On Wednesday 21 November 2007 17:51, Greg Rundlett wrote:
> I really like the indoor batting facility in Salisbury, MA (Extra
> Innings). I wondered how 'fast' the fast cage was....
> Y = Big League pitch speed =
> 60.5 feet / .45 seconds = Y feet / 1 second
> Y = 134.444 feet / second * 3600 / 5280 = 91.66 mph
I did figure it out - approximately. The Reynold's number is
180000, assuming the ball is a smooth sphere of 70mm diameter (I didn't
look up the actual size). The drag coefficient is .5, which results in
a retarding force of 1.8 Newtons.
The drag reduces the energy of the ball by 34 joules in its flight
from the mound to plate (taken as 19 meters). The energy of the ball
when crossing home plate is 160J, assuming a weight of 200 grams (which
I didn't look up either).
That means the initial velocity must be 44m/s to arrive at the plate
at 40m/s (90mph). So, the hydrodynamic drag is not very significant.
Using the average speed, my calculations show you would have .435
seconds to react.
So, congratulations on your fast reflexes! And, it goes to show how
enlightening even an approximate calculation can be. Or, more
particularly, that an approximate calculation is often close enough.
The fancy physics is not needed.
Insidently, the drag force drops suddenly by a factor of 2 just
above 90mph. Thus, a 92mph pitch would arrive in perhaps .40 seconds.
Pitching just above or just below that change must be some part of
making those big league pitchers so hard to hit.
Jim Kuzdrall
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