It's a good thing baseball home run kings Mark McGwire and Sammy Sosa don't have to run the equations before they decide whether to swing for the fences, or Roger Maris's record of 61 home runs would have faced no threat.
Considered as a matter of physics and physiology, using a bat to smack a fast-moving baseball over a stadium fence is a stunningly complicated feat to calculate and achieve even once, much less with the regularity that the St. Louis Cardinals' McGwire and Chicago Cubs' Sosa have been doing it this year.``It's just a tremendous feat to hit a ball 400 feet,' says Yale University physics professor Robert K. Adair, who has written a book on the subject, called ``The Physics of Baseball.' ``It requires a phenomenal concentration of energy.'
A popular shibboleth of sports journalism holds that no task in sport is harder than hitting a baseball with a bat. Back in the late 1980s, the late A. Bartlett Giamatti, a Yale president and baseball nut who went on to be National League president and then baseball commissioner after leaving New Haven, encouraged Adair to bring his loves of physics and baseball to bear on explaining just how it is done.
Through research that included developing a complex equation explaining the physics of a home run, Adair showed that to drive a fastball coming at you at 90 mph over a big-league stadium fence requires swinging a bat at better than 70 mph. McGwire and Sosa, Adair thinks, probably often exceed 80 mph.
Not only that, but given that a fastball reaches the plate in less than half a second, a batter must decide in a fifth of a second after the ball's release whether to swing.
Mis-timing his swing by 1/100th of a second will mean the difference between a foul ball and a four-bagger. A 1/200th second difference will determine whether the ball travels to right, center or left field.
Indeed, not for nothing did legendary Braves pitcher Warren Spahn once observe: ``Hitting is timing. Pitching is upsetting timing.'
Through his research, Adair found that during the 1/1,000th of a second that a slugger like McGwire or Sosa is actually making contact with the ball for a home run, he is exerting something like 8,000 pounds of force on it - the equivalent of an elephant's stepping on the ball.
In the last 1/20th of a second before a slugger makes contact, Adair calculated, his body is generating an astounding 10 horsepower of energy - 70 times as much as a manual laborer might exert during a workday - virtually all of it concentrated in whipping the bat around.
The basic equation involved is that mass times velocity - the weight and speed of the bat - determines the force with which the ball is hit, and the faster the ball is pitched, the faster and therefore farther it's hit.
But history shows there is no such thing as the ideal-sized bat. Babe Ruth was known to use 44- and even 47-ounce bats for his legendary drives. McGwire uses a 36-ounce bat. Sosa and the Seattle Mariners' Ken Griffey Jr. use 31-ounce models.
Nor is there an ideal-sized batter or ideal hitting technique. While McGwire and Sosa have been going head-to-head in the home run race all summer, they are remarkably different physical specimens, McGwire 250 well-muscled pounds on a 6-foot-5 frame, Sosa just 200 pounds and 6 feet tall.
Where McGwire uses fierce power in his swing and an unorthodox one-handed follow-through, Cubs batting coach Jeff Pentland told reporters this year that Sosa ``does it in a different way, with quickness and sharpness. He's certainly a well-built guy, but he's not a physical presence' like McGwire or some of the other big sluggers.
And as hard as McGwire and Sosa swing, much of their effort goes for naught. Adair found that as a general rule, only half the energy in the swing is transmitted to the ball, the rest lost to wind resistance or absorbed by the bat and the batter's hands.
Of the energy that does meet the ball, one-third is lost to distorting and heating the ball through friction (a well-hit ball will get 1 degree Fahrenheit warmer from the impact, and its diameter will briefly shrink to half its normal size).
As a result, only one-third of the force a slugger like McGwire is developing at the plate goes into the ball's ultimate flight - and still he often sends it 450 or 500 feet.
How can anyone possibly decide in 2/10ths of a second, about the minimum time the average person can sensibly react to anything, whether to swing at a pitch?
Theories abound. Adair said he thinks batters work on ``pattern recognition,' seeing in the windup and delivery of pitchers they face over and over again clues that tell them what pitch is coming. (But a pitcher who tips off the hitter that way isn't going to last long). Some hitters claim they can pick up the rotation of the ball in flight and thus know what kind of pitch it is.
Others claim the best batters make an educated guess about what's coming next. Cardinals hitting coach Dave Parker has been quoted as saying McGwire correctly guesses what kind of pitch he'll see 85 percent of the time.
Don't look to either McGwire or Sosa for a detailed explanation of what they do.
``I never talk technical baseball,' McGwire told The Sporting News' Steven Marantz this summer. ``There are things the media don't need to know. There are things my teammates don't know about. I just keep it to myself. ... Someday, when I'm a coach, I'll talk about it.'