Aerodynamics in sports has been studied ever since Newton commented on the deviation of a tennis ball in his paper New theory of light and colours published in 1672. Today, the field of computational fluid dynamics (CFD) studies the effect of aerodynamics in such sports as soccer and NASCAR racing. See Figure 18.1.

Soccer matches are filled with complex aerodynamics as evidenced in the way balls curve and swerve through the air. World class soccer players such as Brazil's Roberto Carlos, Germany's Michael Ballack, and England's David Beckham exploit such behavior, especially in a free kick.

According to research by the University of Sheffield's Sports Engineering Research Group and Fluent Europe Ltd., the shape and surface of a soccer ball, as well as its initial orientation, play a fundamental role in its trajectory. CFD research has increased the understanding of the flight of a knuckleball, which is kicked so as to minimize the spin of the ball and to confuse a goalkeeper. The research group focused on shots resulting from free kicks, in which the ball is placed on the ground after a foul, for instance.

Calculating the trajectories of objects is a common problem in calculus where the absence of air resistance is generally assumed. Drag forces affect the path of a soccer ball and are of two main types: skin friction drag and pressure drag. Skin friction drag occurs when air molecules adhere to the surface of the ball, which results in friction from the interaction of the two bodies.