Una aproximación a la curva de transición Clotoide vista desde Mathematica

Abstract

Clothoids, also known as radius of curvature or Cornu spirals, take their name from the greek word Klotho, meaning, weaver. They are also widely used as transition curves in railroad or highway engineering for connecting and transiting the geometry between a tangent and a circular curve (to join straight sections with curve transitions or to connect two circular sections of different curvatures). This is their most relevant characteristic, since the radius of curvature diminishes in inverse proportion to the distance run over it, and that allows the driver to adapt slowly to the change in the trajectory. The new highways are designed including a series of clothoids with a large curvature which involves a greater visibility in the distance and easy adaptation to the track. In this paper we take into account the geometric property which defines clothoids and we obtain its equation from Fresnel integrals. Secondly, we represent the properties derived geometrically and obtain a numerical approximation of the clothoid. Finally, we use these approximations to present an example.