Path instabilities of streamlined bodies

We study the trajectory and the maximum diving depth of floating axisymmetric streamlined bodies impacting water with a vertical velocity. Three different types of underwater trajectory can be observed. For a centre of mass of the projectile located close to its leading edge, the trajectory is either straight at low velocity or y-shaped at high velocity. When the centre of mass is far from the leading edge, the trajectory has a U-shape, independent of the initial velocity. We first characterize experimentally the aerodynamic properties of the projectile and then solve the equations of motion to recover the three types of trajectories. We finally discuss the transitions between the different regimes.