by John0714 on September 25th, 2006

John0714

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Can you calculate the effect of different bat speeds on the same hypothetical pitch? Say the ball went 200' when hit at x bat speed, how far if hit with 2x speed, everything else being equal?

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  • by looney on September 25th, 2006

    looney

    Need more variables than that. Assume no wind or drag effects, because those are really difficult to calculate. Doubling the bat speed means doubling the bat momentum. This doesn't quite double the ball's momentum, because not all of the bat's momentum is transferred to the ball. But that depends on how the individual batter swings, so it's also inconvenient to calculate for in a theoretical problem. So forget it. Assume the ball's momentum comes out twice what it was the first time, which means its initial velocity is also doubled (since mass is constant).

    Next, we need to know the angle of the ball's initial trajectory relative to the ground. This is necessary to determine how much of the increased speed goes into distance and how much into height. Specifically, vertical velocity is total velocity * sin(angle), whereas horizontal velocity is total v * cos(angle). Once you have the vertical velocity (in feet per second), double it and divide by 32 to get the time (in seconds) that the ball stays in the air. Then multiply by the horizontal velocity to get the distance. Which will be horribly off, because drag and wind effects are quite significant in the trajectory of a baseball, but it'd take a supercomputer to calculate a really accurate result. Which is why nobody bothers to predict the flight of a baseball mathematically. It's much easier to just point a radar gun at it.

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