The Pendulum Rocket Fallacy

By Jim Bowery
Copyright 2001 except for the Goddard photo whose copyright status is unknown.
The author grants the right to copy without modification.

Getting a rocket to lift off and fly straight up is a little like a juggler balancing a pool cue on his chin:

This balancing act is so difficult that many intelligent amateurs have tried building rockets that have their engines at the top.

This is one of the more intelligent amateur rocketeers, standing next to one of his first rockets.

Notice the black engine is at the top and the heavy silver fuel tanks are near the bottom with long pipes going all the way to the top of the engine. He thought placing the engine ahead of the bulk of the rocket would keep the rocket stable as it pulled the rest of the rocket upward.

PS: His name is Robert Goddard. He invented liquid fueled rockets. He even did so when some respected authorities still thought rockets needed a medium against which to push. Newton's third law of motion already told them otherwise, but even respected authorities can be dumb, just like the rest of us. One liquid fueled rocket is the Saturn V you see in the picture of the balancing pool cue above, carrying 3 courageous men to the moon. They are in the tiny white triangular capsule at the top. Like most amateur rocketeers who are inventing new kinds of rockets, Robert Goddard was also courageous in his own way. A lesser risk of inventing things is that a few people who have low self-esteem, or who like things just the way they are, will try to find an excuse to ridicule your efforts. Don't worry about it. Rest assured you will provide them just the excuse they need. Explosions and governments are bigger risks.

Live and learn, stay out of jail, make it work, and tell the tale.

Intuition says that when you lift something from the side, it's center of mass will swing below the point of support and stabilize, like a pendulum that eventually lines up right under your point of support after swinging back and forth a bit.

So far so good.

By putting the engine at the top of their rockets, some amateur rocketeers intend to keep them upright during lift off. They think their rockets won't fall over like a pool cue without the juggler, but will just wobble back and forth under the rocket engine's support, like a pendulum, until it is completely stable:

One of the two main places where intuition goes awry is in forgetting that a rocket engine is rigidly connected to the rest of the vehicle, so the engine's support of the vehicle changes direction along with the center of mass.

The other place where intuition goes awry is assuming that larger masses will fall faster than lighter masses. Galileo showed this false when he dropped two differing weights from the Leaning Tower of Piza and they both hit the ground at the same time. The top and bottom of a pendulum rocket will fall at the same rate so gravity doesn't stabilize it.

That means, if the rocket engine is just a tiny bit misaligned with where the center of mass is, the whole rocket will continue to turn:

Inverting the "pendulum" doesn't really matter.

In both cases the center of mass is misaligned with the direction of thrust.

 

In outer space, such a rocket would just go round and round in a big circle. In Earth's gravity, however, the whole circle falls at 9.8meters/sec**2.

That means the "pendulum rocket" launch profile looks something like this:

If you are wondering how simple model rockets with fins manage to fly straight up, the short answer is, "Because that's the direction they were going when they got going fast enough that the wind on their fins made it hard to turn any other direction." The long answer can be found at Quantum Scientific's Model Rocket Stability page. If that long answer still isn't enough for you, and you have a serious desire to learn, check out The Guidance and Control Systems FAQ.

The author wishes to thank Henry Spencer for telling him three times that the pendulum rocket is fallacious and to Robert Goddard for inventing liquid fueled rockets (and for providing the author with a convenient excuse for being so obtuse).

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