The Kick that Defies Gravity


By Jeff Z. Klein,  New York Times

Soccer has been described as ''the beautiful game,'' a sport that requires flights of magical improvisational genius. Take, for example, free kicks, and the planet's best player at making them, David Beckham of England. Beckham has mastered the art of inducing the ball, from a standing start, to soar over a wall of defenders standing 10 yards away and then seemingly contradict the laws of nature by veering downward at the last second so that it drops beneath the crossbar. It is called bending a free kick, and until recently it was assumed that such mysterious skill could be neither deciphered nor taught.

But this year an international team of researchers managed to solve the mystery of how Beckham bends it -- and in so doing, created the perfect model for the perfect kick. Engineers from the University of Sheffield in England and Yamagata University in Japan, along with researchers at an international engineering-software company called Fluent, used high-speed video analysis, computer models and wind-tunnel simulations to determine the swirl of forces that guided Beckham's famous free kick against Greece that propelled England into the 2002 World Cup. Standing 29 yards in front of the Greek net, the researchers say, Beckham most likely struck the ball about 80 millimeters (3.15 inches) to the right of center with his right foot, sending it off at 80 miles per hour spinning right to left at about 8 revolutions per second.

The ball rose over the wall of defenders, pushed leftward by the sideways pressure, created by spin, that physicists call the Magnus Force. But a few yards from the net, another force took over: atmospheric drag. As the ball slowed, the researchers say, the airflow around it suddenly shifted from ''turbulent'' to ''laminar'' (or in layman's terms, from bumpy to smooth). In a split second, the drag on the ball increased by 150 percent, and that caused the ball to plummet and dip just under the crossbar.

If Beckham had struck the ball with more spin, it would never have cleared the Greek wall; too little spin, and the ball would have sailed harmlessly over the net. ''Beckham was instinctively applying some very sophisticated physics in scoring that great goal,'' reports Matt Carre, an engineer at the University of Sheffield.

So it's simple: kick the ball at just the right point, at just the right speed, creating just the right spin, and you, too, can bend it like Beckham. ''I believe that it would now be possible to design an optimum free kick for any given point,'' Keith Hanna of Fluent says. Of course, designing the ultimate kick and actually performing it on the playing field are two different things -- and that difference is what keeps the beautiful game beautiful.