Curve Balls

Curve Balls Photo Credit: Chris McBrien (c.mcbrien), via Flickr [CC BY-SA 2.0]

About the only math most folks do around a baseball diamond is quoting their favorite player's batting average. But it turns out that baseball may actually have a thing or two to teach mathematicians.


Modeling the perfect pitch. I'm Bob Hirshon and this is Science Update.

Baseball fans aren't the only ones watching the boys of summer play. Chuck Romine, a computational mathematician at Oak Ridge National Lab, says baseball also provides a challenge for scientists.

Take the curve ball pitch. Romine says a curve thrown at Yankee Stadium, which is at sea level, will fly differently than one hurled at the mile-high Coors Field in Denver. He says this phenomenon can be modeled with math.

Most people who have tried to do this kind of model have assumed, for example, that the ball is rotating at a constant velocity. And that's clearly not the case, because the air is going to slow down the rotation during the flight of the ball.

But Romine says a member of his team, Joey Huang, invented a new mathematical method that more accurately describes the flight path of the curve ball.

What his work does goes far beyond just trying to determine the trajectory of a baseball. It's a basic advance in the area of computational fluid dynamics.

And that could have uses beyond the ballpark, like modeling the aerodynamics of an airplane wing or the potentially destructive flow of water around a deep-sea oil rig. So one day, the work not only could benefit big-league pitchers but could be a hit with engineers as well.

For the American Association for the Advancement of Science, I'm Bob Hirshon.

Making Sense of the Research

The purpose of the curve ball pitch is to impart spin to the baseball so that it veers off to the side. This last minute curvature is difficult for a hitter to anticipate, which is why it's such an effective pitch. Mathematician (and baseball fan) Dr. Joey Huang has developed a new mathematical model for the trajectory of a curve ball. What makes his model different from previous ones is the fact that it takes into account both the air's effect on the ball and the ball's effect on the air. Earlier models assumed that the ball is rotated at a constant speed, ignoring the fact that air friction is going to slow it down. They also ignored the impact of drag. In Dr. Huang's simulation, you can actually see the effect that the ball has on the surrounding air in the form of vortices and whirlpools.

Dr. Huang modeled the curve ball using two different types of systems of equations—a mathematical model of the flow of any type of fluid (in this case, the air) and an equation specifying the motion of a solid (in this case, the baseball). Once he coupled these equations, he was able to solve for the trajectory of the ball in a fluid. This same model can be used to explain phenomena such as why paper oscillates when it falls, representing an advance in the field of fluid dynamics.

This model also helps to explain to frustrated pitchers why their curve ball seems so temperamental. Most pitchers are accustomed to pitching in parks near or at sea level. When visiting a park such as Denver's Mile High Stadium, which is 5,280 feet above sea level, the ball curves differently. Dr. Huang's model shows why the curve ball pitch, perfected at sea level, will start curving earlier due, in part, to the lower air density at that high altitude—giving the batter ample time to adjust to it.

Now try to answer the following questions:

  1. Describe the mathematical model that Dr. Huang has developed. How is it different from previous models?
  2. Where would a curve ball be more effective, Yankee Stadium or Denver's Mile High Stadium? Why?
  3. How might the differences in air density affect hitters?
  4. What other factors affect the trajectory of the ball?
  5. What are some other applications for Dr. Huang's work?

For Educators

For more on the mathematics and science behind baseball, visit the Science of Baseball from the Exploratorium. For more information on the how and why of curve balls, go to Putting Something on the Ball. For information and photos on how to throw an effective curve ball, see Thrown for a Curve or Why Does Spinning a Ball Make it Curve?

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