Consequently, integrated servo-mechanisms, capable of training the turrets and elevating the guns automaticaly, based upon the firing solution provided by the computation machine provide faster and more accurate overall response.
RPC was a useful tool in that it automated keeping the guns on target for elevation and (in the USN, train as well), thus eliminating the human element at the gun mountings, at least within the capabilities of the system. If the ship is on a steady course or maneuvering slowly, the system could keep up with the fire control solutions as they were generated. It certainly helped relieve the gun layers and mount pointers of a great deal of work. Essentially, these two would have only to oversee the train and elevation when the mount was under RPC, and apply fine corrections as needed. This was actually more often than one would think in the USN system as the synchros could over or under compensate for course and range changes and for pitch and roll under certain conditions. The German thyratron system was a bit more precise and with less lag time, which is why they chose to use it only for elevation: since they used a tight bracket system for ranging, they probably made the right decision in their RPC system, but one has to admit that it would have been useful to have it for train as well. Post war the USN investigated the German system when they examined the Prinz Eugen and found it had some advantages, leading to adoption of thyratrons in the late 40s and 50s.
RPC was not necessarily faster nor more accurate than follow the pointer, but it was a lot less work. In follow the pointer with the latest systems, the British layers and pointers could keep the guns on target as rapidly and as smoothly as RPC, provided their training and experience levels were of a high order. If you had relatively untrained or inexperienced crews, RPC was much better.
The main reason that RPC was not used for the turrets and guns in most navies, apart from the German and US navies, was most of the world utilized DC current instead of AC for domestic and military power supplies. DC can be used in simple modes, as was the case with the British H and P sights, but it could not provide the power output necessary for managing guns and turrets. In the USA, Tesla's AC had almost completely replaced DC in most power applications, and so the US had rather more experience with it than most.
Steve: I see what you are talking about now--mostly a matter of data flow within the system. I know in the German Schusswertrechner, enemy course and speed were fed into the A component of the FC computer which calculated it as one part of the rate of change formula, and with inclination from the director pointer and own course and speed from the pitot log, combined to form a flow of prediction data for relative range and rate of change. This was then taken up by the ballistic component which used the predictions from the A Component to generate continuous true gun range . I am sure in the USN computers and rangekeepers, it was handled in much the same manner. Both the German and USN used a closed loop data flow system whereby generated data was directed to the director whose crews would check for errors in train and elevation and apply corrections. However, there was a diffence in those old analog systems compared to the more modern FC systems.
In modern ones, a step by step calculation is used to generate the solution. When a correction or change is required to adjust the solution, it forces the computer to start over again and recalculate the solution. In analog, once it was running, corrections could be applied without stopping the data flow. It was rather like an old scale which uses a spring and hook to weigh something, with a pointer to show the weight. You could hang a bucket of water on the scale and it would show the weight. If you poke holes in the bucket, it will continue to show the weight as it changes when water runs out. On a digital scale, change the weight and the scale must recalculate everything.