Mathematics Colloquia and Seminars
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Safe Ski Jump Landing Slope DesignMathematical Biology
|Speaker: ||Mont Hubbard, Sports Biomechanics Lab, UC Davis|
|Location: ||2112 MSB|
|Start time: ||Mon, Apr 21 2008, 4:10PM|
Skiing has evolved to become more acrobatic, with the use of terrain park jumps and other features playing a prominent role in an increase in serious spinal cord injuries. Yet these jumps are rarely, if ever, designed or engineered. This paper presents a coherent methodology for the design of ski jump landing surfaces. Landing impact severity is characterized by skier velocity perpendicular to the slope Vp or, more understandably, equivalent fall height (EFH). The requirement that EFH be small is satisfied by making the landing surface slope nearly equal to the skier flight path slope at landing. Safe landing surfaces are shown to satisfy a first order ordinary differential equation (ode). Having chosen an EFH deemed safe enough, 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 a design variable, it is possible to choose one member of this family to fit on almost any available jump site. The formulation incorporates the fact that skiers can modify velocity direction and magnitude at takeoff by jumping. Such "safe" surfaces can still yield exhilarating flight experiences with relatively long flight times and large air height above the surface before landing, but without the danger posed by jumps created in an ad hoc manner.