Newton In the Batter’s Box

Isaac Newton wouldn't seem to have much in common with Derek Jeter. But in one respect the Yankee has lived up to the physicist's expectations better than today's physicists, who (I regret to say) have let Newton down—dropped the ball, so to speak—on the matter of the Magnus force. It was 1671 when Newton, having observed many tennis games at Cambridge University, wrote that he "had often seen a Tennis ball … describe such a curve line. For, a circular as well as a progressive motion being communicated to it by that stroak, its parts on that side, where the motions conspire, must press and beat the contiguous Air more violently than on the other …" Or, in modern English, spin (Newton's "circular motion") makes balls do weird things. Spin creates a force that makes curveballs curve, and sliders cut to the outside of the plate, and infield pop-ups—which are hit with mad backspin—follow loop-the-loop trajectories. But while infielders like Jeter have intuitively mastered this Magnus force well enough to track pop-ups, physicists have not mastered it scientifically.

If Newton is watching from the ultimate skybox, he must be appalled at how the Magnus force, once dismissed as an optical illusion, continues to stymie physicists (including the one who won naming rights, Heinrich Magnus, 150 years later). "We can't calculate it from basic principles," says physicist Alan Nathan of the University of Illinois. "The equations are very complicated. Using computers to solve them by brute force doesn't work too well, but we are finally getting good experimental data quantifying how spin affects the flight of a hit baseball." There is a silver lining in this cloud of ignorance. The Magnus mystery means that baseball fans can argue endlessly over which pitches are more likely to be walloped for a home run, and scientists are still discovering such basics as why infield pop-ups follow the paths they do.

Consider the conventional wisdom that a fastball is more likely to be smashed for a home run than a curveball is. The faster a batted ball travels, goes the reasoning, the more likely it is to clear the fence. The speed of a batted ball is proportional to the speed of the pitch: faster pitch, faster hit, greater distance. But a second factor also influences the distance a batted ball travels—spin. A ball hit with backspin rotates so that its top surface spins in the direction opposite of flight. Air pressure is therefore greater on the bottom surface than the top, which produces lift, and hence distance. (Balls with topspin, in contrast, feel a force pressing down.) A fastball reaches the plate with backspin; when it is hit, the spin direction reverses, and the ball flies off with backspin. A curveball, on the other hand, arrives at the plate with topspin; that is actually the same spin direction as a hit ball with backspin. Since no reversing of spin is necessary, a hit curveball has greater backspin and therefore a greater Magnus force, and more lift, than a hit fastball. Which factor wins out, the greater speed of a batted fastball or the greater lift of a batted curveball?

To find out, Mont Hubbard at the University of California, Davis, compared well-hit curveballs and well-hit fastballs. In home-run parlance, "well hit" means the batted ball leaves the batter's box on an angle of 30 to 35 degrees. Hubbard concludes that a curveball is more likely to get home-run distance than a fastball is. That is, the Magnus force lifting the batted ball counts for more than the ball's speed. That has incited almost as much passion in baseball chat rooms as the question of whether Babe Ruth could have hit Sandy Koufax. The dean of baseball physicists, Robert Adair of Yale, argues that the UC team overestimated the effect of spin, and therefore exaggerated how much lift—and hence distance—a hit curveball would have.

The reason physicists can't agree on the effect of spin is that the equation of the Magnus force has an embarrassing fudge factor. The equation says that lift equals one-half times the crosssection of the ball, times the square of its speed, times the density of air, times … well, times a number. The number is called the lift coefficient, and there is no way to calculate it from fundamentals. Physicists have therefore tried to measure it, using video cameras to track the path of a ball pitched by machine or human, and high-speed cameras to capture the ball's spin. Alas, different scientists get different coefficients, 50 percent or more apart. Most recently, Illinois's Nathan (a lifelong Red Sox fan) set up 10 cameras operating at 700 frames per second, and shining infrared light on the ball, to track its trajectory and therefore measure lift. The lift coefficient increased linearly with spin and speed, he found; if spin or speed doubled, so did lift. But the Magnus force at 100 miles per hour and 200rpm was about double what models predicted, he finds. Memo to pitchers: at higher speeds your fastball will rise much more sharply, and your curve drop more sharply, than scientists thought.

Analyzing pop-ups, Nathan finds that their monstrous backspin creates a strong Magnus force that is initially directed backward, toward home plate. After the ball reaches its apex and starts falling, the Magnus reverses direction and pushes the ball toward the outfield. "This crazy trajectory breaks different ways on the way up and down," says Nathan, "so the ball loops back on itself and the fielder has to run in and then out." As Jeter knows.

© 2008