U.S. patent number 3,743,818 [Application Number 05/202,449] was granted by the patent office on 1973-07-03 for ballistic computer.
This patent grant is currently assigned to Hughes Aircraft Company, The United States of America as represented by the Secretary of the Army. Invention is credited to Millard M. Frohock, Jr., Paul M. Marasco, William E. McAdam, Jr..
United States Patent |
3,743,818 |
Marasco , et al. |
July 3, 1973 |
**Please see images for:
( Certificate of Correction ) ** |
BALLISTIC COMPUTER
Abstract
A ballistic computer comprising a first section for computing
the ballistic levation angle signal by the mechanization of a power
series as a function of target range, the selected ammunition type,
and variations in firing conditions from standard values; and a
second section for computing a time of flight signal as the sum of
the ballistic elevation angle signal and target range, with the
scale factors of the summation circuit being a function of the
selected ammunition type.
Inventors: |
Marasco; Paul M. (Cherry Hill,
NJ), Frohock, Jr.; Millard M. (Thousand Oaks, CA),
McAdam, Jr.; William E. (Thousand Oaks, CA) |
Assignee: |
The United States of America as
represented by the Secretary of the Army (Washington, DC)
Hughes Aircraft Company (Culver City, CA)
|
Family
ID: |
22749911 |
Appl.
No.: |
05/202,449 |
Filed: |
November 26, 1971 |
Current U.S.
Class: |
235/404; 235/417;
708/802; 708/845 |
Current CPC
Class: |
G06G
7/80 (20130101) |
Current International
Class: |
G06G
7/00 (20060101); G06G 7/80 (20060101); G06g
007/26 (); G06g 007/80 () |
Field of
Search: |
;235/61.5R,61.5E,193,197
;89/41R |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Gruber; Felix D.
Claims
What is claimed is:
1. In a ballistic computer for providing fire control signals as a
function of a target range signal, an ammunition type signal
representative of a selected ammunition type, and signals
representative of nonstandard firing conditions and comprising
elevation angle generator means adapted to receive and responsive
to said target range signal, said ammunition type signal and said
nonstandard firing conditions signals, for producing a first signal
representative of the ballistic elevation angle for a selected
ammunition type and nonstandard firing conditions, and time of
flight generator means for producing a signal representative of the
time of flight for the selected ammunition and the nonstandard
firing conditions, wherein the improvement comprises said time of
flight generator means comprising: multiplication means for
multiplying said first signal and the target range signal by first
and second coefficient values, respectively, with said
multiplication means including means, adapted to receive and
responsive to said ammunition type signal, for selecting the values
of the first and second coefficients, respectively, as a function
of the selected ammunition type; and means for combining the
product signals from said multiplication means to produce a signal
representative of the time of flight for the given ammunition and
the nonstandard firing conditions.
2. In the ballistic computer of claim 1 wherein said multiplication
means includes a first amplifier coupled to receive the first
signal, means for selectively establishing the gain of said first
amplifier as a function of the signals representative of the
selected ammunition type; a second amplifier coupled to receive the
target range signal; and means for selectively establishing the
gain of said second amplifier as a function of the signal
representative of the selected ammunition type.
3. In the ballistic computer of claim 2 wherein said means for
combining includes a summing amplifier having input circuits
coupled to the output circuits of said first and second
amplifiers.
4. In a ballistic computer for providing fire control signals as a
function of a target range signal, and firing conditions signals,
the combination of:
means, adapted to receive and responsive to said target range
signal and said firing conditions signals, for producing a first
signal representative of the target range signal compensated for
the difference between the initial velocity value for a given
ammunition with nonstandard firing conditions, and an initial
velocity value for standard firing conditions;
means, adapted to receive and responsive to said target range
signal, and said firing conditions signals, for producing a second
signal representative of the target range signal compensated for
the difference between the drag value for the given ammunition with
the nonstandard firing conditions and a drag value for standard
firing conditions;
power series forming means responsive to said first and second
signals for forming a power series approximation of the ballistic
elevation angle signal for the given ammunition and nonstandard
firing conditions;
means, coupled to receive said first and second signals, for
forming a third signal as a function of the product of said first
and second signals;
multiplication means, coupled to said power series forming means so
as to receive said ballistic elevation angle signal and adapted to
receive said target range signal, and coupled to receive said third
signal, for multiplying said ballistic elevation angle signal, the
target range signal and said third signal by first, second and
third coefficient values, respectively; and
means for combining the product signals from said multiplication
means to produce a signal representative of the time of flight for
the selected ammunition and nonstandard firing conditions.
5. In the ballistic computer of claim 4 wherein said multiplication
means includes means, adapted to receive signals indicative of a
selected ammunition type, for selecting the values of the first,
second and third coefficients, respectively, as a function of the
selected ammunition type.
6. In the ballistic computer of claim 4 wherein said means for
producing the first signal includes means for producing a fourth
signal as a function of the product of the target range signal and
the difference between the initial velocity for a given ammunition
with the nonstandard firing conditions and an initial velocity
value for standard firing conditions; and wherein said
multiplication means includes means for multiplying said fourth
signal by a fourth coefficient value; and said combining means
includes means for combining the product signals resulting from the
multiplications by the first, second, third and fourth coefficients
to produce the signal representative of the time of flight for the
given ammunition and nonstandard firing conditions.
7. In the ballistic computer of claim 6 wherein said multiplication
means includes means adapted to receive signals indicative of a
selected ammunition type for selecting the values of the first,
second, third and fourth coefficients, respectively, as a function
of the the selected ammunition type.
Description
BACKGROUND OF THE INVENTION
The invention relates generally to ballistic computers and more
particularly to such computers which are adaptable for use with a
plurality of ammunition types, and which provide fire control
signals compensated for nonstandard firing conditions.
Some prior art ballistic computers have mechanized solutions to the
ballistic equations by simulating with analog function generators,
the functions associated with each set of nonstandard firing
conditions. For example, such prior art computers have incorporated
complex arrangements of nonlinear potentiometers, with switchable
pad networks employed to compensate for the nonstandard firing
conditions. Although this type of system has been in extensive use
for many years, it has inherent shortcomings from the standpoint of
reliability and cost effectiveness. Other systems have reduced
equipment complexity by using straight line approximations to
mechanize the superelevation and time of flight ballistic signals,
but this reduction in complexity has been at the cost of decreased
accuracy.
Recent advances in fire control computers, such as those described
in U.S. Pat. No. 3,575,085, have produced normalization techniques
whereby only a single nonlinear electronic function generator is
required for each ballistic signal; i.e., one function generator
associated with the superelevation signal, and another function
generator associated with the time of flight signal. This
normalization technique has significantly reduced the complexity
and increased the accuracy of fire control systems; however, an
important aspect of the subject invention is the recognition of the
fact that even further reductions in equipment complexity and
improved accuracy may be obtained by a power series mechanization
in accordance with the compensation techniques of the subject
invention.
SUMMARY OF THE INVENTION
It is therefore an object of the subject invention to provide an
improved ballistic computer of increased accuracy and reduced
equipment complexity.
A more specific object is to provide a ballistic computer of
reduced complexity which is adaptable for use with a multiplicity
of ammunitions and which provides accurate fire control signals
over a wide range of nonstandard firing conditions.
A further object is to provide an improved ballistic computer
wherein the time of flight signal for a particular selected
ammunition and nonstandard firing conditions is generated by a
relatively noncomplex scaling and summing mechanization.
Briefly, the invention involves the mechanization of the
superelevation signal by a power series of target range, with the
first order range term of the series being compensated for the
difference in the initial velocity of the round from a value for
standard firing conditions, and the second and higher order terms
being compensated for both initial velocity and drag effect
variations from standard condition values. The time of flight
signal is mechanized by means for forming the weighted sum of the
range signal, the superelevation signal, and intermediate terms
produced during the computation of the superelevation signal.
BRIEF DESCRIPTION OF THE DRAWINGS
The novel features of this invention, as well as the invention
itself, will be better understood from the accompanying description
taken in connection with the accompanying drawings in which like
reference characters refer to like parts and in which:
FIG. 1 is a block diagram of a fire control system having a
ballistic computer incorporating the concepts of the subject
invention;
FIG. 2 is a block diagram of a ballistic computer in accordance
with the subject invention;
FIG. 3 is a block diagram of the superelevation section of the
computer of FIG. 2;
FIG. 4 is a block and schematic diagram showing the sensor bridge
circuits of FIG. 3 in greater detail;
FIG. 5 is a block and schematic diagram of an amplifier-multiplier
arrangement suitable for use in the circuits of FIG. 3; and
FIG. 6 is a block diagram of the time of flight generator section
of the computer of FIG. 2.
DESCRIPTION OF THE PREFERRED EMBODIMENT
Reference is first directed to FIG. 1 which shows a fire control
system having a ballistic computer mechanized in accordance with
the concepts of the subject invention. As there shown, range finder
10 which may be a laser range finder, for example, provides target
range information to a computer 14. Control signals, such as those
indicative of the selected type and model of ammunition, are
applied to computer 14 from a control unit 16; and signals
representative of the normalized deviation of the firing conditions
from standard values are applied from sensor unit 18.
The subject invention is not limited to any particular type or
arrangement of fire control systems. For example, it is equally
applicable to the various configurations of disturbed, nondisturbed
or director type systems described in U.S. Pat. No. 3,575,085, as
well as other types of fire control systems. The fire control
system shown in FIG. 1 is of the disturbed type whereby the
computer's output signals control a sight drive unit 20. In this
arrangement the operator adjusts the gun positioning controls 22 to
maintain the target within the field of view of the sight; whereby
the gun is positioned at the proper elevation and deflection angle
for a target hit. The sight 12 is referenced either mechanically or
by means of servo systems, to the gun boresight axis; and the path
of the laser ranging beam may be referenced to the sight by means
of a common optical assembly, for example.
Reference is now directed primarily to FIG. 2 which shows the
computer 14 in greater detail. The range signal (R) and signals
representative of the deviation of firing conditions from standard
conditions are applied from the range finder 10 and sensor unit 18,
respectively, to superelevation generator section 30. In response
to these input signals, as well as to ammunition selection signals
applied from control unit 16, section 30 produces a superelevation
signal .epsilon.. The .epsilon. signal is applied to a coordinate
converter and output unit 32, and to a time of flight generator
section 34. The superelevation signal, .epsilon., sometimes
hereinafter referred to as the ballistic elevation angle signal, is
indicative of the initial elevation angle of the trajectory of the
shell with respect to the horizontal line of sight to the
target.
The superelevation signal as well as intermediate terms (R.sub.s
R.sub.m and RV) produced in the computation thereof and described
hereinafter relative to FIGS. 3 and 6, are applied to the time of
flight generator section 34 on composite lead 36. As used herein
the term "composite lead" means a plurality of individual
conductors, e.g. a cable, with each conductor being used for
applying a separate signal. In response to these signals and to the
target range term applied from laser range finder 10, unit 34
provides a signal, t.sub.f, representative of the time of flight of
the round to the target.
The t.sub.f signal is multiplied within a lead angle and windage
generator 42 by a term representative of the relative target and
wind rates. The relative target rate, .omega., is applied to
generator 42 from a rate sensor unit 38, and the wind value,
V.sub.w, from wind sensor unit 40. The resultant lead angle signal
produced by the multiplication of the t.sub.f and rate signals, is
combined within coordinate converter and output unit 32, with a
drift term K.sub.d .epsilon. which relates to the spin of the
round, to produce a combined drift term .eta.. .eta. is defined by
the equation: .eta. = (V.sub.w K.sub.w - .omega.) t.sub.f - K.sub.d
.epsilon. and the coefficients K.sub.w and K.sub.d are selected as
a function of the ammunition type. Further details of the
mechanization of the term .eta. are presented in U.S. Pat. No.
3,575,085. Also, as explained in the just cited patent, the terms
.eta. and .epsilon. may be processed through a coordinate
transformation unit, e.g., a CANT unit in tank applications; and
the output signals therefrom combined with other correction terms
such as a parallax term from parallax function generator 44 and
"jump" and "zeroing" terms. The output signals from coordinate
converter and output unit 32 are the deflection fire control
signal, D, and the elevation fire control signal E; which signals
are applied to sight drive unit 20 (FIG. 1).
The operation of the coordinate converter and output unit 32 is
summarized by the below two equations:
E = cos C - .eta. sin C + P.sub.E + J.sub.E + Z.sub.E (1)
d = .eta. cos C + .epsilon. sin C + P.sub.d + J.sub.D + Z.sub.D
(2)
where:
E = angle of sight reticle below boresight axis
D = angle of sight reticle to left of boresight axis
C = angle of Cant, left side of turret down
.epsilon. = "superelevation"
.eta. = "windage" + "drift" + "lead".
J.sub.E, J.sub.D ; Z.sub.E, Z.sub.D ; and P.sub.E, P.sub.D are
jump, zeroing and
parallax terms, respectively.
FIG. 3 illustrates one embodiment of superelevation generator
section 30 which mechanizes a cubic power series approximation of
the superelevation angle .epsilon., as a function of target range,
the selected ammunition and variations in firing conditions from
standard condition values. Also shown in FIG. 3 is one embodiment
of nonstandard conditions sensor 18 (FIG. 2) which comprises a
grain temperature sensor 64, and EFC control unit 60, an air
temperature transducer 68, air pressure transducer 74, bridge
circuits 52, 54 and 56 and a potentiometer 50. In accordance with
the illustrated embodiment, the superelevation signal, .epsilon.,
is mechanized in accordance with the equation:
.epsilon. = aR (1-V) + bR.sup.2 (1-V) (1 + A) + cR.sup.3 (1-V) (1 +
A).sup.2 (3)
and the time of flight signal, t.sub.f, is mechanized by the
equation:
t.sub.f = K.sub.T1 .epsilon. + K.sub.T2 R + K.sub.T3 R.sup.2 (1-V)
(1+A) + K.sub.T4 RV (4)
where V = .beta. + K.sub.Tg T + K.sub.gw EFC
a = .gamma. + k.sub.ta (T.sub.a - V) - T.sub.a + P
r.sub.s = R (1 - V)
r.sub.m = R (1 + A)
Hence equations (3) and (4) may be rewritten as
.epsilon. = aR.sub.s + bR.sub.s R.sub.m + cR.sub.s R.sub.m.sup.2 ;
and (5)
t.sub.f = K.sub.T1 .epsilon. + K.sub.T2 R + K.sub.T3 R.sub.s
R.sub.m + K.sub.T4 RV (6)
a, b, c, K.sub.T1, K.sub.T2, K.sub.T3, K.sub.T4, K.sub.tg,
K.sub.gw, and K.sub.ta
are coefficients dependent upon the ammunition type selected; and
.beta. and .gamma. are dependent of the model number of the
selected ammunition. T.sub.g, EFC, T.sub.a and P are normalized
deviations from standard values of grain temperature, gun wear, air
temperature, and air pressure, respectively. For example,
T.sub.a = [T.sub.a (.degree.K) - T.sub.aSTD
(.degree.K)]/[T.sub.aSTD (.degree.K)]
where T.sub.a is equal to the normalized difference between the
sensed air temperature, and the standard condition air temperature
for which the firing tables were derived.
The term V of Equation 3 is related to variations in the initial
velocity of the shell from an initial velocity value for standard
firing conditions. The coefficient, .beta., is dependent upon the
model number of the selected ammunition and compensates for the
difference in initial velocity of the various models within an
ammunition type. The term K.sub.Tg T.sub.g takes into consideration
the change in initial velocity due to the grain (powder)
temperature; with the ammunition dependent constant K.sub.Tg
providing the correct scale factor for each of the ammunition
types. The term K.sub.gw EFC compensates for changes in initial
velocity due to the effective full charge of the round resulting
from wear of the launch tube (gun barrel). For example, in the tank
fire control systems EFC has been defined as equal to (400 -
EFC;)/400 where EFC is equal to 400 - .SIGMA..DELTA.EFC, and
.SIGMA..DELTA.EFC is the accumulated wear of the barrel. As
explained in U.S. Pat. No. 3,575,085, .SIGMA..DELTA.EFC may be
computed as a function of the number of rounds fired by a
particular gun; with scale factors applied to take into
consideration the different types of ammunication fired -- i.e.
certain types of ammunition cause considerably greater gun wear
than other types. The ammunition dependent constant K.sub.gw
compensates for the differing effect of EFC on the initial velocity
of the various ammunition types.
The term A of Equation 3 relates to drag variations resulting from
differences in atmospheric conditions and ammunition
characteristics from standard values. The coefficient .gamma. is
dependent upon the particular model number of the selected
ammunition and compensates for differences in drag characteristics
between model numbers of the same ammunition type. The term
K.sub.Ta (T.sub.a - V) compensates for differences in atmospheric
drag due to variations in mach number, with K.sub.Ta being an
ammunition dependent constant. The terms T.sub.a and P correct for
drag variations due to air temperature and pressure changes,
respectively, and a scale factor coefficient is not associated with
the terms T.sub.a and P because in the illustrated embodiment the
value of such coefficients is approximately unity.
DETERMINATION OF COEFFICIENTS
Associated with each model number of each ammunition type is a set
of firing table which give "standard condition" values of .epsilon.
and t.sub.f for each value of range (usually at 100 meter
intervals). Standard condition values could be, for example,
21.degree. C, 15.degree. C, and 0.0765 lbs./ft..sup.2 for grain
temperature, air temperature and air pressure, respectively. The
standard condition for gun wear (EFC) is a new gun tube.
Additionally, "unit effect" and/or "unit correction" tables give
the delta effect on .epsilon. and t.sub.f of deviations of air
temperature, air pressure, and muzzle velocity from "standard
conditions" at selected range intervals, such as at 250 meter
intervals. Additional data relates grain temperature and gun wear
(EFC) to muzzle velocity.
For many applications, such as the 105mm tank gun, not only are
several ammunition types used but also there are different models
of each type. Although the ammunition developers usually try to
match the ballistics within a given ammunition type, this is not
always accomplished. However, the basic "shape" of the trajectory
is maintained and only corrections to the computation of .epsilon.
and t.sub.f are required to accommodate variations between models
of the same ammunition type.
The first step in deriving the above listed ammunition dependent
constants is to select a model number of a given type of ammunition
which will be considered the primary model for that type, and for
which the primary coefficients will be developed. Using the
standard condition firing tables of .epsilon. versus R in the range
interval of interest, such as from 500 meters to 3,000 meters, for
example, the values of a, b, and c are determined by the
"least-squares-fit" technique and the equation:
.epsilon. = aR + bR.sup.2 + cR.sup.3
The least-squares-fit technique is explained in Volume 1, Chapter
2, of the text "The Approximation of Functions" by John R. Rice,
Addison Wesley Publishing Company, 1964.
Step 2 is to use the standard condition t.sub.f versus R data to
solve for coefficients K.sub.T1, K.sub.T2, and K.sub.T3 by the
least-squares-fit technique in the equation:
t.sub.f = K.sub.T1 (aR + bR.sup.2 + cR.sup.3) + K.sub.R2 R +
K.sub.T3 R.sup.2.
In step 3 the "unit effect" tables for the selected primary model
are used to obtain a table of .DELTA..epsilon. versus R for a unit
change in air temperature. Then the unit value of T.sub.a .ident.
T.sub.a (.mu.) is derived in accordance with the equation, T.sub.a
(.mu.) = (unit change in T.sub.a (.degree. C)/288; and the value of
K.sub.Ta is determined by the least-squares-fit technique from the
equation:
.DELTA..epsilon..sub.(T2) = [bR.sup.2 + 2cR.sup.3 ] [T.sub.a
(.mu.)] [K.sub.Ta - 1]
In step 4 the unit effect tables for the primary model are used to
obtain the table of .DELTA..epsilon. versus R for a unit change in
muzzle velocity .ident..DELTA.V (.mu.). A term K.sub.V is derived
by using the least-squares-fit technique and the following
equation
.DELTA..epsilon..sub.(v) = -K.sub.v .DELTA.V(.mu.) [aR + bR.sup.2 +
cR.sup.3 + K.sub.Ta bR.sup.2 + 2K.sub.Ta cR.sup.3 ]
For step 5 the "unit effect" tables for the primary ammunition
model are used to obtain a table of .DELTA.t.sub.f versus R for a
unit change in muzzle velocity. Thus the value of the coefficient
K.sub.T4 is obtained by the least-squares-fit technique and the
following equation:
.DELTA.t.sub.f = K.sub.v .DELTA.V(.mu.) [K.sub.T4 R - K.sub.T1 (aR
+ bR.sup.2 + cR.sup.2 + K.sub.Ta bR.sup.2 + 2K.sub.Ta cR.sup.3
-K.sub.T3 (R.sup.2 + K.sub.ta R.sup.2)]
In step 6 the ballistic tables are used to derive a linear function
of muzzle velocity with T.sub.g in accordance with the
equation:
.DELTA.V.sub.o = m(T.sub.g)
then
K.sub.Tg = mK.sub.v
In step 7, a linear function of muzzle velocity with EFC is derived
from the gun data and the equation:
.DELTA.V.sub.o = h (EFC)
then
K.sub.gw = hK.sub.v
During step 8 using the standard condition .epsilon. versus R data
for a secondary model of the particular ammunition type and
employing the least-squares-fit technique, the coefficients .beta.
and .gamma. are determined for the secondary model number of the
particular ammunition type in accordance with the equation:
.epsilon. = (1 + .beta.) [aR + bR.sup.3 (1 + .gamma.) + cR.sup.3
(1+ .gamma.).sup.2 ].
Step 8 is repeated for each model number of the particular
ammunition type; and steps 1 through 8 are repeated for each
ammunition type.
Returning now to an analysis of Equation 3, it is noted that the
first term of the equation is a first order function of target
range compensated for first order variations in the shell's initial
velocity; that the second term of the equation is a quadratic
function of range with a first order correction for variations in
initial velocity and for variations in atmospheric drag; and that
the third term is a cubic function of range having a first order
correction for initial velocity variations and a quadratic
correction for variations in drag characteristics. In applications
where greater accuracy is desired the equation may be carried out
to additional terms. For example, the fourth term of the equation
would have range to the fourth power with a first order correction
for initial velocity, and a cubic drag compensation term.
The mechanization of the superelevation term, .epsilon., in
accordance with an embodiment relating to Equation 3 above, is
shown in FIG. 3. Terms R.sup.. EFC; R.sup.. T.sub.g ; RT.sub.a ;
and RP are mechanized by potentiometer circuit 50, bridge circuits
52 and potentiometer circuits 54 and 56, respectively. These
circuits are shown in greater detail in FIG. 4 to which reference
is now momentarily directed. The range signal R is applied from a
buffer amplifier 58 (FIG. 3) to the EFC potentiometer 50 and to
circuits 52, 54 and 56.
The EFC control unit 60 positions the wiper of potentiometer 50 as
a function of the number and type of rounds previously fired by the
gun; and the signal from the wiper is applied through an amplifier
62 to provide an output signal equal to R EFC.
The grain temperature bridge 52 includes a temperature sensitive
thermistor element 63 as one of the resistance elements of the
bridge; and the difference between the signal level from the two
output terminals of bridge 52 is formed within differential
amplifier 66 to provide the term R T.sub.g.
The wiper of the potentiometer of the air temperature circuit 54 is
positioned by an air temperature transducer 68; and the standard
condition air temperature value, as represented by the signal at
tap 69, is subtracted from the signal from the wiper in a
differential amplifier 70 to provide the term R T.sub.a. Similarly,
the term R P is formed by potentiometer circuit 56 and differential
amplifier 72, with the wiper of potentiometer 56 being positioned
by an air pressure transducer 74.
It is noted that in the formation of the terms R T.sub.g, R
T.sub.a, and RP the division operation required for normalization
by the standard value is performed by the gain selected for the
associated differential amplifier. For example, in regard to the
term T.sub.a, the gain of amplifier 70 is selected to perform the
operation 1/T.sub.a (Std.).
Returning now to FIG. 3, the terms R T.sub.g, R and R EFC are
multiplied by the factors K.sub.Tg, .beta., and K.sub.gw in
multipliers 76, 78 and 80 respectively. The output signals from
units 76, 78 and 80 are summed by summing amplifier 82 to provide
the term R V of Equation 3. Since the terms K.sub.Tg .beta., and
K.sub.gw are a function of the ammunition selected, the multipliers
76, 78 and 80 are mechanized as a function of the ammunition
selection. For example each of these multipliers could be an
operational amplifier arrangement in which an appropriate value of
feedback resistance is selected in response to the ammunition
selection signals (not shown in FIG. 3) applied from control unit
16 (FIG. 1). One such device suitable for performing the
multiplication functions indicated in FIG. 3 is shown in FIG. 5.
The gain (multiplication factor) of amplifier 81 is established by
the ratio of the feedback resistor 83 to the input resistor 85. The
feedback resistor is selected by the ammunition selection signals
applied to FET switches 87. The output signals from units 76, 78
and 80 are summed by summing amplifier 82 to provide the term R V
of Equation 3.
Again considering FIG. 3, the term R V is subtracted in amplifier
83 from the term RT.sub.a and the output signal therefrom is
multiplied by the term K.sub.Ta within a multiplier 84. Also, the
range signal is multiplied by the term .gamma. in multiplier 86 and
the output signal therefrom is combined in amplifier 88 with the
terms (RT.sub.a - RV), T.sub.a and RP to form the term RA =
R[.gamma. + K.sub.Ta (T.sub.a - V) - T.sub.a + P].
The term RV from amplifier 82 and the target range signal are
applied as input signals to a summing amplifier 90, which produces
the output signal R(1 - V); equal by definition to R.sub.s. The
term R.sub.s is multiplied by the scaling factor "a" in
multiplication unit 92 to form the first term of Equation 5, i.e.,
aR(1 - V) .ident. aR.sub.s.
In a similar manner the term RA is combined with the target range
signal within a summing amplifier 94 to produce the term R(1 + A)
.ident. R.sub.m. The term R.sub.m is applied through a demodulation
unit 95 to the control input terminal of a master time division
multiplier 96. Master time division multiplier 96 controls two
slave multipliers 98 and 100. One type of suitable time division
multiplication arrangement is shown in FIG. 25 of U.S. Pat. No.
3,575,085; however, any suitable multiplication arrangement may be
utilized instead of multipliers 96, 98 and 100. The master unit 96
of FIG. 3, provides a chain of output signal pulses whose duty
factor is controlled as a direct function of the magnitude of the
input signal to the master multiplication unit. The output signal
pulses from the master unit are applied to one or more slave units,
such as 98 and 100 in FIG. 3; and the output signal from a slave
unit is equal to the average value of a chain of pulses whose duty
factor is controlled by the master unit and whose amplitude is a
direct function of the second input signal applied to the slave
unit. Hence the output signal from a slave unit is equal to the
product of the signal applied to the master and the second input
signal applied to the slave unit.
Considering first slave multiplier 98 of FIG. 3, the term R.sub.s
is applied as the multiplicand input signal and the term R.sub.m
from master unit 96, as the multiplier input term. The product
signal from slave unit 98, therefore, is R.sub.s R.sub.m and this
signal is multiplied by the coefficient "b" in multiplier unit 103
to form the second term of Equation 5, i.e., bR.sub.s R.sub.m.
The output signal from slave multiplier 98 is also applied as the
multiplicand input signal of slave multiplier 100 wherein it is
multiplied by the term R.sub.m to produce the output signal
therefrom R.sub.s R.sub.m.sup.2. The output signal from slave
multiplier 100 is multiplied by the coefficient "c" in multiplier
unit 104 to form the third term of Equation 5, i.e., cR.sub.s
R.sub.m.sup.2. The output signals from multipliers 92, 103 and 104
are combined within suming amplifier 106 to form the sum indicated
by Equation 5, i.e., the superelevation (ballistic elevation
angles) signal, .epsilon..
An important advantage of the subject invention relates to the
mechanization of the time of flight signal by scaling and combining
the superelevation signal, the target range signal, and
intermediate terms produced during the computation of the
superelevation signal. One such embodiment of time of flight
generator 34 (FIG. 2) is shown in FIG. 6 as comprising a group of
multiplier units 108 through 111 and a summing amplifier 112. Unit
108 multiplies the superelevation signal, .epsilon., by the
coefficient K.sub.T1 ; unit 109 multiplier target range, R, by
K.sub.T2 ; unit 110 multiplies the output signal from slave
multiplier 98 (FIG. 3), R.sub.s R.sub.m, by K.sub.T3 ; and unit 111
multiplies the output signal from summing amplifier 82 (FIG. 3), RV
by K.sub.T4. Summing amplifier 112 combines the output signals of
multiplier 108 through 111 to form the signal t.sub.f in accordance
with the Equation 6 wherein
t.sub.f = K.sub.T1 .epsilon. + K.sub.T2 R + K.sub.T3 R.sub.s
R.sub.m + K.sub.T4 RV.
As explained above, the coefficients K.sub.T1 , K.sub.T2, K.sub.T3,
and K.sub.T4 are dependent on the ammunition type selected, and the
scale factors of multipliers 108 through 111 are set in response to
ammunition selection signals applied from unit 16 of FIG. 1. The
ammunition selection portion of computer controls unit 16 may
comprise a four position switch which applies an enable signal to
one of four output leads, in accordance with the ammunition type
manually selected. The four output leads from said switch are
coupled in parallel to each of the multipliers 108 through 111 on a
composite lead (cable) 107. The multipliers 108 through 111 may be
of the type described above relative to FIG. 5.
The effects on the time of flight due to variations in initial
velocity and drag from standard values are partially compensated by
the term .epsilon. of Equation 6. The mechanization of the terms
K.sub.T3 R.sub.s R.sub.m, and K.sub.T4 RV provides a better
approximation of the t.sub.f signal for the selected ammunition and
nonstandard firing conditions. However, for many applications, the
signal t.sub.f can be approximated to sufficient accuracy by the
equation: t.sub.f = K.sub.T1 .epsilon. + K.sub.T2 R and for these
instances multiplier 110 and 111 of FIG. 6 and their associated
connections may be eliminated.
In the disclosed embodiment, the superelevation signal, .epsilon.,
is implemented by the mechanization of a cubic order power series
of range. Although a cubic order series has been determined to be
adequate for certain type of applications, such as tank fire
control systems for example, it should be understood that the
invention is not restricted to power series of any particular
order, and that the series may be modified in accordance with the
concepts of the inventions to include as many terms as required for
the desired degree of accuracy.
Hence, there has been described a novel ballistic computer of
increased accuracy and reduced equipment complexity. These
advantages are obtained by mechanization of the superelevation
signal (ballistic elevation angle signal) for a given ammunition
type and model number by a power series of target range terms
modified to compensate for nonstandard firing conditions; and by
mechanizing the time of flight signal as the sum of the range
signal, the superelevation signal, and intermediate terms produced
during the computation of the superelevation signal, scaled as a
function of the given ammunition type.
* * * * *