How the Physics of Baseball Works

Yogi Berra once said, "I never blame myself when I'm not hitting. I just blame the bat, and if it keeps up, I change bats." In youth ball, changing bats usually means grabbing more aluminum. In the Majors, it's wood, or it's nothing. This may not seem significant, but bat construction has important implications for the game.

First, aluminum bats are hollow, while wooden bats are solid. That means you can make aluminum bats longer or fatter through the barrel without making them unnecessarily heavy. Not so with wooden bats, which get heavier as you make them longer or thicker. Another key difference is the location of a bat's center of mass, or CM. For aluminum bats, the CM is closer to the handle; for wooden bats, it's closer to the end. As a result, aluminum bats are much easier to swing, which means batters get them around faster.

Does this affect batted balls? As it turns out, increasing the mass of a bat increases batted ball speed, or BBS, but not nearly as much as increasing the velocity of the bat. According to some research, doubling the weight of a bat increases BBS by about 17 percent. Doubling the swing speed, however, leads to a 35 percent increase in BBS. In fact, for every 1 mile per hour you add to your swing speed, the ball travels an additional 8 feet [source: Coburn].

For these reasons, governing bodies at all levels of baseball closely regulate bat specifications. In Little League Baseball, the bat "shall not be more than thirty-three (33) inches in length nor more than two and one-quarter (2¼) inches in diameter. Non-wood bats shall be labeled with a BPF (bat performance factor) of 1.15 or less." BPF measures the increase in the liveliness of a ball hitting a bat compared to throwing a ball against a solid wall. So, if a ball has a 20 percent faster rebound coming off a bat, its BPF would be 1.20. Major League rules are more restrictive: "The bat shall be a smooth, round stick not more than 2¾ inches in diameter at the thickest part and not more than 42 inches in length. The bat shall be one piece of solid wood."

The material of a bat has no effect on its sweet spot, at least as it's defined in physical terms. Players know they've engaged the sweet spot when their hands feel no sting during the bat-ball collision. Or, as Ryan Zimmerman, the third baseman for the Washington Nationals, describes it: "Every ball I've hit that I haven't felt, I knew I hit well." Physicists now know that this sensation (or lack of sensation) is related to how a bat vibrates when it strikes a ball.

Yes, just like guitar strings, bats vibrate at multiple frequencies. When they vibrate at their fundamental, or lowest, frequency, they have a node -- a point at which the amplitude of vibration is zero -- about 6.5 inches (16.5 centimeters) from the barrel end. A second node, related to another frequency, appears 4.5 inches (11.4 centimeters) down the barrel. The space between these two nodes is the sweet spot, and hits involving the narrow zone produce less vibration and transfer more energy to the ball.