An Optimal Oval

Abstract

SummaryIn designing horse race tracks and velodromes, clothoids, also called Euler spirals, have been used to achieve a smooth transition between straight and circular track segments. This is also a well-known technique for the construction of roads, railways, and roller coasters. Clothoids provide a steady increase in curvature, preventing participants from experiencing a “centripetal shock.” We suggest a track with a smoother curvature behavior, expressed by a single formula. We call the track optimal since the optimization criteria we apply might well agree with how participants would perceive track quality.