The Art of the Shot:
Modeling and Analysis of Free Kicks in Soccer Based on Initial Conditions
Soccer is a sport with a relatively simple goal- put the ball in the back of the other team’s net. However, it can be difficult to actually achieve that goal, so when players are afforded opportunities like free kicks (a spot-kick to restart or resume play with opponents 10 yards from the ball) close to goal, they need to be prepared to make the most of the chances they get. The most skilled strikers spend hours every week practicing their shots, varying initial conditions of the ball’s motion in order to make their shots almost impossible to stop. My project involves calculating trajectories of shots with varying initial conditions, including angular velocity, launch angle, and initial velocity that will affect the forces acting on them, most notably the Magnus Force. By using vector functions for forces acting on the ball as it travels through time and space in combination with kinematic equations of motion, I will map the trajectories of the shots through three-dimensional space and time. I will use these models, as well as data drawn from them, to determine things about soccer shots in general, including but not limited to what set of initial conditions puts the ball into the goal fastest or slowest and what set lets the ball fly the farthest or shortest, in both space and time.