05-22-2014 / By:
The trampoline effect is quite well known in hollow metal bats. The thin metal shell actually compresses during the collision with the ball and springs back, much like a trampoline, resulting in much less loss of energy (and therefore a higher batted ball speed) than would be the case if the ball hit a completely rigid surface. The loss of energy that I referred to comes mostly from the ball. During the collision, the ball compresses much like a spring. The initial energy of motion (kinetic energy) gets converted to compressional energy (potential energy) that is stored up in the spring. The spring then expands back out again, pushing against the bat, and converting the compressional energy back into kinetic energy. This is a very inefficient process in that only about 25% of the stored compressional energy is returned to the ball in the form of kinetic energy. The rest is lost due to frictional forces, deformation of the ball, etc. You can see the effect of this energy loss for yourself. Drop a baseball onto a hard rigid surface, such as a solid wood floor. The ball bounces back up to only a small fraction of its initial height because energy was lost in the collision of the ball with the floor. The loss mainly came from compressing and then expanding the ball. When a ball collides with a flexible surface, like the thin wall of an aluminum bat, the ball compresses less than it does when colliding with a rigid surface, since the thin wall does some of the compressing instead. Less energy is stored and ultimately lost in the ball, whereas the flexible surface is very efficient at returning its compressional energy back to the ball in the form of kinetic energy. The net effect is that the ball bounces off the flexible surface with higher speed than it does off the rigid surface. This is the essence of the trampoline effect. By the way, the trampoline effect is well known to tennis players, where the effect comes from the strings of the racket. All tennis players know that to hit the ball harder, you should decrease rather than increase the tension in the strings. Many people who do not play tennis find this counterintuitive, but it really is true. The lower tension makes the strings more flexible, just like a trampoline. You can even try the following experiment. Drop a baseball from the floor and measure the ratio of final height to initial height. Now drop a baseball from the strings of a tennis racket, making sure that the frame of the racket is clamped down so it does not vibrate. You should find that the ratio of final to initial height is higher than when the ball is dropped onto the floor. That is the trampoline effect in action.
With that long introduction, we come back to our question: Is there a trampoline effect from the hollowed-out wood bat or the cork filler? My own understanding of the physics of the ball-bat collision suggests that the answer is “no”. Why not? A 1”-diameter hole in a 2-1/2” diameter wood bat means the wall thickness is ¾”, which is at least 7 times thicker than that of a typical aluminum bat. It requires much greater force to compress such a bat than it does to compress an aluminum bat. In the technical parlance of physics, the spring constant of the hollow wood bat is much larger than that of a typical aluminum bat. Therefore, very little compressional energy is stored in the hollow wood bat during the collision, so that any trampoline effect is minimal at best.
In order to test this idea, I did an experiment several years ago with Professor Jim Sherwood at the Baseball Research Center (which Jim directs) at the University of Massachusetts/Lowell. We took two identical Louisville Slugger R161 wood bats, each with a length of 34” and a weight of 32.5 oz. Into one bat I drilled a 7/8 diameter hole, 9-1/4 deep into the barrel, removing a total of 2.0 oz. of wood. We then measured the ball exit speed when a 70 mph ball impacted the bat at a point 6 from the end of the bat. The speed of the bat at that point was set at 66 mph. Using the measured exit speed, the known inertial properties of the bats, and appropriate kinematic formulas, we extracted the ball-bat coefficient of restitution (COR), which is a measure of the liveliness of the ball-bat combination. We found the COR to be identical for the two bats, at least within the overall precision of the experiment. Had there been a trampoline effect, one would have found a larger COR for the hollowed bat. Armed with this information, I then did a calculation of hit ball speed that one would expect in the field, assuming a pitch speed of 90 mph and a bat speed that was slightly higher for the hollowed bat, based on a model for the relationship between bat swing speed and the swing weight of the bat. The model is based on the (unpublished) experimental study of Crisco and Greenwald, which gives a definite relationship between the MOI of the bat and the swing speed. The calculation shows that the unmodified bat actually performs slightly better than the hollowed bat (see figure below).
Moreover, filling the cavity with cork, which is much more easily compressed than the wood itself, is not likely to help. The response time of the cork is much too slow to provide a trampoline effect. The typical ball-bat collision time is less than 1/1000 of a second, which is much faster than the natural vibrational period of the cork. During the short collision time, the cork barely has time to compress. In effect, energy gets transferred to the cork in the form of an impulse, which actually results in more energy dissipation than would be the case if the cavity were empty. Moreover, adding cork restores some of the weight that had been removed, thereby at least partially negating the increase in swing speed that had resulted. It would seem that leaving the cavity hollow would be better than filling it with cork.
Figure 1. Calculation of hit ball speed from two otherwise identical wood bats. Relative to the normal bat, the corked bat had a cavity in the barrel of diameter 0.875” and depth 9.25”, thereby removing a total mass of 2 oz. from the barrel of the bat. The calculation assumes that the ball-bat COR is the same for each bat, as shown from experiment, and assumes a particular relationship between the bat swing speed and the moment of inertia of the bat. The calculation shows that the normal bat slightly outperforms the corked bat.