A design rationale for safer terrain park jumps that limit equivalent fall height

Ski jump landing surface shapes can be created to cushion jumper landing by specifying a value of equivalent fall height (EFH) but, because the shape is calculated by integrating a differential equation, an infinite number of solutions results from the arbitrary boundary conditions. This paper provides a natural rationale for selection of the least expensive (minimum snow budget) one of these that nevertheless satisfies other design constraints, mainly limited normal acceleration and jerk during approach and landing transitions. Choosing the maximum allowable normal acceleration during the approach transition brings the entire infinite family of landing surfaces as close as possible to the parent slope. Limiting the rate of change of normal acceleration (jerk) decreases the likelihood of loss of balance at takeoff and consequent catastrophic spinal cord injuries on landing. An analogous choice, satisfying limited normal acceleration during the landing transition, selects the single member of the infinite family (providing the desired EFH) that lies closest to the parent slope and is therefore least costly to build. Software in the form of a graphical user interface is described that implements these algorithms and is appropriate for inexperienced users to calculate design details before actual fabrication of landing surfaces at a specific jump site.