US3526754A

US3526754A - Control apparatus

Info

Publication number: US3526754A
Application number: US741716A
Authority: US
Inventors: Hans Max Ingfried Graefe; Rolf Dieter Pfeiffer; Helmut Heinrich Spahn
Original assignee: Honeywell GmbH
Current assignee: Honeywell GmbH
Priority date: 1968-07-01
Filing date: 1968-07-01
Publication date: 1970-09-01
Anticipated expiration: 1987-09-01

Description

Sept. 1, 1970 H. M. l. GRAEFE ETAI- 3,526,754

CONTROL APPARATUS 3 Sheets-Sheet 1 Filed July 1, 1968 INVENTORS HANS MAX INGFRIED GRAEFE ROLF DIETER \PFEIFER HELMUT HEINRICH SPAHN BY ATTORNEY S pt 1 H. M. l. GRAEFE ET AL CONTROL APPARATUS Filed July 1, 1968 5 SheetsSheet 2 FIG. '4

INVENTORS HANS MAX INGFRIED GRAEFE ROLF DIETERPFEIFER HELMUT HEINRICH SPAHN MLM ATTORNEY United States Patent Cffice 3,526,754 Patented Sept. 1, 1970 US. Cl. 235-615 11 Claims ABSTRACT OF THE DISCLOSURE A dynamic biaxial lead computer for the lateral and vertical lead angles of tank-mounted anti-aircraft guns.

SUMMARY OF THE INVENTION The present invention pertains to the field of geometrical instruments and, more particularly, to automatic gun movement compensators.

The present invention is intended for use with fire control systems including a biaxially directionable weapon and a biaxially directionable sight or fire director, both mounted on a mobile platform such as a tank or ship, and interconnected electrically as by servo systems such that the sight line determines the weapon line of fire.

The present disclosure concerns a lead angle computer to be interposed in the electrical interconnections to automatically provide an angle of lead between the weapon line of fire and the sight line to compensate for target speed, direction, projectile speed, and projectile ballistics or trajectory.

The present invention provides a lead angle computer especially suited to anti-aircraft guns, mounted on tanks or ships, which are directed toward and which follow a moving target. The invention evaluates the necessary lead angles with respect to the sight line. The lead angle can be computed by using the lateral lead angle together with the vertical lead angle or the lateral lead angle together with the whole elevation angle. The target may be aligned with the sight by means of a directioning handle positioned by the operator. Movements of the supporting frame as would be found with ship or tank mounting can be compensated for by an automatically operating target holding system.

The automatic target holding system would be a necessary element in an application of the present invention wherein an anti-aircraft weapon is mounted on a rotatable turret containing a primary weapon. For this embodiment, it is desired that the secondary weapon be turned and elevated without regard to the motion of the turret which directs the primary weapon. The fire director or sight is also mounted on the turret. The stabilization system provides that the line of sight remains stable with respect to a space reference in spite of turret or vehicle movements without requiring corrections by the gun operator.

It is, of course, also desired that the method of stabilization not affect operation and direction of the weapon by the operator. To this end, the preferred embodiment utilizes direct stabilization of the fire director which in turn maintains the weapon in alignment. The system consists of a directioning handle affected by gyros necessary for stabilization controlling the fire director or sight. The lead angle computer is connected between the fire director and the weapon directing mechanism.

The lead angle is computed in two components, the lateral lead angle 6 and the vertical lead angle 6 For purposes of determination it is assumed that the target moves with a constant V along a straight line path and that the projectile follows a straight line path with a decreasing speed, determinable from a firing table for the particular kind of ammunition used. Curvature of the path of the projectile under the influence of gravity is compensated for by enlarging a to allow for the ballistic super elevation A6.

The average projectile speed V due to the decreasing instantaneous speed, depends on the distance e which the projectile must travel to reach the target.

According to the invention, transducers generate signals proportional to the angular rates of the sight line in the lateral direction (C and the vertical direction (C In one embodiment of the invention, the signals are produced by a rate gyro firmly aligned with the sight line. The rate gyro for the lateral angular speed simultaneously follows the turning motion in the vertical direction. An alternate embodiment derives the signals from a directioning handle for the sight line.

The angular rate signals are combined with signals proportional to the target distance e along the sight line r and the average projectile speed V for determination of the vertical and lateral lead angles 6 and 6 of the weapon with respect to the sight line which is assumed to be constantly directed to the target. The lateral and vertical lead angle equations are e sin 6 C' (1) and For small lead angles:

cos 6 1 sin 6 5 The equations for the lateral and vertical lead angles therefore become and sin 6 sin 58 K cos 0 For small angles 5 a N a K cos 0 cos a H is the elevation angle of the weapon with respect to the turning plane of the turret and B is the elevation angle of the sight line with respect to the turning plane of the turret.

The invention provides a method of continuous evaluation of the target distance e. An integration arrangement is used wherein the initial distance e is adjusted and the distance thereafter is computed depending on the angle a of the sight line r with respect to the line at the time of initial distance estimate. The instantaneous distance with respect to the initial distance is computed according to the equation care of by the. stabilization system.

An important feature of the present invention lies in the fact that evaluation of the lead quantities not only considers motions of the sight line in following the target but also that when the target is kept along the sight line, the lead quantities are automatically corrected for rotational motions of the vehicle around the sight line. Turning motions of the vehicle around other axes are taken An additional feature of the present invention lies in the modification of the vertical lead angle 6 of the weapon to allow for the ballistic super-elevation A of the munition:

wherein g=earths acceleration,

6 =the elevation angle of the sight line with respect to the turning plane of the turret carrying the weapon,

e=target distance along the sight line r, and

v =average projectile speed along the projectile path.

With consideration of the ballistic super-elevation, the total vertical lead angle 6 becomes It is evident from

Equations

1 and 2 that the target diestance enters proportionally into the evaluated lead angles. Errors in distance (dependent on measurement of the initial distance e alfect the lead angle in their full magnitude. The present invention provides an improvement whereby the hit probability may be increased to allow for inaccuracies in the distance measurements. A periodically varying signal is heterodyned to the calculated lead signals. The periodically varying signal is of such an amplitude to cause sweeping of the target area to allow for errors in distance measurement.

The objects of the present invention are:

To provide apparatus for and methods of fire control for ordnance devices, particular anti-aircraft ordnance.

To provide apparatus for and methods of computation of lead angles for anti-aircraft weapons.

To provide a lead computer having means for continuous evaluation of the target distance.

To provide a lead computer which corrects for rotational motions of a gun platform about the axis of the sight line.

To provide means for modification of the vertical lead angle to allow for the ballistic super-elevation of the munition.

To provide means for increasing the hit probability to allow for inaccuracies in distance measurements.

Other advantages of the present invention will become apparent from the specification taken in connection with the drawings.

In the drawings the following reference symbols are used to facilitate an understanding of the invention.

Z position of the target at the moment of firing r sight line at the moment of firing e target distance along the sight line P position of the weapon T point at Which the projectile contacts the target s projectile path 2 projectile flight distance along s t projectile flight time v average projectile speed v target speed (assumed constant) AE turning plane of turret BE reference plane defined by sight line r and a line perpendicular to the line r, at point P, in plane AE. This plane is seen as a line parallel to the turning plane AE of the turret when viewed along the sight line r. (horizontal line in a cross hair sight) a angle passed by sight line with respect to sight line position at time of initial distance C input FE plane defined by target path f and weapon position A angle between target path 1 and field of view plane GE 0 elevation angle of sight line with respect to turning plane of turret 6 total lead angle between projectile path s and sight line r a lateral lead angle component 8 vertical lead angle component 0 elevation angleof weapon with respect tothe turning plane of the turret K inclination angle of projection of target path 1 on plane GE with respect to reference plane BE.

FIG. 1 is a view perpendicular to plane FE;

FIG. 2 is a spatial representation of the pertinent geometry necessary for an explanation of the invention;

FIGS. 3A and 3B represent the field of view of the gun pointer as seen through the sight with mutually perpendicular cross hairs F and F FIG. 4 is a vector diagram illustrating the geometrical addition of two perpendicular components of the directioning signal C; and,

FIG. 5 is a block diagram of the preferred embodiment of the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT In the preferred embodiment shown in FIG. 5, a signal C proportional to the lateral angular speed of the sight line is applied to an input terminal 1. A signal C proportional to the vertical angular speed of the sight line is connected to an input terminal 2.

Inputs

1 and 2 are further connected to the input of a geometrical addition circuit 3 having an output lead 4. Output lead 4 is further connected to the input of an integrator circuit 5 having an output connected to a sine transformer 8 by lead 31. The output of sine transformer 8 is connected by lead 32 to a first input of a divider circuit 9 having an output lead 26 and a second input.

An input terminal 30 is connected to a constant signal source U Input terminal 30 is connected to the input of an integrator circuit 7, the output of which is connected by means of a lead 33 to one of two inputs of a multiplier circuit 6. A lead 34 connects output terminal 4 of circuit 3 to the second input of the multiplier circuit 6. The output of multiplier circuit 6 is connected through a lead 35 to the second input of divider circuit 9'. The output of divider circuit 9 is connected to a first input of a multiplier circuit 11 through a lead 26.

An input terminal 10 is connected to a signal 2 proportional to the initial range of the target. Input terminal 10 is further connected to a sine modulator 12 having an output lead 27 connected to a second input of multiplier circuit 11. The output of multiplier circuit 11 is connected to the input of a non-linear circuit 13 by means of lead 36-. The output of non-linear circuit 13 is connected to a first input of a multiplier circuit 14 (having a second input) through a lead 37. A lead 38 connects input terminal 1 to the second input of a multiplier circuit 14. The output of multiplier circuit 14 is connected to an input of a divider circuit 20 through a lead 39.

A mechanical input 16 to a resolver 17 is driven by the elevation mechanism of the sight. The output of resolver 17 is coupled to a demodulator circuit 18 through a lead 40. The demodulator circuit 18 output is connected to an amplifier circuit 22 through a lead 41. The output of demodulator circuit 18 is also coupled through a lead 19 to a second input of divider circuit 20. The output of divider circuit 20 is conducted through a lead 21 to the turret drive to align the weapon with reference to the sight line in accordance with the calculated lateral lead angle.

The output of amplifier 22 is connected through a lead 24 to an input of a summing amplifier 23. A second input of summing amplifier 23 is connected to the second input terminal for the vertical angular speed signal through a lead 25. The output of summing amplifier 23 is connected through a lead 42 to an input of a multiplier circuit 15. A second input to multiplier circuit 15 is connected to the output of non-linear amplifier 13 through a lead 43. The output of multiplier circuit 15 is conducted through a lead 28 to the elevation mechanism for the weapon to control the elevation with respect to the sight line in ac cordance with the calculated vertical lead angle.

OPERATION With reference to FIG. 1, the distance 1 traveled by the target during the time of projectile flight along the path s and the average projectile speed VG may be computed in the following equations:

f=l l=vzG (7 Referring to FIG. 2, the following lead angle relations can be derived:

DZ s1n 6 HG cos A cos x (9) It will be noted that

Equations

8 and 9 for the lead angles and 5 have no dependence upon the position of the weapon or the elevation angle H When following a target through the optical sight, the target speed vector V is projected on the field of view plane GE. The apparent velocity as seen through the optical sight is therefore v cos A where A is the angle of the target path with respect to the view plane GB. The angular speed of the sight line is determined by dividing the projection of the speed on the view plane by the associated radius distance, in other words, the target distance e. The angular speed therefore becomes COS 5 Uz-COS A and must be proportional to the total directioning signal C for the weapon to track the target:

7)z-COS A e (10) 2)z-0OS A sin 1:

v -cos A cos K e 12 Rearrangement of these equations yields:

v cos A. sin K=CH. (11a) v cos A. cos K=Cs.6 (12a) Equations 11a and may be substituted into the lead angle Equations 8 and 9:

Because the lead angles are small, the following approXimations can be made:

and

sin 8: 6

The final equations for the lead angle components are then 5H CH o and where e =initial distance,

t=time,

C=total directioning signal composed of two perpendicular components, and

r=total angle passed by the sight line since the beginning of calculation.

The total angle through which the sight line is rotated t =f Cat The total directioning signal C is c= Cs +CH (4b) The initial distance e corresponds to an amplification factor in the computer. When the initial value of the distance is available, the amplification factor is adjusted and the distance calculation starts at the time t=0.

Still unknown in the speed angle equation is the projectile speed v dependent on the kind of ammunition and on the distance e the projectile must travel. For a particular kind of ammunition, the projectile speed v will depend on the target distance e along the sight line, the position A of the target path with relation to the weapon position and the speed v of the target. A reasonable approximation formula for the relation between the sight line distance e and the projectile speed v arrived at through calculations of the projectile speed for realistic values of e, v and A is The left side of the equation can be divided into two factors:

where v =firing speed w=constant with dimensions of tlme sight distance projectile path distance less than 1 will not be considered as this would only be the case when the target was departing from the weapon position. The practical maximum value In for the ratio is 1.25 which results at the greatest distance (2 with maximum target speed and a direct approach ()\=90). It is therefore reasonable to represent e/e by a function having a value between 1 and the maximum value m for the greatest distance 2 diminishing towards 1 at decreasing distance e. For instance:

Values of the ratio Substituting this equation into Equation 12a:

e e 8G 6 further resulting in i" e(m1) 1+ 2e 13) If the left side of the above equation is plotted with respect to e, a smooth, slightly curved function will result which may be duplicated electronically.

Equations have thus been provided for calculation of the desired vertical and lateral lead angles in a computer from the directioning signals C and C and the initial distance s Consideration must now be given to the target path rectangular speed components as viewed through the optical sight. The relationship between the two components determine the direction of the resulting motion of the sight line necessary to follow the target due to the inclination of the target path plane. Components of the inertial angular speed of the sight line necessary for target tracking indicate the inclination K of the target path plane by:

Qs tan K CS FIG. 3a is a representation of the target path as seen through the optical sight under normal conditions, i.e., the supporting means for the weapon in a level condition. In this condition, of course, cross hair F will be vertical (along a radius line of the earth) and cross hair F will be horizontal (tangent to the earths surface).

In following the target with the cross hair the inertial angular speeds of the sight line in the two orthogonal directions are indicative of the instantaneous inclination angle at any point. For target movement in the field of sight plane GE in the direction f, the orthogonal inertial angular speeds generated by movement of the sight line in the direction 1" are indicative of the inclination angle K1.

As previously mentioned, the two orthogonal angular speed components of the sight line may be generated by means of a single rate gyro fixedly mounted along the axis of the sight line.

It is also possible to derive the angular speed signals from the control voltages generated by the sight optic drive. For example, stabilization systems utilizing integrating rate gyros to correct for changes in orientation of the turning plane of the weapon (due to a tank-mounted weapon traversing hilly ground, for example) require that the control signals to the sight drive be proportional to the angular speed of the sight line. The inclination angle of the target path plane may therefore be evaluated according to the Equation 14 using these signals.

It is also necessary that the lead computer give the correct values when the weapon is in motion. As the normal target is an airplane and the weapon is mounted on a surface craft, the relative speed between target and weapon is almost entirely determined by the speed of the target. The speed of the weapon may be neglected. Rotation of the weapon support vehicle can be taken as a vector consisting of three components in mutually perpendicular planes. The axes of rotation for the three components are the sight line r, a line it perpendicular to r and parallel to the turning plane AE, and the axis w which is perpendicular to both r and u. Rotational components around axes other than the sight line r may be easily compensated for by a stabilization system. The system is not explained in detail here since it is not a part of the present invention. In general, rotation around the sight line r is not of interest for stabilization purposes. Therefore, no sensing means (gyro) is provided for this purpose. Rotation of the weapon support vehicle around the sight line r can be expected to cause no reaction by the stabilization system.

In the absence of the lead computer, the weapon would be directed in a line parallel to the sight line. With the interconnection of the lead computer, the axis of the weapon has a lead angle inclination with respect to the sight line. Rotation of the craft around the sight line axis causes the axis of the weapon to trace a cone shaped shell around the sight line. As long as the target is maintained in the cross hair by the gun pointer, this condition has no effect. This is explained with reference to the drawings.

FIG. 3a represents the view through the optical sight with the horizontal cross hair F (parallel to turning plane AB) in a horizontal position with respect to the earth. To maintain the target at the point of intersection of the cross hairs, the sight must be moved along the line 1" at an angle K1 with respect to the horizontal F For the condition illustrated in FIG. 3a, that is, horizontal cross hair F (which is parallel to the turning plane of the weapon) level, the inertial angular speeds in the vertical and lateral direction for maintaining the target at the intersection of the cross hairs will have the ratio Referring now to FIG. 3b, a roll motion through the angle Alc around the sight line causes the cross hairs of the optical sight to be positioned relative to a horizontal line as shown. Moving the optical sight along the pre viously correct line as determined by the angle K1 would lose the target moving along the line f. To maintain the sight on target, the gun pointer must change the relationship of the angular speeds of the sight line so that the sight line again moves along the line f. The line f is now defined in position by the relationship This change in the angle 1: necessary for following of the target is automatically calculated within the lead computer. The lead computer therefore not only computes the necessary lead angle but also the absolute direction of the lead for any position of the weapon turning plane (e.g., tank traversing hilly ground or ship in rolling seas) and automatically adjusts the weapon position according to the calculations.

The signals which are generated with a change of the directioning handle by the gun pointer correspond to new nominal values of the angular rotation speeds C and C of the weapon which are fed to the lead computer. Signals proportional to the inertial angular speeds may be taken from a rate gyro which is fixedly aligned with respect to the line of sight. Rolling motion of the sight optic around the sight line does not change the ratio of the inertial angular speed components because, with the change of orientation of the rate gyro, the turning speed of the sight line as represented by two orthogonal components also changes.

With reference to FIG. 5, the operation of the preferred embodiment of the lead computer will be described. As previously described with respect to Equations la and 2a, evaluation of the lead angle requires that the quantities C C and e/v be fed into the lead computer. The signal C is proportional to the angular speed 1; of the sight line in the lateral direction and the signal C is proportional to the angular speed 0. in the vertical direction. Utilizing Equation 4a for the total directioning handle signal C the resultant angular speed is given by FIG. 5 does not show the source of the signals which are proportional to the angular speeds. The block diagram begins with the signals applied to

terminals

1 and 2 in the form of electrical control signals. It has previously been explained with reference to FIG. 4a that these signals representing the two components of the total directioning handle signal C can be used to calculate the total directioning signal C by geometrical addition according to Equation 4b. In FIG. 5, the two signals C and C are geometrically added in the circuit 3 providing on output lead 4 the signal C. The method of geometrical addition is not important and can be achieved in different ways as by squaring the input signals with subsequent adding and taking the square root or by addition of two AC voltages subjected to a ninety degree phase shift and rectification.

The signal on output lead 4 is representative of the angular speed of the sight line as shown in Equations 4b and 40. This signal is integrated in circuit 5 and is also multiplied by a time proportional signal I in multiplier circuit 6. Generation of the signal t is accomplished in integrator circuit 7 which is fed by constant signal U On lead 31 at the output of integrator the signal 0' is available which in a subsequent sine transformer 8 is transformed to the signal sin a appearing on lead 32. We now have available the dividend sin a and the divisor t-C of the fraction in the Equation 4a which are fed toa divider circuit 9 to derive the quantity sin 6/ C -t on lead 26. It is necessary to have a signal which is proportional to the initial distance e along the sight line as shown in Equation 4a. Multiplication circuit 11 is fed with an initial distance signal e which is multiplied with the signal on lead 26.

It will be realized that the hit probability of the weapon system will be increased with a periodically varying signal corresponding to distance heterodyned with the lead signals. In the present embodiment, this is accomplished through modulation of the signal corresponding to the initial distance e before it is fed to the multiplication circuit 11. e is applied to terminal which is connected to the input of a modulation circuit 12 providing on output lead 27 the signal corresponding to the equation The output of multiplier circuit 11 on lead 36 is now a function of time wherein e is proportional to the target distance along the sight line.

Reference to the Equations la and 2a necessary for the calculation of the lead angles 5 and 6 show that the signal e must still be divided by the averaged projectile speed v and subsequently be multiplied by the respective directioning handle signal C and C As previously noted, the average projectile speed VG depends on several quantities and, for the lead angle calculations, the speed is not needed explicitly, but only together with the target distance in the fraction e/v The dependence of v and e/v on the dilferent param eters 'was investigated. It was found that the function can be represented by a group of curves approximated by third degree parabolas. It is therefore possible to determine the desired quantity e/v without evaluating the average projectile speed v using only the target distance e. This is accomplished by feeding the signal e(t) to a non-linear circuit 13 having the characteristic transfer 'function f(e). The output of non-linear circuit 13 appears on lead 37: the signal e/v previously modulated in circuit 12.

In accordance with Equations la and 2a, it is necessary to multiply the signal with the associated directioning signals C and C to arrive at the signal corresponding to the lead angle of the weapon in the vertical and lateral directions respectively. It is to be remembered that the lead angles of the weapons are always with reference tothe sight line which is directed towards the target. Two multiplication circuits are provided in 14 and 15. Multiplier circuit 14 has as inputs the quotient e/v and the lateral directioning signal C providing at the output on lead 39 the lateral lead signal of the weapon It would be possible to feed this signal directly to the weapon, however, as the weapon itself cannot be turned in a lateral direction, but only can be elevated within a rotatable turret, it is necessary to recalculate the lead signal with respect to the lateral lead angle 6 of the turret according to Equation 3a. Equation 3a shows that the elevation angle 0 of the sight line with respect to the horizontal turning plane of the turret must be known. To provide this input information, the input of resolver 17 is coupled mechanically to provide a signal proportional to the elevation angle H The resolver 17, provided with an alternating voltage of constant frequency and amplitude, provides an output signal modulated in accordance with the cosine of the elevation angle G The resolver output signal is fed to a demodulator 18 through lead 40 where it is rectified to provide cos O on lead 41. Cos Q is also fed to the division circuit 20 through lead 19, providing on lead 21 at the output of divider circuit 20 the lateral lead angle 6;; of the turret according to the Equation 3a:

K COS 05 It will be noted with reference to the previously cited Equation 5 that the factor e/v has been extracted from the product. The quantity VG remains as a factor in the denominator of the fraction. In the above equation it has been designated V which has an average value corresponding to the average projectile speed at the main battle distance. Due to this simplification, the calculation of A requires only that the signal cos O (already calculated in the circuits 17 and 18) and the value of e/v (at the output 37 of circuit 13) be multiplied with a constant factor g/ZV The angle including the ballistic superelevation is determined by adding Equations 1a and 5a resulting in:

*=1( l. H vs CH+ZUGI Q V1: The signal cos 0 is multiplied by constant factor is present while on the other input line 25, the directioning signal C in the vertical direction is applied from input terminal 2 through lead 25. The sum of the two input signals is connected to multiplication circuit through lead 42. The signal e/v is multiplied with the sum of the two signals providing, on lead 28 at the output of the multiplier circuit, the vertical lead signal 5 including the ballistic superelevation according to the Equation 4a. The signal 5 determines the lateral lead of the weapon with respect to the sight line. The lateral lead angle 6 of the turret determines the angle between the turret and the sight line. Due to the modulation of the initial distance signal 2 the lateral lead angle as well as the vertical lead angle vary in accordance with the amplitude of the modulation, which is dependent on the initial distance e It is to be realized in accordance with the present invention, that the modulation may be omitted completely or it may be introduced at another point in the circuit. In the embodiment shown in FIG. 5, the lateral variation and the vertical variation of the lead angles are always at an equal percentage. This appears to be the desirable situation, however it can be modified.

In accordance with the invention, it shall be noted that the computations accomplished with the embodiment shown in FIG. 5 can also be realized with other electrical circuits. The equations could be solved, for example, by means of an analog computer. The trigonometric transformation could be accomplished by resolvers or coordinate changers or a sine or cosine potentiometer. The servo-circuits are not to be limited to operation on alternating currents but also can be operated using direct current. The operation with DC causes a change of rotational direction of the motors in response to a change in polarity of the applied current. With AC operation, the change of the motor direction is achieved by altering the phase of the carrier frequency in relation to a reference phase. In both cases it is desirable to introduce a low frequency alternating current to the direct current or the carrier frequency. The present invention provides a system for computation of the lead angle but is not to be limited in scope by the embodiment shown. Various modifications of the system will be evident to those skilled in the art while maintaining the essence of the present invention. It is our intention to be limited in scope only by the appended claims.

We claim:

1. A weapon fire control system wherein a biaxial directionable weapon and a biaxial directionable sight mounted on a movable platform are interconnected electrically, including a lead angle computer interposed in e @kClIical interconnection whereby, in accordance with electrical signals processed in said lead computer, said weapon is directed toward a target seen through said sight, said lead computer comprising:

first and second input means for receiving a signal proportional to the inertial angular speed of the sight line in a lateral and vertical direction respectively; time dependent input; geometrical addition means connected to said first and second input means, having an output, for computing the geometrical sum of said signals; integrator means connected to said time dependent input, having an output, for providing a signal proportional to time which is the integral of a signal 7 applied to said time dependent input; computer means, connected to said output of said geometrical addition means and to said output of said integrator means, having an output for providing a signal directly proportional to the sine of said signal at said output of said geometrical addition means and inversely proportional to the product of said signals at said output of said integrator and said output of said geometrical addition means; first multiplier circuit having a first input connected to said output of said computer means and having a second input, further having an output; initial distance input means for receiving an electrical signal proportional to the target distance, connected to said second input of said first multiplier circuit, whereby said output of said multiplier circuit provides a signal directly proportional to the product of the signal applied to said first input and said signal applied to said initial distance input means; non-linear circuit means with a predetermined transfer characteristic having input and output whereby a signal at said input provides an output signal at said output in accordance with a predetermined nonlinear function approximating a parabola of the third degree, whereby the signal at said output means of said non-linear circuit means is directly proportional to the distance of the target and inversely proportional to the average speed of the projectile; second multiplier circuit having first and second input further having an output, said first input connected to said output of said non-linear circuit means and said second input connected to said first input means for receiving a signal proportional to said inertial angular speed of said sight line in said lateral direction, whereby a signal is provided at said output of said second multiplier circuit proportional to the desired lateral lead angle of the weapon with respect to the sight line; resolver means having a mechanical input connected to said sight, further having an electrical output, whereby the signal at said electrical output is proportional to the cosine of the elevation angle of said sight; first divider means connected to said output of said second multiplier circuit and further connected to said output of said resolver means, having an output coupled to the lateral directioning apparatus of said weapon whereby the signal at said output is directly proportional to said signal at said output of said second multiplier circuit and is inversely proportional to said signal at said electrical output of said resolver means; amplifier means, having an input and an output, said input connected to said output of said resolver means, for providing a signal at said output of said amplifier means directly proportional to a signal at said input in accordance with a predetermined multiplication -factor; summing amplifier having first and second inputs and an output, said first input connected to said second input means for receiving a signal proportional to the inertial angular speed of said sight line in a vertical direction, said second input connected to said output of said amplifier means, said output of said summing amplifier providing a signal equal to the sum of the signals at said first and second inputs; and

third multipler circuit means, having a first input connected to said output of said non-linear circuit means, having a second input connected to said output of said summing amplifier, having an output connected to the vertical directioning apparatus for said weapon, for providing a signal to position said weapon in the vertical direction with respect to said sight line, whereby the combination of said lateral and said vertical directioning signals provides direction of the weapon with respect to said sight line at the correct angle for maximum bit probability.

2. Apparatus as recited in claim 1 including means for modulating said lateral and said vertical directioning signals.

3. Apparatus as recited in claim 1 wherein said predetermined multiplication factor of said amplifier means is adjusted in accordance with the ballistic super elevation needed for a projectile fired from said weapon.

4. A lead computer for an electrically positioned antiaircraft weapon system including a biaxially directionable Weapon and a biaxially directionable sight line comprising:

input means for receiving signals proportional to the inertial angular speeds C and C of said sight line; initial distance input means for receiving a signal proportional to target distance at first contact; first signal processing means, connected to said initial distance input means and to said input means, for evaluating the instantaneous target distance e;

second signal processing means, connected to said input means and to said first signal processing means, for evaluating the vertical lead angle 6 of said weapon using the equation where VG is the average projectile speed;

third signal processing means, connected to said input means and to said first signal processing means, for evaluating the lateral lead angle 6 of said weapon using the equation 14 turret carrying said weapon in accordance with the equation sin 6 SlIl 5 evK 6. Apparatus as recited in claim 4 wherein said second signal processing means and said third signal processing means include non-linear circuit means for calculating the ratio e/v 7. Apparatus as recited in claim 4 including modulating means for modulating said vertical lead angle and said lateral lead angle.

8. Apparatus as recited in claim 7 wherein said modulating means is connected to said initial distance input means for modulating said signal proportional to target distance at first contact.

9. Apparatus as recited in claim 4 wherein said signals proportional to the inertial angular speeds C and C of said sight line are generated by a rate gyro fixedly mounted with respect to said sight line.

10. Apparatus as recited in claim 4 wherein said signals proportional to the inertial angular speeds C and C of said sight line are derived from an electric directioning handle for said sight line.

11. Apparatus as recited in claim 4 wherein said vertical lead angle o of said weapon is evaluated according to the approximate equation for small lead angles 6 5H CH and said lateral lead angle 6 of said weapon is evaluated according to the approximate equation for small lead angles EUGENE G. BOLTZ, Primary Examiner R. W. WEIG, Assistant Examiner U.S. Cl. X.R. 89-l, 41