{"id":3332,"date":"2024-08-30T17:38:11","date_gmt":"2024-08-30T12:08:11","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=3332"},"modified":"2025-07-16T14:59:39","modified_gmt":"2025-07-16T09:29:39","slug":"length-of-summit-curve","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/ce\/highway-engineering\/length-of-summit-curve","title":{"rendered":"Length of Summit Curve"},"content":{"rendered":"<p style=\"text-align: justify;\">For summit curve, the most important consideration in determining length of curve is requirement of sight distance. Length of summit curve depends on whether sight distance is lesser or greater than length of curve.<\/p>\n<h2 style=\"text-align: justify;\">Length of summit curves for both cases are given below<\/h2>\n<p style=\"text-align: justify;\"><strong>Case 1 :<\/strong> Consider a summit curve as shown in figure below.<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3333 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/summit-curve.jpg\" alt=\"Summit Curve\" width=\"676\" height=\"584\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/summit-curve.jpg 676w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/summit-curve-300x259.jpg 300w\" sizes=\"auto, (max-width: 676px) 100vw, 676px\" \/><\/p>\n<p style=\"text-align: justify;\">(a) If stopping sight distance, i.e., SSD is used as a sight distance, then<br \/>\nh<sub>1<\/sub> = 1.2 m and h<sub>2<\/sub> = 0.15 m.<br \/>\nPutting the values in above equation, we get<\/p>\n<p style=\"text-align: justify;\">Ls = NS<sup>2<\/sup> \/ 4.4<\/p>\n<p style=\"text-align: justify;\">(b) If overtaking or intermediate sight distance, i.e., OSD or ISD is used as a sight distance, then<br \/>\nh<sub>1<\/sub> = 1.2 m, h<sub>2<\/sub> = 1.2 m.<br \/>\nPutting values in above equation, we get<\/p>\n<p style=\"text-align: justify;\">Ls = NS<sup>2<\/sup> \/ 9.6<\/p>\n<p style=\"text-align: justify;\"><strong>Case 2 :<\/strong> When length of curve is less than sight distance S provided on the road.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3334 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/sight-distance-1.jpg\" alt=\"Sight Distance\" width=\"636\" height=\"450\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/sight-distance-1.jpg 636w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/sight-distance-1-300x212.jpg 300w\" sizes=\"auto, (max-width: 636px) 100vw, 636px\" \/><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3335 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/summit-curve-1.jpg\" alt=\"Summit curve\" width=\"649\" height=\"430\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/summit-curve-1.jpg 649w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/summit-curve-1-300x199.jpg 300w\" sizes=\"auto, (max-width: 649px) 100vw, 649px\" \/><\/p>\n<p style=\"text-align: justify;\">(a) If stopping sight distance is provided on road, then h1 = 1.2 m, h2 = 0.15 m. Putting values in eqn. (iv), we get<\/p>\n<p style=\"text-align: justify;\">Ls = 2S &#8211; 4.4\/N<\/p>\n<p style=\"text-align: justify;\">(b) If overtaking or intermediate sight distance, i.e., OSD or ISD is provided on road, then h1 = 1.2 m, h2 = 1.2 m. Putting values, we get<\/p>\n<p style=\"text-align: justify;\">Ls = 2S &#8211; 9.6\/N<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_79_1 ez-toc-wrap-left counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.madeeasy.in\/study\/ce\/highway-engineering\/length-of-summit-curve\/#Length-of-Valley-Curve\" >Length of Valley Curve<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.madeeasy.in\/study\/ce\/highway-engineering\/length-of-summit-curve\/#a-Length-of-valley-curve-as-per-comfort-condition\" >(a) Length of valley curve as per comfort condition<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.madeeasy.in\/study\/ce\/highway-engineering\/length-of-summit-curve\/#b-Length-of-valley-curve-based-on-head-light-sight-distance\" >(b) Length of valley curve based on head light sight distance :\u00a0<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.madeeasy.in\/study\/ce\/highway-engineering\/length-of-summit-curve\/#Case-1-When-length-of-valley-curves-LV-is-greater-than-stopping-sight-distance-SSD\" >Case-1: When length of valley curves, LV is greater than stopping sight distance SSD<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.madeeasy.in\/study\/ce\/highway-engineering\/length-of-summit-curve\/#Case-2-When-length-of-valley-curve-is-lesser-than-stopping-sight-distance-SSD\" >Case-2: When length of valley curve is lesser than stopping sight distance SSD<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.madeeasy.in\/study\/ce\/highway-engineering\/length-of-summit-curve\/#Lowest-Point-on-Valley-Curve\" >Lowest Point on Valley Curve<\/a><\/li><\/ul><\/nav><\/div>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Length-of-Valley-Curve\"><\/span>Length of Valley Curve<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">These curves are designed mainly to serve two criteria :<\/p>\n<p style=\"text-align: justify;\">(a) Allowable rate of change of centrifugal acceleration.<br \/>\n(b) The required head light sight distance for night driving.<\/p>\n<p style=\"text-align: justify;\">Length of valley curve is calculated on basis of both the criteria and higher length is adopted as length of valley curve.<\/p>\n<p style=\"text-align: justify;\">Hence, shape of valley curve is chosen as combination of transition curve. Two similar transition curves of equal length (without circular curve in between) where, Lt = Lv \/2, having radius R at common point of meeting of transition curves are adopted as valley curve.<\/p>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"a-Length-of-valley-curve-as-per-comfort-condition\"><\/span><strong>(a) Length of valley curve as per comfort condition<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\">Length of transition curve so as to provide a limit on the rate of change of centrifugal acceleration, Lt is given by<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3336 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/centrifugal-acceleration.jpg\" alt=\"Centrifugal Acceleration\" width=\"592\" height=\"513\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/centrifugal-acceleration.jpg 592w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/centrifugal-acceleration-300x260.jpg 300w\" sizes=\"auto, (max-width: 592px) 100vw, 592px\" \/><\/p>\n<p style=\"text-align: justify;\">It is to be kept in mind that minimum radius of curvature of transition curve, R is given by, R = Lt \/ N<br \/>\nwhere Lt = length of transition curve.<br \/>\nSo, minimum radius of valley curve,<\/p>\n<p style=\"text-align: justify;\">R = LV \/ 2N<\/p>\n<p style=\"text-align: justify;\">where, LV = Length of valley curve<\/p>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"b-Length-of-valley-curve-based-on-head-light-sight-distance\"><\/span><strong>(b) Length of valley curve based on head light sight distance :\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\">Length of valley curve based on headlight sight distance is calculated in the following two cases :<\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Case-1-When-length-of-valley-curves-LV-is-greater-than-stopping-sight-distance-SSD\"><\/span><strong>Case-1: When length of valley curves, LV is greater than stopping sight distance SSD<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">It is assumed that length of valley curve LV is greater than headlight sight distance which is at least taken equal to stopping sight distance. To calculate length of valley curve, consider a valley curve<\/p>\n<p style=\"text-align: justify;\">which is assumed to be parabolic in shape having equation y = ax<sup>2<\/sup> where a = N \/ 2L<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3337 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/parabolic.jpg\" alt=\"Parabolic\" width=\"378\" height=\"176\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/parabolic.jpg 378w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/parabolic-300x140.jpg 300w\" sizes=\"auto, (max-width: 378px) 100vw, 378px\" \/><\/p>\n<p style=\"text-align: justify;\">From figure, we can say that available sight distance for vehicle will be minimum when it is at lowest point on curve. So, while calculating required length of curve, vehicle is assumed to be on lowest point so that the calculated length of curve is sufficient for vehicle when it is not on lowest point.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3340 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/valley-curve.jpg\" alt=\"Valley Curve\" width=\"598\" height=\"274\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/valley-curve.jpg 598w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/valley-curve-300x137.jpg 300w\" sizes=\"auto, (max-width: 598px) 100vw, 598px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Case-2-When-length-of-valley-curve-is-lesser-than-stopping-sight-distance-SSD\"><\/span><strong>Case-2: When length of valley curve is lesser than stopping sight distance SSD<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">Here, length of valley curve is less than available sight distance. To calculate length of valley curve, consider a valley curve of parabolic profile with vehicle at starting of curve so that available sight distance for vehicle is minimum.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3342 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/08\/sight-distance-2.jpg\" alt=\"Sight Distance\" width=\"584\" height=\"402\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/sight-distance-2.jpg 584w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/sight-distance-2-300x207.jpg 300w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/08\/sight-distance-2-130x90.jpg 130w\" sizes=\"auto, (max-width: 584px) 100vw, 584px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Lowest-Point-on-Valley-Curve\"><\/span>Lowest Point on Valley Curve<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">This point is located on curve to provide cross drainage to water. This point will be on bisector of angle between the grades, if the curve is symmetrical.<br \/>\nWhen the valley curve is unsymmetrical, then lowest point lies on flatter grade, and this point is X<sub>o<\/sub> distance from starting point, i.e., first tangent point of curve.<\/p>\n<p style=\"text-align: justify;\">X<sub>o<\/sub> = L \u221an<sub>1<\/sub>\/2N<\/p>\n<p style=\"text-align: justify;\">It is obtained by assuming the curve to be of cubic parabola profile.<\/p>\n<p style=\"text-align: center;\"><a class=\"btn btn-danger\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ce\/highway-engineering\/set-back-distance\/\" target=\"_blank\" rel=\"noopener\">&lt;&lt; Previous<\/a> | <a class=\"btn btn-success\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ce\/highway-engineering\/traffic-studies\/\" target=\"_blank\" rel=\"noopener\"> Next &gt;&gt;<\/a><br \/>\n<strong> Must Read: <\/strong> <a href=\"https:\/\/study.madeeasy.in\/subjects\/what-is-highway-engineering\/\" target=\"_blank\" rel=\"noopener\"><strong>What is Highway Engineering?<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>For summit curve, the most important consideration in determining length of curve is requirement of sight distance. Length of summit<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[921,2],"tags":[933,482,932],"class_list":["post-3332","post","type-post","status-publish","format-standard","hentry","category-highway-engineering","category-ce","tag-length-of-valley-curve","tag-sight-distance","tag-summit-curve"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/3332","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=3332"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/3332\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=3332"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=3332"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=3332"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}