Characterisation of football trajectories for assessing flight performance

Abstract

Much discussion surrounds the flight of association footballs (soccer balls), particularly where the flight may be perceived as irregular. This is particularly prevalent in high-profile competitions due to increased camera coverage and public scrutiny. All footballs do not perform in an identical manner in flight. This article develops methods to characterise the important features of flight, enabling direct, quantitative comparisons between ball designs. The system used to generate the flight paths included collection of aerodynamic force coefficient data in a wind tunnel, which were input into a flight model across a wide range of realistic conditions. Parameters were derived from these trajectories to characterise the in-flight deviations across the range of flights from which the aerodynamic performance of different balls were statistically compared. The amount of lateral movement in flight was determined by calculating the final lateral deviation from the initial shot vector. To quantify the overall shape of the flight, increasing orders of polynomial functions were fitted to the flight path until a good fit was obtained with a high-order polynomial indicating a less consistent flight. The number of inflection points in each flight was also recorded to further define the flight path. The orientation dependency of a ball was assessed by comparing the true shot to a second flight path without considering orientation-dependent forces. The difference between these flights isolated the effect of orientation-dependent aerodynamic forces. The article provides the means of quantitatively describing a ball’s aerodynamic behaviour in a defined and robust mathematical process. Conclusions were not drawn regarding which balls are good and bad; these are subjective terms and can only be analysed through comprehensive player perception studies.