Modelling the “Pop” in Winter Terrain Park Jumps

Epidemiological studies of injuries at ski resorts have found that jumping generally poses a significantly greater risk of spine and head injuries to patrons. Jumping activities in resorts are now focused in terrain parks over man-made features which provides an opportunity to mitigate injury rates through better engineering design. However, the use of engineering design has been questioned by the NSAA due to the issue of rider variability [1], a view implicitly supported in a recent paper by Shealy, et al. [2] who studied jumper trajectories for two terrain park jumps and reported no correlation between the takeoff speeds and landing distances. While their theoretical analysis was flawed, the undeniable fact remains that rider actions can substantially influence the trajectory. In particular riders can “pop”, i.e. jump (or drop) before takeoff, thereby changing the initial velocity in both direction and magnitude. In this paper I expand on an earlier Newtonian analysis to include this effect and use the field data of Shealy et al. to constrain the range of realistic “pop” speeds. I find that “pop” speeds in the range of −2.48 → +1.12 m/s account for the range of landing distances measured by Shealy, et al. Since the rider variability due to “pop” is bounded, similar Newtonian analyses can therefore provide bounds on the range of trajectories, landing positions, landing velocities, and equivalent fall heights which could be useful to winter terrain park designers.