Re: .Bernoulli and curve balls.

["Paul Camp" <pjcamp@coastal.edu>]

>  It is what happens with golf balls (backspin causes the ball to rise and
> overspin to stay low), and I think tennis balls as well.  I've never been
> sure about baseball pitchers though.  Since a right- handed pitcher is more
> effective against left-handed batters (I think that's the way it goes),
> then the ball should curve AWAY from the batter.  

That's mostly due to the fact that they can get inside on the batter. 
They actually want the ball to curve either toward the batter or 
down. Mostly, a downward curve is desired rather than a sideways one 
since that makes the batter aim too high.

Tom Seaver used to advise throwing a curve by: a.) putting the seams 
perpendicular to the direction of the throw (b.) putting the ends of 
your index and middle fingers on a seam and (c.) throwing in a 
motion, for a right hand pitcher, from behind your right ear 
following through to the outside of your left leg. This would tend to 
impart a clockwise rotation as seen by the pitcher; i.e. a horizontal 
topspin. Most pitchers also cock the wrist to add to the clockwise 
rotation (Nolan Ryan is the only one I know of to throw a curve 
without doing that but he is a pretty unusual example all around).

In addition to that horizontal rotation is a backward rotation 
imparted when the ball rolls off the fingers so all told the top of 
the ball, as seen by a right-hander, is coming back and to the right. 
If you do this, the ball curves down and to the right 
which brings it low and inside to a left-handed batter. Low and 
inside is good. It is hard to hit to begin with and if the ball is 
hit, tends to hook foul.

The ball curves mostly due to the Magnus force which arises out of 
differential air resistance on each side of the rotating ball -- the 
resistive force is proportional to the square of the velocity of the 
air stream passing the ball and so is larger on the side spinning 
into the air than on the other side. For balls pitched at speeds 
above about 75 mph, one must worry about how the drag coefficient 
varies with velocity since that is on the cusp of changing from 
laminar to turbulent air flow. It can begin to decrease -- throwing 
too fast makes a very bad curve ball.

The stitches also play a role (note how Seaver instructed the pitcher 
to hold the ball) as they entrain some of the passing air and affect 
the drag coefficient strongly. 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.

Variations include the slider, a kind of fast curve in which the ball 
rotates almost in a horizontal plane, breaking more nearly left-right 
but not nearly so sharply as the curve (which, as noted before, is 
really more of a drop); and the screwball, a kind of reverse curve 
thrown by a right handed pitcher to break away from rather than 
toward a left handed batter.

Interesting historical note: Isaac Newton discussed the curve of 
tennis balls in basically the same terms, as did Rayleigh, and P.G. 
Tait as well (who may have been trying to understand and cure a 
wicked slice).

This information ultimately comes from Robert Adair's wonderful book 
The Physics of Baseball which I recommend to all. Sadly, I have been 
told that it is now out of print. This is too bad since, as we all 
know, baseball is the perfect game.

> If the ball is spinning
> clockwise (viewed from the top as it moves towards the batter) AND if the
> ball does curve in the direction of spin, then the pitcher's release would
> have the ball come off the fingers in a kind of sliding motion with the
> wrist open.  If the ball curves toward the batter then the wrist would have
> to snap to the pitchers left, across the body.  Any BASEBALL experts out
> there to explain (with authority) HOW to throw a curve and in what
> direction it does curve (with or against the spin)?
>
> *****************************************************
> Richard W. Tarara                  
 

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