Free Kick Parameter Study

A computational model is developed to determine the success rate of a free kick, which refers to the probability of scoring an unassisted goal from a free kick. Four-dimensional parameter space volumes are used to determine success rates. It has been found that one out of ten free kicks is successful. Our paper looks at one of the scoring opportunities, the free kick, and presents a mathematical model to illustrate it. To determine a realistic estimation of the probability of an unassisted goal being scored by a free kick, this study aims to determine reasonable estimates. The model is described in terms of the geometry and flight dynamics of the soccer ball. We present findings based on a computational analysis of successful and total kicks parameter space ratios. The flight simulation of a soccer ball takes into account gravity, drag due to air resistance, Magnus force due to spin, and Newton s second law to derive the dynamic equations of motion and determine the trajectory of the soccer ball. The goal of a free kick is to score without the assistance of a teammate. We place the wall on the left side of the goal and allow the goalkeeper to defend the right half. Four parameters determine the trajectory of a kick: the initial speed of the ball, its rotational speed, its angle of launch, and its azimuthal angle. After establishing a reasonable set of ranges for them, we construct a four-dimensional parameter space volume that contains each point representing a different kick. Our parameter space represents the number of kicks by the number of discrete points. In the second step of our analysis, we determine the fraction of the volume of the parameter space that is occupied by good kicks after all kicks have been evaluated and good kicks have been counted. Two factors determine this fraction: the number of successful kicks and the total number of kicks. Among all free kicks, ۹.۶۳% hit their target. For each of the four parameters, we have used ranges that are reasonable representations of the error ranges that may occur in free kicks performed by professional soccer players. By comparing these ranges with the total kick parameter space volume, we were able to determine the likelihood of success. A future study will focus on how best to weigh each parameter.

کلیدواژه ها:

soccer ، free kick ، dynamic modeling ، aerodynamic forces ، four-dimensional parameter space