The V2

For those of us who grew up during or at the tail end of the Buck Rodgers era (yes, I’m over 50) the V2 is the iconic image of Rocket. The classic V2 was a German terror instrument dubbed the Vergeltungswaffe 2, or retaliation weapon 2. After the capture of several rockets and many German scientists at the end of the European war it was popularly V2 and Tunarenamed the Victory weapon 2. It  was a short, fat, ballistic missile. It had an onboard guidance system to keep it on a straight trajectory to where it was aimed but, much like an immense artillery shell it could only get close to the calculated target. It would then explode.

Most of the American testing on the rocket (designated A4 by the US Army) was conducted near where I live at White Sands Missile Range in New Mexico. This rocket actually took the first image of earth from space, in October of 1942.

On the one hand, the rocket is really, really fun to look at. It is just sooo rocket like. But as I said, it is short and bulbous, designed to be hauled through narrow German streets on a truck bed. The thing has terrible aerodynamic characteristics which must somehow be compensated for. The designers of the real thing did this with large steering vanes on the fins and a second set in the motor thrust channel, using both aerofoil management and thrust vectoring to keep the beast stable in flight. We amateur rocketeers do not have these options. Our hobby comes to a close the moment our rocket becomes a missile. But we do love to fly a V2.

I will use this article to explain how we attain dynamic flight stability in a somewhat ungainly situation. You will note that no one building an efficient rocket today is building anything that looks like a V2.

Take a look at the V2 pictured here. You will notice that the large nose cone and large forward swept fins present a lot of surface area, shifting the center of pressure forward on the rocket. The fins, being large, are also heavy, shifting the center of gravity to the rear of the rocket. The relationship between center of gravity (Cg) and center of pressure (Cp) is counter-intuitive if most of your experience is with ground vehicles at low velocities. On your bicycle, you know the the lower the center of gravity, the more stable you are. When a rocket is sitting on the launch pad you might also assume that a high center of gravity would be a problem. A stiff gust of wind might blow it over. Well, when we design a rocket to fly our primary concern is how it will FLY.

While static stability would indicate the center of mass should be closest to the earth, dynamic stability is a different animal. At rest, the center of pressure is a non factor. Under thrust and in flight, the center of pressure becomes a major issue. At velocity, the center of pressure must always be behind the center of gravity, by not less than 1.25 calibres (a calibre being the diameter of the body of the rocket) in the direction of flight. Even when I thought I knew this, I had to see violations of the rule fail before I actually believed it. A rocket that violates this rule will corkscrew in flight or go totally out of control, endangering people and property.

The V2 model is an aerodynamic turkey. One way to address the instability is to make it really long. But then it does not look like a V2. Again, the large surface area presented by the nose cone and fins make the rocket very draggy off the pad. You have to compensate for this by adding a larger motor with higher average thrust, else it will arc over right away. This translates to a heavier motor (more fuel) which adds more mass to the tail end of the rocket thus shifting the center of gravity towards the rear, where those heavy fins are. So, assuming that we insist on our model looking just like an historic V2, our options are pretty simple. Nose weight. I like to use birdshot and epoxy. Others, especially on smaller models, use modeling clay. Adding this much nose weight makes the rocket very heavy. Thus the final system is very inefficient. If you want best altitude, then you do not build a V2 model.

On the other hand, if you want people to jump up and down and cheer and applaud, you can hardly do better than to build and fly a V2 model. They lift off slow, with lots of fire and smoke, and if you get the thrust to weight ratio right, they fly straight and true. Ever seen a turkey take off and fly? It is a sight to behold!