Impact dynamics of a flying soccer ball with consideration of variable characteristic of coefficient of restitution

This paper deals with the impact dynamics of a soccer ball. The trajectory of the ball is decided according to its initial velocity, launch angle, and some aerodynamic effect. Specially, the initial velocity is created by an instant impulse given to the ball. The external impulse exerted on a ball by a kicking robot is a function of the robot´s geometry and dynamic parameters. Here, the coefficient of restitution (COR) is an important parameter to calculate the impulse applied to the ball when the collision is occurred. Usually, COR has been assumed a constant value. We derive an analytical model of COR for the pendulum model colliding with a soccer ball, and show that COR varies according to the velocity. The drag force is taken into account in the COR model. The velocity-dependent characteristic of COR is applied to simulation of a soccer ball traveling a long distance. It is shown that the velocity-dependent COR considerably affects the traveling distance of the flying ball.