Browse all


Mathematical physics

Mathematical physics

How physics can improve your football

24 Jan 2006 Belle Dumé

New research on the mechanics of throwing could allow football teams to make greater use of "throw-ins". Two scientists at the University of Brunel in the UK have calculated that to launch a football as far as possible from a throw-in, the best angle to release the ball is 30 degrees to the horizontal. The result differs significantly from the figure quoted in most physics textbooks (Sports Biomechanics in press).

Throw-ins are awarded in football when the ball goes out of play, and involves the thrower holding the ball with both hands behind his or her head and launching it forward back onto the field of play. Some footballers, such as Dave Challinor of Stockport County in England, are able to throw the ball far enough into the goal area so that their team mates have a significant chance of scoring. The trick is to be able to throw the ball fast enough and at the right angle.

To work out the optimum angle between the initial direction of the ball and the horizontal, Nicholas Linthorne and David Everett first used a video camera to film a player throwing a football at angles between 10 and 60 degrees. They then used biomechanical software to measure the launch velocity and launch angle of the ball as recorded on the video. Combining this information with the equation of flight of a spherical projectile, they calculated the optimum launch angle to be 30 degrees. Most physics textbooks, on the other hand, quote an angle of 45 degrees. Moreover, the researchers found that the ball could travel a few metres further if it was thrown with a “backspin” at slightly lower angles.

The researchers say that that the techniques used in this study could be applied to any sport that involves projecting a ball or launching the human body. Linthorne is now working out the optimum angle at which football goal kicks should be taken.


Copyright © 2018 by IOP Publishing Ltd and individual contributors
bright-rec iop pub iop-science physcis connect