Soccer's free kick is one of the most dramatic moments in sport—a player strikes the ball with all his might, just 27 meters away from the goal keeper. Meanwhile, a trembling line of defenders stand shoulder to shoulder in front of him, trying to block the shot, and covering their crotches to protect themselves.
Highlight films from last month's World Cup soccer tournament in Korea and Japan show that a few players have found a way to score. They spin the ball as they kick it, so it bends in the air—like a baseball pitcher's curveball—and travels around the wall of defenders into the net. But how can players control the curve so precisely? Three groups of researchers have used wind tunnels, high-speed cameras, trajectory simulations, stress analysis, and computational fluid dynamics (CFD) to explain the effect.
British soccer star David Beckham's free kick can curve in mid-air, moving nine feet side-to-side and dropping three feet vertically in a sudden hook, as shown in this trajectory simulation by researchers at the University of Sheffield (U.K.).
The curve begins with the Magnus Force, a phenomenon that causes any spinning ball to move sideways as it goes through the air. That's because there's a high-pressure area on the side of the ball spinning against air flow, and a low-pressure area on the side spinning with the flow.
This force is fairly constant for much of the ball's flight, but has a much greater effect when the ball slows down, says Matt Carre, from the University of Sheffield's Sports Engineering Group. At that point, air flow around the ball changes from turbulent to laminar flow, boosting total drag by 150% almost instantly.
Carre and his team applied their theory by analyzing one of the game's most famous free-kicks: David Beckham's goal for England in an Oct., 2001 world cup qualifying game against Greece. Beckham's kick moved at 80 mph as it cleared the defenders by a foot and a half and continued to rise. It moved laterally about nine feet during that path, thanks to the enormous spin he put on it. Suddenly, it slowed to about 42 mph, and dipped sharply into the upper left corner of the net. Without that dip, it would have missed the goal entirely, Carre says.
A soccer ball can curve so radically because of its changing drag coefficient. Researchers at the University of Sheffield compared soccer and golf balls to a smooth sphere.
High-speed video testing confirmed the importance of ball spin. Takeshi Asai at Yamagata University (Japan), Sports Science Laboratory, used MSC.Patran (from MSC.Software, Santa Ana, CA) to analyze the stresses that deform both foot and ball at the point of impact. He showed that a ball struck 80 mm off-center will spin at eight rev/sec—twice as fast as a ball struck 40 mm off-center.
"The computer modeling techniques my group has developed will help us design better soccer [cleats] in the near term," Asai says. "This has important implications for preventing injuries to the foot, and could improve the overall understanding of the science of soccer."
That analysis is also supported by Fluent, a CFD company headquartered in Lebanon, NH. It's a complex problem for analysis, says Fluent's Keith Hanna. CFD programs typically analyze CAD models by building a theoretical mesh around them. But to handle the rapidly-changing drag and lift conditions of a spinning ball, researchers at the company's Belgium office built a hybrid mesh—prismatic shapes near the surface, and tetrahedral away from the ball.
The results showed a very thin boundary layer between air and ball, and helped provide an answer to soccer fans everywhere who ask "How did he do that?"
Soccer spin animations
free kick by Roberto Carlos of Brazil, in an April, 1998 world cup tune-up game
Beckham's free kick goal in an October 2001 world cup qualifying game between
England and Greece
animation of the same kick
Animation of air
flow around a ball
High speed film
of foot striking ball
foot imparting spin to ball during strike, w/ MSC.Patran
with MSC.Patran of foot and ball deformation
with MSC.Patran of skeletal and ball deformation
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