Jal said:
But that's what has me flummoxed. If you look at the integral of a pure sine wave over time, the most cue speed is obtained when impact occurs at a phase angle of 113 degrees ("accelerating through" so to speak), rather than at 180 degrees (coasting through). In fact, I think it works out to about 95-98% of the speed you would get if you applied the peak force throughout (but I'll have to look at this more). This is for a fixed distance (fixed bridge length).
Granted, we don't execute a pure sine wave, but you do get an increase in cue speed for a variety of "impure" wave forms. I'm probably not the mathematician to prove for which class of wave forms this holds true, and which ones it doesn't, but I think it's likely to be true for the "sine-like" strokes we probably generate (judging from some of the accelerometer data).
Jim
This is off the subject of this thread, but ....
I think we have two different ways of viewing this sensitivity thing.
Both are of the form
Assuming fixed AAAA, ball speed is least sensitive to BBBB when condition CCCC is met.
For Jewett,
AAAA = maximum stick speed
BBBB = errors in forearm angle at impact
CCCC = the intended forearm angle at impact has zero force
For Jal,
AAAA = maximum force during the stroke
BBBB = errors in stroke timing
CCCC = the force at impact is at a particular spot past maximum at impact
Both seem to me to be true statements as far as they go. Their value though depends on
--- whether AAAA, the thing that's assumed fixed, is really something we're trained to readily fix at a certain value.
--- whether BBBB/CCCC refer to a variable we readily control.
I think Jal's interesting approach suffers under this kind of analysis.
I think it's the time integral of the force and not the maximum value of the force that we're trained to summon at a certain value. What we know how to do is get the stick going at a certain maximum speed, and we intuitively use more force when we use a shorter backstroke and less force when we use a longer backstroke. I don't think summoning a certain maximum force is what we're good at.
I don't think Jal's "timing" variable, essentially the period/frequency of the force sine function is a reasonable variable that is under our control. I think the timing is too tied to the stroke geometry.