Lesson #231: The Physics of the Bent Ball

Autobiographical note: It’s actually kind of funny that this should be today’s lesson because I had a dream last night involving Diego Forlan and Slavia Prague’s (for whom Diego Forlan does not play, so I’m not quite sure how the two things are related) not-so-new-anymore stadium, Eden. A bunch of friends too, but they were sort of incidental to the whole thing.

I read about six different football blogs. And all but one of them has linked to this story today. I expect the last will follow before the day is out.

A team of physicists in Paris, in an article entitled “The Spinning Ball Spiral” published today in the New Journal of Physics, have analyzed the effects of spin and drag on a ball and concluded that, “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 L where the ball speed is significantly affected by the drag, the bending of the trajectory increases.”

The study specifically addresses the ability of footballers like David Beckham (most famously) and Roberto Carlos (most incredibly) to curl a free kick and the physics that allows for the movement of the ball. The team was able to verify the long-known Magnus effect (which is responsible for the curved trajectory of a spinning ball over a short distance — 80′ or less — like a free kick in football or the curveball in baseball) and examine the trajectory of a spinning ball over a longer distance like Carlos’ free kick, which was taken at 115′). What they found was that, “when shot from a large enough distance, and with enough power to keep an appreciable velocity as approaching the goal, the ball can have an unexpected trajectory.” In addition, “provided that the shot is powerful enough, another characteristic of Roberto Carlos’ abilities, the ball trajectory brutally bends towards the net, at a velocity still large enough to surprise the keeper.”*

*Quoted text is from the article “The Spinning Ball Spiral” by Guillaume Dupeux, Anne Le Goff, David Quéré
and Christophe Clanet, New Journal of Physics Volume 12, the text of which can be found here.

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