A Fly in the Curveball

As the 103rd Major League baseball season opens,
physicists have now shown that a well-hit curveball
trumps a well-hit fastball. Pitchers must be so scared.

By Adam Summers ~ Illustrations by Patricia J. Wynne

There is a morbid fascination in watching a Little League pitcher who develops a good curveball at a tender age; more than one talented young fastball hitter has switched to basketball after facing that aerodynamic phenomenon, which can turn the most powerful swing into physical comedy. Some youngsters find the rhythm of this evasive pitch and learn to hit it with the same authority as they do a fastball. But for most batters (even at the highest levels of competition) the curve is a devil to hit-not quite as bad as trying to swat a flying mosquito with a toothpick, but almost.

Conventional baseball wisdom has long held that even if the bat does meet the curveball, the batter is still at a disadvantage; many observers maintain that even if a batter manages to crush both curveball and fastball with equal force on the sweet spot of the bat, the curveball won't sail as far as the fastball. But that clubhouse conviction has now fallen victim to a careful analysis of the physics of pitched baseballs. It turns out that good wood on a slow curve will carry the ball deeper into the cheap seats than it will Roger Clemens's best fastball.

As a boy I never got beyond the "keep your eye on the ball" stage of hitting, which led to a pretty abbreviated career in organized baseball. But now that engineers Gregory S. Sawicki of the University of Michigan in Ann Arbor, Mont Hubbard of the University of California, Davis, and William J. Stronge of the University of Cambridge have shown what it takes to accomplish the task, I don't feel so bad about my early retirement. To get the job done in the batter's box, they show, "all" the batter has to do is integrate at least fifteen variables and constants that define several physical characteristics of the bat, the ball, the atmosphere, and the world at large.

Hubbard and his colleagues have built a computerized model that gives a fascinating account of the dynamic between pitcher and batter. Standing just sixty feet, six inches away from home plate, the pitcher delivers a ball that may move at more than ninety miles an hour and spin at more than 1,900 revolutions per minute.

Of course, different pitches arrive at wildly different speeds and spins. A fastball can cross the plate in excess of a hundred miles an hour; expert pitchers can throw one with a backspin that exceeds 1,800 revolutions per minute. (In backspin, the top of the ball spins away from the direction the ball is traveling.) The curveball, by contrast, travels toward the batter at a far more sedate seventy miles an hour, but it can have topspin (the reverse of backspin) that exceeds 1,900 revolutions per minute.

The reason a curveball curves is that its spin drags a layer of air across one surface of the ball faster than it does across the opposite surface. Where air moves faster, its density is lower, and the difference in the density of the air surrounding the spinning ball pushes, or "lifts," the ball toward the lower-density air. Thus the backspin on a fastball causes the air on top of the ball to move faster and the air on the bottom to move slower; the net effect is to push the ball up. The topspin on a curveball pushes the ball down.

Physics of an optimally batted ball shows that the longest home runs should come off curveball pitches.  Click drawing to view full size (65 Kb).

Of course, the faster a ball moves, the greater its kinetic energy: a fast fastball brings more energy to the collision between bat and ball than a slower fastball does, and so the well-hit fast fastball travels farther. A swing that sends a fifty-five-mile-an-hour fastball 410 feet would smack an eighty-five-mile-an-hour burner an extra thirty feet. Similarly, higher bat speed yields better distance. An extra mile an hour in bat speed translates to an extra seven and a half feet on the ground.

But the usual difference in speed between fastball and curveball pitches still doesn't mean that batters should hit fastballs farther than curveballs. The real keys to distance are two related variables: the spin of the hit ball and the undercut of the bat. When the bat hits the ball, the spin of the ball changes dramatically. Its final spin velocity depends on its initial speed and spin, the speed of the bat, and the undercut, which is the vertical distance between the centers of mass of the bat and the ball.

Undercut has a big effect on the ball's spin, and thus on the distance the batted ball travels. With a level swing, a ninety-four-mile-an-hour fastball hit with a half-inch undercut scarcely spins at all, and travels only about 160 feet. Increasing the undercut to roughly an inch, though, increases the spin to 1,800 revolutions per minute and sends the ball 390 feet. Curiously, swing angle has a much smaller effect on flight distance than undercut distance has. If the undercut is correct, even swinging slightly down on the ball will send it 390 feet. That's often long enough for a home run.

Perhaps the most counterintuitive result of the engineers' model is that an optimally hit seventy-eight-mile-an-hour curveball travels about 455 feet. In contrast, the same hit off a ninety-four-mile-an-hour fastball carries 442 feet, thirteen feet less. Spin makes all the difference. The initial backspin of the fastball is abruptly reversed by the undercut of the bat, whereas the initial topspin of the curveball is augmented by the bat. The net result is that the batted curveball spins some 800 revolutions per minute faster than the batted fastball, and that extra spin provides a bit more lift as the curveball sails out of the park.

So even if some precocious master of the curveball manages to make most of his opponents look bad, he'd better be careful. A pitcher never knows when the next player with the great eyes of Ted Williams will show up to demonstrate what a curveball hitter can really do.

Adam Summers (asummers@uci.edu) is an assistant professor of ecology and evolutionary biology at the University of California, Irvine.