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How Piston Engined Bombers Can Outrun Jet Fighters (related to Douglas Model 416)


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Full bibliographic data for the document referenced below is:
"Interception and Escape Techniques at High Speed and High Altitude (Model 416)", W.B. Lklemperer, Office of Scientific Research and Development, NDRC, Division Applied Mathematics Panel, Douglas Aircraft Co., Inc., Santa Monica, Calif., July 24, 1941, Lib. No. 1978" (CONFIDENTIAL)

From Summary Technical Report of Division 5 NDRC, Volume I: Guided Missiles and Techniques

During 1941, under contract from the U. S. Army Air Forces, Douglas Aircraft Company undertook a study to determine the effects of high speed at high altitudes on the problem faced by fighters when attacking bombardment aircraft. The report which arose from that work comprises the body of Appendix A. The problem of maneuvering a fighter plane against a high-speed bomber so as to bring the fixed guns to bear is one of flying a pursuit course. The work of Douglas, therefore, involved a searching analysis of the dynamics of pursuit curves, and although the content of the contract involved no work on guided missiles, its outcome has become a fundamental classic, which has been invaluable to all the Division’s contractors concerned with the development of homing missiles. [Editor]

The study which led to the essay, Interception and Escape Techniques at High Speed and High Altitude, was originally undertaken in 1941 in conjunction with a design study of a fast long-range bombardment airplane in an effort to arrive by theoretical analysis at some judgment of the merits of a design trend toward safety through high performance which was then beginning to take shape in the minds of visionary engineers. The idea was still a bit ahead of contemporary concepts of immediate necessities of the military situation, in which England was seen as hard pressed and in need of relief while America was not yet actively embroiled in the world conflict. The high-performance bomber project was shelved at the time, but the principle was eventually incorporated in the later development of the B-29 bomber.

The report on interception and escape techniques was written at the time as a part of the project proposal and not intended to be published by itself or to pose as a comprehensive treatise on the subject. It is indeed but a very incomplete part of a survey of the field that could be covered or implied by the title.

In retrospect, presentation of the report without a bibliography of the subject matter which has been a fruitful field for many investigators would seem somewhat presumptive. As a matter of fact, no time at all was allowed for a literature search in view of deadlines for the submittal of the project proposal.

This fact also contributed to the decision of coining code words for technical terms which are peculiar to the science of pursuit, and for which more common words were in rather lax and ambiguous usage, though some of them (e.g., pursuit curve, dog curve, squinting, vector sight, and many others) have since been adopted more generally, while others have entered the language of gunsight, radar, and antiaircraft fire-director techniques.


OCR'ers note: Do the following performance characteristics sound similar?

"Let us assume (a) the bomber’s speed v = 450 mph at 40,000 ft and (b) that it is not diminished in combat and that he continues in straight level flight.

Let us assume (a) the interceptor’s speed V = 500 mph at 40,000 ft and (b) that it is not appreciably diminished in combat. (Taking this speed loss into account will favor tail combat phases.)"



The point has been made that the chances of an interceptor’s destroying a straight-flying, ultra-high-speed, high-altitude bomber from any quarter but an acute cone around the tail are remote and that it would therefore appear justified and economical to provide the bomber with defense for the tail cone only.

What now if the enemy became wise to such limited defense and if he developed the technique and practice of slant (brachydromic) attack to the point of a menace? The bomber might then be forced to change his tactics, abandon the straight-course flight plan and dodge the interceptor.

It is at once obvious that a drastic change of altitude would avail the bomber nothing, as the bomber and interceptor would suffer similar performance changes. Any loss of altitude would only aggravate the danger of later interception by other fighters. The following study will therefore first be directed to the effect of veering maneuvers in a horizontal plane. We shall consider three distinct types of maneuvers: luring the interceptor into the tail cone (see Section A.5.1), foiling the interceptor’s attack by spoiling his aim or lead (see Section A.5.2) and heading toward the interceptor to deprive him of maneuvering time (see Section A.5.3).

A 51 Veering Away to Force Tail Combat

The most obvious maneuver to thwart an attack from an undefended angle is to veer away from the interceptor. This automatically brings the interceptor into the tail cone where strong defense is assumed available. Any attempt on the part of the interceptor to avoid the tail-cone defense zone would of necessity spoil his aim, increase his range, and practically ruin his chances.

Aerodynamic Ballistic Advantage

If the interceptor’s forward guns are of the same fire power, caliber, and muzzle velocity as the tail defense guns of the bomber, then the bomber is at a great advantage over the interceptor, for the following reasons: (1) The bomber’s tail guns being flexible (though within limits), the bomber pilot need not aim the entire airplane whereas the fighter pilot must do just that; at high speed this is much more difficult than at conventional speed because of the high accelerations or inertia forces accompanying every control movement. (2) The bomber’s rearward fire is more accurate and the projectile has greater impact energy left because of the lesser trajectory drop and lesser air resistance as the projectile speed against air is u — V for the rearward fire versus u -f- v for forward fire; the ratio of these bullet speeds is almost 1:2 so that the air resistance of the attacker’s bullets is several times that of the bomber’s. This is important because at the larger ranges at which combat will probably have to begin at the higher flight speed, trajectory drop is quite pronounced. As an example, the deflection of a .50-in. bullet is tabulated in Table 12 as computed by extrapolation from Aberdeen Proving Grounds Ballistic Research Laboratory Report No. 117 for various ranges and for u0 = 2,700 fps initial muzzle velocity and for firing backwards from a bomber flying 450 mph and forward from an interceptor flying at 500 mph.

Disparity of Arms

If the interceptor carries guns of larger caliber and /or much greater muzzle velocity than the bomber, then this may offset the interceptor’s handicap. The bomber pilot will then have to resort to other tactics to shake off the attacker. He can still veer away from him as long as he is out of the attacker’s range in order to gain time, especially if the speed differential is small. However, it will be essential for the bomber’s commander to know the armament and performance characteristics of the attacker. The bomber commander may even decide to enter a mock dogfight and emerge from it into tail combat at a short enough range to bring his own tail defense armament into most effective action.

A'52 Dogfight

If the bomber wishes to avoid tail combat, he can accept a dogfight before the attacker has approached to within his firing range.
Attempts to express the phoronomy of such a dogfight in analytical terms indicate that the results are too complicated and cumbersome to evaluate load factors and lead angles. Even in the simple idealized case of the bomber flying in a steady circle and the pursuer following in a scopodromic spiral, the equations describing the pursuer’s path are rather unmanageable. However, some insight into the effect of various maneuvers can be gained by graphical construction of the pursuer’s path.

Acceleration Handicap of Pursuer

It is immediately apparent that if the pursuer continues at full power scopodromically, ballodromically, or somewhere in between after the bomber has turned toward his side in front of the pursuer, then the pursuer’s path tightens up and reaches a much higher load factor than the steadily turning bomber.

If the pursuer is unable to stand more than a certain load factor in combat, say 4 or 5, then he has to relinquish his quarry and let it pass.

The success of an escape turn on the part of the bomber depends a lot on the ratio of the turning radius to the range at which the turn is begun. If the radius is large compared to the initial range, then the chase might develop into an advantage for the pursuer who would essentially trail the bomber, just slightly cutting short to properly lead the target. Thus the pursuer would catch up eventually and his load factor would be but slightly higher than that suffered by the bomber—in fact, little more than in proportion to the square of his speed advantage.

If, however, the turning radius is commensurable to the initial range, i.e., if the bomber does not let the attacker approach closer than a couple of thousand yards, then the attack can possibly be out-maneuvered by turning toward the attacker. If this maneuver is judiciously executed, it can be made to lead to a close-range encounter passage in which, it is true, the attacker has an exceedingly brief chance of a burst, but under exceedingly unfavorable aiming conditions. Immediately afterwards, however, the bomber’s tail defense has a chance of hitting the pursuer under much better aiming conditions, safe from return fire. The next phase following the encounter offers the bomber a gain of range before the pursuer can turn around and resume the chase. The bomber may so maneuver that the pursuer blacks out in the chase or, if the bomber does not want to pass a given certain load factor, he loses his pursuer before he arrives at firing range. This sort of maneuver effectively shakes the pursuer off while the bomber passes ahead of him. If the pursuer attempts an S turn after passage, then the bomber will straighten out its course when in opposite position and put so much distance between himself and the pursuer that the engagement is broken off.

Tracking in Circular Flight

The pursuer may, of course, prefer to follow the pursued in his track rather than cut short across the turn and avoid the higher load factor in the later phases. He would then simply creep up behind him though it would take a little longer. However, this is easier said than done. For one thing, the flight path does not usually remain visible, and when it does leave a condensation track, it is preferable not to fly through it. Secondly, when tracking along a curved path, the aim is very far off, unless a very large gun elevation is available. Obviously, tracking 1,000 yd behind on a 1,000-yd radius places the target 30 degrees off the pursuer’s flight-path tangent, to which a lead correction still has to be added.

Initiative of Escape

Once the bomber has taken the initiative and started to turn in the direction to force the higher load factor upon the pursuer, the sense of turn in the dogfight must not be changed because the first one to make an S turn suffers a tactical disadvantage, except when the bomber decides to accept tail combat in a flight direction favorable to him with regard to the sun, clouds, or reinforcements.

A 5 3 Head-on Parry

If the interceptor is detected while still in a forward quadrant, then the bomber may choose to head directly for the attacker. Even though the latter may not be flying at top speed, the range will now diminish so fast (say at 400 to 450 yd per sec) that only one to two seconds are available for combat.

Snag Dodge

The bomber allows the attacker to come on to within about 2,000 yd, or almost within long-range firing distance, and then veers out of his way to spoil his aim. An effective escape maneuver now consists in an S snag so close to the enemy that he has no time to turn after the bomber and cannot turn sharply enough to lead properly. Then the bomber gets away before the pursuer can complete a 180-degree turn. The chances of a destructive hit in such a delayed veering maneuver from a head-on encounter are very slim indeed.

The interceptor may choose to attack ballodromic-ally during the encounter but he will get only a few rounds in and these under very unfavorable lead conditions, practically at “cross paths,” which means about 20-degree lead. (At 600 yd, this is 6 to 8 bomber’s lengths.) During or immediately after the frustrated close-range passage, the bomber reverses his banking angle and returns to his original course heading. While the pursuer completes his more than 180-degree turn, he loses about 3,000 yd in distance before he can resume the tail chase which will bring him within a few degrees of the bomber’s tail by the time (almost 2 minutes) he may again arrive within firing range, unless he has lost his quarry in the melee.

Head-on Passage

On the other hand, the interceptor may choose a second alternative, namely, that of foregoing all chance to hit or fire at the bomber during the first encounter, and passing the bomber’s course ahead of him merely in order to lose less distance for a subsequent tail attack. This, however, the bomber can foil by starting to trail the interceptor. The trick here will be to avoid being dragged away from the original objective or lured into the fire of other fighters.

A 5 4 Vertical Escape Maneuvers

The question may be raised if vertical escape maneuvers or their combination with horizontal ones have merits for the bomber.

Not in Tail Chase

In the tail chase the answer apparently is no. Most likely, the pursuer would suffer the lesser load factor and he would be in a favorable position whenever the bomber levels off.


Only if the bomber were to start looping just before the pursuer has arrived at his maximum firingrange would the attack be foiled. However, the pursuer could probably follow suit and be right on the bomber’s tail after the loop is completed or when the bomber rolls out at the top of the loop. To continue looping would theoretically be a possible defense tactic but it is hardly practical and would only serve to let other fighters catch up and join the chase.

Zooming Up Behind

The pursuer, however, may benefit from vertical maneuvers. For instance, if in catching up fast he fails to bring his quarry down, he may instead of veering out of the way, zoom up behind him to kill speed only to utilize the potential energy thus gained in diving after the quarry in a subsequent attack. However, the only effect of such a maneuver as compared with merely throttling would seem to be the interruption of fire which may be desirable while changing ammunition drums or clearing jams. Otherwise, between a fixed gun pursuer and a limitedly flexible tail gun of the bomber, the advantage would usually be on the side of the latter.

Descent for Lower-Altitude Bombing

The bomber may be tempted or forced to descend to lower altitudes to fulfill his mission when poor visibility obscures the target at great height. During the descent itself he does not necessarily enhance his risk because in the descent he picks up extra speed. The proximity of the compressibility limits his gain, just as it does to the interceptor who may be trailing him down. The interceptor may perhaps gain a little more if it has thinner wings but this advantage may be balanced by the fact that the interceptor is probably already designed to have its best performance at a lesser lift coefficient than the bomber so that the same speed-up would increase its drag more. At the higher descent speeds, load factors in any curved pursuit increase with the square of the true speed so that the hazards of angular fire are still further reduced until the advantage is absorbed by the greater air density.

The time the bomber has to stay at lower altitudes can be very brief. The descent can be made very flat and may take 50 miles, certainly enough to correct for a reasonable navigation error. After delivery of the bombs, the bomber’s climbing speed is increased and he may still have excess kinetic energy to retrieve several thousand feet before being slowed down to the steady climb rate. During the remainder of the climb to the stratosphere he would have little to fear from those interceptors that might be taking-off to go after him. Only in case other interceptors have been hovering above and dive after him would he be at a speed disadvantage. However, he could have known of their presence if he was equipped with sufficiently long-range detecting apparatus and could have decided to stay up until he might have shaken off or outlasted the interceptors or chosen an alternative target for which he would not have to descend.

A-5-5 Recapitulation

To summarize the results of the maneuveringstudy thus far, it may be said:

The best plan undoubtedly is to provide the bomber with sufficiently powerful tail. armament so that it can accept a tail chase on better than equal terms with whatever interceptor is fast enough to catch up with him before running out of fuel. Better than equal terms does not necessarily mean more powerful weapons because of the aerodynamical bullet speed advantage for the rear fire, as has been explained in Section A.5.1 under Aerodynamic Ballistic Advantage.

At a speed differential of only 50 mph (or 25 mph) it takes the tail chaser fully 5 minutes (or 10 minutes) to creep up from 7,000 yds into firing range.

Any attack from a forward quarter can be turned into an almost head-on encounter and foiled short of firing range.

The bomber can so maneuver that any attack will eventually wind up as a tail chase and that the attacker will drop behind whenever he tries any other trick. The bomber cannot be sure of shaking a tail chaser off permanently, but he can probably turn any angular attack into a tail combat whenever he wants to.

The bomber can accept a dogfight and may outlast the interceptor.

A 5 6 Maneuvers with Slant Gun

The most effective countermeasure to improve the interceptor’s chances in a dogfight near the load factor limits would appear to be its provision with some elevated guns. This will permit the interceptor to fire across a chord of the dogfight circle without running into excessive load factors—without, in fact, having to cut too much across the victim’s path. In such a sharp turn, both ships are steeply banked so that the gun elevation becomes essentially an azimuth correction. The slight lateral correction, consisting of the gun elevation times the sine of the banking angle, can be compensated by the pursuer circling slightly lower than the pursued and by trajectory drop. Visibility for aiming such a gun elevated at, say, 15 degrees can be easily provided for the pilot. This arrangement will also come in very handy in a stalking straight attack from below the tail without dogfighting. However, such an elevated gun requires means for proper lead correction for the own-speed vector, and it does not by any means assure superiority of the pursuer against a bomber equipped with tail guns covering similar cone angles and similar lead correction devices.

The consequences of the presence of a slant gun on the interceptor have already been mentioned. If a high-speed fighter version of the high-speed bomber prototype were eventually developed, it might to good advantage also be equipped with a slant gun of moderate caliber or one that can be elevated in turns.


The question now arises whether concerted pursuit by several interceptors having fixed guns may become unduly dangerous to a lone bomber.

A 61 Multiple Brachydromic Approach

If an interceptor squadron flying in close formation tries to attack the fast bomber in brachydromic approach from some odd angle, the individual interceptors would be forced to peel off as the rear ones would have to head more ahead of the bomber. Therefore, if all the interceptors were to participate in the fire their formation would become loosened up. As for the bomber’s defense, the situation hardly differs from , the brachydromic attack by a single interceptor because the individual fighters come into range one by one and all from the same quarter, almost from the same angle.

A-6-2 Multiple Tail Chase

If several interceptors were to come up from the rear and tried to place themselves simultaneously around the tail—say one to the right, another to the left, one above and another below—and if they were now to press into firing range together or in such rapid syncopation that the bomber’s defense gunnery could not cope with all of them, then the bomber might veer slightly to the side of the nearest attacker just before he comes into firing range. This maneuver brings all the attackers into the same quarter, and they would lose a lot of time if they rearranged themselves.

A 6 s Multiple Ballodromic Approach

In ballodromic approach a squadron of interceptors would be more handicapped by high load factors, aggravated by the requirements of maintaining formation, than a single interceptor. Otherwise the situation for the bomber’s defense winds up in a tail chase or can be turned into a tail chase prematurely whenever the bomber veers to run away.

A 6 4 Multiple Clinoballodrome

A situation annoying to the bomber can possibly arise from simultaneous attack by two pursuers approaching ballodromically, but one in or above and the other below the bomber’s level. Of course, they would quickly get into each other’s way if both were equipped with fixed-level guns only. However, if at least the lower one is equipped with an elevated gun, they can attack simultaneously without interference. The bomber might then try to turn in order to hamper the two closely flying attackers by high load factors. Such a tactical turn may be especially indicated where the two attackers make it a habit to fly in a staggered formation, the one above slightly ahead of the lower one, leaving the burden of avoiding interference to the lower one who has the better visibility. In the escape turn, the upper forward one becomes the inner one and gets into the firing line of the rear lower one, which has to take the outer line, and there is not much the latter can do about it but cease firing.

A*6,5 Simultaneous Interception

Now what if several interceptors were to make concerted attacks from entirely different sides and angles timed to arrive simultaneously? Such tactics are highly improbable. It would seem almost impossible to spot the bomber so accurately, to disseminate the information to all concerned, and to work out and transmit a timed multiple interception plan to the several fighter units, all of which were moving at a rapid pace while these preparations were taking place. Then they would have to approach from stations several miles apart in space. The least error in their calculations or any deliberate course change on the part of the bomber would completely upset the schedule. It seems certain that most of the interceptors, insofar as they do not miss the engagement altogether, would wind up in a tail chase. The small speed differential would make it difficult and tedious for them to sneak up at once.

A66 Multiple Frontal Attack

Multiple frontal attack is dismissed as impractical because of lack of maneuvering room and time.


Navigating a fleet of bombers together toward a common objective or toward different objectives may offer each bomber some measure of protection.

A 71 Decoy Action

To what extent such protection may be secured by decoy action, drawing the interceptors to a feint and away from the real raid, is a matter of strategy which is considered outside the scope of the present study, except insofar as it may have a bearing on the armament requirements for the bomber. If some of the decoy bombers were equipped with extra armament instead of full bomb loads, a bluff might be perpetrated which might discourage the enemy from attacking the real bombers from undefended angles or ranges. Such extra armament should then be so designed that it is not easily distinguishable and that the standard and specially armed aircraft cannot be told apart in the air.

A 7,2 Lateral Attack

In a mass formation raid by a fleet of fast high bombers, dodging of interception would be impractical. The chances for slant attack by interception appear somewhat enhanced because, if the interceptor aims to intercept one airplane, he may miss it but catch another, but the interceptor would also risk drawing fire from several of the bombers.

The vulnerability of a mass formation could undoubtedly be reduced by providing special armament and/or armor for the airplanes assigned the extreme positions in the formation at the expense of their bomb load. This has the design disadvantage of a duplicity of type and the tactical disadvantage of more replacement parts and limitations of the tactical disposition of the units. However, if mass formation raids are contemplated, it may be well worth while to create not only the full-load bomber but also a protective fighter having the same performance and range with reduced or even with no bomb loads.

The fighter version would have some forward-firing guns, possibly capable of elevation, and possibly armor for the occupants. The elevated guns need not be continuously movable in elevation. It may suffice to provide two elevation positions: for instance, (1) parallel to the high-speed flight path and (2) at 10 or 15 degrees elevation therefrom.

In view of the probability of most interceptions’ winding up in a tail chase, the bombers—or at least those assigned the rear positions in the formations— might deserve rear armor.

A 7 3 Formation Shape

The shape of the mass formation has an influence upon the mutual assistance between units. At high speed, considerations of the prevalence of tail attack may call for different formation shapes than at speeds at which the interceptors can attack from all quarters.

Lone stragglers behind would have to rely on their own fire power to ward off pursuit.

A compact phalanx with many bombers abreast along the trailing edge of the formation has the obvious advantage of drawing any tail attacker into the defense fire of the adjacent bombers at good azimuths and almost at the same range with almost no lead correction requirements.

A dense packing of bombers in several tiers above each other (three-dimensional formation), all terminating in one huge vertical trailing plane, would further enhance mutual assistance against the tail chase into which any persistent interception must develop.

Single leaders or navigators ahead of the main phalanx may not be particularly endangered, provided some of the bombers in the front line of the main formation are equipped with a forward-firing gun.

If some such forward-firing guns are distributed throughout the formation, it might serve to discourage any interceptors from trying to break into the formation from above or below in case any of them have enough extra ceiling or climb (or rocket boost).

A-7 4 Formation Density

The safest density of the formation will probably depend not only on the degree of mass formation training attainable under combat conditions but also very much upon the concentration of interceptors loosed against a mass raid.

Obviously, any three-dimensional pattern with several bombers in tiers above each other would have to open up upon arrival at the objective in order to avoid hitting the lower ships with bombs from the upper ones. The technique of this maneuver would hardly differ much from that of similar situations of bombers at lesser speeds, so that no new problem seems to arise from a boost of airspeed or altitude.

If the rear bombers are to derive tactical aid from the firing power of their formation neighbors, then their spacing must remain dense enough; it should be but a fraction of the dangerous firing range. For example, assuming the bomber’s tail armament covers a cone of 30 degrees semiapex angle (i.e., 30 degrees off the fuselage axis), a spacing of more than 200 yd would render the bomber powerless to assist his neighbor when the pursuer approaches within 350 yd.

A very much more scattered formation, with several hundreds or thousands of yards spacing between bombers, would cover a huge area. For instance, 400 bombers in a single-layer square lattice of 2,000 yd spacing would cover 500 square miles of surface. This would be highly confusing to any ground organization trying to dispatch interceptors. However, once the interceptor squadron encounters any part of the raiding force, a man-to-man duel is likely to result, with no further immediate advantage to the bomber; on the contrary, in order to prevent disorganization of the raid schedule, the individual bomber will refrain from escape maneuvers and stay on his job.

Mass raids in waves of bomber groups, in dense formation of each group, timed to arrive at the interception gateways at intervals intended to exhaust the interceptor force will probably have even greater merits at ultra-high speeds than they have at current moderate speeds. If they are timed to arrive at intervals equivalent to the interceptors’ flight duration, then all the fighters sent up to intercept the first wave will be out of fuel and out of commission for the next alarm. Furthermore, while they land they are making so many airports less available for take-off of the next lot. It may even be a good trick to disperse the first wave into several spaced groups 50 or 100 miles apart in order to arouse interceptors from many places so as to disorganize many stations when the next, more concentrated wave comes through. Strategic choice of targets for various waves may aid in creating further confusion of ground defense measures. The opportunities for such long-range strategy increase rapidly with the speed and range of the craft as distances shrink and decoy and evasion detours become more feasible. They force the defender to spread his interception out thinner. Similarly, the long-range and high-speed bombers cooperating in a mass raid can be directed to disperse and feign repulsion—only to reunite, after the fuel supply of the interceptors has been exhausted, to complete the bombing raid and return to their bases.


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I just found something while reading about the Douglas ROC:

Preliminary design work was undertaken by W. B. Klemperer, who had come to Douglas from the Goodyear-Zeppelin Corporation. One of his early contributions had been an esoteric study of pursuit curves, a study pertinent to the Roc problem, but primarily applied to the interception of bombing planes. It was the philosophy expounded in this study which is exemplified in the latest Douglas bomber, the XB-42, familiarly known as the “Mixmaster.”


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