Over at Wired, David Dobbs has a very nice post on famed pitcher Sandy Koufax -- excuse me, "the greatest pitcher ever" -- and the curve ball, a nasty (if you're the batter) trick whereby the baseball dives downward suddenly just before it reaches the plate, faking out the batter. It's fast, too, traveling at least 75 mph and spinning at an angle of around 1500 rpm. It only takes about 0.6 seconds to get from pitcher's hand to home plate -- not a lot of time to react. David's post focuses on the perceptual illusion created as the ball travels towards the batter, and it's that optical illusion that makes the curve ball so bloody hard to hit. Or, as the decidedly salty Mickey Mantle said after being struck out by one of Koufax's infamous curve balls in the 1963 World Series: "How the fuck is anybody supposed to hit that shit?" How indeed? I'll let David explain what's going on perceptually:
[T]he curveball kills you two ways: first, through actual movement; and second, through an extra perceived movement — illusory — that further complicates the task of getting the tiny strip of sweet spot on your bat onto the ball.
The extra perceived movement rises from a difference between the neural dynamics of central vision and those of peripheral vision. This effect of this difference is that a baseball that is rotating horizontally but falling straight down as it comes toward you will appear to fall vertically if you’re looking straight at it — but appear to move sideways if it’s in your peripheral vision. ... This in turn happens because your eyes simply can’t keep up with a pitch as it approaches you and effectively accelerates its path across your field of vision. The ball goes from moving at you to moving past you. At the crucial moment — the last few feet of the ball’s half-second, 60-foot trip to the plate — you must of necessity switch from seeing the ball with your central vision to seeing it with your peripheral vision.
To add to your troubles, it is in this tenth of a second or so that the curveball also moves the most in reality. ... So just as the ball’s real downward and sideways motion is greatest, the curve’s apparent break is exaggerated by visual dynamics.
But there's some terrific physics involved here, too, and Jen-Luc Piquant also uncovered a little-known slice of 20th century history where baseball and science came together for one shining moment to prove that the curve ball really does curve. (For links to everything you could possibly want to know about the physics of baseball, check out this site.)
The man who brought those worlds together was Lyman Briggs who served as director of the National Bureau of Standards (today it's known as the National Institute of Standards and Technology) from 1933 to 1945. Born on a farm in Battle Creek, Michigan, Briggs was an esteemed physicist, despite never attending high school; he won admission to Michigan State College by examination, graduating second in his class four years later. He was also a lifelong baseball fan, having played outfield on the college baseball team during the 1890s.
This was a period when the question of whether the curve ball actually curved was hotly debated. Among the true believers was St. Louis Cardinals pitcher Dizzy Dean. "Ball can't curve?" he famously declared during the 1930s. "Shucks, get behind a tree and I'll hit you with an optical illusion." But anecdotes aren't a substitute for scientific data. So once Briggs officially retired, he decided to do the experiments to settle the matter. And he was well-connected enough to enlist the aid of the pitching staff of the Washington Senators and their manager, Cookie Lavagetto, to do so. It wasn't just a question of baseball, either: the question related to NIST's ongoing research into ballistics and projectiles: the rate of spin is related to how much the ball (or projectile) is deflected at different speeds. Apparently the NSB (now NIST) conducted lots of experiments with golf balls and baseballs; one of Briggs' publications was a 1945 paper entitled, "Methods for Measuring the Coefficient of Restitution and the Spin of the Ball."
So really, Briggs was the perfect man to take on the question of the curveball. Based on his earlier research, he already knew that, in 1852, a German enigneer named Heinrich Magnus had accounted for the curved path of a cannon ball by describing a kind of "whirlpool of air" created around the projectile. This is now known as the "Magnus effect." (That said, Magnus wasn't the first to notice this. In 1672, Isaac Newton correctly inferred the cause after observing tennis players in his Cambridge college, while a British artillery engineer named Benjamin Robins used a similar concept to explain deviations in the trajectories of musket balls in 1742. Isn't the Internet an amazing place?) Per Wikipedia:
Generally the Magnus effect describes the laws of physics that make a curveball curve. A fastball travels through the air with backspin, which creates a high-pressure zone in the air ahead of and under the baseball. The baseball's raised seams augment the ball's ability to churn the air and create high pressure zones. The effect of gravity is partially counteracted as the ball rides on and into energized air. Thus the fastball falls less than a ball thrown without spin (neglecting knuckleball effects) during the 60 feet 6 inches it travels to home plate. On the other hand, a curveball, thrown with topspin, creates a high-pressure zone on top of the ball, which deflects the ball downward in flight. Instead of counteracting gravity, the curveball adds additional downward force, thereby gives the ball an exaggerated drop in flight.
Briggs took things a few steps further and set out to explore how much the curve of a baseball depends on its spin and its speed. Ideally, he wanted to study balls thrown by actual pitchers but it proved too difficult to photograph the flight path, even with a strobe camera flashing 20 times per second. So he switched to rotating a baseball on a rubber tree thereby giving it spin, and the ball was then struck by wood projectiles shot from a large mounted airgun. By doing so, he managed to to measure the speed and the curve; he just couldn't figure out how to measure the spin as well. Per his own notes, the images captured were so small "that the marks put on the ball to measure the spin could not be seen." And spin was looking to be the critical variable when it came to determining how much a ball curved.
To measure the spin of a pitched ball, he enlisted the pitching staff of the Washington Senators at Griffith Stadium. (Historical documents give us the names of those who helped: pitchers included Pedro Ramos and Camilio Pascual; Ed FitzGerald was the catcher for the experiments.) He attached one end of a light flat tape to the ball and then laid the rest of the tape -- a very long piece of tape, 60 feet or so -- loosely along the ground between the mound and home plate, making sure there were no twists. After the pitched curveball was caught, he simply counted the number of twists that had appeared in the tape. The number ranged from 15 or 16 down to 7 or 8 twists in the tape. Knowing the distance the ball traveled (60 feet), Briggs could deduce the pitch speed was 100 feet per second, and concluded that the maximum spin would be 1600 rpm.
But Briggs still wasn't satisfied; the dude was thorough. How could he mark the ball in such a way as to determine the spin most precisely? It just so happens that NSB had a wind tunnel -- maybe they still do -- specifically for the purpose of studying aerodynamics. This allowed him to precisely control most of the variables. He tossed baseballs into the wind tunnel, and let them freefall against the horizontal wind streams, which naturally caused the ball to curve. When a baseball finally hit the ground after the requisite 0.6 seconds, it bounced off a sheet of cardboard treated with lampblack, which left a smear on the ball, indicating point of impact. His conclusion: "An increase in the speed of the pitch beyond 100 feet per second reduced the curve only slightly and the important thing was the spin." Spin rather than speed was the critical factor in causing a pitched ball to break. And a curveball can curve up to 17-1/2 inches as it travels from the pitcher's mound to home plate.
NSB announced the results on March 29, 1959, and Briggs subsequently published his results in the American Journal of Physics. What does it all mean? Well, it's probably not going to help star pitchers perfect their curveballs, unless they're really fast at doing calculations in their heads. That kind of skill comes with practice, practice, practice. But knowing the precise relationship between all those variables and the forces acting on the ball is extremely useful in its own right -- if not for baseball, then most definitely for ballistics. And hey -- baseball players got to contribute to the forward march of science.