NORTH America's baseball season has opened and, once again, the "crack" of the bat is heard throughout the land. But there's more to the encounter of bat and ball than appears to the casual eye.
It turns out that the impact can set up vibrations that make the seemingly stiff bat wriggle like a snake. Therein lies the secret of some of baseball's subtle features, including the fact that wooden bats tend to break on the side opposite the impact point.
Physicist Lonnie L. Van Zandt of Purdue University in West Lafayette, Ind., details this in a paper in the American Journal of Physics.
Commenting on his research in a telephone interview, he noted that, after more than a century of use, the baseball bat "is a finely tooled artifact." But that doesn't mean that one can't still learn interesting things about it by looking at it from a physicist's point of view.
A bat has a series of normal modes of vibration that Dr. Van Zandt says "is entirely analogous to the harmonics of ... an organ pipe."
He used a mathematical model in a computer to study these modes for a bat shaped to major league specifications and confirmed his results by experiment with a real bat borrowed from his son. He found that the first 20 such vibrational modes have implications for the game.
Everyone who has swung a baseball bat in earnest knows about the "sweet spot." That's the spot where a direct hit on the ball drives the ball fastest. It's the spot where a hit doesn't make the bat sting one's hands. It's also the spot, more or less, where a hit sets up the least vibrational activity.
For example, a hit inside of that spot can set up a complexity of vibrations. In the lowest frequency mode, a bat bends in a simple curve that can cause it to break on the side away from the pitcher. A combination of modes can make the handle whip about and sting the batter.
Describing this stinging action in his paper, Van Zandt says: "A right-handed batter will feel the initial slap on his left palm and right fingers at about 2.5 ms [milliseconds] after the hit.... the handle comes back at between 4 and 5 ms to slap the opposite hand."
There are implications for the ball also. If the ball hits the sweet spot defined as the node or point of no motion for the lowest frequency vibration, the bat imparts maximum momentum to the ball and can knock it out of the park.
A hit elsewhere sets up elastic vibrations that absorb some of the impact energy. The bat is a bit "mushy" and doesn't hit the ball as far.
On the other hand, some of the vibrations are so fast they actually return some of the lost energy to the ball.
This effect is especially favorable for balls hit beyond the sweet spot. Van Zandt notes that this "shows quantitatively how important to the batter it is to strike the ball with the outer end of the bat."
Van Zandt acknowledges that professional players know all this intuitively from experience. So he has little advice to give them except he suspects the current fondness for skinny-handle bats is misplaced. "You really pay a penalty for that," he says.