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<div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Mathematically-calculated curve in which a straight section changes into a curve</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Easement_curve.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Easement_curve.svg/220px-Easement_curve.svg.png" decoding="async" width="220" height="123" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Easement_curve.svg/330px-Easement_curve.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/54/Easement_curve.svg/440px-Easement_curve.svg.png 2x" data-file-width="575" data-file-height="321" /></a><figcaption>The red <a href="/wiki/Euler_spiral" title="Euler spiral">Euler spiral</a> is an example of an easement curve between a blue straight line and a circular arc, shown in green.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Parabolic_transition_curve.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Parabolic_transition_curve.JPG/220px-Parabolic_transition_curve.JPG" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Parabolic_transition_curve.JPG/330px-Parabolic_transition_curve.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/13/Parabolic_transition_curve.JPG/440px-Parabolic_transition_curve.JPG 2x" data-file-width="1025" data-file-height="770" /></a><figcaption>This sign aside a railroad (between <a href="/wiki/Ghent" title="Ghent">Ghent</a> and <a href="/wiki/Bruges" title="Bruges">Bruges</a>) indicates the start of the transition curve. A <a href="/wiki/Parabolic_curve" class="mw-redirect" title="Parabolic curve">parabolic curve</a> (<i>POB</i>) is used.</figcaption></figure> <p>A <b>transition curve</b> (also, <b>spiral easement</b> or, simply, <b>spiral</b>) is a spiral-shaped length of highway or <a href="/wiki/Track_(rail_transport)" class="mw-redirect" title="Track (rail transport)">railroad track</a> that is used between sections having different profiles and radii, such as between straightaways (<a href="/wiki/Tangent" title="Tangent">tangents</a>) and curves, or between two different curves.<sup id="cite_ref-pwayblog_1-0" class="reference"><a href="#cite_note-pwayblog-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <table class="wikitable" style="width:200px"> <tbody><tr> <th>Centripetal force on vehicles on roads without and with a transition curve </th></tr> <tr> <td><figure class="mw-default-size mw-halign-center" typeof="mw:File/Frameless"><a href="/wiki/File:Straight-circle.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Straight-circle.gif/260px-Straight-circle.gif" decoding="async" width="260" height="195" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Straight-circle.gif/390px-Straight-circle.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Straight-circle.gif/520px-Straight-circle.gif 2x" data-file-width="960" data-file-height="720" /></a><figcaption></figcaption></figure> Straight sections of road connected directly by a circular arc. | </td></tr> <tr> <td><figure class="mw-default-size mw-halign-center" typeof="mw:File/Frameless"><a href="/wiki/File:Straight-cornu.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Straight-cornu.gif/260px-Straight-cornu.gif" decoding="async" width="260" height="195" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Straight-cornu.gif/390px-Straight-cornu.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Straight-cornu.gif/520px-Straight-cornu.gif 2x" data-file-width="960" data-file-height="720" /></a><figcaption></figcaption></figure> Straight section connected to a circular arc via a Cornu spiral| </td></tr> <tr> <td>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. </td></tr></tbody></table> <p>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 <a href="/wiki/Centripetal_acceleration" class="mw-redirect" title="Centripetal acceleration">lateral (centripetal) acceleration</a> that would otherwise occur without a transition curve. Similarly, on highways, transition curves allow drivers to change steering gradually when entering or exiting curves. </p><p>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 <a href="/wiki/Cant_(road/rail)" class="mw-redirect" title="Cant (road/rail)">bank</a> for the curve. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Track_transition_curve&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>On <a href="/wiki/History_of_rail_transport" title="History of rail transport">early railroads</a>, because of the low speeds and wide-radius curves employed, the surveyors were able to ignore any form of easement, but during the 19th century, as speeds increased, the need for a track curve with gradually increasing curvature became apparent. <a href="/wiki/William_John_Macquorn_Rankine" class="mw-redirect" title="William John Macquorn Rankine">Rankine's</a> 1862 "Civil Engineering"<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> cites several such curves, including an 1828 or 1829 proposal based on the "<a href="/wiki/Sine_wave" title="Sine wave">curve of sines</a>" by <a href="/wiki/William_Gravatt" title="William Gravatt">William Gravatt</a>, and the <i>curve of adjustment</i> by <a href="/wiki/William_Froude" title="William Froude">William Froude</a> around 1842 approximating the <a href="/wiki/Elastica_theory" title="Elastica theory">elastic curve</a>. The actual equation given in Rankine is that of a <a href="/wiki/Polynomial#Graphs" title="Polynomial">cubic curve</a>, which is a polynomial curve of degree 3, at the time also known as a cubic parabola. </p><p>In the UK, only from 1845, when legislation and land costs began to constrain the laying out of rail routes and tighter curves were necessary, were the principles beginning to be applied in practice. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Brusio_Viaduct_(158241421).jpeg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Brusio_Viaduct_%28158241421%29.jpeg/220px-Brusio_Viaduct_%28158241421%29.jpeg" decoding="async" width="220" height="124" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Brusio_Viaduct_%28158241421%29.jpeg/330px-Brusio_Viaduct_%28158241421%29.jpeg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Brusio_Viaduct_%28158241421%29.jpeg/440px-Brusio_Viaduct_%28158241421%29.jpeg 2x" data-file-width="2048" data-file-height="1152" /></a><figcaption><a href="/wiki/Brusio_spiral_viaduct" title="Brusio spiral viaduct">Brusio spiral viaduct</a> and railway (Switzerland, built 1908), from above</figcaption></figure> <p>The 'true spiral', whose curvature is exactly linear in arclength, requires more sophisticated mathematics (in particular, the ability to integrate its <a href="/wiki/Intrinsic_equation" title="Intrinsic equation">intrinsic equation</a>) to compute than the proposals that were cited by Rankine. Several late-19th century civil engineers seem to have derived the equation for this curve independently (all unaware of the original characterization of the curve by <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a> in 1744). Charles Crandall<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> gives credit to one Ellis Holbrook, in the Railroad Gazette, Dec. 3, 1880, for the first accurate description of the curve. Another early publication was <i>The Railway Transition Spiral</i> by <a href="/wiki/Arthur_N._Talbot" class="mw-redirect" title="Arthur N. Talbot">Arthur N. Talbot</a>,<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> originally published in 1890. Some early 20th century authors<sup id="cite_ref-higgins_5-0" class="reference"><a href="#cite_note-higgins-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> call the curve "Glover's spiral" and attribute it to James Glover's 1900 publication.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>The equivalence of the railroad transition spiral and the <a href="/wiki/Clothoid" class="mw-redirect" title="Clothoid">clothoid</a> seems to have been first published in 1922 by Arthur Lovat Higgins.<sup id="cite_ref-higgins_5-1" class="reference"><a href="#cite_note-higgins-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Since then, "clothoid" is the most common name given the curve, but the correct name (following standards of academic attribution) is 'the <a href="/wiki/Euler_spiral" title="Euler spiral">Euler spiral</a>'.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Geometry">Geometry</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Track_transition_curve&action=edit&section=2" title="Edit section: Geometry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Track_transition_curve" title="Special:EditPage/Track transition curve">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">January 2010</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>While railroad <a href="/wiki/Track_geometry" title="Track geometry">track geometry</a> is intrinsically <a href="/wiki/Three-dimensional_space" title="Three-dimensional space">three-dimensional</a>, for practical purposes the vertical and horizontal components of track geometry are usually treated separately.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>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 <a href="/wiki/Quadratic_equation" title="Quadratic equation">quadratically</a> 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 <a href="/wiki/Tangent" title="Tangent">tangent</a>) and curve (i.e. a <a href="/wiki/Circular_arc" title="Circular arc">circular arc</a>) segments connected by transition curves. </p><p>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 <a href="/wiki/Cant_(road/rail)" class="mw-redirect" title="Cant (road/rail)">superelevation</a>. Such difference in the elevation of the rails is intended to compensate for the <a href="/wiki/Centripetal_acceleration" class="mw-redirect" title="Centripetal acceleration">centripetal acceleration</a> 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). </p><p>It is important to note that superelevation is not the same as the roll angle of the rail which is used to describe the "tilting" of the individual rails instead of the banking of the entire track structure as reflected by the elevation difference at the "top of rail". Regardless of the horizontal alignment and the superelevation of the track, the individual rails are almost always designed to "roll"/"cant" towards gage side (the side where the wheel is in contact with the rail) to compensate for the horizontal forces exerted by wheels under normal rail traffic. </p><p>The change of superelevation from zero in a tangent segment to the value selected for the body of a following curve occurs over the length of a transition curve that connects the tangent and the curve proper. Over the length of the transition the curvature of the track will also vary from zero at the end abutting the tangent segment to the value of curvature of the curve body, which is numerically equal to one over the radius of the curve body. </p><p>The simplest and most commonly used form of transition curve is that in which the superelevation and horizontal curvature both vary linearly with distance along the track. <a href="/wiki/Cartesian_coordinates" class="mw-redirect" title="Cartesian coordinates">Cartesian coordinates</a> of points along this spiral are given by the <a href="/wiki/Fresnel_integral" title="Fresnel integral">Fresnel integrals</a>. The resulting shape matches a portion of an <a href="/wiki/Euler_spiral" title="Euler spiral">Euler spiral</a>, which is also commonly referred to as a "clothoid", and sometimes "Cornu spiral". </p><p>A transition curve can connect a track segment of constant non-zero curvature to another segment with constant curvature that is zero or non-zero of either sign. Successive curves in the same direction are sometimes called progressive curves and successive curves in opposite directions are called reverse curves. </p><p>The Euler spiral provides the shortest transition subject to a given limit on the rate of change of the track superelevation (i.e. the twist of the track). However, as has been recognized for a long time, it has undesirable dynamic characteristics due to the large (conceptually infinite) roll acceleration and rate of change of centripetal acceleration at each end. Because of the capabilities of personal computers it is now practical to employ spirals that have dynamics better than those of the Euler spiral. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Track_transition_curve&action=edit&section=3" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Degree_of_curvature" title="Degree of curvature">Degree of curvature</a></li> <li><a href="/wiki/Minimum_railway_curve_radius" title="Minimum railway curve radius">Minimum railway curve radius</a></li> <li><a href="/wiki/Railway_systems_engineering" class="mw-redirect" title="Railway systems engineering">Railway systems engineering</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Track_transition_curve&action=edit&section=4" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-pwayblog-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-pwayblog_1-0">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFConstantin2016" class="citation web cs1">Constantin (2016-07-03). <a rel="nofollow" class="external text" href="https://pwayblog.com/2016/07/03/the-clothoid/">"The Clothoid"</a>. <i>Pwayblog</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2023-06-07</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Pwayblog&rft.atitle=The+Clothoid&rft.date=2016-07-03&rft.au=Constantin&rft_id=https%3A%2F%2Fpwayblog.com%2F2016%2F07%2F03%2Fthe-clothoid%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATrack+transition+curve" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRankine1883" class="citation book cs1"><a href="/wiki/William_John_Macquorn_Rankine" class="mw-redirect" title="William John Macquorn Rankine">Rankine, William</a> (1883). <a rel="nofollow" class="external text" href="https://archive.org/details/amanualcivileng02rankgoog"><i>A Manual of Civil Engineering</i></a> (17th ed.). Charles Griffin. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/amanualcivileng02rankgoog/page/n656">651</a>–653.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Manual+of+Civil+Engineering&rft.pages=651-653&rft.edition=17th&rft.pub=Charles+Griffin&rft.date=1883&rft.aulast=Rankine&rft.aufirst=William&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Famanualcivileng02rankgoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATrack+transition+curve" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCrandall1893" class="citation book cs1">Crandall, Charles (1893). <a rel="nofollow" class="external text" href="https://archive.org/details/transitioncurve02crangoog"><i>The Transition Curve</i></a>. Wiley.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Transition+Curve&rft.pub=Wiley&rft.date=1893&rft.aulast=Crandall&rft.aufirst=Charles&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Ftransitioncurve02crangoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATrack+transition+curve" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTalbot1901" class="citation book cs1">Talbot, Arthur (1901). <a rel="nofollow" class="external text" href="https://archive.org/details/railwaytransiti01talbgoog"><i>The Railway Transition Spiral</i></a>. Engineering News Publishing.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Railway+Transition+Spiral&rft.pub=Engineering+News+Publishing&rft.date=1901&rft.aulast=Talbot&rft.aufirst=Arthur&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Frailwaytransiti01talbgoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATrack+transition+curve" class="Z3988"></span></span> </li> <li id="cite_note-higgins-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-higgins_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-higgins_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHiggins1922" class="citation book cs1">Higgins, Arthur (1922). <a rel="nofollow" class="external text" href="https://archive.org/details/cu31924031215142"><i>The Transition Spiral and Its Introduction to Railway Curves</i></a>. Van Nostrand.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Transition+Spiral+and+Its+Introduction+to+Railway+Curves&rft.pub=Van+Nostrand&rft.date=1922&rft.aulast=Higgins&rft.aufirst=Arthur&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fcu31924031215142&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATrack+transition+curve" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGlover1900" class="citation conference cs1">Glover, James (1900). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=aQsAAAAAMAAJ&pg=PA161">"Transition Curves for Railways"</a>. <i>Minutes of Proceedings of the Institution of Civil Engineers</i>. pp. 161–179.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.atitle=Transition+Curves+for+Railways&rft.btitle=Minutes+of+Proceedings+of+the+Institution+of+Civil+Engineers&rft.pages=161-179&rft.date=1900&rft.aulast=Glover&rft.aufirst=James&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DaQsAAAAAMAAJ%26pg%3DPA161&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATrack+transition+curve" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFArchibald1917" class="citation journal cs1"><a href="/wiki/Raymond_Clare_Archibald" class="mw-redirect" title="Raymond Clare Archibald">Archibald, Raymond Clare</a> (June 1917). <a rel="nofollow" class="external text" href="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"</a>. <i>American Mathematical Monthly</i>. <b>25</b> (6): 276–282 – via Glassblower.Info.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Mathematical+Monthly&rft.atitle=Euler+Integrals+and+Euler%27s+Spiral--Sometimes+called+Fresnel+Integrals+and+the+Clothoide+or+Cornu%27s+Spiral&rft.volume=25&rft.issue=6&rft.pages=276-282&rft.date=1917-06&rft.aulast=Archibald&rft.aufirst=Raymond+Clare&rft_id=http%3A%2F%2Fwww.glassblower.info%2FEuler-Spiral%2FAMM%2FAMM-1918.HTML&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATrack+transition+curve" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLautalaDick" class="citation web cs1">Lautala, Pasi; Dick, Tyler. <a rel="nofollow" class="external text" href="http://www.engr.uky.edu/~jrose/RailwayIntro/Modules/Module%206%20Railway%20Alignment%20Design%20and%20Geometry%20REES%202010.pdf">"Railway Alignment Design and Geometry"</a> <span class="cs1-format">(PDF)</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Railway+Alignment+Design+and+Geometry&rft.aulast=Lautala&rft.aufirst=Pasi&rft.au=Dick%2C+Tyler&rft_id=http%3A%2F%2Fwww.engr.uky.edu%2F~jrose%2FRailwayIntro%2FModules%2FModule%25206%2520Railway%2520Alignment%2520Design%2520and%2520Geometry%2520REES%25202010.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATrack+transition+curve" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLindamoodStrongMcLeod2003" class="citation book cs1">Lindamood, Brian; Strong, James C.; McLeod, James (2003). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20161130162616/http://www.engsoc.org:80/~josh/AREMA/chapter6%20-%20Railway%20Track%20Design.pdf">"Railway Track Design"</a> <span class="cs1-format">(PDF)</span>. <i>Practical Guide to Railway Engineering</i>. <a href="/wiki/American_Railway_Engineering_and_Maintenance-of-Way_Association" title="American Railway Engineering and Maintenance-of-Way Association">American Railway Engineering and Maintenance-of-Way Association</a>. Archived from <a rel="nofollow" class="external text" href="http://www.engsoc.org/~josh/AREMA/chapter6%20-%20Railway%20Track%20Design.pdf">the original</a> <span class="cs1-format">(PDF)</span> on November 30, 2016.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Railway+Track+Design&rft.btitle=Practical+Guide+to+Railway+Engineering&rft.pub=American+Railway+Engineering+and+Maintenance-of-Way+Association&rft.date=2003&rft.aulast=Lindamood&rft.aufirst=Brian&rft.au=Strong%2C+James+C.&rft.au=McLeod%2C+James&rft_id=http%3A%2F%2Fwww.engsoc.org%2F~josh%2FAREMA%2Fchapter6%2520-%2520Railway%2520Track%2520Design.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATrack+transition+curve" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Sources">Sources</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Track_transition_curve&action=edit&section=5" title="Edit section: Sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSimmonsBiddle,_Gordon1997" class="citation book cs1">Simmons, Jack; Biddle, Gordon (1997). <i>The Oxford Companion to British Railway History</i>. Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-19-211697-5" title="Special:BookSources/0-19-211697-5"><bdi>0-19-211697-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Oxford+Companion+to+British+Railway+History&rft.pub=Oxford+University+Press&rft.date=1997&rft.isbn=0-19-211697-5&rft.aulast=Simmons&rft.aufirst=Jack&rft.au=Biddle%2C+Gordon&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATrack+transition+curve" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBiddle1990" class="citation book cs1">Biddle, Gordon (1990). <i>The Railway Surveyors</i>. Chertsey, UK: Ian Allan. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7110-1954-1" title="Special:BookSources/0-7110-1954-1"><bdi>0-7110-1954-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Railway+Surveyors&rft.place=Chertsey%2C+UK&rft.pub=Ian+Allan&rft.date=1990&rft.isbn=0-7110-1954-1&rft.aulast=Biddle&rft.aufirst=Gordon&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATrack+transition+curve" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHickerson1967" class="citation book cs1">Hickerson, Thomas Felix (1967). <i>Route Location and Design</i>. New York: McGraw Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-07-028680-9" title="Special:BookSources/0-07-028680-9"><bdi>0-07-028680-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Route+Location+and+Design&rft.place=New+York&rft.pub=McGraw+Hill&rft.date=1967&rft.isbn=0-07-028680-9&rft.aulast=Hickerson&rft.aufirst=Thomas+Felix&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATrack+transition+curve" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFColeand_HarbinAndrew_L2006" class="citation book cs1">Cole, George M; and Harbin; Andrew L (2006). <i>Surveyor Reference Manual</i>. Belmont, CA: Professional Publications Inc. p. 16. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-59126-044-2" title="Special:BookSources/1-59126-044-2"><bdi>1-59126-044-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Surveyor+Reference+Manual&rft.place=Belmont%2C+CA&rft.pages=16&rft.pub=Professional+Publications+Inc&rft.date=2006&rft.isbn=1-59126-044-2&rft.aulast=Cole&rft.aufirst=George+M&rft.au=and+Harbin&rft.au=Andrew+L&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATrack+transition+curve" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="http://www.arema.org/eseries/scriptcontent/custom/e_arema/Practical_Guide/PGChapter6.pdf"><i>Railway Track Design</i></a> pdf from The American Railway Engineering and Maintenance of Way Association, accessed 4 December 2006.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKellogg1907" class="citation book cs1">Kellogg, Norman Benjamin (1907). <a rel="nofollow" class="external text" href="https://archive.org/details/transitioncurve01nrgoog"><i>The Transition Curve or Curve of Adjustment</i></a> (3rd ed.). New York: McGraw.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Transition+Curve+or+Curve+of+Adjustment&rft.place=New+York&rft.edition=3rd&rft.pub=McGraw&rft.date=1907&rft.aulast=Kellogg&rft.aufirst=Norman+Benjamin&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Ftransitioncurve01nrgoog&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATrack+transition+curve" class="Z3988"></span></li></ul> </div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output 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href="/wiki/Special:EditPage/Template:Rail_tracks" title="Special:EditPage/Template:Rail tracks"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Rail_infrastructure" style="font-size:114%;margin:0 4em">Rail <a href="/wiki/Infrastructure#Transport_infrastructure" title="Infrastructure">infrastructure</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Railway_track" title="Railway track">Tracks</a><small> <a href="/wiki/Permanent_way_(history)" class="mw-redirect" title="Permanent way (history)">(history)</a> </small></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Axe_ties" class="mw-redirect" title="Axe ties">Axe ties</a></li> <li><a href="/wiki/Track_ballast" title="Track ballast">Ballast</a></li> <li><a href="/wiki/Baulk_road" title="Baulk road">Baulk road</a></li> <li><a href="/wiki/Breather_switch" title="Breather switch">Breather switch</a></li> <li><a href="/wiki/Cant_(road/rail)" class="mw-redirect" title="Cant (road/rail)">Cant</a></li> <li><a href="/wiki/Clip_and_scotch" title="Clip and scotch">Clip and scotch</a></li> <li><a href="/wiki/Date_nail" title="Date nail">Date nail</a></li> <li><a href="/wiki/Rail_fastening_system" title="Rail fastening system">Fastening system</a></li> <li><a href="/wiki/Fishplate" title="Fishplate">Fishplate</a></li> <li><a href="/wiki/Ladder_track" title="Ladder track">Ladder track</a></li> <li><a href="/wiki/Minimum_railway_curve_radius" title="Minimum railway curve radius">Minimum radius</a></li> <li><a href="/wiki/Rail_profile" title="Rail profile">Profile</a></li> <li><a href="/wiki/Railroad_tie" title="Railroad tie">Tie/Sleeper</a></li> <li><a class="mw-selflink selflink">Transition curve</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Trackwork</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Balloon_loop" title="Balloon loop">Balloon loop</a></li> <li><a href="/wiki/Classification_yard" title="Classification yard">Classification yard</a></li> <li><a href="/wiki/Headshunt" title="Headshunt">Headshunt</a></li> <li><a href="/wiki/Pocket_track" title="Pocket track">Pocket track</a></li> <li><a href="/wiki/Junction_(rail)" title="Junction (rail)">Junction</a></li> <li><a href="/wiki/Gauntlet_track" title="Gauntlet track">Gauntlet track</a></li> <li><a href="/wiki/Guide_bar" title="Guide bar">Guide bar</a></li> <li><a href="/wiki/Passing_loop" title="Passing loop">Passing loop</a></li> <li><a href="/wiki/Track_gauge" title="Track gauge">Track gauge</a> <ul><li><a href="/wiki/Dual_gauge" title="Dual gauge">dual gauge</a></li></ul></li> <li><a href="/wiki/Track_(rail_transport)" class="mw-redirect" title="Track (rail transport)">Rail track</a> <ul><li><a href="/wiki/Tramway_track" title="Tramway track">tramway track</a></li></ul></li> <li><a href="/wiki/Rail_yard" title="Rail yard">Rail yard</a></li> <li><a href="/wiki/Railway_electrification" title="Railway electrification">Railway electrification</a> <ul><li><a href="/wiki/Overhead_line" title="Overhead line">overhead lines</a></li> <li><a href="/wiki/Third_rail" title="Third rail">third rail</a></li> <li><a href="/wiki/Ground-level_power_supply" title="Ground-level power supply">ground-level power supply</a></li></ul></li> <li><a href="/wiki/Railway_turntable" title="Railway turntable">Railway turntable</a></li> <li><a href="/wiki/Transfer_table" title="Transfer table">Transfer table (traverser)</a></li> <li><a href="/wiki/Roll_way" title="Roll way">Roll way</a></li> <li><a href="/wiki/Siding_(rail)" title="Siding (rail)">Siding</a> <ul><li><a href="/wiki/Refuge_siding" title="Refuge siding">refuge siding</a></li></ul></li> <li><a href="/wiki/Railroad_switch" title="Railroad switch">Switch</a></li> <li><a href="/wiki/Track_geometry" title="Track geometry">Track geometry</a></li> <li><a href="/wiki/Water_crane" title="Water crane">Water crane</a></li> <li><a href="/wiki/Water_trough" title="Water trough">Water trough</a></li> <li><a href="/wiki/Wye_(rail)" title="Wye (rail)">Wye</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Railway_signalling" title="Railway signalling">Signalling</a><br />and safety</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Anti-trespass_panels" title="Anti-trespass panels">Anti-trespass panels</a></li> <li><a href="/wiki/Block_post" title="Block post">Block post</a></li> <li><a href="/wiki/Buffer_stop" title="Buffer stop">Buffer stop</a></li> <li><a href="/wiki/Catch_points" title="Catch points">Catch points</a></li> <li><a href="/wiki/Defect_detector" title="Defect detector">Defect detector</a></li> <li><a href="/wiki/Derail" title="Derail">Derailer</a></li> <li><a href="/wiki/Guard_rail_(railroad)" class="mw-redirect" title="Guard rail (railroad)">Guard rail</a></li> <li><a href="/wiki/Interlocking" title="Interlocking">Interlocking</a></li> <li><a href="/wiki/Level_crossing" title="Level crossing">Level crossing</a></li> <li><a href="/wiki/Loading_gauge" title="Loading gauge">Loading gauge</a></li> <li><a href="/wiki/Platform_screen_doors" title="Platform screen doors">Platform screen doors</a></li> <li><a href="/wiki/Railway_signal" title="Railway signal">Railway signal</a></li> <li><a href="/wiki/Signalling_control" title="Signalling control">Signalling control</a></li> <li><a href="/wiki/Structure_gauge" title="Structure gauge">Structure gauge</a></li> <li><a href="/wiki/Railroad_signal_bridge" class="mw-redirect" title="Railroad signal bridge">Signal bridge</a></li> <li><a href="/wiki/Tell-tale_(bridges)" title="Tell-tale (bridges)">Tell-tale</a></li> <li><a href="/wiki/Train_stop" title="Train stop">Train stop</a></li> <li><a href="/wiki/Wayside_horn" title="Wayside horn">Wayside horn</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Structures</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Coaling_tower" title="Coaling tower">Coaling tower</a></li> <li><a href="/wiki/Motive_power_depot" title="Motive power depot">Motive power depot</a>/<a href="/wiki/Railway_workshop" title="Railway workshop">Railway workshop</a></li> <li><a href="/wiki/Railway_platform" title="Railway platform">Platform</a></li> <li><a href="/wiki/Railway_roundhouse" title="Railway roundhouse">Roundhouse</a></li> <li>Shed <ul><li><a href="/wiki/Train_shed" title="Train shed">for trains</a></li> <li><a href="/wiki/Goods_shed" title="Goods shed">for goods</a></li></ul></li> <li><a href="/wiki/Train_station" title="Train station">Station</a> <ul><li><a href="/wiki/Station_building" title="Station building">building</a></li> <li><a href="/wiki/Station_clock" title="Station clock">clock</a></li> <li><a href="/wiki/Ghost_station" title="Ghost station">ghost</a></li> <li><a href="/wiki/List_of_railway_stations" title="List of railway stations">list</a></li></ul></li> <li><a href="/wiki/Water_stop" title="Water stop">Water stop</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Types</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Industrial_railway" title="Industrial railway">Industrial</a></li> <li><a href="/wiki/Military_railways" title="Military railways">Military</a></li> <li><a href="/wiki/Private_railway" title="Private railway">Private</a> <ul><li><a href="/wiki/Private_railway_station" title="Private railway station">station</a> <ul><li><a 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