^{Sports Science Laboratory}

_{Bat-Ball Science Bat Performance Test}

## Bat Performance Test

*The bat performance test measures the bat and ball speeds before and after impact in a controlled laboratory setting. The test may be configured in a variety of ways, although two similar methods involving an initially stationary bat are the most common. (The speeds measured in the test can be used in different ways to quantify bat performance as described in the following section.)*

A number of devices have been implemented over the years to measure the performance of a bat. Nearly all involve a bat that pivots about a fixed point. While the motion of a bat in play involves translation and rotation, the laboratory fixed pivot point turns out to be a very good approximation to the field situation. To accurately describe the field performance of a bat in the laboratory, one needs to approximate the motion of the bat only during the instant it is in contact with the ball (approximately 0.001 seconds). Two consequences of this short duration greatly simplify the experimental requirements. First, the motion of any object at any instant can be described by an instantaneous center of rotation. The location of the center, as well as the speed, may change over time. During the 0.001 second bat-ball contact, it is essentially stationary. Second, the bat-ball contact is sufficiently short that the pivot conditions do not affect the bat at the impact location. In other words, during the 1 ms bat-ball contact, the bat deformation is sufficiently small (the barrel moves less than ½ inch) that the impact location is unaffected by the constraint at the pivot.

The most complex machines used to test bats involve a swinging bat and a pitched ball[k]. This type of device must not only accurately position the bat and ball, it must also time the delivery of both to achieve the desired trajectory. The NCAA used this type of machine to test bats until 2005[l].

A simpler and more common approach to bat testing involves an initially stationary bat or ball. To the lay observer these tests do not appear to describe the motion they were intended to simulate. By considering a moving frame of reference, however, they can be shown to be the same. Imagine viewing an impact from a small camera attached to the bat. Just prior to impact the bat would appear stationary, while the ball would appear to travel at the pitch speed plus the bat speed. The speed of the bat and ball (before and after impact) can be correlated in this way with an observer in a moving frame of reference. In the laboratory the reverse must also be true. That is, an initially stationary bat or ball can be correlated with field conditionings by knowing the respective bat or pitch speed.

While it is possible to construct a machine involving a swinging bat and an initially stationary ball, they are generally more complex than a machine involving an initially stationary bat. As shown in the preceding example, the bat must travel at the relative bat-ball speed. For softball this is 110 to 120 mph, while for baseball it is over 140 mph. Many bats will break if they are accelerated from 0 to 140 mph in one revolution. Some devices use multiple revolutions to accelerate the bat. If this is done, the delivery of the ball must be timed as it is brought into the path of the bat. The speed of the batted ball also poses challenges for initially stationary ball machines. The batted ball speed will approach 200 mph (in the laboratory frame of reference), which complicates ball containment, speed measurement, and promotes ball damage.

Currently all certified bat performance tests involve an initially stationary bat, as depicted in Fig. 9.1. (Unfortunately, this is the only aspect that is common among the various associations regulating bat performance.) The balls are accelerated using an air cannon, and travel inside a “sabot.” The sabot is sized to the cannon barrel which improves speed control, position accuracy, and prevents ball rotation. (The sabot remains inside the cannon and does not travel with the ball toward the bat.) After the ball exits the cannon, it passes through light gates which measure its incoming speed. After impact the speed of either the rebounding ball (“ball out” or ASTM F2219) or the recoiling bat (“bat out” or ASTM F1890) is measured. Angular momentum about the pivot is conserved during the bat-ball impact. It is easier and more accurate to measure two speeds and use angular momentum to find the third speed. The angular momentum balance of a bat-ball impact of a pivoted bat is

(9.1)

where *m* and *v* are the mass and speeds of the ball, respectively, *I* and *V* are the *MOI*and speeds of the bat, respectively, *Q* is the impact location relative to the pivot point, and the subscripts *i* and *r* refer to the inbound and rebound speeds, respectively. All speeds are taken as numerically positive. For the case of an initially stationary bat, *Vi*=0, so Eq. (9.1) may be readily solved for the unknown rebound ball or bat speed according to ASTM F1890 or ASTM F2219, respectively.

Fig. 9.1. Schematic of a bat test fixture involving an initially stationary bat.

While in principle the “ball out” and “bat out” methods described above appear identical, the following will show three reasons why the “ball out” measure is usually preferred. First, after impact the bat will vibrate as it rotates. The magnitude of the vibrations increase with impacts away from the sweet spot. The vibrations reduce the accuracy of the bat speed measurement. Second, “ball out” measurements tend to be self calibrating. Consider, for instance, light gates that are supposed to be 12 inches apart but are actually 11 inches apart. These gates will report a lower inbound and rebound speed, but their ratio will be correct. As will be shown below, the ratio of the ball speeds is used to determine bat performance, so error in the light gate spacing cancel. Third, the constants in the angular momentum balance (Eq. 9.1) tend to amplify the “bat out” experimental error. To solve Eq. 9.1 for *vr*, the measured quantity, *Vr*, is multiplied by *I/mQ2*which is approximately three. Conversely, to solve Eq. 9.1 for *Vr*, the measured quantity *vr* is multiplied by *mQ2/I*which is approximately 1/3. Given the same variation in measured *vr* or *Vr* (all other factors equal), for a typical bat-ball impact, a “bat out” test would have approximately 4 times the variation as the “ball out” test.

In fairness, the “ball out” method has a distinct disadvantage. Light weight bats with low performance can have slow rebound ball speeds. In some cases it is not possible to get the ball to rebound through the light gates. Without a rebound ball speed, it is not possible to measure bat performance using “ball out.” Fortunately these bats represent a relatively small portion of the market. They are also typically not close to the performance limit, so an accurate measure of bat performance is often not needed for this group of bats.

*Journal of Testing and Evaluation*, 31.3:210-214

*.*

[l] Sherwood, J.A., Mustone, T.J., and Fallon, L.P., 2000, “Characterizing the Performance of Baseball Bats using Experimental and Finite Element Methods,” Proceedings of the 3rd International Conference on the Engineering of Sport, June, Sydney, Australia