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<span>Toggle Longitudinal elevation subsection</span> </button> <ul id="toc-Longitudinal_elevation-sublist" class="vector-toc-list"> <li id="toc-Track_gradient" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Track_gradient"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Track gradient</span> </div> </a> <ul id="toc-Track_gradient-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vertical_curve" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Vertical_curve"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Vertical curve</span> </div> </a> <ul id="toc-Vertical_curve-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Curvature" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Curvature"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Curvature</span> </div> </a> <button aria-controls="toc-Curvature-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Curvature subsection</span> </button> <ul id="toc-Curvature-sublist" class="vector-toc-list"> <li id="toc-Cant" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cant"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Cant</span> </div> </a> <ul id="toc-Cant-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cant_gradient" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cant_gradient"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Cant gradient</span> </div> </a> <ul id="toc-Cant_gradient-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cant_deficiency" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cant_deficiency"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Cant deficiency</span> </div> </a> <ul id="toc-Cant_deficiency-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Alignment" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Alignment"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Alignment</span> </div> </a> <ul id="toc-Alignment-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled 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searchaux" style="display:none">Three-dimensional geometry of track layouts and associated measurements</div> <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 .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · 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.den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><table class="sidebar nomobile nowraplinks"><tbody><tr><th class="sidebar-title" style="background:#bebebe;"><a href="/wiki/Track_gauge" title="Track gauge">Track gauge</a></th></tr><tr><th class="sidebar-heading" style="background:#ddd;"> By transport mode</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Rapid_transit_track_gauge" title="Rapid transit track gauge">Rapid transit</a></li> <li><a href="/wiki/List_of_tram_systems_by_gauge_and_electrification" title="List of tram systems by gauge and electrification">Tram</a></li> <li><a href="/wiki/Ridable_miniature_railway" title="Ridable miniature railway">Miniature</a></li> <li><a href="/wiki/Rail_transport_modelling_scales" title="Rail transport modelling scales">Scale model</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#ddd;"> By size (<a href="/wiki/List_of_track_gauges" title="List of track gauges">list</a>)</th></tr><tr><td class="sidebar-content hlist"> <table class="nowrap"> <tbody><tr> <td colspan="4"><span typeof="mw:File"><a href="/wiki/File:Track_gauge.svg" class="mw-file-description" title="Graphic list of track gauges"><img alt="Graphic list of track gauges" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Track_gauge.svg/240px-Track_gauge.svg.png" decoding="async" width="240" height="69" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Track_gauge.svg/360px-Track_gauge.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Track_gauge.svg/480px-Track_gauge.svg.png 2x" data-file-width="2110" data-file-height="610" /></a></span> </td></tr> <tr> <td colspan="4"><hr /> </td></tr> <tr> <td> </td> <td colspan="3" style="text-align:left;"><b><a href="/wiki/Minimum-gauge_railway" title="Minimum-gauge railway">Minimum</a></b> </td></tr> <tr> <td style="background-color:#b0b0b0;"> </td> <td style="text-align:left;"><a href="/wiki/Fifteen-inch_gauge_railway" class="mw-redirect" title="Fifteen-inch gauge railway">Fifteen inch</a></td> <td style="text-align:right;">381 mm</td> <td style="text-align:left;">(15 in) </td></tr> <tr> <td colspan="4"><hr /> </td></tr> <tr> <td> </td> <td colspan="3" style="text-align:left;"><b><a href="/wiki/Narrow-gauge_railway" title="Narrow-gauge railway">Narrow</a></b> </td></tr> <tr> <td rowspan="3" style="background-color:#E5C4A1;"> </td> <td style="text-align:left;"><a href="/wiki/2_ft_and_600_mm_gauge_railways" title="2 ft and 600 mm gauge railways">600 mm</a></td> <td style="text-align:right;">600 mm</td> <td style="text-align:left;">(1 ft <span class="frac">11<span class="sr-only">+</span><span class="num">5</span>⁄<span class="den">8</span></span> in) </td></tr> <tr> <td style="text-align:left;"><a href="/wiki/2_ft_and_600_mm_gauge_railways" title="2 ft and 600 mm gauge railways">Two foot</a></td> <td style="text-align:right;">610 mm</td> <td style="text-align:left;">(2 ft) </td></tr> <tr> <td style="text-align:left;"><a href="/wiki/List_of_2_ft_3_in_gauge_railways" title="List of 2 ft 3 in gauge railways">Two foot three inch</a></td> <td style="text-align:right;">686 mm</td> <td style="text-align:left;">(2 ft 3 in) </td></tr> <tr> <td rowspan="3" style="background-color:#ff8a37;"> </td> <td style="text-align:left;"><a href="/wiki/750_mm_gauge_railways" title="750 mm gauge railways">750 mm</a></td> <td style="text-align:right;">750 mm</td> <td style="text-align:left;">(2 ft <span class="frac">5<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span> in) </td></tr> <tr> <td style="text-align:left;"><a href="/wiki/Bosnian-gauge_railways" title="Bosnian-gauge railways">Bosnian gauge</a></td> <td style="text-align:right;">760 mm</td> <td style="text-align:left;">(2 ft <span class="frac">5<span class="sr-only">+</span><span class="num">15</span>⁄<span class="den">16</span></span> in) </td></tr> <tr> <td style="text-align:left;"><a href="/wiki/2_ft_6_in_gauge_railways" title="2 ft 6 in gauge railways">Two foot six inch</a></td> <td style="text-align:right;">762 mm</td> <td style="text-align:left;">(2 ft 6 in) </td></tr> <tr> <td rowspan="4" style="background-color:#e1392f;"> </td> <td style="text-align:left;"><a href="/wiki/Swedish_three_foot_gauge_railways" class="mw-redirect" title="Swedish three foot gauge railways">Swedish three foot</a></td> <td style="text-align:right;">891 mm</td> <td style="text-align:left;">(2 ft <span class="frac">11<span class="sr-only">+</span><span class="num">3</span>⁄<span class="den">32</span></span> in) </td></tr> <tr> <td style="text-align:left;"><a href="/wiki/900_mm_gauge_railways" title="900 mm gauge railways">900 mm</a></td> <td style="text-align:right;">900 mm</td> <td style="text-align:left;">(2 ft <span class="frac">11<span class="sr-only">+</span><span class="num">7</span>⁄<span class="den">16</span></span> in) </td></tr> <tr> <td style="text-align:left;"><a href="/wiki/3_ft_gauge_railways" title="3 ft gauge railways">Three foot</a></td> <td style="text-align:right;">914 mm</td> <td style="text-align:left;">(3 ft) </td></tr> <tr> <td style="text-align:left;"><a href="/wiki/Narrow-gauge_railways_in_Italy#Italian_metre-gauge_lines_(950_mm)" title="Narrow-gauge railways in Italy">Italian metre</a></td> <td style="text-align:right;">950 mm</td> <td style="text-align:left;">(3 ft<span class="frac">1<span class="sr-only">+</span><span class="num">13</span>⁄<span class="den">32</span></span> in) </td></tr> <tr> <td style="background-color:#c55e8d;"> </td> <td style="text-align:left;"><a href="/wiki/Metre-gauge_railway" title="Metre-gauge railway">Metre</a></td> <td style="text-align:right;">1,000 mm</td> <td style="text-align:left;">(3 ft <span class="frac">3<span class="sr-only">+</span><span class="num">3</span>⁄<span class="den">8</span></span> in) </td></tr> <tr> <td style="background-color:#6a51b7;"> </td> <td style="text-align:left;"><a href="/wiki/3_ft_6_in_gauge_railways" title="3 ft 6 in gauge railways">Three foot six inch</a></td> <td style="text-align:right;">1,067 mm</td> <td style="text-align:left;">(3 ft 6 in) </td></tr> <tr> <td style="background-color:#6a51b7;"> </td> <td style="text-align:left;"><a href="/wiki/Narrow-gauge_railway#Around_4_ft_gauge" title="Narrow-gauge railway">Four foot</a></td> <td style="text-align:right;">1,219 mm</td> <td style="text-align:left;">(4 ft) </td></tr> <tr> <td style="background-color:#6a51b7;"> </td> <td style="text-align:left;"><a href="/wiki/4_ft_6_in_gauge_railway" title="4 ft 6 in gauge railway">Four foot six inch</a></td> <td style="text-align:right;">1,372 mm</td> <td style="text-align:left;">(4 ft 6 in) </td></tr> <tr> <td style="background-color:#6a51b7;"> </td> <td style="text-align:left;"><a href="/wiki/Standard-gauge_railway#Modern_almost_standard_gauge_railways" title="Standard-gauge railway">1432 mm</a></td> <td style="text-align:right;">1,432 mm</td> <td style="text-align:left;">(4 ft <span class="frac">8<span class="sr-only">+</span><span class="num">3</span>⁄<span class="den">8</span></span> in) </td></tr> <tr> <td colspan="4"><hr /> </td></tr> <tr> <td style="background-color:#568dd0; width:20px;"> </td> <td style="text-align:left;"><b><a href="/wiki/Standard-gauge_railway" title="Standard-gauge railway">Standard</a></b></td> <td style="text-align:right;">1,435 mm</td> <td style="text-align:left;">(4 ft <span class="frac">8<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span> in) </td></tr> <tr> <td colspan="4"><hr /> </td></tr> <tr> <td> </td> <td colspan="3" style="text-align:left;"><b><a href="/wiki/Broad-gauge_railway" title="Broad-gauge railway">Broad</a></b> </td></tr> <tr> <td rowspan="2" style="background-color:#335c33;"> </td> <td style="text-align:left;"><a href="/wiki/Track_gauge_in_Italy" title="Track gauge in Italy">Italian broad gauge</a></td> <td style="text-align:right;">1,445 mm</td> <td style="text-align:left;">(4 ft <span class="frac">8<span class="sr-only">+</span><span class="num">7</span>⁄<span class="den">8</span></span> in) </td></tr> <tr> <td style="text-align:left;"><a href="/wiki/Trams_in_Dresden" title="Trams in Dresden">Dresden gauge</a></td> <td style="text-align:right;">1,450 mm</td> <td style="text-align:left;">(4 ft <span class="frac">9<span class="sr-only">+</span><span class="num">3</span>⁄<span class="den">32</span></span> in) </td></tr> <tr> <td style="background-color:#335c33;"> </td> <td style="text-align:left;"><a href="/wiki/Trams_in_Leipzig" title="Trams in Leipzig">Leipzig gauge</a></td> <td style="text-align:right;">1,458 mm</td> <td style="text-align:left;">(4 ft <span class="frac">9<span class="sr-only">+</span><span class="num">13</span>⁄<span class="den">32</span></span> in) </td></tr> <tr> <td style="background-color:#335c33;"> </td> <td style="text-align:left;"><a href="/wiki/Toronto-gauge_railways" title="Toronto-gauge railways">Toronto gauge</a></td> <td style="text-align:right;">1,495 mm</td> <td style="text-align:left;">(4 ft <span class="frac">10<span class="sr-only">+</span><span class="num">7</span>⁄<span class="den">8</span></span> in) </td></tr> <tr> <td rowspan="2" style="background-color:#335c33;"> </td> <td style="text-align:left;"><a href="/wiki/5_ft_and_1520_mm_gauge_railways" title="5 ft and 1520 mm gauge railways">1520 mm</a></td> <td style="text-align:right;">1,520 mm</td> <td style="text-align:left;">(4 ft <span class="frac">11<span class="sr-only">+</span><span class="num">27</span>⁄<span class="den">32</span></span> in) </td></tr> <tr> <td style="text-align:left;"><a href="/wiki/5_ft_and_1520_mm_gauge_railways" title="5 ft and 1520 mm gauge railways">Five foot</a></td> <td style="text-align:right;">1,524 mm</td> <td style="text-align:left;">(5 ft) </td></tr> <tr> <td rowspan="3" style="background-color:#5abf56;"> </td> <td style="text-align:left;"><a href="/wiki/Track_gauge_in_the_United_States#Pennsylvania_trolley_gauges" title="Track gauge in the United States">Pennsylvania gauge</a></td> <td style="text-align:right;">1,581 mm</td> <td style="text-align:left;">(5 ft <span class="frac">2<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">4</span></span> in) </td></tr> <tr> <td style="text-align:left;">Pennsylvania gauge</td> <td style="text-align:right;">1,588 mm</td> <td style="text-align:left;">(5 ft <span class="frac">2<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span> in) </td></tr> <tr> <td style="text-align:left;"><a href="/wiki/5_ft_3_in_gauge_railways" title="5 ft 3 in gauge railways">Five foot three inch</a></td> <td style="text-align:right;">1,600 mm</td> <td style="text-align:left;">(5 ft 3 in) </td></tr> <tr> <td style="background-color:#bbdf94;"> </td> <td style="text-align:left;"><a href="/wiki/Baltimore_Streetcar_Museum#Streetcar_service" title="Baltimore Streetcar Museum">Baltimore gauge</a></td> <td style="text-align:right;">1,638 mm</td> <td style="text-align:left;">(5 ft <span class="frac">4<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span> in) </td></tr> <tr> <td rowspan="2" style="background-color:#bbdf94;"> </td> <td style="text-align:left;"><a href="/wiki/Iberian-gauge_railways" title="Iberian-gauge railways">Iberian gauge</a></td> <td style="text-align:right;">1,668 mm</td> <td style="text-align:left;">(5 ft <span class="frac">5<span class="sr-only">+</span><span class="num">21</span>⁄<span class="den">32</span></span> in) </td></tr> <tr> <td style="text-align:left;"><a href="/wiki/5_ft_6_in_gauge_railway" title="5 ft 6 in gauge railway">Five foot six inch</a></td> <td style="text-align:right;">1,676 mm</td> <td style="text-align:left;">(5 ft 6 in) </td></tr> <tr> <td style="background-color:#dceba3;"> </td> <td style="text-align:left;"><a href="/wiki/Track_gauge_in_the_United_States#Broad_gauges" title="Track gauge in the United States">Six foot</a></td> <td style="text-align:right;">1,829 mm</td> <td style="text-align:left;">(6 ft) </td></tr> <tr> <td style="background-color:#dceba3;"> </td> <td style="text-align:left;"><a href="/wiki/Great_Western_Railway#Brunel's_7-foot_gauge_and_the_"gauge_war"" title="Great Western Railway">Brunel</a></td> <td style="text-align:right;">2,140 mm</td> <td style="text-align:left;">(7 ft <span class="frac"><span class="num">1</span>⁄<span class="den">4</span></span> in) </td></tr> <tr> <td style="background-color:#dceba3;"> </td> <td style="text-align:left;"><a href="/wiki/Breitspurbahn" title="Breitspurbahn">Breitspurbahn</a></td> <td style="text-align:right;">3,000 mm</td> <td style="text-align:left;">(9 ft 10<span class="frac"><span class="num">1</span>⁄<span class="den">8</span></span> in) </td></tr></tbody></table></td> </tr><tr><th class="sidebar-heading" style="background:#ddd;"> Change of gauge</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Bogie_exchange" title="Bogie exchange">Bogie exchange</a></li> <li><a href="/wiki/Break_of_gauge" title="Break of gauge">Break of gauge</a></li> <li><a href="/wiki/Dual_gauge" title="Dual gauge">Dual gauge</a></li> <li><a href="/wiki/Track_gauge_conversion" title="Track gauge conversion">Conversion</a> <ul><li><a href="/wiki/List_of_gauge_conversions" title="List of gauge conversions">list</a></li></ul></li> <li><a href="/wiki/Variable_gauge" title="Variable gauge">Variable gauge</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#ddd;"> By location</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Track_gauge_in_North_America" title="Track gauge in North America">North America</a></li> <li><a href="/wiki/Track_gauge_in_South_America" title="Track gauge in South America">South America</a></li> <li><a href="/wiki/Track_gauge_in_Europe" title="Track gauge in Europe">Europe</a></li> <li><a href="/wiki/Rail_gauge_in_Australia" title="Rail gauge in Australia">Australia</a></li></ul></td> </tr><tr><td class="sidebar-content hlist"> <span typeof="mw:File"><a href="/wiki/File:Rail_gauge_world.svg" class="mw-file-description" title="World map, rail gauge by region"><img alt="World map, rail gauge by region" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Rail_gauge_world.svg/264px-Rail_gauge_world.svg.png" decoding="async" width="264" height="134" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Rail_gauge_world.svg/396px-Rail_gauge_world.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Rail_gauge_world.svg/528px-Rail_gauge_world.svg.png 2x" data-file-width="2754" data-file-height="1398" /></a></span></td> </tr></tbody></table> <p><b>Track geometry</b> is concerned with the properties and relations of points, lines, curves, and surfaces<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> in the three-dimensional positioning of <a href="/wiki/Railroad" class="mw-redirect" title="Railroad">railroad</a> <a href="/wiki/Track_(rail_transport)" class="mw-redirect" title="Track (rail transport)">track</a>. The term is also applied to measurements used in design, construction and maintenance of track. Track <a href="/wiki/Geometry" title="Geometry">geometry</a> involves standards, speed limits and other regulations in the areas of <a href="/wiki/Track_gauge" title="Track gauge">track gauge</a>, alignment, elevation, <a href="/wiki/Curvature" title="Curvature">curvature</a> and track surface.<sup id="cite_ref-fra-sheet_2-0" class="reference"><a href="#cite_note-fra-sheet-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability"><span title="The material near this tag failed verification of its source citation(s). (October 2021)">failed verification</span></a></i>]</sup> Standards are usually separately expressed for <a href="/wiki/Horizontal_plane" class="mw-redirect" title="Horizontal plane">horizontal</a> and <a href="/wiki/Vertical_direction" class="mw-redirect" title="Vertical direction">vertical</a> layouts although track geometry is three-dimensional. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Layout">Layout</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Track_geometry&action=edit&section=1" title="Edit section: Layout"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Horizontal_layout">Horizontal layout</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Track_geometry&action=edit&section=2" title="Edit section: Horizontal layout"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure 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/240px-Easement_curve.svg.png" decoding="async" width="240" height="134" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Easement_curve.svg/360px-Easement_curve.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/54/Easement_curve.svg/480px-Easement_curve.svg.png 2x" data-file-width="575" data-file-height="321" /></a><figcaption>Tangent track in blue with transition spiral in red and curved track in green.</figcaption></figure> <p>Horizontal layout is the track layout on the horizontal plane. This can be thought of as the <a href="/wiki/Multiview_orthographic_projection#Plan" title="Multiview orthographic projection">plan view</a> which is a view of a 3-dimensional track from the position above the track. In track geometry, the horizontal layout involves the layout of three main track types: <i>tangent track</i> (straight line), <i>curved track</i>, and <i><a href="/wiki/Track_transition_curve" title="Track transition curve">track transition curve</a></i> (also called <i>transition spiral</i> or <i>spiral</i>) which connects between a tangent and a curved track. Curved track can also be categorized into three types. The first type is simple curve which has the same radius throughout that curved track. The second type is compound curve which comprises two or more simple curves of different radii that have the same direction of curvature. The third type is <a href="/wiki/Reverse_curve" title="Reverse curve">reverse curve</a> which comprises two or more simple curves that has the opposite direction of curvature (sometime known as "S" curve or serpentine curve).<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><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> </p><p>In Australia, there is a special definition for a <i>bend</i> (or a <i>horizontal bend</i>) which is a connection between two tangent tracks at almost 180 degrees (with deviation not more than 1 degree 50 <a href="/wiki/Minute_of_arc" class="mw-redirect" title="Minute of arc">minutes</a>) without an intermediate curve. There is a set of speed limits for the bends separately from normal tangent track.<sup id="cite_ref-aus_5-0" class="reference"><a href="#cite_note-aus-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Vertical_layout">Vertical layout</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Track_geometry&action=edit&section=3" title="Edit section: Vertical layout"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Vertical layout is the track layout on the vertical plane. This can be thought of as the <a href="/wiki/Multiview_orthographic_projection#Elevation" title="Multiview orthographic projection">elevation view</a> which is the side view of the track to show track elevation. In track geometry, the vertical layout involves concepts such as crosslevel, cant and gradient. </p> <div class="mw-heading mw-heading3"><h3 id="Reference_rail">Reference rail</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Track_geometry&action=edit&section=4" title="Edit section: Reference rail"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The reference rail is the base rail that is used as a reference point for the measurement. It can vary in different countries. Most countries use one of the rails as the reference rail. For example, North America uses the reference rail as the <i>line rail</i> which is the east rail of tangent track running north and south, the north rail of tangent track running east and west, the outer rail (the rail that is further away from the center) on curves, or the outside rails in multiple track territory.<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> For Swiss railroad, the reference rail for tangent track is the center line between two rails, but it is the outside rail for curved track.<sup id="cite_ref-swiss_7-0" class="reference"><a href="#cite_note-swiss-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Track_gauge">Track gauge</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Track_geometry&action=edit&section=5" title="Edit section: Track gauge"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Track_gauge" title="Track gauge">Track gauge</a></div> <p><i>Track gauge</i> or <i>rail gauge</i> (also known as <i>track gage</i> in North America<sup id="cite_ref-usarmy_8-0" class="reference"><a href="#cite_note-usarmy-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup>) is the distance between the inner sides (gauge sides) of the heads of the two <a href="/wiki/Rail_profile" title="Rail profile">load bearing rails</a> that make up a single railway line. Each country uses different gauges for different types of trains. However, the <span class="nowrap">1,435 mm</span> (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="nowrap">4 ft <span class="frac">8<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span> in</span>) gauge is the basis of 60% of the world's railways. </p> <div class="mw-heading mw-heading2"><h2 id="Transverse_elevation">Transverse elevation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Track_geometry&action=edit&section=6" title="Edit section: Transverse elevation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Crosslevel">Crosslevel</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Track_geometry&action=edit&section=7" title="Edit section: Crosslevel"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Crosslevel_in_track_geometry.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Crosslevel_in_track_geometry.svg/350px-Crosslevel_in_track_geometry.svg.png" decoding="async" width="350" height="106" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Crosslevel_in_track_geometry.svg/525px-Crosslevel_in_track_geometry.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Crosslevel_in_track_geometry.svg/700px-Crosslevel_in_track_geometry.svg.png 2x" data-file-width="825" data-file-height="250" /></a><figcaption>The measurement of crosslevel between two rails</figcaption></figure> <p><i>Crosslevel</i> (or 'cross level') is the measurement of the difference in elevation (height) between the top surface of the two rails at any point of railroad track. The two points (each at the head of each rail) are measured at by the right angles to the <i>reference rail</i>. Since the rail can slightly move up and down, the measurement should be done under load. </p><p>It is said to be <i>zero crosslevel</i> when there is no difference in elevation of both rails. It is said to be <i>reverse crosslevel</i> when the outside rail of curved track has lower elevation than the inside rail. Otherwise, the crosslevel is expressed in the unit of height. </p><p>The speed limits are governed by the crosslevel of the track. In tangent track, it is desired to have zero crosslevel. However, the deviation from zero can take place. Many regulations have specification related to speed limits of certain segment of the track based on the crosslevel.<sup id="cite_ref-usarmy_8-1" class="reference"><a href="#cite_note-usarmy-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-fra_9-0" class="reference"><a href="#cite_note-fra-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>For curved track, most countries use the term <i><a href="/wiki/Cant_(road/rail)" class="mw-redirect" title="Cant (road/rail)">cant</a></i> or <i>superelevation</i> to express the difference in elevation and related regulations. </p> <div class="mw-heading mw-heading3"><h3 id="Warp">Warp</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Track_geometry&action=edit&section=8" title="Edit section: Warp"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>Warp</i> is the difference in crosslevel of any two points within the specific distance along the track. The warp parameter in the track geometry is used to specify the maximum in the crosslevel difference of the track in any segment (tangents, curves and spirals). </p><p>Without the maximum warp parameter, the regulation on crosslevel alone may not be sufficient. Consider rails with a positive crosslevel followed by a negative crosslevel followed by a sequence of alternating positive and negative crosslevels. Although, all of those crosslevels are in permissible parameter, when operating a train along such track, the motion will be rocking left and right. Therefore, the maximum warp parameter is used to prevent the critical <a href="/wiki/Harmonic" title="Harmonic">harmonic</a> rock-off condition that may result in the trains rocking back and forth and <a href="/wiki/Derailment" title="Derailment">derailing</a> following wheel climb.<sup id="cite_ref-fra_9-1" class="reference"><a href="#cite_note-fra-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>In North America, the specific distance used for measurement to ensure that the difference in crosslevel of the track is within the permissible warp parameter is 62 feet. The design warp is zero for both tangent and curved track. That means, ideally, the crosslevel should not change between any two points within 62 feet. There are some deviations to allow crosslevels along the track to change (such as change for superelevation in curves). Different levels of those deviations from the zero warp specify the speed limits.<sup id="cite_ref-usarmy_8-2" class="reference"><a href="#cite_note-usarmy-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>The specification that focuses on the rate of change in crosslevels of curved track is contained within the area related to <i>cant gradient</i>. </p> <div class="mw-heading mw-heading2"><h2 id="Longitudinal_elevation">Longitudinal elevation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Track_geometry&action=edit&section=9" title="Edit section: Longitudinal elevation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Track_gradient">Track gradient</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Track_geometry&action=edit&section=10" title="Edit section: Track gradient"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Track_gradient.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Track_gradient.svg/250px-Track_gradient.svg.png" decoding="async" width="250" height="102" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Track_gradient.svg/375px-Track_gradient.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/01/Track_gradient.svg/500px-Track_gradient.svg.png 2x" data-file-width="400" data-file-height="163" /></a><figcaption><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="plainlist"><ul><li><i>d</i>: distance traveled horizontally</li><li>Δ<i>h</i>: rise</li><li><i>l</i>: slope length</li><li><i>α</i>: angle of inclination</li></ul></div></figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Grade_(slope)#Railways" title="Grade (slope)">Grade (slope) § Railways</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Ruling_gradient" title="Ruling gradient">Ruling gradient</a></div> <p>The term <i>track gradient</i> is relative elevation of the two rails along the track. This can be expressed in the distance traveled horizontally for a rise of one unit, or in terms of an angle of inclination or a percentage difference in elevation for a given distance of the track. </p><p>The allowable gradients may be based on the <i>ruling gradient</i> which is the maximum gradient over which a tonnage train can be hauled with one locomotive. In some countries, <i>momentum gradient</i> which is a steeper but shorter gradient may be allowed. This is usually when a track gradient connects to a leveled tangent track long enough and with no signal between them such that a train can build momentum to push through a steeper grade than it can without the momentum gained on the leveled tangent track. </p><p>In curved track (with or without cant), there will be curve resistance to push the trains through the curve. The allowable gradients may be reduced on curves to compensate for the extra curve resistance.<sup id="cite_ref-aus_5-1" class="reference"><a href="#cite_note-aus-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> The gradient should be uniform along the track. </p> <div class="mw-heading mw-heading3"><h3 id="Vertical_curve">Vertical curve</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Track_geometry&action=edit&section=11" title="Edit section: Vertical curve"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>Vertical curve</i> is the curve in vertical layout to connect two track gradients together whether it is for changing from an <a href="/wiki/Grade_(slope)" title="Grade (slope)">upgrade</a> to a downgrade (summit), changing from a downgrade to an upgrade (sag or valley), changing in two levels of upgrades or changing in two levels of downgrades. </p><p>Some countries do not have specification on the exact geometry of vertical curves beyond general specification on vertical alignment. Australia has specification that the shape of vertical curves should be based on <a href="/wiki/Parabola" title="Parabola">quadratic parabola</a> but the length of a given vertical curve is calculated based on circular curve.<sup id="cite_ref-aus_5-2" class="reference"><a href="#cite_note-aus-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Curvature">Curvature</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Track_geometry&action=edit&section=12" title="Edit section: Curvature"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Amtrak_Keystone_Corridor_Rosemont_Curve.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/Amtrak_Keystone_Corridor_Rosemont_Curve.jpg/300px-Amtrak_Keystone_Corridor_Rosemont_Curve.jpg" decoding="async" width="300" height="192" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/Amtrak_Keystone_Corridor_Rosemont_Curve.jpg/450px-Amtrak_Keystone_Corridor_Rosemont_Curve.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/08/Amtrak_Keystone_Corridor_Rosemont_Curve.jpg/600px-Amtrak_Keystone_Corridor_Rosemont_Curve.jpg 2x" data-file-width="850" data-file-height="545" /></a><figcaption>Curve with superelevation of tracks on the <a href="/wiki/Keystone_Corridor" title="Keystone Corridor">Keystone Corridor</a> near Rosemont, Pennsylvania</figcaption></figure><p><i>Curvature</i> refers to the amount by which a curve deviates from being a straight line. In the context of railway tracks, it is the measure of how much the track deviates from a straight path. It is essential in designing safe and efficient rail systems. In railways, curvature impacts the speed and safety of trains, as sharper curves require slower speeds to avoid derailment. The formula for curvature in a curve is typically defined as the inverse of the radius of the curve. </p><p>Curves are essential in railway tracks as they allow trains to navigate various geographical and urban obstacles that make straight routes impractical or impossible. Natural terrains, such as mountains, valleys, and rivers, require railways to adapt to existing landscapes, which is achieved through carefully designed curves. Additionally, in cities and populated areas, tracks must curve to fit within limited spaces or avoid buildings and other infrastructure. Curved tracks help railways maintain an efficient layout that minimizes land disruption and follows the natural or urban environment. </p><p>In most countries, the measurement of <a href="/wiki/Curvature" title="Curvature">curvature</a> of curved track is expressed in <a href="/wiki/Radius" title="Radius">radius</a>. The shorter the radius, the sharper the curve is. For sharper curves, the speed limits are lower to prevent an outward horizontal <a href="/wiki/Centrifugal_force" title="Centrifugal force">centrifugal force</a> to overturn the trains by directing its weight toward the outside rail. Cant may be used to allow higher speeds over the same curve. </p><p>The curvature of railway tracks significantly affects train dynamics by influencing stability, safety, and performance. </p> <ol><li>Centrifugal force and stability: When a train navigates a curve, centrifugal force acts outward, which can destabilize the train. To counter this, tracks are often tilted (superelevation) to balance the force.</li> <li>Wheel-rail interaction: Tight curves can cause higher lateral forces between wheels and rails, increasing wear and the risk of derailment.</li> <li>Speed limitations: Curves require speed restrictions to ensure the train remains stable and comfortable for passengers.</li> <li>Transition curves: Gradual transition curves, such as <a href="/wiki/Euler_spiral" title="Euler spiral">Euler spirals</a>, are used to minimize sudden changes in curvature, reducing acceleration shocks and improving ride quality.</li></ol> <p>In North America, the measurement of curvature is expressed in <a href="/wiki/Degree_of_curvature" title="Degree of curvature">degree of curvature</a>. This is done by having a <a href="/wiki/Chord_(geometry)" title="Chord (geometry)">chord</a> of 100 feet (30.48 m) connecting to two points on an arc of the reference rail, then drawing radii from the center to each of the chord's end points. The angle between the radii lines is the degree of curvature.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> The degree of curvature is <a href="/wiki/Inverse_function" title="Inverse function">inverse</a> of radius. The larger the degree of curvature, the sharper the curve is. Expressing the curve in this way allows surveyors to use estimation and simpler tools in curve measurement. This can be done by using a 62-foot (18.90 m) string line to be a chord to connect the arc at the gauge side of the reference rail. Then at the midpoint of the string line (at the 31st foot), a measurement is taken from the string line to the gauge of the reference rail. The number of inches in that measurement is approximated to be the number of degrees of curvature.<sup id="cite_ref-usarmy_8-3" class="reference"><a href="#cite_note-usarmy-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>Due to the limitation of how specific train equipment can make a turn at maximum speeds, there is a limitation of <i><a href="/wiki/Minimum_railway_curve_radius" title="Minimum railway curve radius">minimum curve radius</a></i> to control the sharpness of all curves along a given route. Although most countries use radius for measurement of curvature, the term <i>maximum degree of curvature</i> is still used outside North America such as in India, but with the radius as the unit.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Cant">Cant</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Track_geometry&action=edit&section=13" title="Edit section: Cant"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Cant_(road/rail)" class="mw-redirect" title="Cant (road/rail)">Cant (road/rail)</a></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:5_inch_track_superelevation.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9a/5_inch_track_superelevation.jpg/300px-5_inch_track_superelevation.jpg" decoding="async" width="300" height="181" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9a/5_inch_track_superelevation.jpg/450px-5_inch_track_superelevation.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9a/5_inch_track_superelevation.jpg/600px-5_inch_track_superelevation.jpg 2x" data-file-width="1137" data-file-height="687" /></a><figcaption>Railroad track spirit level in place indicating 5 in (130 mm) of superelevation between the inside and outside rails of a curve along the <a href="/wiki/Keystone_Corridor" title="Keystone Corridor">Keystone Corridor</a> near <a href="/wiki/Narberth,_Pennsylvania" title="Narberth, Pennsylvania">Narberth, Pennsylvania</a></figcaption></figure><p>In curved track, it is usually designed to raise the outer rail, providing a <a href="/wiki/Banked_turn" title="Banked turn">banked turn</a>, thus allowing trains to maneuver through the curve at higher speeds that would otherwise be not possible if the surface was flat or level. It also helps a train steer around a curve, keeping the wheel flanges from pressing the rails, minimizing friction and wear. The measurement of the difference in elevation between the outer rail and the inner rail is called <i>cant</i> in most countries. Sometime the cant is measured in term of angle instead of height difference.<sup id="cite_ref-uk_12-0" class="reference"><a href="#cite_note-uk-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> In North America, it is measured in height difference and called crosslevel, even for the curved track. </p><p>When the outside rail is at higher elevation than the inside rail, it is called <i>positive cant</i>. This is normally the desired layout for curved track. Most counties achieve the desired level of positive cant by raising the outside rail to that level which is called <i>superelevation</i>. For Swiss railroads, the cant is done by rotating at the <i>track axis</i> (center of the two rails) to have outside rail super elevated (raised) at the half rate of the desired cant and the inside rail under elevated (lowered) at the same half rate of the desired cant. </p><p>When the outside rail is at lower elevation than the inside rail, it is called <i>negative cant</i> (or reverse crosslevel in North America). This is not usually a desired layout but it may be unavoidable in some situations such as curves involving <a href="/wiki/Railroad_switch" title="Railroad switch">turnouts</a>. </p><p>There are regulations which limit the maximum cant. This is to control the unloading of the wheels on the outside rail (high rail), especially at low speeds. </p> <div class="mw-heading mw-heading3"><h3 id="Cant_gradient">Cant gradient</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Track_geometry&action=edit&section=14" title="Edit section: Cant gradient"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>Cant gradient</i> is the amount by which cant is increased or decreased in a given length of track. The change in cant is required in order to connect a tangent track (no cant) to a curved track (with cant) through a transition curve. The <i>rate of change of cant</i> is used to determine the suitable cant gradient for a given design speed. <i>Track twist</i> may also be used to describe cant gradient which may be expressed in percentage of cant change per length unit.<sup id="cite_ref-swiss_7-1" class="reference"><a href="#cite_note-swiss-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> However, in the UK, the term track twist is normally used in the context of cant gradient with higher values which are considered to be faults.<sup id="cite_ref-uk_12-1" class="reference"><a href="#cite_note-uk-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>In North America, the required cant gradient on a transition curve to achieve smooth connection between superelevation of curved track and the zero crosslevel of tangent track is called <i>superelevation runoff</i>. In addition to the runoff specification, the regulations related to allowable rate of change in the cant is also part of the general specification on the rate of change in crosslevel called warp parameter. The warp parameter and superelevation runoff help calculate the required length of the runoff for a transition curve.<sup id="cite_ref-fra_9-2" class="reference"><a href="#cite_note-fra-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Cant_deficiency">Cant deficiency</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Track_geometry&action=edit&section=15" title="Edit section: Cant deficiency"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Cant_deficiency" title="Cant deficiency">Cant deficiency</a></div> <p>As described, cant may be used to reduce lateral acceleration on trains traveling on curved track. This is to balance the <a href="/wiki/Centrifugal_force" title="Centrifugal force">centrifugal force</a> (force pushing outward the curve) and <a href="/wiki/Centripetal_force" title="Centripetal force">centripetal force</a> (force pushing inward the curve). At a higher speed, the centrifugal force is higher. On the contrary, higher cant creates the higher centripetal force. The calculation for this assumes a constant train speed on a constant radius curve. </p><p>When the speed of the train and the amount of cant are in <i>balance</i> (centrifugal matches centripetal), it is called <i>equilibrium</i>. This would make the components of wheel to rail force normal to the plane of the track having the same in aggregate for the outside rail as for the inside rail. This would also make the passengers in the train not to perceive any lateral acceleration (a push toward sideway). </p><p>For a fixed amount of cant, the speed that creates balance is called <i>equilibrium speed</i>. For a constant speed of a running train, the amount of required cant to achieve the balance is called <i>equilibrium cant</i>.<sup id="cite_ref-uk_12-2" class="reference"><a href="#cite_note-uk-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>In practice, trains are not running on equilibrium cants at curves. The situation is called <i>unbalance</i>, which can be in one of the two following ways. For a given speed, if the actual cant is less than the equilibrium cant, the amount of cant difference is called <i>cant deficiency</i>. In the other word, it is the amount of missing cant to achieve the balance. On the contrary, for a given speed, if the actual cant is higher than the equilibrium cant, the amount of over cant from the balance is called <i>cant excess</i>. </p><p>In a shared track configuration for trains with different operating speeds such as freight and <a href="/wiki/Higher_speed_rail" class="mw-redirect" title="Higher speed rail">higher-speed rail</a> passenger services, the cant on a curve should be considered for both high and low speeds. The higher-speed trains would experience cant deficiency and the lower-speed trains would experience cant excess. These parameters have a significant effect on curve performance which includes safety, passenger comfort, and <a href="/wiki/Wear_and_tear" title="Wear and tear">wear and tear</a> of equipment and rails.<sup id="cite_ref-interface_13-0" class="reference"><a href="#cite_note-interface-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Alignment">Alignment</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Track_geometry&action=edit&section=16" title="Edit section: Alignment"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The term <i>alignment</i> is used in both horizontal and vertical layouts to describe the line uniformity (straightness) of the rails. </p><p>The horizontal alignment (or <i>alinement</i> in the United States) is done by using a predefined length of string line (such as 62-foot in the US and 20 meters in Australia<sup id="cite_ref-aus_5-3" class="reference"><a href="#cite_note-aus-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>) to measure along the gauge side of the reference rail. It is the distance (in inches or millimeters) from the midpoint of the string line to the gauge of the reference rail. The design horizontal alignment for tangent track is zero (perfect straight line on the horizontal layout). The design horizontal alignment on the curved track in North America is 1 inch for each degree of curvature. Any other readings indicate deviations. </p><p>The vertical alignment (or <i>profile</i> in North America, but not to be confused with <a href="/wiki/Rail_profile" title="Rail profile">rail profile</a>) is the surface uniformity in the vertical plane. The measurement of uniformity is done using a predefined length of string line (normally the same length used in horizontal alignment) along the track. If the midpoint of the measurement has higher elevation, it is called <i>hump deviation</i>. On the other hand, if the midpoint has lower elevation, it is called <i>dip deviation</i>.<sup id="cite_ref-fra_9-3" class="reference"><a href="#cite_note-fra-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>These deviations from design alignment are used as parameters to assign speed limits. </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_geometry&action=edit&section=17" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Geometric_design_of_roads" title="Geometric design of roads">Geometric design of roads</a></li> <li><a href="/wiki/Jim_crow_(tool)" title="Jim crow (tool)">Jim crow</a>, a tool for bending rails</li> <li><a href="/wiki/Track_geometry_car" title="Track geometry car">Track geometry car</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_geometry&action=edit&section=18" 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 mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://dictionary.cambridge.org/dictionary/english/geometry">"geometry"</a>. <i>Cambridge Dictionary</i>. Cambridge University Press. 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">21 October</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Cambridge+Dictionary&rft.atitle=geometry&rft.date=2021&rft_id=https%3A%2F%2Fdictionary.cambridge.org%2Fdictionary%2Fenglish%2Fgeometry&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATrack+geometry" class="Z3988"></span></span> </li> <li id="cite_note-fra-sheet-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-fra-sheet_2-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.fra.dot.gov/downloads/PubAffairs/Track_Standards_fact_sheet_FINAL.pdf">"Federal Railroad Administration Federal Track Safety Standards Fact Sheet"</a> <span class="cs1-format">(PDF)</span>. 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Retrieved <span class="nowrap">8 November</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Federal+Railroad+Administration+Federal+Track+Safety+Standards+Fact+Sheet&rft.pub=Federal+Railroad+Administration&rft_id=http%3A%2F%2Fwww.fra.dot.gov%2Fdownloads%2FPubAffairs%2FTrack_Standards_fact_sheet_FINAL.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATrack+geometry" 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="CITEREFMundrey2000" class="citation book cs1">Mundrey (2000). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=PzA3N6eP4TYC&pg=PA164"><i>Railway Track Engineering</i></a>. <a href="/wiki/McGraw-Hill_Education" class="mw-redirect" title="McGraw-Hill Education">McGraw-Hill Education</a>. pp. <span class="nowrap">164–</span>179. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780074637241" title="Special:BookSources/9780074637241"><bdi>9780074637241</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Railway+Track+Engineering&rft.pages=%3Cspan+class%3D%22nowrap%22%3E164-%3C%2Fspan%3E179&rft.pub=McGraw-Hill+Education&rft.date=2000&rft.isbn=9780074637241&rft.au=Mundrey&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DPzA3N6eP4TYC%26pg%3DPA164&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATrack+geometry" 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="CITEREFDuggal2004" class="citation book cs1">Duggal, S. K. (2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=NYUEeDJcVbEC&q=%22compound+curve%22"><i>Surveying</i></a> (2nd ed.). New Delhi: Tata McGraw-Hill. pp. <span class="nowrap">480–</span>481. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780070534704" title="Special:BookSources/9780070534704"><bdi>9780070534704</bdi></a><span class="reference-accessdate">. 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Department of Planning Transport, and Infrastructure - Government of South Australia. 2008.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=PART+1025+Track+Geometry&rft.edition=Issue+2+%E2%80%93+07%2F10%2F08&rft.pub=Department+of+Planning+Transport%2C+and+Infrastructure+-+Government+of+South+Australia&rft.date=2008&rft_id=http%3A%2F%2Fwww.dpti.sa.gov.au%2F__data%2Fassets%2Fword_doc%2F0004%2F40684%2FPart_1025_Rail_Track_geometry.doc&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATrack+geometry" 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 class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.allenrailroad.com/consulting/Railroad_Glossary.htm">"Railroad Glossary and Definitions"</a>. Allen Railroad<span class="reference-accessdate">. Retrieved <span class="nowrap">12 November</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Railroad+Glossary+and+Definitions&rft.pub=Allen+Railroad&rft_id=http%3A%2F%2Fwww.allenrailroad.com%2Fconsulting%2FRailroad_Glossary.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATrack+geometry" class="Z3988"></span></span> </li> <li id="cite_note-swiss-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-swiss_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-swiss_7-1"><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="CITEREFGlaus2006" class="citation book cs1">Glaus, Ralph (2006). 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Federal Railroad Administration. 1 April 2007. Archived from <a rel="nofollow" class="external text" href="http://www.fra.dot.gov/downloads/safety/tss_compliance_manual_chapter_5_final_040107.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 28 May 2008<span class="reference-accessdate">. Retrieved <span class="nowrap">13 November</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=5&rft.btitle=Federal+Railroad+Administration+Track+Safety+Standards+Compliance+Manual&rft.pub=Federal+Railroad+Administration&rft.date=2007-04-01&rft_id=http%3A%2F%2Fwww.fra.dot.gov%2Fdownloads%2Fsafety%2Ftss_compliance_manual_chapter_5_final_040107.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATrack+geometry" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://trn.trains.com/en/Railroad%20Reference/Ask%20Trains/2011/01/Measuring%20track%20curvature.aspx">"Measuring track curvature"</a>. <i>ASK TRAINS</i>. Trains magazine<span class="reference-accessdate">. Retrieved <span class="nowrap">13 November</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=ASK+TRAINS&rft.atitle=Measuring+track+curvature&rft_id=http%3A%2F%2Ftrn.trains.com%2Fen%2FRailroad%2520Reference%2FAsk%2520Trains%2F2011%2F01%2FMeasuring%2520track%2520curvature.aspx&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATrack+geometry" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMundrey2000" class="citation book cs1">Mundrey, J.S. (2000). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=PzA3N6eP4TYC&pg=PA165"><i>Railway track engineering</i></a> (3rd ed.). New Delhi: Tata McGraw-Hill Pub. p. 165. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-463724-1" title="Special:BookSources/978-0-07-463724-1"><bdi>978-0-07-463724-1</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">14 November</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Railway+track+engineering&rft.place=New+Delhi&rft.pages=165&rft.edition=3rd&rft.pub=Tata+McGraw-Hill+Pub.&rft.date=2000&rft.isbn=978-0-07-463724-1&rft.aulast=Mundrey&rft.aufirst=J.S.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DPzA3N6eP4TYC%26pg%3DPA165&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATrack+geometry" class="Z3988"></span></span> </li> <li id="cite_note-uk-12"><span class="mw-cite-backlink">^ <a href="#cite_ref-uk_12-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-uk_12-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-uk_12-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20120131143623/http://www.rgsonline.co.uk/Railway_Group_Standards/Infrastructure/Railway%20Group%20Standards/GCRT5021%20Iss%205.pdf"><i>Track Standards Manual - Section 8: Track Geometry</i></a> <span class="cs1-format">(PDF)</span>. Railtrack PLC. December 1998. Archived from <a rel="nofollow" class="external text" href="http://www.rgsonline.co.uk/Railway_Group_Standards/Infrastructure/Railway%20Group%20Standards/GCRT5021%20Iss%205.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2012-01-31<span class="reference-accessdate">. Retrieved <span class="nowrap">28 May</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Track+Standards+Manual+-+Section+8%3A+Track+Geometry&rft.pub=Railtrack+PLC&rft.date=1998-12&rft_id=http%3A%2F%2Fwww.rgsonline.co.uk%2FRailway_Group_Standards%2FInfrastructure%2FRailway%2520Group%2520Standards%2FGCRT5021%2520Iss%25205.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATrack+geometry" class="Z3988"></span></span> </li> <li id="cite_note-interface-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-interface_13-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKlauser2005" class="citation journal cs1">Klauser, Peter (October 2005). <a rel="nofollow" class="external text" href="http://www.interfacejournal.com/features/09-05/cant/1.html">"Operating at High Cant Deficiency"</a>. <i>Interface - the Journal of Wheel/Rail Interaction</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Interface+-+the+Journal+of+Wheel%2FRail+Interaction&rft.atitle=Operating+at+High+Cant+Deficiency&rft.date=2005-10&rft.aulast=Klauser&rft.aufirst=Peter&rft_id=http%3A%2F%2Fwww.interfacejournal.com%2Ffeatures%2F09-05%2Fcant%2F1.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATrack+geometry" class="Z3988"></span></span> </li> </ol></div></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output 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title="Rail transport">Railway</a> track layouts</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Railway_track" title="Railway track">Railway track</a></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/Single-track_railway" title="Single-track railway">Single track</a></li> <li><a href="/wiki/Passing_loop" title="Passing loop">Passing loop</a></li> <li><a href="/wiki/Double-track_railway" title="Double-track railway">Double track</a></li> <li><a href="/wiki/Quadruple-track_railway" title="Quadruple-track railway">Quadruple track</a></li> <li><a href="/wiki/Railroad_switch#Crossover" title="Railroad switch">Crossover</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Siding_(rail)" title="Siding (rail)">Rail sidings</a></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/Headshunt" title="Headshunt">Headshunt</a></li> <li><a href="/wiki/Pocket_track" title="Pocket track">Pocket track</a></li> <li><a href="/wiki/Refuge_siding" title="Refuge siding">Refuge siding</a></li> <li><a href="/wiki/Rail_yard" title="Rail yard">Rail yard</a></li> <li><a href="/wiki/Classification_yard" title="Classification yard">Classification yard</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Junction_(rail)" title="Junction (rail)">Junctions</a></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/Flying_junction" title="Flying junction">Flying junction</a></li> <li><a href="/wiki/Level_junction" title="Level junction">Level junction</a></li> <li><a href="/wiki/Double_junction" title="Double junction">Double junction</a></li> <li><a href="/wiki/Facing_and_trailing" title="Facing and trailing">Facing and trailing</a></li> <li><a href="/wiki/Grand_union" title="Grand union">Grand union</a></li> <li><a href="/wiki/Tram_roundabout" title="Tram roundabout">Grand circle / roundabout</a></li> <li><a href="/wiki/Wye_(rail)" title="Wye (rail)">Wye</a></li> <li><a href="/wiki/Railroad_switch" title="Railroad switch">Switch / turnout / points</a></li> <li><a href="/wiki/Swingnose_crossing" title="Swingnose crossing">Swingnose crossing</a></li> <li><a href="/wiki/Level_crossing" title="Level crossing">Level crossing</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Train_station" title="Train station">Stations</a></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/Railway_platform" title="Railway platform">Railway platform</a> <ul><li><a href="/wiki/Bay_platform" title="Bay platform">Bay</a></li> <li><a href="/wiki/Island_platform" title="Island platform">Island</a></li> <li><a href="/wiki/Side_platform" title="Side platform">Side</a></li> <li><a href="/wiki/Split_platform" title="Split platform">Split</a></li></ul></li> <li><a href="/wiki/Terminal_station" class="mw-redirect" title="Terminal station">Terminal station</a></li> <li><a href="/wiki/Balloon_loop" title="Balloon loop">Balloon loop</a></li> <li><a href="/wiki/Spanish_solution" title="Spanish solution">Spanish solution</a></li> <li><a href="/wiki/Cross-platform_interchange" title="Cross-platform interchange">Cross-platform interchange</a></li> <li><a href="/wiki/Interchange_station" title="Interchange station">Interchange station</a></li> <li><a href="/wiki/Infill_station" title="Infill station">Infill station</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Hillclimbing_(railway)" title="Hillclimbing (railway)">Hillclimbing</a></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/Horseshoe_curve" title="Horseshoe curve">Horseshoe curve</a></li> <li><a href="/wiki/Zig_zag_(railway)" title="Zig zag (railway)">Zig Zag / Switchback</a></li> <li><a href="/wiki/Spiral_(railway)" title="Spiral (railway)">Spiral</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a class="mw-selflink selflink">Track geometry</a></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/Track_gauge" title="Track gauge">Track gauge</a></li> <li><a href="/wiki/Ruling_gradient" title="Ruling gradient">Ruling gradient</a></li> <li><a href="/wiki/Minimum_railway_curve_radius" title="Minimum railway curve radius">Minimum curve radius</a></li> <li><a href="/wiki/Cant_(road/rail)" class="mw-redirect" title="Cant (road/rail)">Cant</a></li> <li><a href="/wiki/Cant_deficiency" title="Cant deficiency">Cant deficiency</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Rail_infrastructure212" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a 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<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 href="/wiki/Track_transition_curve" title="Track transition curve">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 class="mw-selflink selflink">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 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