13 July 2010

In the Spirit of the MLB All-Star Break: Curve-ball Physics

I thought I would take a break from the kind of science that you have to think really hard about, and reflect on the simple physics behind the curve-ball.  We're talking about a pitch that is SO counterintuitive that for years, baseball experts couldn't even agree on its existence.  Well it turns out the pitch exists in a major way.  A good curve-ball can arc a solid foot and a half away from its original path, and be close to impossible to hit.  Vin Scully called Clayton Kershaw's curve, which he's about to lob in the photo below, "public enemy number one"; this pitch is no joke.

In 1852, a German-Jewish physicists named Heinrich Magnus (below) was the first to describe the way objects spinning in a fluid create a kind of whirlpool around themselves, which has the effect of pushing them slightly off course.  This phenomenon, known as the "Magnus Effect," is what makes curve balls curve.

But WAIT, you say.  That's in a fluid!  A baseball moves through the air, and air is a gas!

A fluid (as we all learned in Atmospheres and Gases at Astrocamp) is defined simply as something that flows. Therefore gases like air can be fluids, just as liquids like water can.  Air definitely flows, or else we wouldn't have weather!  So it's a fluid.

But back to baseball.  I'll simplify for the example and pretend Kershaw is a side-arm pitcher; that way we only have to work in two dimensions.  When the ball leaves Kershaw's hand, he puts a clockwise spin on it (counterclockwise for right-handers, and clockwise for southpaws I believe--correct me if I am wrong somebody).  As the ball moves toward the plate, air flows over it, which I like to imagine as a velocity vector pointing back toward the mound.  Meanwhile, the spin of the ball means that on the first base side the ball is moving against the velocity of the air, while on the third base side the ball is moving with the velocity vector of the air.  On the side where the ball is moving in the same direction as the air, there is less drag, so less air builds up.  On the other side, there is more drag, so more air builds up.  All of a sudden we have a pressure differential, with a surplus of air on one side of the baseball pushing it into the pocket of low-pressure toward third base.  The ball curves toward the low pressure...the batter watches it zoom over the plate...STEEERIKE!

It's easy to generalize to three dimensions.  The effect works the same way in the up-down dimension as it does in the first base-third base one.

As a side note, remember all that fuss at the beginning of the 2010 World Cup about the "Jabulani," the official match ball that the players complained moved through the air the wrong way?  The controversy was quickly drowned out by vuvzelas and the screams of angry soccer fans pledging eternal hatred to slow witted referees, but the issue was the Magnus Effect.  The Jabulani didn't produce as much of a Magnus Effect as the soccer balls the players were used to, so it went farther, and curved less.  Maybe if they had used a normal ball, the U.S.A. wouldn't have sucked so much in the first half against Ghana?

(Go Dodgers!)


Anonymous said...

Neat post. Just FYI, Kersh is gripping for a four-seamer fastball in that photo.

zbuck said...

Thanks anonymous! I'll look for a replacement picture.