I thought that this was pretty cool. Somewhere my high school algebra teacher is smiling, more proof of math in the real world.

“Years ago, physicist Seville Chapman proposed a model to explain how players manage the path of a fly ball so that they arrive to intercept it at just the right time. His theory, called Optical Acceleration Cancellation (OAC), used the acceleration of the ball through the vision field as a guide for player movement.

As a fielder watches the ball rise, he moves either forward or backwards so that the ball moves at a constant speed through his field of vision. If he moves too far forward, the ball will rise faster and may eventually fly over his head. If he takes too many steps back, the ball will appear to rise slower and will drop in front of him.

By managing the ball’s position with his movement, a fielder will end up at the right spot at the right time. This explains why the stationary fielders could not predict where the ball would land, as they did not have the benefit of OAC.If we ask real fielders how they knew where to run to catch a ball, they may not respond with, “Well, I simply adjusted my relative field position to keep the tangent of the vertical optical angle to the ball increasing at a constant rate.” So, to test the OAC geometric equations against real life, researchers led by Dinant Kistemaker of the University of Western Ontario, compared the predicted running paths from their mathematical simulation with the real running paths of fielders observed in a previous study.

“We have found that running paths are largely consistent with those observed experimentally,” Kistemaker told LiveScience. “Largely, and not completely, because the start of fielders is somewhat strange: They tend to step forward first, irrespective of the fact that they have run either forward or backwards to catch that fly ball.”

The research is detailed this month in the journal Human Movement Science.”

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