Safer Ski Jumps: Design of Landing Surfaces and Clothoidal In-Run Transitions

摘要

This thesis explores the recent rise of skiing and snowboarding injuries from jumps fabricated with no scientific design process. It summarizes a previous method to develop a first order ordinary differential equation (ODE) for the landing surface shape, based on kinematics and dynamics, which limits the equivalent fall height (EFH) on landing. These are compared with theoretical expressions for EFH in tabletop jumps, which are shown to have linearly increasing and possibly large EFH values near the ends of the tabletop and linear landing surface portions. Finding solutions to the ODE is explored, with a large emphasis on determining the singular point where the ODE numerical integration can begin. Analysis is conducted to determine a good way to design a curved in-run transition portion of the jump that limits the additional centripetal acceleration on a particle undergoing the required velocity change of direction of a given amount. This turn can be accomplished using a unique curve known as a clothoid, which minimizes jerk along the path. The final topics include a plan for providing maintenance for safe terrain park ski jumps, and an algorithm that will assist a manager in planning where and how to build a jump.