Vannevar Bush Letter
about the Physics of Baseball

Transcription of letter | Page from Edgerton's laboratory notebook

Bush letter

Page 1 of Bush letter

Page 2 of Bush letter


Transcription of Bush letter

S. Dennis
Aug 1, [19]65

Dear Harold--

Those pictures have lots of interest. We will have to talk it over when we get back this fall. I've written a [satire] on baseball, and maybe we ought to write a technical one.

The picture of the line drive seems to check out all right. As I see it the ball should leave at a velocity equal to the incoming velocity plus twice the velocity of the bat. This when there are no losses due to lack of elasticity of ball and bat, rotation of bat when not hit a[t] center of impact, vibration of bat due to bending at time of impact. It's a bit difficult to read the picture since apparently two images nearly coincided. But, if I read it right it says that bat speed was about .6 of ball speed, and ball left at about twice the speed at which it arrived.

This is interesting for one thing because it indicates good ball elasticity, much better than one would get by just letting a ball bounce when dropped from a height. One should not be surprised, I think, if elasticity were better for a sharp blow than for a soft one.

The large picture, with the chap with the whiskers[,] tends to bear this out. Here bat speed is lower, and ball leaves at a speed not much greater than incoming speed.

The foul tip picture is harder to reason about. I like to do it this way, which I think is legitimate. First I reason what things would look like to a man travelling at the speed of the bat. Then, having this result, add the bat speed. Let's call incoming speed Si, leaving speed So, bat speed Sb. Now, to a moving observer in the case of the line drive, incoming speed appears to be Si+Sb. After a perfect bounce leaving speed is the same. For a stationary observer we add Sb, and get for the leaving speed Si+2Sb. This is a maximum, and the extent to which leaving speed falls below this shows amount of losses.

In the case of the foul, incoming speed [as before] to the moving observer. Ball leaving bat at this same speed but at an angle. Then one adds Sb horizontally to the result. The geometry is a bit tough and I haven't worked it out. Qualitatively it seems all right. If I get a chance I'll try to work it out.

One thing is strange in this foul tip picture. The ball must be rotating rapidly after leaving the bat. It should curve, but its path is very straight. Perhaps this is tied in with the "breaking" of a curve pitched ball. I believe "breaking" is real, not just an optical illusion. It takes time to set up the flow around a rotating ball to cause it to curve.

More later perhaps. At any rate this is interesting stuff.




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Photographs © Harold E. Edgerton 1992 Trust

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