Stadium Dugout Announcer's Booth Batting Cage Bullpen Behind the Plate

## II. Why Does a Curveball Curve? - The Physics Principles

I'm working on a new pitch. It's called a strike.
- Jim Kern, Cleveland Indians pitcher, 1986
Dr. Dell says lets go further!

Warning: Physics Alert! This next section is highly technical and is provided only for those who want to learn about the physics principles behind a curveball. Others are free to browse at their own risk.

What is this imbalance of the force? It is actually called the Magnus effect in the honor of the person who first observed it. Now a little history...

Newton actually recognized the effect earlier than Magnus did. Newton saw that a tennis ball "struck with an oblique racket" would curve. Bernoulli also determined that as speed of a fluid is increased, its pressure decreases as stated in his famous Bernoulli's Principle. Later on people who were playing golf found out that rough balls actually traveled farther than smooth balls.

Now for more recent times...

For a long time, people have argued whether or not a curveball is really curving or if it is just an optical illusion. The argument was settled with the advent of fast photography. Using cameras, people were able to determine that, indeed, a curveball does curve. People (mostly physics professors) began wondering why a curveball curved and used Magnus' work to explain why.

Now for some more physics to bash your brain...

When you reach out of the window of a moving car, you can feel the wind rushing into your hand. On an airplane, the wind rushing through top of the wings will move faster than the bottom thus pushing the wings and airplane upward. That was a demonstration of Bernoulli's Principle.

Magnus Force is similar to Bernoulli's Principle, but not quite (or we would be calling it Bernoulli's Principle). For a spinning ball, the stitches on the ball will cause pressure on one side to be less than on its opposite side. This will force the ball to move faster on one side than the other and will force the ball to "curve." This is the Magnus Effect.

 Nonspinning baseball Spinning baseball

When a pitcher throws a curveball, he will throw it such that the axis of rotation is not perpendicular to the ground, as it is in a fastball. Because it is spinning in a skewed axis, the Magmus force will force the ball to curve in a horizontal direction instead of vertical "curve" of a fastball.

How much will a baseball curve?.
The equation is as follows (from Prof. Adair's book Physics of Baseball):
FMagnus Force = KwVCv
where:

• FMagnus Force is the Magnus Force
• K is the Magnus Coefficient
• w is the spin frequency measured in rpm
• V is the velocity of the ball in mph
• Cv is the drag coefficient