[Gulauur]

Incidentally, one other issue the earlier Apollo missions had to deal with was avoiding the Service Module during re-entry. Several minutes before hitting the atmosphere, the crew cast off the SM from the Command Module. The SM's retro-rockets were fired continuously to push it well away, as well as giving it a roll. However, a few startled crews reported seeing their SMs drifting in the opposite direction to which they had been despatched, and re-entering the Earth's atmosphere disturbingly close to the CM.

The Apollo Flight Journal for Apollo 15 explains:
Early Apollo missions (Apollo 7 through 12) revealed an unexpected problem with this technique. At first glance, firing the translational thrusters to back the SM away, and using the roll thrusters to stabilize it would seen to be a perfectly adequate solution for this maneuver. Imagine the surprise then, when the crews of the earlier missions looked out the window and saw that the SM had somehow "boomeranged" around and was tumbling alongside the Command Module! After extensive analysis engineers discovered that the residual fuel and oxidizer in the Service Module sump tanks acted as a sort of "spring", taking the energy imparted onto them from the RCS jets, and releasing it against the tank walls as it sloshed about.

In a paper (Prediction of Apollo Service Module Motion after Jettison [J. Spacecraft and Rocket, June 1971]), a chart implies that any minus-X burn longer than about 200 seconds will result in the SM changing direction. Now, the direction reversal is not due simply to propellant sloshing. Because the SM's mass is not symmetrical over it's axis, any translational/rotational firing will start it tumbling. Since it is still tumbling while the minus-X thrusters are firing, eventually it orients itself to where the minus-X thrusters now have a posigrade (towards the CM) component. This, combined with the propellant slosh, was sufficient to cause the SM to reverse direction and head in the direction of the CM.

Remember that the propellants are just floating "loose" in the tank, which of course, is the reason for ullage before most burns. Let's try a simple scenario, where the minus-X thrusters fire for a short time, say 1 second. When the minus-X thrusters fire, the fuel essentially "stands still", and the SM accelerates around it. Now, you have inside the tank, a mass with some velocity. Eventually, the fuel smacks into a tank upper dome, and imparts its kinetic energy to the SM structure.

Now, remember these are the RCS jets, not the SPS, and they are not capable of any serious acceleration. Longer minus-X burns will eventually force the propellants down to the top of the tank, but not as much as you might think. Ullage before burns was enough to settle some of the fuel, but not enough to "pin" it down at the bottom of the tank with any certainty. There is lots of propellant still in the lines to the engine, enough to get a good engine start, which in turn, would provide enough acceleration to ensure that the propellants were always at the bottom end of the tank.

The problem with the SM jettison was twofold - First, the RCS jets created insufficient acceleration to eliminate the bouncing back and forth of the propellants. Second, The offset CG of the SM, along with the roll burn, caused tumbling which worked against any effort to settle the propellants at the "bottom" of the tank.