Track transition curve: Difference between revisions

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Revision as of 17:29, 16 April 2016

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[[File:CornuSprialAnimation.gif|thumb|Animation depicting evolution of a Cornu spiral with the tangential circle with the same radius of curvature as its tip (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 [[Track (rail transport)|railroad track]], where a straight section changes into a curve. It is designed to prevent sudden changes in [[centripetal acceleration|lateral (or centripetal) acceleration]]. In plan (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, thus forming 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 [[Cantcant (road/rail)|bank]] is reached.

If such easement were not applied, the lateral acceleration of a rail vehicle would change abruptly at one point – 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, using the same principle.

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The equivalence of the railroad transition spiral and the [[clothoid]] seems to have been first published in 1922 by Arthur Lovat Higgins.<ref name="higgins"/> Since then, "clothoid" is the most common name given the curve, even though the correct name (following standards of academic attribution) is "the Euler spiral".<ref>[http://www.glassblower.info/Euler-Spiral/AMM/AMM-1918.HTML Euler Integrals and Euler's Spiral--Sometimes called Fresnel Integrals and the Clothoide or Cornu's Spiral.] American Mathematical Monthly, Volume 25 (1918), pp. 276 - 282276–282. Raymond Clare Archibald</ref>

==Geometry==

{{unreferenced section|date=January 2010}}

While railroad [[track geometry]] is intrinsically [[Threethree-dimensional space|three-dimensional]], for practical purposes the vertical and horizontal components of track geometry are usually treated separately.<ref>http://www.engr.uky.edu/~jrose/RailwayIntro/Modules/Module%206%20Railway%20Alignment%20Design%20and%20Geometry%20REES%202010.pdf</ref><ref>http://www.engsoc.org/~josh/AREMA/chapter6%20-%20Railway%20Track%20Design.pdf</ref>

The overall design pattern for the vertical geometry is typically a sequence of constant grade segments connected by vertical transition curves in which the local grade varies linearly with distance and in which the elevation therefore varies [[Quadraticquadratic equation|quadratically]] with distance. Here grade refers to the tangent of the angle of rise of the track. The design pattern for horizontal geometry is typically a sequence of straight line (i.e., a [[tangent]]) and curve (i.e. a [[circular arc]]) segments connected by transition curves.

The degree of banking in railroad track is typically expressed as the difference in elevation of the two rails, commonly quantified and referred to as the [[superelevation]]. Such difference in the elevation of the rails is intended to compensate for the [[centripetal acceleration]] needed for an object to move along a curved path, so that the lateral acceleration experienced by passengers/the cargo load will be minimized, which enhances passenger comfort/reduces the chance of load shifting (movement of cargo during transit, causing accidents and damage).

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== See also ==

* [[Degree of curvature]]

* [[Euler spiral]]

* [[Minimum railway curve radius]]

* [[Railway systems engineering]]