Studies on the dynamics of a supercavitating projectile

Due to imperfect water entry, a high speed supercavitating projectile, while moving in the forward direction, rotates inside the cavity. This rotation leads to a series of impacts between the projectile tail and the cavity wall. The impacts affiect the trajectory as well as the stability of motion of the projectile. The present paper discusses the in-fiight dynamics of such a projectile. Equations of motion of the projectile are developed for two distinct phases of motion - Phase I: the projectile moves in the cavity without interaction with the cavity wall, and Phase II: the tail impacts on the cavity wall.The equations are found to be coupled and nonlinear. A simple model based on the concepts of flow planes is used to determine the forces acting on the projectile during impact. The effect of the mass distribution on the projectile dynamics is also studied. The results show that despite the impacts with the cavity wall, the projectile nearly follows a straight line path. The frequency of the impacts between the projectile tail and cavity boundary increases initially,reaches a maximum, and then decreases gradually. The results also indicate that the frequency of impacts decreases with the projectile's moment of inertia. It is also shown that the impact of the projectile with the cavity wall can be modelled as an impact with a rigid barrier with variable coefficient of restitution. A functional form of the coefficient of restitution is proposed, and it is shown that the proposed form predicts the impact behaviour quite well