The Physics of Baseball 2: "The Seven Per Cent Knuckleball"
Last weekend, I found myself in Chicago with a free Sunday evening. (I had been presenting at the AAPT conference, and moderating a panel discussion at the University of Chicago in charming Hyde Park.) So, as is often my wont, I wended my way up to Wrigley Field to see the Chicago Cubbies play against the Boston Red Sox, a game many of you saw on E$PN. I did not have a way to get in, so I was forced to purchase a very expensive ticket outside from a tattooed gentleman with the lovely sobriquet of Cobra Phase Two; once inside, I found that someone else already had that seat, so I suspect some kind of skullduggery from Mr. Two. Will I ever learn?
Eventually, however, I found a seat next to some high-spirited young ladies, purchased a frosty beverage for $8, and settled back to watch a gem of a game turned in by Tim Wakefield. Although the Red Sox are somewhat of a non-event for me, I had to admire the skill and aplomb with which Wakefield tosses the only legitimate knuckleball left in the major leagues. (Mike Mussina's knuckle-curve does not count. This is unfortunate because he is one of baseball's truly intelligent and soulful pitchers, but ultimately fine, because he is on the Yankees, who suck.)
I am probably asked about the knuckleball more than about any other pitch. The physical principle is simple enough. When a baseball is thrown or hit, it must overcome several factors: wind resistance, air density, and gravity being chief among them. The force that works "against" a moving ball is called the Magnus force, and has been documented for years.
Pitchers are able to influence how the ball moves on the vertical and horizontal planes by manipulating their grips and their release points, thereby imparting a spin to the ball. This spin can work any number of ways, from the curves and nickel-curves (a.k.a. "sliders") that we often hear about to the relatively exotic (and dare I say erotic) variations on same: sliders, slurves, scroogies (known as "screwballs" or "fadeaways" in the past), cut fastballs (which are actually half-curves), sliced fastballs (technically half-sliders), slinkers (half slurve, half sinker), clurves (half curve, half slurve), scroorves (three-quarters curve, one-quarter scroogie), palm jobs (one-third curve, one-third cut fastball, one third sinker, thrown with the palm), and the like. There is a finite but very large number of combinations.
An amusing anecdote: while taking notes for this article, one of the heavily perfumed and tipsy young ladies came over to me and asked, "What are you writing?" When she noticed the words "palm job" and "scroogie" on my notebook, she yelled out, "Oh my god, this old dude is a FREAK!" and ran away, giggling, her cheap perfume floating on the wind like a scarf. In retrospect, I see what she meant. Oh, my!
The knuckleball is a different creature altogether. It is, first of all, a misnomer: the knuckleball is actually propelled by the fingertips, or the ends of the fingers if the pitcher has accidentally lost his fingertips. The knuckler is thrown without spin, causing asymmetric stitch configurations and trajectoral turbulence relative to the ball's flight. The wind resistance is directed from the smooth side of the ball to the rougher, stitched side. Therefore the balance of Magnus forces is thrown into imbalance, and the ball's flight is given over to chaos theory.
I don't really want to get into chaos theory here, as one needs to study it carefully for a number of years before even beginning to understand it. I try not to talk over my students' heads, and I will not write over yours. Instead, let me put it in terms that any layperson can understand: Given the Brownian motion of air molecules, the Earth's rotation and position relative to the Sun, and the time of day, we can come up with a simple iteration formula of g(x) = (x+3)/2. Knowing as we do that we must re-iterate this based on the velocity of the thrown baseball, and that Wakefield generally throws his knuckleball at an average of 70 mph, we come up with g (g(x)) = ((x+3)/2 +3)/2 = (x +3+6)/4 = (x+9)/4. A third iteration produces g (g(g(x))) =((x+9)/4)+3)/2 = (x+9+12)/8= (x+21)/8, which happens to correspond exactly with the distance 60 feet and 6 inches divided by 70 mph according to the formula often called Sierpinski's Triangle, or the "Infinite Perimeter" principle. Therefore, the limit of D (V+8 / 60.5) as x approaches H = 11.2 inches.
Or, to put it simply, that shiznit is FILTHY. He had the Cubs looking like they were blind miners in a coalshaft. No one knew where the ball was traveling: not Derrek Lee, not Jason Varitek, not Tim Wakefield, not Robert K. Adair, Ph.D., not the zaftig young women heckling me and my equations for three innings of a baseball game, not the kind security guards who eventually led me out of my seat and into a taxi back home (I must remember that four beers on a warm night are 98.4% more likely to get me crunked up double quick!), not even God Himself knew where that knuckleball was headed. Such is the nature of chaos theory, of Magnus forces, of what my Mexican friends call "las gorditas lindas," and of malt liquor in the bloodstream of an old fool like myself.
As to the question of why Wakefield is the only knuckleball pitcher left, I can only assume it is because he is the only pitcher whose arm is weak enough to throw the pitch slow enough so that the break is optimal. Other than that, I have no idea. I am but a gentle, and fragile, physicist. If there were more knuckleball pitchers in the major leagues, it would be a more interesting place for people like me who get a thrill from graphing equations instead of yelling "HEY" when they play that benighted Gary Glitter song. But Major League Baseball would, I am certain, sell fewer jerseys. When Tim Wakefield passes from this earth, this skill will be gone forever. The passing of an era, the end of an age; so quickly are my favorite things disappearing from this earth!
Robert K. Adair, Ph.D., is the author of The Physics of Baseball (Perennial/Harper Collins) and the Sterling Professor Emeritus of Physics at Yale University. He is a lifelong Brooklyn Dodgers fan.