[{"data":1,"prerenderedAt":3074},["ShallowReactive",2],{"blog-\u002Fblog\u002Fthe-bowditch-method-a-deep-dive-into-traverse-adjustment-math":3,"blog-surround-\u002Fblog\u002Fthe-bowditch-method-a-deep-dive-into-traverse-adjustment-math":3063},{"id":4,"title":5,"author":6,"body":7,"category":3039,"description":3040,"extension":3041,"image":3042,"meta":3043,"navigation":3055,"path":3056,"publishedAt":3057,"readTime":3058,"seo":3059,"sitemap":3060,"stem":3061,"__hash__":3062},"blog\u002Fblog\u002F5.the-bowditch-method-a-deep-dive-into-traverse-adjustment-math.md","The Bowditch Method: A Deep Dive into Traverse Adjustment Math","Surveyiiing Expert",{"type":8,"value":9,"toc":3017},"minimark",[10,15,33,37,43,47,149,153,235,858,861,1106,1110,1805,1809,1941,2331,2335,2659,2663,2761,2765,2996,3000,3003,3007],[11,12,14],"h2",{"id":13},"overview","Overview",[16,17,18,19,23,24,28,29,32],"p",{},"No surveying measurement is perfect. When you run a \"closed traverse\" (returning to your starting point), the coordinates will never match perfectly due to small random errors ",[20,21,22],"span",{},"9, 45",". The ",[25,26,27],"strong",{},"Bowditch Rule"," is the industry-standard method for distributing this error ",[20,30,31],{},"45, 46",".",[11,34,36],{"id":35},"why-this-matters","Why This Matters",[16,38,39,40,32],{},"If you don't adjust your traverse, your maps will have \"gaps\" and your structures won't fit. The Bowditch rule is preferred because it considers that both linear and angular measurements are equally prone to error ",[20,41,42],{},"46",[11,44,46],{"id":45},"theory","Theory",[16,48,49,50,52,53,109,110,148],{},"Named after Nathaniel Bowditch (1807), the rule assumes that the error in a line is proportional to its length ",[20,51,42],{},". This means a ",[20,54,57,84],{"className":55},[56],"katex",[20,58,61],{"className":59},[60],"katex-mathml",[62,63,65],"math",{"xmlns":64},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[66,67,68,79],"semantics",{},[69,70,71,75],"mrow",{},[72,73,74],"mn",{},"200",[76,77,78],"mtext",{}," m",[80,81,83],"annotation",{"encoding":82},"application\u002Fx-tex","200 \\text{ m}",[20,85,89],{"className":86,"ariaHidden":88},[87],"katex-html","true",[20,90,93,98,102],{"className":91},[92],"base",[20,94],{"className":95,"style":97},[96],"strut","height:0.6444em;",[20,99,74],{"className":100},[101],"mord",[20,103,106],{"className":104},[101,105],"text",[20,107,78],{"className":108},[101]," leg will receive twice the correction of a ",[20,111,113,130],{"className":112},[56],[20,114,116],{"className":115},[60],[62,117,118],{"xmlns":64},[66,119,120,127],{},[69,121,122,125],{},[72,123,124],{},"100",[76,126,78],{},[80,128,129],{"encoding":82},"100 \\text{ m}",[20,131,133],{"className":132,"ariaHidden":88},[87],[20,134,136,139,142],{"className":135},[92],[20,137],{"className":138,"style":97},[96],[20,140,124],{"className":141},[101],[20,143,145],{"className":144},[101,105],[20,146,78],{"className":147},[101]," leg.",[11,150,152],{"id":151},"mathematical-principles","Mathematical Principles",[16,154,155,156,197,198,234],{},"The correction to the Eastings (",[20,157,159,178],{"className":158},[56],[20,160,162],{"className":161},[60],[62,163,164],{"xmlns":64},[66,165,166,175],{},[69,167,168,172],{},[169,170,171],"mi",{},"δ",[169,173,174],{},"E",[80,176,177],{"encoding":82},"\\delta E",[20,179,181],{"className":180,"ariaHidden":88},[87],[20,182,184,188,193],{"className":183},[92],[20,185],{"className":186,"style":187},[96],"height:0.6944em;",[20,189,171],{"className":190,"style":192},[101,191],"mathnormal","margin-right:0.0379em;",[20,194,174],{"className":195,"style":196},[101,191],"margin-right:0.0576em;",") and Northings (",[20,199,201,218],{"className":200},[56],[20,202,204],{"className":203},[60],[62,205,206],{"xmlns":64},[66,207,208,215],{},[69,209,210,212],{},[169,211,171],{},[169,213,214],{},"N",[80,216,217],{"encoding":82},"\\delta N",[20,219,221],{"className":220,"ariaHidden":88},[87],[20,222,224,227,230],{"className":223},[92],[20,225],{"className":226,"style":187},[96],[20,228,171],{"className":229,"style":192},[101,191],[20,231,214],{"className":232,"style":233},[101,191],"margin-right:0.109em;",") for any given leg of the traverse is:",[16,236,237,575,855,856],{},[20,238,240,301],{"className":239},[56],[20,241,243],{"className":242},[60],[62,244,245],{"xmlns":64},[66,246,247,298],{},[69,248,249,251,259,263,289,292],{},[169,250,171],{},[252,253,254,256],"msub",{},[169,255,174],{},[169,257,258],{},"i",[260,261,262],"mo",{},"=",[264,265,266,281],"mfrac",{},[69,267,268,279],{},[269,270,271,275],"msup",{},[169,272,274],{"mathvariant":273},"normal","Δ",[260,276,278],{"mathvariant":273,"lspace":277,"rspace":277},"0em","′",[169,280,174],{},[69,282,283,286],{},[260,284,285],{},"∑",[169,287,288],{},"L",[260,290,291],{},"×",[252,293,294,296],{},[169,295,288],{},[169,297,258],{},[80,299,300],{"encoding":82},"\\delta E_i = \\frac{\\Delta' E}{\\sum L} \\times L_i",[20,302,304,382,527],{"className":303,"ariaHidden":88},[87],[20,305,307,311,314,370,375,379],{"className":306},[92],[20,308],{"className":309,"style":310},[96],"height:0.8444em;vertical-align:-0.15em;",[20,312,171],{"className":313,"style":192},[101,191],[20,315,317,320],{"className":316},[101],[20,318,174],{"className":319,"style":196},[101,191],[20,321,324],{"className":322},[323],"msupsub",[20,325,329,361],{"className":326},[327,328],"vlist-t","vlist-t2",[20,330,333,356],{"className":331},[332],"vlist-r",[20,334,338],{"className":335,"style":337},[336],"vlist","height:0.3117em;",[20,339,341,346],{"style":340},"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;",[20,342],{"className":343,"style":345},[344],"pstrut","height:2.7em;",[20,347,353],{"className":348},[349,350,351,352],"sizing","reset-size6","size3","mtight",[20,354,258],{"className":355},[101,191,352],[20,357,360],{"className":358},[359],"vlist-s","​",[20,362,364],{"className":363},[332],[20,365,368],{"className":366,"style":367},[336],"height:0.15em;",[20,369],{},[20,371],{"className":372,"style":374},[373],"mspace","margin-right:0.2778em;",[20,376,262],{"className":377},[378],"mrel",[20,380],{"className":381,"style":374},[373],[20,383,385,389,516,520,524],{"className":384},[92],[20,386],{"className":387,"style":388},[96],"height:1.4935em;vertical-align:-0.52em;",[20,390,392,397,512],{"className":391},[101],[20,393],{"className":394},[395,396],"mopen","nulldelimiter",[20,398,400],{"className":399},[264],[20,401,403,503],{"className":402},[327,328],[20,404,406,500],{"className":405},[332],[20,407,410,437,448],{"className":408,"style":409},[336],"height:0.9735em;",[20,411,413,417],{"style":412},"top:-2.655em;",[20,414],{"className":415,"style":416},[344],"height:3em;",[20,418,420],{"className":419},[349,350,351,352],[20,421,423,430,434],{"className":422},[101,352],[20,424,285],{"className":425,"style":429},[426,427,428,352],"mop","op-symbol","small-op","position:relative;top:0em;",[20,431],{"className":432,"style":433},[373,352],"margin-right:0.1952em;",[20,435,288],{"className":436},[101,191,352],[20,438,440,443],{"style":439},"top:-3.23em;",[20,441],{"className":442,"style":416},[344],[20,444],{"className":445,"style":447},[446],"frac-line","border-bottom-width:0.04em;",[20,449,451,454],{"style":450},"top:-3.394em;",[20,452],{"className":453,"style":416},[344],[20,455,457],{"className":456},[349,350,351,352],[20,458,460,497],{"className":459},[101,352],[20,461,463,466],{"className":462},[101,352],[20,464,274],{"className":465},[101,352],[20,467,469],{"className":468},[323],[20,470,472],{"className":471},[327],[20,473,475],{"className":474},[332],[20,476,479],{"className":477,"style":478},[336],"height:0.8278em;",[20,480,482,486],{"style":481},"top:-2.931em;margin-right:0.0714em;",[20,483],{"className":484,"style":485},[344],"height:2.5em;",[20,487,491],{"className":488},[349,489,490,352],"reset-size3","size1",[20,492,494],{"className":493},[101,352],[20,495,278],{"className":496},[101,352],[20,498,174],{"className":499,"style":196},[101,191,352],[20,501,360],{"className":502},[359],[20,504,506],{"className":505},[332],[20,507,510],{"className":508,"style":509},[336],"height:0.52em;",[20,511],{},[20,513],{"className":514},[515,396],"mclose",[20,517],{"className":518,"style":519},[373],"margin-right:0.2222em;",[20,521,291],{"className":522},[523],"mbin",[20,525],{"className":526,"style":519},[373],[20,528,530,534],{"className":529},[92],[20,531],{"className":532,"style":533},[96],"height:0.8333em;vertical-align:-0.15em;",[20,535,537,540],{"className":536},[101],[20,538,288],{"className":539},[101,191],[20,541,543],{"className":542},[323],[20,544,546,567],{"className":545},[327,328],[20,547,549,564],{"className":548},[332],[20,550,552],{"className":551,"style":337},[336],[20,553,555,558],{"style":554},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[20,556],{"className":557,"style":345},[344],[20,559,561],{"className":560},[349,350,351,352],[20,562,258],{"className":563},[101,191,352],[20,565,360],{"className":566},[359],[20,568,570],{"className":569},[332],[20,571,573],{"className":572,"style":367},[336],[20,574],{},[20,576,578,626],{"className":577},[56],[20,579,581],{"className":580},[60],[62,582,583],{"xmlns":64},[66,584,585,623],{},[69,586,587,589,595,597,615,617],{},[169,588,171],{},[252,590,591,593],{},[169,592,214],{},[169,594,258],{},[260,596,262],{},[264,598,599,609],{},[69,600,601,607],{},[269,602,603,605],{},[169,604,274],{"mathvariant":273},[260,606,278],{"mathvariant":273,"lspace":277,"rspace":277},[169,608,214],{},[69,610,611,613],{},[260,612,285],{},[169,614,288],{},[260,616,291],{},[252,618,619,621],{},[169,620,288],{},[169,622,258],{},[80,624,625],{"encoding":82},"\\delta N_i = \\frac{\\Delta' N}{\\sum L} \\times L_i",[20,627,629,688,809],{"className":628,"ariaHidden":88},[87],[20,630,632,635,638,679,682,685],{"className":631},[92],[20,633],{"className":634,"style":310},[96],[20,636,171],{"className":637,"style":192},[101,191],[20,639,641,644],{"className":640},[101],[20,642,214],{"className":643,"style":233},[101,191],[20,645,647],{"className":646},[323],[20,648,650,671],{"className":649},[327,328],[20,651,653,668],{"className":652},[332],[20,654,656],{"className":655,"style":337},[336],[20,657,659,662],{"style":658},"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;",[20,660],{"className":661,"style":345},[344],[20,663,665],{"className":664},[349,350,351,352],[20,666,258],{"className":667},[101,191,352],[20,669,360],{"className":670},[359],[20,672,674],{"className":673},[332],[20,675,677],{"className":676,"style":367},[336],[20,678],{},[20,680],{"className":681,"style":374},[373],[20,683,262],{"className":684},[378],[20,686],{"className":687,"style":374},[373],[20,689,691,694,800,803,806],{"className":690},[92],[20,692],{"className":693,"style":388},[96],[20,695,697,700,797],{"className":696},[101],[20,698],{"className":699},[395,396],[20,701,703],{"className":702},[264],[20,704,706,789],{"className":705},[327,328],[20,707,709,786],{"className":708},[332],[20,710,712,732,740],{"className":711,"style":409},[336],[20,713,714,717],{"style":412},[20,715],{"className":716,"style":416},[344],[20,718,720],{"className":719},[349,350,351,352],[20,721,723,726,729],{"className":722},[101,352],[20,724,285],{"className":725,"style":429},[426,427,428,352],[20,727],{"className":728,"style":433},[373,352],[20,730,288],{"className":731},[101,191,352],[20,733,734,737],{"style":439},[20,735],{"className":736,"style":416},[344],[20,738],{"className":739,"style":447},[446],[20,741,742,745],{"style":450},[20,743],{"className":744,"style":416},[344],[20,746,748],{"className":747},[349,350,351,352],[20,749,751,783],{"className":750},[101,352],[20,752,754,757],{"className":753},[101,352],[20,755,274],{"className":756},[101,352],[20,758,760],{"className":759},[323],[20,761,763],{"className":762},[327],[20,764,766],{"className":765},[332],[20,767,769],{"className":768,"style":478},[336],[20,770,771,774],{"style":481},[20,772],{"className":773,"style":485},[344],[20,775,777],{"className":776},[349,489,490,352],[20,778,780],{"className":779},[101,352],[20,781,278],{"className":782},[101,352],[20,784,214],{"className":785,"style":233},[101,191,352],[20,787,360],{"className":788},[359],[20,790,792],{"className":791},[332],[20,793,795],{"className":794,"style":509},[336],[20,796],{},[20,798],{"className":799},[515,396],[20,801],{"className":802,"style":519},[373],[20,804,291],{"className":805},[523],[20,807],{"className":808,"style":519},[373],[20,810,812,815],{"className":811},[92],[20,813],{"className":814,"style":533},[96],[20,816,818,821],{"className":817},[101],[20,819,288],{"className":820},[101,191],[20,822,824],{"className":823},[323],[20,825,827,847],{"className":826},[327,328],[20,828,830,844],{"className":829},[332],[20,831,833],{"className":832,"style":337},[336],[20,834,835,838],{"style":554},[20,836],{"className":837,"style":345},[344],[20,839,841],{"className":840},[349,350,351,352],[20,842,258],{"className":843},[101,191,352],[20,845,360],{"className":846},[359],[20,848,850],{"className":849},[332],[20,851,853],{"className":852,"style":367},[336],[20,854],{}," ",[20,857,42],{},[16,859,860],{},"Where:",[862,863,864,992,1033],"ul",{},[865,866,867,991],"li",{},[20,868,870,901],{"className":869},[56],[20,871,873],{"className":872},[60],[62,874,875],{"xmlns":64},[66,876,877,898],{},[69,878,879,885,887,890,896],{},[269,880,881,883],{},[169,882,274],{"mathvariant":273},[260,884,278],{"mathvariant":273,"lspace":277,"rspace":277},[169,886,174],{},[260,888,889],{"separator":88},",",[269,891,892,894],{},[169,893,274],{"mathvariant":273},[260,895,278],{"mathvariant":273,"lspace":277,"rspace":277},[169,897,214],{},[80,899,900],{"encoding":82},"\\Delta' E, \\Delta' N",[20,902,904],{"className":903,"ariaHidden":88},[87],[20,905,907,911,945,948,952,956,988],{"className":906},[92],[20,908],{"className":909,"style":910},[96],"height:0.9463em;vertical-align:-0.1944em;",[20,912,914,917],{"className":913},[101],[20,915,274],{"className":916},[101],[20,918,920],{"className":919},[323],[20,921,923],{"className":922},[327],[20,924,926],{"className":925},[332],[20,927,930],{"className":928,"style":929},[336],"height:0.7519em;",[20,931,933,936],{"style":932},"top:-3.063em;margin-right:0.05em;",[20,934],{"className":935,"style":345},[344],[20,937,939],{"className":938},[349,350,351,352],[20,940,942],{"className":941},[101,352],[20,943,278],{"className":944},[101,352],[20,946,174],{"className":947,"style":196},[101,191],[20,949,889],{"className":950},[951],"mpunct",[20,953],{"className":954,"style":955},[373],"margin-right:0.1667em;",[20,957,959,962],{"className":958},[101],[20,960,274],{"className":961},[101],[20,963,965],{"className":964},[323],[20,966,968],{"className":967},[327],[20,969,971],{"className":970},[332],[20,972,974],{"className":973,"style":929},[336],[20,975,976,979],{"style":932},[20,977],{"className":978,"style":345},[344],[20,980,982],{"className":981},[349,350,351,352],[20,983,985],{"className":984},[101,352],[20,986,278],{"className":987},[101,352],[20,989,214],{"className":990,"style":233},[101,191]," = Total coordinate misclosure.",[865,993,994,1032],{},[20,995,997,1013],{"className":996},[56],[20,998,1000],{"className":999},[60],[62,1001,1002],{"xmlns":64},[66,1003,1004,1010],{},[69,1005,1006,1008],{},[260,1007,285],{},[169,1009,288],{},[80,1011,1012],{"encoding":82},"\\sum L",[20,1014,1016],{"className":1015,"ariaHidden":88},[87],[20,1017,1019,1023,1026,1029],{"className":1018},[92],[20,1020],{"className":1021,"style":1022},[96],"height:1em;vertical-align:-0.25em;",[20,1024,285],{"className":1025,"style":429},[426,427,428],[20,1027],{"className":1028,"style":955},[373],[20,1030,288],{"className":1031},[101,191]," = Total length of the traverse.",[865,1034,1035,1105],{},[20,1036,1038,1056],{"className":1037},[56],[20,1039,1041],{"className":1040},[60],[62,1042,1043],{"xmlns":64},[66,1044,1045,1053],{},[69,1046,1047],{},[252,1048,1049,1051],{},[169,1050,288],{},[169,1052,258],{},[80,1054,1055],{"encoding":82},"L_i",[20,1057,1059],{"className":1058,"ariaHidden":88},[87],[20,1060,1062,1065],{"className":1061},[92],[20,1063],{"className":1064,"style":533},[96],[20,1066,1068,1071],{"className":1067},[101],[20,1069,288],{"className":1070},[101,191],[20,1072,1074],{"className":1073},[323],[20,1075,1077,1097],{"className":1076},[327,328],[20,1078,1080,1094],{"className":1079},[332],[20,1081,1083],{"className":1082,"style":337},[336],[20,1084,1085,1088],{"style":554},[20,1086],{"className":1087,"style":345},[344],[20,1089,1091],{"className":1090},[349,350,351,352],[20,1092,258],{"className":1093},[101,191,352],[20,1095,360],{"className":1096},[359],[20,1098,1100],{"className":1099},[332],[20,1101,1103],{"className":1102,"style":367},[336],[20,1104],{}," = Length of the current leg.",[11,1107,1109],{"id":1108},"traverse-workflow","Traverse Workflow",[1111,1112,1113,1118,1273,1277,1508,1512,1719,1723,1728,1732],"steps",{},[1114,1115,1117],"h3",{"id":1116},"angular-adjustment","Angular Adjustment",[16,1119,1120,1121,1237,1238,1269,1270,32],{},"Sum your internal angles. They must equal ",[20,1122,1124,1163],{"className":1123},[56],[20,1125,1127],{"className":1126},[60],[62,1128,1129],{"xmlns":64},[66,1130,1131,1160],{},[69,1132,1133,1137,1140,1143,1146,1149,1152],{},[260,1134,1136],{"stretchy":1135},"false","(",[72,1138,1139],{},"2",[169,1141,1142],{},"n",[260,1144,1145],{},"−",[72,1147,1148],{},"4",[260,1150,1151],{"stretchy":1135},")",[269,1153,1154,1157],{},[72,1155,1156],{},"90",[260,1158,1159],{},"∘",[80,1161,1162],{"encoding":82},"(2n-4)90^\\circ",[20,1164,1166,1190],{"className":1165,"ariaHidden":88},[87],[20,1167,1169,1172,1175,1178,1181,1184,1187],{"className":1168},[92],[20,1170],{"className":1171,"style":1022},[96],[20,1173,1136],{"className":1174},[395],[20,1176,1139],{"className":1177},[101],[20,1179,1142],{"className":1180},[101,191],[20,1182],{"className":1183,"style":519},[373],[20,1185,1145],{"className":1186},[523],[20,1188],{"className":1189,"style":519},[373],[20,1191,1193,1196,1199,1202,1206],{"className":1192},[92],[20,1194],{"className":1195,"style":1022},[96],[20,1197,1148],{"className":1198},[101],[20,1200,1151],{"className":1201},[515],[20,1203,1205],{"className":1204},[101],"9",[20,1207,1209,1213],{"className":1208},[101],[20,1210,1212],{"className":1211},[101],"0",[20,1214,1216],{"className":1215},[323],[20,1217,1219],{"className":1218},[327],[20,1220,1222],{"className":1221},[332],[20,1223,1226],{"className":1224,"style":1225},[336],"height:0.6741em;",[20,1227,1228,1231],{"style":932},[20,1229],{"className":1230,"style":345},[344],[20,1232,1234],{"className":1233},[349,350,351,352],[20,1235,1159],{"className":1236},[523,352],". Distribute any \"angular misclosure\" (",[20,1239,1241,1255],{"className":1240},[56],[20,1242,1244],{"className":1243},[60],[62,1245,1246],{"xmlns":64},[66,1247,1248,1253],{},[69,1249,1250],{},[169,1251,1252],{},"W",[80,1254,1252],{"encoding":82},[20,1256,1258],{"className":1257,"ariaHidden":88},[87],[20,1259,1261,1265],{"className":1260},[92],[20,1262],{"className":1263,"style":1264},[96],"height:0.6833em;",[20,1266,1252],{"className":1267,"style":1268},[101,191],"margin-right:0.1389em;",") equally among all angles before calculating bearings ",[20,1271,1272],{},"47",[1114,1274,1276],{"id":1275},"calculate-coordinates","Calculate Coordinates",[16,1278,1279,1280,1314,1315,1349,1350,1430,855,1505],{},"Using the corrected bearings and measured distances, calculate the ",[20,1281,1283,1299],{"className":1282},[56],[20,1284,1286],{"className":1285},[60],[62,1287,1288],{"xmlns":64},[66,1289,1290,1296],{},[69,1291,1292,1294],{},[169,1293,274],{"mathvariant":273},[169,1295,174],{},[80,1297,1298],{"encoding":82},"\\Delta E",[20,1300,1302],{"className":1301,"ariaHidden":88},[87],[20,1303,1305,1308,1311],{"className":1304},[92],[20,1306],{"className":1307,"style":1264},[96],[20,1309,274],{"className":1310},[101],[20,1312,174],{"className":1313,"style":196},[101,191]," and ",[20,1316,1318,1334],{"className":1317},[56],[20,1319,1321],{"className":1320},[60],[62,1322,1323],{"xmlns":64},[66,1324,1325,1331],{},[69,1326,1327,1329],{},[169,1328,274],{"mathvariant":273},[169,1330,214],{},[80,1332,1333],{"encoding":82},"\\Delta N",[20,1335,1337],{"className":1336,"ariaHidden":88},[87],[20,1338,1340,1343,1346],{"className":1339},[92],[20,1341],{"className":1342,"style":1264},[96],[20,1344,274],{"className":1345},[101],[20,1347,214],{"className":1348,"style":233},[101,191]," for each leg:\n",[20,1351,1353,1383],{"className":1352},[56],[20,1354,1356],{"className":1355},[60],[62,1357,1358],{"xmlns":64},[66,1359,1360,1380],{},[69,1361,1362,1364,1366,1368,1371,1374,1377],{},[169,1363,274],{"mathvariant":273},[169,1365,174],{},[260,1367,262],{},[169,1369,1370],{},"D",[169,1372,1373],{},"sin",[260,1375,1376],{},"⁡",[169,1378,1379],{},"α",[80,1381,1382],{"encoding":82},"\\Delta E = D \\sin \\alpha",[20,1384,1386,1407],{"className":1385,"ariaHidden":88},[87],[20,1387,1389,1392,1395,1398,1401,1404],{"className":1388},[92],[20,1390],{"className":1391,"style":1264},[96],[20,1393,274],{"className":1394},[101],[20,1396,174],{"className":1397,"style":196},[101,191],[20,1399],{"className":1400,"style":374},[373],[20,1402,262],{"className":1403},[378],[20,1405],{"className":1406,"style":374},[373],[20,1408,1410,1413,1417,1420,1423,1426],{"className":1409},[92],[20,1411],{"className":1412,"style":1264},[96],[20,1414,1370],{"className":1415,"style":1416},[101,191],"margin-right:0.0278em;",[20,1418],{"className":1419,"style":955},[373],[20,1421,1373],{"className":1422},[426],[20,1424],{"className":1425,"style":955},[373],[20,1427,1379],{"className":1428,"style":1429},[101,191],"margin-right:0.0037em;",[20,1431,1433,1460],{"className":1432},[56],[20,1434,1436],{"className":1435},[60],[62,1437,1438],{"xmlns":64},[66,1439,1440,1457],{},[69,1441,1442,1444,1446,1448,1450,1453,1455],{},[169,1443,274],{"mathvariant":273},[169,1445,214],{},[260,1447,262],{},[169,1449,1370],{},[169,1451,1452],{},"cos",[260,1454,1376],{},[169,1456,1379],{},[80,1458,1459],{"encoding":82},"\\Delta N = D \\cos \\alpha",[20,1461,1463,1484],{"className":1462,"ariaHidden":88},[87],[20,1464,1466,1469,1472,1475,1478,1481],{"className":1465},[92],[20,1467],{"className":1468,"style":1264},[96],[20,1470,274],{"className":1471},[101],[20,1473,214],{"className":1474,"style":233},[101,191],[20,1476],{"className":1477,"style":374},[373],[20,1479,262],{"className":1480},[378],[20,1482],{"className":1483,"style":374},[373],[20,1485,1487,1490,1493,1496,1499,1502],{"className":1486},[92],[20,1488],{"className":1489,"style":1264},[96],[20,1491,1370],{"className":1492,"style":1416},[101,191],[20,1494],{"className":1495,"style":955},[373],[20,1497,1452],{"className":1498},[426],[20,1500],{"className":1501,"style":955},[373],[20,1503,1379],{"className":1504,"style":1429},[101,191],[20,1506,1507],{},"48, 49",[1114,1509,1511],{"id":1510},"find-the-misclosure","Find the Misclosure",[16,1513,1514,1515,1314,1548,1581,1582,1314,1649,855,1716,32],{},"Sum all ",[20,1516,1518,1533],{"className":1517},[56],[20,1519,1521],{"className":1520},[60],[62,1522,1523],{"xmlns":64},[66,1524,1525,1531],{},[69,1526,1527,1529],{},[169,1528,274],{"mathvariant":273},[169,1530,174],{},[80,1532,1298],{"encoding":82},[20,1534,1536],{"className":1535,"ariaHidden":88},[87],[20,1537,1539,1542,1545],{"className":1538},[92],[20,1540],{"className":1541,"style":1264},[96],[20,1543,274],{"className":1544},[101],[20,1546,174],{"className":1547,"style":196},[101,191],[20,1549,1551,1566],{"className":1550},[56],[20,1552,1554],{"className":1553},[60],[62,1555,1556],{"xmlns":64},[66,1557,1558,1564],{},[69,1559,1560,1562],{},[169,1561,274],{"mathvariant":273},[169,1563,214],{},[80,1565,1333],{"encoding":82},[20,1567,1569],{"className":1568,"ariaHidden":88},[87],[20,1570,1572,1575,1578],{"className":1571},[92],[20,1573],{"className":1574,"style":1264},[96],[20,1576,274],{"className":1577},[101],[20,1579,214],{"className":1580,"style":233},[101,191],". The totals should be zero for a closed loop. Any deviation is your ",[20,1583,1585,1605],{"className":1584},[56],[20,1586,1588],{"className":1587},[60],[62,1589,1590],{"xmlns":64},[66,1591,1592,1602],{},[69,1593,1594,1600],{},[269,1595,1596,1598],{},[169,1597,274],{"mathvariant":273},[260,1599,278],{"mathvariant":273,"lspace":277,"rspace":277},[169,1601,174],{},[80,1603,1604],{"encoding":82},"\\Delta' E",[20,1606,1608],{"className":1607,"ariaHidden":88},[87],[20,1609,1611,1614,1646],{"className":1610},[92],[20,1612],{"className":1613,"style":929},[96],[20,1615,1617,1620],{"className":1616},[101],[20,1618,274],{"className":1619},[101],[20,1621,1623],{"className":1622},[323],[20,1624,1626],{"className":1625},[327],[20,1627,1629],{"className":1628},[332],[20,1630,1632],{"className":1631,"style":929},[336],[20,1633,1634,1637],{"style":932},[20,1635],{"className":1636,"style":345},[344],[20,1638,1640],{"className":1639},[349,350,351,352],[20,1641,1643],{"className":1642},[101,352],[20,1644,278],{"className":1645},[101,352],[20,1647,174],{"className":1648,"style":196},[101,191],[20,1650,1652,1672],{"className":1651},[56],[20,1653,1655],{"className":1654},[60],[62,1656,1657],{"xmlns":64},[66,1658,1659,1669],{},[69,1660,1661,1667],{},[269,1662,1663,1665],{},[169,1664,274],{"mathvariant":273},[260,1666,278],{"mathvariant":273,"lspace":277,"rspace":277},[169,1668,214],{},[80,1670,1671],{"encoding":82},"\\Delta' N",[20,1673,1675],{"className":1674,"ariaHidden":88},[87],[20,1676,1678,1681,1713],{"className":1677},[92],[20,1679],{"className":1680,"style":929},[96],[20,1682,1684,1687],{"className":1683},[101],[20,1685,274],{"className":1686},[101],[20,1688,1690],{"className":1689},[323],[20,1691,1693],{"className":1692},[327],[20,1694,1696],{"className":1695},[332],[20,1697,1699],{"className":1698,"style":929},[336],[20,1700,1701,1704],{"style":932},[20,1702],{"className":1703,"style":345},[344],[20,1705,1707],{"className":1706},[349,350,351,352],[20,1708,1710],{"className":1709},[101,352],[20,1711,278],{"className":1712},[101,352],[20,1714,214],{"className":1715,"style":233},[101,191],[20,1717,1718],{},"50",[1114,1720,1722],{"id":1721},"apply-bowditch","Apply Bowditch",[16,1724,1725,1726,32],{},"Calculate the correction for each leg based on its length and add it algebraically to the coordinates ",[20,1727,42],{},[1114,1729,1731],{"id":1730},"final-coordinates","Final Coordinates",[16,1733,1734,1735,1314,1768,1801,1802,32],{},"Add the corrected ",[20,1736,1738,1753],{"className":1737},[56],[20,1739,1741],{"className":1740},[60],[62,1742,1743],{"xmlns":64},[66,1744,1745,1751],{},[69,1746,1747,1749],{},[169,1748,274],{"mathvariant":273},[169,1750,174],{},[80,1752,1298],{"encoding":82},[20,1754,1756],{"className":1755,"ariaHidden":88},[87],[20,1757,1759,1762,1765],{"className":1758},[92],[20,1760],{"className":1761,"style":1264},[96],[20,1763,274],{"className":1764},[101],[20,1766,174],{"className":1767,"style":196},[101,191],[20,1769,1771,1786],{"className":1770},[56],[20,1772,1774],{"className":1773},[60],[62,1775,1776],{"xmlns":64},[66,1777,1778,1784],{},[69,1779,1780,1782],{},[169,1781,274],{"mathvariant":273},[169,1783,214],{},[80,1785,1333],{"encoding":82},[20,1787,1789],{"className":1788,"ariaHidden":88},[87],[20,1790,1792,1795,1798],{"className":1791},[92],[20,1793],{"className":1794,"style":1264},[96],[20,1796,274],{"className":1797},[101],[20,1799,214],{"className":1800,"style":233},[101,191]," to the starting point to get the final adjusted positions ",[20,1803,1804],{},"51",[11,1806,1808],{"id":1807},"step-by-step-example","Step-by-Step Example",[16,1810,1811,1814,1815,1853,1854,1898,1899,1937,1938],{},[25,1812,1813],{},"Problem:"," A traverse has a total length of ",[20,1816,1818,1835],{"className":1817},[56],[20,1819,1821],{"className":1820},[60],[62,1822,1823],{"xmlns":64},[66,1824,1825,1832],{},[69,1826,1827,1830],{},[72,1828,1829],{},"1239",[76,1831,78],{},[80,1833,1834],{"encoding":82},"1239 \\text{ m}",[20,1836,1838],{"className":1837,"ariaHidden":88},[87],[20,1839,1841,1844,1847],{"className":1840},[92],[20,1842],{"className":1843,"style":97},[96],[20,1845,1829],{"className":1846},[101],[20,1848,1850],{"className":1849},[101,105],[20,1851,78],{"className":1852},[101]," and an Easting misclosure of ",[20,1855,1857,1876],{"className":1856},[56],[20,1858,1860],{"className":1859},[60],[62,1861,1862],{"xmlns":64},[66,1863,1864,1873],{},[69,1865,1866,1868,1871],{},[260,1867,1145],{},[72,1869,1870],{},"0.55",[76,1872,78],{},[80,1874,1875],{"encoding":82},"-0.55 \\text{ m}",[20,1877,1879],{"className":1878,"ariaHidden":88},[87],[20,1880,1882,1886,1889,1892],{"className":1881},[92],[20,1883],{"className":1884,"style":1885},[96],"height:0.7278em;vertical-align:-0.0833em;",[20,1887,1145],{"className":1888},[101],[20,1890,1870],{"className":1891},[101],[20,1893,1895],{"className":1894},[101,105],[20,1896,78],{"className":1897},[101],". What is the correction for a leg that is ",[20,1900,1902,1919],{"className":1901},[56],[20,1903,1905],{"className":1904},[60],[62,1906,1907],{"xmlns":64},[66,1908,1909,1916],{},[69,1910,1911,1914],{},[72,1912,1913],{},"155",[76,1915,78],{},[80,1917,1918],{"encoding":82},"155 \\text{ m}",[20,1920,1922],{"className":1921,"ariaHidden":88},[87],[20,1923,1925,1928,1931],{"className":1924},[92],[20,1926],{"className":1927,"style":97},[96],[20,1929,1913],{"className":1930},[101],[20,1932,1934],{"className":1933},[101,105],[20,1935,78],{"className":1936},[101]," long? ",[20,1939,1940],{},"46, 50",[1942,1943,1944,2134],"ol",{},[865,1945,1946,1980],{},[25,1947,1948,1949,1979],{},"Calculate the Constant (",[20,1950,1952,1966],{"className":1951},[56],[20,1953,1955],{"className":1954},[60],[62,1956,1957],{"xmlns":64},[66,1958,1959,1964],{},[69,1960,1961],{},[169,1962,1963],{},"K",[80,1965,1963],{"encoding":82},[20,1967,1969],{"className":1968,"ariaHidden":88},[87],[20,1970,1972,1975],{"className":1971},[92],[20,1973],{"className":1974,"style":1264},[96],[20,1976,1963],{"className":1977,"style":1978},[101,191],"margin-right:0.0715em;","):",[20,1981,1983,2027],{"className":1982},[56],[20,1984,1986],{"className":1985},[60],[62,1987,1988],{"xmlns":64},[66,1989,1990,2024],{},[69,1991,1992,1994,1996,1999,2001,2004,2006,2008,2011,2013],{},[169,1993,1963],{},[260,1995,262],{},[260,1997,1998],{},"+",[72,2000,1870],{},[169,2002,2003],{"mathvariant":273},"\u002F",[72,2005,1829],{},[260,2007,262],{},[72,2009,2010],{},"4.4",[260,2012,291],{},[269,2014,2015,2018],{},[72,2016,2017],{},"10",[69,2019,2020,2022],{},[260,2021,1145],{},[72,2023,1148],{},[80,2025,2026],{"encoding":82},"K = +0.55 \u002F 1239 = 4.4 \\times 10^{-4}",[20,2028,2030,2048,2070,2088],{"className":2029,"ariaHidden":88},[87],[20,2031,2033,2036,2039,2042,2045],{"className":2032},[92],[20,2034],{"className":2035,"style":1264},[96],[20,2037,1963],{"className":2038,"style":1978},[101,191],[20,2040],{"className":2041,"style":374},[373],[20,2043,262],{"className":2044},[378],[20,2046],{"className":2047,"style":374},[373],[20,2049,2051,2054,2057,2061,2064,2067],{"className":2050},[92],[20,2052],{"className":2053,"style":1022},[96],[20,2055,1998],{"className":2056},[101],[20,2058,2060],{"className":2059},[101],"0.55\u002F1239",[20,2062],{"className":2063,"style":374},[373],[20,2065,262],{"className":2066},[378],[20,2068],{"className":2069,"style":374},[373],[20,2071,2073,2076,2079,2082,2085],{"className":2072},[92],[20,2074],{"className":2075,"style":1885},[96],[20,2077,2010],{"className":2078},[101],[20,2080],{"className":2081,"style":519},[373],[20,2083,291],{"className":2084},[523],[20,2086],{"className":2087,"style":519},[373],[20,2089,2091,2095,2099],{"className":2090},[92],[20,2092],{"className":2093,"style":2094},[96],"height:0.8141em;",[20,2096,2098],{"className":2097},[101],"1",[20,2100,2102,2105],{"className":2101},[101],[20,2103,1212],{"className":2104},[101],[20,2106,2108],{"className":2107},[323],[20,2109,2111],{"className":2110},[327],[20,2112,2114],{"className":2113},[332],[20,2115,2117],{"className":2116,"style":2094},[336],[20,2118,2119,2122],{"style":932},[20,2120],{"className":2121,"style":345},[344],[20,2123,2125],{"className":2124},[349,350,351,352],[20,2126,2128,2131],{"className":2127},[101,352],[20,2129,1145],{"className":2130},[101,352],[20,2132,1148],{"className":2133},[101,352],[865,2135,2136,2139,855,2329],{},[25,2137,2138],{},"Apply to Leg:",[20,2140,2142,2191],{"className":2141},[56],[20,2143,2145],{"className":2144},[60],[62,2146,2147],{"xmlns":64},[66,2148,2149,2188],{},[69,2150,2151,2153,2155,2157,2159,2161,2163,2173,2175,2177,2179,2181,2183,2186],{},[169,2152,171],{},[169,2154,174],{},[260,2156,262],{},[260,2158,1136],{"stretchy":1135},[72,2160,2010],{},[260,2162,291],{},[269,2164,2165,2167],{},[72,2166,2017],{},[69,2168,2169,2171],{},[260,2170,1145],{},[72,2172,1148],{},[260,2174,1151],{"stretchy":1135},[260,2176,291],{},[72,2178,1913],{},[260,2180,262],{},[260,2182,1998],{},[72,2184,2185],{},"0.07",[76,2187,78],{},[80,2189,2190],{"encoding":82},"\\delta E = (4.4 \\times 10^{-4}) \\times 155 = +0.07 \\text{ m}",[20,2192,2194,2215,2236,2293,2311],{"className":2193,"ariaHidden":88},[87],[20,2195,2197,2200,2203,2206,2209,2212],{"className":2196},[92],[20,2198],{"className":2199,"style":187},[96],[20,2201,171],{"className":2202,"style":192},[101,191],[20,2204,174],{"className":2205,"style":196},[101,191],[20,2207],{"className":2208,"style":374},[373],[20,2210,262],{"className":2211},[378],[20,2213],{"className":2214,"style":374},[373],[20,2216,2218,2221,2224,2227,2230,2233],{"className":2217},[92],[20,2219],{"className":2220,"style":1022},[96],[20,2222,1136],{"className":2223},[395],[20,2225,2010],{"className":2226},[101],[20,2228],{"className":2229,"style":519},[373],[20,2231,291],{"className":2232},[523],[20,2234],{"className":2235,"style":519},[373],[20,2237,2239,2243,2246,2281,2284,2287,2290],{"className":2238},[92],[20,2240],{"className":2241,"style":2242},[96],"height:1.0641em;vertical-align:-0.25em;",[20,2244,2098],{"className":2245},[101],[20,2247,2249,2252],{"className":2248},[101],[20,2250,1212],{"className":2251},[101],[20,2253,2255],{"className":2254},[323],[20,2256,2258],{"className":2257},[327],[20,2259,2261],{"className":2260},[332],[20,2262,2264],{"className":2263,"style":2094},[336],[20,2265,2266,2269],{"style":932},[20,2267],{"className":2268,"style":345},[344],[20,2270,2272],{"className":2271},[349,350,351,352],[20,2273,2275,2278],{"className":2274},[101,352],[20,2276,1145],{"className":2277},[101,352],[20,2279,1148],{"className":2280},[101,352],[20,2282,1151],{"className":2283},[515],[20,2285],{"className":2286,"style":519},[373],[20,2288,291],{"className":2289},[523],[20,2291],{"className":2292,"style":519},[373],[20,2294,2296,2299,2302,2305,2308],{"className":2295},[92],[20,2297],{"className":2298,"style":97},[96],[20,2300,1913],{"className":2301},[101],[20,2303],{"className":2304,"style":374},[373],[20,2306,262],{"className":2307},[378],[20,2309],{"className":2310,"style":374},[373],[20,2312,2314,2317,2320,2323],{"className":2313},[92],[20,2315],{"className":2316,"style":1885},[96],[20,2318,1998],{"className":2319},[101],[20,2321,2185],{"className":2322},[101],[20,2324,2326],{"className":2325},[101,105],[20,2327,78],{"className":2328},[101],[20,2330,42],{},[11,2332,2334],{"id":2333},"practical-tips","Practical 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0 400000 1080","xMinYMin slice",[2579,2580],"path",{"d":2581},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[20,2583,360],{"className":2584},[359],[20,2586,2588],{"className":2587},[332],[20,2589,2592],{"className":2590,"style":2591},[336],"height:0.1266em;",[20,2593],{},"). Compare this to the total traverse length to get your ",[25,2596,2597],{},"Accuracy Ratio"," (e.g., ",[20,2600,2602,2625],{"className":2601},[56],[20,2603,2605],{"className":2604},[60],[62,2606,2607],{"xmlns":64},[66,2608,2609,2622],{},[69,2610,2611,2613,2615,2617,2619],{},[72,2612,2098],{},[169,2614,2003],{"mathvariant":273},[72,2616,2017],{},[260,2618,889],{"separator":88},[72,2620,2621],{},"000",[80,2623,2624],{"encoding":82},"1\u002F10,000",[20,2626,2628],{"className":2627,"ariaHidden":88},[87],[20,2629,2631,2634,2638,2641,2644],{"className":2630},[92],[20,2632],{"className":2633,"style":1022},[96],[20,2635,2637],{"className":2636},[101],"1\u002F10",[20,2639,889],{"className":2640},[951],[20,2642],{"className":2643,"style":955},[373],[20,2645,2621],{"className":2646},[101],") ",[20,2649,1718],{},[865,2651,2652,2655,2656,32],{},[25,2653,2654],{},"Constrained Centring:"," Use a \"Three-Tripod System\" to minimize centring errors on short legs, which can ruin a traverse before you even start the math ",[20,2657,2658],{},"52-56",[11,2660,2662],{"id":2661},"common-mistakes","Common Mistakes",[862,2664,2665,2683],{},[865,2666,2667,2675,2676,2679,2680,32],{},[25,2668,2669,2670,2674],{},"Adjusting Angles ",[2671,2672,2673],"em",{},"After"," Coordinates:"," You must always balance your angles ",[2671,2677,2678],{},"first",". Coordinate adjustment assumes the bearings are already as good as they can be ",[20,2681,2682],{},"57",[865,2684,2685,2688,2689,2723,2724,2758,2759,32],{},[25,2686,2687],{},"Sign Confusion:"," If your sum is ",[20,2690,2692,2708],{"className":2691},[56],[20,2693,2695],{"className":2694},[60],[62,2696,2697],{"xmlns":64},[66,2698,2699,2705],{},[69,2700,2701,2703],{},[260,2702,1145],{},[72,2704,1870],{},[80,2706,2707],{"encoding":82},"-0.55",[20,2709,2711],{"className":2710,"ariaHidden":88},[87],[20,2712,2714,2717,2720],{"className":2713},[92],[20,2715],{"className":2716,"style":1885},[96],[20,2718,1145],{"className":2719},[101],[20,2721,1870],{"className":2722},[101],", your correction must be ",[20,2725,2727,2743],{"className":2726},[56],[20,2728,2730],{"className":2729},[60],[62,2731,2732],{"xmlns":64},[66,2733,2734,2740],{},[69,2735,2736,2738],{},[260,2737,1998],{},[72,2739,1870],{},[80,2741,2742],{"encoding":82},"+0.55",[20,2744,2746],{"className":2745,"ariaHidden":88},[87],[20,2747,2749,2752,2755],{"className":2748},[92],[20,2750],{"className":2751,"style":1885},[96],[20,2753,1998],{"className":2754},[101],[20,2756,1870],{"className":2757},[101],". Always reverse the sign of the error to find the correction ",[20,2760,1718],{},[11,2762,2764],{"id":2763},"faq","FAQ",[2766,2767,2768,2778],"accordion",{},[2769,2770,2772],"accordion-item",{"label":2771},"When should I use Least Squares instead?",[16,2773,2774,2775,32],{},"Least Squares is more rigorous for complex networks with multiple loops, but Bowditch is perfectly adequate (and much faster) for simple engineering traverses ",[20,2776,2777],{},"58, 59",[2769,2779,2781],{"label":2780},"What is an acceptable misclosure?",[16,2782,2783,2784,2854,2855,2926,2927,2956,2957,2992,2993,32],{},"This depends on the instrument count. For a ",[20,2785,2787,2809],{"className":2786},[56],[20,2788,2790],{"className":2789},[60],[62,2791,2792],{"xmlns":64},[66,2793,2794,2806],{},[69,2795,2796],{},[269,2797,2798,2800],{},[72,2799,2017],{},[69,2801,2802,2804],{},[260,2803,278],{"mathvariant":273},[260,2805,278],{"mathvariant":273},[80,2807,2808],{"encoding":82},"10''",[20,2810,2812],{"className":2811,"ariaHidden":88},[87],[20,2813,2815,2818,2821],{"className":2814},[92],[20,2816],{"className":2817,"style":929},[96],[20,2819,2098],{"className":2820},[101],[20,2822,2824,2827],{"className":2823},[101],[20,2825,1212],{"className":2826},[101],[20,2828,2830],{"className":2829},[323],[20,2831,2833],{"className":2832},[327],[20,2834,2836],{"className":2835},[332],[20,2837,2839],{"className":2838,"style":929},[336],[20,2840,2841,2844],{"style":932},[20,2842],{"className":2843,"style":345},[344],[20,2845,2847],{"className":2846},[349,350,351,352],[20,2848,2850],{"className":2849},[101,352],[20,2851,2853],{"className":2852},[101,352],"′′"," theodolite, the angular misclosure should be within ",[20,2856,2858,2881],{"className":2857},[56],[20,2859,2861],{"className":2860},[60],[62,2862,2863],{"xmlns":64},[66,2864,2865,2878],{},[69,2866,2867],{},[269,2868,2869,2872],{},[72,2870,2871],{},"110",[69,2873,2874,2876],{},[260,2875,278],{"mathvariant":273},[260,2877,278],{"mathvariant":273},[80,2879,2880],{"encoding":82},"110''",[20,2882,2884],{"className":2883,"ariaHidden":88},[87],[20,2885,2887,2890,2894],{"className":2886},[92],[20,2888],{"className":2889,"style":929},[96],[20,2891,2893],{"className":2892},[101],"11",[20,2895,2897,2900],{"className":2896},[101],[20,2898,1212],{"className":2899},[101],[20,2901,2903],{"className":2902},[323],[20,2904,2906],{"className":2905},[327],[20,2907,2909],{"className":2908},[332],[20,2910,2912],{"className":2911,"style":929},[336],[20,2913,2914,2917],{"style":932},[20,2915],{"className":2916,"style":345},[344],[20,2918,2920],{"className":2919},[349,350,351,352],[20,2921,2923],{"className":2922},[101,352],[20,2924,2853],{"className":2925},[101,352]," for a ",[20,2928,2930,2944],{"className":2929},[56],[20,2931,2933],{"className":2932},[60],[62,2934,2935],{"xmlns":64},[66,2936,2937,2942],{},[69,2938,2939],{},[72,2940,2941],{},"5",[80,2943,2941],{"encoding":82},[20,2945,2947],{"className":2946,"ariaHidden":88},[87],[20,2948,2950,2953],{"className":2949},[92],[20,2951],{"className":2952,"style":97},[96],[20,2954,2941],{"className":2955},[101],"-station traverse at ",[20,2958,2960,2978],{"className":2959},[56],[20,2961,2963],{"className":2962},[60],[62,2964,2965],{"xmlns":64},[66,2966,2967,2975],{},[69,2968,2969,2972],{},[72,2970,2971],{},"95",[169,2973,2974],{"mathvariant":273},"%",[80,2976,2977],{"encoding":82},"95\\%",[20,2979,2981],{"className":2980,"ariaHidden":88},[87],[20,2982,2984,2988],{"className":2983},[92],[20,2985],{"className":2986,"style":2987},[96],"height:0.8056em;vertical-align:-0.0556em;",[20,2989,2991],{"className":2990},[101],"95%"," confidence ",[20,2994,2995],{},"60",[11,2997,2999],{"id":2998},"conclusion","Conclusion",[16,3001,3002],{},"The Bowditch method is the surveyor's best tool for ensuring internal consistency in a control network. By linking error distribution to line length, it provides a logical and robust framework for any site-scale survey.",[11,3004,3006],{"id":3005},"references","References",[16,3008,3009,3010,3013,3014,32],{},"Schofield, W. (2001). ",[2671,3011,3012],{},"Engineering Surveying",". 5th ed. Butterworth-Heinemann. ",[20,3015,3016],{},"45-56, 60, 61",{"title":3018,"searchDepth":3019,"depth":3019,"links":3020},"",2,[3021,3022,3023,3024,3025,3033,3034,3035,3036,3037,3038],{"id":13,"depth":3019,"text":14},{"id":35,"depth":3019,"text":36},{"id":45,"depth":3019,"text":46},{"id":151,"depth":3019,"text":152},{"id":1108,"depth":3019,"text":1109,"children":3026},[3027,3029,3030,3031,3032],{"id":1116,"depth":3028,"text":1117},3,{"id":1275,"depth":3028,"text":1276},{"id":1510,"depth":3028,"text":1511},{"id":1721,"depth":3028,"text":1722},{"id":1730,"depth":3028,"text":1731},{"id":1807,"depth":3019,"text":1808},{"id":2333,"depth":3019,"text":2334},{"id":2661,"depth":3019,"text":2662},{"id":2763,"depth":3019,"text":2764},{"id":2998,"depth":3019,"text":2999},{"id":3005,"depth":3019,"text":3006},"Control Surveys","How to balance horizontal control traverses using the Bowditch rule to distribute coordinate misclosures.","md","\u002Fimages\u002Fbowditch-adjustment.jpg",{"authorCredentials":3044,"tags":3045,"sources":3050},"LS",[3046,3047,3048,3049],"Traverse","Adjustment","Bowditch","Accuracy",[3051],{"title":3052,"type":3053,"note":3054},"Engineering Surveying (Fifth Edition)","Book","Primary source for traverse computation and the Bowditch rule.",true,"\u002Fblog\u002Fthe-bowditch-method-a-deep-dive-into-traverse-adjustment-math","2024-03-24",12,{"title":5,"description":3040},{"loc":3056},"blog\u002F5.the-bowditch-method-a-deep-dive-into-traverse-adjustment-math","R0ZCnHHXopsWlp0HOxXU_UtKer4FUzCYJt0ZYnYdYeo",[3064,3069],{"title":3065,"path":3066,"stem":3067,"description":3068,"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.",{"title":3070,"path":3071,"stem":3072,"description":3073,"children":-1},"The Gyro-Theodolite: Mastering True North Underground","\u002Fblog\u002Fgyro-theodolite-underground-orientation","blog\u002F6.gyro-theodolite-underground-orientation","A comprehensive technical guide to the theory, observation, and calculation of true azimuths using suspended gyroscopes in tunnel and mine surveying.",1783851951706]