Evaluating the Vaunted V-2

by Willy Ley,
Formerly Vice-President, German Rocket Society

Here's a revealing analysis of this rocket-weapon's intriguing technical aspects, its war-worth, and its importance as a transitional factor in aerial research.

Such extreme speculation was aroused concerning an RAF Bomber Command operational flight during the night of Aug 17-18, 1943, that Prime Minister Churchill reported on the nature of the air attack to the House of Commons.

It had been an unusually heavy blow, yet had been directed against an obscure fishing village — Peenemünde on the Baltic, situated at the extreme northwest tip of the Island of Usedom, the westerly of two islands sheltering the Bay of Stettin.

Churchill then disclosed that the Nazis had built a large research laboratory near Peenemünde, which had been "the main experiment station both of the flying bomb and the long-range rocket." The report had it that the laboratory was virtually destroyed in the attack, with 5,000 of its 7,000 scientists and technicians killed.

The flying bomb mentioned by Churchill is the now well-known V-l, essentially a jet-propelled robot-directed flying torpedo, carrying a warhead of 1,000 kg, that is, 2,200 lb.

Churchill's mention of the long-range rocket was the first official confirmation that there was a kernel of truth in the innumerable rumors then extant. But the long-range rocket, now known as V-2, failed to materialize for a considerable length of time. In spite of all rumors and so-called eye-witness reports, in spite even of Churchill's reference to such a weapon, it seemed to many observers as if V-2 were merely a Nazi propaganda claim, or, at best, an experiment that had miscarried.

But after some of the V-1 bases were captured by the Allied armies, easing the stress on England from these 150-mi-range weapons, the long-range rocket did materialize. On Nov 10, 1944, Churchill, in another report to the House of Commons, stated that V-2 rockets had been falling on England for "several weeks", landing "at widely scattered points."

In discussing V-2 it is necessary to consider its various aspects separately, since proper evaluation of the importance of this invention is otherwise impossible. V-2 can be considered as a weapon creating terror, tied up with propaganda and psychological warfare; on the other hand, it can be studied simply as a rocket.

Considered as a weapon, V-2 is comparatively ineffectual and there is reason to doubt whether a long-range rocket bombardment would ever be an effective means of assault, even if regarded only as a substitute for air bombardment.

Considered as a terror or propaganda weapon its chief value is that it strikes without warning. Another aspect of terror value is, peculiarly, that V-2 is not accurate. Under conventional air bombardment, populations living at a distance from railroad yards, bridges, junctions, airports, factories, and power plants know they are relatively safe. Long-range rockets, however, may terrorize large sections of such populations because they are just as likely to crash on a stretch of land devoid of any military target as to fall on or near a vital objective.

But because populations of warring countries have become somewhat hardened to air attack — whether by bomber, flying bomb, or rocket — the terror value of the V-2 type of weapons is hard to estimate. Since actual damage and loss of life resulting from long-range bombardment is small, the psychological attitude of the population is conjectural. The reasonable conclusion, at present, is that V-2 still has to prove that its value as a terror or propaganda device is worth the expenditure.

Considered, however, in the light of rocket research and engineering in general, V-2 must be acclaimed a masterpiece. Enemy development or not, V-2 represents one of the greatest technological advances made during the last two decades.

It is advisable to admit this for our own good, especially since on this side of the water we have, in the past, generally displayed remarkable persistence in neglecting the value, or even the existence, of rocket research.

V-2 is a development which opens limitless possibilities, especially so since its performance is in incredibly close agreement with rocket theory as it was developed before liquid-fuel rockets even existed. V-2 can, therefore, be regarded as large-scale experimental proof for the general validity of rocket theory and also as encouragement that other predications of rocket theory may come true with added experimentation.

The fundamental conceptions required to understand rocket theory are: First, the role and importance of the exhaust velocity (c) and its relationship to the velocity (v) of the rocket; and second, the conception of the mass-ratio which expresses this relationship.

The rocket principle consists of movement in accordance with Newton's Third Law of Motion, by the reaction of a continuous jet of gases produced by continuous combustion of fuel. The oxygen required for fuel combustion is not derived from the air during flight but is taken along in the form of a so-called carrier — the most efficient being liquefied oxygen.

In fireworks and projectile rockets, the fuel is a compressed powder mixture containing the oxygen, required for combustion, in the form of chemical compounds. The disadvantage of powder rockets is that the "combustion chamber" and "fuel tank" are one and the same. This not only limits the amount of fuel which can be efficiently carried, but it also leaves the designer with no safeguard against premature explosion other than the compactness of the compressed powder designed to permit burning only at its surface.

In liquid-fuel rockets, combustion chamber and fuel tanks are separate units so that only the fuel and oxygen fed into the combustion chamber unite chemically. It is obvious that the rocket velocity (v) increases with an increase in exhaust velocity (c); also that a rocket with longer burning time will attain a higher v than a rocket with a shorter burning time, although c and the thrust (P) are given and are the same in both cases.

Factor c is supplied by the nature of the fuel, assuming that the design of the rocket motor is reasonably efficient. The accompanying Table I shows, for a number of fuels the theoretical values for c and the values which may be reasonably expected.

Whereas fireworks and projectile rockets utilize powder mixtures, V-2 is known to burn alcohol and liquid oxygen. The choice of alcohol instead of gasoline is a matter of practical consideration — 1 lb of alcohol needing 2.1 lb of liquid oxygen for complete combustion, while 1 lb of gasoline requires 3.5 lb of liquid oxygen.

Exhaust velocity for alcohol-oxygen, attained with V-2, seems to be about 2,000 m per sec, or roughly, 6,550 ft per sec. The significance of this value for c will become apparent when mass-ratio has been discussed.

The mass of the rocket at takeoff, when both the fuel and oxygen tanks are still full, is usually called M0, and the mass after all fuel has been consumed is termed M1. In turn, M1 equals MP + MR — "payload" and the empty rocket, respectively. The mass-ratio is M0/M1, and for all fireworks and projectile rockets the numerical value of this expression is only slightly greater than 1.

The thrust P of a rocket has to be greater than M0, since the rocket obviously could not rise if the thrust developed by the rocket motor were less than the weight of the rocket. P is determined by the value for c in a given case and by the amount of fuel consumed during a given interval of time. The formula, then, reads:

P = c × dm/dt

Since the molecules of the exhaust may be considered infinitesimal as compared to the mass of the rocket, it is permissible to use the expression —

v = c × ln M0/M1
for the relationship between v and c. Consequently v = c when M0/M1 = c, so that it is possible to arrive at a general for the interdependence of v, c and M0/M1 by writing —
M0 /M1 = ev/c

It is this formula which permits determining the mass-ratio requirements for a desired performance, and it is of great interest to compare actual artillery performance with hypothetical rocket performance derived from this formula.

Three cases, which may serve as examples of such comparisons are given in Table II.

If the same weight of shell were to be transported over the same range by means of rockets, we would find the required mass-ratios given in the following paragraphs. (It was assumed for these calculations that the rocket is a powder rocket with a propelling charge delivering c = 900 m/sec. For simplicity, the muzzle velocity of the gun and the greatest velocity of the rocket at the instant when all fuel has been consumed were considered equivalent. Actually, a rocket would have traveled some distance when that velocity is attained.)

Case I would require a mass-ratio of approximately 1.15. M1 would be MP (118 kg) + MR (12 kg), and M0, would be M1 × 1.15, or 149.5 kg.

Case II would require a mass-ratio of e1/3 or about 1.4. MR would have to be somewhat greater because of this higher mass-ratio, so that M1 , would be, say, 135 instead of 130 kg. M0 would then be 189 kg.

Case III would require a mass-ratio of e1.75 or e7/4 which amounts to approximately 5.76. For such high mass-ratio, MR would at least have to be equal to MP so that the lowest possible value for M1 would be 236 kg. M0 would assume a value of 1,360 kg — meaning that a rocket would require a powder charge of 1,124 kg for the same weight of shell, and the same range which the gun could handle with an expenditure of 300 kg of powder.

Despite this difference, a rocket might be preferable from point of view of financial expenditure. Guns are expensive, rockets comparatively inexpensive, and powder is cheap. The rocket would involve more weight of materials, but less in cash.

But because of engineering considerations mentioned earlier, it is doubtful whether a mass-ratio higher than 1.5/1 would ever he employed with powder used as fuel. When liquid fuels are taken into consideration, a different picture is presented. Liquid fuels not only yield much higher values for c (roughly twice as much), but also permit much higher mass-ratios.

In experimental liquid-fuel rockets of relatively small size, it is customary to force the liquid from the fuel tanks into the combustion chamber simply by the use of compressed nitrogen. This permits mass-ratios of 2/1 and 2.5/1 but hardly beyond that, since the fuel tanks are necessarily heavy in order to withstand the internal pressure used to force the liquids into the rocket motor.

If higher mass-ratios are desired, it is necessary to provide a pumping mechanism which can force the fuel into the combustion chamber from low pressure tanks which are just strong enough to hold the fuel, and are, consequently, rather light. The problem is, of course, to build the pump and pump drive sufficiently light so that introduction of the unit results in a saving in weight.

It is likely that, to do the job, such pumping mechanism would have a minimum size limitation — and as a weight-saving device it could be applied only to large rockets. In V-2, the designers seem to have utilized two centrifugal pumps driven by a gas turbine fed from the same fuel tanks which feed the rocket motor.

This required a large scale design coupled with a high mass-ratio because of the speed this rocket had to attain to span the desired range.

V-2 is generally cigar shaped, with a warhead, of the same weight as that of V-l, forming the nose. The alcohol tank is located behind the warhead — below it if we imagine the rocket upright. The oxygen tank is below the alcohol tank and the pumping mechanism is below the oxygen tank. The motor is in the bottommost part of the rocket, and various auxiliary devices are grouped around the upper part of the motor and around the pump. These auxiliary devices consist in the main of means to control the vanes which keep the rocket ascending at an angle. If there were just rigid stabilizers, the rocket would tend to deviate from the angle at which it was fired, and approach the vertical.

Performance of V-2, according to British sources, includes a range close to 300 mi with peak altitude of about 70 mi. Most of the trajectory is located in high-altitude media so rarefied that there is an approach to a good laboratory vacuum. Because of this, V-2 approaches so-called ideal conditions in elementary ballistics, wherein formulas state that the maximum range for a given gun will be attained when it is fired with an elevation of 45°. In such case, the range is v2g, and the peak altitude along the trajectory is (v2/4)g; in other words, range equals four times maximum altitude.

Since these formulas neglect air resistance, they never actually hold true, except with some pieces of trench artillery where the shell is so heavy and the muzzle velocity so low that air resistance is less than the gunner's error in estimating the distance to the target.

Because more than 90% of V-2's trajectory is located in near-vacuum these elementary formulas are almost applicable. With the maximum range being just about four times the peak altitude, it is likely that V-2 is fired at an angle of 45° or slightly more. (The Paris Gun of 1918 had an 80-mi range mainly because the greater portion of the trajectory was in highly rarefied strata. Utilizing this feature, the designers did, in fact, call for firing the gun at an elevation of 54° in order that the shell would more rapidly leave the denser layers of the atmosphere. The 54° elevation actually produced a longer range than did the 45°.)

V-2 Values

With V-2, MP is 1 metric ton, MR is probably the same, and therefore M1 may be assumed to be 2 metric tons. Mass-ratio for the range actually spanned would have to be 6/1 — bringing M0 to 12 metric tons, assuming c to be 2 km/sec. Reports from Germany and England state that the takeoff weight of V-2 is 12-15 tons, which is in substantial agreement with theoretical figures.

Having a reasonable assumption of the value of c and knowing the mass-ratio, it is easy to calculate some other features. Reported dimensions — length of about 45' and maximum diameter of about 15' — agree well with the known weight and the average density, which cannot be much greater than 1.1 or 1.2.

The fuel load of 10 metric tons must be apportioned as 3¼ tons for the alcohol and 6¾ tons for the liquid oxygen. The thrust of the rocket motor is probably about 18,000 kg — about 40,000 lb, producing an initial acceleration of 0.5 g, which is probably the lower limit required for reasons of stability. With P=18,000 kg and c=2,000 m/sec, the fuel consumption per sec must be 90 kg — about 200 lb.

Since it is likely that the fuel consumption is constant, being probably equal to the maximum capacity of the fuel pumps, the maximum burning time (Tmax ) will be 111 sec, and because c is constant the thrust will remain the same throughout this interval of 111 sec. But the rocket weight is decreasing steadily (at the rate of 90 kg per sec) so that P/M is increasing steadily covering any value between 0.5 g and 8 g, referring to the effective acceleration.*.

It would be possible to increase the range of V-2 by increasing the mass-ratio or the exhaust velocity, or both. The easier method is to increase the mass-ratio — accomplished most easily by reducing the weight of the warhead. But slashing the weight of the warhead to half a ton would not double the mass-ratio, as may be thought at first glance — M1 = MP + MR , and the value for MR would remain unchanged. Doubling the mass-ratio would necessitate discarding the warhead!

An impressive increase of mass-ratio (and range) could he accomplished by replacing the warhead with a 1-ton rocket of similar mass-ratio, provided that the pumping mechanism can be built small enough. If that could not be done, this smaller rocket could at best have a mass-ratio of 3/1 instead of 6/1. But even such lower mass-ratio for the smaller rocket would still result in a total range of 500-550 miles. The warhead would then weigh only 300-350 lb, would reach a total altitude of approximately 400 mi — which means it would touch interplanetary space. And a payload of 300-350 lb could accommodate a substantial number of self-recording scientific instruments — and even, hypothetically, a human observer.

This certainly is the real importance of V-2.

As a war weapon V-2 is quite ineffectual — as could be predicted on theoretical grounds — and propaganda value is doubtful. But V-2 has demonstrated that liquid-fuel rockets of mass-ratio of about 6/1 can be built now; that the problem of the fuel pump can be solved; and that rocket motors with a fuel consumption of 90 kg/sec, and thrust of 18,000 kg plus, are possible.

And there is little doubt that such a rocket can be a research instrument of decided value.

* A report received from England since the foregoing calculations were completed, gives 85° as the angle at which V-2 is fired so as to quickly penetrate the dense layers of atmosphere. The rocket is tilted slowly while ascending, attaining an angle of 45° for maximum range at about 12 mi. The report assumes an effective acceleration of 1 g at take off, which requires a thrust P = 36,000 kg — about 80,000 lb. The rate of fuel consumption, consequently, is assumed to be about 400 lb/sec. Burning time, however, is given as 71 sec (instead of 55.5 sec.). Presumably a mass-ratio slightly greater than 6:1 was assumed by the British

TABLE I — Theoretical and Expected Values of Exhaust Velocity (c) far Various Fuels
Fuele — theoretical
(m/sec)
o — expected
m/sec)
Black powder2,420900-1,000
Smokeless powder3,2401,500-1,800
Dynamite3,300(?)
Gasoline + liquid oxygen4,4502,000-2,500
Gasoline + liquid ozone4,9602,500-3,000
Alcohol + liquid oxygen4,180 2,000-2,500
Alcohol + liquid ozone4,6302,500-3,000
Hydrogen + liquid oxygen5,1703,500-4,000
Hydrogen + liquid ozone5,6704,000-4,500
Note. No experiments with liquid ozone have been made because of its instability. Hydrogen is difficult to handle because of its extremely low boiling point but control would be mostly a matter of practice.

TABLE II — Examples of Artillery Performance
Weight
of shell
(kg)
Weight of
propelling
charge
(kg)
Range
attained
(km)
Muzzle
velocity
(m/sec)
Gun used
Case I1181.1350.60090French 220 mm mortar model 1887
Case II1186.1263.200230French 220 mm mortar model 1887
Case III120300.0126.01,500German Paris Gun Mar 1918

This article was originally printed in the February, 1945, issue of Aviation magazine, vol 44, no 2, pp 212-214.
The original article includes 1 photo of wreckage of a V-2 engine and the tables above.
Photo credited to Associated Press