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I've wondered about how the Apollo spacecraft could rotate to a specified roll angle (for example) and remain there. I know there were two dead bands available, 5 degrees and a much smaller value that I have forgotten.

Say they wanted to rotate by firing two opposing RCS thrusters (a coupled burn). After the roll was begun, they would have to fire again to stop the rotation, but I would imagine it being difficult to control the thrust of a rocket finely enough to simply make it stop rolling, exactly. I think of repeated opposite-direction bursts to make the rotational motion finally stop.

Through a friend, I met one of the engineers who worked on LM RCS, and Fred Haise, at the same time (in Houston, at the Apollo 11 movie on IMAX). I wish I had thought to ask them. :-)

I hope the question is clear...

Thanks,

Tom

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I'm not totally sure what kind of answer you're looking for here.

As far as the limits of the hardware, we can work out what the minimum change in roll rate is that could be achieved from the RCS thrusters.

The change in roll rate for a 4-thruster burn for the CSM would be on the order of 4º per second per second for a fully loaded CSM, nearly twice that for an empty CSM, and less for the CSM mated to the LM.

(4x 490N thrusters 2 meters from center of mass = 3920 N⋅m torque; roll moment of inertia for a uniform cylinder is m × R² / 2, mass is 28,000 kg for the fully loaded CSM, so 56,000 kg⋅m²; dividing we get 0.07 radians/s²).

The thrusters were capable of firing pulses as short as 15 milliseconds, which would change the roll rate by about 0.06º/s. For two thrusters instead of four, and with the LM attached, the change in roll rate would be much smaller, of course, more like 0.02º/s. I don't know if RCS roll was normally done on two thrusters or 4, or if it changed depending on whether a large or small roll change was needed.

According to Apollo Stabilization System Block II Detailed Training Program, the maximum expected error after the computer performed an attitude change was around 1º.

The attitude hold deadband could be set to as little as ±0.2º:

ATT DEADBAND (1811): The ATT DEADBAND switch controls the attitude deadband excursion to ±4.2º in the MAX position or ±0.2º in the MIN position when the SC CONT switch is in the SCS position and the RATE switch is in the LOW position. With the Rate switch in the high position the attitude deadband is ±8º or ±4º with 1811 in the MAX and MIN positions respectively.

RATE (1812): The RATE switch controls the maximum proportional rate command available from the Rotation Control with the S/C under SCS control. These proportional rates will be available in a particular axis only if the respective MANUAL ATTITUDE switch is in the RATE CMD position. The maximum rates obtainable in the HIGH position are 20º/sec in roll and 7º/sec in pitch and yaw. The maximum rates in the LOW position are 0.7º/sec in roll, pitch, and yaw. The HIGH and LOW positions also set the autopilot rate deadbands to ±2º/sec and ±0.2º/sec respectively.

To achieve an 0.2º/sec roll rate deadband, the guidance computer would have to command those 15-millisecond minimum-impulse burns until the measured roll rate was within limits.

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  • $\begingroup$ Thanks for the detailed answer. That amount of fine control (0.06 deg/s^2) is better than I imagined it would be. $\endgroup$ Commented Aug 14 at 23:56
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    $\begingroup$ @TomDickens and of course in practice the goal is simply to get the rates close enough to zero that you don't have to correct your attitude "for a reasonable length of time", and fuel consumption stays acceptable. They more than accomplished that goal. $\endgroup$ Commented Aug 15 at 14:42

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