Euler Spiral

An Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the radius). Euler spirals are also commonly referred to as spiros, clothoids or Cornu spirals.

Euler spirals have applications to diffraction computations. They are also widely used as transition curve in railroad engineering/highway engineering for connecting and transiting the geometry between a tangent and a circular curve. The principle of linear variation of the curvature of the transition curve between a tangent and a circular curve defines the geometry of the Euler spiral:

• Its curvature begins with zero at the straight section (the tangent) and increases linearly with its curve length.
• Where the Euler spiral meets the circular curve, its curvature becomes equal to that of the latter.