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Патент USA US2404011

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July 15, 1946'
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w. T. WHITE
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2,404,011
PREDI GTI ON APPARATUS
Filed June 2l, 1943
'
ÍNVENTOR
MALTE@ Z- /l//WTE «
BY
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MÃÉRNE .
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Patented July 16, 1946
2,404,011
UNITED sTATEs PATENT oFFicE
2,404,011
PREDICTION APPARATUS
Walter T. White, Hempstead, N. Y., assigner to
Sperry Gyroscope Company, Inc., a corpora
tion of New York
Application June 21, 1943, Serial No. 491,637`
5 Claims. (Cl. 2535-615)
1
2
This invention relates generally to the art of
terms of two angular coordinates and one dis
tance or range coordinate, such as by an optical
gun ñre control and, more particularly, to novel
prediction apparatus which combines the sim
sight and rangeñnder. The two angular coordi
nates ‘are usually elevation and azimuth, and
since these are identically treated, at least inso
plicity of previously known approximate predic
tion solutions with the accuracy of previously
known true prediction solutions.
One object of the invention is to provide sim
ple and accurate prediction apparatus for gun
far as the prediction problem is concerned, a gen
eral angular coordinate (6) will hereinafter be
referred to. The prediction component of the
whole nre control solution involves determining
the prediction angle (A0) by which the guns must
be offset from the line of sight to the target in
order to compensate for the motion of the target
ñre control.
Another object of the invention is to provide
prediction apparatus which is comparable in slm
plicity to an “angular rate by time” system but
having a greater accuracy.
Still another object of the invention is to pro
during the projectile time of flight (tp).
The simplest and most approximate type of
vide a prediction system comparable in simplicity 15 prediction solution is commonly known as the
to an “angular rate by time” system but having
“angular rate multiplied by time” solution. This
an accuracy comparable to more complicated sys
tems such as those based on Taylor’s series.
solution finds its greatest application in inter
aircraft and short range anti-aircraft fire control
An object of the invention is to provide pre
systems wherein a certain amount of accuracy in
diction apparatus which takes account not only 20 the solution may be sacrificed for simplicity of
of the angular rate of change of a target coordi
equipment and rapidity in the solution.
nate, but also the time rate of change of that
In such “angular rate by time” prediction sys
rate during the time of night of the projectile,
tems, data corresponding to the angular coordi
A further object of the invention is to provide
nate (0) is continuously supplied to the predic
an “angular rate by time” prediction system 25 tion apparatus from the sight. This angular co
wherein the angular rate is corrected by a factor
ordinate data is diñerentiated to obtain data cor
proportional to the time rate of change of the
angular rate and also to the average value of
the time of flight likely to be encountered in
responding to the time rate of change of the an
gular coordinate, hereafter referred to as the
practice.
angular rate
30
‘
A still further object of the invention is to pro
dt
vide simple prediction apparatus which takes into
This angular rate data is then multiplied by the
account the acceleration of the target position
projectile time of flight (tp), and the resulting
coordinate during the projectile time of flight.
Other objects and advantages will become ap 35 product is taken as the required prediction angle
(A0). Thus the solution is based on the following`
parent from the specification, taken in connec
approximation for the prediction angle:
tion with the accompanying drawing wherein the
invention is embodied in concrete form.
In the drawing:
Fig. 1 is a schematic diagram of mechanical 40 Referring now to Fig. 3, the solid line 3 repre
apparatus embodying the principles of the inven
sents a portion of a typical curve which might be
tion;
-
Fig. 2 is a wiring diagram of the analogous
electrical apparatus embodying the principles of
obtained by plotting the angular rate
(if)
45
dt
_
the invention; and
Fig. 3 is a graph useful in explaining the theory
as a function of time (t) for a particular target.
of the prediction solution employed in the in
Point I indicates the angular rate at the time
vention.
(To) at which the projectile leaves the gun, and
Similar characters of reference are used in
point 2 the angular rate at the time (Tp) at which
all of the above iigures to indicate correspond 50 the projectile strikes the target.
ing parts. Arrows are used to indicate the di
In the simple “angular rate by time” solution
rection of flow of information or control influ
the assumption is made that the angular rate is
ences.
constant during the time of flight (tp). In other
In all known nre control systems the position
words it is assumed that curve 3 follows the dot
of the target in space is continuously located in 55 ted line 4 from the time (To) to the time (Tp).
2,404,011
3
4
In practice this assumption is rarely, if ever, valid
Referring to Fig. 3, such a solution is equivalent
to assuming that the average value of the angu
lar rate is at point 6 on dotted line 5 which value
may be obtained by taking the angular rate at
the time (To) and adding thereto the product of
one-half the time of ilight (tp) and the time rate
of change of the angular rate at the time (To).
since in order to create such a condition the tar
get would have to fly at a constant speed in a
circle having the sight as its center. The solu
tion for the prediction angle (A0), is in error
then because no account has been taken of the
change of the angular rate during the time of
night.
In other words, it is assumed that the angular
acceleration is constant during the time of flight
and that curve 3 therefore travels along the dot
ted line 5 which is tangent to curve 3 at point I.
In order to obtain an accurate solution for the
prediction angle (A0), such as is required for long
range antiaircraft ñre control systems, it has been
proposed to make no assumptions at all concern
Obviously, such an assumption is more valid than
ing the motion- of the target, but to compute the
true prediction angle (A0) based upon the true
the assumption of a constant angular rate, and
a more accurate solution for the prediction angle
will be obtained than in an “angular rate by
time” system. However, even this solution is
more or less complicated since it is necessary to
mode of motion of the target in accordance with
the following expression based on Taylor’s series:
obtain the iirst and second derivatives, the first
and second powers of time of night, and to per
form two multiplications.
In the present invention, it is proposed to ob
tain an approximate value for the average angu
Correlating the above equation with Fig. 3, it will
lar rate by adding to the angular rate at time
(To) a correction proportional to the angular ac
ing the true average value of the angular rate
celeration
'
during the time of night, and multiplying this
average angular rate by the time of flight in or
der to obtain the true prediction angle (A0).
However, in order to accomplish such a solution
Thus, the expression for the prediction angle
it is necessary to take not only the iirst deriva
30 (A0) as solved for in the present apparatus may
tive
be written:
v be seen that such a solution amounts to obtain
di)
d0
dt
of the angular coordinate (0), but also the sec
ond derivative
(n
dit)
35
dt2
and the third derivative
and so on.
than that of a simple “angular rate by time” solu
tion, and will approach the accuracy obtained by
taking the first two terms of Taylor’s series.
However, by making K equal to 1/2tp (average)
one multiplication by time of ñight is eliminated
in the prediction apparatus. Accordingly by the
because of the necessity of solving for the higher
derivatives, the higher powers of time of flight,
and the respective product terms of the series.
In the above described system based on Taylor
scribed may be considered as an approximation
product
d0
ne)
is used and all subsequent products are considered
negligible.
A better approximation for the prediction angle
(A6) than that obtained in an “angular rate
by time” system could be realized by using thev
ñrst two terms of Taylor’s series, the approxi
mation then being:
The value of K is chosen so as to be equal to
one-half of the average values of al1 the time of
flight likely to be encountered, that is K=1/2tp
(average). In many applications the time of
flight varies within rather small limits and there
approximation to 1/21§p. Accordingly, the solution
involve considerable complication of equipment V
based upon Taylor series in which only the first
d20
for the prediction angle will be more accurate
lthen be multiplied by the corresponding powers
of the time of night, and the respective result
ing products must be added together to obtain
`the prediction angle (A0). Such a prediction sys
vtem, although it would provide a very accurate
solution for the prediction angle, would take a
long time to accomplish the solution, and would
prediction angle (A6). Accordingly the process
can be stopped whenever the desired degree of
accuracy has been attained. Indeed, the simple
“angular rate multiplied by time” system ñrst de
d0
40 fore the predetermined value of K may be a good
d t3
These respective derivatives must
series, the successive terms of the series intro
duce successively smaller components of the true
d20
M_ dt+Kdt2>tVd `t"+Kdt2`t”
present invention a certain degree of accuracy
is obtained with the minimum complication, and
in cases where just this degree of accuracy is
required the apparatus of the present invention
may be found very useful.
Referring now to Fig. 1 wherein mechanical
55
apparatus for solving for the prediction angle
(A0) based upon the above analysis is shown, data
corresponding to the angular rate
dt
is received as a. proportional rotation of input
shaft I0 from other portions of the ñre control
system (not shown). Shaft I0 is connected to
actuate one input member of a differential II,
the output member of which is connected to ac
tuate the ball carriage I2 of a variable speed
device I3, as by rack I4 and pinion I5. The vari
able speed device is shown as the usual disc ball
carriage, and cylinder type wherein a constant
speed motor I6 drives a disc I'I., which in turn
drives a cylinder I8 through the interconnecting
ball carriage I2 at a rate proportional to the
speed of the motor I6 and to the displacement of
the ball carriage I2 from its central position with
respect to disc I1. Cylinder I8 is connected by
shaft I9 to drive the second input member of
OIL-rinvii
2,404,011
'6
diñ'erential II which operates t'o displace the
.and will therefore be displaced by an amount
proportional to the prediction angle (A9) in ac
cordance with the above derived equation:
pinion I5 an amount proportional to the differ
ence in the displacements of shafts II) and I9.
As it well known, this arrangement of varia
ble speed device I3 and differential I I operates to
attain a condition of equilibrium at which the
rates of rotation of shafts I0 and I9 are equal.
A@ =
d20
t,
In the apparatus of Fig. 1 the value of K may
be made equal to one-half the average time of
night, as is required, by choosing the proper
When this condition has been reached, the dis
placement of ball carriage I2 is proportional to
the time rate of change of the angular displace
d0
10 speed of motor I6 and proper values of the vari
ous gear ratios involved.
Referring now to Fig. 2, wherein an electrical
ment of shaft III, and is therefore proportional to
the acceleration or second derivative
embodiment of the invention is shown, it is4 as
sumed that a direct voltage signal correspond
dt2
15 ing in polarity and magnitude to the angular rate
of the angular coordinate (0). This can be seen
by a consideration of the fact that should shafts
I0 and I9 not be rotating at the same rate, the
has been generated in other portions of the fire
third member of differential I I will be additionally
displaced, causing a corresponding displacement 20 control system and is applied across input leads
30, 3D’. »These input leads are respectively con
of ball carriage I2 in such a direction as to in
nected to the grids 32, 32’ 0f electron tubes 33,
crease or decrease the angular rate of shaft I 9
33'. yA plate supplyvoltage, indicated as a bat
until it does equal that of shaft Ill. Since the
tery 34, is connected at its negative end, which
rate of rotation of shaft I9 is proportional to
the displacement of `ball carriage I2 because of 26 may be grounded, as shown, to cathodes 35, 35’
and at its positive end to the plates 36, 36'
the nature of operation of variable speed device
di@
through equal resistors 31, 31'. A grid bias volt
I3, the displacement of ball carriage I2 may be
age is provided, indicated as battery 39, having
taken as proportional to the time rate of change
of the angular displacement of shaft Il), and
its positive side Aconnected to cathodes 35, 35’
therefore proportional to the time rate of change 30 and its negative side connected to grids 32, 32'
giif)
<3)
dt2
of the angular rate
dt
,through equal resistors 38, 38’.
The electric circuit so far described is simply
an amplifying circuit adapted to produce across
the opposing terminals of the series circuit con
35 sisting of resistors 31, 31' a voltage of the op
This second derivative, appearing as a propor
tional displacement of ball carriage I2, is intro
posite polarity to that appearing across input
leadsBII, 30', and having a proportional but great
er magnitude.
If it is assumed that zero signal
voltage is received across leads 30, 3U', it will
put member of differential 20, as by rack 2I and 40 be apparent that equal plate currents flow in
tubes 33, 33’ and thence through resistors 31, 31'
pinion 22. A second input member of differen
in opposite directions. Accordingly, the total
tial 20 is displaced by an amount proportional
voltage across the series circuit consisting of these
to the angular rate
duced as a proportional displacement of one in
two resistors would be zero. However, should an
input voltage signal be received of a polarity
such that lead 30 is positive with respect to lead
by being directly actuated from shaft III thr‘ough
3U', the grid of tube 33 will be rendered more
shafts 23, 24, and 25, and the associated gearing.
positive and the grid of tube 33’ will be rendered
Differential 20 operates to angularly displace its
less positive than their quiescent values. Ac
output shaft 26 by an amount proportional to 50 cordingly, more current will flow through resistor
the sum of the angular displacements of its two
31 than through resistor 31’, and the potential of
input shafts. Accordingly, output shaft 26 is
the upper terminal of resistor 31 will become
angularly displaced by an amount proportional to
more negative than the potential 0f the lower
the quantity
terminal of resistor 31'. A resulting voltage will
d0
d20
55 thus be produced across the opposing terminals
dt
of resistors 31, 31' havinga polarity opposite to
that of the input voltage signal received across
The angular displacement of shaft 26 is in
leads 30, 30', and an amplified magnitude. In
troduced into a mechanical multiplier unit 21,
the same manner, should an input signal be re
into which there is also introduced the time of
ceived having opposite polarity to that just as
flight (tp) as an angular displacement of shaft
sumed such that lead 3U’ is positive with respect
28 from other portions of the ñre control system.
to lead 30, an opposite polarity voltage would
The multiplier unit 21 may be of the type dis
be produced across resistors 31, 31’ such that
closed in U. S. Patent No. 2,194,477 for a Multiply
ing machine, issued in the names of W. L. Max 65 the lower terminal of resistor 31’ is negative with
respect to the upper terminal of resistor 31 by a
son and P. J. McLaren, dated March 26, 1940.
proportional amount. 'I'hus the voltage across
As disclosed in that patent, the multiplier unit
is adapted to produce an angular displacement
resistors 31, 31', corresponding to the input volt
of an output shaft equal to the product of the
age across leads 30, 30', is proportional in mag
angular displacements of two input shafts. Ac
nitude and opposite in polarity to the magnitude
cordingly, output shaft 29 will be displaced by 70
an amount equal to the product of the time of
flight (tp) and the quantity
and sense of the angular rate ‘
Q
dt
This voltage is lapplied across a series network
consisting of condenser 4I) and resistor 4I con
“www
‘2,404,011
7
nected in parallel, resistor 42, lresistor 42', and
comes more and more accurate, the greater the
value of y, provided
the condenser 40' and resistor 4|’ connected in
parallel. Neglecting `for the moment the `eiïect
of condensers 40, 4D', it will be apparent that re
sistors 4l, 4l', 42, 42’ comprise a simple voltage 5
divider network so that a voltage Will be devel
Raw”
and the accuracy is quite satisfactory for lire
control applications.
This voltage is then applied to the grids of elec
tron tubes 43, 43’ which, in conjunction with their
oped across the opposite terminals of resistors 42,
42', proportional in magnitude to that across re
sistors 31, 31', and therefore also proportional in
magnitude to the angular rate
10 associated circuit elements, form an amplifying
circuit having exactly the same operation as the
QQ>
amplifying circuit described with respect to elec
tron tubes 33, 33’. ThisI latter amplifying circuit
therefore operates to produce an output voltage
40' upon the current through the resistors 42, 42'
across terminals 44, 44’ having a polarity oppo
it will be seen that an additional component of
site to that across resistors 42, 42', and having
an amplified magnitude. There is thus produced
current will flow through these resistors When
ever the voltage across resistors 31, 31' is chang
across the output terminals 44, 44’ of this am
plifying circuit a voltage having an amplitude
ing. If condenser 40, 40’ and resistors 42, 42' are
chosen such that the time constant of their series 20 proportional to and polarity corresponding to
circuit is small, this added component of current
the magnitude and sense of the quantity
will be proportional in magnitude to the time
d0
d20
rate of change of the voltage across resistors 31,
31’ and will therefore be pl‘OpOrtional in magní
This voltage is then applied across the termi
tude to the second time derivative
25 nals of the linearly wound resistor 45 of poten
dt
Considering now the elïect of condensers 40,
@23)
tiometer unit 46 which has a movable contact arm
diz
of the angular coordinate (a) .
41 actuated in accordance with time of flight
Accordingly, the
(tp) received as a proportional rotation of shaft
total voltage across the grids of tubes 43 and 43'
48 from other portions of the fire control sys
30 tem. The final voltage generated across output
is proportional in magnitude to the quantity
leads 49, 49’ will be proportional to the voltage
d0
d20
impressed upon the -resistor 45 and also propor
tional to the angular displacement of shaft 48.
The values of resistors 4I, 4|', 42, 42" and con
Therefore, the voltage across output leads 49, 49'
densers 40, 40’ in this case also are chosen so 35 will loe proportional in a magnitude and will cor
that K will have a value equal to one-half the
respond in polarityßto the magnitude and sense
average time of ñight. These values can be de
of the quantity
termined in any suitable manner. For example,
d0
d20
the relation between the input (e) to tubes 36_
and 36' and the voltage before grids of tubes 43 40
and 43' (Eg) can be .chosen to be
and will therefore correspond to the prediction
at Kir)
et+ Km»
angle (A6) .
where p is the differential operator
45
It will be apparent that should the received sig
nal corresponding to the angular rate
i
v
dt
be represented -by the amplitude and phase of an
p. is the amplification factor of each of tubes 36
alternating voltage rather than the magnitude
and 36', and the resistances R, and the condens 50 and polarity of a direct voltage, as has been as
\ ers C are identified by subscripts corresponding to
the reference characters used in Fig. 2.
Substitution of
i
dt
gg
dt
.
l
Eg=llRî-î gi'i'Rlzolod-tg]
R
d0
d20
NOW
_B_n
R42
can be adjusted to equal a; so that
d0
d20
E,= îl-¿JfRtCtä-z]
Then, if We let K =R42C40,
d0
and differentiating circuits could be substituted
for those shown in Fig- 2 to produce an alter
nating .current output signal corresponding to the
55 prediction angle (A0).
Although the invention has been described as
applied to a ñre control system wherein the pre
for 11 and
for e gives
sumed, suitable alternating current amplifying
d20
Eg= gi-l- K W
diction is accomplished in terms of spherical co
ordinates, it will be apparent that a linear coordi
80 nate (rc) of the target’s position could as well be
substituted for the angular coordinate (0) with
equally advantageous results in computing a lin
ear prediction (Ax).
Since many changes could be made in the above
65 construction and many apparently widely differ
ent embodiments of this invention could be made
without departing from the scope thereof, it is
intended that al1 matter contained in the above
description or shown in the accompanying draw
70 ing shall be interpreted as illustrative and not in
a limiting sense.
What is claimed is:
l. In a lire control system, wherein a measure
of the time rate of change of a coordinate of the
The first of the above equations for Eg results
from some simplifying approximations. It be-- 75 target position is received as the magnitude of a
OlLH “D i l
2,404,011
9
10
ñrst variable voltage, and a measure of the pro
jectile time of ilight is received as an angular
vdisplacement of a shaft, prediction apparatus
comprising an electrical network receiving said
ñrst voltage and consisting of a iirst resistor con
nected in series with a parallel arrangement of a
second resistor and a condenser, a potentiometer
unit having a linearly wound resistive winding
connected to receive the voltage across said first
resistor, and a rotating contact arm cooperating
age angular rate as a multiplicand whereby a
with the potentiometer winding actuated from
said shaft.
2. A ñre control system `having an apparatus
for computing close approximations of predic
tion angles, comprising means controlled accord
ing to the variable angular rate of a target, other
means for further controlling said means to add
to said angular rate a linear correction to obtain
an approximate value for the average angular
rate of the target, said correction being the prod
uct of a derivative of said angular rate and a
constant, a multiplying device for multiplying
by a time of flight value, means for actuating
said multiplying device in accordance with 'said
approximate average angular rate whereby a
product is obtained from the multiplying device
product is obtained from the multiplying device
which is closely proportional to the required pre
diction angle.
4. A fire control system having means for com
puting prediction angles, comprising an ampli
fier, an input circuit therefor energized by a volt
age proportional to the angular rate of the target,
circuit means in the amplifier for computing a
correction voltage and adding said correction
voltage to the angular rate voltage to obtain a ‘
voltage approximately proportional to the aver
age angular rate of the target, said correction
voltage being a ñrst derivative of the angular rate
multiplied by a constant equal to one-half of an
average time of flight value, multiplying means
connected to the output of the amplifier adapted
to multiply the average angular rate voltage by
a time of ilight factor whereby a voltage is pro
duced at the output of the multiplying means
proportional to the required prediction angle.
5. A fire control system having means for com
puting prediction angles, comprising an ampli
fier, an input circuit therefor energized by a
voltage proportional to the angular rate of the
tion angle.
3. A fire control system having an apparatus
target, circuit means in the amplifier comprising
a resistor and condenser network for producing
a voltage proportional in magnitude to the ñrst
derivative of the angular rate of the target multi
for computing close approximations of predic
plied by a constant, the network components
tion angles, comprising means controlled accord
ing to the variable angular rate of a target, other
means for further controlling said means to add
to said rate a correction to obtain an approximate
being so chosen that the constant is equal to one
half of the average time of ñight, means in the
network for adding this voltage to an amplified
which closely approximates the required predic
value for the average angular rate of the target,
said correction being the product of a derivative
of said angular rate and a constant, said constant
being equal to one half of the average time of
flight of the projectile, a multiplying device,
means for operating said device with a time of
ñight value as a multiplier and said value of aver
voltage proportional to the input voltage to pro
duce a voltage proportional to the approximate
average angular rate of the target, and means
for multiplying the average angular rate voltage
by a factor proportional to time of ñight in order
to obtain a voltage proportional to the required
prediction angle.
WALTER T. WHITE.
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