mikepage said:
What am I missing here? Isn't acceleration by definition the sensitivity (derivative) of the speed of the stick with respect to time?
Sorry for the delay but I had to re-familiarize myself with some old work.
My argument is that the cue's speed is a function of the entire force profile (over time), which I'm sure you'll agree with. As such, what's happening during the last few moments before impact (accelerating vs not vs decelerating) has very little effect, just as continuing to apply a force during impact produces, by itself, negligible gain.
If you model the force applied during the forward stroke as Asin(wt), I'm interpreting and error in
timing to mean an unintended deviation in w, where w = 2pi/T, T = one full cycle period. The cue's speed sensitivity to deviations in w is less when impact occurs such that the phase angle wt is less than pi (ie, accelerating at impact), compared to wt=pi (zero acceleration at impact), which in turn is less than when wt>pi (decelerating during impact). Reducing w reduces wt, all else being equal. It also increases stroke length. These are the results spit out by a program, but I've just spent some time getting an analytical expression for it, as a double check.
Several other sources of error are also reduced when "accelerating through" as well. But speed sensitivity to variations in bridge length (given the exact same stroke) are greater when accelerating or decelerating at impact. The question is, when you set up with a different bridge length, are you aware of it and try to adjust stroke length accordingly? If so, then errors in this adjustment are less when "accelerating through". If not, speed errors are greater when accelerating.
The model Asin(wt), with a smattering of harmonics, is a pretty good representation of at least one stroke where we have accelerometer sampling. But even if this is typical of your average stroke, it's not been established that accelerating up to impact is tantamount to simply reducing w, ie, neatly stretching out the sine function.
I've done a lot of work on this but am trying to keep this short. Here is a graphical description of why stretching out (flattening) the sine function does what it does.
http://ww2.netnitco.net/users/gtech/StrokeSens.jpg
And here is why it should produce gains in cue speed if peak amplitude (A) is kept constant (theoretically):
http://ww2.netnitco.net/users/gtech/Fsins.jpg
I can get more draw, for instance, by moving my grip hand back, as Deadon mentioned earlier. Alternately, less peak force is needed to achieve the same speed.
I'm not pushing accelerating at impact, just offering up what I think are some benefits. A disadvantage is that energy is wasted...and then there's the bridge length thing.
Jim