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Mueller T J Aerodynamic Measurements At Low Reynolds Numbers For Fixed Wing Micro-Air Vehicles 19

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Aerodynamic Measurements at Low Reynolds Numbers for Fixed
Wing Micro-Air Vehicles
By
Thomas J. Mueller
to be presented at the
RTO AVT/VKI Special Course on
Development and Operation of UAVs for Military and Civil Applications
September 13-17, 1999
VKI, Belgium
Hessert Center for Aerospace Research
University of Notre Dame
AerodynamicMeasurementsatLowReynoldsNumbers
forFixedWingMicro-AirVehicles
ThomasJ.Mueller
Roth-GibsonProfessor
HessertCenterforAerospaceResearch
DepartmentofAerospaceandMechanicalEngineering
UniversityofNotreDame
NotreDame,IN46556
USA
Summary
Adescriptionofthemicro-airvehicle(MAV)con-
ceptanddesignrequirementsispresented.Thesevehicles
areverysmallandthereforeoperateatchordReynolds
numbersbelowwhereverylittledataisavail-
ableontheperformanceofliftingsurfaces,i.e.,airfoils
andlowaspect-ratiowings.Thispaperpresentsthere-
sultsofacontinuingstudyofthemethodsthatcanbeused
toobtainreliableforceandmomentdataonthinwingsin
windandwatertunnels.Tothisend,anewplatformforce
andmomentbalance,similartoanalreadyexistingbal-
ance,wasdesignedandbuilttoperformlift,dragandmo-
mentmeasurementsatlowReynoldsnumbers.Balance
characteristicsandvalidationdataarepresented.Results
showagoodagreementbetweenpublisheddataanddata
obtainedwiththenewbalance.Resultsforlift,dragand
pitchingmomentaboutthequarterchordwiththeexist-
ingaerodynamicbalanceonaseriesofthinflatplates
andcamberedplatesatlowReynoldsnumbersarepre-
sented.Theyshowthatthecamberedplatesofferbetter
aerodynamiccharacteristicsandperformance.Moreover,
itappearsthatthetrailing-edgegeometryofthewings
andtheturbulenceintensityuptoabout inthewind
tunneldonothaveastrongeffectontheliftanddrag
forthinwingsatlowReynoldsnumbers.However,the
presenceoftwoendplatesfortwo-dimensionaltestsand
oneendplateforthesemi-infinitetestsappearstohave
anundesirableinfluenceontheliftcharacteristicsatlow
Reynoldsnumbers.Thedragcharacteristicsforthinflat-
platewingsofaspectratiogreaterthanonedonotappear
tobeaffectedbytheendplates.Theeffectoftheendplates
onthedragcharacteristicsofcambered-platewingsisstill
underinvestigation.Itisknown,however,thatendplates
dohaveaneffectonthedragandliftcharacteristicsofa
camberedEppler61airfoil/wing.
Copyright
c
1999byThomasJ.Mueller.PublishedbyRTOwith
permission.
Nomenclature
Symbols
full-spanaspectratio
dragcoefficient(3D)
sectiondragcoefficient(2D)
liftcoefficient(3D)
sectionliftcoefficient(2D)
or
lift-curveslope
enduranceparameter
pitchingmomentcoefficientabout
thequarterchord
slopeofpitchingmomentcurve
lift-to-dragratio
resolutionofA/Dconverter
or root-chordReynoldsnumber
freestreamvelocity
lift-curveslope
2Dlift-curveslope
wingspan
root-chordlength
quantizationerror
semi-spanaspectratio
wingthickness
angleofattack
zero-liftangleofattack
stallangleofattack
Glauertparameter
Subscripts
maxmaximum
minminimum
Abbreviations
2Dtwo-dimensional(airfoil)
3Dthree-dimensional(wing)
A/Danalog-to-digital
TEtrailingedge
UND-FB1oldNotreDameaerodynamicforcebalance
UND-FB2newNotreDameaerodynamicforcebalance
1
Introduction
Thereisaseriousefforttodesignaircraftthatare
assmallaspossibleforspecial,limited-durationmilitary
andcivilmissions.Theseaircraft,calledmicro-airve-
hicles(MAVs)(Davisetal,1996;Ashley,1998;Wilson
1998;Dornheim,1998;Mraz,1998;andFulghum,1998),
areofinterestbecauseelectronicsurveillanceanddetec-
tionsensorequipmentcannowbeminiaturizedsothat
theentirepayloadmassisabout18grams.Theadvan-
tagesofaMAVincludecompactsystemtransportableby
asingleoperator,rapiddeployment,real-timedata,low
radarcross-section,difficulttoseeandveryquiet.The
potentialforlowproductioncostisalsoanadvantage.
TheprimarymissionsofinterestforfixedwingMAVs
includesurveillance,detection,communications,andthe
placementofunattendedsensors.Surveillancemissions
includevideo(dayandnight)andinfraredimagesofbat-
tlefields(referredtoasthe“overthehill”problem)and
urbanareas(referredtoas“aroundthecorner”).These
real-timeimagescangivethenumberandlocationofop-
posingforces.Thistypeofinformationcanalsobeuse-
fulinhostagerescueandcounter-drugoperations.Be-
causeoftheavailabilityofverysmallsensors,detection
missionsincludethesensingofbiologicalagents,chemi-
calcompoundsandnuclearmaterials(i.e.,radioactivity).
MAVsmayalsobeusedtoimprovecommunicationsin
urbanorotherenvironmentswherefull-timelineofsight
operationsareimportant.Theplacementofacousticsen-
sorsontheoutsideofabuildingduringahostagerescue
orcounter-drugoperationisanotherpossiblemission.
TherequirementsforfixedwingMAVscoverawide
rangeofpossibleoperationalenvironmentsincludingur-
ban,jungle,desert,maritime,mountainsandarcticenvi-
ronments.Furthermore,MAVsmustbeabletoperform
theirmissionsinallweatherconditions(i.e.,precipita-
tion,windshear,andgusts).Becausethesevehiclesfly
atrelativelylowaltitudes(i.e.,lessthan )where
buildings,trees,hills,etc.maybepresent,acollision
avoidancesystemisalsorequired.
Thelongtermgoalofthisprojectistodevelopair-
craftsystemswithamassoflessthan30grams,have
aboutaneightcentimeterwingspanthatcanflyfor20
to30minutesatbetween30and .Thecur-
rentgoalistodevelopaircraftwitha15centimeterwing
spanthathaveamassofabout90grams.Thegross
massofmicro-airvehiclesandotherflyingobjectsver-
susReynoldsnumberisshowninFigure1,withthedata
fromJackson(1996-97),Taylor(1969-70),andTennekes
(1996).Sinceitisnotpossibletomeetallofthedesign
requirementsforamicro-airvehiclewithcurrenttechnol-
ogy,researchisproceedingonallofthesystemcompo-
nentsatvariousgovernmentlaboratories,companiesand
universities.
Designaims
Thedesignrequirementscoverawiderangewhen
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+031.E+041.E+051.E+061.E+071.E+08
Reynolds Number
Mass (kg)
Butterfly
Pheasant
Cessna 210
B747
MAV
Figure1:Reynoldsnumberrangeforflightvehicles
oneconsidersthediversityofpossibleapplicationsfor
micro-airvehicles.TheMAVmustbedesignedasa
systemconsistingofairframe,propulsion,payloadand
avionics.Althoughmuchsmallerthancurrentlyopera-
tionalUAVs,electricallypoweredMAVswillhaveap-
proximatelythesameweightfractions,thatis, for
theairframe, fortheengine, forthebattery,
forthepayload,and foravionicsandmiscellaneous
items.Minimumwingareaforeaseofpackagingand
pre-launchhandlingisalsoimportant.Figure2presents
thepayloadmassversuswingspanforMAVsandother
largerUAVs.
Figure2:UAVpayloadvswingspan(Davis,1999)
(ReprintedwithpermissionofMITLincoln
Laboratory,Lexington,Massachusetts)
AtypicalfixedwingMAVmission(Morris,1997)
couldincludethefollowingsequenceofevents:
1.Launchandclimbto100meters
2.Highspeeddash( IndicatedAirSpeed)to
target(at headwind)
2
3.Loiterovertargetarea
4.Maneuverovertargetduringloiterwhileturningat
theminimumradius
5.Descendandclimbovertargetarea
6.Climbto100meters
7.Highspeeddash( IndicatedAirSpeed)to
launchpoint(tailwind ).
Missionconstraintsinthissimulationincludedura-
tion,operationalradius,minimumturningradius,min-
imumclimbangle,maximumaltitudeandnumberof
climbs.SeveralMAVdesignshavebeenbuiltandflown
withthistypeofmissioninmind.A ,squareplan-
forminternalcombustionenginepoweredvehiclecalled
theFlyswatterhasbeenflownbyMorris(1997).Arudder
andelevatorsurfacesareusedtocontrolthisMAV.The
firstelectricpowered MAVwithproportionalradio
controlcarryingavideocamerawasdesignedandflown
byMatthewT.KeennonofAeroVironment.Thisvehicle
calledtheBlackWidowcurrentlyholdstherecordfor
enduranceat22minutes(Keennon,1999).OtherMAVs
withlargerdimensionshavebeendesignedandflownto
helpdeveloptheelectronicpackagesandcontrolsystems
(Harris,1999;andAilinger,1999).Althoughtheseare
examplesofcurrentvehicles,furtherimprovementswill
bemadewhenmoredataonlowReynoldsnumberaero-
dynamicsisavailableandsmaller,moreefficientelectric
motorsandpropellershavebeendeveloped.
Theairfoilsectionandwingplanformofthelifting
surfaceoccupyacentralpositioninalldesignprocedures
forflyingvehicles.Therefore,alllowReynoldsnum-
bervehiclessharetheultimategoalofastableandcon-
trollablevehiclewithmaximumaerodynamicefficiency.
Aerodynamicefficiencyisdefinedintermsofthelift-to-
dragratio.Airfoilsection
,
and asafunctionofReynoldsnumberareshowninFig-
ures3a,3b,and3cafterMcMastersandHenderson
(1980).Itisclearfromthisfigurethatairfoilperfor-
mancedeterioratesrapidlyasthechordReynoldsnum-
berdecreasesbelow.Whilethemaximumlift-
to-dragratioformostlow-speedfixed-wingaircraft(
)isgreaterthan10,valuesforinsects
andsmallbirdsareusuallylessthan10.Furthermore,to
achievethesevaluesforMAVsatlowReynoldsnumbers,
thewingsmustemulatebirdandinsectwingsandbevery
thin(i.e., )withamodestamountofcamber.
RequirementsforatypicalpropellerdrivenMAV,
forexample,includelongflightduration(i.e.,highvalue
of
atspeedsupto atchordReynolds
numbersfromabout toandaltitudes
from30to100meters).Sincethesevehiclesarees-
sentiallysmallflyingwings,thereisaneedtodevelop
efficientlowReynoldsnumber,lowaspect-ratiowings
whicharenotoverlysensitivetowindshear,gusts,and
theroughnessproducedbyprecipitation.Furthermore,
(a)Maximumliftcoefficient
(b)Minimumdragcoefficient
(c)Maximumlift-to-dragratio
Figure3:Airfoilperformance
(McMastersandHenderson,1980)
3
confidencethattheoperationalvehiclewillperformas
designedisimportantinallapplications.
Flowproblems
Althoughdesignmethodsdevelopedoverthepast
35yearsproduceefficientairfoilsforchordReynolds
numbersgreaterthanabout,thesemethodsare
generallyinadequateforchordReynoldsnumbersbelow
,especiallyforverythinairfoils.Inrelationto
theairfoilboundarylayer,importantareasofconcernare
theseparatedregionswhichoccurneartheleadingand/or
trailingedgesandtransitionfromlaminartoturbulent
flowifitoccurs.Itiswellknownthatseparationand
transitionarehighlysensitivetoReynoldsnumber,pres-
suregradient,andthedisturbanceenvironment.Transi-
tionandseparationplayacriticalroleindeterminingthe
developmentoftheboundarylayerwhich,inturn,affects
theoverallperformanceoftheairfoil.Theaerodynamic
characteristicsofthewingandothercomponentsinturn
affectthestatic,dynamicandaeroelasticstabilityofthe
entirevehicle.Thereforethesuccessfulmanagementof
thesensitiveboundarylayerforaparticularlowReynolds
numbervehicledesigniscritical.
ThesurveyoflowReynoldsnumberairfoilsby
Carmichael(1981),althoughalmosttwodecadesold,is
averyusefulstartingpointinthedescriptionofthechar-
acteroftheflowoverairfoilsovertherangeofReynolds
numbersofinteresthere.Thefollowingdiscussionof
flowregimesfrom isamodi-
fiedversionofCarmichael’soriginalwork.
Intherangebetween ,the
boundarylayerflowislaminaranditisverydifficult
tocausetransitiontoturbulentflow.Thedragonfly
andthehouseflyareamongtheinsectsthatflyin
thisregime.Thedragonflywinghasasawtooth
singlesurfaceairfoil.Ithasbeenspeculatedthat
eddiesinthetroughshelpkeeptheflowfromsepa-
rating.Thehouseflywinghaslargenumbersoffine
hair-likeelementsprojectingnormaltothesurface.
Itisspeculatedthatthesepromoteeddy-induceden-
ergytransfertopreventseparation.IndoorMicaFilm
typemodelairplanesalsoflyinthisregime.Ithas
beenfoundthatbothbluntleadingandtrailingedges
enhancetheaerodynamicperformance.
ForchordReynoldsnumbersbetweenand
,theboundarylayeriscompletelylaminar
andartificialtrippinghasnotbeensuccessful.Ex-
periencewithhand-launchedglidermodelsindicates
thatwhentheboundarylayerseparatesitdoesnot
reattach.
Therange isofgreatin-
teresttoMAVdesignersaswellasmodelaircraft
builders.Thechoiceofanairfoilsectionisveryim-
portantinthisregimesincerelativelythickairfoils
(i.e., andabove)canhavesignificanthysteresis
effectscausedbylaminarseparationwithtransition
toturbulentflow.AlsobelowchordReynoldsnum-
bersofabout,thefreeshearlayerafterlami-
narseparationnormallydoesnottransitiontoturbu-
lentflowintimetoreattach.Neartheupperendof
thisrange,thecriticalReynoldsnumbercanbede-
creasedbyusingboundarylayertrips.Thinairfoil
sections(i.e.,lessthan thick)attheupperend
ofthisregimecanexhibitreasonableperformance.
AtReynoldsnumbersaboveandbelow
,extensivelaminarflowcanbeobtainedand
thereforeairfoilperformanceimprovesalthoughthe
laminarseparationbubblemaystillpresentaprob-
lemforaparticularairfoil.Smallradiocontrolled
modelairplanesflyinthisrange.
Above
of,airfoilperformanceim-
provessignificantlyandthereisagreatdealofex-
perienceavailablefromlargesoaringbirds,largera-
diocontrolledmodelairplanes,humanpoweredair-
planes,etc.
Laminarseparationbubblesoccurontheuppersur-
faceofmostairfoilsatReynoldsnumbersaboveabout
.ThesebubblesbecomelargerastheReynolds
numberdecreases,usuallyresultinginarapiddeteriora-
tioninperformance,i.e.,substantialdecreasein.
Inprinciplethelaminarseparationbubbleandtransition
canbeartificiallycontrolledbyaddingthepropertypeof
disturbanceattheproperlocationontheairfoil.Wires,
tapestrips,grooves,steps,grit,orbleed-throughholesin
theairfoilsurfacehaveallbeenusedtohaveapositive
influenceontheboundarylayerinthiscriticalReynolds
numberregion.Thetypeandlocationoftheseso-called
“turbulators”andtheiractualeffectontheairfoilbound-
arylayerhasnotbeenwelldocumented.Furthermore,the
additionofaturbulatordoesnotalwaysimprovetheair-
foilperformance.Infact,howthedisturbancesproduced
byagiventypeofturbulatorinfluencetransitionisnot
completelyunderstood.
Asaresultofthiscriticalboundarylayerbehavior,
severalimportantquestionsmustbeaddressed:
1.Whatisthefreestreamdisturbancelevelandflight
environmentforagivenlowReynoldsnumberap-
plication?
2.Iftheflightconditionsareknownandasuitable
designtechniquewasavailable,couldtheresulting
vehicleorcomponentbeadequatelyevaluatedina
windtunnelwhich,ingeneral,hasadifferentdis-
turbancelevelandenvironmentthantheflightcon-
dition?
3.Isthehysteresisinaerodynamicforcesobservedin
lowturbulencewindtunnelexperimentspresentin
poweredapplications(i.e.,dostructuralvibrations
originatingwiththepropulsionordrivesystemaffect
boundarylayertransition)?
4
4.Becausethecriticalquantitiesmeasuredinwindtun-
nelexperimentsareverysmall,whatisthelevel
ofaccuracyneededtoimprovedesignandanalysis
methods?
Preliminaryexperiments
ManyoftheproblemsplaguingverylowReynolds
numberresearchinvolvethedifficultiesassociatedwith
makingaccuratewind/watertunnelmodelsandobtain-
ingreliabledata.Becausetheboundarylayersaresen-
sitivetosmalldisturbances,accuratewind/watertunnel
modelsareveryimportantintheevaluationofagiven
design.Furthermore,becausetheforces,pressurediffer-
encesandvelocitiesareextremelysmall,agreatdealof
caremustbeexercisedtoobtainaccurateandmeaningful
data.LowReynoldsnumberaerodynamicresearchhas
beeninprogressattheUniversityofNotreDamesince
1978.However,chordReynoldsnumbersbelowabout
wereseldomofinterestinthestudiesbefore1996.
Also,mostofthestudieswereforrelativelythickairfoils,
e.g.the thickLissaman7769,the thickMiley
M06-13-128,andthe thickWortmannFX63-137
airfoils.Theonlyrelativelythinairfoilsstudiedwerethe
Eppler61andPfenninger048airfoils.TheEppler61,
showninFigure4,wasoriginallydesignedformodelair-
planeswithachordReynoldsnumbersofabout
andhasathicknessof and camber.Figure5
showsaschematicofthePfenninger048airfoilgeome-
trytestedbyBurns(seeBurns,1981).Thisairfoilhasa
thickness-to-chordratioof anda camber.
Figure4:Eppler61airfoilprofile
Figure5:Pfenninger048airfoilprofile
ThewindtunneldatashowninFigure6forthe
Eppler61andthePfenninger048airfoilswasobtained
in1980andpublishedbyBurns(1981)andMuellerand
Burns(1982).Figure6indicatesthatforchordReynolds
numbersbelow,thethinnerandsharperleading
edgePfenningerairfoilperformsbetterthantheEppler61
airfoil.
(
C
l
/C
d
)
max
Figure6:Maximumlift-to-dragratioversuschord
Reynoldsnumberforthetwo-dimensionalEppler61and
Pfenninger048airfoils(Burns,1981)
BurnsalsostudiedtheflowfieldovertheEppler61
airfoilfordifferentReynoldsnumbersusingthesmoke
wiretechnique.Thelocationoftheboundarylayersepa-
rationcouldbeobtainedfromhisflowvisualizationpho-
tographs.Figure7showstheeffectofchangingtheangle
ofattackontheboundarylayerfor
.
FlowvisualizationwasalsoconductedonthePfen-
ninger048airfoilatdifferentReynoldsnumbersanddif-
ferentanglesofattack.Figure8showsexamplesofthe
flowvisualizationimagesfor
.
Anewseriesofexperimentswasperformedinthe
Springof1997toevaluateseveralthinairfoilshapesus-
ingtheexistingstraingaugeforcebalance(UND-FB1)in
theHessertCenterwatertunnel.Theresultsforliftand
dragfromtheseexperimentsdowntoachordReynolds
of wereveryencouraging.Amorecompleteex-
perimentalstudyofoneoftheseairfoilshapes(i.e.,the
Eppler61)wasperformedduringthesummerof1997
(PrazakandMueller,1997).Theseexperimentscovered
theReynoldsnumberrangefrom to .Hy-
drogenbubbleflowvisualizationwasusedtodetermine
thelocationofboundarylayerseparationandtheexisting
windtunnellift/dragforcebalance(UND-FB1)wasused
tomakeaerodynamicmeasurements.Allofthese2Dex-
perimentsincludedtwoendplates.The for
the2DEppler61fromthesewatertunnelexperimentsis
includedinFigure6( ).TheresultsofthePrazakand
Muellerstudyinthewatertunnelindicatedthatbyadding
acomputerdataacquisitionsystemtotheUND-FB1force
balance,theuncertaintyintheforcemeasurementsdown
to
couldbereducedsignificantlyforthe
fullspanmodels.
Scopeofpresentstudy
Thepurposeofthepresentworkistopresentand
discussthemeasurementproblemsassociatedwithsmall
aspectratiowingsatReynoldsnumbersbelow.
5
Bothwindtunnelandwatertunnelexperimentswereper-
formedinanattempttoacquire2Dairfoilandfinitelow
aspectratiowingdata.Studiesoftheeffectoftwoend-
platesontheresultsfor2Dconfigurationsandoneend-
plateforsemi-spanorhalfmodelswerealsomade.
Apparatusandprocedures
Windtunnel
TheHessertCenterforAerospaceResearchis
equippedwithtwosimilar,horizontal,subsonicopen-
circuitwindtunnels.Eachindrafttunnelhasacontrac-
tionratioof20.6:1.Thecross-sectionsoftheentrance
andtestsectionaresquare.Thelargesttestsectionis
twofeetbytwofeet( by ).Thecontraction
conesaredesignedtoprovideverylowturbulencelevels
inthetestsection.Justaheadofthecontractioncone
aretwelveanti-turbulencescreens.Boththecontraction
coneandthetestsectionsaremountedonrollerstopro-
videaneasymeansofinterchangingthesecomponents.
Downstreamofthetestsectionisthediffuserwhichis
fixedintothewallofthelaboratory.Thediffuserde-
celeratestheairandalsograduallytransformsthesquare
contourtoacircle.Theimpellerisdrivenbyavariable
speedelectricmotor.Byvaryingthespeedofthemotor,
thetunnelspeedmayreachamaximumofapproximately
( )withafoursquarefoottestsection
( ).Thetestsectionsusedaresixfeet(1.82me-
ters)inlength.Allwindtunnelexperimentspresentedin
thisreportwereconductedinoneofthesesubsonicwind
tunnels.Therangeofvelocitiesrequiredfortestsupto
couldeasilybeobtained.Ingeneral,the
minimumvelocityforforcebalancemeasurementswas
keptabove ( ).Figure9isaschematicof
thewindtunnelused.Thefreestreamturbulenceintensity
wasapproximately overtherangeofinterest.
2’ 1’’
4’ 7’’6’ 0’’
2’ 8’’
9’ 8’’
4.2
Exhaust Fan
Air Flow
2’ 0’’
12’ 6’’
Adjustable
Louvers
18.6 kW Motor
and 8 Bladed Fan
Diffuser
Motor Room
Interchangeable
Test Section
Contraction Inlet
12 Screens
Figure9:Schematicofthelow-speedwindtunnel
Watertunnel
Fortestsbetween ,an
Eidetics
free-surfacewatertunnelwitha ( )testsection,picturedinFigure10,
wasused.Thewatertunnelisalsolocatedinthemain
laboratoryoftheHessertCenter.Watervelocitiesupto
( )canbeobtainedinthetest
section.Afreestreamturbulenceintensityoflessthan
hasbeenreportedbythemanufacturerofthewater
tunnel.
7
8
9
KEY:
1. PUMP
2. PERFORATED INLET
3. DELIVERY PLENUM
4. FLOW CONDITIONING ELEMENTS
5. CONTRACTION SECTION
6. TEST SECTION
7. DISCHARGE PLENUM
8. RETURN PIPING (REVERSIBLE)
9. FILTER SYSTEM
6
1
2
3
4
5
Figure10:Schematicoftheflowvisualizationwater
tunnel(Eidetics
)
Flowvisualizationtechniques
Aqualitativevisualexaminationoftheflowasit
passesanairfoiliskeyinunderstandingitsquantitative
aerodynamiccharacteristics.Inthewindtunnel,twodif-
ferentmethodscanbeusedtogeneratesmokeforthis
flowvisualization.Withthefirstmethod,smokeisgen-
eratedbyadevicewhichallowskerosenetodriponto
electricallyheatedfilaments;thesmokeisthenfunneled
toasmokerake.Therakehasafilterbagandcool-
ingcoilswhichreducethesmoketemperaturetoapproxi-
matelyambientbeforepassingthroughtheanti-turbulence
screensandintothetestsection.Withthesecondmethod,
afinewireisplacedupstreamofthemodel.Thiswire
iscoatedwithoilandanelectriccurrentisappliedto
thewire.Asthewiregetsheated,thesmallbeadsofoil
formedonthewireburn,whichgivesrisetofinesmoke
streaklines.Thistechnique,whichhasbeendescribedin
moredetailsbyBatillandMueller(1980),isreferredtoas
thesmoke-wiretechnique.Thewatertunnelisexcellent
forflowvisualizationusingeitherthehydrogenbubble
ordyeinjectiontechnique.AKodakDC120digitalcam-
eraandCCDvideocamerasareavailabletocaptureflow
visualizationresults.
7
DescriptionoftheUND-FB1balance
Mostoftheresultsonthinplateswereobtainedwith
theexistingthree-componentplatformaerodynamicbal-
anceUND-FB1.Thisbalancecanbeusedtomeasurelift,
dragandpitchingmomentabouttheverticalaxis.The
balanceisanexternalbalanceplacedontopofthetest
sectionofeitherofthetwolow-speedwindtunnels.With
thisbalance,liftanddragforcesaretransmittedthrough
thestingwhichismounteddirectlytothemomentsensor.
Themomentsensorisrigidlymountedtotheadjustable
angleofattackmechanismonthetopplatform.Thelift
platformissupportedfromthedragplatformbytwover-
ticalplatesthatflexonlyintheliftdirection.Thelift
anddragplatformsarealsoconnectedwithaflexurewith
bondedfoilstraingaugesmountedonit.Thedragplat-
formissupportedbytwoverticalplatesthatflexonlyin
thedragdirectionandhangfromtwomoreverticalflex-
ibleplatesattachedtothebaseplatformofthebalance.
Thebaseanddragplatformsarealsoconnectedbyaflex-
urewithstraingaugesmountedonit.Forthisbalancea
secondsetofflexures,forbothliftanddrag,areengaged
whentheloadsarelarge.Fortherangeofforcesmea-
suredinthisinvestigation,thesecondsetofflexureswas
neverengaged.Figure11showsaschematicoftheold
balancesetupinthewindtunnel.Thearrangementwith
twoendplatesshowninFigure11isknownasarrange-
mentnumber1.Arrangementnumber2,notshown,has
thelowerendplateremovedforthesemi-infinitetests.
Thin-platemodelsforcurrentinvestigation
Keepinginmindtheobjectiveofthisfirstphase
oftheinvestigationwhichwastostudytheaerodynamic
characteristicsofsmall,lowaspect-ratioflatandcam-
beredwings,severalthin,flatandcamberedrectangu-
laraluminummodelswithathickness-to-chordratioof
werebuilt.Thinmodelswereselectedbecause
birdsandinsectshaveverythinwings.Themodelseither
hada5-to-1ellipticalleadingedgeanda
taperedtrail-
ingedge,or5-to-1ellipticalleadingandtrailingedges.
Thecamberedmodelshadacirculararcshapewith
camber.Thesemi-spanaspectratios( )testedvar-
iedbetween0.50and3.00.Theroot-chordlengthofthe
modelswaseither ( )or ( ).Fig-
ure12showsschematicsoftheairfoilgeometriesforthe
wingswithataperedtrailingedge,whileTable1gives
thedimensionsofthedifferentmodelsused.Withthe
nomenclatureusedforthewingdesignation,thefirstfour
charactersdefinethenominaldimensionsofthemodel.
Forinstance,C8S4meansaChordof andaSpanof
.Thefollowingcharacters,ifany,definetheshape:
aCmeansacamberedplateandEmeansanelliptical
trailingedgeinsteadofataperedtrailingedge.Amax-
imumspanof ( )waschosensothatthese
modelscouldbeusedinboththewindandwatertunnels.
Endplates
U
Lift platform
Drag platform
Base
Sting
Sting
covering
Wing
3/100 in (0.8mm)
Gap
24in (61cm)
24in
(61cm)
Strain
gauges
Drag flexure
12in
(30.5cm)
Figure11:UND-FB1balancearrangement(1)withtwo
endplatesinthewindtunnel
thickness= t
5*t/2
c
0.18c
(a)Flatplate
thickness= t
5*t/2
c
0.18c
(b)Camberedplate
Figure12:Airfoilgeometryformodelswithtapered
trailingedge
8
Designation
Chord( )
Span( )
Thickness( )
Camber(%)
C8S4
7.973
3.998
0.5
0.155
0
C8S8
7.973
8.003
1.0
0.154
0
C8S12
7.985
12.01
1.5
0.157
0
C4S8
3.999
8.019
2.0
0.077
0
C4S12
4
12.014
3.0
0.077
0
C8S4C
7.975
3.995
0.5
0.156
4
C8S8C
7.983
8
1.0
0.156
4
C8S12C
7.908
12.013
1.5
0.156
4
C4S8C
3.995
8
2.0
0.078
4
C4S12C
3.936
11.998
3.0
0.079
4
C8S12E
7.969
12.011
1.5
0.156
0
C8S12CE
7.931
12.011
1.5
0.157
4
C:cambered;E:ellipticaltrailingedge
Table1:Wingdimensions
Tunnelconfigurations
Endplatesweremountedinthewindandwatertun-
nels.Theplatescouldberemovedtosimulateeithera
semi-infinitemodelorafinitemodel.Allwingstested
wereheldatthequarter-chordpointandthestingwascov-
eredbyastreamlinedstingcoveringinthewindtunnel
andacylindricalcoveringinthewatertunnel.Thegaps
betweenthewingandtheendplateswereadjustedtoap-
proximately ( ).MuellerandBurns(1982)
showedthatgapsizesvaryingbetween and
areusuallyacceptableanddonotaffectthere-
sults.Furthermore,RaeandPope(1984)suggestthatthe
gapbelessthan .Fora ( )span
model,thiscorrespondstoamaximumgapsizeof ( ),whichislargerthanthegapusedinthecur-
rentinvestigation.All2Dtests(orinfinitewing/airfoil
tests)wereperformedwithbothendplatespresent.For
semi-infinitewings(denotedbythesemi-spanaspectra-
tiosymbol ),thebottomplatewasremoved.Finally,
forfinitewingtests(denotedbytheaspectratiosymbol
),bothendplatesandthestingcoveringwereremoved.
DataacquisitionsystemwithUND-FB1balance
Signalsfromthestraingaugesweremeasuredwith
verysensitiveinstrumentation.Thestraingaugeswere
configuredinafullWheatstonebridge.Anexcitation
voltageof wasusedforallthestraingaugebridges.
Thebridgesignalswerereadwithaninstrumentationam-
plifiercircuit,withavailablegainsfrom1to8,000.The
amplifiedanalogsignalsweresenttothecomputerwhere
theywerethenconvertedusingafour-channel,12-bitA/D
converterfromUnitedElectronicIndustries(UEI).Four
datachannels(lift,drag,momentanddynamicpressure)
couldbemeasured.AllthedatawasacquiredusingaPC-
baseddataacquisitionsystemrunningtheLABVIEW
5graphicalprogramminglanguage.Theangleofattack
wascontrolledmanuallywiththeUND-FB1balance.
Procedurefordataacquisition
Beforemeasuringanyaerodynamicforceandmo-
mentwitheitherbalance,theamplifiergainsweread-
justedtomaximizetheoutputsignalsthatwereexpected
duringagivensetofexperiments.Thebalancewasthen
calibratedusingknownmasses.Thelift,dragandmo-
mentaxeswereallindependent.
Fortestslookingattheaerodynamiccharacteristics
asafunctionofangleofattack,thetunnelvelocitywas
adjustedwiththemodelat toyieldthedesired
nominalReynoldsnumber.Theangleofattackwasthen,
ingeneral,setto .Datawastakenforangles
ofattackuptoalargepositiveanglebyanincrementof
.Thewingwasthenbroughtbackto byan
incrementof inordertoseeifhysteresiswaspresent.
Offsetreadingsweremeasuredforallfourdataacquisi-
tionchannelsbeforethetunnelwasturnedonwiththe
modelat .Attheendoftherun,thetunnelwas
turnedoffwiththemodelat anddriftreadings
wereobtainedforallchannels.Theoffsetvoltagefora
givenchannelwassubtractedfromallthevoltageread-
ingsforthatchannel.Apercentageofthedriftwasalso
subtractedfromallthereadings.Alinearbehaviorwas
assumedforthedrift.Thismeansthatif anglesofat-
tackweretestedwiththetunnelrunning, was
subtractedfromthefirstpoint, wassubtracted
fromthesecondpoint,andsoforth.Otherproceduresre-
latedtospecificapplicationswillbepresentedinthetext
whenappropriate.
MeasurementuncertaintywithbalanceUND-FB1
Uncertaintiesinthemeasurementswerecomputed
usingtheKline-McClintocktechnique(KlineandMc-
Clintock,1953)forerrorpropagation.Thetwomain
sourcesofuncertaintywerethequantizationerrorand
theuncertaintyarisingfromthestandarddeviationof
9
agivenmeanoutputvoltage.Thequantizationerroris
,where isthenumberofbits
oftheA/Dconverter.Optimizingtherangeoftheoutput
voltagescanhelptoreducetheuncertainties.Ifthegain
isincreased,thestandarddeviationofthemeanwillalso
beincreased,buttheratioofthestandarddeviationto
themeanwillbasicallyremainthesame.However,the
uncertaintyfromthequantizationerrorwillbereduced
becausethequantizationerrorisafixedvalue(afunction
oftherangeandtheresolutionoftheA/Dconverter).
Theratioofthequantizationerrortothemeanvoltage
willthenbesmallerifalargergainisusedandalarger
balanceoutputmeanvoltageisobtained.
Theuncertaintyintheangleofattackwasdeter-
minedtobeontheorderof .Figures13
through15showanexampleofuncertaintiesobtainedat
withthecamberedplates.Errorbarsindi-
catetheuncertaintyin
,
and
.Theaverage
uncertaintiesfrom andupareapproximately
to for
and
and for
.
Newforce/momentaerodynamicbalance
UND-FB2
Description
Anewplatformforce/momentbalancewasdesigned
byMattFasano,ProfessionalSpecialistattheHessert
CenterforAerospaceResearch,andbuiltfortheaerody-
namicstudiesonlowaspect-ratiowingsdowntochord
Reynoldsnumbersof20,000.Thedesignofthisnew
balance(UND-FB2)wasbasedontheexistingbalance
(UND-FB1)andmeasureslift,drag,andpitchingmoment
abouttheverticalaxis.Itisanexternalbalanceplaced
ontopofthetestsectionforeitherofthetwolow-speed
windtunnelsorthewatertunnel.Duetothebettersen-
sitivityofthenewlydesignedbalance(UND-FB2),only
thisbalanceisnowusedwiththewatertunnel.
Withthisbalance,liftanddragforcesaretransmit-
tedthroughthestingwhichismounteddirectlytothe
momentsensor(seeFigure16foraschematicofthenew
balance).Themomentsensorisrigidlymountedtothe
adjustableangleofattackmechanismonthetopplat-
form.Theliftplatformissupportedfromaplatform,
calledthedragplatform,bytwoverticalplatesthatflex
onlyintheliftdirection.Theliftanddragplatforms
arealsoconnectedwitha ( )flexurewithbonded
foilstraingaugesmountedonit.Thedragplatformis
supportedbytwoverticalplatesthatflexonlyinthe
dragdirectionandhangfromtwomoreverticalflexi-
bleplatesattachedtothebaseplatformofthebalance.
Thebaseanddragplatformsarealsoconnectedbya
( )
flexurewithstraingaugesmountedonthisdragflexure.
Bothflexuresactlikecantileverbeamswhenloadsare
appliedtothebalance.
(degrees)
-20-100102030
C
l
, C
L
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2D
sAR= 1.5
Figure13:Uncertaintiesinliftcoefficientforcambered
platesat
withUND-FB1
(degrees)
-20-100102030
C
d
, C
D
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
2D
sAR= 1.5
Figure14:Uncertaintiesindragcoefficientforcambered
platesat
withUND-FB1
(degrees)
-20-100102030
C
m/
4
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
2D
sAR= 1.5
Figure15:Uncertaintiesinpitchingmomentcoefficient
forcamberedplatesat
withUND-FB1
10
DRAG
LIFT
Servomotor
Calibration
pulley Model
U
Lift
platform
Drag platform
Base
Moment sensor
Incidence gear
Positive lift
calibration
Figure16:SchematicofthenewbalanceUND-FB2
Asmentionedearlier,endplatesweremountedin
bothwindandwatertunnels.Figure17showsa
schematicofthenewbalancewiththeendplatesinplace
inthewatertunnel.Allwingstestedwereheldatthe
quarter-chordpointandthestingwascoveredbyastream-
linedstingcoveringinthewindtunnelandacylindrical
coveringinthewatertunnel.
Themomentsensorisa
TransducerTechniques
RTS-25reactiontorquesensor.Thistorquesensoruses
bondedfoilstraingaugesandisratedat
output.
Themaximumratedcapacityis
( )
andatorsionalstiffnessof .Themo-
mentsensorisattachedtoanadjustableangleofattack
mechanismpoweredbyaservomotorwithacontroller.
Electronics
Signalsfromthestraingaugesaremeasuredwith
verysensitiveinstrumentation.Thestraingaugesforthe
dragandliftflexuresare350ohmswithaG-factorof
2.09andareconfiguredinafullWheatstonebridge.An
excitationvoltageof isusedforallthestraingauge
bridges.Thebridgesignalsarereadwithaninstrumenta-
tionamplifiercircuitwithagainashighas8,000.Dueto
thesensitivityofthecircuitmanyprecautionsweremade
toreducenoise.Atfirst,Ni-Cdrechargeablebatteries
wereusedtopowertheamplifiers,analog-to-digitalcon-
verters,andtheexcitationvoltageforthestraingauges.
ADCpowersupplyisnowbeingusedbecauseofthe
quickdischargeofthebatteriesduringdataacquisition.
Wing
Water level
3/100" (0.8mm)
Gap
24in (61cm)
18in
(45.7 cm)
Sting
Sting
covering
Balance
U
Endplates
Strain
gauges
Floor
Lift platform
Drag platform
Base
Drag flexure
Figure17:New-balancearrangement(1)inthewater
tunnelwithtwoendplates
Thebatteriesusedcouldnotprovideaconstantvoltage
forseveralhours.
Theamplifiersandanalog-to-digitalconvertersare
mountedonacircuitboardplacedinacontrolboxwith
switchesandpotentiometers(pots)toadjustthegains,
offsetsandbalancetheWheatstonebridges.Fourdata
channels(lift,drag,momentanddynamicpressurewhen
necessary)canbemeasuredquasi-simultaneously.Thein-
putdifferentialsignalfromeachchannelissentthrough
twoamplifiersfromAnalogDevices:aprecisioninstru-
mentationAD624amplifier(gainof1,100,200or500)
andasoftwareprogrammableAD526gainamplifier(gain
of1,2,4,8or16).Theamplifiedanalogsingle-ended
signalsfromthefourchannelsarethenconvertedtodig-
italsignalsusingaBurr-BrownAD7825,four-channel,
16-bitanalog-to-digitalconverter.Thesignalsarethen
senttoaNationalInstrumentsdigitaldataacquisitioncard
(NIDAQ)inadataacquisitioncomputer.Theamplified
single-endedanalogsignalscanalsobesentdirectlyto
thecomputer,thusbypassingthe16-bitA/Dconverters;
thesignalsarethenconvertedusingthefour-channel,12-
bitA/DUEIconverter,mentionedearlier.Withthe16-bit
A/Dsystem,eachamplifiercircuitisidenticalexceptfor
thefourthchannelwheretheamplifierscanbebypassed
andasingle-endedsignalcanbesentdirectlytothe16-
bitA/Dconverter.Figure18isasimplifiedschematicof
11
theelectroniccircuitryused.
+5V
AD624
AD526
Strain
gauges
+6V
+6V
+5V
2k
2k
1k
5k
Bridge balancing
(if needed)
Force Balance
20k
-6V
+6V
10k
AD7825
Manometer IN
(channel 4 only)
+5V
UEI Card
NIDAQ Card
16-Bit A/D converter
Offset
adjustment
Offset
adjustment
Figure18:UND-FB2balanceelectronics
Dataacquisition
AllthedatawasacquiredusingaPC-baseddata
acquisitionsystemrunningtheLABVIEW
5graphical
programminglanguage.TheNIDAQcardwasfirstused
fordataacquisition.TheUEIcardisnowusedwiththe
newbalancewhenseverenoiseinterfereswiththedata
andtheNIDAQcardcannotbeused.
Thedataacquisitionprocesswiththenewbalance
wasautomated.Theangleofattackcanbeautomatically
variedfromapre-determinedlistofanglesofattack.The
rangeisusuallyadjustedinordertobeabletoobserve
stall.
Specifications
Sincetheforce/momentbalanceincludesverysensi-
tiveflexuresandstraingauges,theappliedforcesandmo-
mentcannotexceedcertainlimits.Theselimitingforces
andmomentweredeterminedconservativelyandarelisted
inTable2.ThelimitingforcesandmomentfortheUND-
FB1balancearealsoincludedforcomparison(seeHuber,
1985).Inordertobeabletomovethebalanceandmount
themodelswithoutpermanentlydeformingtheflexures,
lockingpinsareusedtorestrainthebalance.Theselock-
ingpinsmustberemovedwhentakingdata.
Sourcesofnoise
Forallmeasurements,digitalfilteringin
LABVIEW
wasnecessarytoreducenoisegener-
atedbytheservomotorusedtochangetheangleof
UND-FB2
UND-FB1
Positivelift
Negativelift
Positivedrag
Moment
Table2:Maximumforce/momentbalancespecifications
attack,andalsothemotorofthewatertunnelwhenwater
tunneltestswereperformed.Alow-passButterworth
filterwithacut-offfrequencyof andoforder
5wasused.Astudyontheeffectofthefilterandits
ordershowedthatthemeanvoltageswerebasicallynot
affected,butthestandarddeviationsofthemeanswere
greatlyreduced.Itwasdiscoveredduringpreliminary
calibrationswiththeNIDAQcardthattheservomotor
wascausingnoiseinthedata.WiththemotorON,the
standarddeviationsofthesamples(4,000datapoints
measuredatasamplingfrequencyof )were
largerthanthosewithoutthemotorON,althoughthe
meanvalues,thusthecalibrationcoefficients,werethe
same.Itwasfoundthatisolatingthemotorfromthe
balancehelpedtoreducethestandarddeviations.Athin
plasticsheetwasthenplacedbetweenthealuminum
motorsupportandthealuminumtopplate,liftplatform,
ofthebalance.Moreover,plasticscrewswereusedto
mountthemotorsupporttothebalance.Thiseliminated
anyaluminum/aluminumcontactbetweenthemotorand
thebalance.Noisecausedbyametal-to-metalcontact
betweenaforce/momentbalanceandamotorwasalso
detectedinapreviousinvestigationattheUniversity
ofNotreDame(Pelletier,1998).Figure19showsthe
standarddeviationsofthesamplesforaliftchannel
calibrationexamplewithandwithouttheisolation
plastic.
Lift (N)
-3-2-10123
Standard deviation (volts)
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
With motor OFF
With motor ON (no isolation)
With motor ON (with isolation)
Figure19:Effectofthemotoronthestandarddeviation
withNIDAQdataacquisitioncard
12
Calibration
Afterconstructionofthebalanceandelectronics,
calibrationswereperformedtoascertainthelinearityof
thebalanceforallitsindependentaxes:lift,dragand
moment.Thesecalibrationswereperformedbymoving
theupperplate,liftplatform,ofthebalanceorbyapply-
ingatorquetothemomentsensorbyplacingprecision
weightsofknownmassinacontainerconnectedtothe
plate,ormomentsensor.Thecontainerwasconnectedto
theupperplatebyrunningastringoverthecalibration
pulleyalignedwiththeaxistocalibrate(forliftanddrag)
orperpendiculartothetorqueapplicator(pinconnected
tothestingusedtoapplyaknowntorque)forthemo-
mentcalibration.Forthismomentcalibration,theliftand
draglockingpinswereusedtopreventmovementinthe
liftanddragdirectionasamomentwasappliedtothe
sensor.Severalcalibrationswereperformedtolookfor
repeatabilityandlinearity.Figures20through22show
examplesofthecalibrationcurvesthatwererepeatedly
obtained.
UND-FB2performance
Oncethenewbalanceanditselectronicswerebuilt
andcalibrationshadbeenperformed,itwastestedtosee
iftheresultscomparedtopublisheddata.Allresultspre-
sentedinthispaperhavebeencorrectedforsolidblock-
age,wakeblockageandstreamlinedcurvatureusingtech-
niquespresentedbyPankhurstandHolder(1952)andRae
andPope(1984).Aseriesoftwo-dimensionaltestswere
conductedondifferentmodels.
Models
Inthebalancevalidationphase,twocircularcylin-
dersweretested.Thediametersofthetwocylinderswere
( )and ( )andtheybothhad
alengthof ( ).AnEppler61airfoilmodel,
whoseprofilewasshowninFigure4,wasalsousedto
testthebalance.Themodelalsohadalengthof ( )andachordof ( ).
Cylinderresults
Thenewbalancewasfirsttestedbymeasuringthe
two-dimensionaldragontwocircularcylindersinthe
low-speedwindtunnel.Figure23showsthedragco-
efficientasafunctionofReynoldsnumber.Resultsof
thepresentinvestigationwerecomparedtoresultsby
Wieselsberger,digitizedfromBoundary-LayerTheoryby
Schlichting(1979).Thereisagoodagreementbetween
thetwosetsofdata.
Eppler61airfoilresults
Thebalancewasthentestedbymeasuringthetwo-
dimensionalliftanddragontheEppler61airfoil.Results
Calibration voltage (volts)
-4-3-2-101234
Lift (N)
-4
-2
0
2
4
6
Calibration data
Linear fit
GAIN= 2000
Slope= -1.079
Figure20:Liftcalibrationforthenewbalance
Calibration voltage (volts)
-1012345
Drag (N)
0.0
0.5
1.0
1.5
2.0
Calibration data
Curve fit
GAIN= 2000
Slope= 0.4301
Figure21:Dragcalibrationforthenewbalance
Calibration voltage (volts)
-6-4-20246
Moment (Nm)
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
Calibration data
Curve fit
GAIN= 1000
Slope= -0.0267
Figure22:Pitchingmomentcalibrationforthe
newbalance
13
Re
1e+31e+41e+5
C
d
0.1
1
10
Small cylinder
Large cylinder
Wieselsberger (Schlichting, 1979)
Figure23:2Ddragcoefficientoftwocircularcylinders
withUND-FB2
wereobtainedinthewindtunnelandthewatertunnelfor
severalReynoldsnumbers.Figures24and25showthe
two-dimensionalliftanddragcoefficientsrespectivelyin
thewindtunnelfordifferent
nominal
Reynoldsnumbers,
i.e.,valuesusedtoadjustthevelocityinthetunnelwith
themodelat
.
Resultsfor
indicateasignificantdifferencebe-
tweenresultsat
andthosefor
.Forlarge
,
increasessmoothlywithangle
ofattack.Forsmaller
,thelift-curveslope
issmallerfor
andthereisasharprise
in
at .Similarresultshavebeenobtainedby
Althaus(1980)andshowninFigure26.Althausused
astraingaugebalancearrangementtomeasureliftanda
wakeraketomeasuredrag.Adrawbackofusingawake
rakewillbeaddressedlater.Althausdidobserveasmall
hysteresisloopatlowReynoldsnumbers.Noapparent
hysteresiswasobservedinthecurrentstudy.
Thesharprisein
atlowReynoldsnumbersis
believedtobetheresultofalaminarseparationbub-
bleontheuppersurfaceofthewing.O’Mearaand
Mueller(1987)showedthatthelengthoftheseparation
bubbletendstoincreasewithareductionin
.Are-
ductionintheturbulenceintensityalsotendstoincrease
thelengthofthebubble.Thelift-curveslopeisaffected
byseparationbubbles.Alongerbubbleisusuallyassoci-
atedwithadecreaseinthelift-curveslope(Bastedoand
Mueller,1985).Thisisthekindofbehaviorobserved
withtheEppler61airfoilinthisinvestigation.Flow
visualizationbyMuellerandBurns(1982)showedthe
presenceofaseparationbubbleontheEppler61airfoil
at
.
Inthewatertunnel,theturbulenceintensityislarger
thaninthewindtunnel.Therefore,thesmaller
and
sharprisein
observedinthewindtunnelfor
mightnotbepresentatallinthewatertunnel
dataforthesameReynoldsnumbers.Thisisexactly
(degrees)
-20-100102030
C
l
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Re= 42,000
Re= 46,000
Re= 62,300
Re= 87,000
Figure24:2DliftcoefficientontheEppler61airfoilin
thewindtunnelwithUND-FB2
(degrees)
-20-100102030
C
d
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Re= 42,000
Re= 46,000
Re= 62,300
Re= 87,000
Figure25:2DdragcoefficientontheEppler61airfoil
inthewindtunnelwithUND-FB2
whathappenedfor
and
,as
showninFigure27.Thedragcoefficientappearstobe
lessaffected,withintheuncertaintyofthemeasurements.
Figure28showsthe
curvesobtainedinthewater
tunnelfortheEppler61airfoil.
Figures29through31showcomparisonsofthecur-
rentEppler61resultswithpublisheddata.Thereis,in
general,agoodagreementbetweenthecurrentdataand
publisheddata.Themostsignificantdifferenceisinthe
stallangle;thereappearstobea
differencein
.
MeasurementuncertaintywithUND-FB2
Uncertaintiesinthemeasurementswerecomputed
usingtheKline-McClintocktechnique(KlineandMc-
Clintock,1953)forerrorpropagation.Asindicatedear-
lier,thetwomainsourcesofuncertaintywerethequanti-
zationerrorandtheuncertaintyarisingfromthestandard
deviationofagivenmeanoutputvoltage.Thequantiza-
14
Figure26:Althaus’resultsfor2Dliftcoefficienton
theEppler61airfoil(Althaus,1980)
tionerror,describedearlier,wassmallerwiththeNIDAQ
cardthanwiththeUEIcardduetothebetterresolution
oftheA/Dconverter(16bitscomparedto12bits).The
uncertaintyintheangleofattackwasdeterminedtobeon
theorderof .Theerrorfromtheencoderwas
negligible.Theencoderofferedanexcellentresolution
of2,000countsperdegree,whichgaveanuncertaintyof
.Figures32and33showacomparisonofwind
tunnelandwatertunnelresultsfortheEppler61airfoil
at
.Errorbarsindicatetheuncertaintyin
and
whentheNIDAQcardisused.Theaverage
uncertaintiesfor
and
intherangeofanglesofat-
tacktestedareapproximately inthewatertunneland
inthewindtunnel.
Thenewbalanceinitselfisalsomoresensitivethan
theoldbalance.Thisallowsexperimentsatsmallerve-
locitiesinthewatertunnel.Asofnow,resultswithdif-
ferentwingshaveshownahighdegreeofrepeatabilityfor
Reynoldsnumbersaslowas.Amajorchallenge
inmeasurementsatReynoldsnumbersbelowis
beingabletomeasuredragaccurately.At
,
theminimumdragcanbeaslowas ,whichcorre-
spondstoaloadofapproximately2grams.Afinedrag
calibrationofthebalanceshowedthat1gramwassuf-
ficienttodeflectthedragflexureandyieldareasonable
outputvoltage.However,thisdeflectionisoftenonthe
orderofsignalnoise.
(degrees)
-20-100102030
C
l
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Re= 42,000
Re= 46,000
Figure27:2DliftcoefficientontheEppler61airfoilin
thewatertunnelwithUND-FB2
(degrees)
-20-100102030
C
d
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Re= 42,000
Re= 46,000
Figure28:2DdragcoefficientontheEppler61airfoil
inthewatertunnelwithUND-FB2
Resultsforthinwings
Thissectionwillpresentresultsforthinflatand
camberedwings.Someadditionalissuesassociatedwith
determiningaerodynamiccharacteristicsasafunctionof
Reynoldsnumberswillalsobeaddressed.Accuratemea-
surementsof
and
withendplatesandsmallaspect-
ratiomodelsaredifficulttoobtainatlowReynoldsnum-
bersbecauseoftheinteractionbetweenthethickbound-
arylayersontheendplatesandtheflowaroundthewing,
whichresultsintoathree-dimensionalflowalongthespan
ofthemodel.Thismustbekeptinmindwhenexamining
thefollowingresults.
Flat-platewings
Someresultsfortheflat-platemodels(twoendplates
for2Dtestsandoneendplateforsemiaspect-ratiotests)
15
(degrees)
-20-100102030
C
l
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Re= 46,000 (wind tunnel)
Re= 46,000 (Burns, 1981)
Re= 40,000 (Althaus, 1980)
Figure29:Comparisonof2Dliftcoefficientonthe
Eppler61airfoilandpublisheddatawithUND-FB2
Re= 46,000
(degrees)
-20-100102030
C
d
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Current investigation
Burns (1981)
Figure30:Comparisonof2Ddragcoefficientonthe
Eppler61airfoilandpublisheddatawithUND-FB2
C
d
0.00.10.20.30.40.50.60.7
C
l
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Re= 46,000
Re= 40,000 (Althaus, 1980)
Figure31:Comparisonof2DdragpolarfortheEppler
61airfoilandpublisheddatawithUND-FB2
Re= 42,000
(degrees)
-20-100102030
C
l
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Wind tunnel
Water tunnel
Figure32:Comparisonofthe2Dliftcoefficientonthe
Eppler61airfoilinwindandwatertunnelswithUND-FB2
Re= 42,000
(degrees)
-20-100102030
C
d
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Wind tunnel
Water tunnel
Figure33:Comparisonofthe2Ddragcoefficientonthe
Eppler61airfoilinwindandwatertunnelswithUND-FB2
canbeseeninFigures34through39for
and
.Figures34and37showasignifi-
cantreductioninthelift-curveslope
forsemi-infinite
wings.
Thelift-curveslopevaluesobtainedfromthewind
tunneldataarecomparedtotheoreticalvaluesforthin
wingsofdifferentsemi-spanaspectratiosinFigure40.
Equation1fromAnderson(1991)wasusedtoestimate
thetheoreticalvaluesof
:
(1)
where
isthe2Dlift-curveslopein1/degrees, is
theaspectratioofthefullwing( )and
istheGlauertparameter(equivalenttoaninduceddrag
factor)varyingtypicallybetween0.05and0.25.The2D
value
wasdeterminedtobe
.This
correspondstotheaverageofalltheslopes
(forall
16
(degrees)
-20-100102030
C
l
, C
L
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2D
sAR= 3
sAR= 1
Figure34:Liftcoefficientonflatplatesat
withUND-FB1
(degrees)
-20-100102030
C
d
, C
D
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
2D
sAR= 3
sAR= 1.5
Figure35:Dragcoefficientonflatplatesat
withUND-FB1
(degrees)
-20-100102030
C
m/4
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
2D
sAR= 3
sAR= 1.5
Figure36:Pitchingmomentcoefficientonflatplates
at
withUND-FB1
(degrees)
-20-100102030
C
l
, C
L
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2D
sAR= 3
sAR= 1.5
sAR= 1
sAR= 0.5
Figure37:Liftcoefficientonflatplatesat
withUND-FB1
degrees)
-20-100102030
C
d
, C
D
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
2D
sAR= 3
sAR= 1.5
sAR= 1
sAR= 0.5
Figure38:Dragcoefficientonflatplatesat
withUND-FB1
(degrees)
-20-100102030
C
m/4
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
2D
sAR= 3
sAR= 1.5
sAR= 1
sAR= 0.5
Figure39:Pitchingmomentcoefficientonflatplatesat
withUND-FB1
17
1/sAR
0.000.250.500.751.00
C
L
1/deg)
0.04
0.06
0.08
0.10
0.12
0.14
0.16
×
×
×
×
*
*
*
Re= 200,000
Re= 180,000
Re= 160,000
Re= 140,000
Re= 120,000
Re= 100,000
Re= 80,000
×
Re= 60,000
*
Theory: = 0.05
Theory: = 0.25
a
a
a
aa
0
0
0
1
573
1
2
*.
*
AR
ARsAR
andin degrees
Figure40:Lift-curveslopeforflat-platemodelsinwind
tunnelwithUND-FB1
Reynoldsnumbersconsidered)foraninfiniteaspectra-
tio(
).Thisvaluewaspickedinsteadofthe
conventionalvalueof
givenby
thin-airfoiltheory.Figure40showsaverygoodagree-
mentbetweentheexperimentalvaluesof
andthe
theoreticalvaluesestimatedbyEquation1.
Astheaspectratiowasdecreased,Figures34and37
alsoshowthatthelinearregionofthe
vs curve
becamelongerand
tendedtoincrease.Moreover,
bothfiguresshowthattherewasnoabruptstallforlow
aspect-ratiowings.Fortheselowaspectratios,
often
reachedaplateauandthenremainedrelativelyconstant,
orevenstartedtoincrease,forincreasinganglesofattack.
Changingtheaspectratioofthemodelsdidnot
appeartohaveameasurableeffectonthedragcoef-
ficientat
,asshowninFigure35.At
,increasingtheaspectratiohadtheunex-
pectedeffectofincreasing
foranglesgreaterthan
.
Nomeasurabledifferencewasencounteredintherange
.
Finally,Figures36and39showthepitchingmo-
mentatthequarterchord.Bothfiguresindicateaslightly
positiveslope
around ,evenwhenconsider-
ingtheuncertainty.Thiswouldimplythattheflat-plate
modelswerestaticallyunstablearound .Increas-
ingtheReynoldsnumberfromtotended
toreducetheslopeof
.Themodelwithasemi-
spanaspectratioof3indicatedanirregularbehaviorat
for
;thepitchingmomentwasnot
zeroat .Thiscasewillhavetoberepeated.
Aerodynamiccharacteristicsasafunctionof
Reynoldsnumber:adifferentmethod
Fortestswithoutendplates,anotherbalancearrange-
ment,denotedarrangementnumber3,wasusedandis
presentedinFigure41.Theliftanddragforcesmeasured
bythebalancewereforthewing-stingcombination.The
liftonthestingwasbasicallyzero.However,thedrag
ofthestingalone,whichdominatedthetotalwing-sting
drag,wasnotzeroandwassubtractedfromthewing-sting
valuestogetthe
oftheflat-platewingalone.
U
Sting
Wing
24in
(61cm)
8
in
(20.3cm)
Balance
Strain
gauges
Lift platform
Drag platform
Base
Drag flexure
Figure41:Balancearrangement(3)forfinitewingtests
withthenewbalance
Ingeneral,wheninvestigatorstrytodeterminehow
and
varywithReynoldsnumbers,theydeter-
mine
and
from
vs and
vs curves
atdifferentReynoldsnumbers.Ithasbeenobservedin
thisinvestigationthatthevaluesobtaineddonotalways
matchtheexpectedtrendfordragbecauseofthedifficulty
involvedinmeasuringtheverysmalldragforces.Aslight
offsetinone
vs or
vs curvecanleadtojagged
vs
or
vs
curves.Abettertech-
niquewasfoundtoobtain
vs
(thevaluesof
vs
areoflesserimportancebecausemicro-air
vehicleswillrarelyflyat
).Forthistechnique,the
angleofattackwasfixedtotheangleyieldingthelowest
ina
vs curve,andmeasurementsweretakenfor
aseriesofincreasinganddecreasingReynoldsnumbers
withoutstoppingthetunnel.Resultsobtainedwiththe
newbalanceUND-FB2usingthistechniqueonafinite
wingofaspectratio inthewindtunnel,pre-
sentedinFigures42and43,arepromisingandthetrends
obtainedmatchedtheexpectedreductionin
with
increasingReynoldsnumbers.
18
Re
050000100000150000200000250000
C
L
0.0
0.1
0.2
0.3
0.4
0.5
= 0°
= 3°
= 10°
Figure42:Liftcoefficientvariationwith
for
flat-platewingwithUND-FB2
Re
050000100000150000200000250000
C
D
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
0.045
0.050
0.055
= 0°
= 3°
Theory
C
D
13282.*
Re
(a)
and
Re
050000100000150000200000250000
C
D
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
= 10°
(b)
Figure43:Dragcoefficientvariationwith
for
flat-platewingwithUND-FB2
Resultsattheangleofattackfor
(
)also
showanincreasein
andadecreasein
within-
creasingReynoldsnumber.TheresultsofFigure42at
aresmallerthantheliftcoefficientpresentedin
Figure34foramodelwith
becauseofthelack
ofanendplate.Foragivenmodel,addinganendplate
leadstoanincreaseinliftcomparedtothecasewithout
anendplate,asshowninFigure44.Addingoneend-
platedidnothaveasignificanteffecton
,asshown
inFigure45.Thewingusedforthisseriesoftestshada
nominalchord
andspan
[C8S12].
Re
050000100000150000200000250000
C
L
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
1 endplate
No endplate
Figure44:LiftcoefficientvariationwithRe(C8S12)
withUND-FB2at
Re
050000100000150000200000250000
C
D
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
1 endplate
No endplate
Figure45:LiftcoefficientvariationwithRe(C8S12)
withUND-FB2at
Atanangleofattack
,addingoneortwo
endplatesdidnotaffect
for
;itre-
mainedbasicallyaroundtheexpectedvalueofzero,as
showninFigure46.Moreover,addingendplatesdidnot,
onceagain,haveameasurableeffecton
,aspresented
inFigure47.SinceFigure47isfor
,itrepresents
versusReynoldsnumberforflat-platewings.Ex-
perimentalresultsarealsocomparedtotheory(Blasius:
)andCFDresultsinFigure47.
19
TheCFDresultswerecomputedbyGregBrooks(Air
ForceResearchLaboratory,Wright-PattersonAirForce
Base)usingCOBALT,aparallel,implicit,unstructured,
finitevolumeCFDcodebasedonGodunov’sexactRie-
mannmethod,developedbytheAirForceResearchLab-
oratory(seeStrang,TomaroandGrismer,1999).Allsets
ofdataindicatethesametrend.Theexperimentaldata
wasalwayslargerthantheoryandtheCFDresults.This
couldhavebeencausedbysurfaceroughness,imperfect
flowconditions,andsoforth.Sinceallwindtunneltests
withtheflatandcamberedwingsareusuallyconducted
atReynoldsnumbersgreaterthan,theresultspre-
sentedinFigures42through47for should
beanalyzedwithcaution.Thevelocityinthewindtun-
nelisusuallytoolowfor toyieldreliable
results.
Re
050000100000150000200000250000
C
l
, C
L
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
2 endplates
1 endplate
No endplate
Figure46:LiftcoefficientvariationwithRe(C8S12)
withUND-FB2at Re
050000100000150000200000250000
C
d
, C
D
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
0.045
0.050
0.055
2 endplates
1 endplate
No endplate
Blasius solution
COBALT (Brooks, 1999)
Figure47:DragcoefficientvariationwithRe(C8S12)
withUND-FB2at TheresultsofFigure47seemtoindicatethatfor
thinflat-platewingsat thedragcoefficientacting
onthewingisindependentofaspectratio.Resultsof
Figure47werethencomparedtothedragcoefficients
Re
050000100000150000200000250000
C
d
, C
D
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
0.045
0.050
0.055
2D
sAR= 1.5
AR= 1.5
AR= 1
Blasius solution
COBALT (Brooks, 1999)
Figure48:Minimumdragcoefficientwith for
flat-platewingswithUND-FB2
forthe plateandnodifferencewasobtained,
asshowninFigure48.Foraspectratiosgreaterthan
one,theminimumdragcoefficientisthenindependent
ofmodelsizeandthepresenceofendplates.Forlower
aspectratios,preliminarytestsindicatedalarger
.
Moreworkisinprogresstofullyunderstandthebehavior
of
asafunctionofReynoldsnumbersforthevery
lowaspect-ratiowings( ).Similartestswillalso
havetobeconductedonthecamberedwings.Thenon-
measurabledifferencein
withReynoldsnumbers
mightjustbevalidforflat-platewings.Addingcamber
mightchangetheresults.Preliminaryresultsseemto
indicatethistrend.
Cambered-platewings
Resultswerealsoobtainedforcambered-platemod-
elsusingthebalancearrangementwithoneortwoend-
plates(semi-infiniteor2Dtests).Ingeneral,camber
ledtobetteraerodynamiccharacteristicsduetoanin-
creaseinlift,eventhoughdragalsoincreased.Figures49
through54showsomeresultsforthecamberedplatesat
and
.Withcambered
plates,
wasslightlylargerthanforflatplates.The
maximumliftcoefficientwasalsolarger,asexpected.
Moreover,thevariationin
withangleofattackat
smallangleswaslesslinearforcamberedplatesthanfor
flatplates.Finally,thebehaviorofthemomentcoefficient
forthecamberedplateswasverydifferentthanthe
behaviorwiththeflatplates.Arisein
occurred
after ,leadingtoahumpataround .This
wasnotobservedwiththeflatplates.Flowvisualization
willhopefullyexplainthisbehavior.
Equation1wasalsousedtocomparetheexperi-
mentalvaluesof
at
forthecamberedplates
totheoreticalvalues.The2Dvalue
usedwas
.Figure55showsagoodagreementbetween
theoryandexperiments.
20
(degrees)
-20-100102030
C
l
, C
L
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2D
sAR= 3
sAR= 1.5
Figure49:Liftcoefficientoncamberedplatesat
withUND-FB1
(degrees)
-20-100102030
C
d
, C
D
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
2D
sAR= 3
sAR= 1.5
Figure50:Dragcoefficientoncamberedplatesat
withUND-FB1
(degrees)
-20-100102030
C
m/4
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
2D
sAR= 3
sAR= 1.5
Figure51:Pitchingmomentcoefficientoncambered
platesat
withUND-FB1
(degrees)
-20-100102030
C
l
, C
L
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2D
sAR= 3
sAR= 1.5
sAR= 1
Figure52:Liftcoefficientoncamberedplatesat
withUND-FB1
(degrees)
-20-100102030
C
d
, C
D
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
2D
sAR= 3
sAR= 1.5
sAR= 1
Figure53:Dragcoefficientoncamberedplatesat
withUND-FB1
(degrees)
-20-100102030
C
m/4
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
2D
sAR= 3
sAR= 1.5
sAR= 1
Figure54:Pitchingmomentcoefficientoncambered
platesat
withUND-FB1
21
1/sAR
0.000.250.500.751.00
C
L
(1/deg)
0.04
0.06
0.08
0.10
0.12
0.14
0.16
×
×
*
*
*
Re= 200,000
Re= 180,000
Re= 160,000
Re= 140,000
Re= 120,000
Re= 100,000
Re= 80,000
×
Re= 60,000
*
Theory: = 0.05
Theory: = 0.25
a
a
a
aa
0
0
0
1
573
1
2
*.
*
AR
ARsAR
andin degrees
Figure55:Lift-curveslopeforcambered-platemodels
inwindtunnelwithUND-FB1
Sincethecamberedwingsshowedbetteraerody-
namiccharacteristics,andhencearemoresuitableinthe
designofmicro-airvehicles,onlyperformancedatafor
thecamberedplatesispresented.Figures56through59
showthebehaviorof
,
,
and
asafunctionofReynoldsnumber.Themax-
imum ratioisrelatedtothemaximumrangefora
propellerdrivenairplane,whilethemaximum
isrelatedtobestendurance(longestflyingtimepossi-
ble).Asexpected,
increasedwithReynoldsnumber
andaspectratiointherangeofReynoldsnumberstested.
Thesameexpectedbehaviorwasobtainedfor
and
.Ontheotherhand,
showedanin-
creasewithdecreasingReynoldsnumber,aswasalsoex-
pected.Themaximum generallyoccurredat to
,while
occurredat to
.It
isimportanttorememberthattheendplateshavebeen
showntohaveaneffectontheliftcoefficientsofflat-
platewings,andprobablycambered-platewingsalso.As
mentionedearlier,theeffectoftheendplatesonthedrag
characteristicsofcambered-platewingsisstillunderin-
vestigation.Theresultspresentedinthisreportmustthen
beanalyzedwiththepossibleeffectoftheendplatesin
mind;thenumericalvaluesshouldnotbetakenastheul-
timateresults.Theeffectoftheendplatesonthepitching
momenthasnotbeeninvestigatedforbothflat-plateand
cambered-platewings.
Effectoftrailing-edgegeometry
Fourmodels[ ( )and ( )]weretestedinthewindtunnelatsev-
eralchordReynoldsnumberstoseeifthetrailing-edge
geometryhadanyinfluenceontheaerodynamiccharac-
teristicsofflatplatesandcamberedplatesatlowchord
Re
c
050000100000150000200000
C
l
max
, C
L
max
0.00
0.25
0.50
0.75
1.00
1.25
1.50
2D
sAR= 1.5
sAR= 1
Figure56:Maximumliftcoefficientasafunctionof
forcamberedwingswithUND-FB1
Re
c
050000100000150000200000
C
d
min
, C
D
min
0.00
0.01
0.02
0.03
0.04
0.05
2D
sAR= 1.5
Figure57:Minimumdragcoefficientasafunction
of
forcamberedwingswithUND-FB1
Re
c
050000100000150000200000
(
L/D
)
max
0
5
10
15
20
25
30
2D
sAR= 3
sAR= 1.5
sAR= 1
Figure58:Maximum
ratioasafunctionof
forcamberedwingswithUND-FB1
22
Re
c
050000100000150000200000
(
C
L
3/2
/C
D
)
max
0
5
10
15
20
25
30
2D
sAR= 3
sAR= 1.5
sAR= 1
Figure59:Maximum
ratioasafunction
of
forcamberedwingswithUND-FB1
Reynoldsnumbers.Thefirsttwomodelshadatapered
trailingedge,whiletheothertwomodelshadanellipti-
caltrailingedge.Resultswereobtainedforinfinitemod-
els(2Dcase)andmodelswithasemi-spanaspectratio
.Forbothcases,nosignificantdifferencewas
observedin
or
,and
or
,asafunctionof
trailing-edgegeometry,asshowninFigures60and61for
.Adifferencewashoweverobservedin
themomentcoefficient
.Forasharptrailingedge,
oftenappearedtobepositivearound
,even
withtheuncertaintyconsidered(errorbarsin
are
aboutthesizeofthesymbols).Withtheellipticaltrailing
edge,the2Dcasesat
showedastable
negativevalueof
,asshowninFigure62.Fora
semi-spanaspectratioof1.5,
wasbasicallyzeroat
.Flowvisualizationtobeperformedlatermay
explainthisphenomenon.
Withthecamberedplates,therewasbasicallyno
differencebetweenasharptrailingedgeandanelliptical
trailingedgeat
,asshowninFigures63
through65.Resultswiththecamberedplatesseemto
agreewithLaitone(Laitone,1996and1997),whoshowed
thatatlowReynoldsnumbers,asharptrailingedgeisnot
ascriticalasforlargerReynoldsnumbers.
Theinfluenceoftheleading-edgegeometrywasalso
investigatedbylookingattheliftanddragcharacteristics
ofaflat-platemodelin2Dand
configurations
inthewatertunnelat
and
.
Forthesetests,theexistingC8S12modelwasrotated180
degrees(taperedleadingedgeandellipticaltrailingedge).
Nodifferencewasnoticedintheresultsforliftanddrag.
Laitone(1996and1997)didnoticeasignificantincrease
inliftat
fora
thicker
reversedNACA
0012airfoil(thesharptrailingedgewasfacingtheflow).
Furthertestswillbeconductedinthewindtunnelatlarger
Reynoldsnumbersonflat-plateandcambered-platewings
tocompletethisstudyoftheleading-edgegeometryeffect
(degrees)
-20-100102030
C
l
, C
L
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2D: sharp TE
2D: elliptical TE
sAR= 1.5: sharp TE
sAR= 1.5: elliptical TE
Figure60:Trailing-edgegeometryeffectonlift
coefficientat
onflatplatesinthe
windtunnelwithUND-FB1
(degrees)
-20-100102030
C
d
, C
D
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
2D: sharp TE
2D: elliptical TE
sAR= 1.5: sharp TE
sAR= 1.5: elliptical TE
Figure61:Trailing-edgegeometryeffectondrag
coefficientat
onflatplatesinthe
windtunnelwithUND-FB1
(degrees)
-20-100102030
C
m/
4
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
2D: sharp TE
2D: elliptical TE
sAR= 1.5: sharp TE
sAR= 1.5: elliptical TE
Figure62:Trailing-edgegeometryeffectonpitching
momentcoefficientat
onflatplates
inthewindtunnelwithUND-FB1
23
(degrees)
-20-100102030
C
l
, C
L
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2D: sharp TE
2D: elliptical TE
sAR= 1.5: sharp TE
sAR= 1.5: elliptical TE
Figure63:Trailing-edgegeometryeffectonlift
coefficientat
oncamberedplatesinthe
windtunnelwithUND-FB1
(degrees)
-20-100102030
C
d
, C
D
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
2D: sharp TE
2D: elliptical TE
sAR= 1.5: sharp TE
sAR= 1.5: elliptical TE
Figure64:Trailing-edgegeometryeffectondrag
coefficientat
oncamberedplatesinthe
windtunnelwithUND-FB1
(degrees)
-20-100102030
C
m/4
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
2D: sharp TE
2D: elliptical TE
sAR= 1.5: sharp TE
sAR= 1.5: elliptical TE
Figure65:Trailing-edgegeometryeffectonpitching
momentcoefficientat
oncamberedplates
inthewindtunnelwithUND-FB1
ontheaerodynamiccharacteristicsofthinwings/airfoils.
Effectoffreestreamturbulence
Muelleretal.(1983)showedthatanincreasein
freestreamturbulenceintensityreducedtheminimumdrag
actingonan
thickLissaman7769airfoilat
andslightlyincreased
.Thiswascaused
byanearlierlaminarshearlayertransition,henceearlier
flowreattachment(i.e.,ashorterseparationbubble),with
alargerturbulenceintensity.Atlargeanglesofattack
wheretheflowismostlyseparated,theyobservedanin-
creaseindragcoefficientwithanincreaseinturbulence
intensity.Increasingtheturbulenceintensityalsohelped
toeliminatesomeofthehysteresisencounteredin
and
forthatparticularairfoil.
Pohlen(1983)alsolookedattheinfluenceofturbu-
lenceintensityona
thickMileyairfoil(M06-13-128)
(seeMiley,1972).Hefoundthatincreasingtheturbu-
lenceintensityhelpedtoreducethehysteresisin
and
andslightlyimprovedairfoilperformance.
Testswerethenconductedinthewindtunnelwith
differentscreensupstreamoftheflat-plate
modelsandaflowrestrictordownstreamofthemodelto
seeifadifferenceintheturbulenceintensitycouldresult
indifferentaerodynamicpropertiesforthemodelsused
inthisinvestigation.Theflowrestrictor,orstrawbox,
wasmadeofdrinkingstrawspackedinawoodenframe
andplacedbetweenthetestsectionandthediffuser.The
additionalturbulenceintensitygeneratedbythestrawbox
wasdeterminedtobeapproximately
(Brendeland
Huber,1984).Table3indicatesthemeshsizeandnomi-
nalfreestreamturbulenceintensityinthetestsectionwith
onlyascreenpresent(noflowrestrictor).
Screen
Meshsize
Wire
Turbulence
(
)
diameter
%
( )
Fine
7.09
0.245
0.25
Medium
3.15
0.508
0.45
Coarse
0.64
1.397
1.3
Table3:Turbulencescreendata
(Pohlen,1983;andBrendelandHuber,1984)
Nomeasurabledifferenceswereobservedinthere-
sultsfordifferentturbulenceintensitiesat
onthe flat-platemodel,asshowninFig-
ures66and67.Onlyaslightincreasein
andan
increasein
forlargeanglesofattackwasnoticed
forthecasewiththefinemeshandwiththestrawbox.
Allothercasesgavethesameresults.Therefore,theef-
fectofturbulenceintensityappearedtobeminimalinthe
windtunnelforthemodelstested.Similarresultswere
24
(degrees)
-20-100102030
C
L
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
No screen, no strawbox
No screen, with strawbox
Fine mesh, with strawbox
Medium mesh, with strawbox
Coarse mesh, with strawbox
Figure66:Freestreamturbulenceeffectonliftcoefficient
at
inthewindtunnelforthe
flat-platemodelwithUND-FB1
(degrees)
-20-100102030
C
D
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
No screen, no strawbox
No screen, with strawbox
Fine mesh, with strawbox
Medium mesh, with strawbox
Coarse mesh, with strawbox
Figure67:Freestreamturbulenceeffectondrag
coefficientat
inthewindtunnelforthe
flat-platemodelwithUND-FB1
obtainedat
inthewindtunnel,andat
and
inthewatertunnel.
Effectofendplateson2Dmeasurements
IthasbeenshowninpreviousexperimentsatNotre
Damethatthepresenceoftheendplatesduring2Dtests
usuallyleadstoalarger
.Foran18%thickairfoil
(NACA
),MuellerandJansen(1982)showed
thattheinteractionbetweentheendplatesandthemodel
resultedina20%increasein
atReynoldsnumbers
between
and
.
Sincemostofthetestsinthecurrentinvestiga-
tionwereconductedatverylowspeeds,theinteraction
betweentheboundarylayergrowingontheendplates
andthewingcreatedacornerflow,asdepictedinFig-
ure68,whichactedoverasignificantportionofthewing
spanandsignificantlyalteredthe2-dimensionalityofthe
U
Figure68:Schematicofcornerflowonwing
flowoverthewing.Thisphenomenonofthecorner
flowhasbeeninvestigatedbyseveralauthors,including
Hawthorne(1954)andBarber(1978)wholookedatthe
flowaroundstrutsnearawall.
Inordertoverifytheeffectoftheendplatesonthe
aerodynamiccharacteristicsoftheEppler61airfoil,a
3-pieceEppler61modelwasused.Withthissetup,a
sectionofanEppler61modelwasfreetomovebetween
twoothersectionsofthesameairfoil.Thesetwoother
sectionswerefixedtotheendplatesinthewindtunnel,
asshowninFigure69,atthesameangleofattackas
themiddlesection.Asmallgapwaspresentbetweenthe
endmodelsandthecenterpiececonnectedtotheforce
balance.Figure70showsthethreepiecesofthe3-piece
Eppler61model.
Theangleofattackofthe3-pieceEppler61model
wasadjustedtoacertainvalueandthevelocityinthe
tunnel,hencetheReynoldsnumber,wasvaried.Thebe-
haviorof
and
wasmeasured.Fromtheprevious
2DresultsontheEppler61airfoil,itwasdetermined
that
occurredat
andtheangleforzerolift
wasabout
.Thebehaviorof
vs
was
firstobtainedatthesetwoanglesofattack.Figures71
and72showthatthedragcoefficientwiththe3-piece
Eppler61modelwasmuchsmallerthanwiththefull
model.ThisresultissimilartothatreportedbyMueller
andJansen(1982)fortheNACA
airfoil.The
liftcoefficientwiththe3-piecemodelwashigherthan
withthefullmodel.Theaerodynamiccharacteristicswith
the3-piecemodelwereclosertotrue2-dimensionalre-
sults,wherealarger
andsmaller
wouldnormally
beexpected.Thebehaviorof
and
withReynolds
numbersalsofollowedtheexpectedtrends.Areduction
in
andanincreasein
wereobservedwithincreas-
ingReynoldsnumbers.ResultsfromAlthaus(1980)and
deVriesetal.(1980)arealsoincludedinthefigures
forcomparison.AswasmentionedearlierforAlthaus,
25
Endplates
U
Sting
Sting
covering
Eppler 61
wing
3/100 in (0.8mm)
Gap
24in (61cm)
24in
(61cm)
4.906in
(12.5cm)
Balance
Strain
gauges
Lift platform
Drag platform
Base
Drag flexure
8in
(20.3cm)
Figure69:New-balancearrangementfor3-piece
Eppler61airfoiltestsinwindtunnel
theseinvestigatorsusedastraingaugeforcebalanceto
measureliftandawakeraketomeasuredrag.Sincethe
dragmeasuredwithawakerakeisusuallyobtainedat
themid-spanofthemodel,itdoesnottakeendeffects,
or3Deffects,intoaccount.Theseendeffectscanbesig-
nificantatverylowReynoldsnumbers.Therefore,drag
coefficientresultsfromAlthausanddeVriesetal.were
expectedtobesmallerthanthepresentresultsandthis
trendwasobserved.
Inordertostudytheeffectofendplatesatlow
Reynoldsnumbers,Seligetal.(1995)showedhow
can
varyforatwo-dimensionalairfoilalongthespanofthe
modelatlowReynoldsnumbers.Figures73through76
showdragpolarsonanSD6060airfoilat
,
,
and
,asobtainedusinga
wakerakewiththemomentumtechniquefor
anda
straingaugeforcebalancefor
.For
and
,thedragpolarsvariedsignificantly
alongthespanofthemodel,whichimpliedathree-
dimensionalflow.At
andespeciallyat
,thedragpolarswererelativelyconstant
alongthespanandanearlytwo-dimensionalflowwas
believedtoexist.
Gap
U
(a)Topview
Lower piece
Upper piece
Sting hole
Wing
(b)Individualpieces
Figure70:3-pieceEppler61airfoilmodeltested
inwindtunnel
26
Re
20000400006000080000100000120000
C
l
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
3-piece airfoil
1-piece airfoil
Althaus (1980)
de Vries et al. (1980)
(a)Liftcoefficient
Re
20000400006000080000100000120000
C
d
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
3-piece airfoil
1-piece airfoil
Althaus (1980)
de Vries et al. (1980)
(b)Dragcoefficient
Figure71:Endplateseffecton2Dcharacteristicsof
Eppler61airfoilat
withUND-FB2
Re
20000400006000080000100000120000
C
l
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
3-piece airfoil
1-piece airfoil
Althaus (1980)
(a)Liftcoefficient
Re
20000400006000080000100000120000
C
d
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
3-piece airfoil
1-piece airfoil
Althaus (1980)
(b)Dragcoefficient
Figure72:Endplateseffecton2Dcharacteristicsof
Eppler61airfoilat
withUND-FB2
27
Figure73:DragpolarforSD6060airfoilat
(Seligetal.,1995)
Figure74:DragpolarforSD6060airfoilat
(Seligetal.,1995)
Figure75:DragpolarforSD6060airfoilat
(Seligetal.,1995)
Figure76:DragpolarforSD6060airfoilat
(Seligetal.,1995)
28
Re
20000400006000080000100000120000
C
l
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
3-piece airfoil
1-piece airfoil
Althaus (1980)
de Vries et al. (1980)
(a)Liftcoefficient
Re
20000400006000080000100000120000
C
d
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
3-piece airfoil
1-piece airfoil
Althaus (1980)
de Vries (1980)
(b)Dragcoefficient
Figure79:Endplateseffecton2Dcharacteristicsof
Eppler61airfoilat
withUND-FB2
andbuiltattheUniversityofNotreDame.Thebalance
showsgoodsensitivity,repeatabilityandaccuracy.Tech-
niquestoreducenoiseandincreasetheaccuracyofthe
resultsinthewatertunnelbelowReynoldsnumbersof
arestillbeinginvestigated.
Moreover,ithasbeenshownthatcambered-plate
wingswith
camberofferbetteraerodynamiccharac-
teristicsthanflat-platewingsforagivenReynoldsnum-
ber.ReducingtheReynoldsnumbercanleadtopoor
performanceduetothelargereductionin
and
forbothflat-andcambered-platewings.
Theturbulenceintensityinthetunnelandthe
trailing-edgegeometryhavebeenshowntohaveavery
smalleffectonthemeasurementsoflift,dragandpitch-
ingmomentonthethinmodelstestedinthisinvestigation.
However,thepresenceofendplatescanaffecttheresults
forliftanddragduetotheinteractionbetweenthebound-
arylayergrowingontheendplateandtheflowaroundthe
wing.ThepresenceofendplatesatlowReynoldsnum-
bersreducesthe2Dliftandincreasesthe2Ddragthat
wouldnormallybeobtainedwithatrulyinfinitemodel,
accordingtotestsontheEppler61airfoil.Furthermore,
foragivenmodel,addingoneendplateleadstoanin-
creaseinliftcomparedtothecasewithoutanendplate.
Testingfinitewingmodelswithoutendplatesappearsto
bedesirableatlowReynoldsnumbersbecauseitelim-
inatesendplateeffects.Thefulleffectoftheendplates
isstillunderinvestigation,especiallyforcambered-plate
wings.
Finally,trendsof
versus
shouldbeinves-
tigatedbyfixingthewingattheangleofattackyield-
ing
andthenvaryingthewindvelocity,hencethe
Reynoldsnumber,inthetunnel.Thisseemstohelpto
eliminatescatterintheresults.Testsusingthistechnique
onvariousflatplateshaveindicatedtheexpectedtrends
ofareductionin
andanincreasein
withan
increaseinReynoldsnumber.
Acknowledgements
ThisresearchwassponsoredbytheU.S.Navy,
NavalResearchLaboratory,Washington,D.C.underCon-
tractNo.N00173-98-C-2025andtheRoth-GibsonEn-
dowmentattheUniversityofNotreDame.Theauthor
wouldliketothankAlainPelletierforhiseffortandex-
pertiseintheexperimentalphaseofthisstudyaswellas
hishelpinpreparingthismanuscript.Specialthanksgo
toMatthewKeennonof
AeroVironment
,WilliamDavis,
Jr.of
TheLincolnLaboratory
,JeffreyHarrisof
Sanders,
ALockheedMartinCompany
,andKevinAilingerofthe
NavalResearchLaboratory
forsharingtheresultsoftheir
MAVdevelopmentprojects.PermissionbyDr.M.Selig
tousedhiswakerakedataand
TheLincolnLaboratory
forFigure2isgratefullyacknowledged.
References
Ailinger,K.G.
“U.S.NavyMicroAirVehicleDe-
velopment.”UnmannedAirVehicleSystemsFour-
teenthInternationalConference,April1999:36-1–
36-7.
Althaus,Dieter.
Profilpolarenf
¨
urdenModellflug.
Neckar-Verlag,Institutf
¨
urAerodynamikundGas-
dynamik,UniversityofStuttgart,1980.
Anderson,JohnD.,Jr.
FundamentalsofAerodynam-
ics.
ed.NewYork:McGraw-Hill,1991.
Ashley,S.“Palm-SizeSpyPlanes.”MechanicalEngi-
neering,February1998:74-78.
Barber,T.J.“AnInvestigationofStrut-WallIntersec-
tionLosses.”JournalofAircraft,Vol.15,No.10,
October1978:676-681.
30
Bastedo,W.G.Jr.,andT.J.Mueller.“TheSpan-
wiseVariationofLaminarSeparationBubbleson
FiniteWingsatLowReynoldsNumbers.”AIAA
Paper#85-1590,July1985.
Batill,StephenM.,andThomasJ.Mueller.“Visual-
izationoftheLaminar-TurbulentTransitioninthe
FlowOveranAirfoilUsingtheSmoke-Wiretech-
nique.”AIAAPaper#80-0421,March1980.
Brendel,Michael,andArthurF.HuberII.“AnEx-
perimentalInvestigationofFlowQualityinanIn-
draftSubsonicWindTunnelUsingaSingleHot
WireAnemometer.”UniversityofNotreDame,
November1984.
Brooks,GregoryAirForceResearchLaboratory,Pri-
vateCommunication,June1999.
Burns,ThomasF.“ExperimentalStudiesofEppler
61andPfenninger048AirfoilsatLowReynolds
Numbers.”Master’sThesis,TheUniversityof
NotreDame,January1981.
Carmichael,B.H.“LowReynoldsNumberAir-
foilSurvey.”VolumeI,NASAContractorReport
165803,November1981.
Davis,W.R.,Jr.,B.B.Kosicki,D.M.Boroson,and
D.F.Kostishack.“MicroAirVehiclesforOpti-
calSurveillance.”TheLincolnLaboratoryJournal,
Vol.9,No.2,1996:197-213.
Davis,W.R.,Jr.TheLincolnLaboratory,Private
Communication,June1999.
deVries,J.,G.H.Hegen,andL.M.M.Boermans.
“PreliminaryResultsofWindtunnelMeasurements
atLowReynoldsNumbersonAirfoilSectionE61.”
InternReportLSW80-5,1980.
Dornheim,M.A.“UnmannedAerialVehicles:Tiny
DronesMayBeSoldiers’NewTool.”Aviation
Week&SpaceTechnology,June8,1998:42-48.
Eidetics
.OperationsManual:FlowVisualization
WaterTunnel.
Fulghum,D.A.“MiniatureAirVehiclesFlyInto
Army’sFuture.”AviationWeek&SpaceTechnol-
ogy,November9,1998:37-38.
Harris,J.D.Sanders,ALockheedMartinCompany,
PrivateCommunication,1999.
Hawthorne,W.R.“TheSecondaryFlowAboutStruts
andAirfoils.”JournaloftheAeronauticalSci-
ences,Vol.21,No.1,January1954:588-608.
Huber,ArthurF.,II.“TheEffectsofRoughnesson
anAirfoilatLowReynoldsNumbers.”Master’s
Thesis,TheUniversityofNotreDame,May1985.
Jackson,Paul,ed.Jane’sAlltheWorld’sAircraft.
Jane’sInformationGroup,1996-97.
Keennon,M.AeroVironment,PrivateCommunication,
June1999.
Kline,S.J.,andF.A.McClintock.“Describing
UncertaintiesinSingle-SampleExperiments.”Me-
chanicalEngineering,Vol.75,No.1,January
1953:3-8.
Laitone,E.V.“AerodynamicLiftatReynoldsNum-
bersBelow .”AIAAJournal,Vol.34,No.9,
September1996:1941-1942.
Laitone,E.V.“WindTunnelTestsofWingsat
ReynoldsNumbersBelow70,000.”Experimentsin
Fluids,Vol.23,1997:405-409.
McMasters,J.H.,andM.L.Henderson.“Low
SpeedSingleElementAirfoilSynthesis.”Tech.
Soaring,Vol.2,No.2,1980:1-21.
Miley,S.J.“AnAnalysisoftheDesignofAirfoil
SectionsforLowReynoldsNumbers.”Ph.D.Dis-
sertation,MississippiStateUniversity,1972.
Morris,S.J.“DesignandFlightTestResultsfor
Micro-SignedFixed-WingandVTOLAircraft.”
InternationalConferenceonEmergingTech-
nologiesforMicroAirVehicles,GeorgiaInstitute
ofTechnology,AtlantaGeorgia,February1997:
117-131.
Mraz,S.J.“HoneyIShrunkthePlane.”MachineDe-
sign,October1998:35-42.
Mueller,T.J.,andT.F.Burns.“ExperimentalStud-
iesoftheEppler61AirfoilatLowReynoldsNum-
bers.”AIAAPaper#82-0345,January1982.
Mueller,T.J.,andB.J.Jansen,Jr.“Aerodynamic
MeasurementsatLowReynoldsNumbers.”AIAA
Paper#82-0598,March1982.
Mueller,T.J.,L.JPohlen,P.E.Conigliaro,andB.
J.Hansen,Jr.“TheInfluenceofFree-StreamDis-
turbancesonLowReynoldsNumberAirfoilEx-
periments.”ExperimentsinFluids.Vol.1,1983:
3-14.
O’Meara,M.M.,andT.J.Mueller.“LaminarSepa-
rationBubbleCharacteristicsonanAirfoilatLow
ReynoldsNumbers.”AIAAJournal,Vol.25,No.8,
August1987:1033-1041.
Pankhurst,R.C.,andD.W.Holder.Wind-Tunnel
Technique.London:SirIsaacPitman&Sons,
1952.
31
Peake,DavidJ.,andMurrayTobak.“Three-
DimensionalFlowsAboutSimpleComponentsat
AngleofAttack.”AGARDLectureSeriesNo.121
onHighAngle-of-AttackAerodynamics,PaperNo.
2,1982.
Pelletier,Alain.“AStudyoftheNonlinearAerody-
namicCharacteristicsofaSlenderDouble-Delta
WinginRoll.”Ph.D.Dissertation,TheUniversity
ofNotreDame,April1998.
Pohlen,Lawrence.“ExperimentalStudiesoftheEf-
fectofBoundaryLayerTransitiononthePerfor-
manceoftheMiley(M06-13-128)AirfoilatLow
ReynoldsNumbers.”Master’sThesis,TheUniver-
sityofNotreDame,January1983.
Prazak,M.W.,andT.J.Mueller.“Experimental
StudiesofanEppler61WingatChordReynolds
Numbersfrom12,000to63,000.”TechnicalNote
UNDAS-TN-256-1,July1997.
Rae,WilliamH.Jr.,andAlanPope.Low-SpeedWind
TunnelTesting.
ed.NewYork:JohnWiley&
Sons,1984.
Schlichting,Hermann.Boundary-LayerTheory.
ed.NewYork:McGraw-Hill,1979.
Selig,MichaelS.,etal.SummaryofLow-SpeedAirfoil
Data.Volume1,Virginia:SoarTechPublications,
1995.
Strang,W.Z.,R.F.Tomaro,andM.J.Grismer.
“TheDefiningMethodsofCobalt60:AParallel,
Implicit,UnstructuredEuler/Navier-StokesFlow
Solver.”AIAAPaper#99-0786,January1999.
Taylor,JohnW.R.,ed.Jane’sAlltheWorld’sAircraft.
Jane’sInformationGroup,1969-70.
Tennekes,Henk.TheSimpleScienceofFlight:From
InsectstoJumboJets.Cambridge:TheMITPress,
1996.
Williams,DavidL.,III.“Dynamic,LateralBehavior
ofLow-Aspect-Ratio,RectangularWingsatHigh
AnglesofAttack.”Ph.D.Dissertation,TheUniver-
sityofNotreDame,April1996.
Wilson,J.R.“MiniTechnologiesforMajorImpact.”
AerospaceAmerica,May1998:36-42.
Winkelmann,A.E.,andJ.B.Barlow.“Flowfield
ModelforaRectangularPlanformWingBeyond
Stall.”AIAAJournal,Vol.18,No.8,August1980:
1006-1008.
32
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Redmegaman
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