Free kick goals in football: an unlikely success between failure and embarrassment

We develop and use an advanced numerical model to investigate the window of opportunity of free kicks in association football. The planar multibody forward dynamics model comprises a two segment leg model with joint actuations, a football, a wall and the turf. Contact mechanics is defined to model the impact of the foot and the ball's interaction with the different elements in the environment. The optimum kick is determined using the global optimization algorithm Differential Evolution, requiring millions of kick simulations. The sensitivity of various solutions to parameter perturbation is investigated.

It is concluded that toe kicks are theoretically superior to instep kicks, but are very difficult to perform reliably. The results also show that very small perturbations in parameters can lead to embarrassingly failed kicks.