Modelling the "Pop" in winter terrain park jumps - McNeil, J. A. (Skiing Trauma and Safety: 19th Volume, 2012)
Epidemiological studies of injuries at ski resorts have found that jumping generally poses a significantly greater risk of spine and head injuries to patrons than other actions. Jumping activities in resorts are now centered in terrain parks containing 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 National Ski Areas Association because of the issue of rider variability (Freestyle Terrain Park Notebook, National Ski Areas Association, Lakewood, CO, 2008), and this view was implicitly supported in a recent paper by Shealy et al. ["Jumper Kinematics on Terrain Park Jumps: Relationship between Takeoff Speed and Distance Traveled," J. ASTM Int., Vol. 7(10), 2010, pp. 1-10], who studied jumper trajectories for two terrain park jumps and reported no correlation between takeoff speeds and landing distances. Although their theoretical analysis was flawed, the undeniable fact remains that rider actions can substantially influence trajectory. In particular, riders can "pop," i.e., jump (or drop) before takeoff, thereby changing the initial velocity in terms of 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 to +1.12 m/s account for the range of landing distances measured by Shealy et al. Because the rider variability due to pop is bounded, similar Newtonian analyses can provide bounds on the range of trajectories, landing positions, landing velocities, and equivalent fall heights that might be useful to winter terrain park designers.