Modelling the long throw in soccer using aerodynamic drag and lift.

The long throw in soccer has received little detailed bio mechanical investigation despite the strategic importance of this attacking option. Previous studies have attempted to correlate maximum length of throw with important input variables such as ball release speed and launch angle. In these treatments, ball flight is modelled using 'simple projectile' theory (gravity only). Reasonable agreement with measured ranges is quoted but this is seen to be fortuitous when aerodynamic drag is introduced, calculated ranges then falling short of measured values. Modelling the flight more precisely involves consideration of aerodynamic drag and lift, the latter force arising from backspin applied to the ball in the throwing action. In this paper the flight equations incorporating gravity, drag and lift (Magnus) forces are formulated and solved numerically. The results are compared with the earlier work and good agreement is found between the model and reported ranges, for realistic values of the drag and lift coefficients. Fine-tuning of the model has been achieved by using the results of a series of carefully measured throws, where the influence of backspin in the thrower's action has been quantified. The results show that ball release velocity, launch angle and spin are key parameters in achieving maximum length of throw. Optimum launch angles are found to differ appreciably from simple projectile motion when drag and lift are present. [ABSTRACT FROM AUTHOR]