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arXiv · 1007.1394

The comfortable roller coaster -- on the shape of tracks with constant normal force

Arne B. Nordmark·Hanno Essen
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Abstract

A particle that moves along a smooth track in a vertical plane is influenced by two forces: gravity and normal force. The force experienced by roller coaster riders is the normal force, so a natural question to ask is: what shape of the track gives a normal force of constant magnitude? Here we solve this problem. It turns out that the solution is related to the Kepler problem; the trajectories in velocity space are conic sections.

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Arne B. Nordmark, Hanno Essen. 2010-07-08. The comfortable roller coaster -- on the shape of tracks with constant normal force. https://doi.org/10.1088/0143-0807%2F31%2F6%2F001

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