I like to send Mr Science mind-candy when I find it on the web …
http://www.npr.org/templates/story/story.php?storyId=130777556
but Mr Science Says:
They're making a convoluted scenario out of a high-school geometry problem.
The path of the ball is a simple circular curve. It doesn't "fall off the table" at the end, it simply continues accelerating in the same direction at the same rate.
Consider a circular automobile race track. You stand just outside the outer wall watching cars go by. As a car comes into your view, almost 90 degrees away around the circle, it is traveling straight toward a point off to your left, like the curve ball (or fast ball) just released by the pitcher. In fact, you can't tell if that car is going to stay on the track, or hit the wall because it fails to hold the curve.
As the car gets closer to you, you begin to see that it is in fact turning, and will stay on the track. It's not moving much sideways, but still coming closer very quickly, and is now coming straight at you. Like that curve ball when it's halfway to the plate.
Then, as the car gets close to you, you begin to see that it's no longer coming toward you very much, but is turning very quickly and will pass by you without hitting you or going off the track. Like the curve ball when it's 2 feet in front of the plate, and "falling off" the table.
The driver of the car hasn't moved his steering wheel the whole time. He's turning at a constant rate, the same as the circular track. The same as the curve ball, the direction of motion is changing at a constant rate.
The batter isn't moving, but the path of the ball is changing as it comes toward him, and his perception of the sideways motion is the sine of the angle between his sightline and the path of the ball. When the ball is coming straight at him, the angle is 0 and the sine is 0. It looks just like a fastball. The longer you wait, the more the path of the ball changes, and the larger is the angle and the sine of the angle. That's the math that explains why a ball that is following a circular path of constant radius seems to "fall off the table" when it gets very close to the batter.
That's also why your draw gradually turns into a duck hook as it approaches the edge of the fairway.
I’m trying not to take it personally, but that “your draw” conclusion stings a little bit . . . 8^D . . . .
