The curve ball

And the slice and hook in golf, etc., etc.

In physics we emphasize how balls travel neglecting the effects of air. This works very well for many cases, but not for the high speed cases (significant air drag) and high speed with spin (drag and curve).

If a ball curves down, it is sending air up. If it curves to the left, it is sending air to the right. The same goes for airplanes, helicopters and birds. They need an upward force, so they push air down. It's an action-reaction thing.

Now how does a spinning ball do that? A ball moving through still air is the same as a ball at rest and the air moving. In the picture below, the ball is spinning counterclockwise and air is moving from right to left. On the top of the ball (toward the top of the page, that is) the surface is moving in the same direction as the air. This enables the air to cling to it farther. (In fluid mechanics jargon it is said that the separation point is farther to the left on the top of the ball than the bottom.) This causes the air on the lee side of the ball (sheltered from the wind: the left side, in this case) to travel toward the bottom of the page, as shown.

This is like the drive in golf, or putting backspin on a pingpong ball. The ball curves upward. Without air, on level ground you get the greatest distance by sending the ball at an initial 45^o. In golf, you get the greatest distance on a drive with an initial angle of way below 45^o, because of the upward curvature initially. The ball quickly slows down and behaves more normally, and its path looks sort of like this, going left to right:

Incidentally, this effect of spin is known as the Magnus effect (after Gustav Magnus). Some people explain this by invoking Bernoulli's equation, but the consensus is that this is not quite right. Bernoulli’s equation is derived for zero air drag and zero turbulence, and that does not quite fit. It could be a reasonable approximation, though. The air above the spinning ball discussed above is moving faster than the air below the ball, so there is a lower pressure above. That is the Bernoulli effect.

The knuckle ball: This is thrown from the finger tips, not the knuckles, and it has approximately no spin. The location of the seam nearest the front of the ball probably has the most effect on how the air flows around the ball. The pitcher does not have good control over that, so the ball curves unpredictably.

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