

Article
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 
AbstractA 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.

