7 ms·
The dynamics problem of balancing an inverted pendulum gets easier as the distance between the COM and the force input is increased. Of course, its also easier
by zardo 11y ago
The dynamics problem of balancing an inverted pendulum gets easier as the distance between the COM and the force input is increased.
Of course, its also easier to have very fast gimballing on a smaller engine, and a taller rocket bends more which makes it harder to detect exactly where it's pointed in the first place.
- NamTaf 11y agoA rocket isn't an inverted pendulum. This is a common mistake. https://en.wikipedia.org/wiki/Pendulum_rocket_fallacy https://en.wikipedia.org/wiki/Pendulum_rocket_fallacy
- gozur88 11y agoThe pendulum fallacy has to do with the tail of the rocket not naturally following the head during launch. Landing really is an inverted pendulum problem.
- jakub_h 11y agoHow is even the landing an inverted pendulum problem? There's no instability of an inclined rocket during the landing; there's an instability of a "gimbaled-away" rocket. That's not the same thing.
- gozur88 11y agoI'm not sure what you mean by that. How is this different, mathematically, from the classic 8th grade textbook picture of a child balancing a yardstick on his nose?
- jakub_h 11y agoEasily. The yardstick is unstable in inclination if it isn't vertical. The rocket is unstable in horizontal position if it isn't vertical. But it doesn't start to rotate as long as the thrust vector goes through the CG. The thrust vector has stable orientation relative to the rocket (if you don't gimbal), whereas the force vector doesn't have stable orientation relative to the yardstick.
- gozur88 11y agoI don't see how that can be true. The rocket will still start to rotate even if the thrust vector goes through the center of gravity, unless that vector is exactly vertical (a point of instability). As I understand it that's the key insight to the pendulum fallacy.
- jakub_h 11y agoNo, it won't, because neither the thrust vector nor the gravity causes a moment in this situation. The key insight to the pendulum fallacy is actually that this situation doesn't create orientation-dependent momentum. That would make it a pendulum, but it isn't like that, hence the "fallacy" part.
- gozur88 11y agoI see what you're saying. That would imply in the absence of an atmosphere a gravity turn isn't really possible. You'd pick up horizontal velocity, relatively slowly, but assuming you didn't exert some kind of control your rocket would always stay at the attitude it had at the end of the pitchover.
- jakub_h 11y agoYes, what is called "gravity turn" turns the velocity vector, but if the rocket didn't actively reorient itself (so as to keep in line with the velocity vector), gravity itself wouldn't rotate the rocket (change its attitude), because almost-homogeneous gravity field won't impart (meaningful) momentum. (Satellites can actually use it that way, but the time constants are substantial and not really relevant for an ascending rocket on a timescale of minutes.) However, this is independent of the presence of the atmosphere. In real life, both scenarios need active control of attitude.
- zardo 11y agoNote: This is completely wrong. The yard stick has a normal force vector from the hand passing through its center of mass. It doesn't start to rotate unless an outside force is applied. Of course in the real world it requires active control because the most minute misalignment causes a feedback that moves it further out of alignment. The rocket is exactly the same, if the thrust vector is not directly between the center of mass of the rocket, and the Earth, it starts to tip over. If it were a stable system, misalignment would push the system back into alignment.
- Nutmog 11y agoIf you draw a free body diagram, weight is down and thrust is forward. Both force pass through the center of mass so they don't impart any moment to the rocket. So it has no tendency to fall over. They do impart a net horizontal force so it has a tendency to run away sideways. For the broomstick, weight is down but "thrust" is both up and forward. So there is a moment caused by weight at the CoM and up-force at the base.
- NamTaf 11y agoBoth forces go through the centre of mass, as the engine doesn't stay firing vertically downwards when the rocket rotates. Your finger on the other hand tries to continue pushing upwards as the yardstick rotates about your finger, whcih means the centre of mass of the yardstick moves laterally comapred with the vertical upwards force you apply with your finger. Thus, it creates a moment and rotates.
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- arjie 11y agoAFAIK, that fallacy relates to thinking of a rocket as a normal pendulum. It's got nothing to do with inverted pendulums.
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- molyss 11y agoit feels to me that the fact that most of the weight is at the bottom of the rocket, ie near the pivot point, means that small or tall rocket are pretty much the same thing to land. While the tall guy has more weight far from the pivot point, it also has more weight down (because more fuel to stop a heavier vehicle), more sensitivity to various winds and more physical tensions/torsions all along its body structure. I'm not physicist/rocket scientist, so wondering if I'm missing something