Re: pool table physics (long)

[brian whatcott <inet@INTELLISYS.NET>]

> Brian Whatcott wrote:
>
> > I am fairly sure that the folks who put together the early billiards
> > table were more interested in three visible features:
> > 1) that a ball, hit no matter how hard, would not jump the cushion
> > nor yet bounce off the baize.
> > 2) That the approach angle to the normal and the departure angle
> > were fairly similar.
> > 3) that there was maximal speed conservation.
> > So these are my assumptions for the pool table too.
> > And I assume that these constraints can be met by the usual
> > cushion height ratio.

At 09:43 4/22/01 -0700, Ben Crowell responded:

> #3 would be extremely difficult to measure with the technology of
> centuries ago, nor would there be any easy way to measure the
> amount of kinetic energy that was retained (which is not
> the same thing). ...

Interesting point that Ben makes: that terminal speed is not
a total measure of kinetic energy in a constant mass.
 This might be called the Galilean error that Ben is pointing to,
and I think it bears some examination.

The quantitive analysis is unhelful if the conceptual underpinning
of the model is incomplete, as I expect Ben believes it is.

So here's a suggestion.
Though a billiard ball can be hit with top, side or back spin,
assume a diagonal cushion hit is from a ball with rotation due only
to unslipping movement of the contact patch with the baize.

I expect that there is some upward precession of the horizontal spin
axis nearer the cushion towards the vertical, which effects a
forward roll along the compressed cushion during the rebound.

This is a rather different effect from the "cancelling" frictional
effect Ben has in mind.


brian whatcott <inet@intellisys.net>  Altus OK
                Eureka!