Science Has a Sweet Spot for Baseball

Baseball a Physics Pastime
Scientists Don't Care if They Ever Get Back

The instant when a baseball springs off a wooden bat may rank as the defining experience of American sports -- a moment so laced with adrenaline and sentiment it would seem immune to any scientific analysis.

Yet the official start of the baseball season this week brings theoretical fodder for researchers like University of Illinois particle physicist Alan Nathan, who has made a pastime of using science to understand the national pastime.

It may sound odd for grown men with tenure at prestigious universities to tackle such burning questions as the aerodynamics of Kerry Wood's fastball or bat-to-ball energy transfer. But a growing clique of scientists, from Nathan to Harvard University biologist Stephen Jay Gould, believes that delving into the fine points of baseball can bring new insights to their day jobs.

At a minimum, it's a heck of an excuse to study their favorite sport. And it probably couldn't hurt Chicago's long-suffering teams to get pointers from some ivory-tower types.

Work such as Nathan's may even be of practical use to professional players by revealing secrets of the "sweet spot," the point on the bat where a hurtling ball sends no sting or resistance to the batter's hands.

Nathan has developed elaborate equations to capture that instant when the ball strikes the wood, causing the bat to vibrate in complex patterns like a violin string. Such work suggests the sweet spot most batters notice is different from the point on the bat that sends the ball sailing the farthest--a finding that could warrant subtle changes in batting strategies.

The sweet spot problem reminds Nathan of his main professional pursuit: experiments in which high-energy electrons are shot at an atomic nucleus to determine its structure.

"It's basic physics," Nathan said. "Conservation of momentum, conservation of energy -- these things apply no matter what kind of collision you're talking about."

Not surprisingly, many of the scientists who now probe baseball's secrets say they failed miserably at the plate as children, yet have harbored a lifelong passion for the game. Gould, who describes himself as "a 190-pound guy who can't hit a curveball," concedes there is an element of wish fulfillment in his use of baseball statistics to illustrate the role of variation in biological evolution.

"It's basically a guy thing rationalized as scientific and intellectual," said Gould, a fanatical New York Yankees fan.

But in addition to providing a link to boyhood dreams, some baseball studies may shed important light on poorly understood aspects of the natural world. Gould argues that the disappearance of .400 hittersin baseball stems from decreasing variation in talent, not diminishing player quality -- a distinction he also applies to evolution, where apparent trends of improvement or decline often prove unfounded.

Porter Johnson, a professor of physics at the Illinois Institute of Technology, only half-jokingly describes baseball as full of deep scientific mysteries.

"They say two big problems in physics have resisted solution," Porter said. "One is the unified theory of everything that would account for all the forces in nature. The other is finding a quantitative description of the motion of a baseball through the air."

Efforts to answer such ball-field enigmas date at least to the 1950s, when wind-tunnel experiments proved that curveballs really do curve. Researchers found that the spinning ball's stitches create an imbalance in air pressure that pushes curveballs to the outside of the plate -- though the exact details of that chaotic interaction remain devilishly difficult to model, Johnson noted.

Nathan, the U. of I. physicist, became fascinated three years ago with the moment when a bat makes contact with a ball. What started as a diverting topic to fill lectures for lay audiences grew into a rich research project, yielding a paper on bat dynamics that Nathan has submitted for publication in a major physics journal.

As it turns out, the complex calculations needed to understand the sweet spot resemble those used to analyze the vibration of airplane wings or bridges, Nathan said. Such motion is important in baseball because every vibration in the bat takes away from the ball's speed as it leaves the plate.

"I describe it as different ways that energy is robbed from the ball," Nathan said.

Each bat vibrates at several different low and high frequencies at once, equivalent to the harmonics of a violin string. These frequencies can be silenced individually by striking the bat at "nodes" where the wood produces no vibrations of a given frequency.

The best spot on a bat to hit the ball might seem to be where the combination of different frequencies produces the weakest overall vibrations, Nathan said. But calculations of that ideal point must also include the fact that the bat's circular motion increases toward the tip of the wood, which tends to propel the ball at a faster speed.

When Nathan wrote a computer program to account for all those effects, he concluded that a ball will travel fastest off of a 34-inch bat if it strikes about 6 inches from the tip, with the efficiency dropping off quickly in either direction.

To test his results, Nathan worked with another researcher -- in Australia, of all places -- who recorded the precise speed of a ball connected to a pendulum when it struck various spots on a suspended bat.

"The actual measurements were right at the points predicted by my theory," Nathan said. "Amazing."

The hitch is, no one knows for sure how close the optimal spot for hitting is to the sweet spot that players know and love.

Nathan hopes to test the theory of Robert Adair, a Yale University physics professor and baseball guru, who believes the subjective sweet spot sits on the node where the bat's lowest frequency vibrations drop out. Human hands aren't sensitive enough to feel the bat's higher frequencies, Adair said.

But if Adair is right, the subjective sweet spot would be located more than an inch away from the bat's best point for hitting. The feeling of maximum power that comes from hitting with the sweet spot may be just an illusion -- a finding that would be disappointing to many players.

"I've talked to many athletes who are multisport stars and asked them what is the most wonderful feeling in any sport," said Tom Boswell, a sports columnist for The Washington Post. "Almost uniformly, they say it is the moment of hitting a baseball perfectly."

Some scientific findings may prove helpful to players. Terry Bahill, a professor of systems engineering at the University of Arizona, has developed a method of calculating each batter's ideal bat weight, based on the person's weight, height, bat speed and arm extension during the swing.

Despite the insights science offers, Harvard's Gould doggedly maintains that at least one baseball moment defies rational explanation: Boston Red Sox catcher Carlton Fisk's seeming success in waving a home run into fair territory to win Game 6 of the 1975 World Series.

"He stood up there and, by sheer body English, he transcended the laws of physics and made that ball curve inside the left-field foul pole," Gould said.