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

Authors: Nordmark, A., Essén, H.
Document Type: Article
Pubstate: Published
Journal: European journal of physics
Volume: 31   1307 - 1317
Year: 2010


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.