Hi Bill—I received an email with your question, so let’s give it a shot…

Mr. Lindsey’s answer is quite correct, and I would recommend no changes.

I would just like to add one small detail—The control authority of the F-1 engines was MASSIVE.

In all of the Saturn 5 flights, the amount of actual deflection required of the F-1 engines was very small. Even Apollo 14, which was launched through a substantial wind shear at altitude (the vehicle response to this shear was large enough that it brought a ‘squawk’ from the crew after the fact) used less than 10% of the available F-1 engine gimbal travel for control.

Edit to original answer follows:

Bill, it has just occurred to me that I didn’t talk about a case that you didn’t mention specifically, but is a fairly obvious one to talk about—that of an F-1 engine failure.

If one of the 5 F-1 engines would have failed outright (i.e., simply stopped thrusting) then the situation becomes ‘a whole new ball game’.

Prior to clearing the umbilical tower (at approx T+10 sec) if 1 of the F-1 engines on the ‘tower side’ of the vehicle were to fail, the vehicle would tend to ‘yaw’ into the tower. In this case, an abort using the Launch Escape System (LES) had to be done FAST.

Also prior to approx T+10 seconds, loss of thrust of 1 engine would result in vehicle weight being greater than thrust. This was known as the ‘pad fall-back case’. Similar to the above, an abort using the LES had to be done quickly.

At any time after T+10 seconds, the vehicle could (in principle) continue to fly on 4 engines. In fact, an alternate guidance scheme (called ‘Chi-Freeze’, for those interested) would be brought into effect to try to salvage as much payload performance as possible. Now, flying on 4 engines would cause the vehicle to fly at a non-zero angle of attack, which would increase the structural loads (sometimes greatly) over the ‘nominal’ case. A great deal of effort was spent in design and analysis (as well as structural testing) to try to ensure that the vehicle had a positive margin of safety under these load conditions.

The biggest uncertainty regarding the loss of 1 F-1 engine (after T+10 seconds) had to do with maintaining attitude control during the ‘transient’ that was created when the ‘failed’ engine stopped thrusting, but while the other 4 engines (or 3 gimballed engines) gimballed to the final position they needed to get to in order to stabilize the vehicle. The first flights of the Saturn V (the first 2 or 3) flew with the outer 4 F-1 engines pointed along the long axis of the vehicle, to maximize delivered thrust. However, analysis showed that the attitude transients created in this circumstance by a single engine failure resulted in loss of control in too many instances. Therefore, a strategy was devised such that at some point (soon) after tower clearance, the 4 outboard engines gimballed (in an outboard direction) so that each engine’s thrust vector was nearer to the vehicle’s Center of Gravity. The result of this was that less time was required to stabilize the vehicle during the transient created by a single engine ‘out’, and vehicle control could be maintained with greater assurance.

Sorry for the length of the above ‘edit’, but I thought it was worth talking about.

I hope you find the above helpful.