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A physical explanation of the curvature of balls

Pretty much every article about the curvature of thrown baseballs begins by saying that for decades, people debated whether curveballs really curved or just appeared to do so. Folksy sage Dizzy Dean provides the summary of early twentieth-century practical wisdom on the topic. “Stand behind a tree 60 feet away,” Ol’ Diz reputedly said, “and I’ll whomp you with an optical illusion.”

Dean was right. Curveballs do curve, but in recent years, we’ve learned more about how they work. It turns out there is an optical illusion involved after all, and that soccer kicks add a twist to their motion, and thus to our story.

Curveballs curve thanks to a phenomenon called the Magnus Effect, after a nineteenth-century German physicist, though Isaac Newton understood the principle almost two centuries earlier. As James Gleick’s biography of Newton notes, while watching tennis matches at Cambridge, Newton concluded that tennis balls curved when oblique hits generated spin. Newton wrote in a letter that the ball’s “parts on that side, where the motions conspire, must press and beat the contiguous Air more violently than on the other, and there excite a reluctancy and reaction of the Air proportionately greater.” I leave it to you, reader, to imagine Dizzy Dean whomping Newton with an apple.

Thanks to the Magnus Effect, pitchers can throw a “rising fastball,” which uses backspin to counteract the downward pull of gravity. The rising fastball still sinks relative to a straight line, but it can appear to rise because the batter expects a greater sinking. Contrarily, a curveball spins forward and to the side, and it therefore moves down and sideways relative to the path that gravity alone would produce. (For much more on the effects on spin on baseballs, see Alan Nathan’s website The Physics of Baseball or Robert Adair’s foundational book of the same name.)

Recently, however, scientists have turned their attention to a way in which the curveball does indeed produce an optical illusion. Baseball players and analysts routinely speak of effective curveballs–and other breaking balls, such as the harder-thrown slider—as having a “sharp” or “late” breaking action, whereas the ball actually curves smoothly, at essentially the same rate from the beginning to the end of the pitch. This perception of a late, sharp break is the true illusion. Thus, as a team of scientists recently put it, “a curveball creates a physical effect and a perceptual puzzle.”

Those scientists—Arthur Shapiro, Zhong-Lin Lu, Emily Knight, and Robert Ennis—won the Neural Correlate Society’s 2009 Best Illusion of the Year contest with “The Break of the Curveball,” which you can see online at . Their illusion shows how a spinning ball moving in a straight line appears to shift its position when it moves from the viewer’s foveal to peripheral vision.

Foveal vision is what we use when we maximize acuity by looking straight at something. As Leonardo Da Vinci first discovered, we focus best when we create a line of sight through the pupil to the fovea centralis of the retina. The illusion of a shift in position when an object moves out of foveal vision affects baseball because a batter’s eyes cannot track a pitch from the pitcher’s hand to the bat.

Tangent! The great hitter Ted Williams sometimes claimed to see the ball hit the bat. Malcolm Gladwell addressed this in his book Blink, where he writes that Williams “always said that he could look the ball onto the bat, that he could track it right to the point where he made contact.” And Ron Luciano, a longtime umpire, related a story about Williams seemingly backing up that claim in a 1972 experiment with a pine tar-covered bat that marked the ball on impact. Gladwell says that Williams, confronted by a scientist, backed off, saying, “Well, I guess it just seemed like I could do that.” But there is another angle to the story. I found a 1954 Sports Illustrated article titled “You Can’t Keep Your Eye On The Ball” that quotes Williams saying, “No, I don’t see the ball when it hits the bat. You usually lose sight of it a few feet away. Once or twice in my whole career I’d say I saw the ball hit the bat, but that’s all.” The real question may be how and when the myth of Williams seeing the ball hit the bat took hold.

OK, back to the optical illusion. When the spinning pitch moves from foveal vision to peripheral vision, the difference in perception causes the ball’s apparent position to shift suddenly, producing the perception of a sharp break in the ball’s motion. The batter therefore confronts the actual curvature produced by the Magnus Effect and an additional illusion of a late break.

Soccer balls, however, add a twist to their motion and to the story of the curveball. Whereas the late-breaking action of a pitched baseball is an optical illusion, a long free kick in soccer really does turn away from its established arc with a sudden final break. French scientists published this finding last September, and you can find coverage online at the website for Scientific American. The article there includes links to footage of free kicks, and it also links to a 1998 Physics World article explaining the basic principles that the French researchers further developed in their new study.

The key to the additional curve of the free kick is that a ball’s velocity decreases faster than its spin rate. At a certain point in the kick’s flight, the decrease in velocity causes a relatively sudden increase in the turbulence surrounding the ball, and the resulting drag increases the curve generated by the Magnus Effect. (A pitched baseball does not fly anywhere close to long enough to produce this sudden break.) The Physics World and Scientific American pieces both illustrate this phenomenon with a famous 1997 free kick by Brazil’s Roberto Carlos, one that veers dramatically around a hapless goalkeeper, who relaxes in anticipation of the ball sailing out of bounds, then turns in astonishment to find it in the goal. The keeper has, in fact, the precise look of a man who has been whomped by physics.

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