[[File:CornuSprialAnimation.gif|thumb|Animation depicting evolution of a Cornu spiral with the tangential circle with the same radius of curvature as at its tip, also known as an [[osculating circle]] (click on thumbnail to observe).]]
[[Image:Parabolic transition curve.JPG|thumb|240px|This sign aside a railroad (between [[Ghent]] and [[Bruges]]) indicates the start of the transition curve. A parabolic curve (''POB'') is used.]]
A '''track transition curve''', or '''spiral easement''', is a mathematically-calculated curve on a section of highway, or [[Tracktrack (rail transport)|railroad track]], wherein which a straight section changes into a curve. It is designed to prevent sudden changes in [[centripetal acceleration|lateral (or centripetal) acceleration]]. In planplane (i.e., viewed from above), the start of the transition of the horizontal curve is at infinite radius, and at the end of the transition, it has the same radius as the curve itself,thusand so formingforms a very broad spiral. At the same time, in the vertical plane, the outside of the curve is gradually raised until the correct degree of [[cant (road/rail)|bank]] is reached.
If such an easement were not applied, the lateral acceleration of a rail vehicle would change abruptly at one point –poin (the [[tangent|tangent point]] where the straight track meets the curve –), with undesirable results. With a road vehicle, the driver naturally applies the steering alteration in a gradual manner, and the curve is designed to permit this,that by using the same principle.
