Predicting kinematics and hydrodynamic loading using spray root propagation in wedge water entry

The water entry phenomenon has a wide range of applications in various engineering disciplines, including marine, mechanical, and aerospace engineering fields. In marine engineering, understanding wedge water entry is crucial for the design and safety assessment of high-speed planing craft. Existing theoretical models are developed to estimate hydrodynamic loads during the impact; however, these often rely on rigid body assumptions and constant-entry velocity, limiting their accuracy for flexible structures and realistic impact scenarios. This paper introduces a novel hybrid approach that integrates experimentally measured spray root propagation with re-derived theoretical models to predict hydrodynamic pressure and wedge kinematics during water entry. The method is validated through a case study involving the free fall impact of a flexible wedge, where analytical models are re-derived to account for velocity loss and match experimental conditions. The hybrid approach, particularly when combined with the re-derived Armand and Cointe model, accurately estimates the hydrodynamic impact pressure with errors in peak pressure location and magnitude within 2% and 7%, respectively. When compared with the pure theoretical approaches, the hybrid approach also shows superior performance in predicting hydrodynamic pressure data. This work establishes a foundation for advanced hydrodynamic analysis of highly flexible structures, enabling future applications in early-stage design of small craft and in situ pressure measurement for planing hulls.