TC said:
You're incredibly funny, as you're trying way too hard with the rather handy information we have... It's a matter of dividing one number by another.
Of course, if we all cared, we could all just look at the Vesuvius class in Secret Ops, which actually bothered to give the ship rotation statistics in the engine, and you'll find that it's 6/6/6
I haven't had time to reply until now; I didn't want to come back until I had at least done some of the initial analysis of the imagery, and to perform a few rough estimates. Here's what I've managed to observe so far.
The clip in question is called 3330A on the WC4 DVD, side B. The helmsman begins executing the "full 180" at approximately frame 1187 (before that, the helm control isn't even nudged). The final frame of the sequence is 2031. At 29.97 fps, this is about 28.2 seconds, so the turn rate would seem to be 6.4 degree/second. No big controversy there.
However, the helmsman is still pulling the helm control all the way until approximately frame 1320 (we then cut to an exterior shot, and are unable to see if he pulls it even further). Until then, the Vesuvius is not executing its turn at the maximum rate. In any event, this is a full 4.4 seconds later. With this figure, the turn is actually completed in 23.7 seconds, and the turn rate rises to about 7.6 dps. Somewhat alarming, but still in the ball park. Recall, however, that the beginning and end of the turn are somewhat slower than the middle, executed at the maximum rate, so this is actually a conservative estimate.
Further complicating matters is that we don't know how fast time actually passes, as we don't know how much the various clips overlap (the scene cuts back and forth between exterior shots and the Intrepid and Vesuvius bridges). Thus the only reliable numbers can be derived from watching a single continuous sequence, and using the one where the Vesuvius turns fastest. As far as I can tell, this sequence occurs between frames 1321 and frames 1400. This sequence follows immediately after the helmsman has pulled the control device as far to the left as we ever see.
Here are frames 1321 and 1400:
(there are 5MB/day transfer limits on these two URLs combined, so they may not work later in the day, depending on thread traffic)
The time between these frames is a mere 2.64 seconds. At a strict 6 dps turn rate, the Vesuvius should be able to turn 16 degrees to port in that time. Taking into account possible rounding errors, a 7 dps turn rate would result in about an 18.5 degree turn.
What I have not resolved (and why this is not a simple matter of mere division, and why I need to use trigonometry and to carefully analyze the scene) is what the actual size of the turn is. Somewhat complicating the analysis is that the background starfield moves slightly, implying motion on the part of the Intrepid (although Blair tells the helmswoman at the start of the scene to keep a straight and steady course). However, just to hazard a guess, it would seem like the turn is appreciably more than 16 degrees (which is only 18%, or roughly 1/5th, of a right angle).
I think we might be able to reconcile the fact that the Vesuvius seems to turn faster than the known figures by calling the 6/6/6 dps rate the "standard" tactical rate. It could probably be pushed higher in an emergency, and we do see the actors lean into the turn during the full 180, something that would probably be avoided during regular manuevers. One reason I think this would be a better interpretation of engine figures is because ships in the engine should be performing routine maneuvers, and any extreme manuevers should otherwise be scripted. I didn't check if the Secret Ops turn rates conform to what TC reported.