In the wake of all the hype about Sammy Sosa's "corking" incident there has been little discussion about whether or not there are benefits of corking a bat.
Corking involves drilling a 0.75- to 1.25-inch hole longitudinally down the center of the barrel of a wood bat. The bat is stuffed with cork or other materials expected to improve performance of the bat. The end of the bat is plugged with wood and finished to hide the illegal modification. The perception is that the modification will increase the batted speed of the ball, adding distance. Does it work?
Assume the bat is in pure rotation about a fixed point A with angular speed ¶ō1, and the baseball impacts the bat with speed V1, at distance d from point A. Using conservation of angular momentum about point A and the coefficient of restitution r, we obtain:
V2=[IAd(1+ r)/(IA+ md2)]¶ō1+[(rIA-md2 )/(IA+md2)]V1
IA is the bat mass moment of inertia about point A, m is the mass of the ball, and V2 is the rebound speed of the ball. This neglects spin and drag effects. Since IA is fairly large compared to md2, V2 is approximated by,
This indicates that V2 is loosely related to IA, and more strongly related to d, r, ¶ō1, and V1.
Does the cork provide a boost to the ball? Since r for cork is less than that for wood due to greater internal dissipation of energy under strain, r for a composite of cork and wood should not have a higher r than the unmodified bat. Cork may do no more than make the bat sound normal when hit. Some believe that the removal of the wood from the bat reduces V1. Research on this topic is limited and contradictory. Some statistically insignificant research has shown an increase in V1 for corked bats, but the increase is no more than 2%. There is speculation that the hole may allow a "trampoline" effect due to increased deflection of the bat, giving extra "spring" to the ball similar to that obtained with aluminum bats. This is partially countered by research showing that harder bats provide more distance. Whether the hole or the cork provides a benefit has not been conclusively proven.
Why do players cork their bats? Some have speculated that players cork their bats and see improvement because they "think" it will provide improvement, suggesting a psychological factor. In light of the lack of conclusive evidence for improvement, there is undoubtedly a psychological factor in play here. Cases have been cited where a player used a corked bat and saw improvement only to return to poorer performance later with the same bat.
Three other factors should be considered. First, the removal of the wood core and replacement with a lighter material, makes the bat lighter and IA is decreased. The batter can swing a lighter bat faster, and V1 will be increased. Since V2 is more strongly dependent on V1 than on IA, V2 will increase. Second, because of decreased time to swing the bat, it can be swung later giving more time to observe the flight of the ball prior to swinging. Estimating a reduction in swing time of 0.005 seconds, gives almost 8 additional inches to see the ball prior to swinging.
Why don't players just get a lighter bat or choke up on the bat? One reason is that a larger wood bat usually has a larger diameter in the barrel, providing a larger hitting area. Also, the larger diameter provides less curvature of the barrel. If a ball is hit off-center, the angular error is smaller with the larger bat. The difference in curvature can increase distance by about 5.5 ft.
Does corking make enough difference for Sammy to use a corked bat for practice or to take the risk of being caught with a corked bat? Probably not.