A novel approach for computing planing forces of cavity-riding bodies

Immediately after impact on the water surface, a body develops a cavity and is supported by its nose, behaving like an inverted pendulum. As the dynamics evolve, the body rotates and eventually strikes the cavity wall, generating an unsteady planing force that dominates the subsequent trajectory. Existing models accurately capture the pre-planing dynamics but fail to describe this cavity-riding regime, where complex fluid-body interactions arise. To address this gap, we combine simplified CFD simulations and experimental measurements to systematically investigate how the planing forces depend on the body’s angle and rotation rate relative to the cavity surface. By assuming quasi-steady behavior, we derive a semi-empirical model that normalizes the force response across a wide range of geometries and dynamic conditions. Our results reveal that these forces can be scaled using simple analytical relationships, allowing trajectory predictions without the need for computationally intensive coupled CFD and rigid-body simulations. This model provides a practical tool for the design and analysis of cavity-riding bodies operating in dynamic water entry environments.