US2718355A

US2718355A - Airborne gun sight of the "own speed" type

Info

Publication number: US2718355A
Application number: US483676A
Authority: US
Inventors: Jr Edmund B Hammond; Ervin D Macdonald
Original assignee: Sperry Rand Corp
Current assignee: Sperry Corp
Priority date: 1943-04-19
Filing date: 1943-04-19
Publication date: 1955-09-20
Anticipated expiration: 1972-09-20

Description

Sept. 20, 1955 E. B. HAMMOND, JR., ET AL 2,718,355

AIRBORNE GUN SIGHT OF' THE "OWN SPEED" TYPE Filed April 19, 1943 5 Sheets-Sheet 1 www Sept. 20, 1955 E. B. HAMMOND, JR., ETAL 2,718,355

IRBORNE GUN SIGHT OF THE "OWN SPEED" TYPE Filed April 19, 1943 3 Sheets-Sheet 2 ,43 INVENTORS Sept. 20, 1955 E. B. HAMMOND, JR., ETAL 2,718,355

AIEBOPEE GUN SIGHT 0E THE "owN SPEED" TYPE 3 Sheets-Sheet 3 293 CHM United States Patent O AIRBORNE GUN SIGITTI'IPOF THE OWN SPEED Edmund B. Hammond, Jr., Brooklyn, and Ervin D. MacDonald, East Williston, N. Y., assignors to Sperry Rand Corporation, a corporation of Delaware Application April 19, 1943, Serial No. 483,676

4 Claims. (Cl. 23S-61.5)

This invention relates to a computing mechanism for gun sights of the own speed type.

The armament used on bombardment types of aircraft is usually designed primarily for defensive purposes, that is, to defend the craft against attacks by enemy craft that would prevent the bombardment craft from reaching its objective. The present invention is primarily directed to means for computing the lead angle by which the line of sight must be offset from the axis of the gun in order to effect a hit on the approaching enemy craft.

For guns located in the nose or tail of bombardment type aircraft it is possible to make certain assumptions in computing the lead angle. These assumptions are due, first, to the predetermined path normally followed by an attacking craft and, second, to the restricted cone within which an attacking craft approaches the nose or tail of a bomber. In order to fire at a bomber, an attacking enemy craft usually approaches a bomber in a manner such that its nose continuously points toward the bomber. If the bomber were not moving, the attacking craft would follow a straight line from its position at any given moment through the position of the bomber. Since the bomber is moving, the attacking craft follows a curved path in order to continuously point toward the bomber.

This path may be predetermined and is dependent upon the relative positions of the two crafts and the velocity of each. Since the attacking craft iiies a predetermined course, its position after a given time of flight mayibe determined and the prediction angle between the line of sight and an imaginary line from the gun to the future position readily computed.

Once the prediction angle is acertained, it is possible to determine the position at which the gun must be directed in order to re a projectile toward the future position of the attacking aircraft. The path of the projectile is determined as the resultant of the aircrafts velocity and the muzzle velocity of the projectile.

Sights utilizing the factors just referred to are vector sights and are known by the Air Forces as own speed sights, and are thus distinguished from the more complicated sights using the angular rate-multiplied by time of):

ight solution.

The principle of the computer herein disclosed is to set up vectors mechanically representing the speed and direction of both the target and projectile. The arrangement in space of these two vectors gives the prediction angle.

One distinct advantage to be gained by the own speed method of computation is that the solution is instantaneous. There is no time lag and no amplification of tracking errors. The solution is complete whenever the sight is pointed at the target and there is no delay for tracking or settling. Even though accurate tracking is not necessary for the solution, it would be easier to accomplish than with other types of sights having disturbed reticles and using a rate multiplied by time solution. Sights of the type herein disclosed can be made very simple and 2,718,355 Patented Sept. 20, 1955 compact which is important where space and weight are at a premium.

One object of the invention is to provide an improved apparatus for computing the lead angle to increase the accuracy of aircraft gun sights.

Another object is to provide an improved apparatus for computing lead angle for aircraft gun sights used especially for defensive purposes.

A further object of the invention is to provide an apparatus for computing the lead angle due to the velocity of the plane on which the gun is mounted.

Other objects and advantages of the invention will become apparent from the following specification, taken in connection with the accompanying drawings, in which:

Fig. 1 is a perspective view of an aircraft gun showing a computing aircraft gun sight mounted on the gun.

Fig. 2 is a perspective view of a computing sight for use with a remote gun.

Fig. 3 is a schematic perspective view of the mechanism used in the computing sights shown -in Figs. 1 and 2.

Fig. 4 is a diagram showing the angular relations of the attacking and defending aircraft.

Fig. 5 is a space diagram showing relationships for computing azimuth and elevation components of the lead angle.

Fig. 6 is a flat schematic drawing which provides a simplified showing of a computer mechanism generally similar to that of Fig. 3.

Fig. 1 shows an aircraft gun designated generally at 1 supported by trunnions 2 which are rotatably mounted in a cradle 3 for providing movements of the gun 1 about a horizontal axis. The cradle 3 is rotatably mounted on a shaft 4 that is carried by a suitable pedestal 5 which may be attached to the body of the aircraft. A stationary azimuth gear 6 is rigid with the pedestal 5, whereby movements of the cradle 3 and gun about the vertical axis of shaft 4 causes rotation of a pinion 7 carried by the cradle 3 in a manner to mesh with the azimuth gear 6. This pinion drives a flexible shaft 8 to supply data to computing mechanism 9 in accordance with the azimuth angle of the

axis

11, 11 of the gun 1.

A gear sector 12, that is held rigidly mounted on the cradle 3, causes rotation of a pinion 13 which drives a shaft 14 to supply elevation data to the computing mechanism 9 as the gun is moved in elevation about the horizontal axis of trunnions 2.

Suitable hand grips

15 and 16 are provided for the operator to slew the gun to keep line of

sight

17, 17 of sighting instrument 18 on a target such as an attacking aircraft.

Suitable knobs

21 and 22 are provided for introducing the indicated air speed and altitude, respectively, of the craft carrying gun 1 into thc computing mechanism 9 to obtain a correction of indicated air speed for air density which amounts to setting into the computer a value or function of true air speed.

Knobs

23 and 24 on the upper side of the computing mechanism 9 are connected with the sighting instrument 18 in a manner to align the line of sight 17 with the gun axis 11 by adjusting the azimuth and elevation, respectively, of the line of sight.

A preferred arrangement for introducing air speed and altitude is shown in Fig. 6. The device comprises an indicated air speed knob 21 fixed to a logarithmic scale 200 calibrated in miles per hour. The knob, when adjusted, drives an output shaft 128. Scale 200 cooperates with either of two

lubber lines

201 and 202 marked on a ring or disc 203 mounted for rotation coaxially with respect to scale 200. An arm or knob 204 fixed to ring 203 is used to position the lubber line being used with reference to a relatively fixed logarithmic scale or dial 205 calibrated in terms of altitude. Lubber line 201 is used when firing at aircraft while lubber line 202 is used when strang ground targets. In operation, the lubber line to be used is positioned opposite the appropriate point on the altitude scale and then dial 200 is adjusted by knob 21 to set the indicated air speed value on the dial opposite the lubber line. The multiple dial arrangement described is equivalent to a differential mechanism and when adjusted as described the output shaft 128 thereof is angularly displaced according to the logarithm of a function (Z) which will be referred to below.

Fig. 2 shows a remote gun 1 corresponding to the gun 1 of Fig. l and having an axis 11', 11. The gun 1' is driven by suitable power mechanisms for directing the axis 11', 11' in accordance with the axis 25, 25 of computing mechanism 9 that is remote from the gun.

The computing mechanism is carried in a cradle 26 that is mounted on a shaft 27 which is rotatable in a brace 28 forming a part of the aircraft. Suitable trunnions 29 and 30 are provided for rotatably mounting the computing mechanism 9 in the cradle 26. A sector 12 engages a pinion 13 which rotates a shaft 14" in accordance with movements of the computing mechanism 9' in elevation about the horizontal axis of trunnions 29 and 30. Thus, the shaft 14 drives the elevation position of the axis 25 into the computing mechanism 9 in a manner similar to that which the shaft 14 drives gun elevation data into the computing mechanism 9. The axis 25 of the computing mechanism 9 is maintained coincident with the axis 11', 11 of the gun 1 in a manner subsequently to be explained.

The computing mechanism 9 has a line of sight 17', 17 defined by sighting instrument 18' corresponding to the line of sight and sighting instrument shown in Fig. 1.

Knobs

23 and 24 are also provided for aligning the line of sight 17', 17' with the axis 25 of the computing mechanism 9. Hand grips 15 and 16 correspond to the grips and 16, and knobs 21' and 22 are provided for introducing indicated air speed and altitude of the aircraft into the computing mechanism 9.

As the computing mechanism 9 is moved in azimuth with the vertical shaft 27, a gear 31 on the shaft 27 is rotated and drives a gear 32 which in turn drives a gear 33. Gears 32 and 33 drive through suitable shafts to position the rotors of coarse and line

electrical position transmitters

34 and 35 that are arranged to transmit the azimuth position of the axis for the computing mechanism 9 to coarse and

fine receivers

36 and 37, respectively, at the gun 1'. These receivers rotate the gun in azimuth by a gear 38 which is driven from

gears

39 and 41, respectively, on the fine and

coarse transmitters

37 and 36, respectively.

The elevation position of the axis 25 for the com puting mechanism 9 is transmitted to the gun 1 by coarse and

tine transmitters

42 and 43. The rotors of these transmitters are positioned in accordance with movements of the computing mechanism 9 about the horizontal axis of trunnions 29 and 30. A sector 44 is rotated with trunnion and drives gears 45 and 46 to position the rotors of

transmitters

42 and 43. The

transmitters

42 and 43 supply elevation data of the axis 25 to

receivers

47 and 48 which control the elevation position of the gun 1'. By suitably synchronizing the transmitters and receivers, the axis 11', 11' may be continuously positioned in accordance with the position of the axis 25 for the computing mechanism 9.

As the gear 33 rotates in accordance with the azimuth position of the computing mechanism, a flexible shaft 8 is driven thereby to supply azimuth data to the cornputing mechanism 9 in a manner similar to that in which Ythis data is supplied by the shaft 8 in Fig. l.

Since the axis 11', 11 for the gun 1 is maintained coincident with the axis 25 for the computing mechanism 9', it will be apparent that the azimuth and elevation data supplied to the computing mechanism 9 by shafts 8" and 14 is equivalent to the azimuth and elevation position of the gun 1.

The

computing mechanisms

9 and 9 are substantially identical'. Fig. 3 shows in detail thearrangement and cooperation of the various elements for the computing mechanism. Before describing the operation of the various elements in the computing mechanism, consideration will first be given to the problems involved in determining an accurate lead angle.

As shown in Fig. 4, an attacking craft 52 follows a predetermined curved path 50 in order to continuously maintain its nose directed toward the position of defending craft 51 which is flying in the direction of a line 53 forming its longitudinal axis. Duringany given time'of iiight, the attacking craft 52 will move to a future position 52. The prediction angle (a) is equal to the angle between line of sight 17 and the line connecting the original position of the defending craft 51 with the future position 52 of the attacking craft.

Considering the observed position 52 of the attacking aircraft as point A, lthe future position 52 as point B,-

and the location of the gun on the defending craft 51v as point C, it will be apparent that the prediction angle (a) may be computed from the relation of Sin a- BC wherein S is the distance between the future position 52 and the line of sight to the present position 52. This distance S may be expressed as wherein (Vp) is the velocity of the' attacking aircraft 52, (w) is the angular rate of turn of the pursuit craft at point A, and (Tp) is the time of ight of the projectile from the gun to the point B. The angular rate (w) is a function of the velocity (Vp) of the defending craft 51, the angular position (00) of the attacking craft, which is the angle of the line of sight 17 relative to the longitudinal axis 52 of the defending craft 51, and the range (Do), which is the distance of the target 52 from the gun on the defending craft 51, and may be expressed as in the present range during the time of flight of (Tp) which may be expressed as Bin a= Substituting this value for the line BC in the equation for the prediction angle (a) we have:

As may be seen from Fig. 4, two forces act upon a projectile fired from a gun carried by the defending aircraft 51. These forces are due to the velocity (Vb) of the defending aircraft 51 and the muzzle velocity (Vm) of the projectile as it leaves the gun. In order to direct a projectile toward the future position 52', it is necessary to adjust the angle of the gun relative to the longitudinal axis 53 so the resultant effect of the muzzle vesin a= sin 00 locity (Vm) and the velocity (Vb) of the defending c'raft 51 will be along the line connecting the gun and the future position 52'. axis 11 of the gun and the path of the projectile to the future position 52 may be referred to as a deflection angle which is formed of two components, namely, the prediction angle (a) and a lead angle (A) between the line of sight 17 and the gun axis 11. The lead angle between the line of sight and the axis of the gun is correctly determined when the gun is positioned in a manner such that the component of the velocity (Vb) of the defending craft across the line of fire is equal to the component of the muzzle velocity (Vm) across the line of fire. By equating these two components, we have Vm sin =Vb sin 6p From an inspection of Fig. 4, it will be apparent that =7\+ and that V sm )t cos a-l-eos )t sin a=f-b (sin 00 eos a-l-cos 00 sin a) Since the angles (a) and (A) are always small, it can bey assumed that their cosines are equal to unity, in which case Equation 3 may be written as sin )vl-sin a=% (sin H-I-eos 00 sin a) By combining Equations 1 and 4 Sin The angle between the longitudinal This may be written as where the muzzle velocity is a constant (K1) for any particular gun. By plotting typical courses for the attacking craft, and assuming a time of flight, the value of P may be computed for various sets of circumstances depending upon the relative positions and the velocities of the respective crafts. The value of P is found to be small as compared with the constant (K1) and varies over a fairly small range. For these reasons an average value of P may be selected and used as a constant (K2). The constants (K1) and (K2) may be added to produce a gun constant (K). Using these assumptions, the lead angle (A) may be computed from the equation sin )(:KVb sin 00 (7) The expression (KVb) is a function (Z) of the velocity of the defending aircraft. This function includes the effect of the velocity of the defending aircraft on the path of the attacking aircraft as well as its eiect on the direction of a projectile fired from a gun. The function (Z) being a function of the aircrafts velocity may be computed as the product of functions of indicated airspeed and altitude. In the present invention, functions of indicated airspeed and altitude are multiplied to obtain the function (Z) of the aircrafts velocity. This function is such that it includes consideration of the prediction angle (a) as well as a lead angle (A) by which the line of sight must be offset relative to the axis of the gun in order to direct a projectile along a path displaced from the line of sight by the lead angle (A) In the foregoing description of the calculations necessary to ascertain the proper lead angle, the various angles have all been considered in one plane. However, with gun mountings presently available and in conformance with present practices, it is necessary to introduce angles into the computing mechanism in terms of azimuth and elevation angles and, similarly, to compute the lead angle in terms of azimuth and elevation components.

In other words, the present invention considers that a bullet fired from a gun on an airplane has two velocities imparted to it, the rst being muzzle velocity and the second is due to the forward velocity of the airplane supporting the gun. The path of the bullet to a stationary target is along the resultant vector of these two forces, generally speaking, and the computing mechanism solves for the elevation and azimuth components of this resultant vector. The forward velocity of the plane is multiplied by a constant to correct for the curved path of the pursuing plane which is the target, this being taken care of by suitably locating a lubber line, not shown, for the indicated air speed knob.

Fig. 5 shows in a space diagram the relations of these various angles and the trigonometric constructions necessary in order to obtain azimuth and elevation components for them. By reference to this ligure, it will be apparent that the azimuth and elevation position of the axis 11 for the gun represent the components of the difference angle (6o-a), provided the azimuth angle is measured from the longitudinal axis 53 of the aircraft. Similarly, it will be apparent that angles (xa) and (Ae) represent azimuth and elevation components of the lead angle (x). In the present computing sight, use is made of a reflex sight which utilizes azimuth and elevation components (Na) and (Re) to construct the lead angle (A). For this reason, the following calculations are based on the assumption that (M1) is equal to (ha). Further assuming that the angles (xa) and (Ae) are equal to their respective tangents, it may be shown from Fig. 5 that sin E,T cos A,-K3 eos E'E The details of computing mechanism 9 by which the azimuth component (ha) of the lead angle (A) and the elevation difference angle (Ae-tbs) are determined from the gun azimuth and elevation angles together with values of indicated airspeed and altitude is shown clearly in Fig. 3. As previously described, computing mechanism 9 adjusts the line of sight 17 relative to the gun axis 11 in accordance with azimuth component (Na) vof'the `lead angle and the elevation difference angle (A-ss). 't

and 64 are rotated in accordance with desiredfunctions: of indicated airspeed and altitude, depending upon the values used.

The line of sight is defined by an optical system including a source of light such as incandescentv lamp 65.

Rays from the source 65 pass through a glass having concentric circles marked thereon which form the reticle of the sight. These rays are then reflected by a mirror 67 on to an azimuth deection mirror 68. Rays reflected from the azimuth deection mirror 68 pass through a lens 69 onto elevation reflector 71 which is of the'reex type. The image of the reticle circles on glass 66 is thus superimposed on a target falling along the line of sight. Optical systems of this type are referred toas reex sights and are well known in the art. It should be understood that other forms of sights may be used without departing from the present invention.

The manner in which the computing mechanism 9 utilizes gun azimuth and elevation angles and functions of altitude and indicated airspeed by solving Equations 9 and 10 to adjust the azimuth reflector 68 and the elevation reflector 71 will now be described. As has been described above, the function (Z) of thev velocity of the aircraft 51 is the product of functions of indicated airspeed and altitude. Selected values of indicated airspeed and altitude as determined by instruments on the aircraft S1 are set into the mechanism 9 by arranging pointers on the

knobs

21, 22 to correspond with the selected values as shown by the scales on the casing of the mechanism 9, for these pointers.

These scales are so arranged that the

knobs

21 and 22 are rotated in accordance with logarithms of the desired functions of indicated airspeed and altitude respectively. It will be apparent therefore that the shaft 63 is rotated in accordance with a logarithm of the desired function of indicated airspeed. Similarly, the shaft 64 is rotated in accordance with the logarithm of the desired function of altitude.

The product of the functions of indicated airspeed and altitude is obtained by adding the two logarithms. This is accomplished by rotating input gears 72 and 73 of differential 74 in accordance with the logarithms ofthe desired function. Thus, the shaft 63 rotates a gear` 75 which drives an idler gear 76 to rotate the input gear 72. The input gear 73 is driven by the shaft 64, pinion 77 and idler gear 78. Thus, by suitably selecting gearing ratios, output shaft 79 of the differential 74 is rotated in accordance with the logarithm of the product of the functions of the indicated airspeed and altitude, that is the logarithm of the function (Z) of the velocity of aircraft 51.

Shaft 14, which is rotated in accordance with the gun elevation angle, drives through suitable gearing 81 to rotate shaft 82 in accordance with the gun elevation angle (Eg). The shaft 82 drives through a pinion 83 to rotate a cam gear 84 on the periphery of cam disc 85 to rotate the cam disc in accordance with the gun elevation angle (Eg)- and so designed that a follower 87 having a cam pin 88 riding in the groove 86 will be displaced in accordance with the logarithm of the cosine of the gun elevation angle. This movement of the follower 87 rotates a shaft 89 carrying a pinion 91 which drives through a gear 92 Cam disc 85 has a cam groove 86 formed therein to rotate shaft 93 and pinion 94 in accordance with the logarithm of the cousine of the gun elevation angle.

The produce of the function (Z) of the aircrafts velocity andthe cosine of the gun elevation angle is obtained by adding the logarithms of these two functions. This addition is accomplished by differential 96, one input of which is driven by the shaft 79 in accordance with the logarithm of the function (Z). Input gear 95 of the differential 96 is rotated by the pinion 94 in accordance with the logarithm of the cosine of the gun elevation angie. Thus, output gear 97 of the differential 96 is rotated in accordance with logarithm of the product of the function-(Z) and the cosine of the gun elevation angle This-product is multiplied by the cosine of the gun azimuth angle by adding logarithms of these two factors. Input gear 98 of differential 99 is driven by the gear 97 in accordance with the logarithm of the product of the function (Z) multiplied by the cosine of the gun elevation angle. The other input gear 101 of differential 99 is rotated in accordance with the logarithm of the cosine of the gun azimuth angle in a manner which will now be described.

Pinion 62, which is rotated by shaft 8 in accordance withl the gun azimuth angle, drives a gear 102 on shaft 103 that in turn drives pinion 104 in with a gear 105 on a periphery of cam 106 in accordance with the gun azimuth angle. A cam groove 107 formed in the surface of the cam disc 106 is so designed that a follower 108 having a pin 109 arranged to slide in the groove 107 is moved in accordance with the logarithm of the cosine of the gun azimuth angle. This movement of the follower 108 rotates the shaft 111 carrying a pinion 112 in accordance with said logarithm of the cosine of the gun azimuth angle.

-The rotation of pinion 112 is utilized to drive through gear 113, shaft 114 and pinion 115 to rotate the input gear 101 of differential 99 in accordance with the logarithm of the cosine of the gun azimuth angle.

Thus, output shaft 116 of the differential 99 rotates a pinion 117 in accordance with the logarithm of the product of the function (Z) of the aircraft velocity, cosine of the elevation angle and cosine of the azimuth angle. This may be represented by the expression Log (Z cos Eg cos Ag) By subtracting this expression from unity, it will be apparent that the denominator of the expressions for the azimuth and elevation components of the lead angle as set forth in Equations 8 and 9 will be obtained. To accomplish this, pinion 117 drives gear 118, shaft 119 and pinion 121 in accordance with the above expression. Pinion 121 meshes with a gear 122 on the periphery of cam disc 123. It has a cam groove 124 formed on the surface thereof whereby a follower 125 carrying a cam pin 126 is displaced in accordance with the expression Log (l-Z cos Eg cos Ag) In order to divide this expression into the function (Z) of the aircrafts velocity, the logarithm of the expression is subtracted from the logarithm of the function (Z) by a differential 127. Input shaft 128 of the differential 127 is Adriven by shaft 79 which is rotated in accordance with the logarithm of the function (Z) of the aircrafts velocity. Input gear 131 of the differential 127 is driven in accordance with Log (l-Z cos Eg cos Ag) by.a pinion 132 on shaft 133 which is rotated in accordance with the above expression by the cam follower '125. Asmay be seen in Fig. 3, pinion 132 drives through a gear 134 on shaft 135 and pinion 136 to rotate the gear 131 in accordance with the expression.

The gearing and gear ratios are so arranged that the input'of the differential 127 represented by the gear 131 is subtracted 'from the input of the differential 127 repre- 9 sented by the shaft 128. Thus, the twoinputs are subtracted and output gear 137 is driven in accordancewith the expression Log (I Z cos E,e eos AK It may be seen from the Equation 8 that the azimuth component (Na) of the lead angle (A) is equal to the product of the above expression and the sine of the gun azimuth angle. This product is obtained from a threedimensional cam 141 which is translated in accordance with the above expression and rotated in accordance with the gun azimuth angle (Ag). Translation of the cam 141 is eected by a pinion 142 that meshes with a cylindrical rack 143. The pinion 142 is driven by gear 144 on shaft 145 that meshes with the output gear 137. Thus, the pinion 142 is rotated and translates cam 141 in accordance with the expression g (1-2 Gos Eg eos A,

Shaft 103 drives through suitable gearing 146 to rotate shaft 1 47 and elongated pinion 148 in accordance with the gun azimuth angle (Ag). The pinion 148 meshes with the gear 149 to rotate the cam 141 in accordance with the gun azimuth angle. The surface of the threedimensional cam 141 is so designed that cam follower 151 riding thereon is translated in accordance with the azimuth component (Na) of the lead angle (A) as determined by Equation 8. Cam follower 151 has a worm 152 on one end arranged to engage a worm gear 153 whereby shaft 154 rotates the azimuth reector 68 in accordance with the azimuth component of the lead angle.

As may be seen from Equation 9 the elevation component (he) of the lead angle is equal to the product of the expression l-Z eos Ag cos E',I

by which the cam 141 is translated, the sine of the gun elevation angle (Eg) and the cosine of the gun azimuth angle (Ag). Since the cam 141 is translated in accordance with the above expression and rotated in accordance with the gun azimuth angle, it is evident that a follower 157A angularly displaced by 90 with respect to the follower 151 is moved in accordance with the expression Z .1-Z cos A,z eos Eze This expression is multiplied by the sine of the gun elevation angle (Eg) by a three-dimensional cam 158 that is translated by cam follower 157 in accordance with the above expression and rotated by an elongated pinion 159 on the shaft 82. Since the shaft 82 is rotated in accordance with the gun elevation angle (Eg), the elongated pinion'meshing with a gear 161 on the cam 158 rotates the cam 158 in accordance with the gun elevation angle. The cam 158 may be laid out in a manner suchthat the cam follower 162 riding on the surface thereof is translatedin accordance with the elevation component (Xe) ofthe lead angle as defined by Equation 9.

Since the line of sight 17 is offset vertically with respect to the gun axis 11 in accordance with the elevation component of the lead angle, it is necessary to reduce the amount of this offset angle by the gravity deflection angle (qbs) that is the angle by which a projectile fired from the gun is dellected from a line representing the gun axis due to the force of gravity. As previously explained, this deflection angle is a function of the range and the gun elevation angle.

However, since an average range may be used, the gravity deflection angle (eps) may be determined by multiplying the cosine of the gun elevation angle by.a suitable constant. This deflection angle is therefore a function cos Ag of the gun elevation angle and its.value may be subtracted from the surface of the cam 158. Thus, the surface of the cam 158 is actually laid out in a manner such that the follower 162 is translated in accordance with the elevation difference angle (Ae-pg where the gravity deflection angle (s) is determined as the product of a constant in the cosine of the gun elevation angle.

A worm 163 on the cam follower 162 engages a worm gear 164 on shaft 165 to rotate the elevation reector 71 in accordance with the elevation difference angle.

Since the azimuth and

elevation reflectors

68 and 71 are adjusted in accordance with the azimuth component (Na) Aof the lead angle and the elevation dilerence angle (Xe-) as determined by Equations 8 and 10, the line of sight 17 is offset with respect to the gun axis 11 by these angles. A projectile red from the gun will, therefore, follow approximately the path displaced by the prediction angle (a) from the line of sight at the instant that the projectile is red. The function (Z) of the defending aircrafts velocity, as used in determining the azimuth and elevation components of the-lead angle, makes allowance for the deviation of the attacking craft from the line of sight. The path of a projectile red from the gun will deviate from the line of sight 17 by an amount corresponding to deviation of the attacking craft 52. Obviously, vthe amount of this deviation is dependent to some extent upon range. However, it has Vbeen determined that accurate resultsmay be obtained by using an average value of range in the computations of the lead angle.

Knobs

23 and 24 are arranged to adjust the alignment of the line of sight 17 with the gun axis 11. The knob 23 is mounted on a shaft 171 that carries an elongated pinion 172 adapted to mesh with the gear 173 on the Cam follower 151. Thus, rotation ofthe knob 23 rotates the cam follower 151 and worm 152 thereon. It will be apparent that rotation of the worm 152 causes rotation of the worm gear` 153 and azimuth reiiector 168 to adjust the line of sight in azimuth to align it with the gun axis 11. Similarly, the knob 24 is mounted on a vshaft 175 that carries an elongated pinion 176 which meshes with gear 177 on the cam follower 162. Rotation of the knob 24 acts through pinion 176 and gear 177 to rotate worm 163 on the follower ,162 thereby rotating the worm gear 164 and elevation reflector 71. In this manner, the line of sight 17 may be adjusted into alignment with the axis 11 of the gun.

After this alignment is effected, any movement of the gun in elevation or azimuth causes the line of sight to be offset relative to the gun axis 11. The amount of this offset includes the prediction angle and the lead angle. The amount of the lead angle offset is determined by a function of the velocity of the aircraft, which in turn is equal to the product of functions of indicated airspeed and altitude, and a function of the sighting angle between the line of sight 17 and the longitudinal axis 53 of the defending craft 51. f

The guns may be provided with suitable firing mechanisms (not shown) such as' triggers mounted with the

grips

15 and 16 and arranged to actuate electrical controls for the firing circuit'syl It is only necessary for the gunner to train the gun so the line of sight 17 falls on a selected target. Whenfthisi-occurs, he may operate the tiring mechanism, and the' gun will direct a projectile approximately along theliv of sight, deviating therefrom only to compensate 'follthe deviation of the path of the attacking aircraft, that is the prediction angle (a).

Thedetail mechanism described in connection with Fig. 3 may be mounted integrally with the gun, as shown in Fig. 1, or may be mounted separately therefrom to control a remote gun, as shown in Fig. 2. In each case In the latterl theaxis 25 for the computing mechanism 9. However,4

11 since suitable transmission systems are utilized to maintainthe axis 11', 11' of the gun 1 coincident with the axis 25 of the computing mechanism 9', the shafts 8 and 14' are rotated substantially in accordance with the azimuth and elevation angles of the gun.

As previously explained, the computing mechanism and gun sight herein described is primarily for use on aircraft in defense against attacking aircraft. Although the gun has been described as being used on a bomber, it should be understood that it may be used on any type of aircraft without departing from the invention. The best results may be obtained by using this sight and computing mechanism in the tail or nose of a defending craft because some of the approximations are based upon the conditions existing in firing at targets located within the tail or nose cone of the craft.

Equations 8 and 9 represent computations for the azimuth and elevation component lead angles for the tail cone of the aircraft. As has been explained, the invention may be used in either the tail or the nose of the craft. For the nose cone, Equations 8 and 9 must be revised.

From Equation 7 it is apparent that the lead angle (x) is dependent upon the sine of the sighting angle However, the mechanism is supplied with the position angles of the axis of the gun. For a gun in the tail of the craft, the gun position angle is equal to the difference between the sighting angle (00) and the lead angle (A), whereas the position angle of a gun in the nose is equal to the sum of the sighting angle (00) and the lead angle Equations 8 and 9 automatically compensate for this change in the relationship of the gun position angles and the sighting angle if the gun position angles are measured from the tail of the craft in both instances. As the gun azimuth angle (Ag), for example, exceeds 90, the cosine of this angle becomes the cosine (180-Ag) or a negative value. However, the mechanism 9 uses a logarithmic solution for Equations 8, 9 and 10 thus making it impossible to use the cosine function of angles greater than 90.

In order to use the mechanism for a gun in the nose of the aircraft, it is necessary to change the negative sign in the denominator of Equations 8, 9 and 10. For

a gun in the nose, these equations are written as Z l+Z cos A,cos E. Sm A' (u) Z A, sm E, cos AI (12) =l-l-Z cos Ag cos E,

log (l-l-Z cos Eg cos Ag) Since for a gun in the nose of the aircraft, the azimuth component lead angle (xn) and the elevation difference angle (xe-tps) are subtracted from the gun position angle to determine the line of sight, it is necessary that the

reflectors

68 and 71 be moved to subtract these angles instead of adding them to the gun position angles as is the case for a gun in the tail of the craft. This subtraction may be accomplished by designing cam 141 to have negative lifts, so that

followers

151 and 157 will be displaced to move the line of sight in the opposite direction to that in which it is moved for a tail gun.

It will be obvious to those skilled in the art that the computing mechanism and gun sight described may also be used with great accuracy in tiring from an aircraft toward relatively stationary targets, such as targets on the ground or comparatively slowly moving targets in the air.

As many changes could be made in the above construction and many apparently widely different embodiments of this invention could be made without departing from the scope thereof, it is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative and not in a Hunting sense.

What is claimed is:

l. In an automatic computing mechanism for a gun sight of the own speed type for aircraft, the combination of azimuth and elevation members movable respectively n accordance with the azimuth and elevation movements of a gun on the aircraft, means to convert the movement of the azimuth member to a movement representing the logarithm of a cosine function of gun azimuth, means to convert the movement of the elevation member to a movement representing the logarithm of a cosine function of gun elevation, means settable according to the indicated air speed and altitude of the aircraft to represent the logarithm of a function of the air velocity of the aircraft, means to combine the logarithmic representations, means to convert the combined logarithmic representation to a representation of the logarithm of unity minus the combined logarithmic representation, means to subtract the last recited logarithmic representation from the representation of the logarithm of the function of air velocity, and means to multiply the quantity represented by the resulting logarithm by the sine of gun azimuth.

2. In an automatic computing mechanism for a gun sight of the own speed type for aircraft, the combination of azimuth and elevation members movable respectively in accordance with the azimuth and elevation movements of a gun on the aircraft, means to convert the movement of the azimuth member to a movement representing the logarithm of a cosine function of gun azimuth, means to convert the movement of the elevation member to a movement representing the logarithm of a cosine function of gun elevation, means settable according to the indicated air speed and altitude of the aircraft to represent the logarithm of a function of the air velocity of the aircraft, means to combine the logarithmic representations, means to convert the combined logarithmic representation to a representation of the logarithm of unity minus the combined logarithmic representation, means to subtract the last recited logarithmic representation from the representation of the logarithm of the function of air velocity, means to multiply the quantity represented by the resulting logarithm by the cosine of gun azimuth, and means to multiply the resulting product by the sine of gun elevation.

3. In an automatic computing mechanism for a gun.

the indicated air speed and altitude of the airrcaft tol represent the logarithm of a function of the air velocity of the aircraft, means to combine the logarithmic repre-V sentations, means to convert the combined logarithmic representation to a representation of the logarithm of unity plus the combined logarithmic representation,

means to subtract the last recited logarithmic representation from the representation of the logarithm of the function of air velocity, and means to multiply the quantity represented by the resulting logarithm by the sine of gun p.

azimuth.

4. In an automatic computing mechanism for a gun sight of the own speed type for aircraft, the combination of azimuth and elevation members movable respectively in accordance with the azimuth and elevation movements of a gun on the aircraft, means to convert the movement of the azimuth member to a movement representing the logarithm of a cosine function of gun azimuth, means to convert the movement of the elevation member to a movement representing the logarithm of a cosine function of gun elevation, means settable according to the indicated air speed and altitude of the aircraft to represent the logarithm of a function of the air velocity of the aircraft, means to combine the logarithmic representations, means to convert the combined logarithmic representation to a representation of the logarithm of unity plus the combined logarithmic representation, means to subtract the last recited logarithmic representation References Cited in the file of this patent UNITED STATES PATENTS 1,067,859 Bacon et al. July 22, 1913 1,811,688 Gray June 23, 1931 1,936,442 Willard Nov. 2l, 1933 1,940,518 Watson Dec. 19, 1933 2,012,960 Coupland Sept. 3, 1935 2,385,348 Chafee Sept. 25, 1945 2,403,117 Peters July 21, 1946