27 Different Ways To Strike A Shot

5aheadforpinks said:
Seems to me that there are more things to consider than english and speed. Besides the endless discussion on the infinite cueball... there is also a matter of how straight your strokes follow through is, how far your strokes follow through is, how loose or tight your grip is... most of this has to do with how long the cue tip stays in contact with the cue ball, no matter what speed you shoot at you can get different results from the cueball (even with the same speed)


If you believe the mathematicians, infinite just doesn't cut it. According
to them there are many, many more than an infinite number of
positions...a "transfinite" amount in fact. I can't put an exact number
on it, but it's more than a 100 I'm sure.

I don't think you can have any significant control over how long the
tip contacts the cueball. I'm not an expert at this, but if you assume
a sinusoidal buildup and decay of the compression forces, then the
contact period is independent of the speed of the cue and virtually
independent of how much force you're applying during the impact.
(The length of the contact period decreases ever so slightly as you
apply more force.)

I think a more realistic treatment which takes into account that the
compression forces are not a simple linear function of the amount
of "penetration' of the tip into the cueball, internal damping in the
tip due to friction, and the fact the relaxation forces do not
follow the same curve as the compression forces, predicts even
less of a contact period when you increase the cue's speed or the
force on it at impact.

So what happens to the cueball after impact depends only slightly
on whether or not any force is being applied at that time. To get a
sense of this, let's go with the simpler (and more optimistic model).

To propel the cueball at 20 mph, an average force of 344 Lbs has
to be exerted during the 1/1000 sec of contact. This is the inertial
force that arises simply because the cueball is sitting there and has
mass. Assuming your stroke follows a sinusoidal buildup of force
(see the link below), and I think this is somewhat justified, the peak
force you'll have applied to the cue is 14.9 Lbs. This assumes that
at the moment of contact you're not applying any force (the 14.9 Lbs
has subsided to zero). But suppose you lengthen your stroke by
changing your muscle timing (or by gripping the cue further back)
and manage to apply 10 Lbs of force during the hit. The force the
cueball sees will be the 10 Lbs multiplied by the ratio of the cueball's
mass to the combined mass of the stick and ball (1/4), or 2.5 Lbs.
So the percentage increase in force will be (2.5/344)x100 or 0.7%.
This will add 0.7% to the cueball's spin/speed assuming the total time
of contact does not diminish too much.

But you do in fact get more action (spin/speed) by about 13.5% in
this case. While 13.5% may not itself seem like too much,
it results in the cueball having about a 29% increase in energy,
which means it will travel 29% further, and so will the balls in the
rack it breaks, on average. A picture is worth a thousand words
so hopefully the link below will help explain this.

http://xs.to/xs.php?h=xs28&d=05196&f=Fsins.jpg

The diagram shows the after impact forces as if no impact had occured.
In reality, according to a plot of cue speed vs distance by Bob Jewett
(the Jacksonville Project), the cue accelerates positively after impact
even without any muscle force being applied as the cue kind of catches
up with the arm. But I think the before impact curves are a fair enough,
if somewhat idealized, representation of the force function.

Even harmonic distortions tend to exaggerate the effect of lengthening
a stroke (increasing cue speed), while diminishing the effect of shortening
it (decreasing cue speed), while the presence of odd harmonics have the
opposite effect. Just in case you were curious!

The point is that follow through is an integral part of a stroke: the more
follow through, the longer the stroke, and the more action you get on
the cueball. It has nothing to do with what happens at impact, but
with the the distribution of force over the total time the cue is
accelerating. And these are rather large effects especially when you
compare the differences between strokes which are decelerating vs
accelerating at impact. Moving your grip hand back vs forward by 2",
for instance, without changing anything else, will result in an almost
30% difference in cue speed between these two positions, or 70%
difference in the cueball's energy.

Jim
 
During one of the ring games from Debry City Classic Jim Mataya got into this conversation with his broadcasting partner. I think Jim said he came up with 11 different ways to put english on a ball. He did not get into how he came up with his numbers.
 
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