Diagram of a soccer ball with three trajectories: straight, curving right, and curving left.

Image: Jose-Luis Olivares/MIT

If you’re seeking a tangible application of advanced mathematics, look no further than the  dancing trajectory of a soccer ball off the foot of a master player.

MIT’s John Bush, a professor of applied mathematics, has helped us understand water-walking insects and the dynamics of coughs and sneezes, and developed self-propelled cocktail boats. Now via today’s MIT News, he shines a light on the aerodynamics of “the beautiful game”.

Explained: How does a soccer ball swerve?
The smoothness of a ball’s surface — in addition to playing technique — is a critical factor.
Peter Dizikes | MIT News Office | June 17, 2014

It happens every four years: The World Cup begins and some of the world’s most skilled players carefully line up free kicks, take aim — and shoot way over the goal.

The players are all trying to bend the ball into a top corner of the goal, often over a wall of defensive players and away from the reach of a lunging goalkeeper. Yet when such shots go awry in the World Cup, a blame game usually sets in. Players, fans, and pundits all suggest that the new official tournament ball, introduced every four years, is the cause.

Many of the people saying that may be seeking excuses. And yet scholars do think that subtle variations among soccer balls affect how they fly. Specifically, researchers increasingly believe that one variable really does differentiate soccer balls: their surfaces. It is harder to control a smoother ball, such as the much-discussed “Jabulani” used at the 2010 World Cup. The new ball used at this year’s tournament in Brazil, the “Brazuca,” has seams that are over 50 percent longer, one factor that makes the ball less smooth and apparently more predictable in flight.

“The details of the flow of air around the ball are complicated, and in particular they depend on how rough the ball is,” says John Bush, a professor of applied mathematics at MIT and the author of a recently published article about the aerodynamics of soccer balls. “If the ball is perfectly smooth, it bends the wrong way.”

By the “wrong way,” Bush means that two otherwise similar balls struck precisely the same way, by the same player, can actually curve in opposite directions, depending on the surface of those balls. Sound surprising? Read more, and see a video demonstration…

You can learn more about the beautiful mathematics behind such phenomena in these OCW courses by Prof. Bush: