Perfect pitch

Exploring the physics of throwing.

Gregory Nemec

Gregory Nemec

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When Yale’s own Craig Breslow ’02 takes the mound for the Minnesota Twins, he’s hoping to fire a pitch that is fast, accurate, and unhittable. Unfortunately, Breslow, like anyone who has ever thrown a baseball—or anything else—is forever facing a foe far greater than the best hitters in the major leagues.

“The fundamental physics of how a projectile moves through the air imposes an adverse tradeoff between speed and accuracy,” says Madhusudhan Venkadesan, an assistant professor of mechanical engineering who studies biomechanics. His research, published in Royal Society Open Science, explores why physics makes life so challenging for pitchers, dart throwers, prehistoric spear hunters, and folks trying to chuck paper into a wastebasket.

To find the best throwing strategies, Venkadesan and Harvard applied mathematician L. Mahadevan created a mathematical model with parameters such as overhand versus underhand, arm speed, angle, and release point. They discovered that darts players maximize their accuracy by tossing the dart overhand, with an arm speed of about 5.3 meters per second and a release point between 17 and 37 degrees before the arm becomes vertical. And if you let go a little too early, or a little too late? Venkadesan offers no hope. “Once you launch whatever you’re throwing, there’s nothing you can do. The object’s just going to carry out the consequences of what you did.”

Other takeaways: use a gentle lob to hit the wastebasket, whether it’s close or across the room; and a fast underhand throw maximizes a cricket player’s chances of knocking over wickets at close range.

What about NBA Hall of Famer Rick Barry, who delivered his free throws underhand—with record accuracy? Venkadesan says underhand is a fine strategy: “The so-called ‘granny throw’ is at least as accurate, according to our modeling, as the overhand toss.” As to why the style is neither taught nor seen on the courts anymore, Venkadesan points to the “cultural baggage” of sports. “That’s beyond physics,” he says.

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