(Received 7 December 2007; accepted 18 November 2008)
Published Online: 2008
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Skiing and snowboarding have become more acrobatic with terrain park jumps and other manmade features playing a prominent role in an increase in serious spinal cord injuries. Yet these jumps rarely, if ever, involve formal or detailed design or engineering. This paper presents a coherent theory and methodology for the design of ski jump landing surfaces. The motion of the skier center of mass is modeled. Although jumpers may land in many configurations, we assume that the probability of severe landing injury is correlated with the component of skier velocity perpendicular (normal) to the landing surface v⊥ or, more understandably, with the corresponding equivalent fall height (EFH). The requirement that v⊥ and EFH be small is satisfied by making the landing surface nearly parallel to the skier flight path at landing. Safer landing surfaces that limit EFH to a given value are shown to satisfy a first order ordinary differential equation (ODE). Having chosen an EFH deemed safe enough by the designer, integration of this ODE provides members of an infinite family of landing surfaces that limit the EFH to the desired value, for any jumper in-run velocity. Using the takeoff ramp angle as another design variable, one can choose a member of this family to fit on almost any available jump site. The formulation incorporates the fact that skiers can slightly modify velocity direction and magnitude at takeoff by jumping and is valid for any landing body configuration. Such landing surfaces can still yield exhilarating flight experiences with relatively large flight times and air height above the surface, but without the danger posed by jumps created in an ad hoc manner, which can expose the skier to much larger unsafe equivalent fall heights.
Sports Biomechanics Laboratory, Department of Mechanical and Aeronautical Engineering, University of California, Davis, CA
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