Shuttlecock dynamics

We study experimentally the dynamics of shuttlecocks. We show that their trajectory is completely different from classical parabola: for a same launch, the flight of the shuttlecock quickly curves downwards and almost reaches a vertical asymptote. We solve the equation of motion with gravity and drag at high Reynolds number and find an analytical expression for the range. At high velocity, this reach does not depend on the velocity anymore. This phenomenon, that we call the "aerodynamic wall", is highly observable in badminton. Then we study how the shuttlecock shape influences the badminton game. The shuttlecock always flies the nose forehead, which means after the impact it has to flip. Actually it returns, oscillates and then stabilizes. We understand these damping oscillations by distinguishing the mass and aerodynamic center of a shuttlecock.