Physics and Acoustics of Baseball & Softball Bats
Daniel A. Russell
Science & Mathematics Department, Kettering University, Flint, MI 48504-4898
Unless stated otherwise, all tex and images are ©2003 Daniel A. Russell
I'm still working on the contents of this page. My target date for completion is the end of May 2003.

The Anatomy of the Swing

Bat rotation during a swing

First, let's take a look at the motion of the bat during a typical swing. The images below are still frames from a movie of a college player hitting a slow pitch softball.[1,2] I should note that in this overhead camera view the swing is reduced to a 2-dimensional motion, in which the bat appears to move in a plane parallel to the ground. This is almost never the case - at the point of impact for most ball-bat collisions, the ball is usually moving downwards while the bat is moving upwards during the swing. However, the fundamental aspects of the swing and the effect of mass and inertia on the bat swing speed may be sufficiently described by the overhead images below. Looking at this movie it would appear that the bat undergoes three distinct types of motion during the swing. Let's look at each of these stages of the swing.

[1] As the three frames below illustrate*, the primary component of motion during the first part of the swing is essentially a rotation of the bat-player system about a pivot point near the player's shoulders. The player's arms and the bat keep their relative orientations as they rotate through the first 90o.

[2] During the second part of the swing the bat undergoes two types of motion. There is some translation as the bat moves forward towards the ball. However, the more important motion is a rotation of the bat about a point centered on the player's hands (about 6 inches from the knob at the end of the handle). The player's arms do not move much during this part of the swing. Instead the player's wrists rotate the bat 90o until it makes contact with the ball. This part of the swing, specifically the rotation about the handle of the bat, is what we need to focus on to better understand the physics of the bat-ball collision.

[3] During the follow through, after contact, the motion is again a combined rotation of the bat and the player's arms together pivoting about a point centered on the player's body.

Rotational Inertia and Mass Distribution

As the still frames above illustrate, the primary motion of the bat just before impact is a rotation of the bat about a point roughly 6 inches from the knob end of the bat. The player's hands (wrists) supply the force/torque to cause this rotation.

This pivot point (the 6-inch point) is used for all standardized tests currently used to measure bat performance[3,4] Moment of inertia, Center-of-Percussion, and BPF are all measured with respect to this location on the handle. So, how does the rotation of the bat affect the bat-ball collision and the batted ball velocity?

References
[1] Larry K. Noble, "Elastic and Rigid Body Properties of Bats," Mini-symposium presentation at the Annual Meeting of the American College of Sports Medicine, Baltimore, MD, May 30-June 3 (2001).
[2] L. Noble and D. Zollman, Physics of Sport Videodisk, (Videodiscovery Inc., 1988)
*Permission to reproduce these still frames here was obtained from Larry Noble.
[3] ASTM. F1881-98. Standard Test Method for Measuring Baseball Bat Performance Factor
[4] Alan M. Nathan, "Characterizing the performance of baseball bats," American Journal of Physics, 71(2), 134-143 (2003).
[5] Rod Cross, "A double pendulum swing experiment: In search of a better bat," American Journal of Physics, 73(4), 330-339 (2005).
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