Bending a Soccer Ball with CFD
By Sarah Barber and Timothy P. Chartier
SIAM News, August 2007
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.
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.)
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.
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.