## Influence of Elliptical Arcs on Half-Pipe Performances |

**Peter Bonventre, Steven Neier, Erik Skorina**

2011 Union College Mathematical Contest in Modeling team

May 16, 2011

4:30 pm

Bailey Hall 207

Refreshments will be served in Bailey 204 at 4:15

A half-pipe is a symmetrically curved slope used by snowboarders to perform aerial tricks. The effectiveness of a half-pipe design is typically determined by the height that snowboarders achieve above the far edge of the half-pipe. In the Mathematical Contest in Modeling, we analyzed the change in velocity of a snowboarder in a half-pipe. This was accomplished by iteratively calculating the potential and kinetic energies as well as the work done by friction. This process allowed us to determine the velocity of the snowboarder at the far edge of the half-pipe. This enabled us to determine the optimal dimensions and curvature for a half-pipe in order to optimize the vertical air obtained by a snowboarder. Additionally, we considered the effect of slope, approach angle, and initial velocities of a snowboarder on our optimizations.

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