Ever since reading Willy Ley's highly interesting conjectures about the performance of an improved V-2—{ Astounding Science Fict ion, January 1947)—I have felt it necessary to argue with some of his concepts. First, let's understand that his major two theses are correct; it is possible to achieve improved performance by bettering the weight ratio of the V-2, and it is definitely true that the purpose of the final design determines the form arid configuration of the rocket.

In looking at Ley's article, and my rejoinder, remember that the intent is to improve the V-2 by elimination of "excess" weight in a standard model. We have ruled out any changes in the power plant section because such changes would require additional research. But we're kidding ourselves when we do that, because in the engine compartment lie most of the possibilities for real improvement of the V-2. If we can get better fuel-oxidizer combinations, or lighter and smaller engines, the V-2 will become a far more valuable research tool than it now is.

Perhaps it is not so well known that the performance change of a rocket is more dependent upon changes in the exhaust velocity than changes in weight. This shows up in the classic formula for the final velocity of a rocket in a vacuum.

Final velocity of rocket = (exhaust velocity)
Xlog(e) initial weight
        final weight

So it's apparent that we get more returns by increasing the exhaust velocity than we do by lopping off pounds here and there. Ot this, more will be said later.

We might argue for a while on the sloppy workmanship and crude finish of the V-2. 1 have seen several examples of the V-2 or parts, and was really surprised at the quality of the work. It was far better than I ever expected slave labor to produce. And compared to the standards of United States wartime aircraft finishes, the V-2 was rather lovely. (I exclude here the two classic exceptions—the P-51 Mustang wing finish and the piano-top surface of the P-80 Shooting Star. But, as in all such cases, there are good examples and had examples; Mr. Ley and I undoubtedly saw ones from different batches. And, arguing that the purpose determines the form, siipiwse that the V-2 finish was a poor job—on an expendable missile, who cares? They're not to look at, but to kill with. Paint them to camouflage them, or to stop them from rusting, but let it go at that.

But those perfectly useless fins! Now there is a sore point, because I am an aerodynamicist, and believe mightily in the importance of stability and control. Just suppose that the V-2 had no fins, and that it started to descend through the atmosphere on its way to the target. As soon as the air density got to be appreciable, the missile would experience some kind of an air force on it. Since the V-2 would be descending in a rather tail-down position, at an extremely high angle of attack, there exists the probability that the missile would start to tumble end over end, or even continue on in about a horizontal position: in any event, the drag increase would be terrific. These changes in drag greatly affect the descending path toward the target, and the dispersion of the Y-2 would be ten, fifteen or twenty percent of the range, instead of the one percent the Germans obtained. That alone is good and sufficient reason for the fins on a missile.

An elementary consideration of the aerodynamics of static stability is necessary from here on in. Stability is very worthwhile, like low drag; and having stability, it is also nice to have a certain amount of control, so that the gadget will go where you want it. In an airplane, this is done by the location and design of stabilizing and control surfaces—the stabilizer and fins for stability, the rudder, elevator and ailerons for control. That works line where there is some air for the surface to deflect, but what about a rocket? What happens after the power cut-off that renders the jet vanes completely useless?

It happens that the restoring moment supplied by any stabilizing surface is proportional, among other things, to the dynamic pressure, which is the product of the air density and the square of the velocity. Let's look at the variation of the dynamic pressure for a few typical points along the V-2 flight path. First, at sea level; the rocket is at a standstill, and apart from any airflow induced around it by the jet, the aif velocity is essentially zero. Therefore, the dynamic pressure is zero, and so is the restoring moment. Hence the need for jet vanes, to deflect the high-speed exhaust and make it work at control as well as propulsion. At the three-mile level, where the speed of the V-2 is about that of sound, the dynamic pressure can be calculated as 814 pounds per square foot. At the final point of cut-off, about eighteen miles up. the speed of the. V-2 is five times that of sound, and the dynamic pressure has dropped to only 545 pounds per square foot, which is still a very sizable value. And from here on up, the jet vanes are not working; only the external fins and rudders can supply the necessary forces normal to the flight path to insure that the pre-determined trajectory of the V-2 will be closely followed. This is all closely related to the positions of the centers of pressure and gravity for the V-2.

The center of gravity is well known as the point of application of the resultant weight force on any body. For the V-2. the CG position moves aft with time as the fuel is burned. It is farthest aft when the weight of the remaining fuel equals the weight of the tanks, and from then on, moves a little forward until the fuel is all burned. The center of pressure is similarly the point of application of the resultant air forces acting on the V-2. It so happens that on the V-2 with fins, this CP lies aft of the CG, which is a very essential criterion for stability. This means that if the V-2 assumes some small angle of yaw or pitch because of a disturbance, the* air loads will increase aft of the center of gravity and tend to swine the missile on course again. This principle is more familiarly used in the weather vane.

Tests of the V-2 show that the center of pressure moves forward as the speed increases. We have already seen that the center of gravity moves aft with time, or an increase in speed, and so it is apparent that the most critical condition of near-instability occurs when the V-2 is nearing fuel cut-off. when the C(i is farthest aft. and the C'l' is farthest forward. In the meantime, the jet vanes have been eroding. and their effectiveness has been getting lower, so that as the cut-oil is approached, the external surfaces just have to take over, it is a safe bet that the i/.e of the control surfaces and the tins has been calculated to provide for this condition of high-altitude stability.

Even if the rocket is limited to a vertical trajectory, eliminating the fins is not good. Suppose the V-2 passes power cut-off iiue, and then a little farther up, gets smacked across the nose by a stratospheric wind, and deflected about 10°-off course. What happens? Well, with luck, it might not break up in the air, but it would certainly never get much higher, liut just leave those ''perfectly useless'' tins sticking out in the breeze, and the nose swings back on course.

The next argument concerns the elimination of weight. If the warhead is replaced by only a wind-shield, the center ot gravity is immediately moved aft a considerable distance. By removing the tins, it is true, the CG does move forward again, but by 750/2200 of the distance it moved aft. But worse than that, by removing the (ins, the center of pressure has moved forward by a very considerable amount, and the missile is immediately unstable.

To belabor this problem of weight saving a little farther, where is the extra 550 pounds to be saved "all the way down"? We ruled out (he power plant bay, and have already removed the warhead, four litis, their controls and some insulation. i doubt that the shell structure could be built much lighter, and for any greater accelerations—presupposing the V-2 could be made lighter—the tanks would have 'to be stronger, which makes them heavier. Just where is that 550 pounds to be found? And the instrument allowance of 100 pounds should include a parachute, which must weigh something. If it is a service model, then 20 pounds is good and sufficient, but the Germans, and later the United States Army Air Forces, found that thfc conventional type of chute as we know it was not much good for the parachute recovery of missiles or their contents. So we had better .include the ribbon type chute that the Germans developed for high-speed recovery, and that will surely weigh more than 20 pounds, perhaps even twice that.

It seems that all this has not left much room for improvement, has it? And the reason it hasn't is because there is not a great deal of room for improvement unless we do develop the power plant section, the only item that wre ruled out before. We must look for continual progress in rocket motor technology, and the use of more powerful tuel- oxidizer combinations in order to realize any substantial boost in the performance of the V-2.

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