Stability of Coupled Human and Stand Up Paddle Board

Abstract

This study investigates the rider stability on a stand up paddle board (SUP) based on board dimensions, rider body parameters and skill level using a buoyant body dynamics approach. Although the industry provides board volume recommendations for users accounting for their parameters and skill level, further examination reveals the recommendations differ from one vendor to the other. For this thesis, the system of a rider standing on a SUP is modeled as a planar motion of a rectangular cross-section buoyant body attached with an added mass at a fixed height. The stability condition of the upward equilibrium is derived in analytic equations. Furthermore, the stability map is developed to visualize stability region for system parameters. With the stability map, a new approach of describing user skill level is proposed and compared to the current industrial experience. Lastly, wave tank experiment is conducted to verify the analytic equations. A full-scale experiment explores future applications in real SUP products. Analytical results of the rectangular board show the same trend as the experimental results from a real SUP product. The results of this thesis show that eigenvalue contours may be used to present more uniform and objective rider skill levels than qualitative terms, such as, beginners and professional. Future studies on modeling elliptical buoyant body dynamics and estimating hydrodynamics effects in short aspect ratio will benefit the application in this field.