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Re: .Bernoulli and curve balls.




There exists empirical data on this problem taken in wind tunnel
tests which I believe is reported in the Briggs article previously
cited. It confirms a curve opposite to the direction expected from
the Magnus effect and the wind velocity at which this occurs does
correspond to the transition from laminar to turbulent flow.
Evidently, then, there must be some error in the calculation (though
I must confess I didn't catch it).

It might confirm a force reversing direction in a steady flow for a
mounted spinning ball. We were talking about a curve, however, and
my analysis dealt with a pitch, arguing that a reversal of the curve
could not occur because the ball does not move with constant speed.
I should have made it clearer that the myth I complained about was
the suggestion that the ball might actually be made to curve in the
opposite direction if the spin and speed were adjusted just right,
which is what I thought you were suggesting.

Leigh

It is and it does. A knuckleball, which a slowly spinning pitch, can
do exactly that and in fact may curve in a variety of directions on
the way to the plate.

Adair gives the following argument:

Qualitatively, the force on the ball may be given as:

F= term for low velocity smooth flow + term for high velocity
turbulent flow

In detail, this is wrong but then in detail the only proper way to
analyze the problem is by way of the Navier-Stokes equation and that
is not practical. So:

F=KfvC [1 + 0.5(v/C)dC/dv]

where K is a constant (empirically, about 2x10^-6), f is the
frequency of the spinning ball, v is its velocity and C is the drag
coefficient. The second term arises due to the fact that near the
transition between laminar and turbulent flow, the drag coefficient
varies strongly with the velocity.

If, therefore, the logarithmic derivative of C is less than about -2,
the drag force decreases as the velocity increases.

The important point here is that a curve ball curves not because of
the Bernoulli effect but because of the Magnus effect. Drag is
important, as is turbulence.

As far as the wind tunnel results go, I don't see how the mount on a
mounted spinning ball makes a material amount of difference.




Paul J. Camp "The Beauty of the Universe
Assistant Professor of Physics consists not only of unity
Coastal Carolina University in variety but also of
Conway, SC 29528 variety in unity.
pjcamp@csd1.coastal.edu --Umberto Eco
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