### STP1553: Modeling Terrain Park Jumps: Linear Tabletop Geometry May Not Limit Equivalent Fall Height

Swedberg, Andrew D.

*Dept. of Mathematical Sciences, United States Military Academy, West Point, NY*

Hubbard, Mont

*Professor, Mechanical and Aerospace Engineering, Univ. of California, Davis, Davis, CA*

Swedberg, Andrew D.

*MAJ, Dept. of Mathematical Sciences, United States Military Academy, West Point, NY,*

Hubbard, Mont

*Professor, Mechanical and Aerospace Engineering, Univ. of California, Davis, Davis, CA*

Pages: 16 Published: Nov 2012

**Abstract**

Terrain park tabletop jumps have a shape that is common at many ski areas today. A safe, low-impact landing on any jump with a constant linear landing area requires that the component of jumper velocity perpendicular to the landing surface be small, and when velocities are large, achieving this requires that the jumper flight path angle be nearly equal to the landing surface angle. Landing impact severity can alternatively be measured using the equivalent fall height (EFH). Based on Newton's laws and assumed ballistic flight, this research presents a general expression for the EFH experienced by a jumper when landing at any possible point on any landing surface whatsoever. This general expression is then particularized to show the effects on the EFH of the four physical features of a generic tabletop jump with a flat, horizontal deck and a constant linear landing region: the takeoff angle θ^{0}, the coordinates of the knuckle *xt* and *yt* where the intended constant-slope landing region begins, and the snow landing surface angle ϕ in this region. Numerical results show that tabletop jump EFHs have increasing and possibly large values near the ends of both the tabletop and the linear landing downslope portions. We conclude that tabletop jumps do not exhibit a low impulse on landing everywhere, which increases the likelihood of jumper injuries relative to those jumps for which the EFH is small everywhere.

**Keywords:**

terrain park, tabletop jump, skiing, snowboarding, landing impact

**Paper ID:** STP104335

**Committee/Subcommittee:** F27.30

**DOI:** 10.1520/STP104335

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