Do curveballs really curve?

October 31, 2003

Dear Cecil:

While watching this year's baseball playoffs, I remembered something someone told me a while ago. Curveballs don't really curve. It is an optical illusion. Is this really the case? Also, how many different ways can a pitcher really throw the ball?

Your question comes at a timely moment. I, too, watched the playoffs. My team did not win. My backup didn't win. However, I will have no talk of goats, bambinos, or any other such feeble excuse. We need to get back to basics. Lesson Number One: How to Pitch.

The debate over whether a curveball actually curves began maybe 20 minutes after the pitch was perfected by William "Candy" Cummings in 1867. (I follow the account given by LeRoy Alaways in his 1998 doctoral dissertation for the University of California, Davis, "Aerodynamics of the Curve-Ball: An Investigation of the Effects of Angular Velocity on Baseball Trajectories.") The matter wasn't resolved quickly. As late as May 1941, in a mock letter to the editors of the New Yorker, one R.W. Madden quoted a baseball sage as saying, "Now I'll tell you something, boy. No man alive, nor no man that ever lived, has ever thrown a curve ball. It can't be done." This declaration, though clearly tongue-in-cheek, begat much acrimonious discussion. A few months later Life magazine, apparently figuring that for one week it could forgo the usual fluff about Japanese maneuvers in the Pacific, published a photographic analysis purporting to show that "a baseball is so heavy an object . . . that the pitcher's spinning action appears to be insufficiently strong appreciably to change its course."

Too bad Life hadn't been around a half century earlier--no doubt it would've proclaimed that heavier-than-air flight was impossible. Truth was, the reality of the curve had been demonstrated as early as 1877, when a couple of pitchers--one a lefty, the other a right-hander--threw curveballs around boards that had been set up at intervals along a straight chalk line. (The pitches in question obviously curved more from side to side than up and down.) The scientists who've gotten into the act since the 1940s have used strobe photography, wind tunnels, and other sophisticated technology, but their conclusions have all been the same: Yes, a curveball curves--in the hands (well, having left the hands) of a skilled pitcher, as much as 18 inches.

The reason the ball curves involves something called the Magnus effect. It boils down to this: A pitcher throwing a curve imparts spin to the ball. As the ball flies through the air, it leaves a wake behind it. Were the ball not spinning, the wake would be roughly symmetrical, as shown in the left-hand illustration. Since it does spin, the wake is deflected to one side (the side where the spin is counter to the motion of the air rushing past), as shown in the right-hand illustration. Intuition alone (and that failing, the law of conservation of momentum) should convince us that if the forces acting on the ball are such that they deflect the wake one way, they simultaneously push the ball the opposite way. Thus the curve.

How many different ways can the pitcher throw the ball? There's a seemingly unlimited number of names for pitches: fastball, curve, slider, breaking ball, sinker, changeup, screwball, knuckleball, split-finger fastball, two-seam fastball, four-seam fastball, cut fastball, slurve, forkball, and lots more. (I grant you that some of the preceding are basically synonyms.) I won't attempt to sort them all out, other than to say they involve different grips, release speeds, degrees and angles of rotation, and so on. (For a not-too-technical analysis of common pitches, see The Physics of Baseball by Robert Adair, onetime "physicist to the National League," 1990.) The extreme case is surely the knuckleball, which rotates only a half spin or so en route to the plate (for comparison, fastballs usually spin 9 to 12 times) and whose aerodynamics change so drastically in consequence that it can curve one way and then another.

Pitching isn't illusion free. Despite appearances, breaking balls don't really break--that is, the ball doesn't change trajectory abruptly in midflight ("fall off the table," in baseball parlance). The curve of a spinning ball--i.e., anything but a knuckleball--is always smooth. Likewise, the ball can't speed up on its way to the plate, although if the boys in the dugout think it does, the pitcher is doing his job.

So, think you've got a pretty clear idea how to throw a curveball now? Good. Next week we'll turn to Lesson Number Two, which may be even more useful to certain parties in the baseball business: The Importance of Middle Relief.

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