The Physics of Ball on Bat

While reading the sports page a few days ago, I saw a quote by a teammate of Mark McGwire, the St. Louis Cardinals' slugger who just hit the 500th home run of his major-league career. The player, who watches from the bench as McGwire propels baseballs out of stadiums from New York to San Diego, said of McGwire: "He hits the ball as far as is humanly possible."

Actually, the honor of the farthest-hit baseball goes to Mickey Mantle, who played with the Yankees in the 1950s and 1960s. That tidbit was dug up by of Robert Adair, a professor of physics at Yale University who was once appointed by the commissioner of baseball as "official physicist to the National League."

I suffered from physics phobia in high school and college, but I like it when the science of matter and energy is applied to sports. Adair took a look at the natural laws governing the national pastime in The Physics of Baseball.

Simple physics explains why major-league pitchers have a rough time in Denver, for example. The Colorado Rockies play home games at an elevation of more than a mile above sea level. As mountain climbers know, the higher one goes, the thinner the air becomes. The drag of air molecules on a baseball is less in mile-high Denver than in New York City, close to sea level. Adair calculated a home run that traveled 400 feet at Yankee Stadium on a windless day would fly about 430 feet in Denver. If a batter hit that same home run in Mexico City, at an elevation of 7,800 feet, it would sail 450 feet.

Pitchers also complain that their curve balls don't dance in Denver. Adair figured that thin air causes balls to curve about 25 percent less in Denver than in Boston or New York. Why does a ball curve, anyway? By spinning a baseball as it's released, a pitcher forces the air resistance of the ball to be greater on one side than the other. Reacting to the spin, the ball moves away from the side of greatest resistance, causing it to curve. In 1870, Freddy Goldsmith proved the curve ball wasn't an illusion when he threw one through three aligned rods. The ball passed to the left of one rod, to the right of the second, and to the left of the third.

A baseball is not the perfect flying object. When mashed into an oval during the collision with a bat that takes about 1/1000th of a second, only about 30 percent of the ball's energy returns in the rebound. Though a baseball--two strips of cowhide stitched tightly over a layer of yarn and a cork nucleus--is a dud when compared to a golf ball, the two feature similar alterations that make them fly well enough to add excitement to both games. The raised stitches on a baseball act like the dimples on a golf ball, creating air turbulence that makes them move farther. A baseball hit 400 feet would only travel 300 feet if it didn't have raised stitches, Adair wrote. Figuring the limitations of human strength, air resistance, the hardness of wooden bats and the bounce of a baseball, Adair calculated that the farthest anyone will ever be able to hit a baseball is about 545 feet.

Though McGwire or the Chicago Cubs' Sammy Sosa may drive a ball deeper, Mickey Mantle still holds the record for a ball he hit in 1953. Adair studied the trajectory of Mantle's home run, which cleared the bleachers of Griffith Stadium 460 feet from home plate and struck a beer sign. By retracing the arc of the ball, Adair figured Mantle's homer would have gone 506 feet if it hadn't hit the sign.

Until someone hits one deeper, Mantle's ball was hit as far as is humanly possible.