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Tuesday, May 30, 2006

One thing that cannot have escaped college softball fans is that many of the dominant pitchers are very tall, especially for women. Among the teams playing in the Women's College World Series, which begins Thursday, we have: Cat Osterman of Texas (whom I profiled in yesterday's entry, below), 6-foot-2; Monica Abbott of Tennessee, 6-3; and Brianne McGowan of Oregon State, 6-2.

Given my recreational interest in physics, I've begun to wonder if longer pitching arms produce higher speed on the ball. We first need to establish that taller people have longer arms; indeed, arm span is positively correlated with height. Further, writings on various sports suggest that there may be something going on with height and/or arm length.

Regarding whether 16-year-old female golfer Michelle Wie would ever be good enough to qualify to play on the men's PGA tour full-time, a commentator suggested on's website that:

... there is the fact that she is 6-foot-1 trending toward 6-foot-2. That gives her a big swing arc that can generate impressive club head speed.

Another potentially useful source is Timothy Gay's book, Football Physics (which I've reviewed, here).

On pages 130-139 of Dr. Gay's book, his discussion of the kicking motion (especially Figure 5-1) suggests an analogy between a kicker's leg rotation about the hip and a softball pitcher's arm rotation about the shoulder. Limb length appears to have some role to play, as he includes the punter's leg length (assumed to be 3 feet) in calculating the leg's moment of inertia. One difference, of course, between kicking and pitching is that in the former, one strikes the ball, whereas in the latter, one releases it.

The equations in the upper part of p. 137 appear to suggest that greater leg length is associated with greater speed of the ball coming off the punter's foot. Thus, both the aforementioned golf quote and my reading of Football Physics suggest that height (or limb length) is beneficial for athletes performing tasks of angular (circular) motion.

I've inquired with some physicists (whose identities I don't want to reveal at this time because they've offered me only some tentative thoughts), and none of them has shot down the idea that, everything else held equal, a longer arm would lead to a faster pitch.