[{"data":1,"prerenderedAt":2843},["ShallowReactive",2],{"blog-\u002Fblog\u002Frankines-method-the-definitive-guide-to-setting-out-circular-curves":3,"blog-surround-\u002Fblog\u002Frankines-method-the-definitive-guide-to-setting-out-circular-curves":2832},{"id":4,"title":5,"author":6,"body":7,"category":2781,"description":2809,"extension":2810,"image":2811,"meta":2812,"navigation":2824,"path":2825,"publishedAt":2826,"readTime":2827,"seo":2828,"sitemap":2829,"stem":2830,"__hash__":2831},"blog\u002Fblog\u002F3.rankines-method-the-definitive-guide-to-setting-out-circular-curves.md","Rankine’s Method: The Definitive Guide to Setting Out Circular Curves","Surveyiiing Expert",{"type":8,"value":9,"toc":2786},"minimark",[10,15,33,37,43,47,53,57,171,349,531,535,1138,1142,1442,1446,1643,2259,2263,2510,2514,2672,2676,2765,2769,2772,2776],[11,12,14],"h2",{"id":13},"overview","Overview",[16,17,18,19,23,24,28,29,32],"p",{},"Horizontal circular curves are essential for connecting two straight sections of a road or railway ",[20,21,22],"span",{},"13",". ",[25,26,27],"strong",{},"Rankine’s Method",", also known as the tangential angle method, is the most popular field technique for establishing these curves using a theodolite and tape ",[20,30,31],{},"14",".",[11,34,36],{"id":35},"why-this-matters","Why This Matters",[16,38,39,40,32],{},"Precise curve setting ensures that vehicles can navigate changes in direction safely at design speeds. Rankine’s method is versatile because it allows you to set out points on the curve even if the Intersection Point (IP) is inaccessible ",[20,41,42],{},"14, 15",[11,44,46],{"id":45},"theory","Theory",[16,48,49,50,32],{},"Rankine’s method is based on the geometric principle that the angle between a tangent and a chord is equal to half the angle subtended by the chord at the center of the circle ",[20,51,52],{},"16",[11,54,56],{"id":55},"mathematical-principles","Mathematical Principles",[16,58,59,60,107,108,138,139,170],{},"To calculate the deflection angle (",[20,61,64,87],{"className":62},[63],"katex",[20,65,68],{"className":66},[67],"katex-mathml",[69,70,72],"math",{"xmlns":71},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[73,74,75,82],"semantics",{},[76,77,78],"mrow",{},[79,80,81],"mi",{},"δ",[83,84,86],"annotation",{"encoding":85},"application\u002Fx-tex","\\delta",[20,88,92],{"className":89,"ariaHidden":91},[90],"katex-html","true",[20,93,96,101],{"className":94},[95],"base",[20,97],{"className":98,"style":100},[99],"strut","height:0.6944em;",[20,102,81],{"className":103,"style":106},[104,105],"mord","mathnormal","margin-right:0.0379em;",") for a chord of length ",[20,109,111,125],{"className":110},[63],[20,112,114],{"className":113},[67],[69,115,116],{"xmlns":71},[73,117,118,123],{},[76,119,120],{},[79,121,122],{},"c",[83,124,122],{"encoding":85},[20,126,128],{"className":127,"ariaHidden":91},[90],[20,129,131,135],{"className":130},[95],[20,132],{"className":133,"style":134},[99],"height:0.4306em;",[20,136,122],{"className":137},[104,105]," on a curve of radius ",[20,140,142,156],{"className":141},[63],[20,143,145],{"className":144},[67],[69,146,147],{"xmlns":71},[73,148,149,154],{},[76,150,151],{},[79,152,153],{},"R",[83,155,153],{"encoding":85},[20,157,159],{"className":158,"ariaHidden":91},[90],[20,160,162,166],{"className":161},[95],[20,163],{"className":164,"style":165},[99],"height:0.6833em;",[20,167,153],{"className":168,"style":169},[104,105],"margin-right:0.0077em;",":",[16,172,173,176],{},[25,174,175],{},"1. In Radians:",[20,177,179,215],{"className":178},[63],[20,180,182],{"className":181},[67],[69,183,184],{"xmlns":71},[73,185,186,212],{},[76,187,188,190,194,198],{},[79,189,81],{},[191,192,193],"mtext",{}," rad",[195,196,197],"mo",{},"=",[199,200,201,204],"mfrac",{},[191,202,203],{},"chord",[76,205,206,210],{},[207,208,209],"mn",{},"2",[79,211,153],{},[83,213,214],{"encoding":85},"\\delta \\text{ rad} = \\frac{\\text{chord}}{2R}",[20,216,218,246],{"className":217,"ariaHidden":91},[90],[20,219,221,224,227,234,239,243],{"className":220},[95],[20,222],{"className":223,"style":100},[99],[20,225,81],{"className":226,"style":106},[104,105],[20,228,231],{"className":229},[104,230],"text",[20,232,193],{"className":233},[104],[20,235],{"className":236,"style":238},[237],"mspace","margin-right:0.2778em;",[20,240,197],{"className":241},[242],"mrel",[20,244],{"className":245,"style":238},[237],[20,247,249,253],{"className":248},[95],[20,250],{"className":251,"style":252},[99],"height:1.2251em;vertical-align:-0.345em;",[20,254,256,261,345],{"className":255},[104],[20,257],{"className":258},[259,260],"mopen","nulldelimiter",[20,262,264],{"className":263},[199],[20,265,269,336],{"className":266},[267,268],"vlist-t","vlist-t2",[20,270,273,331],{"className":271},[272],"vlist-r",[20,274,278,302,313],{"className":275,"style":277},[276],"vlist","height:0.8801em;",[20,279,281,286],{"style":280},"top:-2.655em;",[20,282],{"className":283,"style":285},[284],"pstrut","height:3em;",[20,287,293],{"className":288},[289,290,291,292],"sizing","reset-size6","size3","mtight",[20,294,296,299],{"className":295},[104,292],[20,297,209],{"className":298},[104,292],[20,300,153],{"className":301,"style":169},[104,105,292],[20,303,305,308],{"style":304},"top:-3.23em;",[20,306],{"className":307,"style":285},[284],[20,309],{"className":310,"style":312},[311],"frac-line","border-bottom-width:0.04em;",[20,314,316,319],{"style":315},"top:-3.394em;",[20,317],{"className":318,"style":285},[284],[20,320,322],{"className":321},[289,290,291,292],[20,323,325],{"className":324},[104,292],[20,326,328],{"className":327},[104,230,292],[20,329,203],{"className":330},[104,292],[20,332,335],{"className":333},[334],"vlist-s","​",[20,337,339],{"className":338},[272],[20,340,343],{"className":341,"style":342},[276],"height:0.345em;",[20,344],{},[20,346],{"className":347},[348,260],"mclose",[16,350,351,354,528,529],{},[25,352,353],{},"2. In Degrees (The Surveying Standard):",[20,355,357,393],{"className":356},[63],[20,358,360],{"className":359},[67],[69,361,362],{"xmlns":71},[73,363,364,390],{},[76,365,366,374,376],{},[367,368,369,371],"msup",{},[79,370,81],{},[195,372,373],{},"∘",[195,375,197],{},[199,377,378,388],{},[76,379,380,383,386],{},[207,381,382],{},"28.6479",[195,384,385],{},"×",[191,387,203],{},[79,389,153],{},[83,391,392],{"encoding":85},"\\delta^\\circ = \\frac{28.6479 \\times \\text{chord}}{R}",[20,394,396,445],{"className":395,"ariaHidden":91},[90],[20,397,399,402,436,439,442],{"className":398},[95],[20,400],{"className":401,"style":100},[99],[20,403,405,408],{"className":404},[104],[20,406,81],{"className":407,"style":106},[104,105],[20,409,412],{"className":410},[411],"msupsub",[20,413,415],{"className":414},[267],[20,416,418],{"className":417},[272],[20,419,422],{"className":420,"style":421},[276],"height:0.6741em;",[20,423,425,429],{"style":424},"top:-3.063em;margin-right:0.05em;",[20,426],{"className":427,"style":428},[284],"height:2.7em;",[20,430,432],{"className":431},[289,290,291,292],[20,433,373],{"className":434},[435,292],"mbin",[20,437],{"className":438,"style":238},[237],[20,440,197],{"className":441},[242],[20,443],{"className":444,"style":238},[237],[20,446,448,451],{"className":447},[95],[20,449],{"className":450,"style":252},[99],[20,452,454,457,525],{"className":453},[104],[20,455],{"className":456},[259,260],[20,458,460],{"className":459},[199],[20,461,463,517],{"className":462},[267,268],[20,464,466,514],{"className":465},[272],[20,467,469,483,491],{"className":468,"style":277},[276],[20,470,471,474],{"style":280},[20,472],{"className":473,"style":285},[284],[20,475,477],{"className":476},[289,290,291,292],[20,478,480],{"className":479},[104,292],[20,481,153],{"className":482,"style":169},[104,105,292],[20,484,485,488],{"style":304},[20,486],{"className":487,"style":285},[284],[20,489],{"className":490,"style":312},[311],[20,492,493,496],{"style":315},[20,494],{"className":495,"style":285},[284],[20,497,499],{"className":498},[289,290,291,292],[20,500,502,505,508],{"className":501},[104,292],[20,503,382],{"className":504},[104,292],[20,506,385],{"className":507},[435,292],[20,509,511],{"className":510},[104,230,292],[20,512,203],{"className":513},[104,292],[20,515,335],{"className":516},[334],[20,518,520],{"className":519},[272],[20,521,523],{"className":522,"style":342},[276],[20,524],{},[20,526],{"className":527},[348,260]," ",[20,530,52],{},[11,532,534],{"id":533},"field-workflow","Field Workflow",[536,537,538,543,791,795,899,903,981,985,1060,1064],"steps",{},[539,540,542],"h3",{"id":541},"locate-tangent-points","Locate Tangent Points",[16,544,545,546,624,625,695,696,756,757,787,788,32],{},"Fix the first tangent point (",[20,547,549,570],{"className":548},[63],[20,550,552],{"className":551},[67],[69,553,554],{"xmlns":71},[73,555,556,567],{},[76,557,558],{},[559,560,561,564],"msub",{},[79,562,563],{},"T",[207,565,566],{},"1",[83,568,569],{"encoding":85},"T_1",[20,571,573],{"className":572,"ariaHidden":91},[90],[20,574,576,580],{"className":575},[95],[20,577],{"className":578,"style":579},[99],"height:0.8333em;vertical-align:-0.15em;",[20,581,583,587],{"className":582},[104],[20,584,563],{"className":585,"style":586},[104,105],"margin-right:0.1389em;",[20,588,590],{"className":589},[411],[20,591,593,615],{"className":592},[267,268],[20,594,596,612],{"className":595},[272],[20,597,600],{"className":598,"style":599},[276],"height:0.3011em;",[20,601,603,606],{"style":602},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[20,604],{"className":605,"style":428},[284],[20,607,609],{"className":608},[289,290,291,292],[20,610,566],{"className":611},[104,292],[20,613,335],{"className":614},[334],[20,616,618],{"className":617},[272],[20,619,622],{"className":620,"style":621},[276],"height:0.15em;",[20,623],{},") and second tangent point (",[20,626,628,646],{"className":627},[63],[20,629,631],{"className":630},[67],[69,632,633],{"xmlns":71},[73,634,635,643],{},[76,636,637],{},[559,638,639,641],{},[79,640,563],{},[207,642,209],{},[83,644,645],{"encoding":85},"T_2",[20,647,649],{"className":648,"ariaHidden":91},[90],[20,650,652,655],{"className":651},[95],[20,653],{"className":654,"style":579},[99],[20,656,658,661],{"className":657},[104],[20,659,563],{"className":660,"style":586},[104,105],[20,662,664],{"className":663},[411],[20,665,667,687],{"className":666},[267,268],[20,668,670,684],{"className":669},[272],[20,671,673],{"className":672,"style":599},[276],[20,674,675,678],{"style":602},[20,676],{"className":677,"style":428},[284],[20,679,681],{"className":680},[289,290,291,292],[20,682,209],{"className":683},[104,292],[20,685,335],{"className":686},[334],[20,688,690],{"className":689},[272],[20,691,693],{"className":692,"style":621},[276],[20,694],{},") by measuring the tangent length (",[20,697,699,728],{"className":698},[63],[20,700,702],{"className":701},[67],[69,703,704],{"xmlns":71},[73,705,706,725],{},[76,707,708,710,713,716,720,723],{},[79,709,153],{},[79,711,712],{},"tan",[195,714,715],{},"⁡",[79,717,719],{"mathvariant":718},"normal","Δ",[79,721,722],{"mathvariant":718},"\u002F",[207,724,209],{},[83,726,727],{"encoding":85},"R \\tan \\Delta\u002F2",[20,729,731],{"className":730,"ariaHidden":91},[90],[20,732,734,738,741,745,749,752],{"className":733},[95],[20,735],{"className":736,"style":737},[99],"height:1em;vertical-align:-0.25em;",[20,739,153],{"className":740,"style":169},[104,105],[20,742],{"className":743,"style":744},[237],"margin-right:0.1667em;",[20,746,712],{"className":747},[748],"mop",[20,750],{"className":751,"style":744},[237],[20,753,755],{"className":754},[104],"Δ\u002F2",") back from the Intersection Point (",[20,758,760,774],{"className":759},[63],[20,761,763],{"className":762},[67],[69,764,765],{"xmlns":71},[73,766,767,772],{},[76,768,769],{},[79,770,771],{},"I",[83,773,771],{"encoding":85},[20,775,777],{"className":776,"ariaHidden":91},[90],[20,778,780,783],{"className":779},[95],[20,781],{"className":782,"style":165},[99],[20,784,771],{"className":785,"style":786},[104,105],"margin-right:0.0785em;",") ",[20,789,790],{},"14, 17",[539,792,794],{"id":793},"set-up-instrument","Set Up Instrument",[16,796,797,798,867,868,896,897,32],{},"Set up the theodolite at ",[20,799,801,818],{"className":800},[63],[20,802,804],{"className":803},[67],[69,805,806],{"xmlns":71},[73,807,808,816],{},[76,809,810],{},[559,811,812,814],{},[79,813,563],{},[207,815,566],{},[83,817,569],{"encoding":85},[20,819,821],{"className":820,"ariaHidden":91},[90],[20,822,824,827],{"className":823},[95],[20,825],{"className":826,"style":579},[99],[20,828,830,833],{"className":829},[104],[20,831,563],{"className":832,"style":586},[104,105],[20,834,836],{"className":835},[411],[20,837,839,859],{"className":838},[267,268],[20,840,842,856],{"className":841},[272],[20,843,845],{"className":844,"style":599},[276],[20,846,847,850],{"style":602},[20,848],{"className":849,"style":428},[284],[20,851,853],{"className":852},[289,290,291,292],[20,854,566],{"className":855},[104,292],[20,857,335],{"className":858},[334],[20,860,862],{"className":861},[272],[20,863,865],{"className":864,"style":621},[276],[20,866],{}," and sight the Intersection Point (",[20,869,871,884],{"className":870},[63],[20,872,874],{"className":873},[67],[69,875,876],{"xmlns":71},[73,877,878,882],{},[76,879,880],{},[79,881,771],{},[83,883,771],{"encoding":85},[20,885,887],{"className":886,"ariaHidden":91},[90],[20,888,890,893],{"className":889},[95],[20,891],{"className":892,"style":165},[99],[20,894,771],{"className":895,"style":786},[104,105],") with the horizontal circle reading zero ",[20,898,52],{},[539,900,902],{"id":901},"turn-deflection-angle","Turn Deflection Angle",[16,904,905,906,978,979,32],{},"Turn off the first deflection angle (",[20,907,909,927],{"className":908},[63],[20,910,912],{"className":911},[67],[69,913,914],{"xmlns":71},[73,915,916,924],{},[76,917,918],{},[559,919,920,922],{},[79,921,81],{},[207,923,566],{},[83,925,926],{"encoding":85},"\\delta_1",[20,928,930],{"className":929,"ariaHidden":91},[90],[20,931,933,937],{"className":932},[95],[20,934],{"className":935,"style":936},[99],"height:0.8444em;vertical-align:-0.15em;",[20,938,940,943],{"className":939},[104],[20,941,81],{"className":942,"style":106},[104,105],[20,944,946],{"className":945},[411],[20,947,949,970],{"className":948},[267,268],[20,950,952,967],{"className":951},[272],[20,953,955],{"className":954,"style":599},[276],[20,956,958,961],{"style":957},"top:-2.55em;margin-left:-0.0379em;margin-right:0.05em;",[20,959],{"className":960,"style":428},[284],[20,962,964],{"className":963},[289,290,291,292],[20,965,566],{"className":966},[104,292],[20,968,335],{"className":969},[334],[20,971,973],{"className":972},[272],[20,974,976],{"className":975,"style":621},[276],[20,977],{},") calculated for the first sub-chord ",[20,980,52],{},[539,982,984],{"id":983},"range-the-point","Range the Point",[16,986,987,988,1057,1058,32],{},"Measure out the chord length from ",[20,989,991,1008],{"className":990},[63],[20,992,994],{"className":993},[67],[69,995,996],{"xmlns":71},[73,997,998,1006],{},[76,999,1000],{},[559,1001,1002,1004],{},[79,1003,563],{},[207,1005,566],{},[83,1007,569],{"encoding":85},[20,1009,1011],{"className":1010,"ariaHidden":91},[90],[20,1012,1014,1017],{"className":1013},[95],[20,1015],{"className":1016,"style":579},[99],[20,1018,1020,1023],{"className":1019},[104],[20,1021,563],{"className":1022,"style":586},[104,105],[20,1024,1026],{"className":1025},[411],[20,1027,1029,1049],{"className":1028},[267,268],[20,1030,1032,1046],{"className":1031},[272],[20,1033,1035],{"className":1034,"style":599},[276],[20,1036,1037,1040],{"style":602},[20,1038],{"className":1039,"style":428},[284],[20,1041,1043],{"className":1042},[289,290,291,292],[20,1044,566],{"className":1045},[104,292],[20,1047,335],{"className":1048},[334],[20,1050,1052],{"className":1051},[272],[20,1053,1055],{"className":1054,"style":621},[276],[20,1056],{}," along the line of sight to fix the first peg on the curve ",[20,1059,52],{},[539,1061,1063],{"id":1062},"continue-the-curve","Continue the Curve",[16,1065,1066,1067,1100,1101,1105,1106,528,1136,32],{},"For subsequent pegs, turn off cumulative deflection angles (",[20,1068,1070,1088],{"className":1069},[63],[20,1071,1073],{"className":1072},[67],[69,1074,1075],{"xmlns":71},[73,1076,1077,1085],{},[76,1078,1079,1081,1083],{},[79,1080,719],{"mathvariant":718},[79,1082,722],{"mathvariant":718},[207,1084,209],{},[83,1086,1087],{"encoding":85},"\\Delta\u002F2",[20,1089,1091],{"className":1090,"ariaHidden":91},[90],[20,1092,1094,1097],{"className":1093},[95],[20,1095],{"className":1096,"style":737},[99],[20,1098,755],{"className":1099},[104],") and measure chord lengths from the ",[1102,1103,1104],"em",{},"previous"," peg until the curve intersects at ",[20,1107,1109,1123],{"className":1108},[63],[20,1110,1112],{"className":1111},[67],[69,1113,1114],{"xmlns":71},[73,1115,1116,1121],{},[76,1117,1118],{},[79,1119,1120],{},"Y",[83,1122,1120],{"encoding":85},[20,1124,1126],{"className":1125,"ariaHidden":91},[90],[20,1127,1129,1132],{"className":1128},[95],[20,1130],{"className":1131,"style":165},[99],[20,1133,1120],{"className":1134,"style":1135},[104,105],"margin-right:0.2222em;",[20,1137,52],{},[11,1139,1141],{"id":1140},"formula-breakdown","Formula Breakdown",[1143,1144,1145,1237,1324],"ul",{},[1146,1147,1148,528,1151,528,1234],"li",{},[25,1149,1150],{},"Tangent Length:",[20,1152,1154,1189],{"className":1153},[63],[20,1155,1157],{"className":1156},[67],[69,1158,1159],{"xmlns":71},[73,1160,1161,1186],{},[76,1162,1163,1165,1167,1169,1171,1173,1177,1179,1181,1183],{},[79,1164,563],{},[195,1166,197],{},[79,1168,153],{},[79,1170,712],{},[195,1172,715],{},[195,1174,1176],{"stretchy":1175},"false","(",[79,1178,719],{"mathvariant":718},[79,1180,722],{"mathvariant":718},[207,1182,209],{},[195,1184,1185],{"stretchy":1175},")",[83,1187,1188],{"encoding":85},"T = R \\tan(\\Delta\u002F2)",[20,1190,1192,1210],{"className":1191,"ariaHidden":91},[90],[20,1193,1195,1198,1201,1204,1207],{"className":1194},[95],[20,1196],{"className":1197,"style":165},[99],[20,1199,563],{"className":1200,"style":586},[104,105],[20,1202],{"className":1203,"style":238},[237],[20,1205,197],{"className":1206},[242],[20,1208],{"className":1209,"style":238},[237],[20,1211,1213,1216,1219,1222,1225,1228,1231],{"className":1212},[95],[20,1214],{"className":1215,"style":737},[99],[20,1217,153],{"className":1218,"style":169},[104,105],[20,1220],{"className":1221,"style":744},[237],[20,1223,712],{"className":1224},[748],[20,1226,1176],{"className":1227},[259],[20,1229,755],{"className":1230},[104],[20,1232,1185],{"className":1233},[348],[20,1235,1236],{},"17",[1146,1238,1239,528,1242,528,1322],{},[25,1240,1241],{},"Curve Length:",[20,1243,1245,1274],{"className":1244},[63],[20,1246,1248],{"className":1247},[67],[69,1249,1250],{"xmlns":71},[73,1251,1252,1271],{},[76,1253,1254,1257,1259,1261,1263,1266,1268],{},[79,1255,1256],{},"L",[195,1258,197],{},[79,1260,153],{},[79,1262,719],{"mathvariant":718},[191,1264,1265],{}," (with ",[79,1267,719],{"mathvariant":718},[191,1269,1270],{}," in radians)",[83,1272,1273],{"encoding":85},"L = R\\Delta \\text{ (with } \\Delta \\text{ in radians)}",[20,1275,1277,1295],{"className":1276,"ariaHidden":91},[90],[20,1278,1280,1283,1286,1289,1292],{"className":1279},[95],[20,1281],{"className":1282,"style":165},[99],[20,1284,1256],{"className":1285},[104,105],[20,1287],{"className":1288,"style":238},[237],[20,1290,197],{"className":1291},[242],[20,1293],{"className":1294,"style":238},[237],[20,1296,1298,1301,1304,1307,1313,1316],{"className":1297},[95],[20,1299],{"className":1300,"style":737},[99],[20,1302,153],{"className":1303,"style":169},[104,105],[20,1305,719],{"className":1306},[104],[20,1308,1310],{"className":1309},[104,230],[20,1311,1265],{"className":1312},[104],[20,1314,719],{"className":1315},[104],[20,1317,1319],{"className":1318},[104,230],[20,1320,1270],{"className":1321},[104],[20,1323,1236],{},[1146,1325,1326,528,1329,528,1439],{},[25,1327,1328],{},"Apex Distance:",[20,1330,1332,1373],{"className":1331},[63],[20,1333,1335],{"className":1334},[67],[69,1336,1337],{"xmlns":71},[73,1338,1339,1370],{},[76,1340,1341,1343,1346,1348,1350,1352,1355,1357,1359,1361,1363,1366,1368],{},[79,1342,771],{},[79,1344,1345],{},"A",[195,1347,197],{},[79,1349,153],{},[195,1351,1176],{"stretchy":1175},[79,1353,1354],{},"sec",[195,1356,715],{},[79,1358,719],{"mathvariant":718},[79,1360,722],{"mathvariant":718},[207,1362,209],{},[195,1364,1365],{},"−",[207,1367,566],{},[195,1369,1185],{"stretchy":1175},[83,1371,1372],{"encoding":85},"IA = R(\\sec \\Delta\u002F2 - 1)",[20,1374,1376,1397,1427],{"className":1375,"ariaHidden":91},[90],[20,1377,1379,1382,1385,1388,1391,1394],{"className":1378},[95],[20,1380],{"className":1381,"style":165},[99],[20,1383,771],{"className":1384,"style":786},[104,105],[20,1386,1345],{"className":1387},[104,105],[20,1389],{"className":1390,"style":238},[237],[20,1392,197],{"className":1393},[242],[20,1395],{"className":1396,"style":238},[237],[20,1398,1400,1403,1406,1409,1412,1415,1418,1421,1424],{"className":1399},[95],[20,1401],{"className":1402,"style":737},[99],[20,1404,153],{"className":1405,"style":169},[104,105],[20,1407,1176],{"className":1408},[259],[20,1410,1354],{"className":1411},[748],[20,1413],{"className":1414,"style":744},[237],[20,1416,755],{"className":1417},[104],[20,1419],{"className":1420,"style":1135},[237],[20,1422,1365],{"className":1423},[435],[20,1425],{"className":1426,"style":1135},[237],[20,1428,1430,1433,1436],{"className":1429},[95],[20,1431],{"className":1432,"style":737},[99],[20,1434,566],{"className":1435},[104],[20,1437,1185],{"className":1438},[348],[20,1440,1441],{},"18",[11,1443,1445],{"id":1444},"step-by-step-example","Step-by-Step Example",[16,1447,1448,1451,1452,23,1539,1601,1602,1640,1641,32],{},[25,1449,1450],{},"Problem:"," Two straights meet at ",[20,1453,1455,1478],{"className":1454},[63],[20,1456,1458],{"className":1457},[67],[69,1459,1460],{"xmlns":71},[73,1461,1462,1475],{},[76,1463,1464,1466,1468],{},[79,1465,719],{"mathvariant":718},[195,1467,197],{},[367,1469,1470,1473],{},[207,1471,1472],{},"30",[195,1474,373],{},[83,1476,1477],{"encoding":85},"\\Delta = 30^\\circ",[20,1479,1481,1499],{"className":1480,"ariaHidden":91},[90],[20,1482,1484,1487,1490,1493,1496],{"className":1483},[95],[20,1485],{"className":1486,"style":165},[99],[20,1488,719],{"className":1489},[104],[20,1491],{"className":1492,"style":238},[237],[20,1494,197],{"className":1495},[242],[20,1497],{"className":1498,"style":238},[237],[20,1500,1502,1505,1509],{"className":1501},[95],[20,1503],{"className":1504,"style":421},[99],[20,1506,1508],{"className":1507},[104],"3",[20,1510,1512,1516],{"className":1511},[104],[20,1513,1515],{"className":1514},[104],"0",[20,1517,1519],{"className":1518},[411],[20,1520,1522],{"className":1521},[267],[20,1523,1525],{"className":1524},[272],[20,1526,1528],{"className":1527,"style":421},[276],[20,1529,1530,1533],{"style":424},[20,1531],{"className":1532,"style":428},[284],[20,1534,1536],{"className":1535},[289,290,291,292],[20,1537,373],{"className":1538},[435,292],[20,1540,1542,1564],{"className":1541},[63],[20,1543,1545],{"className":1544},[67],[69,1546,1547],{"xmlns":71},[73,1548,1549,1561],{},[76,1550,1551,1553,1555,1558],{},[79,1552,153],{},[195,1554,197],{},[207,1556,1557],{},"200",[191,1559,1560],{}," m",[83,1562,1563],{"encoding":85},"R = 200 \\text{ m}",[20,1565,1567,1585],{"className":1566,"ariaHidden":91},[90],[20,1568,1570,1573,1576,1579,1582],{"className":1569},[95],[20,1571],{"className":1572,"style":165},[99],[20,1574,153],{"className":1575,"style":169},[104,105],[20,1577],{"className":1578,"style":238},[237],[20,1580,197],{"className":1581},[242],[20,1583],{"className":1584,"style":238},[237],[20,1586,1588,1592,1595],{"className":1587},[95],[20,1589],{"className":1590,"style":1591},[99],"height:0.6444em;",[20,1593,1557],{"className":1594},[104],[20,1596,1598],{"className":1597},[104,230],[20,1599,1560],{"className":1600},[104],". Calculate the deflection angle for a ",[20,1603,1605,1622],{"className":1604},[63],[20,1606,1608],{"className":1607},[67],[69,1609,1610],{"xmlns":71},[73,1611,1612,1619],{},[76,1613,1614,1617],{},[207,1615,1616],{},"20",[191,1618,1560],{},[83,1620,1621],{"encoding":85},"20 \\text{ m}",[20,1623,1625],{"className":1624,"ariaHidden":91},[90],[20,1626,1628,1631,1634],{"className":1627},[95],[20,1629],{"className":1630,"style":1591},[99],[20,1632,1616],{"className":1633},[104],[20,1635,1637],{"className":1636},[104,230],[20,1638,1560],{"className":1639},[104]," standard chord ",[20,1642,52],{},[1644,1645,1646,1828,2007,2099],"ol",{},[1146,1647,1648,528,1651],{},[25,1649,1650],{},"Formula:",[20,1652,1654,1685],{"className":1653},[63],[20,1655,1657],{"className":1656},[67],[69,1658,1659],{"xmlns":71},[73,1660,1661,1682],{},[76,1662,1663,1669,1671,1673,1675],{},[367,1664,1665,1667],{},[79,1666,81],{},[195,1668,373],{},[195,1670,197],{},[207,1672,382],{},[195,1674,385],{},[199,1676,1677,1680],{},[79,1678,1679],{},"C",[79,1681,153],{},[83,1683,1684],{"encoding":85},"\\delta^\\circ = 28.6479 \\times \\frac{C}{R}",[20,1686,1688,1732,1751],{"className":1687,"ariaHidden":91},[90],[20,1689,1691,1694,1723,1726,1729],{"className":1690},[95],[20,1692],{"className":1693,"style":100},[99],[20,1695,1697,1700],{"className":1696},[104],[20,1698,81],{"className":1699,"style":106},[104,105],[20,1701,1703],{"className":1702},[411],[20,1704,1706],{"className":1705},[267],[20,1707,1709],{"className":1708},[272],[20,1710,1712],{"className":1711,"style":421},[276],[20,1713,1714,1717],{"style":424},[20,1715],{"className":1716,"style":428},[284],[20,1718,1720],{"className":1719},[289,290,291,292],[20,1721,373],{"className":1722},[435,292],[20,1724],{"className":1725,"style":238},[237],[20,1727,197],{"className":1728},[242],[20,1730],{"className":1731,"style":238},[237],[20,1733,1735,1739,1742,1745,1748],{"className":1734},[95],[20,1736],{"className":1737,"style":1738},[99],"height:0.7278em;vertical-align:-0.0833em;",[20,1740,382],{"className":1741},[104],[20,1743],{"className":1744,"style":1135},[237],[20,1746,385],{"className":1747},[435],[20,1749],{"className":1750,"style":1135},[237],[20,1752,1754,1758],{"className":1753},[95],[20,1755],{"className":1756,"style":1757},[99],"height:1.2173em;vertical-align:-0.345em;",[20,1759,1761,1764,1825],{"className":1760},[104],[20,1762],{"className":1763},[259,260],[20,1765,1767],{"className":1766},[199],[20,1768,1770,1817],{"className":1769},[267,268],[20,1771,1773,1814],{"className":1772},[272],[20,1774,1777,1791,1799],{"className":1775,"style":1776},[276],"height:0.8723em;",[20,1778,1779,1782],{"style":280},[20,1780],{"className":1781,"style":285},[284],[20,1783,1785],{"className":1784},[289,290,291,292],[20,1786,1788],{"className":1787},[104,292],[20,1789,153],{"className":1790,"style":169},[104,105,292],[20,1792,1793,1796],{"style":304},[20,1794],{"className":1795,"style":285},[284],[20,1797],{"className":1798,"style":312},[311],[20,1800,1801,1804],{"style":315},[20,1802],{"className":1803,"style":285},[284],[20,1805,1807],{"className":1806},[289,290,291,292],[20,1808,1810],{"className":1809},[104,292],[20,1811,1679],{"className":1812,"style":1813},[104,105,292],"margin-right:0.0715em;",[20,1815,335],{"className":1816},[334],[20,1818,1820],{"className":1819},[272],[20,1821,1823],{"className":1822,"style":342},[276],[20,1824],{},[20,1826],{"className":1827},[348,260],[1146,1829,1830,528,1833],{},[25,1831,1832],{},"Plug in values:",[20,1834,1836,1866],{"className":1835},[63],[20,1837,1839],{"className":1838},[67],[69,1840,1841],{"xmlns":71},[73,1842,1843,1863],{},[76,1844,1845,1851,1853,1855,1857],{},[367,1846,1847,1849],{},[79,1848,81],{},[195,1850,373],{},[195,1852,197],{},[207,1854,382],{},[195,1856,385],{},[199,1858,1859,1861],{},[207,1860,1616],{},[207,1862,1557],{},[83,1864,1865],{"encoding":85},"\\delta^\\circ = 28.6479 \\times \\frac{20}{200}",[20,1867,1869,1913,1931],{"className":1868,"ariaHidden":91},[90],[20,1870,1872,1875,1904,1907,1910],{"className":1871},[95],[20,1873],{"className":1874,"style":100},[99],[20,1876,1878,1881],{"className":1877},[104],[20,1879,81],{"className":1880,"style":106},[104,105],[20,1882,1884],{"className":1883},[411],[20,1885,1887],{"className":1886},[267],[20,1888,1890],{"className":1889},[272],[20,1891,1893],{"className":1892,"style":421},[276],[20,1894,1895,1898],{"style":424},[20,1896],{"className":1897,"style":428},[284],[20,1899,1901],{"className":1900},[289,290,291,292],[20,1902,373],{"className":1903},[435,292],[20,1905],{"className":1906,"style":238},[237],[20,1908,197],{"className":1909},[242],[20,1911],{"className":1912,"style":238},[237],[20,1914,1916,1919,1922,1925,1928],{"className":1915},[95],[20,1917],{"className":1918,"style":1738},[99],[20,1920,382],{"className":1921},[104],[20,1923],{"className":1924,"style":1135},[237],[20,1926,385],{"className":1927},[435],[20,1929],{"className":1930,"style":1135},[237],[20,1932,1934,1938],{"className":1933},[95],[20,1935],{"className":1936,"style":1937},[99],"height:1.1901em;vertical-align:-0.345em;",[20,1939,1941,1944,2004],{"className":1940},[104],[20,1942],{"className":1943},[259,260],[20,1945,1947],{"className":1946},[199],[20,1948,1950,1996],{"className":1949},[267,268],[20,1951,1953,1993],{"className":1952},[272],[20,1954,1957,1971,1979],{"className":1955,"style":1956},[276],"height:0.8451em;",[20,1958,1959,1962],{"style":280},[20,1960],{"className":1961,"style":285},[284],[20,1963,1965],{"className":1964},[289,290,291,292],[20,1966,1968],{"className":1967},[104,292],[20,1969,1557],{"className":1970},[104,292],[20,1972,1973,1976],{"style":304},[20,1974],{"className":1975,"style":285},[284],[20,1977],{"className":1978,"style":312},[311],[20,1980,1981,1984],{"style":315},[20,1982],{"className":1983,"style":285},[284],[20,1985,1987],{"className":1986},[289,290,291,292],[20,1988,1990],{"className":1989},[104,292],[20,1991,1616],{"className":1992},[104,292],[20,1994,335],{"className":1995},[334],[20,1997,1999],{"className":1998},[272],[20,2000,2002],{"className":2001,"style":342},[276],[20,2003],{},[20,2005],{"className":2006},[348,260],[1146,2008,2009,528,2012],{},[25,2010,2011],{},"Calculation:",[20,2013,2015,2038],{"className":2014},[63],[20,2016,2018],{"className":2017},[67],[69,2019,2020],{"xmlns":71},[73,2021,2022,2035],{},[76,2023,2024,2026,2028],{},[79,2025,81],{},[195,2027,197],{},[367,2029,2030,2033],{},[207,2031,2032],{},"2.86479",[195,2034,373],{},[83,2036,2037],{"encoding":85},"\\delta = 2.86479^\\circ",[20,2039,2041,2059],{"className":2040,"ariaHidden":91},[90],[20,2042,2044,2047,2050,2053,2056],{"className":2043},[95],[20,2045],{"className":2046,"style":100},[99],[20,2048,81],{"className":2049,"style":106},[104,105],[20,2051],{"className":2052,"style":238},[237],[20,2054,197],{"className":2055},[242],[20,2057],{"className":2058,"style":238},[237],[20,2060,2062,2065,2069],{"className":2061},[95],[20,2063],{"className":2064,"style":421},[99],[20,2066,2068],{"className":2067},[104],"2.8647",[20,2070,2072,2076],{"className":2071},[104],[20,2073,2075],{"className":2074},[104],"9",[20,2077,2079],{"className":2078},[411],[20,2080,2082],{"className":2081},[267],[20,2083,2085],{"className":2084},[272],[20,2086,2088],{"className":2087,"style":421},[276],[20,2089,2090,2093],{"style":424},[20,2091],{"className":2092,"style":428},[284],[20,2094,2096],{"className":2095},[289,290,291,292],[20,2097,373],{"className":2098},[435,292],[1146,2100,2101,528,2104,528,2256],{},[25,2102,2103],{},"Convert to DMS:",[20,2105,2107,2145],{"className":2106},[63],[20,2108,2110],{"className":2109},[67],[69,2111,2112],{"xmlns":71},[73,2113,2114,2142],{},[76,2115,2116,2122,2131],{},[367,2117,2118,2120],{},[207,2119,209],{},[195,2121,373],{},[367,2123,2124,2127],{},[207,2125,2126],{},"51",[195,2128,2130],{"mathvariant":718,"lspace":2129,"rspace":2129},"0em","′",[367,2132,2133,2136],{},[207,2134,2135],{},"53",[76,2137,2138,2140],{},[195,2139,2130],{"mathvariant":718},[195,2141,2130],{"mathvariant":718},[83,2143,2144],{"encoding":85},"2^\\circ 51' 53''",[20,2146,2148],{"className":2147,"ariaHidden":91},[90],[20,2149,2151,2155,2184,2188,2220,2223],{"className":2150},[95],[20,2152],{"className":2153,"style":2154},[99],"height:0.7519em;",[20,2156,2158,2161],{"className":2157},[104],[20,2159,209],{"className":2160},[104],[20,2162,2164],{"className":2163},[411],[20,2165,2167],{"className":2166},[267],[20,2168,2170],{"className":2169},[272],[20,2171,2173],{"className":2172,"style":421},[276],[20,2174,2175,2178],{"style":424},[20,2176],{"className":2177,"style":428},[284],[20,2179,2181],{"className":2180},[289,290,291,292],[20,2182,373],{"className":2183},[435,292],[20,2185,2187],{"className":2186},[104],"5",[20,2189,2191,2194],{"className":2190},[104],[20,2192,566],{"className":2193},[104],[20,2195,2197],{"className":2196},[411],[20,2198,2200],{"className":2199},[267],[20,2201,2203],{"className":2202},[272],[20,2204,2206],{"className":2205,"style":2154},[276],[20,2207,2208,2211],{"style":424},[20,2209],{"className":2210,"style":428},[284],[20,2212,2214],{"className":2213},[289,290,291,292],[20,2215,2217],{"className":2216},[104,292],[20,2218,2130],{"className":2219},[104,292],[20,2221,2187],{"className":2222},[104],[20,2224,2226,2229],{"className":2225},[104],[20,2227,1508],{"className":2228},[104],[20,2230,2232],{"className":2231},[411],[20,2233,2235],{"className":2234},[267],[20,2236,2238],{"className":2237},[272],[20,2239,2241],{"className":2240,"style":2154},[276],[20,2242,2243,2246],{"style":424},[20,2244],{"className":2245,"style":428},[284],[20,2247,2249],{"className":2248},[289,290,291,292],[20,2250,2252],{"className":2251},[104,292],[20,2253,2255],{"className":2254},[104,292],"′′",[20,2257,2258],{},"19",[11,2260,2262],{"id":2261},"practical-tips","Practical Tips",[1143,2264,2265,2334],{},[1146,2266,2267,2270,2271,787,2332,32],{},[25,2268,2269],{},"Through Chainage:"," Always calculate your chords based on through chainage to ensure pegs land on round numbers (e.g., ",[20,2272,2274,2300],{"className":2273},[63],[20,2275,2277],{"className":2276},[67],[69,2278,2279],{"xmlns":71},[73,2280,2281,2297],{},[76,2282,2283,2286,2289,2292,2294],{},[207,2284,2285],{},"2200",[195,2287,2288],{"separator":91},",",[207,2290,2291],{},"2220",[195,2293,2288],{"separator":91},[207,2295,2296],{},"2240",[83,2298,2299],{"encoding":85},"2200, 2220, 2240",[20,2301,2303],{"className":2302,"ariaHidden":91},[90],[20,2304,2306,2310,2313,2317,2320,2323,2326,2329],{"className":2305},[95],[20,2307],{"className":2308,"style":2309},[99],"height:0.8389em;vertical-align:-0.1944em;",[20,2311,2285],{"className":2312},[104],[20,2314,2288],{"className":2315},[2316],"mpunct",[20,2318],{"className":2319,"style":744},[237],[20,2321,2291],{"className":2322},[104],[20,2324,2288],{"className":2325},[2316],[20,2327],{"className":2328,"style":744},[237],[20,2330,2296],{"className":2331},[104],[20,2333,1616],{},[1146,2335,2336,2339,2340,2409,2410,2506,2507,32],{},[25,2337,2338],{},"EDM Advantage:"," If using an EDM, you can set out the curve by measuring the total distance from ",[20,2341,2343,2360],{"className":2342},[63],[20,2344,2346],{"className":2345},[67],[69,2347,2348],{"xmlns":71},[73,2349,2350,2358],{},[76,2351,2352],{},[559,2353,2354,2356],{},[79,2355,563],{},[207,2357,566],{},[83,2359,569],{"encoding":85},[20,2361,2363],{"className":2362,"ariaHidden":91},[90],[20,2364,2366,2369],{"className":2365},[95],[20,2367],{"className":2368,"style":579},[99],[20,2370,2372,2375],{"className":2371},[104],[20,2373,563],{"className":2374,"style":586},[104,105],[20,2376,2378],{"className":2377},[411],[20,2379,2381,2401],{"className":2380},[267,268],[20,2382,2384,2398],{"className":2383},[272],[20,2385,2387],{"className":2386,"style":599},[276],[20,2388,2389,2392],{"style":602},[20,2390],{"className":2391,"style":428},[284],[20,2393,2395],{"className":2394},[289,290,291,292],[20,2396,566],{"className":2397},[104,292],[20,2399,335],{"className":2400},[334],[20,2402,2404],{"className":2403},[272],[20,2405,2407],{"className":2406,"style":621},[276],[20,2408],{}," to each peg (",[20,2411,2413,2441],{"className":2412},[63],[20,2414,2416],{"className":2415},[67],[69,2417,2418],{"xmlns":71},[73,2419,2420,2438],{},[76,2421,2422,2424,2426,2429,2431],{},[207,2423,209],{},[79,2425,153],{},[79,2427,2428],{},"sin",[195,2430,715],{},[559,2432,2433,2435],{},[79,2434,81],{},[79,2436,2437],{},"n",[83,2439,2440],{"encoding":85},"2R \\sin \\delta_n",[20,2442,2444],{"className":2443,"ariaHidden":91},[90],[20,2445,2447,2450,2453,2456,2459,2462,2465],{"className":2446},[95],[20,2448],{"className":2449,"style":936},[99],[20,2451,209],{"className":2452},[104],[20,2454,153],{"className":2455,"style":169},[104,105],[20,2457],{"className":2458,"style":744},[237],[20,2460,2428],{"className":2461},[748],[20,2463],{"className":2464,"style":744},[237],[20,2466,2468,2471],{"className":2467},[104],[20,2469,81],{"className":2470,"style":106},[104,105],[20,2472,2474],{"className":2473},[411],[20,2475,2477,2498],{"className":2476},[267,268],[20,2478,2480,2495],{"className":2479},[272],[20,2481,2484],{"className":2482,"style":2483},[276],"height:0.1514em;",[20,2485,2486,2489],{"style":957},[20,2487],{"className":2488,"style":428},[284],[20,2490,2492],{"className":2491},[289,290,291,292],[20,2493,2437],{"className":2494},[104,105,292],[20,2496,335],{"className":2497},[334],[20,2499,2501],{"className":2500},[272],[20,2502,2504],{"className":2503,"style":621},[276],[20,2505],{},") rather than measuring chord-to-chord ",[20,2508,2509],{},"21",[11,2511,2513],{"id":2512},"common-mistakes","Common Mistakes",[1143,2515,2516,2562],{},[1146,2517,2518,2521,2522,2558,2559,32],{},[25,2519,2520],{},"Ignoring the Sub-chord:"," The first and last chords are rarely a full ",[20,2523,2525,2540],{"className":2524},[63],[20,2526,2528],{"className":2527},[67],[69,2529,2530],{"xmlns":71},[73,2531,2532,2538],{},[76,2533,2534,2536],{},[207,2535,1616],{},[191,2537,1560],{},[83,2539,1621],{"encoding":85},[20,2541,2543],{"className":2542,"ariaHidden":91},[90],[20,2544,2546,2549,2552],{"className":2545},[95],[20,2547],{"className":2548,"style":1591},[99],[20,2550,1616],{"className":2551},[104],[20,2553,2555],{"className":2554},[104,230],[20,2556,1560],{"className":2557},[104],". Failing to calculate the specific deflection angle for these \"sub-chords\" will throw off the entire curve ",[20,2560,2561],{},"19, 20",[1146,2563,2564,2567,2568,2637,2638,528,2670,32],{},[25,2565,2566],{},"Cumulative Errors:"," In manual taping, errors in one peg affect all subsequent pegs. Always check into ",[20,2569,2571,2588],{"className":2570},[63],[20,2572,2574],{"className":2573},[67],[69,2575,2576],{"xmlns":71},[73,2577,2578,2586],{},[76,2579,2580],{},[559,2581,2582,2584],{},[79,2583,563],{},[207,2585,209],{},[83,2587,645],{"encoding":85},[20,2589,2591],{"className":2590,"ariaHidden":91},[90],[20,2592,2594,2597],{"className":2593},[95],[20,2595],{"className":2596,"style":579},[99],[20,2598,2600,2603],{"className":2599},[104],[20,2601,563],{"className":2602,"style":586},[104,105],[20,2604,2606],{"className":2605},[411],[20,2607,2609,2629],{"className":2608},[267,268],[20,2610,2612,2626],{"className":2611},[272],[20,2613,2615],{"className":2614,"style":599},[276],[20,2616,2617,2620],{"style":602},[20,2618],{"className":2619,"style":428},[284],[20,2621,2623],{"className":2622},[289,290,291,292],[20,2624,209],{"className":2625},[104,292],[20,2627,335],{"className":2628},[334],[20,2630,2632],{"className":2631},[272],[20,2633,2635],{"className":2634,"style":621},[276],[20,2636],{}," to verify the total deflection angle equals ",[20,2639,2641,2658],{"className":2640},[63],[20,2642,2644],{"className":2643},[67],[69,2645,2646],{"xmlns":71},[73,2647,2648,2656],{},[76,2649,2650,2652,2654],{},[79,2651,719],{"mathvariant":718},[79,2653,722],{"mathvariant":718},[207,2655,209],{},[83,2657,1087],{"encoding":85},[20,2659,2661],{"className":2660,"ariaHidden":91},[90],[20,2662,2664,2667],{"className":2663},[95],[20,2665],{"className":2666,"style":737},[99],[20,2668,755],{"className":2669},[104],[20,2671,2258],{},[11,2673,2675],{"id":2674},"faq","FAQ",[2677,2678,2679,2689],"accordion",{},[2680,2681,2683],"accordion-item",{"label":2682},"What if the Intersection Point (I) is inaccessible?",[16,2684,2685,2686,32],{},"You can establish two points on the straights, measure the distance between them, and use the sine rule to solve for the tangent points ",[20,2687,2688],{},"15, 22",[2680,2690,2692],{"label":2691},"What is the 'Degree of Curve'?",[16,2693,2694,2695,2733,2734,2762,2763,32],{},"It is the angle subtended at the center by a standard arc or chord (usually ",[20,2696,2698,2715],{"className":2697},[63],[20,2699,2701],{"className":2700},[67],[69,2702,2703],{"xmlns":71},[73,2704,2705,2712],{},[76,2706,2707,2710],{},[207,2708,2709],{},"100",[191,2711,1560],{},[83,2713,2714],{"encoding":85},"100 \\text{ m}",[20,2716,2718],{"className":2717,"ariaHidden":91},[90],[20,2719,2721,2724,2727],{"className":2720},[95],[20,2722],{"className":2723,"style":1591},[99],[20,2725,2709],{"className":2726},[104],[20,2728,2730],{"className":2729},[104,230],[20,2731,1560],{"className":2732},[104],"). Modern practice favors using the Radius (",[20,2735,2737,2750],{"className":2736},[63],[20,2738,2740],{"className":2739},[67],[69,2741,2742],{"xmlns":71},[73,2743,2744,2748],{},[76,2745,2746],{},[79,2747,153],{},[83,2749,153],{"encoding":85},[20,2751,2753],{"className":2752,"ariaHidden":91},[90],[20,2754,2756,2759],{"className":2755},[95],[20,2757],{"className":2758,"style":165},[99],[20,2760,153],{"className":2761,"style":169},[104,105],") instead ",[20,2764,1616],{},[11,2766,2768],{"id":2767},"conclusion","Conclusion",[16,2770,2771],{},"Rankine’s method is the \"gold standard\" for manual curve setting. Even in the age of GPS, understanding these geometric foundations is vital for verifying automated designs on-site.",[11,2773,2775],{"id":2774},"references","References",[16,2777,2778,2779,2782,2783,32],{},"Schofield, W. (2001). ",[1102,2780,2781],{},"Engineering Surveying",". 5th ed. Butterworth-Heinemann. ",[20,2784,2785],{},"13-17, 19-21, 23-28",{"title":2787,"searchDepth":2788,"depth":2788,"links":2789},"",2,[2790,2791,2792,2793,2794,2802,2803,2804,2805,2806,2807,2808],{"id":13,"depth":2788,"text":14},{"id":35,"depth":2788,"text":36},{"id":45,"depth":2788,"text":46},{"id":55,"depth":2788,"text":56},{"id":533,"depth":2788,"text":534,"children":2795},[2796,2798,2799,2800,2801],{"id":541,"depth":2797,"text":542},3,{"id":793,"depth":2797,"text":794},{"id":901,"depth":2797,"text":902},{"id":983,"depth":2797,"text":984},{"id":1062,"depth":2797,"text":1063},{"id":1140,"depth":2788,"text":1141},{"id":1444,"depth":2788,"text":1445},{"id":2261,"depth":2788,"text":2262},{"id":2512,"depth":2788,"text":2513},{"id":2674,"depth":2788,"text":2675},{"id":2767,"depth":2788,"text":2768},{"id":2774,"depth":2788,"text":2775},"A step-by-step technical guide to setting out horizontal circular curves using deflection angles and a theodolite.","md","\u002Fimages\u002Frankine-method.jpg",{"authorCredentials":2813,"tags":2814,"sources":2819},"LS",[2815,2816,2817,2818],"Curves","Setting Out","Road Design","Theodolite",[2820],{"title":2821,"type":2822,"note":2823},"Engineering Surveying (Fifth Edition)","Book","Primary source for curve formulas and Rankine's method.",true,"\u002Fblog\u002Frankines-method-the-definitive-guide-to-setting-out-circular-curves","2024-03-22",15,{"title":5,"description":2809},{"loc":2825},"blog\u002F3.rankines-method-the-definitive-guide-to-setting-out-circular-curves","L9n3BY6w5ptBtdi9ss0N5T1qIBSXEchurDXT8uaY9_g",[2833,2838],{"title":2834,"path":2835,"stem":2836,"description":2837,"children":-1},"Combination of Errors: Calculating the Propagation of Uncertainty","\u002Fblog\u002Fcombination-of-errors-calculating-the-propagation-of-uncertainty","blog\u002F2.combination-of-errors-calculating-the-propagation-of-uncertainty","How to mathematically determine the total error in derived surveying quantities like areas, volumes, and coordinates.",{"title":2839,"path":2840,"stem":2841,"description":2842,"children":-1},"Vertical Parabolic Curves: Designing for Sight Distance and Safety","\u002Fblog\u002Fvertical-parabolic-curves-designing-for-sight-distance-and-safety","blog\u002F4.vertical-parabolic-curves-designing-for-sight-distance-and-safety","How to design and calculate vertical parabolic curves to smoothly connect road gradients.",1783851951911]