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Re: .Bernoulli and curve balls.




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.

Knuckleball? This argument refers to the pathological behaviour of a
*seamless* ball, I believe. Is a knuckleball seamless? If not it makes
a poor example.

The argument referred to a physical situation in which one side of a
round spinning object is causing the airflow to become turbulent
while it remains laminar on the other side. The nature of the ball is
immaterial as long as the forces involved are the same. Stitches
cause the airflow to become turbulent at a different velocity and as
they rotate around, can cause the direction of the Magnus force to
change. The latter does not happen with a smooth ball. The same
physics applies to a fast ball as well -- if the ball's translational
velocity is high enough, it is almost impossible to make it curve
very much. This is partly due to the smaller time of flight but
mostly due to a reduction in the Magnus force due to turbulent flow.
The physical effect is the same as that which causes a reversal of
the sign of the force for balls with more uniform surfaces. The
physical principle is more generally applicable than for that
specific example -- it is not a whole new day.


Adair gives the following argument:

I'm having a copy of Adair brought in. I'll look at it.

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:

If Adair's argument is wrong then I see no mitigating value in making
it. I believe the equations of hydrodynamics have been found to be
quite tractable by using supercomputers. This particular problem seems
somewhat simpler than some I've heard have been integrated at NASA's
Ames Laboratory near San Jose. If that is so then it *is* practical to
analyze the problem in the proper manner.

Do not misquote -- the argument is not wrong, the functional form of
the Magnus force near the transition to turbulent flow is wrong IN
DETAIL. However, though the real function is not a simple
superposition of low- and high-velocity limits, it must ultimately
reduce to those limits in the appropriate cases. Therefore, though
Adair's function should not give the correct QUANTITIVE force, it
does provide an adequate tool for QUALITATIVE reasoning.

We do this all the time. Do you use (mu) N for the frictional force?
It too is wrong in detail and gives quantitive predictions that do
not work in even the most rudimentary physics lab. Friction, too, is
a very complicated problem that likely would require a supercomputer
to solve it correctly (if then). This does not prevent us from using
an idealized situation for qualitative reasoning, simply because it
makes the analysis tractable and because it highlights a particular
and relevant physical relationship. This simple form for friction
does have the correct qualitative behavior (friction does depend on
the magnitude of the contact force between two surfaces) and
therefore provides a tool for reasoning about general behavior, even
though if you try to use it for quantitative analysis you get
blatantly wrong results. This will have to suffice until you get
your grant to do a supercomputer analysis of curve balls (real soon
now, I hope -- it would be interesting).

Some people have even won Nobel prizes for doing things that were
arguably wrong but were near enough right to enable useful analysis
to be performed.


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.

Simple. In a wind tunnel the speed of the ball can be maintained
indefinitely and "anomalous" forces due to critical circumstances can
be similarly prolonged. A real curve ball decelerates. That's why I
asked how such a mechanism could be responsible for a reversed curve
ball. I suspect it is not a stable condition over a suitably large
range of velocities.

Leigh


It is interesting to note, however, that the same "faulty" wind
tunnel tests give the correct results for a spinning baseball. Are
they only invalid for smooth balls? If the calculation is at variance
with experimental observation, likely the calculation is the one
which is wrong.

The spin rate of a typical ball decreases by something on the order
of 20% per second. This varies somewhat with the speed of the
ball but for a 60 mph curve ball, which will cross the plate in about
half a second, it isn't very much change. Spin rates are about 1600
rpm and so decrease to around 1400 rpm.

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
pjcamp@postoffice.worldnet.att.net The Name of the Rose
(803)349-2227
fax: (803)349-2926