Free Kick Physics

Roberto Carlos, a Brazillian defender famous for belting free kicks with incredible control (as opposed to Beckham who tended to go for placement over power), hit a pretty memorable free kick against France in the 1998 World Cup. The video is below.

The kick seems to defy the laws of physics. So some scientists have built an equation to explain it. Their work has just been published.

“We discuss the trajectory of a fast revolving solid ball moving in a fluid of comparable density. As the ball slows down owing to drag, its trajectory follows an exponential spiral as long as the rotation speed remains constant: at the characteristic distance where the ball speed is significantly affected by the drag, the bending of the trajectory increases, surprisingly. Later, the rotation speed decreases, which makes the ball follow a second kind of spiral, also described in the paper. Finally, the use of these highly curved trajectories is shown to be relevant to sports.”


Image Credit: Wired Magazine’s story on the study.

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