Track transition curve: Difference between revisions

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{{Short description|Mathematically-calculated curve in which a straight section changes into a curve}}

[[Image:Easement curve.svg|thumb|The red [[Euler spiral]] is an example of an easement curve between a blue straight line and a circular arc, shown in green.]]

[[File:CornuSpiralAnimation.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|This sign aside a railroad (between [[Ghent]] and [[Bruges]]) indicates the start of the transition curve. A [[parabolic curve]] (''POB'') is used.]]

A '''transition curve''' (also, '''spiral easement''' or, simply, '''spiral''') is a spiral-shaped length of highway or [[track (rail transport)|railroad track]] that is used between sections having different profiles and radii, such as between straightaways ([[tangent]]s) and curves, or between two different curves.<ref name="pwayblog">{{Cite web |last=Constantin |date=2016-07-03 |title=The Clothoid |url=https://pwayblog.com/2016/07/03/the-clothoid/ |access-date=2023-06-07 |website=Pwayblog}}</ref>

A '''track transition curve''', or '''spiral easement''', is a mathematically-calculated curve on a section of highway, or [[track (rail transport)|railroad track]], in which a straight section changes into a curve. It is designed to prevent sudden changes in [[centripetal acceleration|lateral (or centripetal) acceleration]]. In plane (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 and so forms 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.

{| class="wikitable" style=width:200px

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! Centripetal force on vehicles on roads without and with a transition curve

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| [[File:Straight-circle.gif|frameless|upright=1.2|center]] Straight sections of road connected directly by a circular arc. |

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| [[File:Straight-cornu.gif|frameless|upright=1.2|center]] Straight section connected to a circular arc via a Cornu spiral|

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| Comparison of a poorly designed road with no transition curve with the sudden application of centripetal force required to move in a circle versus a well-designed road in which the centripetal acceleration builds up gradually on a Cornu spiral before being constant on the circular arc. The second animation shows the increasing curvature of the transition curve which is able to connect to a circular arc of progressively smaller radius.

|}

In the horizontal plane, the radius of a transition curve varies continually over its length between the disparate radii of the sections that it joins—for example, from infinite radius at a tangent to the nominal radius of a smooth curve. The resulting spiral provides a gradual, eased transition, preventing undesirable sudden, abrupt changes in [[centripetal acceleration|lateral (centripetal) acceleration]] that would otherwise occur without a transition curve. Similarly, on highways, transition curves allow drivers to change steering gradually when entering or exiting curves.

Transition curves also serve as a transition in the vertical plane, whereby the elevation of the inside or outside of the curve is lowered or raised to reach the nominal amount of [[cant (road/rail)|bank]] for the curve.

If such an 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, a transition curve allows the driver to alter the steering in a gradual manner.

==History==