Three collaborating groups of researchers have unraveled some of the underlying mysteries of bending a soccer ball during a kick.

Researchers at the University of Sheffield in England, at Yamagata University in Japan, and at Fluent Inc. in Lebanon, N.H., have done scientific and engineering analysis of the soccer ball bend.

The technique of bending the flight of a soccer ball during a free kick may often mean the difference between victory and defeat. A ball that is kicked from a dead stop can move in one direction, then bend to another direction. The phenomenon is due to the way air flows over the spinning ball.

The researchers used a combination of wind-tunnel experiments, high-speed video camera analysis, trajectory simulations, and computer modeling techniques to explain what happens when a soccer ball bends during a free kick.

Takeshi Asai of Yamagata University's Sports Science Laboratory used MSC.Patran, a product of MSC.Software of Los Angeles, to model the stress and deformation of the foot and ball as the player strikes the ball. This simulation was combined with computational fluid dynamics research done by Fluent, and with wind tunnel and trajectory studies done by Matt Carré of the University of Sheffield's Sports Engineering Research Group.

Researchers used scientific and engineering analyses to unravel the physics behind the elite soccer players' soccer-ball bend.

The research may give soccer ball manufacturers better insight into how to design their products, Carré said. It may also help soccer players train and improve their techniques.

Roberto Carlos of Brazil, David Beckham of England, and Michael Ballack of Germany are particularly noted for bending the ball.

In the 1 to 1.5 seconds it takes for a soccer free kick to reach its end point, the ball experiences some very complex physics, said Keith Hanna, marketing communications director at Fluent. The university researchers used the company's CFD software to simulate the flow pathlines around the soccer ball.

"It amazes me that elite soccer players do what they do on a free kick instantaneously and under immense pressure in critical games," Hanna said.

"Their brains must be computing some very detailed trajectory calculations in a few seconds purely from instinct and practice. Our computers take a few hours to do the same thing, and although we can now better explain the science of what they do, it's still magical to watch."

The research team specifically studied Beckham's legendary goal against Greece that put England into the 2002 World Cup tournament.

High-speed cameras showed that Beckham accelerated the ball to 80 miles per hour, after hitting it about 8 centimeters to the right of its center with the instep of his right foot. The ball spun counterclockwise at about eight revolutions per second and started swerving to the left. The ball rose into the air as if it would soar over the goal's crossbar. Then, it slowed to 40 mph, curved further to the left, and dropped into the top left corner for the goal.

To study the forces that act on a flying soccer ball, Carré placed the soccer ball inside a wind tunnel. Changing the speed of the airflow in the tunnel allowed him to measure drag and lift forces acting on the ball.

He discovered that airflow changes when the ball travels below a certain speed. At fast speeds, it experiences turbulent airflow. When it drops below about 23 mph, however, the airflow becomes laminar.

Carré said that when airflow around Beckham's free kick changed from turbulent to laminar, the drag on the ball increased 150 percent in about one second. That caused the ball to slow down suddenly and to drop into the net.

This change from turbulent to laminar airflow, produces the sudden dips of the best free kicks as the ball approaches the goal, Carré said.

The spinning ball moves sideways as it travels because of a phenomenon known as the Magnus force. On the side of a spinning ball moving through the air with rotation and airflow in the same direction, the airspeed increases and pressure decreases. But on the opposite side of the ball, airspeed decreases and pressure increases. The imbalance of pressures produces the Magnus side force, which is quite pronounced at the ends of the ball's flight.

The balance of sideways force and drag force stays about the same for most of the ball's trajectory, but changes a great deal near the goal as the flow around the ball changes, causing it to dip and bend.

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