Aug. 21
LMT 2200Oct. 21Jan. 20Apr. 22July 22
LMT 0000Sept. 22Dec. 22Mar. 23June 22
LMT 0200Aug. 22Nov. 22Feb. 21May 23
LMT 0400July 23Oct. 22Jan 21Apr. 22
LMT 0600June 22Sept. 21Dec. 22Mar. 23
Table 1532. Locating the zenith on the star diagrams.
NAVIGATIONAL ASTRONOMY253
Figure 1533. Stars in the vicinity of Pegasus.
254NAVIGATIONAL ASTRONOMY
tialmeridian,justabovethehorizonofobserversin
latitudesoftheextremesouthernpartoftheUnitedStates.
TheseareAcamar,Achernar,AlNa’ir,andPeacock.These
stars,witheachotherandwithAnkaa,Fomalhaut,and
Diphda,formaseriesoftrianglesasshowninFigure1533.
AlmanacstarsnearthebottomofFigure1533arediscussed
in succeeding articles.
Twootheralmanacstarscanbelocatedbytheirposi-
tionsrelativetoPegasus.TheseareHamalinthe
constellationAries,theram,eastofPegasus,andEnif,west
ofthesouthernpartofthesquare,identifiedinFigure1533.
ThelineleadingtoHamal,ifcontinued,leadstothePleia-
des(theSevenSisters),notusedbynavigatorsforcelestial
observations,butaprominentfigureinthesky,heralding
theapproachofthemanyconspicuousstarsofthewinter
evening sky.
1534. Stars in the Vicinity of Orion
AsPegasusleavesthemeridianandmovesintothe
westernsky,Orion,thehunter,risesintheeast.Withthe
possibleexceptionofUrsaMajor,nootherconfigurationof
starsintheentireskyisaswellknownasOrionanditsim-
mediatesurroundings.Innootherregionaretheresomany
first magnitude stars.
ThebeltofOrion,nearlyonthecelestialequator,is
visibleinvirtuallyanylatitude,risingandsettingalmoston
theprimevertical,anddividingitstimeequallyaboveand
belowthehorizon.Ofthethreesecondmagnitudestars
formingthebelt,onlyAlnilam,themiddleone,islistedon
the daily pages of theNautical Almanac.
Fourconspicuousstarsformaboxaroundthebelt.
Rigel,ahot,bluestar,istothesouth.Betelgeuse,acool,red
starliestothenorth.Bellatrix,brightforasecond
magnitudestarbutovershadowedbyitsfirstmagnitude
neighbors,isafewdegreeswestofBetelgeuse.Neitherthe
secondmagnitudestarformingthesoutheasterncornerof
thebox,noranystarofthedagger,islistedonthedaily
pages of theNautical Almanac.
AlineextendingeastwardfromthebeltofOrion,and
curvingtowardthesouth,leadstoSirius,thebrighteststar
intheentireheavens,havingamagnitudeof–1.6.Only
MarsandJupiteratorneartheirgreatestbrilliance,theSun,
Moon,andVenusarebrighterthanSirius.Siriusispartof
theconstellationCanisMajor,thelargehuntingdogof
Orion.StartingatSiriusacurvedlineextendsnorthward
throughfirstmagnitudeProcyon,inCanisMinor,thesmall
huntingdog;firstmagnitudePolluxandsecondmagnitude
Castor(notlistedonthedailypagesoftheNautical
Almanac),thetwinsofGemini;brilliantCapellainAuriga,
thecharioteer;andbackdowntofirstmagnitude
Aldebaran,thefollower,whichtrailsthePleiades,theseven
sisters.Aldebaran,brighteststarintheheadofTaurus,the
bull,mayalsobefoundbyacurvedlineextending
northwestwardfromthebeltofOrion.TheV-shapedfigure
formingtheoutlineoftheheadandhornsofTauruspoints
towardthirdmagnitudeMenkar.Atthesummersolsticethe
Sun is between Pollux and Aldebaran.
IfthecurvedlinefromOrion’sbeltsoutheastwardto
Siriusiscontinued,itleadstoaconspicuous,small,nearly
equilateraltriangleofthreebrightsecondmagnitudestars
ofnearlyequalbrilliancy.ThisispartofCanisMajor.Only
Adhara,thewesternmostofthethreestars,islistedonthe
dailypagesoftheNauticalAlmanac.Continuingonwith
somewhatlesscurvature,thelineleadstoCanopus,second
brighteststarintheheavensandoneofthetwostarshaving
anegativemagnitude(–0.9).WithSuhailandMiaplacidus,
Canopusformsalarge,equilateraltrianglewhichpartlyen-
closesthegroupofstarsoftenmistakenforCrux.The
brighteststarwithinthistriangleisAvior,nearitscenter.
CanopusisalsoatoneapexofatriangleformedwithAdha-
ratothenorthandSuhailtotheeast,anothertrianglewith
AcamartothewestandAchernartothesouthwest,andan-
otherwithAchernarandMiaplacidus.Acamar,Achernar,
andAnkaaformstillanothertriangletowardthewest.Be-
causeofchartdistortion,thesetrianglesdonotappearinthe
skyinexactlytherelationshipshownonthestarchart.Oth-
erdaily-pagealmanacstarsnearthebottomofFigure1534
are discussed in succeeding articles.
Inthewintereveningsky,UrsaMajoriseastofPolaris,
UrsaMinorisnearlybelowit,andCassiopeiaiswestofit.
MirfakisnorthwestofCapella,nearlymidwaybetweenitand
Cassiopeia.Hamalisinthewesternsky.RegulusandAlphard
arelowintheeasternsky,heraldingtheapproachofthe
configurations associated with the evening skies of spring.
1535. Stars in the Vicinity of Ursa Major
Asiftoenhancethesplendoroftheskyinthevicinity
ofOrion,theregiontowardtheeast,likethattowardthe
west,hasfewbrightstars,exceptinthevicinityofthesouth
celestialpole.However,asOrionsetsinthewest,leaving
CapellaandPolluxinthenorthwesternsky,anumberof
goodnavigationalstarsmoveintofavorablepositionsfor
observation.
UrsaMajor,thegreatbear,appearsprominentlyabove
thenorthcelestialpole,directlyoppositeCassiopeia,which
appearsasa“W”justabovethenorthernhorizonofmost
observersinlatitudesoftheUnitedStates.Oftheseven
starsformingUrsaMajor,onlyDubhe,Alioth,andAlkaid
arelistedonthedailypagesoftheNauticalAlmanac.See
Figure 1535.
Thetwosecondmagnitudestarsformingtheouterpart
ofthebowlofUrsaMajorareoftencalledthepointers
becausealineextendingnorthward(downinspring
evenings)throughthempointstoPolaris.UrsaMinor,the
LittleBear,containsPolarisatoneendandKochabatthe
other.Relativetoitsbowl,thehandleofUrsaMinorcurves
in the opposite direction to that of Ursa Major.
Alineextendingsouthwardthroughthepointers,and
curvingsomewhattowardthewest,leadstofirstmagnitude
Regulus,brighteststarinLeo,thelion.Thehead,
NAVIGATIONAL ASTRONOMY255
Figure 1534. Stars in the vicinity of Orion.
256NAVIGATIONAL ASTRONOMY
Figure 1535. Stars in the vicinity of Ursa Major.
NAVIGATIONAL ASTRONOMY257
shoulders,andfrontlegsofthisconstellationformasickle,
withRegulusattheendofthehandle.Towardtheeastis
secondmagnitudeDenebola,thetailofthelion.Ontoward
thesouthwestfromRegulusissecondmagnitudeAlphard,
brighteststarinHydra,theseaserpent.Adarkskyand
considerableimaginationareneededtotracethelong,
winding body of this figure.
AcurvedlineextendingthearcofthehandleofUrsa
MajorleadstofirstmagnitudeArcturus.WithAlkaidand
Alphecca,brighteststarinCoronaBorealis,theNorthern
Crown,Arcturusformsalarge,inconspicuoustriangle.If
thearcthroughArcturusiscontinued,itleadsnexttofirst
magnitudeSpicaandthentoCorvus,thecrow.The
brighteststarinthisconstellationisGienah,butthreeothers
arenearlyasbright.Atautumnalequinox,theSunisonthe
celestialequator,aboutmidwaybetweenRegulusand
Spica.
Along,slightlycurvedlinefromRegulus,east-
southeasterlythroughSpica,leadstoZubenelgenubiatthe
southwesterncornerofaninconspicuousbox-likefigure
called Libra, the scales.
ReturningtoCorvus,alinefromGienah,extending
diagonallyacrossthefigureandthencurvingsomewhat
toward the east, leads to Menkent, just beyond Hydra.
Fartothesouth,belowthehorizonofmostnorthern
hemisphereobservers,agroupofbrightstarsisaprominent
featureofthespringskyoftheSouthernHemisphere.Thisis
Crux,theSouthernCross.Cruxisabout40°southofCorvus.
The“falsecross”tothewestisoftenmistakenforCrux.
AcruxatthesouthernendofCruxandGacruxatthenorthern
end are listed on the daily pages of theNautical Almanac.
ThetrianglesformedbySuhail,Miaplacidus,andCanopus,
andbySuhail,Adhara,andCanopus,arewestofCrux.Suhailis
inlinewiththehorizontalarmofCrux.AlinefromCanopus,
throughMiaplacidus,curvedslightlytowardthenorth,leadsto
Acrux.Alinethroughtheeast-westarmofCrux,eastwardand
thencurvingtowardthesouth,leadsfirsttoHadarandthento
RigilKentaurus,bothverybrightstars.Continuingon,the
curvedlineleadstosmallTriangulumAustrale,theSouthern
Triangle, the easternmost star of which is Atria.
1536. Stars in the Vicinity of Cygnus
Asthecelestialspherecontinuesinitsapparentwest-
wardrotation,thestarsfamiliartoaspringevening
observersinklowinthewesternsky.Bymidsummer,Ursa
Majorhasmovedtoapositiontotheleftofthenorthceles-
tialpole,andthelinefromthepointerstoPolarisisnearly
horizontal.UrsaMinor,isstandingonitshandle,with
Kochababoveandtotheleftofthecelestialpole.Cassio-
peiaisattherightofPolaris,oppositethehandleofUrsa
Major. See Figure 1536.
TheonlyfirstmagnitudestarinthewesternskyisArc-
turus,whichformsalarge,inconspicuoustrianglewith
Alkaid,theendofthehandleofUrsaMajor,andAlphecca,
the brightest star in Corona Borealis, the Northern Crown.
Theeasternskyisdominatedbythreeverybright
stars.ThewesternmostoftheseisVega,thebrightest
starnorthofthecelestialequator,andthirdbrighteststar
intheheavens,withamagnitudeof0.1.Witha
declinationofalittlelessthan39°N,Vegapasses
throughthezenithalongapathacrossthecentralpartof
theUnitedStates,fromWashingtonintheeasttoSan
FranciscoonthePacificcoast.Vegaformsalargebut
conspicuoustrianglewithitstwobrightneighbors,
DenebtothenortheastandAltairtothesoutheast.The
angleatVegaisnearlyarightangle.Denebisattheend
ofthetailofCygnus,theswan.Thisconfigurationis
sometimescalledtheNorthernCross,withDenebatthe
head.Tomodernyouthitmorenearlyresemblesadive
bomber,whileitisstillwelltowardtheeast,withDeneb
atthenoseofthefuselage.Altairhastwofainterstars
closeby,onoppositesides.ThelineformedbyAltair
anditstwofaintercompanions,ifextendedina
northwesterlydirection,passesthroughVega,andonto
secondmagnitudeEltanin.Theangulardistancefrom
VegatoEltaninisabouthalfthatfromAltairto
Vega.VegaandAltair,withsecondmagnitude
Rasalhaguetothewest,formalargeequilateraltriangle.
ThisislessconspicuousthantheVega-Deneb-Altair
trianglebecausethebrillianceofRasalhagueismuch
lessthanthatofthethreefirstmagnitudestars,andthe
triangle is overshadowed by the brighter one.
FartothesouthofRasalhague,andalittletowardthe
west,isastrikingconfigurationcalledScorpius,thescorpi-
on.Thebrighteststar,formingthehead,isredAntares.At
the tail is Shaula.
Antaresisatthesouthwesterncornerofan
approximateparallelogramformedbyAntares,Sabik,
Nunki,andKausAustralis.WiththeexceptionofAntares,
thesestarsareonlyslightlybrighterthananumberofothers
nearby,andsothisparallelogramisnotastrikingfigure.At
wintersolsticetheSunisashortdistancenorthwestof
Nunki.
NorthwestofScorpiusisthebox-likeLibra,thescales,
of which Zubenelgenubi marks the southwest corner.
WithMenkentandRigilKentaurustothesouthwest,
Antaresformsalargebutunimpressivetriangle.Formost
observersinthelatitudesoftheUnitedStates,Antaresis
lowinthesouthernsky,andtheothertwostarsofthe
trianglearebelowthehorizon.Toanobserverinthe
SouthernHemisphereCruxistotherightofthesouth
celestialpole,whichisnotmarkedbyaconspicuousstar.A
long,curvedline,startingwiththenow-verticalarmof
Cruxandextendingnorthwardandtheneastward,passes
successivelythroughHadar,RigilKentaurus,Peacock,and
Al Na’ir.
Fomalhautislowinthesoutheasternskyofthesouthern
hemisphereobserver,andEnifislowintheeasternskyat
nearlyanylatitude.Withtheappearanceofthesestarsitisnot
longbeforePegasuswillappearovertheeasternhorizon
duringtheevening,andasthewingedhorseclimbseveningby
258NAVIGATIONAL ASTRONOMY
Figure 1536. Stars in the vicinity of Cygnus.
NAVIGATIONAL ASTRONOMY259
eveningtoapositionhigherinthesky,anewannualcycle
approaches.
1537. Planet Diagram
TheplanetdiagramintheNauticalAlmanacshows,for
anydate,theLMTofmeridianpassageoftheSun,forthe
fiveplanetsMercury,Venus,Mars,Jupiter,andSaturn,and
ofeach30°ofSHA.Thediagramprovidesageneralpicture
oftheavailabilityofplanetsandstarsforobservation,and
thus shows:
1.WhetheraplanetorstaristooclosetotheSunfor
observation.
2.Whether a planet is a morning or evening star.
3.Someindicationoftheplanet’spositionduring
twilight.
4.The proximity of other planets.
5.Whetheraplanetisvisiblefromeveningto
morning twilight.
Aband45minuteswideisshadedoneachsideofthe
curvemarkingtheLMTofmeridianpassageoftheSun.Any
planetandmoststarslyingwithintheshadedareaaretoo
close to the Sun for observation.
Whenthemeridianpassageoccursatmidnight,the
bodyisinoppositiontotheSunandisvisibleallnight;
planetsmaybeobservableinbothmorningandevening
twilights.Asthetimeofmeridianpassagedecreases,the
bodyceasestobeobservableinthemorning,butitsaltitude
abovetheeasternhorizonduringeveningtwilightgradually
increases;thiscontinuesuntilthebodyisonthemeridianat
twilight.Fromthenonwardsthebodyisobservableabove
thewesternhorizonanditsaltitudeateveningtwilight
graduallydecreases;eventuallythebodycomestoocloseto
theSunforobservation.Whenthebodyagainbecomesvis-
ible,itisseenasamorningstarlowintheeast.Itsaltitude
attwilightincreasesuntilmeridianpassageoccursatthe
timeofmorningtwilight.Then,asthetimeofmeridianpas-
sagedecreasesto0
h
,thebodyisobservableinthewestin
themorningtwilightwithagraduallydecreasingaltitude,
until it once again reaches opposition.
Onlyaboutone-halftheregionoftheskyalongthe
ecliptic,asshownonthediagram,isabovethehorizonat
onetime.Atsunrise(LMTabout6
h
)theSunand,hence,the
regionnearthemiddleofthediagram,arerisingintheeast;
theregionatthebottomofthediagramissettinginthe
west.Theregionhalfwaybetweenisonthemeridian.At
sunset(LMTabout18
h
)theSunissettinginthewest;the
regionatthetopofthediagramisrisingintheeast.Mark-
ingtheplanetdiagramoftheNauticalAlmanacsothateast
isatthetopofthediagramandwestisatthebottomcanbe
useful to interpretation.
Ifthecurveforaplanetintersectstheverticalline
connectingthedategraduationsbelowtheshadedarea,the
planetisamorningstar;iftheintersectionisabovethe
shaded area, the planet is an evening star.
AsimilarplanetlocationdiagramintheAirAlmanac
representstheregionoftheskyalongtheeclipticwithin
whichtheSun,Moon,andplanetsalwaysmove;itshows,
foreachdate,theSuninthecenterandtherelativepositions
oftheMoon,thefiveplanetsMercury,Venus,Mars,Jupi-
ter,SaturnandthefourfirstmagnitudestarsAldebaran,
Antares,Spica,andRegulus,andalsothepositiononthe
eclipticwhichisnorthofSirius(i.e.Siriusis40°southof
thispoint).ThefirstpointofAriesisalsoshownforrefer-
ence.Themagnitudesoftheplanetsaregivenatsuitable
intervalsalongthecurves.TheMoonsymbolshowsthe
correctphase.Astraightlinejoiningthedateontheleft-
handsidewiththesamedateoftheright-handsiderepre-
sentsacompletecirclearoundthesky,thetwoendsofthe
linerepresentingthepoint180°fromtheSun;theintersec-
tionswiththecurvesshowthespacingofthebodiesalong
theeclipticonthedate.Thetimescaleindicatesroughlythe
localmeantimeatwhichanobjectwillbeontheobserver’s
meridian.
Atanytimeonlyabouthalftheregiononthediagram
isabovethehorizon.AtsunrisetheSun(andhencethere-
gionnearthemiddleofthediagram),isrisingintheeast
andtheregionattheendmarked“West”issettinginthe
west;theregionhalf-waybetweentheseextremesisonthe
meridian,aswillbeindicatedbythelocaltime(about6
h
).
Atthetimeofsunset(localtimeabout18
h
)theSunisset-
tinginthewest,andtheregionattheendmarked“East”is
risingintheeast.Thediagramshouldbeusedinconjunc-
tion with the Sky Diagrams.
1538. Finding Stars for a Fix
Variousdeviceshavebeeninventedtohelpanobserv-
erfindindividualstars.ThemostwidelyusedistheStar
FinderandIdentifier,formerlypublishedbytheU.S.
NavyHydrographicOfficeasNo.2102D.Itisnolongeris-
sued,havingbeenreplacedofficiallybytheSTELLA
computerprogram,butitisstillavailablecommercially.A
navigationalcalculatororcomputerprogramismuch
quicker, more accurate, and less tedious.
Infact,theprocessofidentifyingstarsisnolongernec-
essarybecausethecomputerorcalculatordoesit
automatically.Thenavigatorneedonlytakesightsanden-
tertherequireddata.Theprogramidentifiesthebodies,
solvesfortheLOP’sforeach,combinesthemintothebest
fix,anddisplaysthelat./long.position.Mostcomputerpro-
gramsalsoprintoutaplottedfix,justasthenavigatormight
have drawn by hand.
Thedatarequiredbythecalculatororprogramconsists
oftheDRposition,thesextantaltitudeofthebody,the
time,andtheazimuthofthebody.Thenameofthebodyis
notnecessarybecausetherewillbeonlyonepossiblebody
meetingthoseconditions,whichthecomputerwillidentify.
Computersightreductionprogramscanalsoautomati-
callypredicttwilightonamovingvesselandcreateaplot
260NAVIGATIONAL ASTRONOMY
oftheskyatthevessel’stwilightlocation(oranylocation,
atanytime).Thisplotwillbefreeofthedistortioninherent
inthemechanicalstarfindersandwillshowallbodies,even
planets,Sun,andMoon,intheircorrectrelativeorientation
centeredontheobserver’szenith.Itwillalsoindicatewhich
stars provide the best geometry for a fix.
Computersightreductionprogramsorcelestialnaviga-
tioncalculatorsareespeciallyusefulwhentheskyisonly
brieflyvisiblethoroughbrokencloudcover.Thenavigator
canquicklyshootanyvisiblebodywithouthavingtoiden-
tify it by name, and let the computer do the rest.
1539. Identification by Computation
Ifthealtitudeandazimuthofthecelestialbody,andthe
approximatelatitudeoftheobserver,areknown,thenavi-
gationaltrianglecanbesolvedformeridianangleand
declination.ThemeridiananglecanbeconvertedtoLHA,
andthistoGHA.WiththisandGHAatthetimeofob-
servation,theSHAofthebodycanbedetermined.With
SHAanddeclination,onecanidentifythebodybyrefer-
encetoanalmanac.Anymethodofsolvingaspherical
triangle,withtwosidesandtheincludedanglebeinggiven,
issuitableforthispurpose.Alarge-scale,carefully-drawn
diagramontheplaneofthecelestialmeridian,usingthere-
finementshowninFigure1528f,shouldyieldsatisfactory
results.
Althoughnoformalstaridentificationtablesare
includedinPub.No.229,asimpleapproachtostaridenti-
ficationistoscanthepagesoftheappropriatelatitudes,and
observethecombinationofargumentswhichgivethe
altitudeandazimuthangleoftheobservation.Thusthe
declinationandLHA★aredetermineddirectly.Thestar’s
SHAisfoundfromSHA★=LHA★–LHA.From
thesequantitiesthestarcanbeidentifiedfromtheNautical
Almanac.
Anothersolutionisavailablethroughaninterchangeof
argumentsusingthenearestintegralvalues.Theprocedure
consistsofenteringPub.No.229withtheobserver’slatitude
(samenameasdeclination),withtheobservedazimuthangle
(convertedfromobservedtrueazimuthasrequired)asLHA
andtheobservedaltitudeasdeclination,andextractingfrom
thetablesthealtitudeandazimuthanglerespondents.The
extractedaltitudebecomesthebody’sdeclination;the
extractedazimuthangle(oritssupplement)isthemeridian
angleofthebody.Notethatthetablesarealwaysentered
withlatitudeofsamenameasdeclination.Innorthlatitudes
the tables can be entered with true azimuth as LHA.
IftherespondentsareextractedfromabovetheC-S
Lineonaright-handpage,thenameofthelatitudeis
actuallycontrarytothedeclination.Otherwise,the
declinationofthebodyhasthesamenameasthelatitude.If
theazimuthanglerespondentisextractedfromabovetheC-
SLine,thesupplementofthetabularvalueisthemeridian
angle,t,ofthebody.Ifthebodyiseastoftheobserver’s
meridian,LHA=360°–t;ifthebodyiswestofthe
meridian, LHA = t.
261
CHAPTER 16
INSTRUMENTS FOR CELESTIAL NAVIGATION
THE MARINE SEXTANT
1600. Description and Use
Themarinesextantmeasurestheanglebetweentwo
pointsbybringingthedirectimagefromonepointanda
double-reflectedimagefromtheotherintocoincidence.Its
principaluseistomeasurethealtitudesofcelestialbodies
abovethevisibleseahorizon.Itmayalsobeusedtomeasure
verticalanglestofindtherangefromanobjectofknown
height.Sometimesitisturnedonitssideandusedfor
measuringtheangulardistancebetweentwoterrestrial
objects.
Amarinesextantcanmeasureanglesuptoapproxi-
mately120°.Originally,theterm“sextant”wasappliedto
thenavigator’sdouble-reflecting,altitude-measuring
instrumentonlyifitsarcwas60°inlength,or1/6ofa
circle,permittingmeasurementofanglesfrom0°to120°.
Inmodernusagethetermisappliedtoallmodernnaviga-
tionalaltitude-measuringinstrumentsregardlessofangular
range or principles of operation.
1601. Optical Principles of a Sextant
Whenaplanesurfacereflectsalightray,theangleofre-
flectionequalstheangleofincidence.Theanglebetweenthe
firstandfinaldirectionsofarayoflightthathasundergone
doublereflectioninthesameplaneistwicetheanglethetwo
reflecting surfaces make with each other (Figure 1601).
InFigure1601,ABisarayoflightfromacelestialbody.
TheindexmirrorofthesextantisatB,thehorizonglassatC,
andtheeyeoftheobserveratD.ConstructionlinesEFand
CFareperpendiculartotheindexmirrorandhorizonglass,
respectively.LinesBGandCGareparalleltothesemirrors.
Therefore,anglesBFCandBGCareequalbecausetheir
sidesaremutuallyperpendicular.AngleBGCisthe
inclinationofthetworeflectingsurfaces.TherayoflightAB
isreflectedatmirrorB,proceedstomirrorC,whereitis
againreflected,andthencontinuesontotheeyeofthe
observeratD.Sincetheangleofreflectionisequaltothe
angle of incidence,
Sinceanexteriorangleofatriangleequalsthesumof
the two non adjacent interior angles,
ABC = BDC+BCD, and EBC = BFC+BCF.
Transposing,
BDC = ABC-BCD, and BFC = EBC-BCF.
Substituting2EBCforABC,and2BCFforBCDinthe
first of these equations,
BDC = 2EBC-2BCF, or BDC=2 (EBC-BCF).
Since BFC=EBC - BCF, and BFC = BGC, therefore
BDC = 2BFC = 2BGC.
Thatis,BDC,theanglebetweenthefirstandlast
directionsoftherayoflight,isequalto2BGC,twicethe
angleofinclinationofthereflectingsurfaces.AngleBDC
is the altitude of the celestial body.
Ifthetwomirrorsareparallel,theincidentrayfromany
observedbodymustbeparalleltotheobserver’slineofsight
throughthehorizonglass.Inthatcase,thebody’saltitude
wouldbezero.Theanglethatthesetworeflectingsurfaces
makewitheachotherisone-halftheobservedangle.The
graduationsonthearcreflectthishalfanglerelationship
between the angle observed and the mirrors’ angle.
1602. Micrometer Drum Sextant
Figure1602showsamodernmarinesextant,calleda
micrometerdrumsextant.Inmostmarinesextants,brass
oraluminumcomprisetheframe,A.FramescomeinFigure 1601. Optical principle of the marine sextant.
ABE=EBC, and ABC=2EBC.
BCF=FCD, and BCD=2BCF.
262INSTRUMENTS FOR CELESTIAL NAVIGATION
variousdesigns;mostaresimilartothis.Teethmarkthe
outeredgeofthelimb,B;eachtoothmarksonedegreeof
altitude.Thealtitudegraduations,C,alongthelimb,mark
thearc.Somesextantshaveanarcmarkedinastripof
brass, silver, or platinum inlaid in the limb.
Theindexarm,D,isamovablebarofthesamematerial
astheframe.Itpivotsaboutthecenterofcurvatureofthe
limb.Thetangentscrew,E,ismountedperpendicularlyon
theendoftheindexarm,whereitengagestheteethofthe
limb.Becausetheobservercanmovetheindexarmthrough
thelengthofthearcbyrotatingthetangentscrew,thisis
sometimescalledan“endlesstangentscrew.”Therelease,F,
isaspring-actuatedclampthatkeepsthetangentscrew
engagedwiththelimb’steeth.Theobservercandisengage
thetangentscrewandmovetheindexarmalongthelimbfor
roughadjustment.Theendofthetangentscrewmountsa
micrometerdrum,G,graduatedinminutesofaltitude.One
completeturnofthedrummovestheindexarmonedegree
alongthearc.Nexttothemicrometerdrumandfixedonthe
indexarmisavernier,H,thatreadsinfractionsofaminute.
Theverniershownisgraduatedintotenparts,permitting
readingsto
1
/
10
ofaminuteofarc(0.1').Somesextantshave
verniersgraduatedintoonlyfiveparts,permittingreadingsto
0.2'.
Theindexmirror,I,isapieceofsilveredplateglass
mountedontheindexarm,perpendiculartotheplaneofthe
instrument,withthecenterofthereflectingsurfacedirectly
overthepivotoftheindexarm.Thehorizonglass,J,isa
pieceofopticalglasssilveredonitshalfnearertheframe.
Itismountedontheframe,perpendiculartotheplaneofthe
sextant.Theindexmirrorandhorizonglassaremountedso
thattheirsurfacesareparallelwhenthemicrometerdrumis
setat0°,iftheinstrumentisinperfectadjustment.Shade
glasses,K,ofvaryingdarknessaremountedonthe
sextant’sframeinfrontoftheindexmirrorandhorizon
glass.Theycanbemovedintothelineofsightasneededto
reduce the intensity of light reaching the eye.
Thetelescope,L,screwsintoanadjustablecollarin
linewiththehorizonglassandparalleltotheplaneofthe
instrument.Mostmodernsextantsareprovidedwithonly
onetelescope.Whenonlyonetelescopeisprovided,itisof
the“erectimagetype,”eitherasshownorwithawider
“objectglass”(farendoftelescope),whichgenerallyis
shorterinlengthandgivesagreaterfieldofview.The
secondtelescope,ifprovided,maybethe“invertingtype.”
Theinvertingtelescope,havingonelenslessthantheerect
type,absorbslesslight,butattheexpenseofproducingan
invertedimage.Asmallcoloredglasscapissometimes
provided,tobeplacedoverthe“eyepiece”(nearendof
telescope)toreduceglare.Withthisinplace,shadeglasses
aregenerallynotneeded.A“peepsight,”orcleartube
whichservestodirectthelineofsightoftheobserverwhen
no telescope is used, may be fitted.
Sextantsaredesignedtobeheldintherighthand.
Somehaveasmalllightontheindexarmtoassistin
readingaltitudes.Thebatteriesforthislightarefittedinside
arecessinthehandle,M.NotclearlyshowninFigure1602
are thetangent screw, E, and the three legs.
Figure 1602. U.S. Navy Mark 2 micrometer drum sextant.
INSTRUMENTS FOR CELESTIAL NAVIGATION263
Therearetwobasicdesignscommonlyusedformounting
andadjustingmirrorsonmarinesextants.OntheU.S.Navy
Mark3andcertainothersextants,themirrorismountedsothat
itcanbemovedagainstretainingormountingspringswithin
itsframe.Onlyoneperpendicularadjustmentscrewis
required.OntheU.S.NavyMark2andothersextantsthe
mirrorisfixedwithinitsframe.Twoperpendicularadjustment
screwsarerequired.Onescrewmustbeloosenedbeforethe
other screw bearing on the same surface is tightened.
1603. Vernier Sextant
Mostrecentmarinesextantsareofthemicrometer
drumtype,butatleasttwoolder-typesextantsarestillin
use.Thesedifferfromthemicrometerdrumsextant
principallyinthemannerinwhichthefinalreadingis
made. They are calledvernier sextants.
Theclampscrewverniersextantistheolderofthe
two.Inplaceofthemodernreleaseclamp,aclampscrewis
fittedontheundersideoftheindexarm.Tomovetheindex
arm,theclampscrewisloosened,releasingthearm.When
thearmisplacedattheapproximatealtitudeofthebody
beingobserved,theclampscrewistightened.Fixedtothe
clampscrewandengagedwiththeindexarmisalong
tangentscrew.Whenthisscrewisturned,theindexarm
movesslowly,permittingaccuratesetting.Movementofthe
indexarmbythetangentscrewislimitedtothelengthofthe
screw(severaldegreesofarc).Beforeanaltitudeis
measured,thisscrewshouldbesettotheapproximatemid-
pointofitsrange.Thefinalreadingismadeonavernierset
intheindexarmbelowthearc.Asmallmicroscopeor
magnifyingglassfittedtotheindexarmisusedinmaking
the final reading.
Theendlesstangentscrewverniersextantisidenticalto
themicrometerdrumsextant,exceptthatithasnodrum,and
thefinereadingismadebyavernieralongthearc,aswiththe
clampscrewverniersextant.Thereleaseisthesameasonthe
micrometerdrumsextant,andteetharecutintotheunderside
of the limb which engage with the endless tangent screw.
1604. Sextant Sun Sights
ForaSunsight,holdthesextantverticallyanddirectthe
sightlineatthehorizondirectlybelowtheSun.Aftermoving
suitableshadeglassesintothelineofsight,movetheindex
armoutwardalongthearcuntilthereflectedimageappearsin
thehorizonglassnearthedirectviewofthehorizon.Rockthe
sextantslightlytotherightandlefttoensureitisperpen-
dicular.Asyourockthesextant,theimageoftheSunappears
tomoveinanarc,andyoumayhavetoturnslightlytoprevent
the image from moving off the horizon glass.
ThesextantisverticalwhentheSunappearsatthe
bottomofthearc.Thisisthecorrectpositionformakingthe
observation.TheSun’sreflectedimageappearsatthe
centerofthehorizonglass;onehalfappearsonthesilvered
part,andtheotherhalfappearsontheclearpart.Movethe
indexarmwiththedrumorvernierslowlyuntiltheSun
appearstoberestingexactlyonthehorizon,tangenttothe
lowerlimb.Thenoviceobserverneedspracticeto
determinetheexactpointoftangency.Beginnersoftenerr
by bringing the image down too far.
Somenavigatorsgettheirmostaccurateobservations
bylettingthebodycontactthehorizonbyitsownmotion,
bringingitslightlybelowthehorizonifrising,andaboveif
setting.Attheinstantthehorizonistangenttothedisk,the
navigatornotesthetime.Thesextantaltitudeisthe
uncorrected reading of the sextant.
1605. Sextant Moon Sights
WhenobservingtheMoon,followthesameprocedure
asfortheSun.BecauseofthephasesoftheMoon,theupper
limboftheMoonisobservedmoreoftenthanthatofthe
Sun.Whentheterminator(thelinebetweenlightanddark
areas)isnearlyvertical,becarefulinselectingthelimbto
shoot.SightsoftheMoonarebestmadeduringeither
daylighthoursorthatpartoftwilightinwhichtheMoonis
leastluminous.Atnight,falsehorizonsmayappearbelow
theMoonbecausetheMoonilluminatesthewaterbelowit.
1606. Sextant Star and Planet Sights
WhiletherelativelylargeSunandMoonareeasyto
findinthesextant,starsandplanetscanbemoredifficultto
locatebecausethefieldofviewissonarrow.Oneofthree
methods may help locate a star or planet:
Method1.Settheindexarmandmicrometerdrumon
0°anddirectthelineofsightatthebodytobeobserved.
Then,whilekeepingthereflectedimageofthebodyinthe
mirroredhalfofthehorizonglass,swingtheindexarmout
androtatetheframeofthesextantdown.Keepthereflected
imageofthebodyinthemirroruntilthehorizonappearsin
theclearpartofthehorizonglass.Then,makethe
observation.Whenthereislittlecontrastbetween
brightnessoftheskyandthebody,thisprocedureis
difficult.Ifthebodyis“lost”whileitisbeingbrought
down, it may not be recovered without starting over again.
Method2.Directthelineofsightatthebodywhile
holdingthesextantupsidedown.Slowlymovetheindex
armoutuntilthehorizonappearsinthehorizonglass.Then
invert the sextant and take the sight in the usual manner.
Method3.Determineinadvancetheapproximate
altitudeandazimuthofthebodybyastarfindersuchasNo.
2102D.Setthesextantattheindicatedaltitudeandfacein
thedirectionoftheazimuth.Theimageofthebodyshould
appear in the horizon glass with a little searching.
Whenmeasuringthealtitudeofastarorplanet,bring
itscenterdowntothehorizon.Starsandplanetshaveno
discernibleupperorlowerlimb;youmustobservethe
centerofthepointoflight.Becausestarsandplanetshave
264INSTRUMENTS FOR CELESTIAL NAVIGATION
nodiscerniblelimbandbecausetheirvisibilitymaybe
limited,themethodoflettingastarorplanetintersectthe
horizonbyitsownmotionisnotrecommended.Aswiththe
SunandMoon,however,“rockthesextant”toestablish
perpendicularity.
1607. Taking a Sight
Unlessyouhaveanavigationcalculatororcomputer
thatwillidentifybodiesautomatically,predictexpected
altitudesandazimuthsforuptoeightbodieswhen
preparingtotakecelestialsights.Choosethestarsand
planetsthatgivethebestbearingspread.Trytoselect
bodieswithapredictedaltitudebetween30°and70°.Take
sightsofthebrighteststarsfirstintheevening;takesights
of the brightest stars last in the morning.
Occasionally,fog,haze,orothershipsinaformation
mayobscurethehorizondirectlybelowabodywhichthe
navigatorwishestoobserve.Ifthearcofthesextantis
sufficientlylong,abacksightmightbeobtained,usingthe
oppositepointofthehorizonasthereference.Forthisthe
observerfacesawayfromthebodyandobservesthe
supplementofthealtitude.IftheSunorMoonisobserved
inthismanner,whatappearsinthehorizonglasstobethe
lowerlimbisinfacttheupperlimb,andviceversa.Inthe
caseoftheSun,itisusuallypreferabletoobservewhat
appearstobetheupperlimb.Thearcthatappearswhen
rockingthesextantforabacksightisinverted;thatis,the
highest point indicates the position of perpendicularity.
Ifmorethanonetelescopeisfurnishedwiththe
sextant,theerectingtelescopeisusedtoobservetheSun.A
widerfieldofviewispresentifthetelescopeisnotused.
Thecollarintowhichthesextanttelescopefitsmaybe
adjustedinorout,inrelationtotheframe.Whenmovedin,
moreofthemirroredhalfofthehorizonglassisvisibleto
thenavigator,andastarorplanetismoreeasilyobserved
whentheskyisrelativelybright.Nearthedarkerlimitof
twilight,thetelescopecanbemovedout,givingabroader
viewoftheclearhalfoftheglass,andmakingtheless
distincthorizonmoreeasilydiscernible.Ifbotheyesare
keptopenuntilthelastmomentsofanobservation,eye
strainwillbelessened.Practicewillpermitobservationsto
be made quickly, reducing inaccuracy due to eye fatigue.
Whenmeasuringanaltitude,haveanassistantnoteand
recordthetimeifpossible,witha“stand-by”warningwhen
themeasurementisalmostready,anda“mark”atthe
momentasightismade.Ifaflashlightisneededtoseethe
comparingwatch,theassistantshouldbecarefulnotto
interfere with the navigator’s night vision.
Ifanassistantisnotavailabletotimetheobservations,the
observerholdsthewatchinthepalmofhislefthand,leavinghis
fingersfreetomanipulatethetangentscrewofthesextant.After
makingtheobservation,henotesthetimeasquicklyaspossible.
Thedelaybetweencompletingthealtitudeobservationand
noting the time should not be more than one or two seconds.
1608. Reading the Sextant
Readingamicrometerdrumsextantisdoneinthree
steps.Thedegreesarereadbynotingthepositionofthe
arrowontheindexarminrelationtothearc.Theminutes
arereadbynotingthepositionofthezeroonthevernier
withrelationtothegraduationsonthemicrometerdrum.
Thefractionofaminuteisreadbynotingwhichmarkon
theverniermostnearlycoincideswithoneofthe
graduationsonthemicrometerdrum.Thisissimilarto
readingthetimewiththehour,minute,andsecondhandsof
awatch.Inboth,therelationshipofonepartofthereading
totheothersshouldbekeptinmind.Thus,ifthehourhand
ofawatchwereabouton“4,”onewouldknowthatthetime
wasaboutfouro’clock.Butiftheminutehandwereon
“58,”onewouldknowthatthetimewas0358(or1558),not
0458(or1658).Similarly,ifthearcindicatedareadingof
about40°,and58'onthemicrometerdrumwereopposite
zeroonthevernier,onewouldknowthatthereadingwas
39°58',not40°58'.Similarly,anydoubtastothecorrect
minutecanberemovedbynotingthefractionofaminute
fromthepositionofthevernier.InFigure1608athereading
is29°42.5'.Thearrowontheindexmarkisbetween29°
and30°,thezeroonthevernierisbetween42'and43',and
the0.5'graduationontheverniercoincideswithoneofthe
graduations on the micrometer drum.
Theprincipleofreadingaverniersextantisthesame,but
thereadingismadeintwosteps.Figure1608bshowsatypical
altitudesetting.Eachdegreeonthearcofthissextantis
graduatedintothreeparts,permittinganinitialreadingbythe
referencemarkontheindexarmtothenearest20'ofarc.In
thisillustrationthereferencemarkliesbetween29°40'and
30°00',indicatingareadingbetweenthesevalues.Thereading
forthefractionof20'ismadeusingthevernier,whichis
engravedontheindexarmandhasthesmallreferencemarkas
itszerograduation.Onthisvernier,40graduationscoincide
with39graduationsonthearc.Eachgraduationonthevernier
isequivalentto1/40ofonegraduationof20'onthearc,or0.5',
or30".Intheillustration,theverniergraduationrepresenting2
1/2'(2'30")mostnearlycoincideswithoneofthegraduations
onthearc.Therefore,thereadingis29°42'30",or29°42.5',as
before.Whenavernierofthistypeisused,anydoubtasto
whichmarkontheverniercoincideswithagraduationonthe
arccanusuallyberesolvedbynotingthepositionofthevernier
mark on each side of the one that seems to be in coincidence.
Negativereadings,suchasanegativeindexcorrection,
aremadeinthesamemanneraspositivereadings;the
variousfiguresareaddedalgebraically.Thus,ifthethree
partsofamicrometerdrumreadingare(-)1°,56'and0.3',
the total reading is ( - )1° + 56' + 0.3' = ( - )3.7'.
1609. Developing Observational Skill
Awell-constructedmarinesextantiscapableof
measuringangleswithaninstrumenterrornotexceeding0.1'.
Linesofpositionfromaltitudesofthisaccuracywouldnotbe
INSTRUMENTS FOR CELESTIAL NAVIGATION265
Figure 1608a. Micrometer drum sextant set at 29°42.5'.
Figure 1608b. Vernier sextant set at 29°42'30".
266INSTRUMENTS FOR CELESTIAL NAVIGATION
inerrorbymorethanabout200yards.However,thereare
varioussourcesoferror,otherthaninstrumental,inaltitudes
measuredbysextant.Oneoftheprincipalsourcesisthe
observer.
Thefirstfixastudentcelestialnavigatorplotsislikely
tobedisappointing.Mostnavigatorsrequireagreatamount
ofpracticetodeveloptheskillnecessaryforconsistently
goodobservations.Butpracticealoneisnotsufficient.
Goodtechniqueshouldbedevelopedearlyandrefined
throughoutthenavigator’scareer.Manygoodpointerscan
beobtainedfromexperiencednavigators,buteach
developshisowntechnique,andapracticethatproves
successfulforoneobservermaynothelpanother.Also,an
experiencednavigatorisnotnecessarilyagoodobserver.
Navigatorshaveanaturaltendencytojudgetheaccuracyof
theirobservationsbythesizeofthefigureformedwhenthe
linesofpositionareplotted.Althoughthisissome
indication,itisanimperfectone,becauseitdoesnot
indicateerrorsofindividualobservations,andmaynot
reflectconstanterrors.Also,itisacompoundofanumber
oferrors,someofwhicharenotsubjecttothenavigator’s
control.
Linesofpositionfromcelestialobservationsshouldbe
comparedoftenwithgoodpositionsobtainedbyelectronics
or piloting. Common sources of error are:
1.The sextant may not be rocked properly.
2.Tangency may not be judged accurately.
3.A false horizon may have been used.
4.Subnormal refraction (dip) might be present.
5.The height of eye may be wrong.
6.Time might be in error.
7.Theindexcorrectionmayhavebeendetermined
incorrectly.
8.The sextant might be out of adjustment.
9.An error may have been made in the computation.
Generally,itispossibletocorrectobservation
techniqueerrors,butoccasionallyapersonalerrorwill
persist.Thiserrormightvaryasafunctionofthebody
observed,degreeoffatigueoftheobserver,andother
factors.Forthisreason,apersonalerrorshouldbeapplied
with caution.
Toobtaingreateraccuracy,takeanumberofclosely-
spacedobservations.Plottheresultingaltitudesversustime
andfairacurvethroughthepoints.Unlessthebodyisnear
thecelestialmeridian,thiscurveshouldbeastraightline.
Usethisgraphtodeterminethealtitudeofthebodyatany
timecoveredbythegraph.Itisbesttouseapointnearthe
middleoftheline.Usinganavigationalcalculatoror
computerprogramtoreducesightswillyieldgreater
accuracybecauseoftheroundingerrorsinherentintheuse
ofsightreductiontables,andbecausemanymoresightscan
be reduced in a given time, thus averaging out errors.
Asimplermethodinvolvesmakingobservationsat
equalintervals.Thisprocedureisbaseduponthe
assumptionthat,unlessthebodyisonthecelestial
meridian,thechangeinaltitudeshouldbeequalforequal
intervalsoftime.Observationscanbemadeatequal
intervalsofaltitudeortime.Iftimeintervalsareconstant,
themidtimeandtheaveragealtitudeareusedasthe
observation.Ifaltitudeincrementsareconstant,theaverage
time and mid altitude are used.
Ifonlyasmallnumberofobservationsisavailable,
reduceandplottheresultinglinesofposition;thenadjust
themtoacommontime.Theaveragepositionoftheline
mightbeused,butitisgenerallybetterpracticetousethe
middleline.Rejectanyobservationconsideredunreliable
when determining the average.
1610. Care of the Sextant
Asextantisaruggedinstrument.However,careless
handlingorneglectcancauseitirreparableharm.Ifyou
dropit,takeittoaninstrumentrepairshopfortestingand
inspection.Whennotusingthesextant,stowitinasturdy
andsufficientlypaddedcase.Keepthesextantawayfrom
excessiveheatanddampness.Donotexposeittoexcessive
vibration.Donotleaveitunattendedwhenitisoutofits
case.Donotholditbyitslimb,indexarm,ortelescope.Lift
itonlybyitsframeorhandle.Donotliftitbyitsarcor
index bar.
Nexttocarelesshandling,moistureisthesextant’s
greatestenemy.Wipethemirrorsandthearcaftereachuse.
Ifthemirrorsgetdirty,cleanthemwithlenspaperanda
smallamountofalcohol.Cleanthearcwithammonia;
neveruseapolishingcompound.Whencleaning,donot
apply excessive pressure to any part of the instrument.
Silicagelkeptinthesextantcasewillhelpkeepthe
instrumentfreefrommoistureandpreservethemirrors.
Occasionallyheatthesilicageltoremovetheabsorbed
moisture.
Rinsethesextantwithfreshwaterifseawatergetson
it.Wipethesextantgentlywithasoftcottonclothanddry
the optics with lens paper.
Glassopticsdonottransmitallthelightreceived
becauseglasssurfacesreflectasmallportionoflight
incidentontheirface.Thislossoflightreducesthe
brightnessoftheobjectviewed.Viewinganobjectthrough
severalglassopticsaffectstheperceivedbrightnessand
makestheimageindistinct.Thereflectionalsocausesglare
whichobscurestheobjectbeingviewed.Toreducethis
effecttoaminimum,theglassopticsaretreatedwithathin,
fragile,anti-reflectioncoating.Therefore,applyonlylight
pressurewhenpolishingthecoatedoptics.Blowloosedust
offthelensbeforewipingthemsogritdoesnotscratchthe
lens.
Occasionally,oilandcleanthetangentscrewandthe
teethonthesideofthelimb.Usetheoilprovidedwiththe
sextantoranall-purposelightmachineoil.Occasionallyset
theindexarmofanendlesstangentscrewatoneextremity
ofthelimb,oilitlightly,andthenrotatethetangentscrew
INSTRUMENTS FOR CELESTIAL NAVIGATION267
overthelengthofthearc.Thiswillcleantheteethand
spreadoiloverthem.Whenstowingasextantforalong
period,cleanitthoroughly,polishandoilit,andprotectits
arcwithathincoatofpetroleumjelly.Ifthemirrorsneed
re-silvering, take the sextant to an instrument shop.
1611. Non Adjustable Sextant Errors
Thenon-adjustablesextanterrorsareprismaticerror,
graduationerror,andcenteringerror.Thehigherthequality
of the instrument, the less these error will be.
Prismaticerroroccurswhenthefacesoftheshade
glassesandmirrorsarenotparallel.Errorduetolackof
parallelismintheshadeglassesmaybecalledshadeerror.
Thenavigatorcandetermineshadeerrorintheshade
glassesneartheindexmirrorbycomparinganangle
measuredwhenashadeglassisinthelineofsightwiththe
sameanglemeasuredwhentheglassisnotinthelineof
sight.Inthismanner,determineandrecordtheerrorfor
eachshadeglass.Beforeusingacombinationofshade
glasses,determinetheircombinederror.Ifcertain
observationsrequireadditionalshading,usethecolored
telescopeeyepiececover.Thisdoesnotintroduceanerror
becausedirectandreflectedraysaretravelingtogether
whentheyreachthecoverandare,therefore,affected
equally by any lack of parallelism of its two sides.
Graduationerrorsoccurinthearc,micrometerdrum,
andvernierofasextantwhichisimproperlycutor
incorrectlycalibrated.Normally,thenavigatorcannot
determinewhetherthearcofasextantisimproperlycut,but
theprincipleoftheverniermakesitpossibletodetermine
theexistenceofgraduationerrorsinthemicrometerdrum
orvernier.Thisisausefulguideindetectingapoorlymade
instrument.Thefirstandlastmarkingsonanyvernier
shouldalignperfectlywithonelessgraduationonthe
adjacent micrometer drum.
Centeringerrorresultsiftheindexarmdoesnotpivot
attheexactcenterofthearc’scurvature.Calculate
centeringerrorbymeasuringknownanglesafterremoving
alladjustableerrors.Usehorizontalanglesaccurately
measuredwithatheodoliteasreferencesforthisprocedure.
Severalreadingsbyboththeodoliteandsextantshould
minimizeerrors.Ifatheodoliteisnotavailable,use
calculatedanglesbetweenthelinesofsighttostarsasthe
reference,comparingthesecalculatedvalueswiththe
valuesdeterminedbythesextant.Tominimizerefraction
errors,selectstarsataboutthesamealtitudeandavoidstars
nearthehorizon.Thesameshadeglasses,ifany,usedfor
determiningindexerrorshouldbeusedformeasuring
centering error.
Themanufacturernormallydeterminesthemagnitude
ofallthreenon-adjustableerrorsandreportsthemtothe
userasinstrumenterror.Thenavigatorshouldapplythe
correction for this error to each sextant reading.
1612. Adjustable Sextant Error
Thenavigatorshouldmeasureandremovethe
following adjustable sextant errors in the order listed:
1.PerpendicularityError:Adjustfirstforperpendicu-
larityoftheindexmirrortotheframeofthesextant.Totestfor
perpendicularity,placetheindexarmatabout35°onthearc
andholdthesextantonitssidewiththeindexmirrorupand
towardtheeye.Observethedirectandreflectedviewsofthe
sextantarc,asillustratedinFigure1612a.Ifthetwoviewsare
notjoinedinastraightline,theindexmirrorisnotperpen-
dicular.Ifthereflectedimageisabovethedirectview,the
mirrorisinclinedforward.Ifthereflectedimageisbelowthe
directview,themirrorisinclinedbackward.Makethe
adjustment using two screws behind the index mirror.
2.SideError:Anerrorresultingfromthehorizonglass
notbeingperpendiculariscalledsideerror.Totestforside
error,settheindexarmatzeroanddirectthelineofsightata
star.Thenrotatethetangentscrewbackandforthsothatthe
reflectedimagepassesalternatelyaboveandbelowthedirect
view.If,inchangingfromonepositiontotheother,thereflected
imagepassesdirectlyovertheunreflectedimage,nosideerror
exists.Ifitpassestooneside,sideerrorexists.Figure1612b
illustratesobservationswithoutsideerror(left)andwithside
error(right).Whetherthesextantreadszerowhenthetrueand
reflectedimagesareincoincidenceisimmaterialforthistest.An
alternativemethodistoobserveaverticalline,suchasoneedge
ofthemastofanothervessel(orthesextantcanbeheldonits
sideandthehorizonused).Ifthedirectandreflectedportionsdo
notformacontinuousline,thehorizonglassisnot
perpendiculartotheframeofthesextant.Athirdmethod
involvesholdingthesextantvertically,asinobservingthe
altitudeofacelestialbody.Bringthereflectedimageofthe
horizonintocoincidencewiththedirectviewuntilitappearsas
acontinuouslineacrossthehorizonglass.Thentiltthesextant
rightorleft.Ifthehorizonstillappearscontinuous,thehorizon
glassisperpendiculartotheframe,butifthereflectedportion
appearsaboveorbelowthepartseendirectly,theglassisnot
perpendicular.Maketheappropriateadjustmentusingtwo
screws behind the horizon glass.
3.CollimationError:Ifthelineofsightthroughthe
telescopeisnotparalleltotheplaneoftheinstrument,a
collimationerrorwillresult.Altitudesmeasuredwillbe
greaterthantheiractualvalues.Tocheckforparallelismof
thetelescope,insertitinitscollarandobservetwostars90°
ormoreapart.Bringthereflectedimageofoneinto
coincidencewiththedirectviewoftheotherneareitherthe
rightorleftedgeofthefieldofview(theupperorlower
edgeifthesextantishorizontal).Thentiltthesextantsothat
thestarsappearneartheoppositeedge.Iftheyremainin
coincidence,thetelescopeisparalleltotheframe;ifthey
separate,itisnot.Analternativemethodinvolvesplacing
thetelescopeinitscollarandthenlayingthesextantona
flattable.Sightalongtheframeofthesextantandhavean
assistantplaceamarkontheoppositebulkhead,inlinewith
theframe.Placeanothermarkabovethefirst,atadistance
equaltothedistancefromthecenterofthetelescopetothe
frame.Thissecondlineshouldbeinthecenterofthefield
268INSTRUMENTS FOR CELESTIAL NAVIGATION
ofviewofthetelescopeifthetelescopeisparalleltothe
frame. Adjust the collar to correct for non-parallelism.
4.IndexError:Indexerroristheerrorremainingafter
thenavigatorhasremovedperpendicularityerror,sideerror,
andcollimationerror.Theindexmirrorandhorizonglassnot
beingparallelwhentheindexarmissetexactlyatzeroisthe
majorcauseofindexerror.Totestforparallelismofthe
mirrors,settheinstrumentatzeroanddirectthelineofsightat
thehorizon.Adjustthesextantreadingasnecessarytocause
bothimagesofthehorizontocomeintoline.Thesextant’s
readingwhenthehorizoncomesintolineistheindexerror.If
theindexerrorispositive,subtractitfromeachsextant
reading.Iftheindexerrorisnegative,addittoeachsextant
reading.
1613. Selecting a Sextant
Carefullymatchtheselectedsextanttoitsrequireduses.
Foroccasionalsmallcraftorstudentuse,aplasticsextantmay
beadequate.Aplasticsextantmayalsobeappropriateforan
emergencynavigationkit.Accurateoffshorenavigation
requiresaqualitymetalinstrument.Forordinaryusein
measuringaltitudesofcelestialbodies,anarcof90°orslightly
moreissufficient.Ifbacksightsordetermininghorizontal
anglesareoftenrequired,purchaseonewithalongerarc.An
experiencedmarinerornauticalinstrumenttechniciancan
provide valuable advice on the purchase of a sextant.
1614. The Artificial Horizon
Measurementofaltituderequiresanexacthorizontal
reference,normallyprovidedatseabythevisiblehorizon.If
thehorizonisnotclearlyvisible,however,adifferent
horizontalreferenceisrequired.Suchareferenceiscommonly
termedanartificialhorizon.Ifitisattachedto,orpartof,the
sextant,altitudescanbemeasuredatsea,onland,orintheair,
whenever celestial bodies are available for observations.
Anexternalartificialhorizoncanbeimprovisedbya
carefullylevelledmirrororapanofdarkliquid.Tousean
externalartificialhorizon,standorsitsothatthecelestialbody
isreflectedinthemirrororliquid,andisalsovisibleindirect
view.Withthesextant,bringthedouble-reflectedimageinto
coincidencewiththeimageappearingintheliquid.Foralower
limbobservationoftheSunortheMoon,bringthebottomof
thedouble-reflectedimageintocoincidencewiththetopofthe
imageintheliquid.Foranupper-limbobservation,bringthe
oppositesidesintocoincidence.Ifoneimagecoverstheother,
the observation is of the center of the body.
Aftertheobservation,applytheindexcorrectionandany
otherinstrumentalcorrection.Thentakehalftheremaining
angleandapplyallothercorrectionsexceptdip(heightofeye)
correction,sincethisisnotapplicable.IfthecenteroftheSun
or Moon is observed, omit the correction for semidiameter.
Figure 1612a. Testing the perpendicularity of the index mirror. Here the mirror is not perpendicular.
Figure1612b.Testingtheperpendicularityofthehorizonglass.
Ontheleft,sideerrordoesnotexist.Attheright,sideerrordoes
exist.
INSTRUMENTS FOR CELESTIAL NAVIGATION269
1615. Artificial Horizon Sextants
Varioustypesofartificialhorizonshavebeenused,
includingabubble,gyroscope,andpendulum.Ofthese,the
bubblehasbeenmostwidelyused.Thistypeofinstrumentis
fittedasabackupsystemtoinertialandotherpositioning
systemsinafewaircraft,fulfillingtherequirementforaself-
contained,non-emittingsystem.Onland,askilledobserver
usinga2-minuteaveragingbubbleorpendulumsextantcan
measurealtitudestoanaccuracyofperhaps2',(2miles).
This,ofcourse,referstotheaccuracyofmeasurementonly,
anddoesnotincludeadditionalerrorssuchasabnormal
refraction,deflectionofthevertical,computingandplotting
errors,etc.Insteadyflightthroughsmoothairtheerrorofa
2-minute observation is increased to perhaps 5 to 10 miles.
Atsea,withvirtuallynorollorpitch,resultsshould
approachthoseonland.However,evenagentlerollcauses
largeerrors.Undertheseconditionsobservationalerrorsof
10-16milesarenotunreasonable.Withamoderatesea,
errorsof30milesormorearecommon.Inaheavysea,any
usefulobservationsarevirtuallyimpossibletoobtain.
Singlealtitudeobservationsinamoderateseacanbein
error by a matter of degrees.
Whenthehorizonisobscuredbyiceorhaze,polar
navigatorscansometimesobtainbetterresultswithan
artificial-horizonsextantthanwithamarinesextant.Some
artificial-horizonsextantshaveprovisionformaking
observationswiththenaturalhorizonasareference,but
resultsarenotgenerallyassatisfactoryasbymarinesextant.
Becauseoftheirmorecomplicatedopticalsystems,andthe
needforprovidingahorizontalreference,artificial-horizon
sextantsaregenerallymuchmorecostlytomanufacturethan
marine sextants.
Altitudesobservedbyartificial-horizonsextantsare
subjecttothesameerrorsasthoseobservedbymarine
sextant,exceptthatthedip(heightofeye)correctiondoes
notapply.Also,whenthecenteroftheSunorMoonis
observed, no correction for semidiameter is required.
CHRONOMETERS
1616. The Marine Chronometer
Thespring-drivenmarinechronometerisaprecision
timepieceusedaboardshiptoprovideaccuratetimefor
celestialobservations.Achronometerdiffersfromaspring-
drivenwatchprincipallyinthatitcontainsavariablelever
devicetomaintainevenpressureonthemainspring,anda
specialbalancedesignedtocompensatefortemperature
variations.
Aspring-drivenchronometerissetapproximatelyto
Greenwichmeantime(GMT)andisnotresetuntilthe
instrumentisoverhauledandcleaned,usuallyatthree-year
intervals.ThedifferencebetweenGMTandchronometer
time(C)iscarefullydeterminedandappliedasacorrection
toallchronometerreadings.Thisdifference,called
chronometererror(CE),isfast(F)ifchronometertimeis
laterthanGMT,andslow(S)ifearlier.Theamountby
whichchronometererrorchangesin1dayiscalled
chronometerrate.Anerraticrateindicatesadefective
instrument requiring repair.
Theprincipalmaintenancerequirementisregular
windingataboutthesametimeeachday.Atmaximum
intervalsofaboutthreeyears,aspring-drivenchronometer
shouldbesenttoachronometerrepairshopforcleaning
and overhaul.
1617. Quartz Crystal Marine Chronometers
Quartzcrystalmarinechronometershavereplaced
spring-drivenchronometersaboardmanyshipsbecauseof
theirgreateraccuracy.TheyaremaintainedonGMTdirectly
fromradiotimesignals.Thiseliminateschronometererror
(CE)andwatcherror(WE)corrections.Shouldthesecond
handbeinerrorbyareadableamount,itcanbereset
electrically.
Thebasicelementfortimegenerationisaquartz
crystaloscillator.Thequartzcrystalistemperature
compensatedandishermeticallysealedinanevacuated
envelope.Acalibratedadjustmentcapabilityisprovidedto
adjust for the aging of the crystal.
Thechronometerisdesignedtooperateforaminimum
of1yearonasinglesetofbatteries.Agoodmarine
chronometerhasabuilt-inpushbuttonbatterytestmeter.
Themeterfaceismarkedtoindicatewhenthebattery
shouldbereplaced.Thechronometercontinuestooperate
andkeepthecorrecttimeforatleast5minuteswhilethe
batteriesarechanged.Thechronometerisdesignedto
accommodatethegradualvoltagedropduringthelifeofthe
batteries while maintaining accuracy requirements.
1618. Watches
Achronometershouldnotberemovedfromitscaseto
timesights.Observationsmaybetimedandship’sclocks
setwithacomparingwatch,whichissettochronometer
time(GMT,alsoknownasUT)andtakentothebridge
wingforrecordingsighttimes.Inpractice,awristwatch
coordinatedtothenearestsecondwiththechronometerwill
be adequate.
Astopwatch,eitherspringwoundordigital,mayalso
beusedforcelestialobservations.Inthiscase,thewatchis
startedataknownGMTbychronometer,andtheelapsed
timeofeachsightaddedtothistoobtainGMTofthesight.
Allchronometersandwatchesshouldbechecked
regularlywitharadiotimesignal.Timesandfrequenciesof
radiotimesignalsarelistedinNIMAPub.117,Radio
Navigational Aids.
270INSTRUMENTS FOR CELESTIAL NAVIGATION
1619. Navigational Calculators
Whilenotconsidered“instruments”inthestrictsense
oftheword,certainlyoneoftheprofessionalnavigator’s
mostusefultoolsisthenavigationalcalculatororcomputer
program.Calculatorseliminateseveralpotentialsourcesof
errorincelestialnavigation,andpermitthesolutionof
manymoresightsinmuchlesstime,makingitpossibleto
refineacelestialpositionmuchmoreaccuratelythanis
practical using mathematical or tabular methods.
Calculatorsalsosavespaceandweight,avaluablecon-
siderationonmanycraft.Onesmallcalculatorcanreplace
severalheavyandexpensivevolumesoftables,andisinex-
pensiveenoughthatthereislittlereasonnottocarryaspare
forbackupuseshouldtheprimaryonefail.Thepre-pro-
grammedcalculatorsareatleastasrobustinconstruction,
probablymoreso,thanthesextantitself,andproperlycared
for,willlastalifetimewithnomaintenanceexceptnewbat-
teries from time to time.
Ifthevesselcarriesacomputerforothership’schores
suchasinventorycontrolorpersonneladministration,there
islittlereasonnottouseitforcelestialnavigation.Free-
wareorinexpensiveprogramsareavailablewhichtakeup
littleharddiskspaceandallowrapidsolutionofalltypesof
celestialnavigationproblems.Typicallytheywillalsotake
careofrouteplanning,sailings,tides,weatherrouting,elec-
tronic charts, and numerous other tasks.
Usingacalculatororsightreductionprogram,itispos-
sibletotakeandsolvehalfadozenormoresightsina
fractionofthetimeitwouldnormallytaketoshoottwoor
threeandsolvethembyhand.Thiswillincreasetheaccuracy
ofthefixbyaveragingouterrorsintakingthesights.The
computerizedsolutionisalwaysmoreaccuratethantabular
methods because it is free of rounding errors.
271
CHAPTER 17
AZIMUTHS AND AMPLITUDES
INTRODUCTION
1700. Checking Compass Error
Thenavigatormustconstantlybeconcernedaboutthe
accuracyoftheship’sprimaryandbackupcompasses,and
shouldcheckthemregularly.Aregularlyannotatedcompass
logbookwillallowthenavigatortonoticeadevelopingerror
before it becomes a serious problem.
Aslongasatleasttwodifferenttypesofcompass(e.g.
mechanicalgyroandfluxgate,ormagneticandringlaser
gyro)areconsistentwitheachother,onecanbereasonably
surethatthereisnoappreciableerrorineithersystem.Since
differenttypesofcompassesdependondifferentscientific
principlesandarenotsubjecttothesameerrorsources,their
agreementindicatesalmostcertainlythatnoerrorispresent.
Anavigationalcompasscanbecheckedagainstthe
headingreferenceofaninertialnavigationsystemifoneis
installed.Onecanalsorefertotheship’sindicatedGPStrack
aslongascurrentandleewayarenotfactors,sothatthe
ship’s COG and heading are in close agreement.
Thenavigator’sonlycompletelyindependent
directionalreference(becauseitisextra-terrestrialandnot
man-made)isthesky.Theprimarycompassshouldbe
checkedoccasionallybycomparingtheobservedand
calculatedazimuthsandamplitudesofacelestialbody.The
differencebetweentheobservedandcalculatedvaluesisthe
compass error. This chapter discusses these procedures.
Theoretically,theseproceduresworkwithanycelestial
body.However,theSunandPolarisareusedmostoften
whenmeasuringazimuths,andtherisingorsettingSun
when measuring amplitudes.
Whileerrorscanbecomputedtothenearesttenthofa
degreeorso,itisseldompossibletosteerashipthat
accurately,especiallywhenaseaisrunning,anditis
reasonabletoroundcalculationstothenearesthalfor
perhaps whole degree for most purposes.
Varioushand-heldcalculatorsandcomputerprograms
areavailabletorelievethetediumanderrorsoftabularand
mathematicalmethodsofcalculatingazimuthsandampli-
tudes.NavalnavigatorswillfindtheSTELLAprogram
usefulinthisregard.Chapter20discussesthisprogramin
greater detail.
AZIMUTHS
1701. Compass Error by Azimuth of the Sun
MarinersmayusePub229,SightReductionTablesfor
MarineNavigationtocomputetheSun’sazimuth.They
comparethecomputedazimuthtotheazimuthmeasured
withthecompasstodeterminecompasserror.Incomputing
anazimuth,interpolatethetabularazimuthangleforthe
differencebetweenthetableargumentsandtheactual
valuesofdeclination,latitude,andlocalhourangle.Dothis
triple interpolation of the azimuth angle as follows:
1.EntertheSightReductionTableswiththenearest
integralvaluesofdeclination,latitude,andlocal
hourangle.Foreachofthesearguments,extracta
base azimuth angle.
2.ReenterthetableswiththesamelatitudeandLHA
argumentsbutwiththedeclinationargument1°
greaterorlessthanthebasedeclinationargument,
dependinguponwhethertheactualdeclinationis
greaterorlessthanthebaseargument.Recordthe
differencebetweentherespondentazimuthangle
andthebaseazimuthangleandlabelitasthe
azimuth angle difference (Z Diff.).
3.Reenterthetableswiththebasedeclinationand
LHAarguments,butwiththelatitudeargument1°
greaterorlessthanthebaselatitudeargument,
dependinguponwhethertheactual(usuallyDR)
latitudeisgreaterorlessthanthebaseargument.
Record the Z Diff. for the increment of latitude.
4.Reenterthetableswiththebasedeclinationand
latitudearguments,butwiththeLHAargument1°
greaterorlessthanthebaseLHAargument,
dependinguponwhethertheactualLHAisgreater
orlessthanthebaseargument.RecordtheZDiff.
for the increment of LHA.
5.Correctthebaseazimuthangleforeach
increment.
272AZIMUTHS AND AMPLITUDES
Example:
InDRlatitude33°24.0'N,theazimuthoftheSunis096.5°
pgc.Atthetimeoftheobservation,thedeclinationoftheSun
is20°13.8'N;thelocalhourangleoftheSunis316°41.2'.
Determine compass error.
Solution:
SeeFigure1701Entertheactualvalueofdeclination,
DRlatitude,andLHA.Roundeachargumenttothenearest
wholedegree.Inthiscase,roundthedeclinationandthe
latitudedowntothenearestwholedegree.RoundtheLHA
uptothenearestwholedegree.EntertheSightReduction
Tableswiththesewholedegreeargumentsandextractthe
baseazimuthvaluefortheseroundedoffarguments.
Record the base azimuth value in the table.
Asthefirststepinthetripleinterpolationprocess,
increasethevalueofdeclinationby1°(to21°)becausethe
actualdeclinationvaluewasgreaterthanthebasedeclination.
EntertheSightReductionTableswiththefollowing
arguments:(1)Declination=21°;(2)DRLatitude=33°;(3)
LHA=317°.Recordthetabulatedazimuthforthese
arguments.
Asthesecondstepinthetripleinterpolationprocess,
increasethevalueoflatitudeby1°to34°becausethe
actualDRlatitudewasgreaterthanthebaselatitude.Enter
theSightReductionTableswiththefollowingarguments:
(1)Declination=20°;(2)DRLatitude=34°;(3)LHA=
317°. Record the tabulated azimuth for these arguments.
Asthethirdandfinalstepinthetripleinterpolation
process,decreasethevalueofLHAto316°becausethe
actualLHAvaluewassmallerthanthebaseLHA.Enterthe
SightReductionTableswiththefollowingarguments:(1)
Declination=20°;(2)DRLatitude=33°;(3)LHA=316°.
Record the tabulated azimuth for these arguments.
CalculatetheZDifferencebysubtractingthebase
azimuthfromthetabulatedazimuth.Becarefultocarrythe
correct sign.
Z Difference = Tab Z - Base Z
Next,determinetheincrementforeachargumentby
takingthedifferencebetweentheactualvaluesofeach
argumentandthebaseargument.Calculatethecorrection
foreachofthethreeargumentinterpolationsby
multiplyingtheincrementbytheZdifferenceanddividing
the resulting product by 60.
Thesignofeachcorrectionisthesameasthesignofthe
correspondingZdifferenceusedtocalculateit.Intheabove
example,thetotalcorrectionsumsto-0.1'.Applythisvalue
tothebaseazimuthof97.8°toobtainthetrueazimuth97.7°.
Comparethistothecompassreadingof096.5°pgc.The
compasserroris1.2°E,whichcanberoundedto1°for
steering and logging purposes.
AZIMUTH OF POLARIS
1702. Compass Error By Azimuth Of Polaris
ThePolaristablesintheNauticalAlmanaclistthe
azimuthofPolarisforlatitudesbetweentheequatorand65°
N.Figure2012inChapter20showsthistable.Comparea
compassbearingofPolaristothetabularvalueofPolaristo
determinecompasserror.Theenteringargumentsforthe
table are LHA of Aries and observer latitude.
Example:
OnMarch17,2001,atL33°15.0'Nandλ045°00.0'W,
at02-00-00GMT,Polarisbears358.6°pgc.Calculatethe
compass error.
Solution:
EntertheazimuthsectionofthePolaristablewiththe
Actual
Base
Arguments
Base
Z
Tab*
ZZ Diff.Increments
Correction
(Z Diffx Inc.÷ 60)
Dec.20˚13.8'N20˚ 97.8˚ 96.4˚–1.4˚ 13.8'–0.3˚
DR Lat.33˚24.0'N33˚(Same)97.8˚ 98.9˚+1.1˚ 24.0'+0.4˚
LHA316˚41.2'317˚ 97.8˚ 97.1˚– 0.7˚ 18.8'–0.2˚
Base Z97.8˚ Total Corr.–0.1˚
Corr.
(–)
0.1˚
ZN 97.7˚E
*Respondent for the two base arguments and 1˚
change from third base argument, in vertical
order of Dec., DR Lat., and LHA.
Zn097.7˚
Zn pgc
096.5˚
Gyro Error1.2˚E
Figure 1701. Azimuth by Pub. No. 229.
Date17 March 2001
Time (GMT)02-00-00
GHA Aries204° 43.0'
Longitude045° 00.0'W
LHA Aries159° 43.0'
AZIMUTHS AND AMPLITUDES273
calculatedLHAofAries.Inthiscase,gotothecolumnfor
LHAAriesbetween160°and169°.Followthatcolumn
downandextractthevalueforthegivenlatitude.Sincethe
incrementbetweentabulatedvaluesissosmall,visual
interpolationissufficient.Inthiscase,theazimuthfor
PolarisforthegivenLHAofAriesandthegivenlatitude
is 359.3°.
AMPLITUDES
1703. Amplitudes
Acelestialbody’samplitudeangleisthecomplement
ofitsazimuthangle.Atthemomentthatabodyrisesorsets,
theamplitudeangleisthearcofthehorizonbetweenthe
bodyandtheEast/Westpointofthehorizonwherethe
observer’sprimeverticalintersectsthehorizon(at90°),
whichisalsothepointwheretheplaneoftheequator
intersectsthehorizon(atananglenumericallyequaltothe
observer’s co-latitude). SeeFigure 1703.
Inpracticalnavigation,abearing(pscorpgc)ofabody
canbeobservedwhenitisoneitherthecelestialorthe
visiblehorizon.Todeterminecompasserror,simply
convertthecomputedamplitudeangletotruedegreesand
compare it with the observed compass bearing.
The angle is computed by the formula:
sin A = sin Dec / cos Lat.
Thisformulagivestheangleattheinstantthebodyis
onthecelestialhorizon.Itdoesnotcontainanaltitudeterm
becausethebody’scomputedaltitudeiszeroatthisinstant.
TheangleisprefixedEifthebodyisrisingandWifit
issetting.Thisistheonlyangleincelestialnavigation
referencedFROMEastorWest,i.e.fromtheprime
vertical.Abodywithnortherlydeclinationwillriseandset
Northoftheprimevertical.Likewise,abodywithsoutherly
declinationwillriseandsetSouthoftheprimevertical.
Therefore,theangleissuffixedNorStoagreewiththe
nameofthebody’sdeclination.Abodywhosedeclination
is zero rises and sets exactly on the prime vertical.
TheSunisonthecelestialhorizonwhenitslowerlimb
isapproximatelytwothirdsofadiameterabovethevisible
horizon.TheMoonisonthecelestialhorizonwhenits
upperlimbisonthevisiblehorizon.Starsandplanetsare
onthecelestialhorizonwhentheyareapproximatelyone
Sun diameter above the visible horizon.
Whenobservingabodyonthevisiblehorizon,a
correctionfromTable23mustbeapplied.Thiscorrection
accountsfortheslightchangeinbearingasthebodymoves
betweenthevisibleandcelestialhorizons.Itreducesthe
bearingonthevisiblehorizontothecelestialhorizon,from
which the table is computed.
FortheSun,stars,andplanets,applythiscorrectionto
theobservedbearinginthedirectionawayfromthe
elevatedpole.Forthemoon,applyonehalfofthe
correctiontowardtheelevatedpole.Notethatthealgebraic
signofthecorrectiondoesnotdependuponthebody’s
declination,butonlyontheobserver’slatitude.Assuming
thebodyistheSuntheruleforapplyingthecorrectioncan
be outlined as follows:
Thefollowingtwoarticlesdemonstratetheprocedure
forobtainingtheamplitudeoftheSunonboththecelestial
and visible horizons.
1704. Amplitude of the Sun on the Celestial Horizon
Example:
TheDRlatitudeofashipis51°24.6'N.Thenavigator
observesthesettingSunonthecelestialhorizon.Itsdecli-
Tabulated Azimuth359.2°T
Compass Bearing358.6°C
Error0.6°E
Figure1703.Theamplitudeangle(A)subtendsthearcof
thehorizonbetweenthebodyandthepointwheretheprime
verticalandtheequatorintersectthehorizon.Notethatit
is the compliment of the azimuth angle (Z).
Observer’s Lat.Rising/SettingObserved bearing
NorthRisingAdd to
NorthSettingSubtract from
SouthRisingSubtract from
SouthSettingAdd to
274AZIMUTHS AND AMPLITUDES
nation is N 19° 40.4'. Its observed bearing is 303°pgc.
Required:
Gyro error.
Solution:
InterpolateinTable22fortheSun’scalculated
amplitudeasfollows.SeeFigure1704.Theactualvalues
forlatitudeanddeclinationareL=51.4°Nanddec.=N
19.67°.Findthetabulatedvaluesoflatitudeand
declinationclosesttotheseactualvalues.Inthiscase,these
tabulatedvaluesareL=51°anddec.=19.5°.Recordthe
amplitudecorrespondingtothesebasevalues,32.0°,asthe
base amplitude.
Next,holdingthebasedeclinationvalueconstantat
19.5°,increasethevalueoflatitudetothenexttabulated
value:N52°.Notethatthisvalueoflatitudewasincreased
becausetheactuallatitudevaluewasgreaterthanthebase
valueoflatitude.RecordthetabulatedamplitudeforL=
52°anddec.=19.5°:32.8°.Then,holdingthebaselatitude
valueconstantat51°,increasethedeclinationvaluetothe
nexttabulatedvalue:20°.Recordthetabulatedamplitude
for L = 51° and dec. = 20°: 32.9°.
Thelatitude’sactualvalue(51.4°)is0.4oftheway
betweenthebasevalue(51°)andthevalueusedto
determinethetabulatedamplitude(52°).Thedeclination’s
actualvalue(19.67°)is0.3ofthewaybetweenthebase
value(19.5°)andthevalueusedtodeterminethetabulated
amplitude(20.0°).Todeterminethetotalcorrectiontobase
amplitude,multiplytheseincrements(0.4and0.3)bythe
respectivedifferencebetweenthebaseandtabulatedvalues
(+0.8and+0.9,respectively)andsumtheproducts.The
totalcorrectionis+0.6°.Addthetotalcorrection(+0.6°)
tothebaseamplitude(32.0°)todeterminethefinal
amplitude(32.6°)whichwillbeconvertedtoatruebearing.
Becauseofitsnortherlydeclination(inthiscase),the
Sunwas32.6°northofwestwhenitwasonthecelestial
horizon.Thereforeitstruebearingwas302.6°(270°+
32.6°)atthismoment.Comparingthiswiththegyro
bearingof303°givesanerrorof0.4°W,whichcanbe
rounded to 1/2°W.
1705. Amplitude of the Sun on the Visible Horizon
Inhigherlatitudes,amplitudeobservationsshouldbe
madewhenthebodyisonthevisiblehorizonbecausethe
valueofthecorrectionislargeenoughtocausesignificant
erroriftheobservermisjudgestheexactpositionofthe
celestialhorizon.Theobservationwillyieldpreciseresults
whenever the visible horizon is clearly defined.
Example:
Observer’sDRlatitudeis59°47’N,Sun’sdeclination
is5°11.3’S.AtsunrisetheSunisobservedonthevisible
horizon bearing 098.5° pgc.
Required:
Compass error.
Solution:
Giventhisparticularlatitudeanddeclination,the
amplitudeangleis 10.4° S,sothattheSun’struebearing
is100.4°atthemomentitisonthecelestialhorizon,thatis,
whenitsHcisprecisely0°.ApplyingtheTable23
correctiontotheobservedbearingusingtherulesgivenin
Article1703,theSunwouldhavebeenbearing099.7°pgc
hadtheobservationbeenmadewhentheSunwasonthe
celestial horizon. Therefore, the gyro error is 0.7°E.
1706. Amplitude by Calculation
AsanalternativetousingTable22andTable23,a
visiblehorizonamplitudeobservationcanbesolvedbythe
“altitudeazimuth”formula,becauseazimuthandamplitude
anglesarecomplimentary,andtheco-functionsofcompli-
mentary angles are equal; i.e., cosine Z = sine A.
Sine A = [SinD - (sin L sin H)] / (cos L cos H)
Forshipboardobservations,theSun’s(computed)
altitudeisnegative0.7°whenitisonthevisiblehorizon.
UsingthesameentitiesasinArticle1705,theamplitude
angle is computed as follows:
SinA=[sin5.2°-(sin59.8°Xsin-0.7°)]/(cos59.8°
X cos 0.7°)
ActualBaseBase Amp.Tab. Amp.Diff.Inc.Correction
L=51.4°N51°32.0°32.8°+0.8°0.4+0.3°
dec=19.67°N19.5°32.0°32.9°+0.9°0.3
+0.3
°
Total+0.6°
Figure 1704. Interpolation inTable 22 for Amplitude.
275
CHAPTER 18
TIME
TIME IN NAVIGATION
1800. Solar Time
TheEarth’srotationonitsaxiscausestheSunand
othercelestialbodiestoappeartomoveacrosstheskyfrom
easttowesteachday.IfapersonlocatedontheEarth’s
equatormeasuredthetimeintervalbetweentwosuccessive
transitsoverheadofaverydistantstar,hewouldbe
measuringtheperiodoftheEarth’srotation.Ifhethen
madeasimilarmeasurementoftheSun,theresultingtime
wouldbeabout4minuteslonger.ThisisduetotheEarth’s
motionaroundtheSun,whichcontinuouslychangesthe
apparentplaceoftheSunamongthestars.Thus,duringthe
courseofadaytheSunappearstomovealittletotheeast
amongthestars,sothattheEarthmustrotateonitsaxis
throughmorethan360°inordertobringtheSunoverhead
again.
SeeFigure1800.IftheSunisontheobserver’smeridian
whentheEarthisatpointAinitsorbitaroundtheSun,itwill
notbeontheobserver’smeridianaftertheEarthhasrotated
through360°becausetheEarthwillhavemovedalongits
orbittopointB.BeforetheSunisagainontheobserver’s
meridian,theEarthmustturnalittlemoreonitsaxis.The
Sunwillbeontheobserver’smeridianagainwhentheEarth
hasmovedtopointCinitsorbit.Thus,duringthecourseof
adaytheSunappearstomoveeastwardwithrespecttothe
stars.
Theapparentpositionsofthestarsarecommonly
reckonedwithreferencetoanimaginarypointcalledthe
vernalequinox,theintersectionofthecelestialequatorand
theecliptic.TheperiodoftheEarth’srotationmeasured
withrespecttothevernalequinoxiscalledasiderealday.
TheperiodwithrespecttotheSuniscalledanapparent
solar day.
WhenmeasuringtimebytheEarth’srotation,usingthe
actualpositionoftheSun,ortheapparentSun,resultsin
apparentsolartime.UseoftheapparentSunasatimeref-
erenceresultsintimeofnon-constantrateforatleastthree
reasons.First,revolutionoftheEarthinitsorbitisnotcon-
stant.Second,timeismeasuredalongthecelestialequator
andthepathoftherealSunisnotalongthecelestialequa-
tor.Rather,itspathisalongtheecliptic,whichistiltedatan
angleof23°27'withrespecttothecelestialequator.Third,
rotation of the Earth on its axis is not constant.
Figure 1800. Apparent eastward movement of the Sun with respect to the stars.
276TIME
Toobtainaconstantrateoftime,wereplacetheappar-
entSunwithafictitiousmeanSun.ThismeanSunmoves
eastwardalongthecelestialequatoratauniformspeedequal
totheaveragespeedoftheapparentSunalongtheecliptic.
ThismeanSun,therefore,providesauniformmeasureof
timewhichapproximatestheaverageapparenttime.The
speedofthemeanSunalongthecelestialequatoris15°per
hour of mean solar time.
1801. Equation of Time
Meansolartime,ormeantimeasitiscommonly
called,issometimesaheadofandsometimesbehind
apparentsolartime.Thisdifference,whichneverexceeds
about 16.4 minutes, is called theequation of time.
Thenavigatormostoftendealswiththeequationoftime
whendeterminingthetimeofuppermeridianpassageofthe
Sun.TheSuntransitstheobserver’suppermeridianatlocal
apparentnoon.Wereitnotforthedifferenceinratebetween
themeanandapparentSun,theSunwouldbeontheobserver’s
meridianwhenthemeanSunindicated1200localtime.The
apparentsolartimeofuppermeridianpassage,however,is
offsetfromexactly1200meansolartime.Thistimedifference,
theequationoftimeatmeridiantransit,islistedontherighthand
daily pages of theNautical Almanac.
Thesignoftheequationoftimeisnegativeifthetime
ofSun’smeridianpassageisearlierthan1200andpositive
iflaterthan1200.Therefore:ApparentTime=MeanTime
+ (equation of time).
Example1:DeterminethetimeoftheSun’smeridian
passage (Local Apparent Noon) on June 16, 1994.
Solution:SeeFigure2008inChapter20,theNautical
Almanac’srighthanddailypageforJune16,1994.The
equationoftimeislistedinthebottomrighthandcornerof
thepage.Therearetwowaystosolvetheproblem,
dependingontheaccuracyrequiredforthevalueof
meridianpassage.ThetimeoftheSunatmeridianpassage
isgiventothenearestminuteinthe“Mer.Pass.”column.
For June 16, 1994, this value is 1201.
Todeterminetheexacttimeofmeridianpassage,use
thevaluegivenfortheequationoftime.Thisvalueislisted
immediatelytotheleftofthe“Mer.Pass.”columnonthe
dailypages.ForJune16,1994,thevalueisgivenas00
m
37
s
.
Usethe“12
h
”columnbecausetheproblemaskedfor
meridianpassageatLAN.Thevalueofmeridianpassage
fromthe“Mer.Pass.”columnindicatesthatmeridian
passageoccurs
after1200;therefore,addthe37second
correctionto1200toobtaintheexacttimeofmeridian
passage.TheexacttimeofmeridianpassageforJune16,
1994, is 12
h
00
m
37
s
.
Theequationoftime’smaximumvalueapproaches
16
m
22
s
in November.
IftheAlmanacliststhetimeofmeridianpassageas
1200,proceedasfollows.Examinetheequationsoftime
listedintheAlmanactofindthedividinglinemarkingwhere
theequationoftimechangesbetweenpositiveandnegative
values.Examinethetrendofthevaluesnearthisdividingline
to determine the correct sign for the equation of time.
Example2:SeeFigure1801.Determinethetimeofthe
upper meridian passage of the Sun on April 16, 1995.
Solution:FromFigure1801,uppermeridianpassage
oftheSunonApril16,1995,isgivenas1200.Thedividing
linebetweenthevaluesforupperandlowermeridian
passageonApril16thindicatesthatthesignoftheequation
oftimechangesbetweenlowermeridianpassageandupper
meridianpassageonthisdate;thequestion,therefore,
becomes:doesitbecomepositiveornegative?Notethaton
April18,1995,uppermeridianpassageisgivenas1159,
indicatingthatonApril18,1995,theequationoftimeis
positive.Allvaluesfortheequationoftimeonthesameside
ofthedividinglineasApril18tharepositive.Therefore,the
equationoftimeforuppermeridianpassageoftheSunon
April16,1995is(+)00
m
05
s
.Uppermeridianpassage,
therefore, takes place at 11
h
59
m
55
s
.
TocalculatelatitudeandlongitudeatLAN,thenavigator
seldomrequiresthetimeofmeridianpassagetoaccuracies
greaterthanoneminute.Therefore,usethetimelistedunder
the“Mer.Pass.”columntoestimateLANunlessextraordinary
accuracy is required.
1802. Fundamental Systems of Time
AtomictimeisdefinedbytheSystemeInternational
(SI)second,withadurationof9,192,631,770cyclesof
radiationcorrespondingtothetransitionbetweentwo
hyperfinelevelsofthegroundstateofcesium133.
InternationalAtomicTime(TAI)isaninternationaltime
scale based on the average of a number of atomic clocks.
Universaltime(UT)iscountedfrom0hoursat
midnight,withadurationofonemeansolarday,averaging
out minor variations in the rotation of the Earth.
UT0istherotationaltimeofaparticularplaceof
observation,observedasthediurnalmotionofstarsor
extraterrestrial radio sources.
UT1iscomputedbycorrectingUT0fortheeffectof
polarmotiononthelongitudeoftheobserver,andvaries
because of irregularities in the Earth’s rotation.
CoordinatedUniversalTime,orUTC,usedasa
standardreferenceworldwideforcertainpurposes,iskept
Day
SUNMOON
Eqn. of TimeMer.Mer. Pass.
00
h
12
h
Pass.UpperLowerAgePhase
msmshmhmhmd
160002000512000026125516
170013002012000125135417
180027003311590225145518
Figure 1801. The equation of time for April 16, 17, 18, 1995.
TIME277
withinonesecondofTAIbytheintroductionofleap
seconds.ItdiffersfromTAIbyanintegralnumberof
seconds, but is always kept within 0.9 seconds of TAI.
Dynamicaltimehasreplacedephemeristimein
theoreticalusage,andisbasedontheorbitalmotionsofthe
Earth, Moon, and planets.
Terrestrialtime(TT),alsoknownasTerrestrial
DynamicalTime(TDT),isdefinedas86,400secondson
the geoid.
Siderealtimeisthehourangleofthevernalequinox,
andhasaunitofdurationrelatedtotheperiodoftheEarth’s
rotation with respect to the stars.
Delta T is the difference between UT1 and TDT.
Disseminationoftimeisaninherentpartofvarious
electronicnavigationsystems.TheU.S.NavalObservatory
MasterClockisusedtocoordinateLoransignals,andGPS
signalshaveatimereferenceencodedinthedatamessage.
GPStimeisnormallywithin15nanosecondswithSAoff,
about70nanosecondswithSAon.Onenanosecond(one
one-billionthofasecond)oftimeisroughlyequivalentto
one foot on the Earth for the GPS system.
1803. Time and Arc
OnedayrepresentsonecompleterotationoftheEarth.
Eachdayisdividedinto24hoursof60minutes;each
minute has 60 seconds.
Timeofdayisanindicationofthephaseofrotationof
theEarth.Thatis,itindicateshowmuchofadayhas
elapsed,orwhatpartofarotationhasbeencompleted.
Thus,atzerohoursthedaybegins.Onehourlater,theEarth
hasturnedthrough1/24ofaday,or1/24of360°,or360°÷
24 = 15°
Smallerintervalscanalsobestatedinangularunits;
since1houror60minutesisequivalentto15°ofarc,1
minuteoftimeisequivalentto15°÷60=0.25°=15'ofarc,
and1secondoftimeisequivalentto15'÷60=0.25'=15"
of arc.
Summarizing in table form:
Thereforeanytimeintervalcanbeexpressedasan
equivalentamountofrotation,andviceversa.Intercon-
versionoftheseunitscanbemadebytherelationships
indicated above.
To convert time to arc:
1.Multiply the hours by 15 to obtain degrees of arc.
2.Dividetheminutesoftimebyfourtoobtain
degrees.
3.Multiplytheremainderofstep2by15toobtain
minutes of arc.
4.Dividethesecondsoftimebyfourtoobtain
minutes of arc
5.Multiply the remainder by 15 to obtain seconds of arc.
6.Add the resulting degrees, minutes, and seconds.
Example 1:Convert 14
h
21
m
39
s
to arc.
Solution:
To convert arc to time:
1.Divide the degrees by 15 to obtain hours.
2.Multiplytheremainderfromstep1byfourto
obtain minutes of time.
3.Dividetheminutesofarcby15toobtainminutes
of time.
4.Multiplytheremainderfromstep3byfourto
obtain seconds of time.
5.Dividethesecondsofarcby15toobtainseconds
of time.
6.Add the resulting hours, minutes, and seconds.
Example 2:Convert 215° 24' 45" to time units.
Solution:
Solutionscanalsobemadeusingarctotimeconversion
tablesinthealmanacs.IntheNauticalAlmanac,thetable
givennearthebackofthevolumeisintwoparts,permitting
separateentrieswithdegrees,minutes,andquarterminutes
ofarc.Thistableisarrangedinthismannerbecausethe
navigator converts arc to time more often than the reverse.
Example3:Convert334°18'22"totimeunits,usingthe
Nautical Almanac arc to time conversion table.
1
d
=24
h
=360°
60
m
=1
h
=15°
4
m
=1°=60'
60
s
=1
m
=15'
4
s
=1'=60"
1
s
=15"=0.25'
(1)
14
h
× 15
=210° 00' 00"
(2)
21
m
÷ 4
=005° 00' 00" (remainder 1)
(3)1× 15=000° 15' 00"
(4)
39
s
÷ 4
=000° 09' 00" (remainder 3)
(5)3× 15=000° 00' 45"
(6)
14
h
21
m
39
s
=215° 24' 45"
(1)215°÷ 15=
14
h
00
m
00
s
remainder 5
(2)5× 4=
00
h
20
m
00
s
(3)24'÷ 15=
00
h
01
m
00
s
remainder 9
(4)9× 4=
00
h
00
m
36
s
(5)45"÷ 15=
00
h
00
m
03
s
(6)215° 24' 45"=
14
h
21
m
39
s
278TIME
Solution:
Convertthe22"tothenearestquarterminuteofarcfor
solutiontothenearestsecondoftime.Interpolateifmore
precise results are required.
334° 00.00
m
=22
h
16
m
00
s
000° 18.25
m
= 00
h
01
m
13
s
334° 18' 22"= 22
h
17
m
13
s
1804. Time and Longitude
SupposetheSunweredirectlyoveracertainpointon
theEarthatagiventime.AnhourlatertheEarthwould
haveturnedthrough15°,andtheSunwouldthenbedirectly
overameridian15°fartherwest.Thus,anydifferenceof
longitudebetweentwopointsisameasureoftheangle
throughwhichtheEarthmustrotatetoseparatethem.
Therefore,placeseastofanobserverhavelatertime,and
thosewesthaveearliertime,andthedifferenceisexactly
equaltothedifferenceinlongitude,expressedintimeunits.
Thedifferenceintimebetweentwoplacesisequaltothe
differenceoflongitudebetweentheirmeridians,expressed
in units of time instead of arc.
1805. The Date Line
Sincetimegrowslatertowardtheeastandearliertoward
thewestofanobserver,timeatthelowerbranchofone’s
meridianis12hoursearlierorlater,dependinguponthe
directionofreckoning.AtravelercirclingtheEarthgainsor
losesanentiredaydependingonthedirectionoftravel,and
onlyforasingleinstantoftime,atpreciselyGreenwich
noon,isitthesamedatearoundtheearth.Topreventthedate
frombeinginerrorandtoprovideastartingplaceforeach
newday,adatelineisfixedbyinformalagreement.Thisline
coincideswiththe180thmeridianovermostofitslength.In
crossingthisline,thedateisalteredbyoneday.Ifapersonis
travelingeastwardfromeastlongitudetowestlongitude,
timeisbecominglater,andwhenthedatelineiscrossedthe
datebecomes1dayearlier.Atanyinstantthedate
immediatelytothewestofthedateline(eastlongitude)is1
daylaterthanthedateimmediatelytotheeastoftheline.
Whensolvingcelestialproblems,weconvertlocaltimeto
Greenwichtimeandthenconvertthistolocaltimeonthe
opposite side of the date line.
1806. Zone Time
Atsea,aswellasashore,watchesandclocksare
normallysettosomeformofzonetime(ZT).Atseathe
nearestmeridianexactlydivisibleby15°isusuallyusedas
thetimemeridianorzonemeridian.Thus,withinatime
zoneextending7.5°oneachsideofthetimemeridianthe
timeisthesame,andtimeinconsecutivezonesdiffersby
exactlyonehour.Thetimeischangedasconvenient,
usuallyatawholehour,whencrossingtheboundary
betweenzones.Eachtimezoneisidentifiedbythenumber
oftimesthelongitudeofitszonemeridianisdivisibleby
15°,positiveinwestlongitudeandnegativeineast
longitude.Thisnumberanditssign,calledthezone
description(ZD),isthenumberofwholehoursthatare
addedtoorsubtractedfromthezonetimetoobtain
GreenwichMeanTime(GMT).ThemeanSunisthe
celestial reference point for zone time. See Figure 1806.
ConvertingZTtoGMT,apositiveZTisaddedanda
negativeonesubtracted;convertingGMTtoZT,apositive
ZD is subtracted, and a negative one added.
Example:The GMT is 15
h
27
m
09
s
.
Required:(1) ZT at long. 156°24.4' W.
(2) ZT at long. 039°04.8' E.
Solutions:
1807. Chronometer Time
Chronometertime(C)istimeindicatedbya
chronometer.Sinceachronometerissetapproximatelyto
GMTandnotresetuntilitisoverhauledandcleanedabout
every3years,thereisnearlyalwaysachronometererror
(CE),eitherfast(F)orslow(S).Thechangeinchronometer
errorin24hoursiscalledchronometerrate,ordailyrate,
anddesignatedgainingorlosing.Withaconsistentrateof1
s
perdayforthreeyears,thechronometererrorwouldtotal
approximately18
m
.Sincechronometererrorissubjectto
change,itshouldbedeterminedfromtimetotime,
preferablydailyatsea.Chronometererrorisfoundbyradio
timesignal,bycomparisonwithanothertimepieceofknown
error,orbyapplyingchronometerratetopreviousreadingsof
thesameinstrument.Itisrecordedtothenearestwholeorhalf
second. Chronometer rate is recorded to the nearest 0.1 second.
Example:AtGMT1200onMay12thechronometerreads
12
h
04
m
21
s
. At GMT 1600 on May 18 it reads 4
h
04
m
25
s
.
Required:.1. Chronometer error at 1200 GMT May 12.
2. Chronometer error at 1600 GMT May 18.
3. Chronometer rate.
4. Chronometer error at GMT 0530, May 27.
(1)GMT
15
h
27
m
09
s
ZD
+10
h
(rev.)
ZT
05
h
27
m
09
s
(2)GMT
15
h
27
m
09
s
ZD
–03
h
(rev.)
ZT
18
h
27
m
09
s
TIME279
Figure 1806. Time Zone Chart.
280TIME
Solutions:
BecauseGMTisona24-hourbasisand
chronometertimeona12-hourbasis,a12-hour
ambiguityexists.Thisisignoredinfindingchronometer
error.However,ifchronometererrorisappliedto
chronometertimetofindGMT,a12-hourerrorcan
result.Thiscanberesolvedbymentallyapplyingthe
zonedescriptiontolocaltimetoobtainapproximate
GMT.Atimediagramcanbeusedforresolvingdoubtas
toapproximateGMTandGreenwichdate.IftheSunfor
thekindoftimeused(meanorapparent)isbetweenthe
lowerbranchesoftwotimemeridians(asthestandard
meridianforlocaltime,andtheGreenwichmeridianfor
GMT),thedateattheplacefarthereastisonedaylater
than at the place farther west.
1808. Watch Time
Watchtime(WT)isusuallyanapproximationof
zonetime,exceptthatfortimingcelestialobservationsit
iseasiesttosetacomparingwatchtoGMT.Ifthewatch
hasasecond-settinghand,thewatchcanbesetexactlyto
ZTorGMT,andthetimeissodesignated.Ifthewatchis
notsetexactlytooneofthesetimes,thedifferenceis
knownaswatcherror(WE),labeledfast(F)orslow(S)
toindicatewhetherthewatchisaheadoforbehindthe
correct time.
IfawatchistobesetexactlytoZTorGMT,setitto
somewholeminuteslightlyaheadofthecorrecttimeand
stopped.Whenthesettimearrives,startthewatchand
check it for accuracy.
TheGMTmaybeinerrorby12
h
,butifthewatchis
graduatedto12hours,thiswillnotbereflected.Ifawatch
witha24-hourdialisused,theactualGMTshouldbe
determined.
Todeterminewatcherrorcomparethereadingofthe
watchwiththatofthechronometerataselectedmoment.
ThismayalsobeatsomeselectedGMT.Unlessawatchis
graduatedto24hours,itstimeisdesignatedambeforenoon
and pm after noon.
Eventhoughawatchissettozonetimeapproximately,
itserroronGMTcanbedeterminedandusedfortiming
observations.Inthiscasethe12-hourambiguityinGMT
shouldberesolved,andatimediagramusedtoavoiderror.
Thismethodrequiresadditionalwork,andpresentsa
greaterprobabilityoferror,withoutcompensating
advantages.
Ifastopwatchisusedfortimingobservations,itshould
bestartedatsomeconvenientGMT,suchasawhole5
m
or
10
m
.ThetimeofeachobservationisthentheGMTplusthe
watchtime.Digitalstopwatchesandwristwatchesareideal
forthispurpose,astheycanbesetfromaconvenientGMT
and read immediately after the altitude is taken.
1809. Local Mean Time
Localmeantime(LMT),likezonetime,usesthe
meanSunasthecelestialreferencepoint.Itdiffersfrom
zonetimeinthatthelocalmeridianisusedastheterrestrial
reference,ratherthanazonemeridian.Thus,thelocalmean
timeateachmeridiandiffersfromeveryothermeridian,the
differencebeingequaltothedifferenceoflongitude
expressedintimeunits.Ateachzonemeridian,including
0°, LMT and ZT are identical.
InnavigationtheprincipaluseofLMTisinrising,
setting,andtwilighttables.Theproblemisusuallyoneof
convertingtheLMTtakenfromthetabletoZT.Atsea,the
differencebetweenthetimesisnormallynotmorethan
30
m
,andtheconversionismadedirectly,withoutfinding
GMTasanintermediatestep.Thisisdonebyapplyinga
correctionequaltothedifferenceoflongitude.Ifthe
observeriswestofthetimemeridian,thecorrectionis
added,andifeastofit,thecorrectionissubtracted.If
Greenwich time is desired, it is found from ZT.
Wherethereisanirregularzoneboundary,thelongitude
may differ by more than 7.5° (30
m
) from the time meridian.
IfLMTistobecorrectedtodaylightsavingtime,the
differenceinlongitudebetweenthelocalandtimemeridian
canbeused,ortheZTcanfirstbefoundandthenincreased
by one hour.
ConversionofZT(includingGMT)toLMTisthe
sameasconversionintheoppositedirection,exceptthatthe
signofdifferenceoflongitudeisreversed.Thisproblemis
not normally encountered in navigation.
1810. Sidereal Time
SiderealtimeusesthefirstpointofAries(vernal
equinox)asthecelestialreferencepoint.SincetheEarth
1.GMT
12
h
00
m
00
s
May 12
C
12
h
04
m
21
s
CE
(F)4
m
21
s
2.GMT
16
h
00
m
00
s
May 18
C04 04 25
CE
(F)4
m
25
s
3.GMT
18
d
16
h
GMT
12
d
12h
diff.
06
d
04
h
= 6.2
d
CE
(F)4
m
21
s
1200 May 12
CE
(F)4
m
25
s
1600 May 18
diff.
4
s
(gained)
daily rate
0.6
s
(gain)
4.GMT
27
d
05
h
30
m
GMT
18
d
16
h
00
m
diff.
08
d
13
h
30
m
(8.5
d
)
CE
(F)4
m
25
s
1600 May 18
corr.
(+)0
m
05
s
diff.× rate
CE
(F)4
m
30
s
0530 May 27
TIME281
revolvesaroundtheSun,andsincethedirectionofthe
Earth’srotationandrevolutionarethesame,itcompletesa
rotationwithrespecttothestarsinlesstime(about3
m
56.6
s
ofmeansolarunits)thanwithrespecttotheSun,andduring
onerevolutionabouttheSun(1year)itmakesonecomplete
rotationmorewithrespecttothestarsthanwiththeSun.
Thisaccountsforthedailyshiftofthestarsnearly1°
westwardeachnight.Hence,siderealdaysareshorterthan
solardays,anditshours,minutes,andsecondsare
correspondinglyshorter.Becauseofnutation,siderealtime
isnotquiteconstantinrate.Timebasedupontheaverage
rateiscalledmeansiderealtime,whenitistobedistin-
guishedfromtheslightlyirregularsiderealtime.Theratio
ofmeansolartimeunitstomeansiderealtimeunitsis
1:1.00273791.
Anavigatorveryseldomusessiderealtime.
Astronomersuseittoregulatemeantimebecauseits
celestialreferencepointremainsalmostfixedinrelationto
the stars.
1811. Time And Hour Angle
Bothtimeandhourangleareameasureofthephaseof
rotationoftheEarth,sincebothindicatetheangular
distanceofacelestialreferencepointwestofaterrestrial
referencemeridian.Hourangle,however,appliestoany
pointonthecelestialsphere.Timemightbeusedinthis
respect,butonlytheapparentSun,meanSun,thefirstpoint
of Aries, and occasionally the Moon, are commonly used.
Houranglesareusuallyexpressedinarcunits,andare
measuredfromtheupperbranchofthecelestialmeridian.
Timeiscustomarilyexpressedintimeunits.Siderealtimeis
measuredfromtheupperbranchofthecelestialmeridian,like
hourangle,butsolartimeismeasuredfromthelowerbranch.
Thus,LMT=LHAmeanSunplusorminus180°,LAT=
LHAapparentSunplusorminus180°,andLST=LHAAries.
Aswithtime,localhourangle(LHA)attwoplaces
differsbytheirdifferenceinlongitude,andLHAat
longitude0°iscalledGreenwichhourangle(GHA).In
addition,itisoftenconvenienttoexpresshouranglein
termsoftheshorterarcbetweenthelocalmeridianandthe
body.Thisissimilartomeasurementoflongitudefromthe
Greenwichmeridian.Localhouranglemeasuredinthis
wayiscalledmeridianangle(t),whichislabeledeastor
west,likelongitude,toindicatethedirectionof
measurement.Awesterlymeridianangleisnumerically
equaltoLHA,whileaneasterlymeridianangleisequalto
360°–LHA.LHA=t(W),andLHA=360°–t(E).
Meridianangleisusedinthesolutionofthenavigational
triangle.
Example:FindLHAandtoftheSunatGMT3
h
24
m
16
s
on
June 1, 1975, for long. 118°48.2' W.
Solution:
RADIO DISSEMINATION OF TIME SIGNALS
1812. Dissemination Systems
Ofthemanysystemsfortimeandfrequencydissemi-
nation,themajorityemploysometypeofradio
transmission,eitherindedicatedtimeandfrequency
emissionsorestablishedsystemssuchasradionavigation
systems.Themostaccuratemeansoftimeandfrequency
disseminationtodayisbythemutualexchangeoftime
signalsthroughcommunication(commonlycalledTwo-
Way)andbythemutualobservationofnavigationsatellites
(commonly called Common View).
Radiotimesignalscanbeusedeithertoperforma
clock’sfunctionortosetclocks.Whenusingaradiowave
insteadofaclock,however,newconsiderationsevolve.
Oneisthedelaytimeofapproximately3microsecondsper
kilometerittakestheradiowavetopropagateandarriveat
thereceptionpoint.Thus,auser1,000kilometersfroma
transmitterreceivesthetimesignalabout3milliseconds
laterthantheon-timetransmittersignal.Iftimeisneededto
betterthan3milliseconds,acorrectionmustbemadefor
the time it takes the signal to pass through the receiver.
Inmostcasesstandardtimeandfrequencyemissions
asreceivedaremorethanadequateforordinaryneeds.
However,manysystemsexistforthemoreexacting
scientific requirements.
1813. Characteristic Elements of Dissemination
Systems
Anumberofcommonelementscharacterizemost
timeandfrequencydisseminationsystems.Amongthe
moreimportantelementsareaccuracy,ambiguity,repeat-
ability,coverage,availabilityoftimesignal,reliability,
easeofuse,costtotheuser,andthenumberofusers
served.Nosinglesystemincorporatesalldesiredcharac-
teristics.Therelativeimportanceofthesecharacteristics
willvaryfromoneusertothenext,andthesolutionfor
oneusermaynotbesatisfactorytoanother.These
commonelementsarediscussedinthefollowing
examination of a hypothetical radio signal.
Consideraverysimplesystemconsistingofan
unmodulated10-kHzsignalasshowninFigure1813.This
signal,leavingthetransmitterat0000UTC,willreachthe
receiveratalatertimeequivalenttothepropagation
GMT
3
h
24
m
16
s
June 1
3
h
225°35.7'
24
m
16
s
6°04.0'
GHA231°39.7'
λ
118°48.2'W
LHA112°51.5'
t112°51.5' W
282TIME
delay.Theusermustknowthisdelaybecausethe
accuracyofhisknowledgeoftimecanbenobetterthan
thedegreetowhichthedelayisknown.Sinceallcyclesof
thesignalareidentical,thesignalisambiguousandthe
usermustsomehowdecidewhichcycleisthe“ontime”
cycle.Thismeans,inthecaseofthehypothetical10-kHz
signal,thattheusermustknowthetimeto±50
microseconds(halftheperiodofthesignal).Further,the
usermaydesiretousethissystem,sayonceaday,foran
extendedperiodoftimetocheckhisclockorfrequency
standard.However,ifthedelayvariesfromonedaytothe
nextwithouttheuserknowing,accuracywillbelimited
by the lack of repeatability.
Manyusersareinterestedinmakingtimecoordinated
measurementsoverlargegeographicareas.Theywould
likeallmeasurementstobereferencedtoonetimesystem
toeliminatecorrectionsfordifferenttimesystemsusedat
scatteredorremotelocations.Thisisaveryimportant
practicalconsiderationwhenmeasurementsare
undertakeninthefield.Inaddition,aone-reference
system,suchasasingletimebroadcast,increases
confidencethatallmeasurementscanberelatedtoeach
otherinsomeknownway.Thus,thecoverageofasystem
isanimportantconcept.Anotherimportantcharacteristic
ofatimingsystemisthepercentoftimeavailable.The
manonthestreetwhohastokeepanappointmentneeds
toknowthetimeperhapstoaminuteorso.Although
requiringonlycoarsetimeinformation,hewantsiton
demand,sohecarriesawristwatchthatgivesthetime24
hoursaday.Ontheotherhand,auserwhoneedstimeto
afewmicrosecondsemploysaverygoodclockwhich
onlyneedsanoccasionalupdate,perhapsonlyonceor
twiceaday.Anadditionalcharacteristicoftimeand
frequencydisseminationisreliability,i.e.,thelikelihood
thatatimesignalwillbeavailablewhenscheduled.
Propagationfade-outcansometimespreventreceptionof
HF signals.
1814. Radio Wave Propagation Factors
Radiohasbeenusedtotransmitstandardtimeand
frequencysignalssincetheearly1900’s.Asopposedtothe
physicaltransferoftimeviaportableclocks,thetransferof
informationbyradioentailspropagationofelectromagnetic
energy from a transmitter to a distant receiver.
Inatypicalstandardfrequencyandtimebroadcast,the
signalsaredirectlyrelatedtosomemasterclockandare
transmittedwithlittleornodegradationinaccuracy.Ina
vacuumandwithanoise-freebackground,thesignalsshould
bereceivedatadistantpointessentiallyastransmitted,
exceptforaconstantpathdelaywiththeradiowave
propagatingnearthespeedoflight(299,773kilometersper
second).Thepropagationmedia,includingtheEarth,
atmosphere,andionosphere,aswellasphysicaland
electricalcharacteristicsoftransmittersandreceivers,
influencethestabilityandaccuracyofreceivedradiosignals,
dependentuponthefrequencyofthetransmissionandlength
ofsignalpath.Propagationdelaysareaffectedinvarying
degreesbyextraneousradiationsinthepropagationmedia,
solardisturbances,diurnaleffects,andweatherconditions,
among others.
Radiodisseminationsystemscanbeclassifiedina
numberofdifferentways.Onewayistodividethosecarrier
frequencieslowenoughtobereflectedbytheionosphere
(below30MHz)fromthosesufficientlyhightopenetrate
theionosphere(above30MHz).Theformercanbe
observedatgreatdistancesfromthetransmitterbutsuffer
fromionosphericpropagationanomaliesthatlimit
accuracy;thelatterarerestrictedtoline-of-sight
applicationsbutshowlittleornosignaldeterioration
causedbypropagationanomalies.Themostaccurate
systemstendtobethosewhichusethehigher,line-of-sight
frequencies,whilebroadcastsofthelowercarrier
frequencies show the greatest number of users.
1815. Standard Time Broadcasts
TheWorldAdministrativeRadioCouncil(WARC)
hasallocatedcertainfrequenciesinfivebandsforstandard
frequencyandtimesignalemission.Forsuchdedicated
standardfrequencytransmissions,theInternationalRadio
ConsultativeCommittee(CCIR)recommendsthatcarrier
frequenciesbemaintainedsothattheaveragedaily
fractionalfrequencydeviationsfromtheinternationally
designatedstandardformeasurementoftimeinterval
shouldnotexceed1X10
-10
.TheU.S.NavalObservatory
TimeServiceAnnouncementSeries1,No.2,givescharac-
teristicsofstandardtimesignalsassignedtoallocated
bands, as reported by the CCIR.
Figure 1813. Single tone time dissemination.
TIME283
1816. Time Signals
Theusualmethodofdeterminingchronometererror
anddailyrateisbyradiotimesignals,popularlycalledtime
ticks.Mostmaritimenationsbroadcasttimesignalsseveral
timesdailyfromoneormorestations,andavessel
equippedwithradioreceivingequipmentnormallyhasno
difficultyinobtainingatimetickanywhereintheworld.
Normally,thetimetransmittedismaintainedvirtually
uniformwithrespecttoatomicclocks.TheCoordinated
UniversalTime(UTC)asreceivedbyavesselmaydiffer
from (GMT) by as much as 0.9 second.
Themajorityofradiotimesignalsaretransmitted
automatically,beingcontrolledbythestandardclockofan
astronomicalobservatoryoranationalmeasurement
standardslaboratory.Absolutereliancemaybeplacedon
thesesignalsbecausetheyarerequiredtobeaccuratetoat
least 0.001
s
as transmitted.
Otherradiostations,however,havenoautomatic
transmissionsysteminstalled,andthesignalsaregivenby
hand.Inthisinstancetheoperatorisguidedbythestandard
clockatthestation.Theclockischeckedbyastronomical
observationsorradiotimesignalsandisnormallycorrectto
0.25 second.
Atsea,aspring-drivenchronometershouldbechecked
dailybyradiotimesignal,andinportdailychecksshould
bemaintained,orbegunatleastthreedayspriorto
departure,ifconditionspermit.Errorandrateareenteredin
thechronometerrecordbook(orrecordsheet)eachtime
they are determined.
Thevarioustimesignalsystemsusedthroughoutthe
worldarediscussedinNIMAPub.117,RadioNaviga-
tionalAids,andvolume5ofAdmiraltyListofRadio
Signals. Only the United States signals are discussed here.
TheNationalInstituteofStandardsandTechnology
(NIST)broadcastscontinuoustimeandfrequency
referencesignalsfromWWV,WWVH,WWVB,andthe
GOESsatellitesystem.Becauseoftheirwidecoverageand
relativesimplicity,theHFservicesfromWWVand
WWVH are used extensively for navigation.
StationWWVbroadcastsfromFortCollins,Colorado
attheinternationallyallocatedfrequenciesof2.5,5.0,10.0,
15.0,and20.0MHz;stationWWVHtransmitsfromKauai,
Hawaiionthesamefrequencieswiththeexceptionof20.0
MHz.Thebroadcastsignalsincludestandardtimeand
frequencies,andvariousvoiceannouncements.Detailsof
thesebroadcastsaregiveninNISTSpecialPublication
432,NISTFrequencyandTimeDisseminationServices.
BothHFemissionsaredirectlycontrolledbycesiumbeam
frequencystandardswithperiodicreferencetotheNIST
atomic frequency and time standards.
Figure 1816a. Broadcast format of station WWV.
284TIME
ThetimeticksintheWWVandWWVHemissionsare
showninFigure1816aandFigure1816b.The1-second
UTCmarkersaretransmittedcontinuouslybyWWVand
WWVH,exceptforomissionofthe29thand59thmarker
eachminute.Withtheexceptionofthebeginningtoneat
eachminute(800milliseconds)all1-secondmarkersareof
5millisecondsduration.Eachpulseisprecededby10
millisecondsofsilenceandfollowedby25millisecondsof
silence.Timevoiceannouncementsaregivenalsoat1-
minute intervals. All time announcements are UTC.
Pub.No.117,RadioNavigationalAids,shouldbe
referred to for further information on time signals.
1817. Leap-Second Adjustments
Byinternationalagreement,UTCismaintainedwithin
about0.9secondsofthecelestialnavigator’stimescale,
UT1.Theintroductionofleapsecondsallowsaclockto
keepapproximatelyinstepwiththeSun.Becauseofthe
variationsintherateofrotationoftheEarth,however,the
occurrencesoftheleapsecondsarenotpredictableindetail.
TheCentralBureauoftheInternationalEarthRotation
Service(IERS)decidesuponandannouncestheintroduction
ofaleapsecond.TheIERSannouncesthenewleapsecond
atleastseveralweeksinadvance.Apositiveornegativeleap
Figure 1816b. Broadcast format of station WWVH.
Figure 1817a. Dating of event in the vicinity of a positive leap second.
TIME285
secondisintroducedthelastsecondofaUTCmonth,but
firstpreferenceisgiventotheendofDecemberandJune,
andsecondpreferenceisgiventotheendofMarchand
September.Apositiveleapsecondbeginsat23
h
59
m
60
s
and
endsat00
h
00
m
00
s
ofthefirstdayofthefollowingmonth.
Inthecaseofanegativeleapsecond,23
h
59
m
58
s
is
followedonesecondlaterby00
h
00
m
00
s
ofthefirstdayof
the following month.
Thedatingofeventsinthevicinityofaleapsecondis
effectedinthemannerindicatedinFigure1817aandFigure
1817b.
Wheneverleapsecondadjustmentsaretobemadeto
UTC, mariners are advised by messages from NIMA.
Figure 1817b. Dating of event in the vicinity of a negative leap second.
287
CHAPTER 19
THE ALMANACS
PURPOSE OF ALMANACS
1900. Introduction
Celestialnavigationrequiresaccuratepredictionsofthe
geographicpositionsofthecelestialbodiesobserved.These
predictionsareavailablefromthreealmanacspublished
annuallybytheUnitedStatesNavalObservatoryandH.M.
Nautical Almanac Office, Royal Greenwich Observatory.
TheAstronomicalAlmanacpreciselytabulatescelestial
datafortheexactingrequirementsfoundinseveralscientific
fields.Itsprecisionisfargreaterthanthatrequiredby
celestialnavigation.EveniftheAstronomicalAlmanacis
usedforcelestialnavigation,itwillnotnecessarilyresultin
moreaccuratefixesduetothelimitationsofotheraspectsof
the celestial navigation process.
TheNauticalAlmanaccontainstheastronomical
informationspecificallyneededbymarinenavigators.
Informationistabulatedtothenearest0.1'ofarcand1secondof
time.GHAanddeclinationareavailablefortheSun,Moon,
planets,and173stars,aswellascorrectionsnecessarytoreduce
the observed values to true.
TheAirAlmanacwasoriginallyintendedforair
navigators,butisusedtodaymostlybyasegmentofthe
maritimecommunity.Ingeneral,theinformationissimilarto
theNauticalAlmanac,butisgiventoaprecisionof1'ofarc
and1secondoftime,atintervalsof10minutes(valuesfor
theSunandAriesaregiventoaprecisionof0.1').This
publicationissuitableforordinarynavigationatsea,but
lackstheprecisionoftheNauticalAlmanac,andprovides
GHAanddeclinationforonlythe57commonlyused
navigation stars.
TheMulti-YearInteractiveComputerAlmanac
(MICA)isacomputerizedalmanacproducedbytheU.S.
NavalObservatory.Thisandotherweb-basedcalculatorsare
availablefrom:http://aa.usno.navy.mil.TheNavy’s
STELLAprogram,foundaboardallseagoingnavalvessels,
containsaninteractivealmanacaswell.Avarietyof
privatelyproducedelectronicalmanacsareavailableas
computerprogramsorinstalledinpocketcalculators.These
invariablyareassociatedwithsightreductionsoftwarewhich
replaces tabular and mathematical sight reduction methods.
FORMAT OF THE NAUTICAL AND AIR ALMANACS
1901.Nautical Almanac
ThemajorportionoftheNauticalAlmanacisdevoted
tohourlytabulationsofGreenwichHourAngle(GHA)
anddeclination,tothenearest0.1'ofarc.Oneachsetof
facingpages,informationislistedforthreeconsecutive
days.Ontheleft-handpage,successivecolumnslistGHA
ofAries(),andbothGHAanddeclinationofVenus,
Mars,Jupiter,andSaturn,followedbytheSiderealHour
Angle(SHA)anddeclinationof57stars.TheGHAand
declinationoftheSunandMoon,andthehorizontal
parallaxoftheMoon,arelistedontheright-handpage.
Whereapplicable,thequantitiesvanddaregiventoassist
ininterpolation.Thequantityvisthedifferencebetween
theactualchangeofGHAin1hourandaconstantvalue
usedintheinterpolationtables,whiledisthechangein
declinationin1hour.Bothvanddarelistedtothenearest
0.1'.
TotherightoftheMoondataislistedtheLocalMean
Time(LMT)ofsunrise,sunset,andbeginningandending
ofnauticalandciviltwilightforlatitudesfrom72°Nto
60°S.TheLMTofmoonriseandmoonsetatthesame
latitudesislistedforeachofthethreedaysforwhichother
informationisgiven,andforthefollowingday.Magnitude
ofeachplanetatUT1200ofthemiddledayislistedatthe
topofthecolumn.TheUToftransitacrossthecelestial
meridianofGreenwichislistedas“Mer.Pass.”.Thevalue
forthefirstpointofAriesforthemiddleofthethreedays
islistedtothenearest0.1'atthebottomoftheAries
column.Thetimeoftransitoftheplanetsforthemiddleday
isgiventothenearestwholeminute,withSHA(atUT0000
ofthemiddleday)tothenearest0.1',belowthelistofstars.
FortheSunandMoon,thetimeoftransittothenearest
wholeminuteisgivenforeachday.FortheMoon,both
upperandlowertransitsaregiven.Thisinformationis
tabulatedbelowtherising,setting,andtwilight
information.Alsolisted,aretheequationoftimefor0
h
and
12
h
,andtheageandphaseoftheMoon.Equationoftime
islisted,withoutsign,tothenearestwholesecond.Ageis
given to the nearest whole day. Phase is given by symbol.
Themaintabulationisprecededbyalistofreligious
andcivilholidays,phasesoftheMoon,acalendar,
informationoneclipsesoccurringduringtheyear,and
notes and a diagram giving information on the planets.
288THE ALMANACS
Themaintabulationisfollowedbyexplanationsand
examples.Nextarefourpagesofstandardtimes(zone
descriptions).Starchartsarenext,followedbyalistof173
starsinorderofincreasingSHA.Thislistincludesthestars
givenonthedailypages.ItgivestheSHAanddeclination
eachmonth,andthemagnitude.StarsarelistedbyBayer’s
nameandalsobypopularnamewhereapplicable.Following
thestarlistarethePolaristables.Thesetablesgivethe
azimuthandthecorrectionstobeappliedtotheobserved
altitude to find the latitude.
FollowingthePolaristableisasectionthatgives
formulasandexamplesfortheentryofalmanacdata,the
calculationsthatreduceasight,andamethodofsolution
forposition,allforusewithacalculatorormicrocomputer.
Thisisfollowedbyconcisesightreductiontables,with
instructionsandexamples,forusewhenacalculatoror
traditionalsightreductiontablesarenotavailable.Tabular
precision of the concise tables is one minute of arc.
Nextisatableforconvertingarctotimeunits.Thisis
followedbya30-pagetablecalled“Incrementsand
Corrections,”usedforinterpolationofGHAand
declination.Thistableisprintedontintedpaperforquick
location.Thencometablesforinterpolatingfortimesof
rise,set,andtwilight;followedbytwoindicesofthe57
starslistedonthedailypages,oneindexinalphabetical
order, and the other in order of decreasing SHA.
Sextantaltitudecorrectionsaregivenatthefrontand
backofthealmanac.TablesfortheSun,stars,andplanets,
andadiptable,aregivenontheinsidefrontcoverand
facingpage,withanadditionalcorrectionfornonstandard
temperatureandatmosphericpressureonthefollowing
page.TablesfortheMoon,andanabbreviateddiptable,are
givenontheinsidebackcoverandfacingpage.Corrections
fortheSun,stars,andplanetsforaltitudesgreaterthan10°,
andthediptable,arerepeatedononesideofaloose
bookmark. The star indices are repeated on the other side.
1902.Air Almanac
AsintheNauticalAlmanac,themajorportionoftheAir
AlmanacisdevotedtoatabulationofGHAanddeclination.
However,intheAirAlmanacvaluesarelistedatintervalsof10
minutes,toaprecisionof0.1'fortheSunandAries,andtoa
precisionof1'fortheMoonandtheplanets.Valuesaregivenfor
theSun,firstpointofAries(GHAonly),thethreenavigational
planetsmostfavorablylocatedforobservation,andtheMoon.
Themagnitudeofeachplanetlistedisgivenatthetopofits
column,andthepercentageoftheMoon’sdiscilluminated,
waxing(+)orwaning(-),isgivenatthebottomofeach
page.Valuesforthefirst12hoursofthedayaregivenon
theright-handpage,andthoseforthesecondhalfoftheday
ontheback.Inaddition,eachpagehasatableofthe
Moon’sparallaxinaltitude,andbelowthisthesemidi-
ameteroftheSun,andboththesemidiameterandageofthe
Moon.EachdailypageincludestheLMTofmoonriseand
moonset;andadifferencecolumntofindthetimeof
moonrise and moonset at any longitude.
CriticaltablesforinterpolationforGHAaregivenon
theinsidefrontcover,whichalsohasanalphabeticallisting
ofthestars,withthenumber,magnitude,SHA,anddecli-
nationofeach.Thesameinterpolationtableandstarlistare
printedonaflapwhichfollowsthedailypages.Thisflap
alsocontainsastarchart,astarindexinorderofdecreasing
SHA,andatableforinterpolationoftheLMTofmoonrise
and moonset for longitude.
Followingtheflapareinstructionsfortheuseofthe
almanac;alistofsymbolsandabbreviationsinEnglish,
French,andSpanish;alistoftimedifferencesbetween
Greenwichandotherplaces;skydiagrams;aplanet
locationdiagram;starrecognitiondiagramsfor
periscopicsextants;sunrise,sunset,andciviltwilight
tables;rising,setting,anddepressiongraphs;semidu-
rationgraphsofSunlight,twilight,andMoonlightin
highlatitudes;percentageoftheMoonilluminatedat6
and18hoursUTdaily;alistof173starsbynumberand
Bayer’sname(alsopopularnamewherethereisone),
givingtheSHAanddeclinationeachmonth(toa
precisionof0.1'),andthemagnitude;tablesforinterpo-
lationofGHASunandGHA;atableforconverting
arctotime;asinglePolariscorrectiontable;anaircraft
standarddomerefractiontable;arefractioncorrection
table;aCorioliscorrectiontable;andontheinsideback
cover, a correction table for dip of the horizon.
USING THE ALMANACS
1903. Entering Arguments
Thetimeusedasanenteringargumentinthealmanacs
is12
h
+GHAofthemeanSunandisdenotedbyUT,for-
merlyreferredtoasGMTandsoreferredtointhisbookto
avoidconfusion.Thisscalemaydifferfromthebroadcast
timesignalsbyanamountwhich,ifignored,willintroduce
anerrorofupto0.2'inlongitudedeterminedfromastro-
nomicalobservations.Thedifferencearisesbecausethe
timeargumentdependsonthevariablerateofrotationof
theEarthwhilethebroadcasttimesignalsarenowbasedon
atomictime.Stepadjustmentsofexactlyonesecondare
madetothetimesignalsasrequired(primarilyat24hon
December31andJune30)sothatthedifferencebetween
thetimesignalsandUT,asusedinthealmanacs,maynot
exceed0.9
s
.Ifobservationstoaprecisionofbetterthan1
s
arerequired,correctionsmustbeobtainedfromcodingin
thesignal,orfromothersources.Thecorrectionmaybeap-
pliedtoeachofthetimesofobservation.Alternatively,the
longitude,whendeterminedfromobservations,maybecor-
rected by the corresponding amount shown in Table 1903.
Themaincontentsofthealmanacsconsistofdatafrom
THE ALMANACS289
whichtheGHAandthedeclinationofallthebodiesused
fornavigationcanbeobtainedforanyinstantofUT.The
LHA can then be obtained with the formula:
FortheSun,Moon,andthefournavigationalplanets,
theGHAanddeclinationaretabulateddirectlyinthe
NauticalAlmanacforeachhourofGMTthroughoutthe
year;intheAirAlmanac,thevaluesaretabulatedforeach
whole10mofGMT.Forthestars,theSHAisgiven,and
the GHA is obtained from:
GHA Star = GHA + SHA Star.
TheSHAanddeclinationofthestarschangeslowly
andmayberegardedasconstantoverperiodsofseveral
daysorevenmonthsiflesseraccuracyisrequired.The
SHAanddeclinationofstarstabulatedintheAirAlmanac
maybeconsideredconstanttoaprecisionof1.5'to2'for
theperiodcoveredbyeachofthevolumesprovidingthe
dataforawholeyear,withmostdatabeingclosertothe
smallervalue.GHA,ortheGHAofthefirstpointof
Aries(thevernalequinox),istabulatedforeachhourinthe
NauticalAlmanacandforeachwhole10
m
intheAirAlma-
nac.Permanenttableslisttheappropriateincrementstothe
tabulatedvaluesofGHAanddeclinationfortheminutes
and seconds of time.
IntheNauticalAlmanac,thepermanenttablefor
incrementsalsoincludescorrectionsforv,thedifference
betweentheactualchangeofGHAinonehouranda
constantvalueusedintheinterpolationtables;andd,the
change in declination in one hour.
IntheNauticalAlmanac,visalwayspositiveunlessa
negativesign(-)isshown.Thisoccursonlyinthecaseof
Venus.FortheSun,thetabulatedvaluesofGHAhavebeen
adjustedtoreducetoaminimumtheerrorcausedby
treatingv as negligible; there is nov tabulated for the Sun.
Nosignisgivenfortabulatedvaluesofd,whichisposi-
tiveifdeclinationisincreasing,andnegativeifdecreasing.The
sign of av ord value is also given to the related correction.
IntheAirAlmanac,thetabularvaluesoftheGHAof
theMoonareadjustedsothatuseofaninterpolationtable
basedonafixedrateofchangegivesrisetonegligible
error;nosuchadjustmentisnecessaryfortheSunand
planets.Thetabulateddeclinationvalues,exceptforthe
Sun,arethoseforthemiddleoftheintervalbetweenthe
timeindicatedandthenextfollowingtimeforwhicha
valueisgiven,makinginterpolationunnecessary.Thus,it
isalwaysimportanttotakeouttheGHAanddeclinationfor
the time immediatelybefore the time of observation.
IntheAirAlmanac,GHAandtheGHAand
declinationoftheSunaretabulatedtoaprecisionof0.1'.If
thesevaluesareextractedwiththetabularprecision,the
“InterpolationofGHA”tableontheinsidefrontcover(and
flap)shouldnotbeused;usethe“InterpolationofGHASun”
and“InterpolationofGHAAries’tables,asappropriate.These
tables are found immediately preceding the Polaris Table.
1904. Finding GHA and Declination of the Sun
NauticalAlmanac:Enterthedailypagetablewiththe
wholehourbeforethegivenGMT,unlesstheexacttimeis
awholehour,andtakeoutthetabulatedGHAand
declination.Alsorecordthedvaluegivenatthebottomof
thedeclinationcolumn.Next,entertheincrementsand
correctionstableforthenumberofminutesofGMT.If
thereareseconds,usethenextearlierwholeminute.Onthe
linecorrespondingtothesecondsofGMT,extractthevalue
fromtheSun-Planetscolumn.AddthistothevalueofGHA
fromthedailypage.ThisisGHAoftheSun.Next,enterthe
correctiontableforthesameminutewiththedvalueand
takeoutthecorrection.Givethisthesignofthedvalueand
applyittothedeclinationfromthedailypage.Thisisthe
declination.
ThecorrectiontableforGHAoftheSunisbasedupon
arateofchangeof15°perhour,theaveragerateduringa
year.Atmosttimestheratediffersslightly.Theslighterror
isminimizedbyadjustmentofthetabularvalues.Thed
valueistheamountthatthedeclinationchangesbetween
1200 and 1300 on the middle day of the three shown.
AirAlmanac:Enterthedailypagewiththewhole10
m
precedingthegivenGMT,unlessthetimeisitselfawhole
10
m
,andextracttheGHA.Thedeclinationisextracted
withoutinterpolationfromthesamelineasthetabulated
GHAor,inthecaseofplanets,thetoplineoftheblockof
six.Ifthevaluesextractedareroundedtothenearest
minute,nextenterthe“InterpolationofGHA”tableonthe
insidefrontcover(andflap),usingthe“Sun,etc.”entry
column,andtakeoutthevaluefortheremainingminutes
andsecondsofGMT.Iftheentrytimeisanexacttabulated
value,usethecorrectionlistedhalfalineabovetheentry
time.AddthiscorrectiontotheGHAtakenfromthedaily
page.ThisisGHA.Noadjustmentofdeclinationisneeded.
Ifthevaluesareextractedwithaprecisionof0.1',thetable
forinterpolatingtheGHAoftheSuntoaprecisionof0.1'
mustbeused.Againnoadjustmentofdeclinationisneeded.
Correction to time
signals
Correction to
longitude
-0.7
s
to -0.9
s
0.2' to east
-0.6
s
to -0.3
s
0.1' to east
-0.2
s
to +0.2
s
no correction
+0.3
s
to +0.6
s
0.1' to west
+0.7
s
to +0.9
s
0.2' to west
Table 1903. Corrections to time.
LHA=GHA + east longitude.
LHA=GHA - west longitude.
290THE ALMANACS
1905. Finding GHA and Declination of the Moon
NauticalAlmanac:Enterthedailypagetablewiththe
wholehourbeforethegivenGMT,unlessthistimeisitself
awholehour,andextractthetabulatedGHAand
declination.Recordthecorrespondingvanddvalues
tabulatedonthesameline,anddeterminethesignofthed
value.ThevvalueoftheMoonisalwayspositive(+)and
isnotmarkedinthealmanac.Next,entertheincrements
andcorrectionstablefortheminutesofGMT,andonthe
lineforthesecondsofGMT,taketheGHAcorrectionfrom
theMooncolumn.Then,enterthecorrectiontableforthe
sameminutewiththevvalue,andextractthecorrection.
AddbothofthesecorrectionstotheGHAfromthedaily
page.ThisisGHAoftheMoon.Then,enterthesame
correctiontablewiththedvalueandextractthecorrection.
Givethiscorrectionthesignofthedvalueandapplyitto
the declination from the daily page. This is declination.
ThecorrectiontableforGHAoftheMoonisbased
upontheminimumrateatwhichtheMoon’sGHA
increases,14°19.0'perhour.Thevcorrectionadjustsfor
theactualrate.Thevvalueisthedifferencebetweenthe
minimumrateandtheactualrateduringthehour
followingthetabulatedtime.Thedvalueistheamount
thatthedeclinationchangesduringthehourfollowingthe
tabulated time.
AirAlmanac:Enterthedailypagewiththewhole10
m
nextprecedingthegivenGMT,unlessthistimeisawhole
10
m
,andextractthetabulatedGHAandthedeclination
withoutinterpolation.Next,enterthe“Interpolationof
GHA”tableontheinsidefrontcover,usingthe“Moon”
entrycolumn,andextractthevaluefortheremaining
minutesandsecondsofGMT.Iftheentrytimeisanexact
tabulatedvalue,usethecorrectiongivenhalfalineabove
theentrytime.AddthiscorrectiontotheGHAtakenfrom
thedailypagetofindtheGHAatthegiventime.No
adjustment of declination is needed.
Thedeclinationgiveninthetableiscorrectforthetime
5minuteslaterthantabulated,sothatitcanbeusedforthe10-
minuteintervalwithoutinterpolation,toanaccuracytomeet
mostrequirements.Declinationchangesmuchmoreslowly
thanGHA.Ifgreateraccuracyisneeded,itcanbeobtainedby
interpolation, remembering to allow for the 5 minutes.
1906. Finding GHA and Declination of a Planet
NauticalAlmanac:Enterthedailypagetablewiththe
wholehourbeforethegivenGMT,unlessthetimeisa
wholehour,andextractthetabulatedGHAanddeclination.
Recordthevvaluegivenatthebottomofeachofthese
columns.Next,entertheincrementsandcorrectionstable
fortheminutesofGMT,andonthelineforthesecondsof
GMT,taketheGHAcorrectionfromtheSun-planets
column.Next,enterthecorrectiontablewiththevvalue
andextractthecorrection,givingitthesignofthevvalue.
AddthefirstcorrectiontotheGHAfromthedailypage,
andapplythesecondcorrectioninaccordancewithitssign.
ThisisGHA.Thenenterthecorrectiontableforthesame
minutewiththedvalue,andextractthecorrection.Give
thiscorrectionthesignofthedvalue,andapplyittothe
declinationfromthedailypagetofindthedeclinationatthe
given time.
ThecorrectiontableforGHAofplanetsisbasedupon
themeanrateoftheSun,15°perhour.Thevvalueisthe
differencebetween15°andthechangeofGHAofthe
planetbetween1200and1300onthemiddledayofthe
threeshown.Thedvalueistheamountthedeclination
changesbetween1200and1300onthemiddleday.Venus
is the only body listed which ever has a negative v value.
AirAlmanac:Enterthedailypagewiththewhole10
m
beforethegivenGMT,unlessthistimeisawhole10
m
,and
extractthetabulatedGHAanddeclination,withoutinterpo-
lation.Thetabulateddeclinationiscorrectforthetime30
m
laterthantabulated,sointerpolationduringthehour
followingtabulationisnotneededformostpurposes.Next,
enterthe“InterpolationofGHA”tableontheinsidefront
cover,usingthe“Sun,etc.”column,andtakeoutthevalue
fortheremainingminutesandsecondsofGMT.Iftheentry
timeisanexacttabulatedvalue,usethecorrectionhalfa
lineabovetheentrytime.AddthiscorrectiontotheGHA
fromthedailypagetofindtheGHAatthegiventime.No
adjustment of declination is needed.
1907. Finding GHA and Declination of a Star
IftheGHAanddeclinationofeachnavigationalstar
weretabulatedseparately,thealmanacswouldbeseveral
timestheirpresentsize.Butsincethesiderealhourangleand
thedeclinationarenearlyconstantoverseveraldays(tothe
nearest0.1')ormonths(tothenearest1'),separatetabulations
arenotneeded.Instead,theGHAofthefirstpointofAries,
fromwhichSHAismeasured,istabulatedonthedailypages,
andasinglelistingofSHAanddeclinationisgivenforeach
doublepageoftheNauticalAlmanac,andforanentirevol-
umeoftheAirAlmanac.FindingtheGHAissimilarto
finding the GHA of the Sun, Moon, and planets.
NauticalAlmanac:Enterthedailypagetablewiththe
wholehourbeforethegivenGMT,unlessthistimeisa
wholehour,andextractthetabulatedGHAofAries.Also
recordthetabulatedSHAanddeclinationofthestarfrom
thelistingontheleft-handdailypage.Next,enterthe
incrementsandcorrectionstablefortheminutesofGMT,
and,onthelineforthesecondsofGMT,extracttheGHA
correctionfromtheAriescolumn.Addthiscorrectionand
theSHAofthestartotheGHAonthedailypageto
findtheGHAofthestaratthegiventime.Noadjustment
of declination is needed.
TheSHAanddeclinationof173stars,including
Polarisandthe57listedonthedailypages,aregivenfor
themiddleofeachmonth.Forastarnotlistedonthe
dailypages,thisistheonlyalmanacsourceofthis
information.Interpolationinthistableisnotnecessary
THE ALMANACS291
forordinarypurposesofnavigation,butissometimes
needed for precise results.
AirAlmanac:Enterthedailypagewiththewhole10
m
beforethegivenGMT,unlessthisisawhole10
m
,and
extractthetabulatedGHA.Next,enterthe“Interpo-
lationofGHA”tableontheinsidefrontcover,usingthe
“Sun,etc.”entrycolumn,andextractthevalueforthe
remainingminutesandsecondsofGMT.Iftheentrytime
isanexacttabulatedvalue,usethecorrectiongivenhalfa
lineabovetheentrytime.Fromthetabulationattheleftside
ofthesamepage,extracttheSHAanddeclinationofthe
star.AddtheGHAfromthedailypageandthetwovalues
takenfromtheinsidefrontcovertofindtheGHAatthe
given time. No adjustment of declination is needed.
RISING, SETTING, AND TWILIGHT
1908. Rising, Setting, and Twilight
InbothAirandNauticalAlmanacs,thetimesofsunrise,
sunset,moonrise,moonset,andtwilightinformation,at
variouslatitudesbetween72°Nand60°S,islistedtothe
nearestwholeminute.Bydefinition,risingorsettingoccurs
whentheupperlimbofthebodyisonthevisiblehorizon,
assumingstandardrefractionforzeroheightofeye.Because
ofvariationsinrefractionandheightofeye,computationto
a greater precision than 1 minute of time is not justified.
Inhighlatitudes,someofthephenomenadonotoccur
duringcertainperiods.Symbolsareusedinthealmanacsto
indicate:
1.SunorMoondoesnotset,butremainscontin-
uouslyabovethehorizon,indicatedbyanopen
rectangle.
2.SunorMoondoesnotrise,butremainscontin-
uouslybelowthehorizon,indicatedbyasolid
rectangle.
3.Twilight lasts all night, indicated by 4 slashes (////).
TheNauticalAlmanacmakesnoprovisionforfinding
thetimesofrising,setting,ortwilightinpolarregions.The
Air Almanachas graphs for this purpose.
IntheNauticalAlmanac,sunrise,sunset,andtwilight
tablesaregivenonlyonceforthemiddleofthethreedays
oneachpageopening.Fornavigationalpurposesthis
informationcanbeusedforallthreedays.Bothalmanacs
have moonrise and moonset tables for each day.
ThetabulationsareinLMT.Onthezonemeridian,this
isthezonetime(ZT).Forevery15'oflongitudethe
observer’spositiondiffersfromthezonemeridian,thezone
timeofthephenomenadiffersby1
m
,beinglaterifthe
observeriswestofthezonemeridian,andearlierifeastof
thezonemeridian.TheLMTofthephenomenavarieswith
latitudeoftheobserver,declinationofthebody,andhour
angle of the body relative to the mean Sun.
TheUTofthephenomenonisfoundfromLMTbythe
formula:
UT = LMT + W Longitude
UT = LMT - E Longitude.
Tousethisformula,convertthelongitudetotimeusing
thetableonpageiorbycomputation,andaddorsubtract
asindicated.Applythezonedescription(ZD)tofindthe
zone time of the phenomena.
Sunriseandsunsetarealsotabulatedinthetidetables
(from 76°N to 60°S).
1909. Finding Times of Sunrise and Sunset
TofindthetimeofsunriseorsunsetintheNautical
Almanac,enterthetableonthedailypage,andextractthe
LMTforthelatitudenextsmallerthanyourown(unlessit
isexactlythesame).ApplyacorrectionfromTableIon
almanacpagexxxiitointerpolateforaltitude,determining
thesignbyinspection.ThenconvertLMTtoZTusingthe
differenceoflongitudebetweenthelocalandzone
meridians.
FortheAirAlmanac,theprocedureisthesameasfor
theNauticalAlmanac,exceptthattheLMTistakenfrom
thetablesofsunriseandsunsetinsteadoffromthedaily
page, and the latitude correction is by linear interpolation.
ThetabulatedtimesarefortheGreenwichmeridian.
Exceptinhighlatitudesnearthetimeoftheequinoxes,the
timeofsunriseandsunsetvariessolittlefromdaytoday
thatnointerpolationisneededforlongitude.Inhigh
latitudesinterpolationisnotalwayspossible.Betweentwo
tabulatedentries,theSunmayinfactceasetoset.Inthis
case,thetimeofrisingandsettingisgreatlyinfluencedby
small variations in refraction and changes in height of eye.
1910. Twilight
Morningtwilightendsatsunrise,andeveningtwilight
beginsatsunset.Thetimeofthedarkerlimitcanbefound
fromthealmanacs.Thetimeofthedarkerlimitsofboth
civilandnauticaltwilights(centeroftheSun6°and12°,
respectively,belowthecelestialhorizon)isgiveninthe
NauticalAlmanac.TheAirAlmanacprovidestabulations
ofciviltwilightfrom60°Sto72°N.Thebrightnessofthe
skyatanygivendepressionoftheSunbelowthehorizon
mayvaryconsiderablyfromdaytoday,dependingupon
theamountofcloudiness,haze,andotheratmospheric
conditions.Ingeneral,themosteffectiveperiodfor
observingstarsandplanetsoccurswhenthecenterofthe
Sunisbetweenabout3°and9°belowthecelestialhorizon.
Hence,thedarkerlimitofciviltwilightoccursataboutthe
mid-pointofthisperiod.Atthedarkerlimitofnautical
twilight,thehorizonisgenerallytoodarkforgood
292THE ALMANACS
observations.
Atthedarkerlimitofastronomicaltwilight(centerof
theSun18°belowthecelestialhorizon),fullnighthasset
in.ThetimeofthistwilightisgivenintheAstronomical
Almanac.Itsapproximatevaluecanbedeterminedby
extrapolationintheNauticalAlmanac,notingthatthe
durationofthedifferentkindsoftwilightisproportionalto
thenumberofdegreesofdepressionforthecenterofthe
Sun.Moreprecisedeterminationofthetimeatwhichthe
centeroftheSunisanygivennumberofdegreesbelowthe
celestialhorizoncanbedeterminedbyalarge-scale
diagramontheplaneofthecelestialmeridian,orby
computation.Durationoftwilightinlatitudeshigherthan
65°N is given in a graph in theAir Almanac.
InbothNauticalandAirAlmanacs,themethodof
findingthedarkerlimitoftwilightisthesameasthatfor
sunrise and sunset.
SometimesinhighlatitudestheSundoesnotrisebut
twilightoccurs.ThisisindicatedintheAirAlmanacbya
solidblackrectanglesymbolinthesunriseandsunset
column.Tofindthetimeofbeginningofmorningtwilight,
subtracthalfthedurationoftwilightasobtainedfromthe
durationoftwilightgraphfromthetimeofmeridiantransit
oftheSun;andforthetimeofendingofeveningtwilight,
addittothetimeofmeridiantransit.TheLMTofmeridian
transitneverdiffersbymorethan16.4
m
(approximately)
from1200.Theactualtimeonanydatecanbedetermined
from the almanac.
1911. Moonrise and Moonset
Findingthetimeofmoonriseandmoonsetissimilarto
findingthetimeofsunriseandsunset,withoneimportant
difference.BecauseoftheMoon’srapidchangeof
declination,anditsfasteastwardmotionrelativetotheSun,
thetimeofmoonriseandmoonsetvariesconsiderablyfrom
daytoday.Thesechangesofpositiononthecelestial
spherearecontinuous,asmoonriseandmoonsetoccur
successivelyatvariouslongitudesaroundtheEarth.
Therefore,thechangeintimeisdistributedoverall
longitudes.Forpreciseresults,itwouldbenecessaryto
computethetimeofthephenomenaatanygivenplaceby
lengthycomplexcalculation.Forordinarypurposesof
navigation,however,itissufficientlyaccurateto
interpolatebetweenconsecutivemoonrisesormoonsetsat
theGreenwichmeridian.Sinceapparentmotionofthe
Mooniswestward,relativetoanobserverontheEarth,
interpolationinwestlongitudeisbetweenthephenomenon
onthegivendateandthefollowingone.Ineastlongitudeit
isbetweenthephenomenononthegivendateandthe
preceding one.
TofindthetimeofmoonriseormoonsetintheNautical
Almanac,enterthedaily-pagetablewithlatitude,andextract
theLMTforthetabulatedlatitudenextsmallerthanthe
observer’slatitude(unlessthisisanexacttabulatedvalue).
ApplyacorrectionfromtableIofalmanacpagexxxiito
interpolateforlatitude,determiningthesignofthecorrection
byinspection.Repeatthisprocedureforthedayfollowing
thegivendate,ifinwestlongitude;orforthedaypreceding,
ifineastlongitude.Usingthedifferencebetweenthesetwo
times,andthelongitude,entertableIIofthealmanaconthe
samepageandtakeoutthecorrection.Applythiscorrection
totheLMTofmoonriseormoonsetattheGreenwich
meridianonthegivendatetofindtheLMTatthepositionof
theobserver.Thesigntobegiventhecorrectionissuchasto
makethecorrectedtimefallbetweenthetimesforthetwo
datesbetweenwhichinterpolationisbeingmade.Thisis
nearlyalwayspositive(+)inwestlongitudeandnegative(-)
in east longitude. Convert the corrected LMT to ZT.
TofindthetimeofmoonriseormoonsetbytheAir
Almanacforthegivendate,determineLMTforthe
observer’slatitudeattheGreenwichmeridianinthesame
manneraswiththeNauticalAlmanac,exceptthatlinear
interpolationismadedirectlyfromthemaintables,sinceno
interpolationtableisprovided.Extract,also,thevaluefrom
the“Diff.”columntotherightofthemoonriseandmoonset
column,interpolatingifnecessary.This“Diff.”isthehalf-
dailydifference.Theerrorintroducedbythisapproxi-
mationisgenerallynotmorethanafewminutes,although
itincreaseswithlatitude.Usingthisdifference,andthe
longitude,enterthe“Interpolationofmoonrise,moonset”
tableonflapF4oftheAirAlmanacandextractthe
correction.TheAirAlmanacrecommendstakingthe
correctionfromthistablewithoutinterpolation.Theresults
thusobtainedaresufficientlyaccurateforordinary
purposesofnavigation.Ifgreateraccuracyisdesired,the
correctioncanbetakenbyinterpolation.However,since
the“Diff.”itselfisanapproximation,theNauticalAlmanac
orcomputationshouldbeusedifaccuracyisaconsid-
eration.ApplythecorrectiontotheLMTofmoonriseor
moonsetattheGreenwichmeridianonthegivendateto
findtheLMTatthepositionoftheobserver.Thecorrection
ispositive(+)forwestlongitude,andnegative(-)foreast
longitude,unlessthe“Diff.”onthedailypageispreceded
bythenegativesign(-),whenthecorrectionisnegative(-)
forwestlongitude,andpositive(+)foreastlongitude.Ifthe
timeisnearmidnight,recordthedateateachstep,asinthe
Nautical Almanac solution.
AswiththeSun,therearetimesinhighlatitudeswhen
interpolationisinaccurateorimpossible.Atsuchperiods,the
timesofthephenomenathemselvesareuncertain,butan
approximateanswercanbeobtainedbytheMoonlightgraph
intheAirAlmanac,orbycomputation.WiththeMoon,this
conditionoccurswhentheMoonrisesorsetsatonelatitude,
butnotatthenexthighertabulatedlatitude,aswiththeSun.It
alsooccurswhentheMoonrisesorsetsononeday,butnoton
theprecedingorfollowingday.Thislatterconditionis
indicatedintheAirAlmanacbythesymbol*inthe“Diff.”
column.
BecauseoftheeastwardrevolutionoftheMoonaround
theEarth,thereisonedayeachsynodicalmonth(29
1
/
2
days)whentheMoondoesnotrise,andonedaywhenit
THE ALMANACS293
doesnotset.Theseoccurnearlastquarterandfirstquarter,
respectively.Sincethisdayisnotthesameatalllatitudesor
atalllongitudes,thetimeofmoonriseormoonsetfound
fromthealmanacmayoccasionallybetheprecedingor
succeedingonetothatdesired.Wheninterpolatingnear
midnight, caution will prevent an error.
TheeffectoftherevolutionoftheMoonaroundthe
EarthistocausetheMoontoriseorsetlaterfromdayto
day.Thedailyretardationduetothiseffectdoesnotdiffer
greatlyfrom50
m
.However,thechangeindeclinationofthe
Moonmayincreaseordecreasethiseffect.Thiseffect
increaseswithlatitude,andinextremeconditionsitmaybe
greaterthantheeffectduetorevolutionoftheMoon.
Hence,theintervalbetweensuccessivemoonrisesor
moonsetsismoreerraticinhighlatitudesthaninlow
latitudes.Whenthetwoeffectsactinthesamedirection,
dailydifferencescanbequitelarge.Whentheyactin
oppositedirections,theyaresmall,andwhentheeffectdue
tochangeindeclinationislargerthanthatduetorevolution,
the Moon setsearlier on succeeding days.
ThisconditionisreflectedintheAirAlmanacbyaneg-
ative“Diff.”Ifthishappensnearthelastquarterorfirst
quarter,twomoonrisesormoonsetsmightoccuronthe
sameday,oneafewminutesafterthedaybegins,andthe
otherafewminutesbeforeitends,asonJune8,2002,
wheretwomoonrisesoccuratlatitude72°.Interpolationfor
longitudeisalwaysmadebetweenconsecutivemoonrises
or moonsets, regardless of the days on which they fall.
Beyondthenorthernlimitsofthealmanacsthevalues
canbeobtainedfromaseriesofgraphsgivenneartheback
oftheAirAlmanac.Forhighlatitudes,graphsareusedin-
steadoftablesbecausegraphsgiveaclearerpictureof
conditions,whichmaychangeradicallywithrelativelylit-
tlechangeinpositionordate.Undertheseconditions
interpolationtopracticalprecisionissimplerbygraphthan
bytable.Inthosepartsofthegraphwhicharedifficultto
read,thetimesofthephenomena’soccurrenceareuncer-
tain,beingalteredconsiderablybyarelativelysmallchange
in refraction or height of eye.
Onallofthesegraphs,anygivenlatitudeisrepresented
byahorizontallineandanygivendatebyaverticalline.At
theintersectionofthesetwolinesthedurationisreadfrom
the curves, interpolating by eye between curves.
The“SemidurationofSunlight”graphgivesthe
numberofhoursbetweensunriseandmeridiantransitor
betweenmeridiantransitandsunset.Thedotscalenearthe
topofthegraphindicatestheLMTofmeridiantransit,the
timerepresentedbytheminutedotnearestthevertical
datelinebeingused.Iftheintersectionoccursinthearea
marked“Sunabovehorizon,”theSundoesnotset;andifin
theareamarked“Sunbelowhorizon,”theSundoesnotrise.
The“DurationofTwilight”graphgivesthenumberof
hoursbetweenthebeginningofmorningciviltwilight
(centerofSun6°belowthehorizon)andsunrise,or
betweensunsetandtheendofeveningciviltwilight.Ifthe
Sundoesnotrise,buttwilightoccurs,thetimetakenfrom
thegraphishalfthetotallengthofthesingletwilight
period,orthenumberofhoursfrombeginningofmorning
twilighttoLAN,orfromLANtoendofeveningtwilight.
Iftheintersectionoccursintheareamarked“continuous
twilightorSunlight,”thecenteroftheSundoesnotmove
morethan6°belowthehorizon,andifintheareamarked
“notwilightnorSunlight,”theSunremainsmorethan6°
below the horizon throughout the entire day.
The“SemidurationofMoonlight”graphgivesthe
numberofhoursbetweenmoonriseandmeridiantransitor
betweenmeridiantransitandmoonset.Thedotscalenear
thetopofthegraphindicatestheLMTofmeridiantransit,
eachdotrepresentingonehour.Thephasesymbolsindicate
thedateonwhichtheprincipalMoonphasesoccur,the
opencircleindicatingfullMoonandthedarkcircle
indicatingnewMoon.Iftheintersectionofthevertical
datelineandthehorizontallatitudelinefallsinthe“Moon
abovehorizon”or“Moonbelowhorizon”area,theMoon
remainsaboveorbelowthehorizon,respectively,forthe
entire 24 hours of the day.
Ifapproximationsofthetimesofmoonriseand
moonsetaresufficient,thesemidurationofMoonlightis
takenforthetimeofmeridianpassageandcanbeused
withoutadjustment.Whenanestimatedtimeofrisefallson
theprecedingday,thatphenomenonmayberecalculated
usingthemeridianpassageandsemidurationfortheday
following.Whenanestimatedtimeofsetfallsonthe
followingday,thatphenomenonmayberecalculatedusing
meridianpassageandsemidurationfortheprecedingday.
Formoreaccurateresults(seldomjustified),thetimeson
therequireddateandtheadjacentdate(thefollowingdate
inWlongitudeandtheprecedingdateinElongitude)
shouldbedetermined,andaninterpolationmadefor
longitude,asinanylatitude,sincetheintervalsgivenarefor
the Greenwich meridian.
Sunlight,twilight,andMoonlightgraphsarenotgiven
forsouthlatitudes.Beyondlatitude65°S,thenorthern
hemispheregraphscanbeusedfordeterminingthesemidu-
rationorduration,byusingtheverticaldatelineforaday
whenthedeclinationhasthesamenumericalvaluebut
oppositesign.Thetimeofmeridiantransitandthephaseof
theMoonaredeterminedasexplainedabove,usingthe
correctdate.Betweenlatitudes60°Sand65°S,thesolution
ismadebyinterpolationbetweenthetablesandthegraphs.
Othermethodsofsolutionofthesephenomenaare
available.TheTideTablestabulatesunriseandsunsetfrom
latitude76°Nto60°S.Semidurationordurationcanbe
determinedgraphicallyusingadiagramontheplaneofthe
celestialmeridian,orbycomputation.Whencomputationis
used,solutionismadeforthemeridianangleatwhichthe
requirednegativealtitudeoccurs.Themeridianangle
expressedintimeunitsisthesemidurationinthecaseof
sunrise,sunset,moonrise,andmoonset;andthesemidu-
rationofthecombinedSunlightandtwilight,orthetime
frommeridiantransitatwhichmorningtwilightbeginsor
eveningtwilightends.Forsunriseandsunsetthealtitude
294THE ALMANACS
usedis(-)50'.Allowanceforheightofeyecanbemadeby
algebraicallysubtracting(numericallyadding)thedip
correctionfromthisaltitude.Thealtitudeusedfortwilight
is(-)6°,(-)12°,or(-)18°forcivil,nautical,orastronomical
twilight,respectively.Thealtitudeusedformoonriseand
moonsetis-34'-SD+HP,whereSDissemidiameterand
HPishorizontalparallax,fromthedailypagesofthe
Nautical Almanac.
1912. Rising, Setting, and Twilight on a Moving Craft
Instructionstothispointrelatetoafixedpositionon
theEarth.Aboardamovingcrafttheproblemis
complicatedsomewhatbythefactthattimeofoccurrence
dependsuponthepositionofthecraft,whichitselfdepends
onthetime.Atshipspeeds,itisgenerallysufficiently
accuratetomakeanapproximatementalsolutionanduse
thepositionofthevesselatthistimetomakeamore
accuratesolution.Ifgreateraccuracyisrequired,the
positionatthetimeindicatedinthesecondsolutioncanbe
usedforathirdsolution.Ifdesired,thisprocesscanbe
repeateduntilthesameanswerisobtainedfromtwo
consecutivesolutions.However,itisgenerallysufficientto
alterthefirstsolutionby1
m
foreach15'oflongitudethat
thepositionofthecraftdiffersfromthatusedinthe
solution,addingifwestoftheestimatedposition,and
subtractingifeastofit.Inapplyingthisrule,useboth
longitudestothenearest15'.Thefirstsolutionisthefirst
estimate; the second solution is thesecond estimate.
295
CHAPTER 20
SIGHT REDUCTION
BASIC PROCEDURES
2000. Computer Sight Reduction
Thepurelymathematicalprocessofsightreductionis
anidealcandidateforcomputerization,andanumberof
differenthand-heldcalculatorsandcomputerprograms
havebeendevelopedtorelievethetediumofworkingout
sightsbytabularormathematicalmethods.Thecivilian
navigatorcanchoosefromawidevarietyofhand-held
calculatorsandcomputerprogramswhichrequireonlythe
entryoftheDRposition,altitudeandazimuthofthebody,
andGMT.Itisnotevennecessarytoknowthenameofthe
bodybecausethecomputercanfigureoutwhatitmustbe
basedontheentereddata.Calculatorsandcomputers
providemoreaccuratesolutionsthantabularand
mathematicalmethodsbecausetheycanbebasedonactual
valuesratherthantheoreticalassumptionsanddonothave
inherent rounding errors.
U.S.Navalnavigatorshaveaccesstoaprogramcalled
STELLA(SystemToEstimateLatitudeandLongitudeAs-
tronomically;donotconfusewithacommercialastronomy
programwiththesamename).STELLAwasdevelopedby
theAstronomicalApplicationsDepartmentoftheU.S.Na-
valObservatorybasedonaNavyrequirement.The
algorithmsusedinSTELLAprovideanaccuracyofone
arc-secondontheEarth’ssurface,adistanceofabout30
meters.Whilethisaccuracyisfarbetterthancanbeob-
tainedusingasextant,itdoessupportpossiblenavalneeds
forautomatednavigationsystemsbasedoncelestialob-
jects.Thesealgorithmstakeintoaccounttheoblatenessof
theEarth,movementofthevesselduringsight-taking,and
other factors not fully addressed by traditional methods.
STELLAcanperformalmanacfunctions,positionup-
dating/DRestimations,celestialbodyrise/set/transit
calculations,compasserrorcalculations,sightplanning,
andsightreduction.On-linehelpanduser’sguidearein-
cluded,anditisacomponentoftheBlockIIINAVSSI.
BecauseSTELLAlogsallentereddataforfuturereference,
itisauthorizedtoreplacetheNavyNavigationWorkbook.
STELLAisnowanallowancelistrequirementforNaval
ships, and is available from:
Superintendent
U.S. Naval Observatory
Code: AA/STELLA
3450 Massachusetts Ave. NW
Washington, DC, 20392-5420
or on the Navigator of the Navy Web site at
http://www.navigator.navy.mil/navigator/surface.html.
2001. Tabular Sight Reduction
Theremainderofthischapterconcentratesonsightre-
ductionusingtheNauticalAlmanacandPub.No.229,
SightReductionTablesforMarineNavigation.Themethod
explainedhereisonlyoneofmanymethodsofreducinga
sight.TheNauticalAlmanaccontainsdirectionsforsolving
sightsusingitsownconcisesightreductiontablesorcalcu-
lators, along with examples for the current year
Reducingacelestialsighttoobtainalineofposition
using the tables consists of six steps:
1.Correctthesextantaltitude(hs)toobtainobserved
altitude (ho).
2.Determine the body’s GHA and declination (dec.).
3.Selectanassumedposition(AP)andfinditslocal
hour angle (LHA).
4.Compute altitude and azimuth for the AP.
5.Compare the computed and observed altitudes.
6.Plot the line of position.
TheintroductiontoeachvolumeofPub.229contains
information:(1)discussinguseofthepublicationforava-
rietyofspecialcelestialnavigationtechniques;(2)
discussinginterpolation,explainingthedoubleseconddif-
ferenceinterpolationrequiredinsomesightreductions,and
providingtablestofacilitatetheinterpolationprocess;and
(3)discussingthepublication’suseinsolvingproblemsof
greatcirclesailings.PriortousingPub.229,carefullyread
this introductory material.
Celestialnavigationinvolvesdeterminingacircular
lineofpositionbasedonanobserver’sdistancefromace-
lestialbody’sgeographicposition(GP).Shouldthe
observerdeterminebothabody’sGPandhisdistancefrom
theGP,hewouldhaveenoughinformationtoplotalineof
position;hewouldbesomewhereonacirclewhosecenter
wastheGPandwhoseradiusequaledhisdistancefromthat
GP.Thatcircle,fromallpointsonwhichabody’smeasured
altitudewouldbeequal,isacircleofequalaltitude.There
isadirectproportionalitybetweenabody’saltitudeasmea-
suredbyanobserverandthedistanceofitsGPfromthat
observer;thelowerthealtitude,thefartherawaytheGP.
296SIGHT REDUCTION
Therefore,whenanobservermeasuresabody’saltitudehe
obtainsanindirectmeasureofthedistancebetweenhimself
andthebody’sGP.Sightreductionistheprocessofcon-
verting that indirect measurement into a line of position.
Sightreductionreducestheproblemofscaletoman-
ageablesize.Dependingonabody’saltitude,itsGPcould
bethousandsofmilesfromtheobserver’sposition.The
sizeofachartrequiredtoplotthislargedistancewouldbe
impractical.Toeliminatethisproblem,thenavigatordoes
notplotthislineofpositiondirectly.Indeed,hedoesnot
plottheGPatall.Rather,hechoosesanassumedposition
(AP)near,butusuallynotcoincidentwith,hisDRposition.
ThenavigatorchoosestheAP’slatitudeandlongitudeto
correspondtotheenteringargumentsofLHAandlatitude
usedinPub.229.FromPub.229,thenavigatorcomputes
whatthebody’saltitudewouldhavebeenhaditbeenmea-
suredfromtheAP.Thisyieldsthecomputedaltitude(h
c
).
Hethencomparesthiscomputedvaluewiththeobserved
altitude(h
o
)obtainedathisactualposition.Thedifference
betweenthecomputedandobservedaltitudesisdirectly
proportionaltothedistancebetweenthecirclesofequalal-
titudefortheassumedpositionandtheactualposition.Pub.
229alsogivesthedirectionfromtheGPtotheAP.Having
selectedtheassumedposition,calculatedthedistancebe-
tweenthecirclesofequalaltitudeforthatAPandhisactual
position,anddeterminedthedirectionfromtheassumed
positiontothebody’sGP,thenavigatorhasenoughinfor-
mation to plot a line of position (LOP).
ToplotanLOP,plottheassumedpositiononeithera
chartoraplottingsheet.FromtheSightReductionTables,
determine:1)thealtitudeofthebodyforasighttakenatthe
APand2)thedirectionfromtheAPtotheGP.Then,deter-
minethedifferencebetweenthebody’scalculatedaltitude
atthisAPandthebody’smeasuredaltitude.Thisdifference
representsthedifferenceinradiibetweentheequalaltitude
circlepassingthroughtheAPandtheequalaltitudecircle
passingthroughtheactualposition.Plotthisdifference
fromtheAPeithertowardsorawayfromtheGPalongthe
axisbetweentheAPandtheGP.Finally,drawthecircleof
equalaltituderepresentingthecirclewiththebody’sGPat
thecenterandwitharadiusequaltothedistancebetween
the GP and the navigator’s actual position.
Onefinalconsiderationsimplifiestheplottingoftheequal
altitudecircle.RecallthattheGPisusuallythousandsofmiles
awayfromthenavigator’sposition.Theequalaltitudecircle’s
radius,therefore,canbeextremelylarge.Sincethisradiusisso
large,thenavigatorcanapproximatethesectionclosetohispo-
sitionwithastraightlinedrawnperpendiculartotheline
connectingtheAPandtheGP.Thisstraightlineapproximation
isgoodonlyforsightsatrelativelylowaltitudes.Thehigherthe
altitude,theshorterthedistancebetweentheGPandtheactual
position,andthesmallerthecircleofequalaltitude.Theshorter
thisdistance,thegreatertheinaccuracyintroducedbythis
approximation.
2002. Selection of the Assumed Position (AP)
UsethefollowingargumentswhenenteringPub.229
to compute altitude (h
c
) and azimuth:
1.Latitude (L)
2.Declination (d or Dec.)
3.Local hour angle (LHA)
LatitudeandLHAarefunctionsoftheassumed
position.SelectanAPlongituderesultinginawholedegree
ofLHAandanAPlatitudeequaltothatwholedegreeof
latitudeclosesttotheDRposition.SelectingtheAPinthis
mannereliminatesinterpolationforLHAandlatitudein
Pub. 229.
2003. Comparison of Computed and Observed
Altitudes
Thedifferencebetweenthecomputedaltitude(h
c
)and
the observed altitude (h
o
) is thealtitude intercept (a).
Thealtitudeinterceptisthedifferenceinthelengthof
theradiiofthecirclesofequalaltitudepassingthroughthe
APandtheobserver’sactualposition.Thepositionhaving
thegreateraltitudeisonthecircleofsmallerradiusandis
closertotheobservedbody’sGP.InFigure2004,theAPis
shown on the inner circle. Therefore, h
c
is greater than h
o
.
Expressthealtitudeinterceptinnauticalmilesand
labelitTorAtoindicatewhetherthelineofpositionis
toward or away from the GP, as measured from the AP.
Ausefulaidinrememberingtherelationbetweenh
o
,
h
c
,andthealtitudeinterceptis:
H
o
M
o
T
o
forH
o
More
Toward.AnotherisC-G-A:
Computed
Greater
Away,
rememberedas
Coast
Guard
Academy.Inotherwords,ifh
o
isgreaterthanh
c
,thelineofpositionintersectsapoint
measuredfromtheAPtowardstheGPadistanceequalto
thealtitudeintercept.DrawtheLOPthroughthis
intersectionpointperpendiculartotheaxisbetweentheAP
and GP.
2004. Plotting the Line of Position
PlotthelineofpositionasshowninFigure2004.Plot
theAPfirst;thenplottheazimuthlinefromtheAPtoward
orawayfromtheGP.Then,measurethealtitudeintercept
alongthisline.Atthepointontheazimuthlineequaltothe
interceptdistance,drawalineperpendiculartotheazimuth
line.Thisperpendicularrepresentsthatsectionofthecircle
ofequalaltitudepassingthroughthenavigator’sactual
position. This is the line of position.
Anavigatoroftentakessightsofmorethanone
celestialbodywhendeterminingacelestialfix.After
plottingthelinesofpositionfromtheseseveralsights,
advancetheresultingLOP’salongthetracktothetimeof
thelastsightandlabeltheresultingfixwiththetimeofthis
last sight.
SIGHT REDUCTION297
2005. Sight Reduction Procedures
Justasitisimportanttounderstandthetheoryofsight
reduction,itisalsoimportanttodevelopapractical
proceduretoreducecelestialsightsconsistentlyand
accurately.Sightreductioninvolvesseveralconsecutive
steps,theaccuracyofeachcompletelydependentonthe
accuracyofthestepsthatwentbefore.Sightreduction
tableshave,forthemostpart,reducedthemathematics
involvedtosimpleadditionandsubtraction.However,
carelesserrorswillrendereventhemostskillfully
measuredsightsinaccurate.Thenavigatorusingtabularor
mathematicaltechniquesmustworkmethodicallytoreduce
careless errors.
NavalnavigatorswillmostlikelyuseOPNAV3530,U.S.
NavyNavigationWorkbook,whichcontainspre-formatted
pageswith“stripforms”toguidethenavigatorthroughsight
reduction.Avarietyofcommercially-producedformsarealso
available.Pickaformandlearnitsmethodthoroughly.With
familiaritywillcomeincreasingunderstanding,speedand
accuracy.
Figure2005representsafunctionalandcompleteworksheet
designedtoensureamethodicalapproachtoanysightreduction
problem.Therecommendedprocedurediscussedbelowisnot
theonlyoneavailable;however,thenavigatorwhousesitcanbe
assuredthathehasconsideredeverycorrectionrequiredtoobtain
an accurate fix.
SECTIONONEconsistsoftwoparts:(1)Correcting
sextantaltitudetoobtainapparentaltitude;and(2)
Correctingtheapparentaltitudetoobtaintheobserved
altitude.
Body:Enterthenameofthebodywhosealtitudeyou
havemeasured.IfusingtheSunortheMoon,indicate
which limb was measured.
IndexCorrection:Thisisdeterminedbythecharac-
teristicsoftheindividualsextantused.Chapter16discusses
determining its magnitude and algebraic sign.
Dip:Thedipcorrectionisafunctionoftheheightof
eyeoftheobserver.Itisalwaysnegative;itsmagnitudeis
determinedfromtheDipTableontheinsidefrontcoverof
theNautical Almanac.
Sum:Enterthealgebraicsumofthedipcorrectionand
the index correction.
SextantAltitude:Enterthealtitudeofthebody
measured by the sextant.
ApparentAltitude:Applythecorrectiondetermined
abovetothemeasuredaltitudeandentertheresultasthe
apparent altitude.
AltitudeCorrection:Everyobservationrequiresanalti-
tudecorrection.Thiscorrectionisafunctionoftheapparent
altitudeofthebody.TheAlmanaccontainstablesfordetermin-
Figure 2004. The basis for the line of position from a celestial observation.
298SIGHT REDUCTION
SECTION ONE: OBSERVED ALTITUDE
Body__________________________________
Index Correction__________________________________
Dip (height of eye)__________________________________
Sum__________________________________
Sextant Altitude (h
s
)__________________________________
Apparent Altitude (h
a
)__________________________________
Altitude Correction__________________________________
Mars or Venus Additional Correction__________________________________
Additional Correction__________________________________
Horizontal Parallax Correction__________________________________
Moon Upper Limb Correction__________________________________
Correction to Apparent Altitude (h
a
)__________________________________
Observed Altitude (h
o
)__________________________________
SECTION TWO: GMT TIME AND DATE
Date__________________________________
DR Latitude__________________________________
DR Longitude__________________________________
Observation Time__________________________________
Watch Error__________________________________
Zone Time__________________________________
Zone Description__________________________________
Greenwich Mean Time__________________________________
Date GMT__________________________________
SECTION THREE: LOCAL HOUR ANGLE AND DECLINATION
Tabulated GHA andv Correction Factor__________________________________
GHA Increment__________________________________
Sidereal Hour Angle (SHA) orv Correction__________________________________
GHA__________________________________
+ or - 360° if needed__________________________________
Assumed Longitude (-W, +E)__________________________________
Local Hour Angle (LHA)__________________________________
Tabulated Declination anddCorrection Factor__________________________________
d Correction__________________________________
True Declination__________________________________
Assumed Latitude__________________________________
SECTION FOUR: ALTITUDE INTERCEPT AND AZIMUTH
Declination Increment andd Interpolation Factor__________________________________
Computed Altitude (Tabulated)__________________________________
Double Second Difference Correction__________________________________
Total Correction__________________________________
Computed Altitude (h
c
)__________________________________
Observed Altitude (h
o
)__________________________________
Altitude Intercept__________________________________
Azimuth Angle__________________________________
True Azimuth__________________________________
Figure 2005. Complete sight reduction form.
SIGHT REDUCTION299
ingthesecorrections.FortheSun,planets,andstars,thesetables
arelocatedontheinsidefrontcoverandfacingpage.Forthe
Moon,thesetablesarelocatedonthebackinsidecoverandpre-
ceding page.
MarsorVenusAdditionalCorrection:Asthename
implies,thiscorrectionisappliedtosightsofMarsandVe-
nus.Thecorrectionisafunctionoftheplanetmeasured,the
timeofyear,andtheapparentaltitude.Theinsidefrontcov-
er of theAlmanac lists these corrections.
AdditionalCorrection:Enterthisadditionalcorrection
fromTableA-4locatedatthefrontoftheNauticalAlmanac
whenobtainingasightundernon-standardatmospherictem-
peratureandpressureconditions.Thiscorrectionisa
functionofatmosphericpressure,temperature,andapparent
altitude.
HorizontalParallaxCorrection:Thiscorrectionisunique
toreducingMoonsights.ObtaintheH.P.correctionvaluefrom
thedailypagesoftheAlmanac.EntertheH.Pcorrectiontableat
thebackoftheAlmanacwiththisvalue.TheH.Pcorrectionisa
functionofthelimboftheMoonused(upperorlower),theap-
parentaltitude,andtheH.P.correctionfactor.TheH.P.
correction is always added to the apparent altitude.
MoonUpperLimbCorrection:Enter-30'forthis
correction if the sight was of the upper limb of the Moon.
CorrectiontoApparentAltitude:Sumthealtitude
correction,theMarsorVenusadditionalcorrection,the
additionalcorrection,thehorizontalparallaxcorrection,andthe
Moon’supperlimbcorrection.Becarefultodetermineandcarry
thealgebraicsignofthecorrectionsandtheirsumcorrectly.
Enter this sum as the correction to the apparent altitude.
ObservedAltitude:ApplytheCorrectiontoApparent
Altitudealgebraicallytotheapparentaltitude.Theresultisthe
observed altitude.
SECTIONTWOdeterminestheGreenwichMeanTime
(GMT;referredtointheAlmanacsasUniversaltimeorUT)and
GMT date of the sight.
Date: Enter the local time zone date of the sight.
DRLatitude:Enterthedeadreckoninglatitudeofthe
vessel.
DRLongitude:Enterthedeadreckoninglongitudeofthe
vessel.
ObservationTime:Enterthelocaltimeofthesightas
recorded on the ship’s chronometer or other timepiece.
WatchError:Enteracorrectionforanyknownwatch
error.
ZoneTime:Correcttheobservationtimewithwatch
error to determine zone time.
ZoneDescription:Enterthezonedescriptionofthetime
zoneindicatedbytheDRlongitude.Ifthelongitudeiswestofthe
GreenwichMeridian,thezonedescriptionispositive.
Conversely,ifthelongitudeiseastoftheGreenwichMeridian,
thezonedescriptionisnegative.Thezonedescriptionrepresents
thecorrectionnecessarytoconvertlocaltimetoGreenwich
Mean Time.
GreenwichMeanTime:Addtothezonedescriptionthe
zone time to determine Greenwich Mean Time.
Date:Carefullyevaluatethetimecorrectionappliedabove
anddetermineifthecorrectionhaschangedthedate.Enterthe
GMT date.
SECTIONTHREEdeterminestwoofthethreeargu-
mentsrequiredtoenterPub.229:LocalHourAngle(LHA)
andDeclination.Thissectionemploystheprinciplethatace-
lestialbody’sLHAisthealgebraicsumofitsGreenwich
HourAngle(GHA)andtheobserver’slongitude.Therefore,
thebasicmethodemployedinthissectionis:(1)Determine
thebody’sGHA;(2)Determineanassumedlongitude;(3)
Algebraicallycombinethetwoquantities,rememberingto
subtractawesternassumedlongitudefromGHAandtoadd
aneasternlongitudetoGHA;and(4)Extractthedeclination
ofthebodyfromtheappropriateAlmanactable,correcting
the tabular value if required.
Tabulated GHA and (2)v Correction Factor:
FortheSun,theMoon,oraplanet,extractthevaluefor
thewholehourofGHAcorrespondingtothesight.For
example,ifthesightwasobtainedat13-50-45GMT,extract
theGHAvaluefor1300.Forastarsightreduction,extractthe
valueoftheGHAofAries(GHA),againusingthevalue
corresponding to the whole hour of the time of the sight.
ForaplanetorMoonsightreduction,enterthev
correctionvalue.ThisquantityisnotapplicabletoaSunor
starsight.Thevcorrectionforaplanetsightisfoundatthe
bottomofthecolumnforeachparticularplanet.Thev
correctionfactorfortheMoonislocateddirectlybesidethe
tabulatedhourlyGHAvalues.Thevcorrectionfactorfor
theMoonisalwayspositive.Ifaplanet’svcorrectionfactor
islistedwithoutsign,itispositive.Iflistedwithanegative
sign,theplanet’svcorrectionfactorisnegative.Thisv
correctionfactorisnotthemagnitudeofthevcorrection;it
isusedlatertoentertheIncrementsandCorrectiontableto
determine the magnitude of the correction.
GHAIncrement:TheGHAincrementservesasan
interpolationfactor,correctingforthetimethatthesight
differedfromthewholehour.Forexample,inthesightat
13-50-45discussedabove,thisincrementcorrection
accountsforthe50minutesand45secondsafterthewhole
houratwhichthesightwastaken.Obtainthiscorrection
valuefromtheIncrementsandCorrectionstablesinthe
Almanac.Theenteringargumentsforthesetablesarethe
minutesandsecondsafterthehouratwhichthesightwas
takenandthebodysighted.Extractthepropercorrection
from the applicable table and enter the correction.
SiderealHourAngleorvCorrection:Ifreducinga
starsight,enterthestar’sSiderealHourAngle(SHA).The
SHAisfoundinthestarcolumnofthedailypagesofthe
Almanac.TheSHAcombinedwiththeGHAofAries
resultsinthestar’sGHA.TheSHAentryisapplicableonly
toastar.IfreducingaplanetorMoonsight,obtainthev
correctionfromtheIncrementsandCorrectionsTable.The
correctionisafunctionofonlythevcorrectionfactor;its
300SIGHT REDUCTION
magnitude is the same for both the Moon and the planets.
GHA:Astar’sGHAequalsthesumoftheTabulated
GHAofAries,theGHAIncrement,andthestar’sSHA.
TheSun’sGHAequalsthesumoftheTabulatedGHAand
theGHAIncrement.TheGHAoftheMoonoraplanet
equalsthesumoftheTabulatedGHA,theGHAIncrement,
and thev correction.
+or–360°(ifneeded):SincetheLHAwillbe
determinedfromsubtractingoraddingtheassumed
longitudetotheGHA,adjusttheGHAby360°ifneededto
facilitate the addition or subtraction.
AssumedLongitude:Ifthevesseliswestoftheprime
meridian,theassumedlongitudewillbesubtractedfromthe
GHAtodetermineLHA.Ifthevesseliseastoftheprime
meridian,theassumedlongitudewillbeaddedtotheGHA
todeterminetheLHA.Selecttheassumedlongitudeto
meetthefollowingtwocriteria:(1)Whenaddedor
subtracted(asapplicable)totheGHAdeterminedabove,a
wholedegreeofLHAwillresult;and(2)Itisthelongitude
closest to that DR longitude that meets criterion (1).
LocalHourAngle(LHA):Combinethebody’sGHA
withtheassumedlongitudeasdiscussedaboveto
determine the body’s LHA.
TabulatedDeclinationanddCorrectionfactor:(1)
ObtainthetabulateddeclinationfortheSun,theMoon,the
stars,ortheplanetsfromthedailypagesoftheAlmanac.
Thedeclinationvaluesforthestarsaregivenfortheentire
threedayperiodcoveredbythedailypageoftheAlmanac.
ThevaluesfortheSun,Moon,andplanetsarelistedin
hourlyincrements.Forthesebodies,enterthedeclination
valueforthewholehourofthesight.Forexample,ifthe
sightisat12-58-40,enterthetabulateddeclinationfor1200.
(2)Thereisnodcorrectionfactorforastarsight.Thereare
dcorrectionfactorsforSun,Moon,andplanetsights.
Similartothevcorrectionfactordiscussedabove,thed
correctionfactordoesnotequalthemagnitudeofthed
correction;itprovidestheargumenttoentertheIncrements
andCorrectionstablesintheAlmanac.Thesignofthed
correctionfactor,whichdeterminesthesignofthed
correction,isdeterminedbythetrendofdeclinationvalues,
notthetrendofdvalues.Thedcorrectionfactorissimply
aninterpolationfactor;therefore,todetermineitssign,look
atthedeclinationvaluesforthehoursthatframethetimeof
thesight.Forexample,supposethesightwastakenona
certaindateat12-30-00.Comparethedeclinationvaluefor
1200and1300anddetermineifthedeclinationhas
increasedordecreased.Ifithasincreased,thedcorrection
factorispositive.Ifithasdecreased,thedcorrectionfactor
is negative.
dcorrection:EntertheIncrementsandCorrections
tablewiththedcorrectionfactordiscussedabove.Extract
thepropercorrection,beingcarefultoretaintheproper
sign.
TrueDeclination:Combinethetabulateddeclination
and thedcorrection to obtain the true declination.
AssumedLatitude:Chooseastheassumedlatitude
thatwholevalueoflatitudeclosesttothevessel’sDR
latitude.Iftheassumedlatitudeanddeclinationareboth
northorbothsouth,labeltheassumedlatitude“Same.”If
oneisnorthandtheotherissouth,labeltheassumed
latitude “Contrary.”
SECTIONFOURusestheargumentsofassumed
latitude,LHA,anddeclinationdeterminedinSectionThreeto
enterPub.229todetermineazimuthandcomputedaltitude.
Then,SectionFourcomparescomputedandobservedaltitudes
to calculate the altitude intercept. From this the LOP is plotted.
DeclinationIncrementanddInterpolationFactor:
NotethattwoofthethreeargumentsusedtoenterPub.229,
LHAandlatitude,arewholedegreevalues.SectionThreedoes
notdeterminethethirdargument,declination,asawhole
degree.Therefore,thenavigatormustinterpolateinPub.229
fordeclination,givenwholedegreesofLHAandlatitude.The
firststepsofSectionFourinvolvethisinterpolationfor
declination.Sincedeclinationvaluesaretabulatedeverywhole
degreeinPub.229,thedeclinationincrementistheminutesand
tenthsofthetruedeclination.Forexample,ifthetruedeclination
is 13° 15.6', then the declination increment is 15.6'.
Pub.229alsolistsadInterpolationFactor.Thisisthemag-
nitudeofthedifferencebetweenthetwosuccessivetabulated
valuesfordeclinationthatframethetruedeclination.Therefore,
forthehypotheticaldeclinationlistedabove,thetabulateddin-
terpolationfactorlistedinthetablewouldbethedifference
betweendeclinationvaluesgivenfor13°and14°.Ifthedeclina-
tionincreasesbetweenthesetwovalues,dispositive.Ifthe
declination decreases between these two values,d is negative.
ComputedAltitude(Tabulated):EnterPub.229
withthefollowingarguments:(1)LHAfromSection
Three;(2)assumedlatitudefromSectionThree;(3)the
wholedegreevalueofthetruedeclination.Forexample,if
thetruedeclinationwere13°15.6',thenenterPub.229with
13°asthevaluefordeclination.Recordthetabulated
computed altitude.
DoubleSecondDifferenceCorrection:Usethis
correctionwhenlinearinterpolationofdeclinationfor
computedaltitudeisnotsufficientlyaccurateduetothenon-
linearchangeinthecomputedaltitudeasafunctionof
declination.Theneedfordoubleseconddifferenceinterpo-
lationisindicatedbythedinterpolationfactorappearingin
italictypefollowedbyasmalldot.Whenthisproceduremust
beemployed,refertodetailedinstructionsintheintroduction
toPub. 229.
TotalCorrection:Thetotalcorrectionisthesumof
thedoubleseconddifference(ifrequired)andtheinterpo-
lationcorrections.Calculatetheinterpolationcorrectionby
dividingthedeclinationincrementby60'andmultiplythe
resulting quotient by thedinterpolation factor.
ComputedAltitude(h
c
):Applythetotalcorrection,
beingcarefultocarrythecorrectsign,tothetabulated
computed altitude. This yields the computed altitude.
ObservedAltitude(h
o
):Entertheobservedaltitude
from Section One.
SIGHT REDUCTION301
AltitudeIntercept:Compareh
c
andh
o
.Subtractthe
smallerfromthelarger.Theresultingdifferenceisthe
magnitudeofthealtitudeintercept.Ifh
o
isgreaterthanh
c
,
thenlabelthealtitudeintercept“Toward.”Ifh
c
isgreater
than h
o
, then label the altitude intercept “Away.”
AzimuthAngle:Obtaintheazimuthangle(Z)from
Pub.229,usingthesameargumentswhichdeterminedtab-
ulatedcomputedaltitude.Visualinterpolationis
sufficiently accurate.
TrueAzimuth:Calculatethetrueazimuth(Z
n
)from
the azimuth angle (Z) as follows:
a) If in northern latitudes:
b) If in southern latitudes:
SIGHT REDUCTION
Thesectionabovediscussedthebasictheoryofsight
reductionandpresentedamethodtobefollowedwhen
reducingsights.Thissectionputsthatmethodintopractice
inreducingsightsofastar,theSun,theMoon,andplanets.
2006. Reducing Star Sights to a Fix
OnMay16,1995,atthetimesindicated,thenavigator
takes and records the following sights:
Heightofeyeis48feetandindexcorrection(IC)is
+2.1'.TheDRlatitudeforbothsightsis39°N.TheDR
longitudefortheSpicasightis157°10'W.TheDR
longitudefortheKochabsightis157°08.0'W.Determine
the intercept and azimuth for both sights. See Figure 2006.
First,convertthesextantaltitudestoobserved
altitudes. Reduce the Spica sight first:
Determinethesumoftheindexcorrectionandthedip
correction.GototheinsidefrontcoveroftheNautical
Almanactothetableentitled“DIP.”Thistablelistsdip
correctionsasafunctionofheightofeyemeasuredineither
feetormeters.Intheaboveproblem,theobserver’sheightof
eyeis48feet.Theheightsofeyearetabulatedinintervals,
withthecorrectioncorrespondingtoeachintervallisted
betweentheinterval’sendpoints.Inthiscase,48feetlies
betweenthetabulated46.9to48.4feetinterval;the
correspondingcorrectionforthisintervalis-6.7'.AddtheIC
andthedipcorrection,beingcarefultocarrythecorrectsign.
Thesumofthecorrectionshereis-4.6'.Applythiscorrection
to the sextant altitude to obtain the apparent altitude (h
a
).
Next,applythealtitudecorrection.Findthealtitude
correctiontableontheinsidefrontcoveroftheNautical
Almanacnexttothediptable.Thealtitudecorrectionvaries
asafunctionofboththetypeofbodysighted(Sun,star,or
planet)andthebody’sapparentaltitude.Fortheproblem
above,enterthestaraltitudecorrectiontable.Again,the
correctionisgivenwithinanaltitudeinterval;h
a
inthiscase
was32°30.2'.Thisvalueliesbetweenthetabulated
endpoints32°00.0'and33°45.0'.Thecorrection
correspondingtothisintervalis-1.5'.Applyingthis
correction to h
a
yields an observed altitude of 32° 28.7'.
Havingcalculatedtheobservedaltitude,determinethe
time and date of the sight in Greenwich Mean Time:
Recordtheobservationtimeandthenapplyanywatch
errortodeterminezonetime.Then,usetheDRlongitudeat
thetimeofthesighttodeterminetimezonedescription.In
thiscase,theDRlongitudeindicatesazonedescriptionof
+10hours.Addthezonedescriptiontothezonetimeto
obtainGMT.Itisimportanttocarrythecorrectdatewhen
applyingthiscorrection.Inthiscase,the+10correction
madeit06-11-26GMTonMay
17,whenthedateinthe
local time zone was May
16.
AftercalculatingboththeobservedaltitudeandtheGMT
LHA180°then Z
n
Z
=,>
LHA180°then Z
n
360°
Z–
=,<
LHA180°then Z
n
180°
Z
–=,>
LHA180°then Z
n
180°+
Z
=,<
StarSextant AltitudeZone Time
Kochab47° 19.1'20-07-43
Spica32° 34.8'20-11-26
BodySpica
Index Correction+2.1'
Dip (height 48 ft)-6.7'
Sum-4.6'
Sextant Altitude (h
s
)32° 34.8'
Apparent Altitude (h
a
)32° 30.2'
Altitude Correction-1.5'
Additional Correction0
Horizontal Parallax0
Correction to h
a
-1.5'
Observed Altitude (h
o
)32° 28.7'
Date16 May 1995
DR Latitude39° N
DR Longitude157° 10' W
Observation Time20-11-26
Watch Error0
Zone Time20-11-26
Zone Description+10
GMT06-11-26
GMT Date17 May 1995
302SIGHT REDUCTION
time,enterthedailypagesoftheNauticalAlmanacto
calculatethestar’sGreenwichHourAngle(GHA)and
declination.
First,recordtheGHAofAriesfromtheMay17,1995
daily page: 324° 28.4'.
Next,determinetheincrementaladditionforthe
minutesandsecondsafter0600fromtheIncrementsand
CorrectionstableinthebackoftheNauticalAlmanac.The
increment for 11 minutes and 26 seconds is 2° 52'.
Then, calculate the GHA of the star. Remember:
GHA (star) = GHA + SHA (star)
TheNauticalAlmanacliststheSHAofselectedstarson
eachdailypage.TheSHAofSpicaonMay17,1995:158°45.3'.
Pub.229’senteringargumentsarewholedegreesof
LHAandassumedlatitude.RememberthatLHA=GHA-
westlongitudeorGHA+eastlongitude.Sinceinthis
examplethevesselisinwestlongitude,subtractits
assumedlongitudefromtheGHAofthebodytoobtainthe
LHA.Assumealongitudemeetingthecriterialistedin
Article 2005.
Fromthosecriteria,theassumedlongitudemustendin
05.7minutessothat,whensubtractedfromthecalculated
GHA,awholedegreeofLHAwillresult.SincetheDR
longitudewas157°10.0',thentheassumedlongitude
endingin05.7'closesttotheDRlongitudeis157°05.7'.
Subtractingthisassumedlongitudefromthecalculated
GHA of the star yields an LHA of 329°.
Thenextvalueofconcernisthestar’struedeclination.
ThisvalueisfoundontheMay17thdailypagenexttothe
star’sSHA.Spica’sdeclinationisS11°08.4'.Thereisnod
correctionforastarsight,sothestar’struedeclination
equalsitstabulateddeclination.Theassumedlatitudeis
determinedfromthewholedegreeoflatitudeclosesttothe
DRlatitudeatthetimeofthesight.Inthiscase,theassumed
latitudeisN39°.Itismarked“contrary”becausetheDR
latitude is north while the star’s declination is south.
Thefollowinginformationisknown:(1)theassumed
position’sLHA(329°)andassumedlatitude(39°N
contraryname);and(2)thebody’sdeclination(S11°08.4').
FindthepageintheSightReductionTable
correspondingtoanLHAof329°andanassumedlatitude
ofN39°,withlatitudecontrarytodeclination.Enterthis
tablewiththebody’swholedegreeofdeclination.Inthis
case,thebody’swholedegreeofdeclinationis11°.This
declinationcorrespondstoatabulatedaltitudeof32°15.9'.
Thisvalueisforadeclinationof11°;thetruedeclinationis
11°08.4'.Therefore,interpolatetodeterminethecorrection
toaddtothetabulatedaltitudetoobtainthecomputed
altitude.
Thedifferencebetweenthetabulatedaltitudesfor11°
and12°isgiveninPub.229asthevalued;inthiscase,d=
-53.0.Expressasaratiothedeclinationincrement(inthis
case,8.4')andthetotalintervalbetweenthetabulateddec-
linationvalues(inthiscase,60')toobtainthepercentageof
thedistancebetweenthetabulateddeclinationvaluesrepre-
sentedbythedeclinationincrement.Next,multiplythat
percentagebytheincrementbetweenthetwovaluesfor
computed altitude. In this case:
Subtract7.4'fromthetabulatedaltitudetoobtainthe
final computed altitude: H
c
= 32° 08.5'.
Itwillbevaluableheretoreviewexactlywhath
o
andh
c
represent.Recallthemethodologyofthe
altitude-interceptmethod.Thenavigatorfirstmeasures
andcorrectsanaltitudeforacelestialbody.This
correctedaltitude,h
o
,correspondstoacircleofequal
altitudepassingthroughthenavigator’sactualposition
whosecenteristhegeographicposition(GP)ofthe
body.Thenavigatorthendeterminesanassumed
position(AP)near,butnotcoincidentwith,hisactual
position;hethencalculatesanaltitudeforanobserver
atthatassumedposition(AP).Thecircleofequal
altitudepassingthroughthisassumedpositionis
concentricwiththecircleofequalaltitudepassing
throughthenavigator’sactualposition.Thedifference
betweenthebody’saltitudeattheassumedposition(h
c
)
andthebody’sobservedaltitude(h
o
)isequaltothe
differencesinradiilengthofthetwocorresponding
circlesofequalaltitude.Intheaboveproblem,
therefore,thenavigatorknowsthattheequalaltitude
circle passing through his actual position is:
awayfromtheequalaltitudecirclepassingthroughhis
assumedposition.Sinceh
o
isgreaterthanh
c
,the
navigatorknowsthattheradiusoftheequalaltitude
circlepassingthroughhisactualpositionislessthan
Tab GHA324° 28.4'
GHA Increment2° 52.0'
SHA158° 45.3'
GHA486° 05.7'
+/- 360°not required
Assumed Longitude157° 05.7'
LHA329°
Tabulated Dec/dS 11° 08.4'/n.a.
d Correction—
True DeclinationS 11° 08.4'
Assumed LatitudeN 39° contrary
Dec Inc / + or - d8.4' / -53.0
h
c
(tabulated)32° 15.9'
Correction (+ or -)-7.4'
h
c
(computed)32° 08.5'
8.4
60
-------
53.0–()×7.4–=
SIGHT REDUCTION303
theradiusoftheequalaltitudecirclepassingthrough
theassumedposition.Theonlyremainingquestionis:in
whatdirectionfromtheassumedpositionisthebody’s
actualGP.Pub.229alsoprovidesthisfinalpieceof
information.ThisisthevalueforZtabulatedwiththeh
c
anddvaluesdiscussedabove.Inthiscase,enterPub.229
asbefore,withLHA,assumedlatitude,anddeclination.
Visualinterpolationissufficient.ExtractthevalueZ=
143.3°.TherelationbetweenZandZ
n
,thetrueazimuth,
is as follows:
In northern latitudes:
In southern latitudes:
Inthiscase,LHA>180°andthevesselisinnorthernlati-
tude.Therefore,Z
n
=Z=143.3°T.Thenavigatornowhas
enough information to plot a line of position.
The values for the reduction of the Kochab sight follow:
2007. Reducing a Sun Sight
Theexamplebelowpointsoutthesimilaritiesbetween
reducingaSunsightandreducingastarsight.Italsodem-
onstratestheadditionalcorrectionsrequiredforlowaltitude
(<10°)sightsandsightstakenduringnon-standardtemper-
ature and pressure conditions.
OnJune16,1994,at05-15-23localtime,atDRposi-
tionL30°Nλ45°W,anavigatortakesasightoftheSun’s
upperlimb.Thenavigatorhasaheightofeyeof18feet,the
temperatureis88°F,andtheatmosphericpressureis982
mb.Thesextantaltitudeis3°20.2'.Thereisnoindexerror.
Determine the observed altitude. See Figure 2007.
Applytheindexanddipcorrectionstoh
s
toobtainh
a
.
Becauseh
a
islessthan10°,usethespecialaltitudecorrection
tableforsightsbetween0°and10°locatedontherightinside
front page of theNautical Almanac.
Enterthetablewiththeapparentaltitude,thelimbof
theSunusedforthesight,andtheperiodoftheyear.Inter-
polationfortheapparentaltitudeisnotrequired.Inthis
case,thetableyieldsacorrectionof-29.4'.Thecorrection’s
algebraicsignisfoundattheheadofeachgroupofentries
and at every change of sign.
Theadditionalcorrectionisrequiredbecauseofthe
non-standardtemperatureandatmosphericpressureunder
whichthesightwastaken.Thecorrectionforthesenon-
standardconditionsisfoundintheAdditionalCorrections
tablelocatedonpageA4inthefrontoftheNautical
Almanac.
First,entertheAdditionalCorrectionstablewiththe
temperatureandpressuretodeterminethecorrectzone
letter:inthiscase,zoneL.Then,locatethecorrectioninthe
Lcolumncorrespondingtotheapparentaltitudeof3°16.1'.
Interpolatebetweenthetableargumentsof3°00.0'and3°
30.0'todeterminetheadditionalcorrection:+1.4'.Thetotal
correctiontotheapparentaltitudeisthesumofthealtitude
andadditionalcorrections:-28.0'.Thisresultsinanh
o
of
2°48.1'.
Next,determinetheSun’sGHAanddeclination.
BodyKochab
Index Correction+2.1'
Dip Correction-6.7'
Sum-4.6'
h
s
47° 19.1'
h
a
47° 14.5'
Altitude Correction-.9'
Additional Correctionnot applicable
Horizontal Parallaxnot applicable
Correction to h
a
-9'
h
o
47° 13.6'
Date16 May 1995
DR latitude39°N
DR longitude157° 08.0' W
Observation Time20-07-43
Watch Error0
Zone Time20-07-43
Zone Description+10
GMT06-07-43
GMT Date17 May 1995
Tab GHA324° 28.4'
GHA Increment1° 56.1'
SHA137° 18.5'
h
o
32°28.7′=
h–
c
32°08.5′
20.2NM
--------------------------------=
LHA180°then Z
n
Z
=,>
LHA180°then Z
n
360°
Z–
=,<
LHA180°then Z
n
180°
Z
–=,>
LHA180°then Z
n
180°
Z+
=,<
GHA463° 43.0'
+/- 360°not applicable
Assumed Longitude156° 43.0'
LHA307°
Tab Dec /dN74° 10.6' / n.a.
d Correctionnot applicable
True DeclinationN74° 10.6'
Assumed Latitude39°N (same)
Dec Inc / + or - d10.6' / -24.8
h
c
47° 12.6'
Total Correction-4.2'
h
c
(computed)47° 08.4'
h
o
47° 13.6'
a (intercept)5.2 towards
Z018.9°
Z
n
018.9°
304SIGHT REDUCTION
Figure 2006. Left hand daily page of the Nautical Almanac for May 17, 1995.
SIGHT REDUCTION305
Again,thisprocessissimilartothestarsightsreduced
above.Notice,however,thatSHA,aquantityuniquetostar
sight reduction, is not used in Sun sight reduction.
DeterminingtheSun’sGHAislesscomplicatedthan
determiningastar’sGHA.TheNauticalAlmanac’sdaily
pageslisttheSun’sGHAinhourlyincrements.Inthiscase,
theSun’sGHAat0800GMTonJune16,1994is299°
51.3'.ThevcorrectionisnotapplicableforaSunsight;
therefore,applyingtheincrementcorrectionyieldsthe
Sun’s GHA. In this case, the GHA is 303° 42.1'.
DeterminingtheSun’sLHAissimilartodetermining
astar’sLHA.IndeterminingtheSun’sdeclination,how-
ever,anadditionalcorrectionnotencounteredinthestar
sight,thedcorrection,mustbeconsidered.Thebottomof
theSuncolumnonthedailypagesoftheNauticalAlma-
nacliststhedvalue.Thisisaninterpolationfactorforthe
Sun’sdeclination.Thesignofthedfactorisnotgiven;it
mustbedeterminedbynotingfromtheAlmanacifthe
Sun’sdeclinationisincreasingordecreasingthroughout
theday.Ifitisincreasing,thefactorispositive;ifitisde-
creasing,thefactorisnegative.Intheaboveproblem,the
Sun’sdeclinationisincreasingthroughouttheday.There-
fore, thed factor is +0.1.
Having obtained thed factor, enter the 15 minute
incrementandcorrectiontable.Underthecolumnlabeled
“vordcorr
n
,”findthevaluefordinthelefthandcolumn.
Thecorrespondingnumberintherighthandcolumnisthe
correction; apply it to the tabulated declination. In this
case, the correction corresponding to advalue of +0.1 is
0.0'.
Thefinalstepwillbetodetermineh
c
andZ
n
.EnterPub.
229withanLHAof259°,adeclinationofN23°20.5',andan
assumed latitude of 30°N.
2008. Reducing a Moon Sight
TheMooniseasytoidentifyandisoftenvisibleduring
theday.However,theMoon’sproximitytotheEarthrequires
applyingadditionalcorrectionstoh
a
toobtainh
o
.Thisarticle
will cover Moon sight reduction.
At10-00-00GMT,June16,1994,thenavigatorobtainsa
sightoftheMoon’supperlimb.H
s
is26°06.7'.Heightofeye
is18feet;thereisnoindexerror.Determineh
o
,theMoon’s
GHA, and the Moon’s declination. See Figure 2008.
Thisexampledemonstratestheextracorrections
requiredforobtainingh
o
foraMoonsight.Applytheindex
anddipcorrectionsinthesamemannerasforstarandSun
sights.Thealtitudecorrectioncomesfromtableslocatedon
the inside back covers of theNautical Almanac.
Inthiscase,theapparentaltitudewas26°02.6'.Enterthe
altitudecorrectiontablefortheMoonwiththeabove
apparentaltitude.Interpolationisnotrequired.The
correctionis+60.5'.Theadditionalcorrectioninthiscaseis
notapplicablebecausethesightwastakenunderstandard
temperature and pressure conditions.
ThehorizontalparallaxcorrectionisuniquetoMoon
sights.ThetablefordeterminingthisHPcorrectionisonthe
backinsidecoveroftheNauticalAlmanac.First,gotothe
dailypageforJune16at10-00-00GMT.Inthecolumnfor
theMoon,findtheHPcorrectionfactorcorrespondingto
10-00-00.Itsvalueis58.4.TakethisvaluetotheHP
correctiontableontheinsidebackcoveroftheAlmanac.
NoticethattheHPcorrectioncolumnslineupvertically
withtheMoonaltitudecorrectiontablecolumns.Findthe
HPcorrectioncolumndirectlyunderthealtitudecorrection
tableheadingcorrespondingtotheapparentaltitude.Enter
thatcolumnwiththeHPcorrectionfactorfromthedaily
pages.Thecolumnhastwosetsoffigureslistedunder“U”
and“L”forupperandlowerlimb,respectively.Inthiscase,
tracedownthe“U”columnuntilitintersectswiththeHP
BodySun UL
Index Correction0
Dip Correction (18 ft)-4.1'
Sum-4.1'
h
s
3° 20.2'
h
a
3° 16.1'
Altitude Correction-29.4'
Additional Correction+1.4'
Horizontal Parallax0
Correction to h
a
-28.0'
h
o
2° 48.1'
DateJune 16, 1994
DR LatitudeN30° 00.0'
DR LongitudeW045° 00.0'
Observation Time05-15-23
Watch Error0
Zone Time05-15-23
Zone Description+03
GMT08-15-23
Date GMTJune 16, 1994
Tab GHA /v299° 51.3' / n.a.
GHA Increment3° 50.8'
SHA orv correctionnot applicable
GHA303°42.1'
Assumed Longitude44° 42.1' W
LHA259°
Tab Declination /dN23° 20.5' / +0.1'
d Correction0.0
True DeclinationN23° 20.5'
Assumed LatitudeN30° (same)
Correction (+ or -)+10.8'
Computed Altitude (h
c
)2° 39.6'
Observed Altitude (h
o
)2° 48.1'
Intercept8.5 NM (towards)
Z064.7°
Z
n
064.7°
Declination Increment / + or -d20.5' / +31.5
Tabulated Altitude2° 28.8'
306SIGHT REDUCTION
Figure 2007. Left hand daily page of the Nautical Almanac for June 16, 1994.
SIGHT REDUCTION307
correctionfactorof58.4.Interpolatingbetween58.2and
58.5yieldsavalueof+4.0'forthehorizontalparallax
correction.
Thefinalcorrectionisaconstant-30.0'correctiontoh
a
appliedonlytosightsoftheMoon’supperlimb.Thiscorrection
isalwaysnegative;applyitonlytosightsoftheMoon’supper
limb,notitslowerlimb.Thetotalcorrectiontoh
a
isthesumof
allthecorrections;inthiscase,thistotalcorrectionis+34.5
minutes.
ToobtaintheMoon’sGHA,enterthedailypagesinthe
Mooncolumnandextracttheapplicabledatajustasforastaror
Sunsight.DeterminingtheMoon’sGHArequiresanadditional
correction, thev correction.
First,recordtheGHAoftheMoonfor10-00-00on
June16,1994,fromthedailypagesoftheNauticalAlma-
nac.Recordalsothevcorrectionfactor;inthiscase,itis
+11.3.ThevcorrectionfactorfortheMoonisalwaysposi-
tive.Theincrementcorrectionis,inthiscase,zerobecause
thesightwasrecordedontheevenhour.Toobtainthev
correction,gotothetablesofincrementsandcorrections.In
the0minutetableinthevordcorrectioncolumns,findthe
correctionthatcorrespondstoav=11.3.Thetableyieldsa
correctionof+0.1'.Addingthiscorrectiontothetabulated
GHA gives the final GHA as 245° 45.2'.
FindingtheMoon’sdeclinationissimilartofindingthe
declinationfortheSunorstars.Gotothedailypagesfor
June16,1994;extracttheMoon’sdeclinationanddfactor.
Thetabulateddeclinationandthedfactorcomefrom
theNauticalAlmanac’sdailypages.Recordthedeclination
anddcorrectionandgototheincrementandcorrection
pagestoextractthepropercorrectionforthegivendfactor.
Inthiscase,gotothecorrectionpagefor0minutes.The
correctioncorrespondingtoadfactorof+12.1is+0.1.Itis
importanttoextractthecorrectionwiththecorrect
algebraicsign.Thedcorrectionmaybepositiveornegative
dependingonwhethertheMoon’sdeclinationisincreasing
ordecreasingintheintervalcoveredbythedfactor.Inthis
case,theMoon’sdeclinationat10-00-00GMTon16June
wasS00°13.7';at11-00-00onthesamedatetheMoon’s
declinationwasS00°25.8'.Therefore,sincethe
declinationwasincreasingoverthisperiod,thedcorrection
ispositive.Donotdeterminethesignofthiscorrectionby
notingthetrendinthedfactor.Inotherwords,hadthed
factorfor11-00-00beenavaluelessthan12.1,thatwould
notindicatethatthedcorrectionshouldbenegative.
Rememberthatthedfactorisanalogoustoaninterpolation
factor;itprovidesacorrectionto
declination.Therefore,the
trendindeclinationvalues,notthetrendindvalues,
controlsthesignofthedcorrection.Combinethetabulated
declinationandthedcorrectionfactortodeterminethetrue
declination.Inthiscase,theMoon’struedeclinationisS
00° 13.8'.
HavingobtainedtheMoon’sGHAanddeclination,
calculateLHAanddeterminetheassumedlatitude.Enterthe
SightReductionTablewiththeLHA,assumedlatitude,and
calculateddeclination.Calculatetheinterceptandazimuthin
the same manner used for star and Sun sights.
2009. Reducing a Planet Sight
Therearefournavigationalplanets:Venus,Mars,
Jupiter,andSaturn.Reducingaplanetsightissimilarto
reducingaSunorstarsight,butthereareafewimportant
differences.ThisArticlewillcovertheprocedurefor
determiningh
o
,theGHAandthedeclinationforaplanet
sight.
OnJuly27,1995,at09-45-20GMT,youtakeasight
ofMars.H
s
is33°20.5'.Theheightofeyeis25feet,andthe
indexcorrectionis+0.2'.Determineh
o
,GHA,anddeclina-
tion. See Figure 2009.
Thetableabovedemonstratesthesimilaritybetween
reducingplanetsightsandreducingsightsoftheSunand
stars.Calculateandapplytheindexanddipcorrectionsex-
actlyasforanyothersight.Taketheresultingapparent
altitudeandenterthealtitudecorrectiontableforthestars
andplanetsontheinsidefrontcoveroftheNautical
Almanac.
Inthiscase,thealtitudecorrectionfor33°15.8'resultsin
acorrectionof-1.5'.Theadditionalcorrectionisnotapplicable
becausethesightwastakenatstandardtemperatureandpres-
sure;thehorizontalparallaxcorrectionisnotapplicabletoa
planetsight.AllthatremainsisthecorrectionspecifictoMars
orVenus.ThealtitudecorrectiontableintheNauticalAlma-
nacalsocontainsthiscorrection.Itsmagnitudeisafunctionof
thebodysighted(MarsorVenus),thetimeofyear,andthe
body’sapparentaltitude.Enteringthistablewiththedatafor
thisproblemyieldsacorrectionof+0.1'.Applyingthesecor-
BodyMoon (UL)
Index Correction0.0'
Dip (18 feet)-4.1'
Sum-4.1'
Sextant Altitude (h
s
)26° 06.7'
Apparent Altitude (h
a
)26° 02.6'
Altitude Correction+60.5'
Additional Correction0.0'
Horizontal Parallax (58.4)+4.0'
Moon Upper Limb Correction-30.0'
Correction to h
a
+34.5'
Observed Altitude (h
o
)26° 37.1'
GHA Moon andv245° 45.1' and +11.3
GHA Increment0° 00.0'
vCorrection+0.1'
GHA245° 45.2'
Tabulated Declination / dS 00° 13.7' / +12.1
dCorrection+0.1'
True DeclinationS 00° 13.8'
308SIGHT REDUCTION
Figure 2008. Right hand daily page of the Nautical Almanac for June 16, 1994.
SIGHT REDUCTION309
rections to h
a
results in an h
o
of 33° 14.4'.
TheonlydifferencebetweendeterminingtheSun’sGHA
andaplanet’sGHAliesinapplyingthevcorrection.Calculate
thiscorrectionfromthevordcorrectionsectionoftheIncre-
ments and Correction table in theNautical Almanac.
Findthevfactoratthebottomoftheplanets’GHAcolumns
on the daily pages of theNautical Almanac. For Mars on
July 27, 1995, thev factor is 1.1. If no algebraic sign
precedes thev factor, add the resulting correction to the
tabulatedGHA.Subtracttheresultingcorrectiononlywhen
a negative sign precedes thev factor. Entering thev ord
correction table corresponding to 45 minutes yields a
correctionof0.8'.Remember,becausenosignprecededthe
vfactor on the daily pages, add this correction to the
tabulated GHA. The final GHA is 267°31.4'.
Readthetabulateddeclinationdirectlyfromthedaily
pagesoftheNauticalAlmanac.Thedcorrectionfactoris
listedatthebottomoftheplanetcolumn;inthiscase,the
factoris0.6.Notethetrendinthedeclinationvaluesforthe
planet;iftheyareincreasingduringtheday,thecorrection
factorispositive.Iftheplanet’sdeclinationisdecreasing
duringtheday,thecorrectionfactorisnegative.Next,enter
thevordcorrectiontablecorrespondingto45minutesand
extractthecorrectionforadfactorof0.6.Thecorrectionin
this case is +0.5'.
Fromthispoint,reducingaplanetsightisexactlythe
same as reducing a Sun sight.
MERIDIAN PASSAGE
Thissectioncoversdeterminingbothlatitudeand
longitudeatthemeridianpassageoftheSun,orLocal
ApparentNoon(LAN).Determiningavessel’slatitudeat
LANrequirescalculatingtheSun’szenithdistanceand
declinationandcombiningthemaccordingtotherules
discussed below.
LatitudeatLANisaspecialcaseofthenavigational
trianglewheretheSunisontheobserver’smeridianandthe
trianglebecomesastraightnorth/southline.No“solution”is
necessary,excepttocombinetheSun’szenithdistanceand
its declination according to the rules discussed below.
LongitudeatLANisafunctionofthetimeelapsedsincethe
SunpassedtheGreenwichmeridian.Thenavigatormust
determinethetimeofLANandcalculatetheGHAoftheSunat
thattime.Thefollowingexamplesdemonstratestheseprocesses.
2010. Latitude at Meridian Passage
At1056ZT,May16,1995,avessel’sDRpositionisL
40°04.3'Nandλ157°18.5'W.Theshipisoncourse200°T
ataspeedoftenknots.(1)Calculatethefirstandsecondes-
timatesofLocalApparentNoon.(2)Thenavigatoractually
observesLANat12-23-30zonetime.Thesextantaltitude
atLANis69°16.0'.Theindexcorrectionis+2.1'andthe
height of eye is 45 feet. Determine the vessel’s latitude.
First,determinethetimeofmeridianpassagefromthedaily
pagesoftheNauticalAlmanac.Inthiscase,themeridian
passageforMay16,1995,is1156.Thatis,theSuncrossesthe
centralmeridianofthetimezoneat1156ZTandtheobserver’s
localmeridianat1156localtime.Next,determinethevessel’s
DRlongitudeforthetimeofmeridianpassage.Inthiscase,the
vessel’s1156DRlongitudeis157°23.0'W.Determinethetime
zoneinwhichthisDRlongitudefallsandrecordthelongitude
ofthattimezone’scentralmeridian.Inthiscase,thecentral
meridianis150°W.EntertheConversionofArctoTimetable
intheNauticalAlmanacwiththedifferencebetweentheDR
longitudeandthecentralmeridianlongitude.Theconversionfor
7°ofarcis28
m
oftime,andtheconversionfor23'ofarcis
1
m
32
s
oftime.Sumthesetwotimes.IftheDRpositioniswest
ofthecentralmeridian(asitisinthiscase),addthistimetothe
timeoftabulatedmeridianpassage.Ifthelongitudedifferenceis
totheeastofthecentralmeridian,subtractthistimefromthe
tabulatedmeridianpassage.Inthiscase,theDRpositioniswest
ofthecentralmeridian.Therefore,add29minutesand32
secondsto1156,thetabulatedtimeofmeridianpassage.The
estimated time of LAN is 12-25-32 ZT.
ThisfirstestimateforLANdoesnottakeintoaccountthe
vessel’smovement.TocalculatethesecondestimateofLAN,
firstdeterminetheDRlongitudeforthetimeoffirstestimateof
LAN(12-25-32ZT).Inthiscase,thatlongitudewouldbe157°
25.2'W.Then,calculatethedifferencebetweenthelongitudeof
the12-25-32DRpositionandthecentralmeridianlongitude.
Thiswouldbe7°25.2'.Again,enterthearctotimeconversion
tableandcalculatethetimedifferencecorrespondingtothis
BodyMars
Index Correction+0.2'
Dip Correction (25 feet)-4.9'
Sum-4.7'
h
s
33° 20.5'
h
a
33° 15.8'
Altitude Correction-1.5'
Additional CorrectionNot applicable
Horizontal ParallaxNot applicable
Additional Correction for Mars+0.1'
Correction to h
a
-1.4'
h
o
33° 14.4'
Tabulated GHA /v256°10.6' / 1.1
GHA Increment11° 20.0'
v correction+0.8'
GHA267°31.4'
Tabulated Declination /dS 01° 06.1' / 0.6
dCorrection+0.5'
True DeclinationS 01° 06.6'
310SIGHT REDUCTION
Figure 2009. Left hand daily page of the Nautical Almanac for July 27, 1995.
SIGHT REDUCTION311
longitudedifference.Thecorrectionfor7°ofarcis28'oftime,
andthecorrectionfor25.2'ofarcis1'41"oftime.Finally,apply
thistimecorrectiontotheoriginaltabulatedtimeofmeridian
passage(1156ZT).Theresultingtime,12-25-41ZT,isthe
second estimate of LAN.
Solvingforlatituderequiresthatthenavigatorcalculate
twoquantities:theSun’sdeclinationandtheSun’szenith
distance.First,calculatetheSun’struedeclinationatLAN.The
problemstatesthatLANis12-28-30.(Determiningtheexact
timeofLANiscoveredinArticle2011.)Enterthetimeof
observedLANandaddthecorrectzonedescriptionto
determineGMT.DeterminetheSun’sdeclinationinthesame
mannerasinthesightreductionprobleminArticle2006.Inthis
case,thetabulateddeclinationwasN19°19.1',andthed
correction +0.2'. The true declination, therefore, is N 19° 19.3'.
Next,calculatezenithdistance.RecallfromNavigational
Astronomythatzenithdistanceissimply90°-observedaltitude.
Therefore,correcth
s
toobtainh
a
;thencorrecth
a
toobtainh
o
.
Then,subtracth
o
from90°todeterminethezenithdistance.
NamethezenithdistanceNorthorSouthdependingonthe
relativepositionoftheobserverandtheSun’sdeclination.Ifthe
observeristothenorthoftheSun’sdeclination,namethezenith
distancenorth.Conversely,iftheobserveristothesouthofthe
Sun’sdeclination,namethezenithdistancesouth.Inthiscase,
theDRlatitudeisN39°55.0'andtheSun’sdeclinationisN19°
19.3'.TheobserveristothenorthoftheSun’sdeclination;
therefore,namethezenithdistancenorth.Next,comparethe
namesofthezenithdistanceandthedeclination.Iftheirnames
arethesame(i.e.,botharenorthorbotharesouth),addthetwo
valuestogethertoobtainthelatitude.Thiswasthecaseinthis
problem.BoththeSun’sdeclinationandzenithdistancewere
north; therefore, the observer’s latitude is the sum of the two.
Ifthenameofthebody’szenithdistanceiscontraryto
thenameoftheSun’sdeclination,thensubtractthesmaller
ofthetwoquantitiesfromthelarger,carryingforthename
ofthedifferencethenameofthelargerofthetwo
quantities.Theresultistheobserver’slatitude.The
following examples illustrate this process.
2011. Longitude at Meridian Passage
Determiningavessel’slongitudeatLANisstraight-
forward.Inthewesternhemisphere,theSun’sGHAat
LANequalsthevessel’slongitude.Intheeastern
hemisphere,subtracttheSun’sGHAfrom360°to
determinelongitude.Thedifficultpartliesindetermining
the precise moment of meridian passage.
Determiningthetimeofmeridianpassagepresentsa
problembecausetheSunappearstohangforafinitetime
atitslocalmaximumaltitude.Therefore,notingthetime
ofmaximumsextantaltitudeisnotsufficientfor
determiningtheprecisetimeofLAN.Twomethodsare
availabletoobtainLANwithaprecisionsufficientfor
determininglongitude:(1)thegraphicalmethodand(2)
thecalculationmethod.Thegraphicalmethodis
discussed first below.
SeeFigure2011.Forabout30minutesbeforethe
estimatedtimeofLAN,measureandrecordseveralsextant
altitudesandtheircorrespondingtimes.Continuetaking
sightsforabout30minutesaftertheSunhasdescended
fromthemaximumrecordedaltitude.Increasethesighting
frequencynearthemeridianpassage.Onesightevery20-30
secondsshouldyieldgoodresultsnearmeridianpassage;
less frequent sights are required before and after.
Plottheresultingdataonagraphofsextantaltitude
versustimeanddrawafaircurvethroughtheplotted
data.Next,drawaseriesofhorizontallinesacrossthe
curveformedbythedatapoints.Theselineswill
intersectthefairedcurveattwodifferentpoints.Thex
coordinatesofthepointswheretheselinesintersectthe
fairedcurverepresentthetwodifferenttimeswhenthe
Sun’saltitudewasequal(onetimewhentheSunwas
ascending;theothertimewhentheSunwasdescending).
Drawthreesuchlines,andensurethelineshave
sufficientverticalseparation.Foreachline,averagethe
twotimeswhereitintersectsthefairedcurve.Finally,
averagethethreeresultingtimestoobtainafinalvalue
Date16 May 1995
DR Latitude (1156 ZT)39° 55.0' N
DR Longitude (1156 ZT)157° 23.0' W
Central Meridian150° W
d Longitude (arc)7° 23' W
d Longitude (time)+29 min. 32 sec
Meridian Passage (LMT)1156
ZT (first estimate)12-25-32
DR Longitude (12-25-32)157° 25.2'
d Longitude (arc)7° 25.2'
d Longitude (time)+29 min. 41 sec
Meridian Passage1156
ZT (second estimate)12-25-41
ZT (actual transit)12-23-30 local
Zone Description+10
GMT22-23-30
Date (GMT)16 May 1995
Tabulated Declination /dN 19° 09.0' / +0.6
d correction+0.2'
True DeclinationN 19° 09.2'
Index Correction+2.1'
Dip (48 ft)-6.7'
Sum-4.6'
h
s
(at LAN)69° 16.0'
h
a
69° 11.4'
Altitude Correction+15.6'
89° 60'89° 60.0'
h
o
69° 27.0'
Zenith DistanceN 20° 33.0'
True DeclinationN 19° 09.2'
Latitude39° 42.2'
Zenith DistanceN 25°Zenith DistanceS 50°
True Declination
S 15
°
True Declination
N10
°
LatitudeN 10°LatitudeS 40°
312SIGHT REDUCTION
forthetimeofLAN.FromtheNauticalAlmanac,
determinetheSun’sGHAatthattime;thisisyour
longitudeinthewesternhemisphere.Intheeastern
hemisphere,subtracttheSun’sGHAfrom360°to
determinelongitude.Foraquickerbutlessexacttime,
simplydropaperpendicularfromtheapexofthecurve
and read the time along the time scale.
ThesecondmethodofdeterminingLANissimilarto
thefirst.EstimatethetimeofLANasdiscussedabove,
MeasureandrecordtheSun’saltitudeastheSun
approachesitsmaximumaltitude.AstheSunbeginsto
descend,setthesextanttocorrespondtothealtitude
recordedjustbeforetheSun’sreachingitsmaximum
altitude.NotethetimewhentheSunisagainatthat
altitude.Averagethetwotimes.Repeatthisprocedure
withtwootheraltitudesrecordedbeforeLAN,eachtime
presettingthesextanttothosealtitudesandrecordingthe
correspondingtimesthattheSun,nowonitsdescent,
passesthroughthosealtitudes.Averagethese
correspondingtimes.Takeafinalaverageamongthe
threeaveragedtimes;theresultwillbethetimeof
meridianpassage.Determinethevessel’slongitudeby
determining the Sun’s GHA at the exact time of LAN.
LATITUDE BY POLARIS
2012. Latitude by Polaris
SincePolarisisalwayswithinabout1°oftheNorth
Pole,thealtitudeofPolaris,withafewminorcorrections,
equalsthelatitudeoftheobserver.Thisrelationshipmakes
Polarisanextremelyimportantnavigationalstarinthe
northern hemisphere.
ThecorrectionsarenecessarybecausePolarisorbitsin
asmallcirclearoundthepole.WhenPolarisisattheexact
samealtitudeasthepole,thecorrectioniszero.Attwo
pointsinitsorbititisinadirectlinewiththeobserverand
thepole,eithernearerthanorbeyondthepole.Atthese
pointsthecorrectionsaremaximum.Thefollowing
example illustrates converting a Polaris sight to latitude.
At23-18-56GMT,onApril21,1994,atDRLat.50°
23.8'N,λ=37°14.0'W,theobservedaltitudeofPolaris(h
o
)
is 49° 31.6'. Find the vessel’s latitude.
To solve this problem, use the equation:
whereh
o
isthesextantaltitude(h
s
)correctedasinanyother
starsight;1°isaconstant;andA
0
,A
1
,andA
2
are
correctionfactorsfromthePolaristablesfoundinthe
NauticalAlmanac.Thesethreecorrectionfactorsare
alwayspositive.Oneneedsthefollowinginformationto
enterthetables:LHAofAries,DRlatitude,andthemonth
of the year. Therefore:
EnterthePolaristablewiththecalculatedLHAofAries
Figure 2011. Time of LAN.
Latitude
h
o
1°
A
0
A
1
A
2
+++–=
SIGHT REDUCTION313
Figure 2012. Excerpt from the Polaris Tables.
314SIGHT REDUCTION
(162°03.5').SeeFigure2012.Thefirstcorrection,A
0
,isa
functionsolelyoftheLHAofAries.Enterthetablecolumn
indicatingtheproperrangeofLHAofAries;inthiscase,
enterthe160°-169°column.Thenumbersonthelefthand
sideoftheA
0
correctiontablerepresentthewholedegreesof
LHA;interpolatetodeterminetheproperA
0
correction.
Inthiscase,LHAwas162°03.5'.TheA
0
correctionfor
LHA=162°is1°25.4'andtheA
0
correctionforLHA=163°
is 1° 26.1'. The A
0
correction for 162° 03.5' is 1° 25.4'.
TocalculatetheA
1
correction,entertheA
1
correction
tablewiththeDRlatitude,beingcarefultostayinthe160°-
169°LHAcolumn.Thereisnoneedtointerpolatehere;simply
choosethelatitudethatisclosesttothevessel’sDRlatitude.In
thiscase,Lis50°N.TheA
1
correctioncorrespondingtoan
LHA range of 160°-169° and a latitude of 50°N is + 0.6'.
Finally,tocalculatetheA
2
correctionfactor,stayinthe
160°-169°LHAcolumnandentertheA
2
correction
table.Followthecolumndowntothemonthoftheyear;in
this case, it is April. The correction for April is + 0.9'.
Sumthecorrections,rememberingthatallthreeare
alwayspositive.Subtract1°fromthesumtodeterminethe
totalcorrection;thenapplytheresultingvaluetothe
observed altitude of Polaris. This is the vessel’s latitude.
THE DAY’S WORK IN CELESTIAL NAVIGATION
2013. Celestial Navigation Daily Routine
Thenavigatorneednotfollowtheentirecelestialrou-
tineifcelestialnavigationisnottheprimarynavigation
method.Itisappropriatetouseonlythestepsoftheceles-
tialday’sworkthatarenecessarytoprovideameaningful
checkontheprimaryfixsourceandmaintaincompetency
in celestial techniques.
Thelistofproceduresbelowprovidesacompletedaily
celestialroutinetofollow.Thissequenceworksequally
wellforallsightreductionmethods,whethertabular,math-
ematical,computerprogram,orcelestialnavigation
calculator.SeeFigure2013foranexampleofatypical
day’s celestial plot.
1.Beforedawn,computethetimeofmorningtwilight
and plot the dead reckoning position for that time.
2.Atmorningtwilight,takeandreducecelestialobser-
vationsforafix.Atsunrisetakeanamplitudeofthe
Sun for a compass check.
3.Mid-morning,windthechronometeranddetermine
chronometer error with a radio time tick.
4.Mid-morning,reduceaSunsightforamorningSun
line.
5.CalculateanazimuthoftheSunforacompass
check, if no amplitude was taken at sunrise.
6.AtLAN,obtainaSunlineandadvancethemorning
Sunlineforthenoonfix.Computealongitudedeter-
mined at LAN for an additional LOP.
7.Midafternoon,againtakeandreduceaSunsight.
ThisisprimarilyforusewithanadvancednoonSun
line,orwithaMoonorVenuslineiftheskiesareover-
cast during evening twilight.
8.CalculateanazimuthoftheSunforacompasscheck
ataboutthesametimeastheafternoonSunobserva-
tion.Thenavigatormayreplacethisazimuthwithan
amplitude observation at sunset.
9.Duringeveningtwilight,reducecelestialobserva-
tions for a fix.
10.Bealertatalltimesforthemoonorbrighterplanets
whichmaybevisibleduringdaylighthoursforaddi-
tionalLOP’s,andPolarisattwilightforalatitudeline.
Chapter7,Chapter17,andChapter20containdetailedex-
planationsoftheproceduresrequiredtocarryoutthevarious
functions of this routine.
LHA162° 03.5'
A
0
(162° 03.5')+1° 25.4'
A
1
(L = 50°N)+0.6'
A
2
(April)+0.9'
Sum1° 26.9'
Constant-1° 00.0'
Observed Altitude49° 31.6'
Total Correction+26.9'
LatitudeN 49° 58.5'
Tabulated GHA(2300 hrs.)194° 32.7'
Increment (18-56)4° 44.8'
GHA199° 17.5'
DR Longitude (-W +E)37° 14.0'
SIGHT REDUCTION315
Figure 2013. Typical celestial plot at sea.
317
CHAPTER 21
NAVIGATIONAL MATHEMATICS
GEOMETRY
2100. Definition
Geometrydealswiththeproperties,relations,and
measurementoflines,surfaces,solids,andangles.Plane
geometrydealswithplanefigures,andsolidgeometry
deals with three–dimensional figures.
Apoint,consideredmathematically,isaplacehaving
positionbutnoextent.Ithasnolength,breadth,or
thickness.Apointinmotionproducesaline,whichhas
length,butneitherbreadthnorthickness.Astraightor
rightlineistheshortestdistancebetweentwopointsin
space.Alineinmotioninanydirectionexceptalongitself
producesasurface,whichhaslengthandbreadth,butnot
thickness.Aplanesurfaceorplaneisasurfacewithout
curvature.Astraightlineconnectinganytwoofitspoints
lieswhollywithintheplane.Aplanesurfaceinmotionin
anydirectionexceptwithinitsplaneproducesasolid,
whichhaslength,breadth,andthickness.Parallellinesor
surfacesarethosewhichareeverywhereequidistant.
Perpendicularlinesorsurfacesarethosewhichmeetat
rightor90°angles.Aperpendicularmaybecalleda
normal,particularlywhenitisperpendiculartothe
tangenttoacurvedlineorsurfaceatthepointoftangency.
Allpointsequidistantfromtheendsofastraightlineare
ontheperpendicularbisectorofthatline.Theshortest
distancefromapointtoalineisthelengthoftheperpen-
dicular between them.
2101. Angles
Anangleisformedbytwostraightlineswhichmeetat
apoint.Itismeasuredbythearcofacircleintercepted
betweenthetwolinesformingtheangle,thecenterofthe
circlebeingatthepointofintersection.InFigure2101,the
angleformedbylinesABandBC,maybedesignated
“angleB,”“angleABC,”or“angleCBA”;orbyGreekletter
as“angleα.”Thethreeletterdesignationispreferredif
thereismorethanoneangleatthepoint.Whenthreeletters
areused,themiddleoneshouldalwaysbethatatthevertex
of the angle.
Anacute angle is one less than a right angle (90°).
Aright angle is one whose sides are perpendicular (90°).
Anobtuseangleisonegreaterthanarightangle(90°)
but less than 180°.
Astraightangleisonewhosesidesformacontinuous
straight line (180°).
Areflexangleisonegreaterthanastraightangle
(180°)butlessthanacircle(360°).Anytwolinesmeeting
atapointformtwoangles,onelessthanastraightangleof
180°(unlessexactlyastraightangle)andtheothergreater
than a straight angle.
Anoblique angle is any angle not a multiple of 90°.
Twoangleswhosesumisarightangle(90°)arecomple-
mentary angles, and either is thecomplement of the other.
Twoangleswhosesumisastraightangle(180°)are
supplementaryangles,andeitheristhesupplementofthe
other.
Twoangleswhosesumisacircle(360°)are
explementaryangles,andeithe