I've just watched Scott Manley's video SpaceX's Water Landing Reveals Rocket "Secrets" (or, What We Learned from CRS-16) (again) and there's some rigid body dynamics in there where I'm not sure I am completely understanding exactly what he is saying.

After concluding that this was a single engine burn and so thrust vectoring of the single, central main engine could not address the stuck-grid-fin-induced roll he says:

So I think a lot of the last minute correction comes from the reaction control thrusters. Now another thing to see is that as it gets down, it starts to pitch over. This is what would happen if the engine starts to thrust off center and starts to correct, you would of course get a gyroscopic precession-style effect where the actual rotation would be at 90 degrees to the one the thruster was trying to perform.

  • When he refers to the single engine correction, is it correction for pitch/yaw, or correction for the roll problem, which he seems to indicate would not work as the single engine is on-axis.

  • And what is it exactly that is 90 degrees to what else exactly? If there is a governing equation for this effect, it would be great to add it as well.

  • Did the engine vector 90 degrees to the direction of tilt in order to correct it correctly, or was the correction 90 degrees away from where it was needed because the gyroscopic effect was not properly taken into account?

cued at 05:05

  • $\begingroup$ I've added a new spaceflight-dynamics tag, but not sure if that would be sufficiently covered by math + physics + adcs and a new tag wouldn't be necessary. Thoughts? $\endgroup$ – uhoh Jan 21 '19 at 2:28

When you're trying to rotate something, there are two cases:

1) The torque you're applying is large compared to the angular momentum the body has, i.e. when the body isn't rotating. Then it starts to rotate in the direction of the torque you're applying. This is the more intuitive case.

2) The torque you're applying is small compared to the angular momentum the body has, i.e. when the body already has significant angular velocity and/or has a large moment of inertia. That's the gyroscopic precession case, where the body seems to rotate "as if" the forces had been applied 90 degrees further around the rotation.

A rocket body rapidly rotating around its long axis certainly can be the 2nd situation. In that case, trying to rotate it in pitch or yaw will get tricky; control equations that don't anticipate a lot of roll might not work if they can't apply large torques.

But I'm not at all sure that's what the video shows. The rocket body isn't rotating all that fast, its mass is low, and the moment of inertia around roll of a rocket is much less than the yaw/pitch moments that the thrusters are already meant to deal with. Further, torquing to keep a particular orientation, instead of to causes a rotation, doesn't invoke precession: It's cancelling some other torque, for a net torque of zero.

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  • $\begingroup$ I see, so if the rocket were tilted toward the north for example, and rolling about its axis fairly fast, then we might expect the nozzle to vector in the east-west plane in order to tilt it toward the south? $\endgroup$ – uhoh Jan 21 '19 at 8:33
  • 1
    $\begingroup$ @uhoh yes, that's about correct. The engine would need to vector continuously, matching the roll rate, in order to remain in the East-West plane. It's the same physical system as the classic 'hanging bicycle wheel', just rotated- the wheel is a short flat rocket body and the hanging string provides the (very) vectored engine thrust $\endgroup$ – Jack Jan 21 '19 at 8:47

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