# Do corked bats allow baseball players to hit farther?

Porter Johnson, a physics professor at the Illinois Institute of Technology, explains.

In professional baseball, the bat must be made from a single solid piece of wood thus the use of corked bats during games is illegal. Still, corked bats have turned up several times in major league play, most recently by Sammy Sosa. A definite advantage to this strategy is that lighter bats allow a quicker response by the batter. But the question of whether or not corked bats truly help hitters is a complex one.

Suppose that you could make baseball bats of the same size, shape, structure, and strength, but with different weights. What would be the ideal weight for such a bat, so that a particular player could hit a given pitch farther than he could with a bat of different mass? And just how much difference does it make when the mass is changed?

In fact, it is extremely difficult to calculate an ideal bat weight, which would surely vary from player to player as well as from pitch to pitch. It helps to first examine a much simpler problem such as an elastic collision on a pool table. Consider a moving cue ball striking a second ball initially at rest. Newton's Laws say that the target ball gains the greatest recoil energy if it has the exact same mass as the cue ball. A heavier cue ball will be going more slowly, and will impel the target with a lesser speed. A lighter cue ball will have a greater speed, but it will bounce off the target, transferring less of its energy to the second ball.

Now, back to baseball. For reasons similar to the example with billiards, one might conclude that the ideal weight of a baseball bat should not be dramatically different from the weight of the ball itself, which is about five ounces. But the following factors conspire to make the baseball problem very complicated:

• The bat-ball collision lasts for about one thousandth of a second and the forces involved can be several thousand pounds in magnitude. Because the batter holds the bat on the handle, there will be a reaction force of the same magnitude on the batter, unless the ball hits the bat at the "sweet spot," which is located near the trademark symbol.
• The internal vibrations inevitably created within the bat during the collision dissipate at least two-thirds of its mechanical energy. In fact, the sound produced when the ball strikes the bat is a consequence of this dissipated energy.
• Unlike in the pool example, the ball and bat are both moving rapidly before the collision, and the bat continues to move rapidly afterward. Again, Newton's Laws dictate that in this case only a fraction of the bat's energy can actually be transferred to the ball.

Because of these factors, the ideal bat weight should actually be somewhat greater than the weight of the ball. Some models predict that an ideal bat should weigh about five times as much as the ball, or about 25 ounces but this weight is significantly less than the weights of bats traditionally used in professional baseball. In any event, a few ounces more or less may not make a significant difference in bat dynamics.

Some batsmen may prefer lighter bats simply because they are easier to wield, allowing the batter more time to react to an incoming pitch and adjust his swing. The distance gained by using a corked bat may be very small, if you also assume that you hit the ball at the right place and time. Lightening the bat does increase the probability that you will hit it properly, however. This helps home run sluggers and singles hitters alike.

Indeed, there has been a tendency for major league batters to adopt lighter bats in recent years. In these models, wood is typically removed from the handles, making them quite thin and easily breakable. Of course, another way to make a bat lighter is to drill a hole in the end, insert a piece of cork deep into the hole, and then carefully plug, seal, and cover the hole. The weight of the bat would thereby be reduced, and if expertly done the bat would not be significantly weakened.

Answer originally posted July 28, 2003

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