Cristiano Ronaldo, David Beckham and Roberto Carlos might not be NASA scientists but they implicitly understand how to curve a soccer ball. It’s the best way to get the ball past defenders standing in the way of the goal and to confound the goalkeeper, who expects the ball to take one track and then must react to an unpredicted swerve. Real-life NASA scientists, eager to find intriguing examples of practical physics to educate the public, look in detail at why a kicked soccer ball takes a curved path.
The Kicker
Ronaldo and his fellow soccer artistes are known as free-kick specialists. “For them, a wall means nothing,” writes Iain Macintosh in “Everything You Ever Wanted to Know About Football But Were Too Afraid to Ask,” referring to the row of two or more defenders that line up to impede the path of a free kick. You don’t have to be a professional to curve a free kick. High school and younger players can begin to work on the curve by kicking the ball, toes pointed down so the laces provide contact, slightly off-center.
The Kick
The off-center kick provides spin on the ball, important to creating the curve. The follow-through can determine the type of spin. Swinging the leg across the front of your body provides side spin for a swerve or banana kick as the curve is variously known. Punching the ball with a straight ahead follow through can make it drop suddenly, an effect called knuckling that also leaves the goalie clasping at air. Ronaldo has produced kicks that knuckled or kicked down not just once but twice, including a goal in 2006 versus Fulham, write the authors of a chapter on soccer ball dynamics in “Computational Fluid Dynamics for Sport Simulation.”
The Airflow
As the ball spins, its basic motion and to an extent the seams that hold together its panels create anomalies in the airflow. Aerodynamic forces then cause the ball to bend in the air. The forces can be predicted by an equation that inputs the radius of the ball, its spin, the velocity of the kick, the density of the air and a lift coefficient determined by experimentation, according to NASA.
The Curve
The forces that act on the ball deflect it from the path that its initial location and speed would otherwise have predicted. In simplified terms, the force operates to push the ball perpendicularly. Thus, instead of following a straight path, it follows a curved path ideally designed to make the keeper think it is going wide and then curls at the last instant just inside the goalpost or just underneath the crossbar. The radius of the curvature depends on the strength of the side forces interacting with the velocity of the kick. Even if Ronaldo can’t write the formulas based on Newton’s law, he intuits how to apply the force of the kick to obtain the desired effect. He's bound to figure out that a harder kick creates higher velocity, which produces a relatively straighter curve, and higher spin produces a sharper curve.
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