Track transition curve: Difference between revisions

Revision as of 14:09, 12 November 2018

Revision as of 15:01, 13 November 2018

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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, but the correct name (following standards of academic attribution) is 'the Euler spiral'.<ref>[http://www.glassblower.info/Euler{{Cite journal |last=Archibald |first=Raymond Clare |author-Spiral/AMM/AMM-1918.HTMLlink=Raymond Clare Archibald |date=June 1917 |title=Euler Integrals and Euler's Spiral--Sometimes called Fresnel Integrals and the Clothoide or Cornu's Spiral |url=http://www.]glassblower.info/Euler-Spiral/AMM/AMM-1918.HTML |journal=American Mathematical Monthly, Volume |volume=25 (1918),|issue=6 pp.|pages=276–282 276–282|via=Glassblower. Raymond Clare ArchibaldInfo}}</ref>

==Geometry==

{{unreferenced section|date=January 2010}}

While railroad [[track geometry]] is intrinsically [[three-dimensional space|three-dimensional]], for practical purposes the vertical and horizontal components of track geometry are usually treated separately.<ref>{{Cite web |url=http://www.engr.uky.edu/~jrose/RailwayIntro/Modules/Module%206%20Railway%20Alignment%20Design%20and%20Geometry%20REES%202010.pdf |title=Railway Alignment Design and Geometry |last=Lautala |first=Pasi |last2=Dick |first2=Tyler}}</ref><ref>{{Cite book |title=Practical Guide to Railway Engineering |last=Lindamood |first=Brian |last2=Strong |first2=James C. |last3=McLeod |first3=James |publisher=[[American Railway Engineering and Maintenance-of-Way Association]] |year=2003 |chapter=Railway Track Design |chapter-url=http://www.engsoc.org/~josh/AREMA/chapter6%20-%20Railway%20Track%20Design.pdf |archive-url=https://web.archive.org/web/20161130162616/http://www.engsoc.org:80/~josh/AREMA/chapter6%20-%20Railway%20Track%20Design.pdf |archive-date=November 20, 2016}}</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 [[quadratic 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.