Re: .Bernoulli and curve balls.

[palmer@sfu.ca (Leigh Palmer)]

> > > In fact, for a slowly spinning, slowly
> > > pitched *smooth* ball, the curve can break the opposite way as the
> > > air flow may be laminar on one side and turbulent on the other.
> >
> > The mythology is enhanced! What speed must the ball move (and spin)
> > so that the airflow becomes laminar? To what precision must this
> > condition be established and maintained?
> This is obviously a pretty complicated problem.

And what do physicists do when confronted with a "pretty complicated
problem"? Give up!? Let's have a bash at it and see why this is not a
credible possibility. The Reynolds number for the onset of turbulent
flow is usually taken to be about 200. For an object of size D moving
with velocity v in a fluid of density rho and viscosity eta:

   Re = 200
    D = 10 cm
  eta = 180.0E-6 poise
  rho = 1.29E-3 g/cm^3
                                  eta Re
The critical speed would be v  = -------- = 3 cm/s
                             c    D rho

We conclude that to keep one side of the ball in laminar air flow the
spin must be such that the tangential velocity of the ball (in the
ball's frame of reference) does not differ from the speed of the
passing airstream by more than +/- 3 cm/s, and it must remain so for
the duration of the curve. That is, the speed of the ball must not
diminish by more than 6 cm/s over the distance of the pitch, assuming
the spin remains constant over that same time. If that specification
is not sufficiently discouraging (the ball slows much more rapidly
than that), recognize that the calculation we have done applies to
airflow at a single radial distance from the axis of rotation. I fear
that the range of radii (and hence the fraction of the surface of the
ball) that can be expected to move with the critical surface spin
rate within a range of the critical velocity is very small indeed, of
the order of the ratio of the critical speed to the projectile speed!
In plain language, if it happens that a smooth ball can be made to
curve the other way, fluid mechanics will have to be overhauled.

This problem is difficult. It is also complicated. The answer is
well known, however, and that should be a guide to tell us whether we
are modelling it reasonably or not. The glib "explanations" in terms
of the Bernoulli effect are unsatisfying and unedifying in addition
to being incorrect. I can't find the Hecht explanation of the curve
ball which was cited as 98% correct and I'd like to have that page
number again (I have the Hecht books). We are *not* all agreed, though
I may be a very small minority, but at least I've done a calculation!

Leigh