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On Science: The physics of McGwire's homers

This article first appeared in the St. Louis Beacon, Jan. 13, 2010 - Mark McGwire, past first baseman for the St. Louis Cardinals, is arguably the greatest home run hitter of all time. In 6,187 at-bats in 16 seasons playing first for Oakland and then for St. Louis, McGwire hit 583 home runs - that's one every 10.6 at-bats, a frequency no other player has even approached. In a four-year stretch batting for the Cardinals in the late 1990s, McGwire bashed 245 home runs, 70 of them in one season in 1998.

Mark McGwire is much in the news this week, with his admission Sunday that he had used steroids throughout his career. McGwire, frequently on the disabled list, claims he used the performance-enhancing drugs not to boost performance, but to speed recovery of his damaged muscles. I am in no position to assess his motives, as steroids will both boost performance and speed muscle recovery - steroids simply add muscle mass, whatever the motive for using them.

McGwire's other claim, that he would have hit as many home runs without the steroids, is another matter. Just how much of a role they might have played in his success is a matter of physics, not simply an instinctive assessment.

With that in mind, I thought it would be instructive this week to examine the physics of hitting home runs. I wrote about this previously in a column devoted to Albert Pujols, another gifted St. Louis Cardinals home run hitter. The lessons this sort of analysis teaches us seem right on point in the light of today's controversy.

Before hitting one out of the park, McGwire's muscles are tensed with anticipation, holding a 42-inch wooden bat while he waits for the precise instant to swing at a 3-inch, 5-ounce cowhide-wrapped ball hurtling toward him at more than 90 miles per hour.

At this speed, it will take about four-tenths of a second for the ball to travel the 60 feet, 6 inches from the pitcher's mound to home plate.

In that brief interval, if he decides to swing the bat, and has the good fortune to hit the ball, he will be carrying out a physics experiment on the transformation of energy.

As you can imagine, there is a lot of energy invested in a baseball traveling 90 miles per hour. This energy of motion is called kinetic energy by scientists, and it's easy to appreciate its raw power. Not so evident is the latent power in the muscles of the batter awaiting the pitch. Like coiled springs, the energy in Mark McGwire's muscles is ready to be put into action. This stored energy is called potential energy by scientists, energy ready to be put to work swinging the bat. The more potential energy McGwire's muscles release, the faster the speed of the bat through the swing.

Obviously there is a lot of energy at play here. The batter McGwire must convert a considerable amount of potential energy from his arm and shoulder muscles to the kinetic energy of the swinging bat. Similarly, the pitcher has converted potential energy from his throwing arm to the kinetic energy of the speeding baseball.

What happens in the instant when the ball hits the bat is the difference between a home run and a fly ball, and a lot of scientists' time has been devoted to understanding that brief 1/1,000th of a second, the measured duration of the collision of a pitched baseball on a swinging bat.

The Sports Biomechanics Laboratory at the Davis campus of the University of California has for decades carried out detailed examinations of the scientific principles governing baseball. Many of the researchers in the Lab are graduate and undergraduate students in biomedical engineering. The student researchers have learned a lot about what it takes to hit a home run. The on-the-field mechanics of baseball -- how pitchers throw, how batters swing -- are examined through equations that attempt to simulate what happens when bat meets ball. When a simulation seems to take the laws of physics into account properly, it is then checked by direct measurements to see how well the simulation predicts what actually happens.

What the Pitcher Controls

First, let's look at how the ball is thrown. Three variables turn out to be of particular importance:

Ball velocity. Not surprisingly, balls that are pitched faster travel off the bat further. Much of the kinetic energy of the ball is returned to it by the bat, as kinetic energy of motion in the opposite direction.

Spin. However, even more important is the spin of the pitched ball. Conventional wisdom says a hitter can drive a fastball farther than a curveball -- the fastball travels about 42 meters per second, the curve ball only 35 meters per second, so the fastball has much more kinetic energy to contribute to the ball's flight, they say. Not so, it turns out. A curveball is thrown with topspin, so the top of the ball rotates in the direction of the pitch. Being hit by the bat throws the ball into reverse, giving it backspin and thus lift to carry it further. A fastball is thrown with backspin; it spins the other way when hit, and so has less lift and sinks sooner.

Ball elasticity. When the ball is deformed by its collision with the bat, it tends to bounce back. The more elastic the ball, the more of its kinetic energy is returned by the bat. The cork core of a baseball is wound tightly with yarn to make it bouncy. If the yarn is wound tighter, a more "lively" ball results, one that travels further off the bat.

What the Batter Controls

Now consider how the ball is hit. Again, three variables have been found to be of prime importance:

Bat speed. More than any other variable, the speed with which the hitter swings the bat determines how far the hit ball will travel. As a general rule, increasing the bat velocity of an average home run swing (30 meters per second) by one meter per second increases the distance of the hit five meters.

Bat position on ball. For optimal range, the bat should not contact the ball squarely, but rather 2.65 cm below center. This undercut imparts backspin, creating lift that causes the ball to travel further.

Ball position on bat. The impact of the ball causes the 42 inch wooden bat to vibrate, like plucking a tightly drawn string. This is important, because every vibration of the bat draws energy away from the ball, reducing its speed as it leaves the bat. Each bat vibrates at several low and high frequencies at once, like the harmonics of a violin string. Striking the bat at "nodes" where a frequency produces no vibrations avoids this loss of energy. The optimal position is about 6 inches from the tip. Interestingly, the shape of the shaft and handle makes no difference whatever -- by the time the vibration reaches there, the ball has already left the bat.

The Steroid Affect?

So how much did the use of steroids add to Mark McGwire's home run totals? Was the contribution insignificant, as McGwire has claimed in interviews this week, or did it make all the difference, as some hall-of-fame voters seem to think? This is a question that can be answered, if only approximately. Steroid performance enhancement is limited to the performance benefit obtained by added muscle mass. As you have seen in the analysis above, it comes right down to bat speed. How much did the muscle added by steroid use increase McGwire's bat speed?

The only way to know for sure is to measure McGwire's bat speed before and after his steroid use, which of course we can't do. All we can do now is make a reasonable guess. As McGwire was hitting a lot of home runs before he began steroid use (even as a teenager he was a slugger), it seems fair to assume he had pretty good bat speed from the get-go. So say the added muscle speeded up his swing 5 percent. That would be a lot. The scientific analysis described above suggests that an increase of 5 percent to the average home run bat velocity of 30 meters per second (an added one and a half meters per second) would increase the distance of McGwire's hit by about 25 feet.

So how many of Mark McGwire's home runs landed within 25 feet of the fence? Not many, I'd bet. I have seen a lot of his home runs, at the stadium and on television, and "towering" is the world that leaps to my mind. In the lack of hard data, it is my personal belief that McGwire has a point in what he said in interviews this week: It seems to me unlikely that subtracting the steroid-added bat speed would have deprived him of many home runs.

Because of the enormous kinetic energy invested in the baseball when a big league pitcher throws a 90 mph fast ball, to hit a home run McGwire had to act not only with strength, but very fast, and very precisely. He has less than a quarter second to see the pitch, judge its speed and location, decide what to do, and then start to swing. The bat had to meet the ball within an eighth of an inch of dead center to avoid a foul ball, at precisely the right millisecond to generate the correct arc to send it out of the park.

A home run, by McGwire or any other batter, is all about precision in the application of energy. There can be no doubt that at this McGwire was a master.

George B. Johnson's "On Science" column looks at scientific issues and explains them in anaccessible manner. 

Johnson, Ph.D., professor emeritus of Biology at WashingtonUniversity, has taught biology and genetics to undergraduates for morethan 30 years. Also professor of genetics at Washington University’sSchool of Medicine, Johnson is a student of population genetics andevolution, renowned for his pioneering studies of genetic variability. He has authored more than 50 scientific publications and seventexts.

As the founding director of The Living World, the education center at the St Louis Zoo,from 1987 to 1990, he was responsible for developing innovative high-tech exhibits and new educationalprograms.

Copyright George Johnson