Hydrodynamics and trajectory for vertical water entry of truncated head-type projectiles

A trajectory control method is proposed for the rapid leveling of the projectile after water entry through an asymmetric head-type design. The hydrodynamic and trajectory characteristics of truncated head-type projectiles were investigated using high-speed experiments and numerical simulations based on Reynolds-averaged Navier–Stokes (RANS) equations coupled with the volume of fluid (VOF) method. The effects of truncation angle and water-entry velocity were systematically examined. The results show that all truncated head-type projectiles exhibited rightward-deflected trajectories, with larger truncation angles producing greater lateral deviation and trajectory curvature. This behavior is attributed to asymmetric water impact, where non-uniform flow around the projectile generates distinct cavities at the head and tail, respectively, resulting in lateral forces and yaw moments. The initial impact induced sharp peaks in drag, lateral force, and yaw moment coefficients. As the projectile interacted with the cavity surface, projectiles with larger truncation angles experienced earlier cavity collisions and faster stabilization. In contrast, variations in water-entry velocity had little influence on centroid trajectories and hydrodynamic coefficients at comparable penetration depths. An empirical trajectory model was developed by decoupling the equations of motion to relate trajectory curvature to truncation angle. The model demonstrated excellent agreement with numerical results, providing a reliable predictive tool for the design and control of water-entry projectiles.