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United States’ Jermaine Jones celebrates with his teammates after scoring against Portugal at the World Cup.
Associated Press

RIO DE JANEIRO—When Jermaine Jones scored his ripper of a goal in the U.S.’s second World Cup game against Portugal, John Bush celebrated along with millions of Americans. He also took note of how the ball curved around a Portuguese defender.

“It would definitely have gone wide had it followed its initial trajectory,” Mr. Bush says.

Mr. Bush is a professor of applied math and fluid dynamics at MIT. He’s also a big soccer fan, and he’d like the world to understand a bit more about how a soccer ball moves through the air.

“I remember when I was kicking the soccer ball around as a kid thinking, ‘Why does it curve in the air a certain way, what causes that?’” Mr. Bush says.

While at college at the University of Toronto, Mr. Bush studied fluid dynamics and started to understand more deeply that as a ball flies through the air, there are flow patterns that determine how it moves.

Jones struck the ball with his right foot, and the spin and curvature of the ball were consistent, causing it to bend it to the left.

“A standard ‘chute de curva,’” Mr. Bush says, referring to the Brazilian phrase for that type of shot. (When the ball changes directions more than once, it’s called a ‘Pombo Sem Asa,’ or a dove without wings.)

Mr. Bush got his PhD in geophysics from Harvard, but the science of soccer was a steady hobby. At MIT, he gives a talk on the subject every year to his fluid dynamics class. And last year, he contributed a paper titled “The aerodynamics of the beautiful game,” for a book called Sports Physics.

A section of that paper is devoted entirely to the unique style of Brazilian free kicks.

Here’s a sample paragraph from that paper, for those who can understand it:

The pressure drag is thus dominant for most sports balls, including footballs, and a good approximation for the drag is a force opposing motion with magnitudeCDρU2πa2/2, where a is the ball radius, ρ is the air density, and U is the ball speed. The drag coecient CD is in general a function of both Re and surface roughness, but is an order 1 constant at the high Re appropriate for ball sports. The empirical dependence of CD on Re has been well characterized for a smooth ball, for which CD 0.4 for 103 &lt; Re &lt; 2×105 (Smith et al., 1999). As Re is further increased, CD decreases dramatically to a value of approximately 0.1 before recovering to a value of approximately 0.4 for Re &gt; 107. This precipitous drop in CD, termed the dragcrisis, plays a critical role in many ball sports (Mehta 1985, Mehta & Pallis 2001),including football.

Perhaps the U.S. should look to develop players who can kick the ball hard and understand drag coefficients.

“It was sort of a culmination of my life in sport and science,” Mr. Bush says of the paper. “As a player you develop an intuition of how to do it, but you don’t really necessarily know why it works. So it’s kind of fun to have the two come together, intuition and science.”

He’s become well-known in the small overlapping worlds of math and soccer. After giving a talk in France, a local journalist called him “The Zidane of Fluid Dynamics.” He was even approached to do a TV show about the science behind free kicks, but he backed out when the producers couldn’t get soccer superstar David Beckham to participate.

Mr. Bush is in Brazil for June and July as a visiting professor at the National Institute for Pure and Applied Math in Rio de Janeiro. His visit, Mr. Bush admits, was “carefully timed” so he could attend some World Cup matches and soak up the festive atmosphere in Brazil.

As for his talk on the science of soccer, Mr. Bush calls it a “party piece” that he dusts off from time to time. Dusts off, and dumbs down.

The version of the talk he gives to his fluid dynamics class wasn’t going to work when he gave the talk at the MIT Museum earlier this year.

“I realized that no one in the front row was older than six,” he says. “So I give various versions of it.”

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