Calculating Angular Momentum Reduction in Rotating Rockets

[darkdave3000]

how do i calculate the gradual reduction of angular momentum a rocket initially has before it fires its main rocket engines? I am assuming if the thrust is high enough then the rocket should eventually stop rotating and travel in a straight line. assume the rocket is in a universe without planets and is just floating in space. would the shape and mass distribution of this hypothetical spacecraft matter? for example, if its a sphere like in hitch hikers guide to the galaxy as the heart of gold vs a saturn V rocket?

 

[A.T.]

how do i calculate the gradual reduction of angular momentum

https://en.wikipedia.org/wiki/Torque#Definition_and_relation_to_angular_momentum

 

[CWatters]

how do i calculate the gradual reduction of angular momentum a rocket initially has before it fires its main rocket engines?

Perhaps I'm being a bit slow today but can you explain what causes the "reduction of angular momentum"?

I mean before a rocket fires it's main engines it's usually just sitting there on the launch pad and nothing is changing. I suppose it might be boiling off some liquid oxygen, reducing it's mass. Is that what you are referring to? Don't they normally keep it topped up?

 

[rcgldr]

If the thrust from the rocket provides no torque, then the angular momentum of the rocket does not change, and it continues to rotate at the same rate as it initially did. Since it's in empty space (no aerodynamic drag), the shape doesn't matter.

 

[CWatters]

I'm wondering if the OP is thinking about the possibility of a rocket "falling over" until they are going fast enough for aerodynamics to keep them straight? In fact many use steerable engines (vectored thrust) to balance until aerodynamics takes over.

 

[darkdave3000]

If the thrust from the rocket provides no torque, then the angular momentum of the rocket does not change, and it continues to rotate at the same rate as it initially did. Since it's in empty space (no aerodynamic drag), the shape doesn't matter.

Hi thanks for this. Youre the first to fully understand the problem and answer it. It seems counter intuitive though, so I am going to ask you: are you sure about this? Remember that the vector of rocket exhaust will also be rotating as the rocket rotates.

Imagine a satun V rocket in empty space rotating about 1 degree per minute(very slowly) and then it fires its engines... you mean to say that even by the time it achieves say 8km/s it will still be rotating at 1 degree per minute? The rocket thrust will not overwhelm it and reduce/cancel it out? That is the rocket will not fly in a straight line but in a curve? Remember no RCS is fired after the initial rotation starts, so there will be no RCS maintaining rotation and no RCS countering it either.

Note: please ignore reduction in mass and change in COG as a result of fuel and propellant being spent.

 

[darkdave3000]

https://en.wikipedia.org/wiki/Torque#Definition_and_relation_to_angular_momentum

Hi I read this but I am not sure how i can use this to solve my problem of calculating the reduction in RPM.

 

[rcgldr]

If the thrust from the rocket provides no torque, then the angular momentum of the rocket does not change, and it continues to rotate at the same rate as it initially did. Since it's in empty space (no aerodynamic drag), the shape doesn't matter.

are you sure about this?

To be technically correct, assume the rocket and its fuel as an isolated system, free from any external forces or external torques. The center of mass of the rocket and fuel can be used as a non-accelerating frame of reference. From this frame, angular momentum of rocket and fuel is conserved. If it's assumed that the thrust provides no torque on the rocket, then the rocket continues to rotate at the same rate. In reality, as the fuel moves outwards from inside a rotating rocket, the fuel would normally exert an internal opposing torque from within the rocket, but you could assume that the thrust is vectored so that the thrust never generates any net torque on the rocket. So with no net torque from within the rocket, and with no external forces or external torques involved, the rocket continues to rotate at the same rate. The path would initially be spiral like, but I don't know if the path would converge to a specific shape.

 

[A.T.]

Hi I read this but I am not sure how i can use this to solve my problem of calculating the reduction in RPM.

Compute the net torque from all froces around the rockets center of mass. This is the change of the rockets angular momentum per time.

 

[jbriggs444]

To be technically correct, assume the rocket and its fuel as an isolated system, free from any external forces or external torques. The center of mass of the rocket and fuel can be used as a non-accelerating frame of reference. From this frame, angular momentum of rocket and fuel is conserved. If it's assumed that the thrust provides no torque on the rocket, then the rocket continues to rotate at the same rate. In reality, as the fuel moves outwards from inside a rotating rocket, the fuel would normally exert an internal opposing torque from within the rocket, but you could assume that the thrust is vectored so that the thrust never generates any net torque on the rocket. So with no net torque from within the rocket, and with no external forces or external torques involved, the rocket continues to rotate at the same rate. The path would initially be spiral like, but I don't know if the path would converge to a specific shape.

We are asked to assume that there is no reduction in craft mass due to expelled exhaust. You asking us to consider the center of mass of rocket and fuel and consider that the expelled exhaust carries momentum and counts against the center of mass. In order to make these two viewpoints consistent, we must assume an infinite exhaust velocity and a negligible exhaust mass. Accordingly, no thrust vectoring is required.

 

[CWatters]

Imagine a satun V rocket in empty space rotating about 1 degree per minute(very slowly) and then it fires its engines... you mean to say that even by the time it achieves say 8km/s it will still be rotating at 1 degree per minute? The rocket thrust will not overwhelm it and reduce/cancel it out? That is the rocket will not fly in a straight line but in a curve? Remember no RCS is fired after the initial rotation starts, so there will be no RCS maintaining rotation and no RCS countering it either.

You don't say which axis the rocket is rotating about but flying "in a curve" implies it's rotating about a horizontal axis rather than a vertical axis.

You are correct. The rocket will continue to rotate unless something provides a torque to slow and then stop the rotation. If the thrust line of the main engines acts through the centre of mass (eg they can't be vectored) then they cannot provide that torque.

On the Saturn V the outer four engines were steerable and the inner one was fixed. I've not been able to find a video on youtube that shows vectoring at launch but I suspect that's the only time it happened?

 

[darkdave]

Compute the net torque from all froces around the rockets center of mass. This is the change of the rockets angular momentum per time.

Only two acceleration will be
1. Initial spin of the rocket along a 2D plane
2. The main rockets firing as the rocket continues to spin

Will I discover that the rocket will continue to spin as the rocket engine provides the 2nd form of acceleration?
Everyone on this thread seems to think so and I would prefer not to waste time with calculations to come to the same conclusion.

 

[A.T.]

Will I discover that the rocket will continue to spin as the rocket engine provides the 2nd form of acceleration?

If there is not torque from the thrust force around the CoM, then it will continue to spin.

 

[TurtleMeister]

Based on the OPs conditions, I agree with the other posters. The rocket will continue to spin around a center point. It's speed or RPM around the center point will remain constant if the thrust remains constant. One analogy is to attach the front tip of a model rocket to a string and swing it around your head. Your head is the center point. The rocket thrust is always pointed toward the center point. The force produced by the rocket engine would be the same as the centripetal force required to keep it in the circular path.

edit: The rocket thrust has no effect on the RPM, which will always be the same as the initial rotation or spin. Changing rocket thrust will affect the distance between the rocket and the center point, or circumference.

edit2: The center point along with the circling rocket may have a steady motion relative to the observer, in which case the rockets motion would appear to be moving with a spiraled motion.

 

[CWatters]

Only two acceleration will be
1. Initial spin of the rocket along a 2D plane
2. The main rockets firing as the rocket continues to spin

Will I discover that the rocket will continue to spin as the rocket engine provides the 2nd form of acceleration?
Everyone on this thread seems to think so and I would prefer not to waste time with calculations to come to the same conclusion.

The initial spin is not a torque.

The main rocket thrust might provide a torque but only if it is vectored. If the thrust acts through the centre of mass then it won't provide a torque either.