Physics

How does a football swerve?

Print edition : July 25, 2014

Argentina’s Lionel Messi scores with a swerving free kick in the 2014 World Cup Group F match against Nigeria at the Beira Rio stadium in Porto Alegre on June 25. Photo: STEFANO RELLANDINI/REUTERS

THE football World Cup is on and it is a common sight to see players trying to shoot the ball by bending it into a top corner of the net, often over a wall of defensive players and away from the reach of a lunging goalkeeper. Yet when such shots go awry, players, fans and experts all suggest that the new official tournament ball, introduced every four years, is the cause.

One might think that this is just an excuse. But scientists think that subtle variations among footballs do affect how they fly. Specifically, researchers increasingly believe that one variable that really does differentiate footballs is the surface. It is harder to control a smoother ball, such as the much-discussed “Jabulani” used at the 2010 World Cup. The new ball used in the current World Cup, the “Brazuca”, has seams that are over 50 per cent 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 the Massachusetts Institute of technology (MIT) and the author of a recently published article, “The Aerodynamics of the Beautiful Game”, about the aerodynamics of footballs in “Sports Physics”, published by Les Editions de L’Ecole Polytechnique in France. “If the ball is perfectly smooth, it bends the wrong way.”

That is, 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!

The question of how a spinning ball curves in flight has a textbook answer: the Magnus Effect. This phenomenon was first described by Isaac Newton, who noticed that in tennis, topspin causes a ball to dip, while backspin flattens out its trajectory. A curveball in baseball is another example from sports. In cricket, this is the cause of the drift that many spinners achieve.

In football, the same thing usually occurs with free kicks, corner kicks, crosses from the wings, and other kinds of passes or shots: The player kicking the ball applies spin during contact, creating rotation that makes the ball curve. But this kind of a shot—the Brazilians call it the “chute de curva”—depends on a ball with some surface roughness, points out Bush.

“The fact is that the Magnus Effect can change sign,” Bush says. “People don’t generally appreciate that fact.” Given an absolutely smooth ball, the direction of the curve may reverse: the same kicking motion will not produce a shot or pass curving in a right-to-left direction, but in a left-to-right direction.

It is due to the way the surface of the ball creates motion at the “boundary layer” between the spinning ball and the air, says Bush. The rougher the ball, the easier it is to create the textbook version of the Magnus Effect, with a “positive” sign: The ball curves in the expected direction.

If the reversing of the Magnus Effect has largely eluded detection it is because footballs are not absolutely smooth, but they have been moving in that direction over the decades, Bush points out. While other sports, such as baseball and cricket, have strict rules about the stitching on the ball, football does not, and advances in technology have largely given balls sleeker, smoother designs —until the introduction of the Brazuca, at least.

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