A few months ago, the television program “Mythbusters” tackled a series of baseball myths, ranging from whether a corked bat makes a difference to the performance of a hitter, to whether sliding into a base is faster than just slowing down and landing on it. Overall, I was pretty impressed with the experiments they devised. More than once, the Mythbusters remarked on how the data they were collecting were the real story, where the real science happens. That kind of recognition of the importance of gathering and analyzing data warms my heart.
One myth they tried to tackle was the following: it’s possible to knock the hide off a baseball in a normal pitching/hitting environment. In their setup, they loaded baseballs into an air cannon and fired them at a stationary bat. The technical reason for doing so, I suspect, was that this pitching/hitting rig was not wholly reliable and the precision timing needed to hit the faster pitches was beyond the rig’s capability. They concluded from this setup – fast ball, fixed bat – that it was not possible to knock the skin off a baseball under normal conditions. In their experiment, the ball had to be traveling at about 437 mph in order to lose its skin after striking the bat.
As a particle physicist, I see this as a unique opportunity to think about fixed-target vs. colliding beam experiments. When you’re attempting to go for raw collision energy, without expending more energy than is necessary in any one part of the experiment, you should go for a “colliding beam” experiment. This is when both the target and the bullet are moving toward one another, relative to the reference frame of the laboratory. In baseball, the lab frame is the stadium, and in that frame we know that the bat and the ball are both moving when the ball gets hit.
Colliding beam experiments are typically held in contrast to the “fixed-target” experiment, in which the target is stationary (in the lab frame) and the bullet is moving. The Mythbusters conducted the experiment which doesn’t happen in baseball (unless the hitter bunts): they fired baseballs at a stationary, rather than a moving, bat. Could this explain why they concluded that the pitcher would have to be super-human in order to get the energy needed to part hide from baseball?
To make progress on this question, we have to start with physics. In particular, we want to answer the following question: in order to achieve the energy required to strip the skin off the baseball in the “fixed-target” scenario, how fast must the batter swing and how much slower can the pitcher pitch? Here, we need some assumptions. First, we assume that the bat connects with the ball at the maximum point of the swing; that is, when the bat’s motion is entirely directed into the flight path of the ball, with no deviation from that line of travel. This energy sweet spot is the point at which the most energy can be delivered by the batter to the ball, and if you can’t achieve the conditions there, you can’t achieve them anywhere else.
We need the Mythbusters’ data. They found that a ball moving at 437 mph, hitting the stationary bat, was enough to part the skin from the baseball. The fastest pitch ever recorded was 103 mph. Now, let’s do some math and see the energy in this collision. Then we can figure out whether it’s possible for a batter to swing at a reasonable speed, and a pitcher to pitch at a reasonable speed, and achieve the same energy.
Energy is given by a simple formula. The ball’s energy of motion is E, which is equal to 1/2mvv – one-half times the mass of the baseball, times its velocity-squared. A baseball weighs between 140-150 grams (g), so let’s call it 145 g. Therefore, the energy (in Joules, or J) of a baseball traveling at 437 mph (195.4 m/s) is 2768 J. Now, let’s turn the problem around – given that the bat is also moving, what is the relationship between the bat and the ball needed to achieve 2768 J?
Here again we appeal to kinetic energy, and the conservation of energy. The total energy (Etotal) of the collision must be 2768 J. If the bat and ball are moving, we can write the equation :
Etotal = 1/2 (MVV + mvv)
where M is the mass of the bat and V its velocity. If we know that the mass of a wooden baseball bat is between 20 – 40 ounces, and that a heavier bat will impart more energy to the collision, we can plug in a 40 ounce bat (1.13 kg) and 103 mph for the baseball pitching speed (46 m/s). What do we learn? The velocity of the bat must be V = SQRT( (2*Etotal – mvv)/M) = 68 m/s = 152 mph.
Can a human swing that fast? The answer is no. A Major League power hitter swinging a 40 ounce bat can only swing at about 60 mph, about a third the speed needed to achieve this energy. It seems that while the setup the Mythbusters devised was not real-world accurate, the conclusion from a real setup would likely be the same. It’s just not possible to part hide from baseball with a human pitcher and a human batter.
References:
http://www.kettering.edu/~drussell/bats-new/batw8.html
http://hypertextbook.com/facts/1999/ChristinaLee.shtml
