Soccer balls curved and swerved through the air in the 2006 FIFA World Cup as players worked to confuse opposing goalkeepers and send the balls to the back of the net. Among world-class soccer players who have perfected the "bending" of a ball from a free kick are Brazil's Roberto Carlos, Germany's Michael Ballack, and England's David Beckham.

Recent results in computational fluid dynamics from the University of Sheffield's Sports Engineering Research Group and Fluent Europe indicate that the shape and surface of a soccer ball, as well as its initial orientation, play a fundamental role in the ball's trajectory through the air. In particular, the CFD researchers have increased understanding of the "knuckleball" effect, a technique sometimes used to confuse an opposing goalkeeper. The research group focused on shots resulting from "free kicks," in which the ball is placed on the ground, as after a foul.

Figure 1. An important step in CFD simulations at the University of Sheffield is capturing the geometry of a soccer ball with a 3D non-contact laser scanner. This mesh has approximately 9 million cells.

To facilitate such results, a soccer ball was digitized down to its stitching, as shown in Figure 1. Especially important is the refinement near the seams, which is required for proper modeling of the boundary layer. Since 1970, Adidas has produced the official ball for the World Cup competition, which is held every four years. From this set of soccer balls, the researchers selected four balls with different panel designs for scanning. Among the digitized balls was the new Adidas Teamgeist ball used in the 2006 World Cup.

A free kick in soccer can have an initial velocity of almost 70 mph. Wind tunnel experiments have demonstrated that air flow around a soccer ball transitions from laminar to turbulent at speeds between 20 and 30 mph, depending on the surface structure and texture of the ball. (See Figures 2 and 3.)

Figure 2. Left: Wind tunnel smoke test of a non-spinning soccer ball. Right: CFD stimulation showing wake-flow pathlines of a non-spinning soccer ball; air speed is 27 mph.

 

Figure 3. High-speed air-flow pathlines colored by local velocity over the 2006 Teamgeist soccer ball.

The techniques developed in Sheffield facilitated detailed analysis of a memorable goal scored by David Beckham of England in a match against Greece during the World Cup qualifiers in 2001. A foul on an English player resulted in a free kick about 29 yards from the goal. A group of defenders was standing side by side on the field between the ball and Greece's goal. Beckham's shot left his foot at about 80 mph. The ball cleared the defensive wall by about one and a half feet, rising above the height of the goal. As it ended its flight, the ball slowed to 42 mph and dipped into the corner of the net. Calculations showed that the flow around the ball transitioned from turbulent to laminar several yards from the goal; otherwise, the ball would have missed the net and gone over the goal's crossbar.

In a sense, Beckham's kick represents a sophisticated application of physics. Although the CFD simulations at Sheffield can accurately model only turbulent flow that has been averaged over time, and as such cannot detect vortex shedding, such research could affect soccer players, from beginner to professional. For instance, ball manufacturers could exploit such results to produce more consistent or interesting balls, possibly tailored to the needs and levels of different groups of players. Such work could also affect the training of players.

To this end, researchers at the University of Sheffield have developed a simulation program called Soccer Sim. The program predicts the flight of a ball from given input conditions, which can be acquired from the CFD and wind tunnel tests, as well as from high-speed videotapes of actual players' kicks. The software can then be used to compare the trajectories of a ball with varying initial orientations or with different spins induced by the kick. The trajectories of different soccer balls can also be compared.

Scientists have been studying the aerodynamics of sports balls at least since Newton commented on the deviation of a tennis ball in his paper "New Theory of Light and Colours," which was published in 1672.

The impact of the CFD research briefly described here will be seen only with time. The work may well give new insight into ways to bend a soccer ball--regardless or possibly because of its design.

Acknowledgments
Images courtesy of Fluent Inc. and the University of Sheffield.

Sarah Barber received a master's degree in mechanical engineering jointly from Cambridge University and MIT; for her thesis, she studied air flow around speed skaters using CFD. An avid football player who plays for the Sheffield Ladies FC, she is currently completing a doctorate at the University of Sheffield in the Sports Engineering Research Group. Tim Chartier, an assistant professor of mathematics at Davidson College, frequently collaborates with research scientists at Lawrence Livermore and Los Alamos National Laboratories. Once an avid soccer player, he currently plays the game with his four-year-old son.