Generating football C_d profiles without a wind tunnel

摘要

Wind tunnels have been used extensively to obtain the aerodynamic characteristics of many objects, including sports balls. However, as an expensive piece of equipment, wind tunnels are not always appropriate. This paper describes a method which was used to obtain a football's coefficient of drag (C_d) profile without the use of a wind tunnel. A football was launched at a variety of velocities and its flight recorded with high speed video cameras in 2D. An aerodynamic model was used to generate a series of displacements to compare with the recorded trajectories. In order to simulate aerodynamic drag, a sigmoid function was developed which mimics the shape of a typical aerodynamic profile. A simplex optimisation process was used to generate a number of C_d profiles which result in a minimum error between the modelled and recorded displacements. It was found that the ball had a C_d of around 0.275 in the turbulent regime and 0.525 in the laminar.