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How to throw a soccer ball

January 25, 2006 By Philip Ball This article courtesy of Nature News.

Physicists reveal how best to get speed and distance with a throw-in.

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Researchers have managed to confirm what many football players have already worked out: when it comes to throwing a soccer ball far and fast, the usual rules of projectile maths don't necessarily apply.

The study, by sports scientists Nicholas Linthorne and David Everett at Brunel University in Uxbridge, UK, also holds some tips for soccer coaches as to how to get the best from their long-throwing players.

The 'long throw-in' is a classic, useful move in soccer: chucking a ball from the touchline into the opponents' goalmouth can catch defenders off guard, and an attacker receiving the ball from a throw can't be caught out by the offside rule.

If all of that sounds like gibberish, rest assured that the ability to overhand throw a ball a long distance is a very good thing. But the mechanics of it seems to defy standard wisdom in physics.

Cannon fire

The players have already worked it out by trial and error.
Nicholas Linthorne
Brunel University
Every physics undergraduate knows that to get the maximum range from a projectile shot from a cannon, the barrel should be tilted at 45° to the ground. But footballers, as well as shot putters and javelin and discus throwers, usually release their projectiles at much lower angles, closer to around 30-35°1.

"People haven't been able to explain it," Linthorne says. He and Everett have now made a detailed study of the football throw-in, videoing a player making a series of throws at different release angles. They fitted the resulting release speeds, throwing distances and flight times to mathematical equations.

This enabled the researchers to find the best release angle for producing a long throw. The answer, it seems, is that it doesn't matter too much, provided that the angle is between about 20 and 35°. They report their findings in Sports Biomechanics2.

Body works

Why the difference to what conventional mechanics predicts? Because, says Linthorne, that neglects the skeletal and muscular structure of the human body, which makes it easier to apply a lot of force to the ball at lower angles than at higher ones, and so to release it at a faster speed.

It's this speed, he says, that mostly determines the distance thrown. "The human body has a built-in bias to low release-angles," he says.

But Linthorne doesn't expect to be deluged by professional players looking to improve their throw-in technique with help from physics. "They've already worked it out by trial and error," he says. "The science is only now catching up." He says that players can typically keep their release angle to within a few degrees of what they've found to be the best.

Fast and furious

He adds that sometimes it's not distance that counts, but flight time. Delivering the ball faster to the target player capitalizes on the element of surprise. He and Everett find that making the release angle just a few degrees shallower makes almost no difference to the distance that can be achieved, but can decrease the flight time by a crucial few tenths of a second.

"These are all well-rehearsed tactics," Linthorne explains. "Most teams have a specialist long-thrower." Figuring out how they do it, he says, might help to deter coaches from trying to apply some misinformed elementary physics to the problem.

But perhaps the primary value of the study will be to high-school teachers trying to get the kids excited about physics. "Anything to do with sports gets the students interested," says Linthorne.

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  1. Linthorne N. P. Am. J. Phys. submitted (2006).
  2. Linthorne N. P. & Everett D. J. Sports Biomechanics (in press).


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