US 3743818 A
A ballistic computer comprising a first section for computing the ballistic elevation 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.
Description (OCR text may contain errors)
. 1 i ea 397439818 1 it.
United Stat a Marasco et al. U I a July 3, 1973 1 41 BALLISTIC COMPUTER 3.426.357 2/1969 Paulus 23s/193x 1751 Mammary Hm, Ni; 3,551,238 #511313 352F232... 235%? Millard -F h- M William E 3,339,457 7/1967 Pun 23s/61.s R
McAdam, Jr., both of Thousand Oaks, Calif.
 Assignees: The United States of America as Primary Examiner-Felix D. Gruber "Presented y the wretary of the A t'torney W. H. MacAllister, Jr. and Lawrence V.
Army, Washington, DC. by said Li k J,- et Marasco; Hughes Aircraft Company,
Culver City, Calif. by said Frohock and McAdam 221 Filed: Nov. 26, 1971 21 Appl. No.2 202,449
[5 '7] ABSTRACT A ballistic computer comprising a first section for computing the ballistic elevation angle signal by the mecha- 52] CL 235/615 R, 235/615 nization of a power series as a function of target range,
$235119} the selected ammunition type, and variations in firing 51 Int. Cl. G06g 7/26, (566 7/80 cnditins fmm Standard Values; and sewn! Swim 581 Field 61 Search 235/6l.5 R, 61.5 E, m time of flight Signal a the Sum of the 235/193, 197; 89/41 R ballistic elevation angle signal and target range, with the scale factors of the summation circuit being a func- 56] References Cited tion of the selected ammunition type.
UNITED STATES PATENTS 3,591,790 7/1971 Couture.. 235/193 7 Claims, 6 Drawing Figures Ammunition Select a R R ,RV
Superelevotion Time of R Generator Flight -+-R Section Section Norrsmndord Conditions oo d Lead Angle Sensors COfiVeTlBF 9 and Windoge Output Unit Generator J fi i g. Rate Wind ig Sensor Sensor Patented July 3, 1973 3 Sheets-Sheet 2 d :2 Jo
BALLISTIC COMPUTER 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 tire 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 sumof 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 tire 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 ized deviation of the firing conditions from standard values are applied from sensor unit 18. I
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 sys tern shown in FIG. 1 is of the disturbed type whereby the computers output signals control a sight drive unit 20. In this arrangement the operator adjusts the gun po-.
sitioning 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; I and the path of the laser ranging beam may be referenced to the sight by means of a common optical asv sembly, 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 l0 and sensor unit [8, 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 e. The e signal is applied to'a coordinate converter and output unit 32, and to a time of flight generator section 34. The superelevation signal, e, sometimes hereinafter referred to as the ballistic elevation angle signal, isrindicative 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,R,, 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,, representative of the time of flight of the round to the target.
The r, 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, to, is applied to generator 42 from a rate sensor unit 38, and the wind value, V,,,, from wind sensor unit 40. The resultant lead angle signal produced by the multiplication of the t, and rate signals, is combined within coordinate converter and output unit 32, with a drift term K e which relates to the spin of the round, to produce a combined drift term 1 1 is defined by the equation: 1; (V,, K,, w) t, K e and the coefficients K and K,, are selected as a function of the ammunition type. Further details of the mechanization of the term '1; are presented in U.S. Pat. No. 3,575,085. Also, as explained in the just cited patent, the terms 1; and c 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=cosC1;sinC+P +J +Z D=ncosC+esinC+P +J +Z 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, 6, is mechanized in accordance with the equation:
e=aR (1-V)+bR(l-\Z) (l +A)+cR (1V) (l A) and the time of flight signal, I is mechanized by the equation:
t,= K e K R K R (l-V) (1+1) K RV I-Ience equations (3) and (4) may be rewritten as e aR, bR R cR,R,,, and
11, 12, n 14, m ara and m are coefficients dependent upon the ammunition type selected; and B and 'y are dependent of the model number of the selected ammunition. T EFC, T, and F are normalized deviations from standard values of grain temperature, gun wear, air temperature, and air pressure, respectively. For example,
o a 0 aSTD )]I[ aSTD where T, 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, [3, 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 T, takes into consideration the change in initial velocity due to the grain (powder) temperature; with the ammunition dependent constant K providing the correct scale factor for each of the ammunition types. The term K FIT, 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 EFG has been defined as equal to (400 EFC,')/400 where EFC is equal to 400 EAEF C, and EAEF C is the accumulated wear of the barrel. As explained in U.S. Pat. No. 3,575,085, EAEFC 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 compensates for the differing effect of EFG 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 y 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 (T, V) compensates for differences in atmospheric drag due to variations in mach number, with K being an ammunition dependent constant. The terms T and F correct for drag variations due to air temperature and pressure changes, respectively, and a scale factor coefficient is not associated with the terms T and F 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 conditionvalues of e and t, for each value of range (usually at 100 meter intervals). Standard condition values could be, for example, 21 C, C, and 0.0765 lbs/ft. for grain temperature, air temperature and air pressure, respectively. The standard condition for gun wear (EF C) is a new gun tube. Additionally, unit effect and/or unit correction tables give the delta effect on e and t, 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 (EF C) 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 fshape of the trajectory is maintained and only corrections to the computation of e and t, 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 6 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:
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, versus R data to solve for coefficients K K and K by the least-s'quares-fit technique in the equation;
In step 3 the "unit effect" tables for the selected primary model are used to obtain a table of Ae versus R for a unit change in air temperature. Then the unit value .of T 1 T 1.) is derived in accordance with the equation, T, (u) (unit change in T C)/288; and the value of K is determined by the least-squares-fit technique from the equation:
In step 4 the unit effect tables for the primary mode] are used to obtain the table of Ae versus R for a unit change in muzzle velocity E AV(p.). A term Kv is derived by using the least-squares-fit technique and the following equation For step 5 the unit effect tables for the primary ammunition model are used to obtain a table of At, versus R for a unit change in muzzle velocity. Thus the value of the coefficient K is obtained by the leastsquares-fit technique and the following equation:
In step 6 the ballistic tables are used to derive a linear function of muzzle velocity with T, in accordance with the equation:
Av, m T,
Tn v In step 7, a linear function of muzzle velocity with EFC is derived from the gun data and the equation:
AV, h (EFC) then K hit,
Step 8 is repeated for each model number of the particular ammunition type; and steps 1 through time repeated for each ammunition type. I
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 thefourth power with a first order correction' for initial velocity, and a'cubic drag co'mpensa- 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 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 Similarly, the term R R 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,, R T,,, and RF 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 the gain of amplifier 70 is selected to perform the operation I/T,,(Std.). Returning now to FIG. 3, the terms R T,,, R and R EFC are multiplied by the factors K 5, and K 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 I of Equation 3. Since the terms K B, and K,,,, 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 I is subtracted in amplifier 83 from the term RT and the output signal therefrom is multiplied by the term Kmwithlin a multiplier 84. Also, the range signal is multiplied by the term 7 in multiplier 86 and the output signal therefrom is combined in amplifier 88 with the terms (RT, RV T, and RF to form the term RA My K,,,( T, V)
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(l V); equal by definition to R,. The term R, is multiplied by the scaling factor a" in multiplication uni t 92 to form the first term of Equation 5, i.e., aR(I V) I aR,.
In a similar manner the term RA is combined with the target range signal within a summing amplifier 94 to produce the term R(l A) s R,,,. The term R,, 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 US. 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, is applied as the multiplicand input signal and the term R,,, from master unit 96, as the multiplier input term. The product signal from slave unit 98, therefore, is R, R,,, and this signal is multiplied by the coefficient b in multiplier unit 103 to form the second term of Equation 5, i.e., bR, R,,,.
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,, to produce the output signal therefrom R, R,,,*. 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, R,,,*. 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, e.
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, 6, by the coefficient K unit 109. multiplier target range, R, by K unit 110 multiplies the output signal from slave multiplier 98 (FIG. 3), R, R,,,, by K and unit 111 multiplies the output signal from summing amplifier 82 (FIG. 3), R7 by K Summing amplifier 1 12 combines the output signals of multiplier 108 through 111 to form the signal t, in accordance with the Equation 6 wherein t K1 K R. R, K RV- As explained above, the coefficients K K K and K 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 of Equation 6. The mechanization of the terms K R, R,,,, and K RV provides a better approximation of the t, signal for the selected ammunition and nonstandard firing conditions. However, for many applications, the signal t, can be approximated to sufficient accuracy by the equation: t;= K 6 K 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, e, 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.
What is claimed is:
1. In a ballistic computer for providing fire control signals as a function of a traget range signal, an ammunition type signal respresentative 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 theballistic 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 sig-' nals, 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 difierence 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.
* =l l l UNITED STATES PATENT OFFICE Patent No. 3 Dated July 3, 1973 lnventofls) Paul M. Mar'asco et a1.
above-identified patent t error appears in the d as shown below:
It is certified the ereby correcte and that said Letters Patent are h F Col. 1, before "Background of the Invention" insert the '1 following paragraph: The invention claimed herein was made in the subcontract thereunder course of or under a contract or with the United States Army.-- Col. 3, line 40, equation 1, insert -e-- before "cos".
Signed and sealed this 5th day of March 19 714..
(SEAL) Attes t2 7 v c MARSHALL DANN Commissioner of Patents EDWARD M.FLETC HEJR JR. Atte sting Officer