Also known as clothoids, spiros or Cornu spirals They are curves whose curvature changes linearly with curve length (curvature of a circular circle is the reciprocal of it’s radius) eg: Railway tracks where the curve changes into a straight track

Derived using Fresnel Integrals

Usages

Track Transition Curves Used in Optics to describe diffraction patterns Rollercoaster clothoids Velodromes (bicycle curves) - for rapid entry and gradual exit

Tags: Jerk clothoids