As the U.S. women’s football team face Japan in the Olympics gold medal match, scientist John D. Barrow, author of Mathletics, explains the physics of an unstoppable free kick.
One of the skills that soccer players seek to master from an early age is how to “bend” the ball. For those ignorant of the game, we should say this simply means learning how to kick the ball so that it swerves in the air. This skill can deceive opposing defenders and goalkeepers and is especially potent when a free kick is awarded close to the edge of the opponents’ penalty area.
The defending team will set up a wall of players at the requisite 10 yards from the ball (closer if they can get away with it) to block a direct shot at their goal. The attacking team may well have a prized player like David Beckham, who can bend the ball around or over this defensive wall so that the initial trajectory of the ball heads past the edge, or over the top of the wall of defenders, only for it to swing back in, or down, and end up in the goal. Alas, the poor goalkeeper finds that his wall of defenders does nothing more than block his view of the ball until it is too late to respond. How is this done and why is it possible?
When you kick a soccer ball off-center it will spin. If you kick the right-hand side of the ball with the inside of your right foot, then it will spin in a counterclockwise direction, but kick it on the left-hand side with the outside of your right foot and it will spin clockwise. The greater the spin you can put on the ball, the more it will swerve.
The most famous example of this skill was a free kick taken by Roberto Carlos for Brazil in a 1997 match against France. He struck the ball initially from a spot 115 feet from the goal, close to the corner of the D on the edge of the penalty area, at a velocity of about 80 mph. The subsequent swerve was so dramatic that a ball boy standing 33 feet to the side of the goal jumped out of the way because he thought the ball was heading straight for him before it swerved suddenly away from him and beat the goalkeeper.
Carlos hit the ball so hard that gravity never had a chance to damp down the aerodynamic motion. This effect is not unique to soccer. It can be seen across the whole sporting spectrum. Volleyballs, baseballs, cricket balls, tennis balls—all can be given a spin that will result in them following a curved trajectory that a non-spinning ball would not. The reason for the swerve can be understood by looking at the air flowing past the ball. When the airflow impinges on the ball the flow lines are pushed together, so the pressure drops and the speed of the air passing the surface of the ball increases.
If the ball is spinning, then the flow lines of the air near the surface of the ball are significantly altered. If the ball has been given a clockwise spin,at the top the air movement very close to the surface of the ball is in the opposite direction to the oncoming air, whereas at the bottom it is in the same direction. This means that the net speed of the air near the top of the ball is less than that near the bottom. Therefore the pressure on the ball is greater at the top than the bottom and there is a net downward force. A ball with topspin will swerve downward. A ball struck with the outside of the right foot will swerve to the right.
During the last men’s World Cup in South Africa, there was considerable controversy and much complaining by goalkeepers about the introduction of a new, lighter ball that displayed unfamiliar aerodynamic properties. Yet it was very noticeable that the world’s leading attacking players never really mastered the behavior of the ball, and there were almost no goals scored by long-range shots or free kicks. Players were simply unable to control the swerve of the ball.
Excerpted from MATHLETICS: A Scientist Explains 100 Amazing Things about the World of Sports by John D. Barrow. Copyright © 2012 by John D. Barrow. With permission of the publisher, W.W. Norton & Company, Inc.