US2805601A - Toss bombing apparatus - Google Patents

Description

Sept. 10, 1957 H. s. MORTON TOSS BOMBING APPARATUS 5 Sheets-Sheet 1 Filed June 1, 1944 gwuc/wbom Hurnld IE]- M ar a an T "known L w ouuhav ubw ukw MCKELV. E 3% x fi wmm Sept. 10, 1957 H. s. MORTON 2,805,601

TOSS BOMBING APPARATUS Filed June 1, 1944 3 Sheets-Sheet 2 gnaw bow Hurnlpl E1- Murctlii @294 a flmmm 4% Sept. 10, 1957 H. s. MORTON TOSS BOMBING APPARATUS 3 Sheets-Sheet 3 Filed June 1, 1944 A 2 WW gwuc/vvto'r/ l-luruld E1- Mar-"c an 2,805,60l Patented Sept. 10, 1957 1 2,805,601 TOSS BOMBING APPARATUS Harold S. Morton, Takoma Park, Md., assignor to the United States of America as represented by the Sec= retary of War Application June 1, 1944, Serial No. 538,311 Claims. (Cl. 89-15) (Granted under Title 35, U. S. Code (1952), sec. 266) The invention described herein may be manufactured and used by or for the Government for governmental purposes without the payment to me of any royalty thereon.

This invention relates to a method of bombing by aircraft and particularly to a method of plane-to-plane bombing.

Close formations of heavily armed bombing planes have recently been signally successful in their ability to perform their mission in spite of heavy attacks by enemy planes. At the same time such formations are able to inflict severe losses on the attacking planes. There is therefore a need for technique which will damage :or destroy the individual planes in such bomber formations, or force the dispersion of the formation so that pursuit planes can deal with the bombing planes individually, without exposing the attacking plane to the concentrated fire of the formation at short ranges.

The bombing of such a formation by an attacking plane has been heretofore suggested. The suggested method however generally involved the attacking plane flying parallel to and at a greater altitude than the bomber formation, hence requiring a vertical fall of the bombs of the attacking plane. Such a method when employing bombs equipped with contact fuses cannot be successful against an alert enemy for the following reasons: a. When the bomb is released from a safe distance above the enemy bomber formation, the time of fall of the bomb permits time enough for evasion by the bomber formation. For example, neglecting air resistance, in the first second the bomb falls only sixteen feet, in the first two seconds, sixty-four feet, etc. so that if the attacking plane stays at a relatively safe distance of 3000 feet above the bomber formation, approximately eleven seconds are required for the bomb to fall to the target. b. With contact fuse bombs, a direct hit on one of the bombersin the formation is necessary and of course is extremely diflicult to achieve. c. The determination of the proper point of release by systems of sighting which must take into consideration relative velocity, range, and difference of altitude tends to be a very difficult process requiring complicated apparatus.

Accordingly, it is an object of this invention to provide an improved method of bombing by plane, particularly effective against flying targets but equally applicable to targets on land or water.

A particular object of this invention is to provide apparatus for carrying out the bombing method disclosed herein.

The specific nature of the invention as well as other objects and advantages thereof will clearly appear from a description of a preferred embodiment as shown in the accompanying drawings in which:

Fig. l is a schematic diagram showing the path of a projectile released from an attacking plane flying a horizontal course after such plane has pulled upwardly with an acceleration of 2g or greater and released a projectile at the point R.

Fig. 2 is a schematic diagram showing an attacking plane flying on a collision course with respect to a target plane, illustrating the line of sight between the attacking plane and target plane at successive time intervals t1, 12 etc.

Fig. 3is a view similar to Fig. 2 but showing the path of the projectile after the release of such projectile at the point R with coordinates based on the horizontal.

Fig. 4 is an enlarged diagrammatic view of a portion of Fig. 3. i

.Fig. 5 is likewise a diagrammatic view of a portion of 1 Fig. 3.

Fig. 6 is a view similar to Fig. 4 but with the horizontal coordinate axis parallel to the line of flight of the target plane.

Fig. 7 is a diagrammatic view showing the last plane in the flight'nearest to the attacking plane utilized for sighting purposes when releasing the bomb on a steep dive approach. The path of such released bomb is also shown.

Fig. 8 is a diagrammatic view showing a generalized condition of an attacking plane flying a collision course at A and then pulling up to release the projectile at a point B and also showing the projected path of such projectile after release at point B.

Fig. 9 shows diagrammatically a simple form of integrating delayed release mechanism.

Fig. 10 is an elevational sectional view of an airplane carrying the toss bombing mechanism of this invention.

In the bombing method comprising the present invention, the pilot of the bombing plane flies, at uniform velocity, on a straight line course which, if continued indefinitely, would cause him to collide with the target. While still a safe distance from the target, he determines, in any conventional manner, how far away he is in terms of time from the target. Knowing this information, the bombing plane is given a proper vertically upward acceleration for a long enough period of time to insure that the velocity of the bomb, when the latter is released shortly thereafter, will be such as to cause the bomb to cross the original line of flight of the bombing plane close enough to the theoretical collision point of the planes to insure proper functioning of the fuze on the target, assuming that the latter, i-f moving, has not changed its speed or direction of flight. Acceleration integrating means is provided, according to the invention, for delaying the release of the bomb during the acceleration of the plane until the proper bomb velocity has been reached to accomplish the desired result.

My invention may be used with any bomb carrying airplane. As suggested in Fig. 10, the bomb 30 is normally carried along the belly of the airplane 31 and is detachably connected thereto by fasteners 32. The fasteners 32 operate to release the bomb in response to functiming of the bomb release mechanism 33. Bomb release mechanism 33 is in turn responsive to the acceleration integrator 34. In the palticular integrator, shown in detail in Fig. 9, a predetermined rotational displacement of shaft 22 depends upon an integration of vertical accelerations of the airplane over a period of time to give the necessary vertical component of the velocity to the airplane and its bomb. Upon attainment of this velocity the bomb is released and its flight to a target is assured. Angle of flight with respect to the actual horizontal is indicated by a conventional artificial horizon 36.

It will be apparent that the present method can be utilized in bombing stationary or moving targets on land or sea or in the air. In the case of a stationary target, the line of flight of the bombing plane will be a straight line to the target. For a target moving in a straight line at uniform velocity, which will be the usual case, the line of flight of the bombing plane and the course of the target will be straight lines intersecting at the collision point.

The method of bombing in accordance with this invention is particularly effective with bombs equipped with proximity fuses. The specific nature of such fuses forms no part. of this invention and such fuses may be any of several known constructions. In general such fuses have an arming time on the order of several seconds which permits the plane releasing the bomb to get sufficiently faraway from the bomb after it is released'that'the releasing plane will not accomplish the detonation of the bomb, Such fuses are generally effective to detonate the bomb'when they approach within one hundred fifty feet or less of thetarget object, which. of course is well within the effective destruction range of a 500 pound or larger bomb. i

The technique of flying a collision course toward the target applies not only to direct head-on attack from the same level and directly in front of the target, as where the target is an enemy airplane, but also to ap proaches at' an angle, in which the bombing plane and the target have straight line intersecting courses, and *to approaches from above, in a dive bombing attack or l,

even from a lower level in a climbing approach; The method constituting this invention is most clearly understood when applied to conditions where the attacking plane is flown straight into the face of oncoming enemy planes, at the same level and flying directly down means in the line of sight of the attacking plane will 7 serve the same purpose. Upon reaching a predetermined range from the approaching enemy, which range will be shown to be not very critical, the attacking plane pulls up sharply and-by means of apparatus to be described, releases his bomb slightly after beginning the pull-up. The eflfect of this maneuver is to give the bomb a slight upward toss whereby the bomb first rises slightly above the line of flight of the approaching enemy plane, reaches zero upward velocity and then falls below such line of flight in accordance with the gravity forces. operative on the bomb. However, the bomb has a horizontal velocity of approach to the enemy plane equal to the sum of the velocities of the attacking and target planes.

. The desirability of this method will be clearly evident from the following table. In this table there has been calculated for pull-up accelerations of the attacking plane ranging from 2% g to 4 /2 g the necessary time delay 'in release of the bomb from the beginning of the upward acceleration to produce upward velocities of the bomb of 64, 72, and 80 feet per second. The vertical positions of the bomb with respect to the original line of flight of the attacking plane is also tabulated showing the height of the bomb at release, the maximum height attained, and the height at 4, 5, and 6 seconds respectively after release with respect to the horizontal path of the target.

From above table, it will be apparent that the released bomb will lie within a hundred and fifty feet vertically of the line of flight of the enemy' plane formation for at least five seconds after release of the bomb, and with the eighty foot-seconds upward velocity at release, for six full seconds. As has'already' been mentioned the bomb is approaching the target'plane with a horizontal velocity equal to the sum of the velocities of the attacking and target planes. If each plane. is assumed to be flying at the rate of three hundred miles per hour, the rate of approach is 880 feet per second. Neglecting the retarding etfect of air friction (which in the case of heavy bombs. has been found to reduce the range less than forty feet at 300 miles per hours), a bomb may be released 4400 feet horizontally from the target and reach the new horizontal positionof the target infive seconds. In this example, the attacking plane thus could release its bomb elevent times 'as far away' from the target in accordance with this method than an attacking plane relying solely on the vertical fall of the b01111). V r

The limiting factor in determining how close the attacking plane can approachthe target before releasing a bomb with a proximity fuse 'is the time necessary for theattacking plane to get a reasonably safe distance away from its own bomb before it becomes armed and operates on the. target. As has been shown, it is not suflicient for an attacking plane to rely solely on gravity to put distance between it and the bomb. However, in accordance' with this invention the attacking plane pulls'upward away from the bomb with an acceleration of at least 2 /2 g. The following table has been Eomputed to show the separation between the attacking plane and the bomb if the attacking plane pulls sharply upward immediately after release of the bomb.

TABLE B Separation from. released bomb 5 The foregoing table would indicate that an arming delay time on the order of four seconds will provide. ample safety for the attacking plane if the'pilot pulls upward with an acceleration of at least 2 /z' g. If the pilot is willing to pull up with a higher? acceleration,

the arming time may be still further reduced. 1

Referring to Tables A and B with the specific exam- TABLE A Total Acceleration 2% g 3 g 3% a 4 g 4% a a Time to Release 1.33 1.0 0.8 0.67 O. 57

- aximum eig Upward Venom Height 4 sec. after Releas 43 32 2e 22 11s 9- Height 5 see. after Release- -a7 -48 -54 -58 -e2 Height 6 see. after Release .do -149 --160 166 170 174' Time to Release .seconds 1. 5 1.12 0. 9 0.76 0. 64 V I I et. 54 40 32 27 2g 72lsec. Upward Velocity 2 g g; 2 r at Release. 1 1 13 -89 ,1o5 -111 116 --12a 1. 67 1.25 1.0 0. 0. 71 67 50 4O 33 28 80lsee. Upward Velocity g 167 150 133 128 at Release Height 4 see. after Releas 131 114 104 97 92 Height 5 see. after Release- .d 67 5O 4O 33 28 Height 6 sec'. after Release do -29 46 56 -63 68 Height 7 see. after Release do 157 -174 -J .84 191 -198 ple of both attacking and flying planes flying at 300 miles per hour, the advantages of bombing methods in accordance with this invention are apparent. If the bomb fuse is set to produce a four-second arming time delay and the pilot pulls up with an acceleration of from 2 to 4 /2 g, releasing the bomb with an upward velocity of 72 feet per second, then as illustrated in Fig. 1, his bomb may be released at a range varying from 3520 feet to 5280 feet from the target and the bomb will nevertheless be armed and within 150 feet vertically of the target when it reaches the same horizontal position as the target. Furthermore, the attacking plane will be safely out of range of harm both from its own bomb and the fire of the target plane. Since the proximity fuse will cause detonation of the bomb at an approach of 150 feet or less to the target, the probability of damage to the attacking plane, and particularly to a formation of attacking planes, is very high.

The enemy must take sharp evasive action within a very short time to avoid the effective area of the bomb. It is obviously an advantage for the attacking plane to keep the time between the release of the bomb and its reaching the vicinity of the target as low as is consistent with the safety of the attacking plane. If the time is kept low, a formation will not have suflicient time to make any efiective change of pace or direction after the bomb is released. The enemy may start to turn as soon as he sees any planes making a frontal approach. This can readily be defeated by flying several attacking planes abreast of each other, so that no matter which way the enemy plane turns, some one attacking plane is in front of him. Movements of the enemy up or down can be matched by the attacker and even if the enemy at the last moment takes a course at the last line between him and the enemy plane, the latter can aim, not at the enemy plane itself, but at the imaginary spot where the enemy plane will be if it continues its new course until the bomb meets it.

Following is a mathematical analysis of the uniform level-head-on attack method. Referring to Fig. 1 the attacking plane A is flying horizontally maintaining a uniform level-head-on approach to enemy plane E. The attacking plane A is equipped with a delayed release mechanism on its bomb rack, which will be described later, to delay the release of the bomb until a predetermined upward vertical velocity is attained by the attacking plane. At point B the pilot presses the release trigger and immediately pulls up sharply with an acceleration of 2 g or more. The delayed release mechanism holds on to the bomb until it reaches point R, at which point it has a vertical velocity v and has been lifted a distance L above the original line of flight.

At the time of release the bomb has the same speed as the plane in a direction tangent to the line of flight. This velocity V is resolved into its vertical component v and its horizontal component V11.

In precise calculations of the trajectory consideration must be given to the fact that Vh is one or two percent less than V. For this presentation secondary effects of minor character will be disregarded, while a general conception of flight characteristics is developed.

Let

then

pulling up.

A mechanical delayed release mechanism will be later described which will in effect integrate the above relationship and hold up the release until a predetermined upwardly velocity is reached, regardless of whether the pull-up be gentle or abrupt.

Let 0 be the origin of a system of rectangular coordinates; and let t=time in seconds after release at point R whose coordinates are x=o y=L Properly chosen values of v will cause the bomb trajectory to cross the original line of flight (and line of sight) any desired number of seconds after release, as shown at x .(Fig. 1). Anywhere between points C and D is close enough to the line of flight to be effective, so there can be considerable error in determination of range or velocity of approach without causing a miss, because of the flatness of the trajectory.

For example a trajectory will be calculated for V='440/sec. v='/sec. a=96'/sec./sec. from Equation 3 above L=50 feet.

TABLE C [Time (1!) seconds] z 1,760 1,980 2,200 2, 420 2, 640 2, 860 3,080 11 114 86 50 0 -4a 10B 174 The crossing point is just past 5 /2 seconds or 2420 feet after release, but the trajectory is at no point more than feet off the line of flight until just before 7 seconds has elapsed.

If the enemy is approaching at 440/ sec. and assuming an arming time of 4 seconds, the distance between the two planes at time of release might vary from about 3520' to about 6000 feet, a difference of nearly /2 mile, without causing a miss.

The principles of this invention are equally applicable to all other approach situations to both moving and stationary targets in addition to the uniform level-head-on approach already discussed. concepts of this invention are involved in the angular approach. The method of the invention may be stated in the following general terms. Assuming that the enemy plane has been sighted and is moving in a fixed course at a uniform velocity, the attacking plane need only assume a flight direction and velocity whether level flight, climbing, or diving which if maintained uniformly will intersect the enemy plane. In other words the attacking plane flies a collision course with respect to the enemy plane. The attacking plane now may consider itself as a fixed reference point of a system of coordinates. The target then appears as an object approaching the fixed reference point at a uniform velocity along a straight line. To the pilot of the attacking plane, it appears that the approaching object will strike him if he does not move out of the way. Accordingly, by apparatus to be described, the pilot ascertains the exact length of time existing prior to the impending collision. He then moves 01f his course to avoid the collision and thereby moves In fact the most general.

' right angles to the collision course.

away. from the fixed reference point. As he does so, he tosses. thebomb vertically upward with just sufiicient velocity. that it .will rise, stop, and fall back to the fixed reference point in exactly the same number of seconds that will be taken by the target to reach the same point.

With this concept of the method of bombing in accordance with this invention, it is thereforeimmaterial whether the path of the attacking plane is horizontal, diving, orclimbing so long as the attacking plane is fast enough to fly on a course which will eventually collide V with the target.

The attacking plane may readily fly on the necessary collision course without requiring special instruments or computing mechanisms. Referring to Fig. 2, an attacking plane at A observes, an enemy plane at E. When first observed the enemy plane in general has an apparent angular motion about the attacking plane. The attacking plane is turned in'such a way as to head off the apparent movement of the enemy which is accomplished by getting on'a'c'ourse at B such that the line of sight A enemy continues to maintain the same absolute orientation with respect to the attacker, the two must inevitably collide, if the courses are continued.

The principle is the same as that habitually used in navigating to reach a certain destination in a cross-wind. The plane does not point toward its destination at all, butit does maintain a constant orientation which ultimately brings it'directly to the destination. The same principle applies to, a plane approaching another, not directly head-on, but at an angle from the side. For each condition of relative speeds and angle of orientation, the attacking plane can swing to a line of flight which constantly'maintains the other plane in the same absolute orientation, just as long as both continue to fly a straightline, uniform speed course. It makes no difference whether the geometric plane containing the two intersecting flight lines is horizontal, vertical or oblique.

Under any of these conditions, when the attacking plane on its collision course is considered as the reference point, the target will appear to be approaching along a straightline at a uniform velocity. There is however, a marked difference in the direction of toss of the bomb obtained by merely pulling up, according towhether the attacking plane is flying level or at an angle with respect 'to the gravity'axis. An attacking plane flying level and then pulling up off the collision course imparts only a vertical upward velocity of the bombwith respect to the reference point. 'When the attacking plane is diving or diagonally climbing, a bombtossed by pull up will not have a resultant velocity vertically upward but will be directed at Under such conditions, it is more difficult to toss the bomb with only a resultant vertical upward velocity with respect to the reference point. It is however possible to obtain such a resultant velocity in a diving plane by a simultaneous change in direction of the plane, such as by pulling out of the dive, and simultaneously reducing the speed of the dive by throttling the motor and/or lowering the wing flaps. Proper coordination between the rate of pullup and rate of reduction of speed will give a resultant toss which is straight up, relative to the fixed reference point. If a toss of this type is accomplished then the relationships computed in Tables A and B are still accurate and hence the same advantages are obtained independent of direction of approach to target.

It will now be demonstrated that only a small, readily compensated erroroccurs in the application of the bombinamet pd 0.1": t s inventiqato an ns a appma o the In the vertically upward toss of the, bomb, the superelevation? causes the resulting evolute' bombtrajectory to lie above the projected linefof flight for a certain nurnberrof seconds until gravity pulls it backacross thelline. In the toss perpendicular to an angular collision course, two new factors enter into. the problem: a. The trajectory does not curve back toward the original line of flight of the releasing plane as fast as in the case of horizontal flight because only a part of the force of gravity acts as a restoring force in this direction. b. The bomb does not travel abreast of the corresponding positions on the releasing planes collision course as time goes by; but it accelerates its velocitydue to the component of gravity and runs further and further ahead of the projected plane positions (which are predicated on constant speed).

Referring to Fig. 3, the family of parallel lines t1, t2, ts, etc., are called isochronous lines, and represent the orientation of the target with respect to thejattacking plane at various times. (Note: The exact position of the target on any one of these lines is not known, and hence the exact time at which the collision-point of the two courses is reached will require instrument determination by apparatus to be described.) It is necessary to examine the parabolic trajectory of the bomb and see Whether, at successive times, :1, t2, t3, etc., it is reasonably close tothe isochronous lines corresponding to the same respective times.

. It will be noted from Fig.3 that at a time the bomb t4 will reach its closest approach to the target plane at a point G before the target reaches the collision-point on the intersection of the two flight lines, and at a lower level than the corresponding point H on the attacking planes projected course. This shows that the two new factors discussed under a and b, above,'produce compensating effects which make it possible to score hits (or be within fuze radius) over a-considerable range of time'intervals, in dive-bombing attacks, just as in level flight attack.

This effect can be investigated mathematically by setting up'equations for the parabola and the isochronous lines, in a system of rectangular coordinates with point 0 (Fig.

3) on the projected path of theattacking plane as the Equations for. the parabolic trajectory of the bomb by application of'well known formulae are then: V

x=L sin or+vl sin a +Vt cos at T (6) Equations for the family of isochronous lines:

y=x tan 0n When t and n are bothzero tion of Fig. 3 at any time t, the value ofn is represented by GA.

AB=BD tan 0=Vt cos 0: tan 0 Assigning proper algebraic sign to the several terms the equation for the isochronous lines becomesz y=x tan 0+Vt cos or tan t2-Vt sin or (9) Any given values of t define a particular point 011 the parabola, and give the equation of a particular line when substituted in the isochronous line formula. It becomes of interest to determine the value of y on the isochronous line t for the value of X as found on the parabola for t and then to see what the difierence is between the y point L of the parabola and the y point K of the isochronous line. Such difierence is illustrated graphically as the line KL on Fig. 5 which is a view of a portion of Fig. 3.

Substitute in the formula for the isochronous lines, the value of x for the parabola as follows:

isochrone: y=x tan 0+Vt cos a tan -Vt sin a x of parabola: x=L sin u+vt sin a-f-Vl cos a (6) Substitution: i

y=--L sin oz tan 9-vt sin a tan 9-- V2 cos a tan 0+Vt cos 0c tan 0-4 1 sin a =L sin or tan 0vt sine tan 0-Vt sin a Subtract this value of y from the value of y for the parabola which is:

in order to get the value of KL- the difierence in values of y for various values of t. The closest approach to the path of target is the line LM and is found by multiplying KL by cos 0.

KL=L cos 06+Vt cos oc-Vt sin u- /zgr L sin a tan 0+vt sin a tan 0-l-Vt sin a KL=(L+vt) (cos oc-I-Sifl a tan i9) /2gt (10) The relationships between or and 0 obviously depend on the relative velocities of the two planes. Referring to Fig. 6 where the x coordinate axis is taken parallel to the flight of the target plane B:

Let

Sin 0:

tan 0= (11) cos ark- In order to adjust the constants in the trajectory equations to the proper values, let the y=ditferences, or KL of Fig. 5, equal zero at the value of t at which greatest accuracy is desired.

KL=(L+vt) (cos ut+sin a tan 0)- /2gt 12 =0(L+vt) (cos a+sin a tan 6l)= /2g1:

Now substitute value of tan 0 in terms of a derived in (11) above Solving for Sin 0:

t (1 cos a+ cos cplranging from one to zero.

In this table the time from bomb release to reaching of collision point has been selected as six seconds and a net pull out acceleration of 3gs has been assumed.

TABLE D [Values of 11.]

Indications of the above table, drawn up for maximum accuracy six seconds after release of the bomb are that when the velocities of both planes are equal, or

V 1 the angle of dive at has no effect on the required velocity of the bomb produced by the delayed release mechanism; but when the target plane is at a lesser velocity, the perpendicular component of bomb velocity v should be reduced as the angle of dive increases. The lower the target velocity, the greater is the reduction in velocity v with increased angle of dive. This correction to the delayed release mechanism obviously could be made manually by the pilot of the attacking plane in anticipation of the probable relative speeds of the target plane and the attacking plane.

The following numerical example is presented to illustrate how close the bomb will come to the isochronous lines, each of which is intersected by the target plane, at various times from four to eight seconds after its release when the value of v corresponds to that shown in the preceding table.

The perpendicular distance between the bomb and any isochronous line is of course LM of Fig. 5. Let plane and target velocities be equal or Let at equal 40; then from Table D v=87 feet per second and L=54 feet.

sin a Substituting in Equation '10 sin a KL-(L+Ut)(COS a+m)}gt =Llvtygt and I, W.

MK=(L+vt-%gt cos a 14) From Equation 14 the following. table has been com puted: V

.11 TABLE E"' Distance between bomb and isochronous lines to-target plane as function of time [t (seconds)] 44 5 5% 66% vw's LM (feet).. 137 115 85 45 0 64 114 181 257 It will be understood that when a steep dive-bombing attack is made with an approach from a quartering posia tion instead of directly in front, the over-run of the bomb discussed above will cause it to carry beyond the course of the enemy plane. It will tend to make the hit on the second or third plane on the flank of the formation opposite the attacker, unless some corrective measures are taken. This phenomenon resembles the effect of angle of lag on cross-wind bombing, and will only eflect this technique on angular approaches across the enemys course.

Note that this effect is not present if a cross-course approach is made at the same level; and it is not significant at moderate angles of dive. 7 It only becomes noticeable in steep dives considerably to one side of a head-on ap proach. In order to evaluate the importance of this effect, an analysis will be made of the over reach by which the bomb trajectory lies ahead of the projected line of the dive-bombers course at various times after release of the bomb.

The projected line of flight of the plane (Fig. 6) is at an angle at below the x-axis and starts from the origin. Its equation may be written:

y=x tan a or x=y cot a (15) Substitute for y the value for the parabola from Equation y=L cos a+t1t cos aVt sin 01%;]? (7) Then, a2: L cos a cot a-Ui cos a cot (1+ Vt sin a cot. a-Hgt cot a cos 0: cos a 2 :v-- L sin a vt sin a cos Obi- 19 cot a Subtract this from the value of x for the parabola from Equation 6 to obtain the-horizontal over reachz x=Lsin a+vt sin oH-Vi boso (6) Over reach= The preceding table illustrates how far thebomb over reaches horizontally the isochronous lines to the enemy plane. Thus the enemy plane is always short of .its: collision-point? with the course of the bombing plane, because, in the oblique attack. the over-reac of the bomb, and its accelerated downward speed cause it to meet thetarget sooner than the attacking plane would reach the collision-poin and sooner than the enemy 12 plane would reach the attacking planes coursel- There-v fore, in the oblique approach, dive-bombing attack, the bomb falls beyond the collision-point in prolongation of the attacking planes course, and the enemy plane is short of reaching the theoretical collision-point. It is noted from the table in the preceding paragraph that at six seconds the distance of over-reach is 206 feet which is just a little more than fuze ranges. The amount by which the enemy plane falls short of the collision-point is closely related quantitatively to the over-reach of the bomb, as in the head-on approach; this is what guarantees the hit.

The foregoing complication is the only one that arises in the application of the bombing method in accordance with this invention to the general problemof approaching the target plane from any angle. Such error of course does not exist if the velocity component imparted to the bomb at release is. vertically upward instead. of perpendicular to theplanescollision course. Such an error could of course be eliminated by introducing a computing sight mechanism. However, 'one of the outstanding advantages of this method of bombing is the elimination of such complex devices. The following solution is therefore suggested which is based on the premise that plane-to-plane bombing attacks will be made against formations of enemy planes as generally will be the case. approaching on a steep diving course and desiring to detonate his bomb in the vicinity of the leading plane of a V-formation, which point offers the most possibility of damage toall of the planes, instead of aiming to hit the leading plane, the attacking plane takes thelast plane on the nearest side to him as the target (Fig. 7). Dis-. regarding all the rest of the formation, he keeps this one flank plane in the constant orientation which establishes converging courses toward the collision-point. This procedure, due to the deviation discussed above, will then cause the bomb to reach the vicinity of the leading plane.

Thus far the proper operation of the delayed release mechanism has been assumed. Analysis of the mathematical factors covering this operation will now be presented. V

Such analysis will be based upon the simplified concept of the method of bombing wherein the attacking plane flying its collision course is considered a fixed reference point. It should be remembered in connection with the following analysis, that when the attacking plane is flying an angular course with respect to the gravity axis, then the analysis is absolutely correct only if a resultant vertically upward toss is imparted to the bomb thru the comattacking plane until a resultant component of velocity v' directed vertically upward has been attained. In level flight approach, such velocity component v will be per-,

k=the number of gs of total vertical acceleration, as-

sumed to'be uniform between points A and B;

t =the time in seconds that the bomb is released after initiation of the pull-up.

Let I a v=-the vertical componentof velocity of the bomb at the instant of its release at point B.

Under such circumstances the attacking plane' H +L=the total distance of the fall from the apex of the trajectory back to the level of the original line of flight.

If the total acceleration is kg, the net upward acceleration is g(k1). Hence oand Analysis can now be made of the proper release delay time l'p which will accomplish the delivery of the bomb to a point D on the projection of the original line of flight at a time T1 seconds after the start of the pull-up.

The above derived Equation 26 is an accurate expression for the functioning of the integrator. The physical significance of the expression is that an integrator which is pre-set to deliver the bomb at the collision point at the projection of the original line of flight of the plane at T1 seconds after initiation of pull-up by the attacking plane, must delay the release of the bomb by a time t which is determined by the rate of acceleration k at which the pull-up is accomplished, -in accordance with the above derived equation. The relationship between i and k is obviously a non-linear function and simple means whereby the integrator could react to various values of k exactly in accordance with the above equations are not immediately obvious. However, an examination of the function k+k /1-l/k discloses that it develops into a very flat, practically linear curve for values of k above 1.5. Since the criteria could be readily established that every attacking plane should pull-up with an acceleration greater than 1.5g (and as a practical manner the values of k will more likely be greater than 2) the behavior of the above k-function for values of k below 1.5 is of little interest or concern. It is therefore possible to select a linear function of k which so closely approximates the above derived k function that the error is negligible be- 14 tween values of k greater than 1.5 and less than 4. Such linear function has been found to be 2.035 (k.322.). Thus the relationship between t for k for a. fixed value of T1 becomes the following:

It will be noted that the analysis heretofore was based on an assumed uniform constant acceleration during pull-up of some value greater than 1.5g. As a practical matter the acceleration builds up from one g to the final value over a finite period of time. The error caused by \such'gradual build-up over the whole period amounts to less than two-tenths of :a second with the above equation. This error is fully compensated if the equation is modified as follows:

Obviously other compromise adjustments are possible involving modifying the co-efficient 2.035 as well as the value .322 until the combination which best fits the usual flight conditions of an attacking plane is obtained.

The analysis heretofore developed demonstrates clearly that the only factor which need be determined by the pilot of the attacking plane is the time remaining before he will collide with the target, so that he may initiate his deviation from the collision course at exactly the time T1 for which integrating delay release mechanism is set. Having begun his build-up or pull-out as the case may be, at the proper time T1, the integrating delayed release mechanism will accomplish the release of the bomb at a proper velocity v determined by the rate of pull-up k. A pilot therefore does not need to know how big the enemy plane is, how fast it is flying, or its exact range at any given instant. He needs to know only the time to target.

The time to target may be determined by any of several known methods. Indicator means 35 carried by the airplane 31, Fig. 10, for determining the time-to-target comprises radar equipment, for example, which will yield instantaneous determination of range and hence rate of change of range. A simple division of the range at any instant by the rate of change of range which will generally be quite uniform will yield the time to target. Alternatively, and for utmost simplicity of instrumentation, the reversing clock technique may be utilized. In accordance with this technique, the pilot views the approaching target thru a sight having a target mil-scale or possibly a pair of concentric sighting circles. A clock is started when the approaching target subtends a certain angle determined by the scale on the sight or by the target filling the smaller one of the sighting rings. When the target is one-half as far away, the angle then subtended is readily determinable by application of trigonometry and may be indicated on the mil-scale of the sight or by the point at which the view of the target fills the larger sighting circle. At this point the clock is reversed and starts running backward. The clock is then measuring time to target and will read zero at the instant of collision if the attacking planes course is maintained. When the clock reads the value T1, for which the integrating release mechanism is set, the pilot energizes the integrating release mechanism :and begins to pull-up with a uniform acceleration kg of at least 2g. Release of the bomb is accomplished by the integrating release mechanism when the bomb has attained a proper vertical component velocity v in accordance with the relationship between v and k heretofore derived.

Fig. 9 illustrates a simple form of integrating delayed, release mechanism which will function in accordance with. Equation 28 heretofore derived, namely,

the airplane.

The mechanismcomprises a disk driven at a constant speed about a horizontal axis by any suitable means (not shown). Preferably the speed of such drivingis adjustable Which has the effect of permitting a variation in the values of T1 of Equation 28. The disk 10 drives a second disk 20 which is rotatably supported with its axis vertical and hence perpendicular to the driving disk 10. The disk 20 is driven by friction by disk 10 but will of course only receive a driving force when it is displaced from the center of driving disk 10. The disk 20 is normally supported in a frame 21 which is in turn secured to a weight 26. The weight 26 is suspended from a fixed support 24 by a spring 23. Inertia means, such as Weight 26, is guided along thepath perpendicular to the nose-to-tail center line of A stop 25 is provided to prevent upward movement of weight 26 at accelerations less than one'g. The arrangement is such that when the airplane is in level flight, the disk 20 is supported atthe center of driving disk 10 and hence is not rotated by driving disk 10. An upward acceleration of the plane will impart a vertically downward force to weight 26, which during the existence of such acceleration will assume a lower position determined by the characteristics of spring 23. The extension of spring 23, has the effect of moving the disk 20 radially from the center of driving disk 10. Hence disk 20 is now rotated by driving disk 10 at a rate depending upon the deflection of spring 23 and hence upon the upward accel eration produced by the plane. The disk 20 thereby rotates a suitable shaft 22 which is connected thru gearing mechanism represented by 27 to a conventional bomb release mechanism 33, diagrammatically shown in Fig.

10 in such a manner that a fixed extent of rotation of the shaft 22 accomplishes the release of the bomb. Ob-

' viously the time required for the shaft 22 to accomplish such fixed extent of rotation depends directly upon the radial position of the disk 20 with respect to the center of driving disk 10. Thus under level flight conditions, or with a force of one g operative upon the weight 26, there is no rotation of disk 20. During upward acceleration of the plane the disk 20 is rotated at a speed proportional to (a g), where a is the acceleration of the plane, and the time required for the shaft 22 to complete the fixed number of revolutions is thus inversely proportional to the acceleration. By suitable selection of the mass of weight 26, the proportions of spring 23, and the speed of driving disk 10, this mechanism will readily produce a delay release time in accordance with the relation It will therefore be apparent that this invention provides. a simple yet extremely accurate method of bombing of any type target requiring only the determination by simple instrumentation of time to target. The integrating delayed release mechanism performs all necessary calculations and accomplishes release of the bomb with proper velocity to reach the theoretical collision point with the target at the same instant that the target arrives at such point. Furthermore, I have provided a simple and yet rugged form of integrating delayed release mechanism which will. accomplish the necessary functions required by the bombing method with a high degree of accuracy over the entire range of flying conditions which would be most practical for the application of the bombing method of this invention. V I claim:

l. The combination for bombing at target by airplane,

' upward velocity component at a fixed time to target, a

bomb, a bomb release mechanismon said airplane detachably carrying said bomb, acceleration integratin 3. 1'5 means so oriented in said airplane as to be responsive to vertical accelerations ,of the airplane, said integrating means being operatively coupled to said bombrelease mechanismand adapted to actuateisaid' mechanism in re-:

sponse to a predetermined attained vertical component of:

velocity, said predetermined velocity component being proportioned to the said fixed time to target.

2. In a toss-bombing combination, a releasable missile,

a controllable carrier carrying said releasable missile on a substantially collision course on a line of flight to a target,

said carrier being capable of executing an excursive' maneuver at a predetermined time before the collision to impart a'v elocity component to the missile perpendicular to the original line of flight, 'anacceleration integrator for integrating changes in said, peipendicular 'velocity component, and means responsive to said. intemechanism on said airplane detachably carrying said bomb, and an acceleration integrating means responsive to changes in said vertically upward velocity component, operatively coupled to said bomb release mechanism for releasing said bomb from the airplane when a predetermined vertically upward velocity 'is attained by the airplane, said integrating means being so constructed and arranged as to operate said bomb release mechanism in response to attainment of saidpredetermined vertica component of velocity.

4. The combination for bombing a target by airplane flying a collision course with respect to the target, comprising an airplane, a bomb carried by the airplane, a

bomb release mechanism, means for determining the time T1 k+k 1l/k Where T1 is said time'remaining before collision and where k is said predetermined constant.

5. In the art-of toss bombing, the combination of an airplane, a missile detachably carried by said airplane, a release mechanism for dropping said missile, an accelera tion responsive inertia means mounted in'and responsive to changes of altitude of said airplane, means for integrating changes in vertical acceleration coupled to said inertia means, said integrating'means being coupled to the release mechanism and being adapted to operate the release mechanism upon and only upon attainment by said-airplane of a predetermined component of upward velocity.

References Cited in the file of this patent UNITED STATES PATENTS 1,216,382 Wenyon -1 Feb. 2, 1917 1,433,596 Binfield Oct. 31, 1922 1,728,904 Herr Sept; 17, 1929 1,823,044 Holmberg Sept. 15; 1931 2,266,449 Ullich et :al Dec. 16, 1941 2,309,686 Winters Feb. 2, 1943. 2,410,097 Morgenthaler et al. Oct. 29, 1946 (FOREIGN PATENTS I V 1 801,194 France May 16, '1936,

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