Fresnel Integrals and Euler Spirals in the Construction of Track Transition Curves

by Trent Callahan

Submitted : Spring 2017

In order to connect a straight line and an arc together, one will need a transitional curve. In order to model this curve most efficiently, Euler Spirals can be employed due to their linear properties - specifically that the curvature of the spiral (1/R) increases linearly with its length. In order to determine the values of the coordinates of Euler Spirals, it is necessary to compute some special integrals (called Fresnel integrals). These integrals cannot be computed using the Fundamental Theorem of Calculus, so we will make use  of the Taylor series expansion to provide estimates. The purpose of this project is to describe how to go about determining the ideal transitional curves, applicable to a range of different scenarios, using concepts familiar to engineering students.

[ Back ]