# Solving the Rocket Pendulum Fallacy?

## Main Question or Discussion Point

I have been researching the rocket pendulum fallacy and have gotten into some spirited debate on the subject.

If I understand correctly...
1. if the thrust is perfectly in line with the centerline (and no outside forces act on the craft other than gravity) it does not matter where the source of the propulsion is located, forward or aft, the craft will behave the same.
BUT
2. if the thrust is not perfectly in line with the centerline of the craft, the craft will be unbalanced both forward and aft, but it will behave unbalanced in different ways relative to the location/direction of gravity acting on the craft.
3. the reason why this is not a "pendulum" effect is that the thrust is a force of fixed angular acceleration rather than a fixed pivot point.

One question I have is, if the thrust remained always directionally opposed to gravity regardless of the direction of the rocket (I know this isn't practical but for theoretical discussion), would this then result in a pendulum effect (again, with no outside forces effecting the rocket other than gravity)?

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russ_watters
Mentor
One question I have is, if the thrust remained always directionally opposed to gravity regardless of the direction of the rocket (I know this isn't practical but for theoretical discussion), would this then result in a pendulum effect (again, with no outside forces effecting the rocket other than gravity)?
You mean gimballing the engine to remain vertical while the rest of the rocket sways under it? Sure, it would -- you can draw a free body diagram and verify what the forces are doing to it.

Also remember that "perfect" does not exist, so any non'stabilized rocket will tip eventually, it's just a matter of how fast.

Thanks!

So to clarify, the self-correcting gimbaling of the motor would in essence be allowing a pendulum effect to happen and "pendulum" would be the correct term to describe it?

I have been unclear if the definition of pendulum required a "fixed point" meant that the fixed point needed to be fixed in relation to the earth or if it is fixed in relation to the object.

To my mind, if I spin my keys around my finger on a vertical axis, my centrifugal force is acting the whole time but there is a pendulum effect working on the keys... it is just overpowered by my centrifugal force. Is that an accurate way to describe it?

berkeman
Mentor
So to clarify, the self-correcting gimbaling of the motor would in essence be allowing a pendulum effect to happen and "pendulum" would be the correct term to describe it?
I think "inverted pendulum" would be more accurate...
To my mind, if I spin my keys around my finger on a vertical axis, my centrifugal force is acting the whole time but there is a pendulum effect working on the keys... it is just overpowered by my centrifugal force. Is that an accurate way to describe it?
I'm not understanding the analogy, sorry. Probably a better way to visualize it is to think about how you balance a vertical stick on your outstretched hand...

russ_watters
Mentor
I think "inverted pendulum" would be more accurate...
Er....I don't...
I'm not understanding the analogy, sorry. Probably a better way to visualize it is to think about how you balance a vertical stick on your outstretched hand...
Goddard's first rocket had the fuel tank slung under the rocket motor. It was literally a [attempted] normal pendulum configuration.

russ_watters
Mentor
So to clarify, the self-correcting gimbaling of the motor would in essence be allowing a pendulum effect to happen and "pendulum" would be the correct term to describe it?

I have been unclear if the definition of pendulum required a "fixed point" meant that the fixed point needed to be fixed in relation to the earth or if it is fixed in relation to the object.

 ....thinking about this a bit more, I think there is a bit of difference from one sitting on a table: with nothing to absorb lateral forces, the rocket motor would have to oscillate (but not rotate) back and forth above the center of gravity.
Well the way you describe it, the motor remains always vertical and the gimbal acts as a pivot point. It is exactly a top-mounted pendulum, no different from a one sitting on a table except in magnitude of g.
To my mind, if I spin my keys around my finger on a vertical axis, my centrifugal force is acting the whole time but there is a pendulum effect working on the keys... it is just overpowered by my centrifugal force. Is that an accurate way to describe it?
Kind of, though I don't see how it relates to this problem. Usually a pendulum is oscillating and that example is usually examined in a non-oscillating state.

berkeman
Mentor
russ_watters
Mentor
Ah, I missed that you were discussing having the rocket engine at the top of the rocket...

When the rocket engine is at the bottom, it's an inverted pendulum type of control system, right?
Yes/agreed.

Thanks for all the help. I have crafted my understanding of what I've learned here. Let me know if there are any inaccuracies in the following:

The pendulum fallacy only applies when the points of thrust are at a fixed angle in relation to the centerline of the craft. As the craft rotates, the thrust rotates at the same rate creating fixed angular acceleration, not a pivot point and thus not a pendulum effect.

However, when the angle of thrust is variable to the centerline and is adjusted (by either pilot input or gimbal input) to remain oppositional/angular to the directional force of gravity, the thrust creates a pivot point. This introduces the pendulum effect to the craft. Therefore, a forward-mounted point of thrust would be more stable (pendulum) as it would take less thrust to correct for unwanted trajectories than aft thrust (inverse pendulum).

If you want context for my need for understanding, it is in relation to this video: At around 2:50 I said the word "pendulum" and people in the comments went nuts. We want to make sure our science is right for a pinned comment and for info in a following video. If I am incorrect in my physics we want to correct it to give our audience good information.
Thanks again for the help!

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russ_watters
Mentor
However, when the angle of thrust is variable to the centerline and is adjusted (by either pilot input or gimbal input) to remain oppositional/angular to the directional force of gravity, the thrust creates a pivot point. This introduces the pendulum effect to the craft. Therefore, a forward-mounted point of thrust would be more stable (pendulum) as it would take less thrust to correct for unwanted trajectories than aft thrust (inverse pendulum).
I don't see how you reached either of those conclusions. The whole point of the fallacy is that there is no difference between the two scenarios: an inverted pendulum configuration doesn't cause any instability and an upright (normal) pendulum doesn't add any stability in rockets. That's the main reason forward-mounted thrust was quickly abandoned. An off-axis force creates the same torque for the same angle/distance from the center of gravity whether it is above or below.

Well the way you describe it, the motor remains always vertical and the gimbal acts as a pivot point. It is exactly a top-mounted pendulum, no different from a one sitting on a table except in magnitude of g.
This is what confuses me. Since you say there is a pendulum effect in this scenario where the thrust is always keeping opposition to gravity, why would it not matter if it became a pendulum (top mounted thrust) vs inverted pendulum (bottom mounted thrust)? Wouldn't a pendulum would naturally return to vertical where an inverted pendulum would naturally want to swing away from vertical?

cjl
Only if you're steering it such that the thrust directly opposes gravity. There's no reason why you'd do that in the inverted pendulum case though - you'd steer the opposite way instead. In either case, you need active control to keep it stable.

russ_watters
Mentor
This is what confuses me. Since you say there is a pendulum effect in this scenario where the thrust is always keeping opposition to gravity, why would it not matter if it became a pendulum (top mounted thrust) vs inverted pendulum (bottom mounted thrust)? Wouldn't a pendulum would naturally return to vertical where an inverted pendulum would naturally want to swing away from vertical?
Well think about what is making it sway to begin with; it's asymmetric thrust that causes the sway, so in the very odd scenario you described, if there's an asymmetric thrust starting the oscillation (such as a delay in the actuation of the gimbal) you'd get a series of increasing oscillations until you exceed the gimbal limit of the motor.

And I say "very odd scenario" because if you have the ability to control a gimballing motor, why would you use it to make or allow the rocket oscillate instead of using it to make the rocket fly straight? Why make it artificially simulate a pendulum?

 Let's talk through what a rocket with a control system like you describe would do. Let's say it starts straight vertical and intends to fly perfectly vertical, with the engine perfectly aligned with the COG. A bit of wind blows it off vertical to the right (clockwise), which means the engine is also pointing off-vertical (to the left). Now, in your system the gimbal swings the motor to the right (counterclockwise) to make the engine align vertically as you want, applying a torque to push the nose back to the left. The angle between the rocket and motor decreases as the rocket swings back vertical, but the rotational speed continues to increase as the rocket approaches vertical, causing the rocket to sway back in the opposite direction. These oscillations will increase or decrease at the whim of the wind or control system delay until eventually they topple the rocket over.

Instead, as the rocket rotates back to vertical the motor should pivot in the opposite direction to stop the rotation when the rocket gets to vertical. Again, if you have a control system capable of controlling orientation, why program it to make the rocket behave like a pendulum when you could just as easily program it to make the rocket fly straight?

[edit2] Thinking through your control system on a normal rocket with the motor at the bottom, your control system would definitely perform worse on a normal rocket than a rocket with the motor on top. But I don't know why that buys you anything.

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Thanks. I'm getting a better understanding here...
My question then is, with the motors pivoting to adjust for the craft being out-of-vertical alignment, doesn't that introduce a pendulum effect (or inverse pendulum with them on the bottom)? If it does, is there still a pendulum effect?

If there is pendulum effect happening, is there still pendulum effect in your below scenario?

Instead, as the rocket rotates back to vertical the motor should pivot in the opposite direction to stop the rotation when the rocket gets to vertical.
My understanding is that there is a pendulum effect but that there are other things happening in addition to the pendulum effect.

Take the example of a small boat in a moving river. If the boat is at anchor, then it will orient itself, hanging from the anchor, downstream of the anchor-point, facing directly upstream. That's the "pendulum effect".

But if it's not at anchor, then what happens ? Well, then it will remain at whatever its original angle of orientation was, as it floats downstream. Even if you run the engine, it still won't turn (unless the engine's thrust is off-centreline). It doesn't matter if the engine is at the front or the back.

If you want a rocketship to use the "pendulum effect", then the attachment point to the motor has to be a free gimbal(/universal joint). Then the ship will hang from the engine, as a proper pendulum.

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cjl
If you want a rocketship to use the "pendulum effect", then the attachment point to the motor has to be a free gimbal(/universal joint). Then the ship will hang from the engine, as a proper pendulum.
And you need some mechanism to keep the motor always pointed straight up. If the motor is free to rotate, you'll just end up with an unpredictable and unstable rocket.

And you need some mechanism to keep the motor always pointed straight up.
It doesn't need to be pointed straight up, though - with a horizontal acceleration (component) - pendling won't be to the vertical.

If the motor is free to rotate, you'll just end up with an unpredictable and unstable rocket.
The joint between engine and ship needs to be free gimballing.

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cjl
It doesn't need to be pointed straight up, though - with a horizontal acceleration (component) - pendling won't be to the vertical.

The joint between engine and ship needs to be free gimballing.
If it's just a free gimbal, what keeps the rocket motor pointing in the direction you want to go though? You still need a control system here, and in many ways, it's a more complicated one than if you just put the motor at the bottom and controlled the rocket as a whole.

If it's just a free gimbal, what keeps the rocket motor pointing in the direction you want to go though? You still need a control system here, and in many ways, it's a more complicated one than if you just put the motor at the bottom and controlled the rocket as a whole.
Which could sertve to explain why you don't see many rocketships with the engine at the top.

Of course, this all begs the question of why you want a penduluming rocketship in the first place.