[{"data":1,"prerenderedAt":7571},["ShallowReactive",2],{"learn-\u002Flearn\u002Ftools\u002Ftraverse-and-bowditch":3,"learn-\u002Flearn\u002Ftools\u002Ftraverse-and-bowditch-surround":7560},{"id":4,"title":5,"body":6,"category":7550,"description":7551,"extension":7552,"meta":7553,"navigation":7554,"order":7523,"path":7555,"seo":7556,"sitemap":7557,"stem":7558,"__hash__":7559},"learn\u002Flearn\u002Ftools\u002Ftraverse-and-bowditch.md","Traverse Closure & Bowditch Adjustment",{"type":7,"value":8,"toc":7521},"minimark",[9,14,18,21,96,100,103,115,130,133,137,203,206,353,359,481,546,919,922,1191,1194,1447,1450,1668,1730,1734,1766,2091,2155,2187,2191,2194,2272,2309,2426,2574,2578,2581,2584,2588,2602,2734,3302,3305,3804,4012,4466,4469,4812,5084,5089,5093,5288,5293,5354,5358,5479,5483,5832,5836,5909,6102,6106,6171,6175,6231,6235,6890,6894,6901,7072,7075,7079,7083,7381,7385,7455,7459,7462,7466,7469,7473],[10,11,13],"h2",{"id":12},"introduction","Introduction",[15,16,17],"p",{},"Establishing a reliable horizontal control network is fundamental in civil engineering, boundary determination, and construction monitoring. Horizontal traversing remains the most versatile field method for extending coordinates and checking spatial consistency. Traversing yields connected lines whose directions and lengths are measured successively.",[15,19,20],{},"Professional traverse resolution splits into two phases: analyze raw measurements for geometric closure, then apply a systematic adjustment to distribute random measurement error. Surveying Core provides:",[22,23,24,82,89],"ul",{},[25,26,27,28,33,34,81],"li",{},"The ",[29,30,32],"a",{"href":31},"\u002Ftools\u002Ftraverse-closure","Traverse closure calculator"," — departures and latitudes, linear misclosure, and relative precision (1:",[35,36,39,61],"span",{"className":37},[38],"katex",[35,40,43],{"className":41},[42],"katex-mathml",[44,45,47],"math",{"xmlns":46},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[48,49,50,57],"semantics",{},[51,52,53],"mrow",{},[54,55,56],"mi",{},"N",[58,59,56],"annotation",{"encoding":60},"application\u002Fx-tex",[35,62,66],{"className":63,"ariaHidden":65},[64],"katex-html","true",[35,67,70,75],{"className":68},[69],"base",[35,71],{"className":72,"style":74},[73],"strut","height:0.6833em;",[35,76,56],{"className":77,"style":80},[78,79],"mord","mathnormal","margin-right:0.109em;",").",[25,83,27,84,88],{},[29,85,87],{"href":86},"\u002Ftools\u002Fbowditch-traverse","Bowditch adjustment calculator"," — compass-rule corrections, closed coordinates, adjusted bearings and distances.",[25,90,27,91,95],{},[29,92,94],{"href":93},"\u002Ftools\u002Fbearing-distance","Bearing & distance calculator"," — auxiliary coordinate and orientation conversions.",[10,97,99],{"id":98},"closed-traverses-in-engineering-surveying","Closed Traverses in Engineering Surveying",[15,101,102],{},"A horizontal traverse is a sequence of legs between control stations. The goal is plane rectangular coordinates (eastings and northings) relative to a project grid or geodetic datum.",[15,104,105,106,110,111,114],{},"Traverses are ",[107,108,109],"strong",{},"open"," (start known, end unknown — no redundancy) or ",[107,112,113],{},"closed",":",[116,117,118,124],"ol",{},[25,119,120,123],{},[107,121,122],{},"Closed-loop (polygon)"," — starts and ends at the same station; interior-angle and coordinate sums check against theory.",[25,125,126,129],{},[107,127,128],{},"Closed-link (connecting)"," — starts at known control, runs through new stations, closes on a different known point — common for corridors anchored to geodetic control.",[15,131,132],{},"Field data per station: clockwise horizontal angles (backsight to foresight) and horizontal distances (EDM or tape). Slope reduction and curvature\u002Frefraction are pre-processing steps before the horizontal model discussed here.",[10,134,136],{"id":135},"computing-traverse-closure","Computing Traverse Closure",[15,138,139,140,172,173,202],{},"Project each leg onto the horizontal plane using grid azimuth ",[35,141,143,158],{"className":142},[38],[35,144,146],{"className":145},[42],[44,147,148],{"xmlns":46},[48,149,150,155],{},[51,151,152],{},[54,153,154],{},"θ",[58,156,157],{"encoding":60},"\\theta",[35,159,161],{"className":160,"ariaHidden":65},[64],[35,162,164,168],{"className":163},[69],[35,165],{"className":166,"style":167},[73],"height:0.6944em;",[35,169,154],{"className":170,"style":171},[78,79],"margin-right:0.0278em;"," (clockwise from north, decimal degrees) and horizontal distance ",[35,174,176,190],{"className":175},[38],[35,177,179],{"className":178},[42],[44,180,181],{"xmlns":46},[48,182,183,188],{},[51,184,185],{},[54,186,187],{},"D",[58,189,187],{"encoding":60},[35,191,193],{"className":192,"ariaHidden":65},[64],[35,194,196,199],{"className":195},[69],[35,197],{"className":198,"style":74},[73],[35,200,187],{"className":201,"style":171},[78,79],".",[15,204,205],{},"Departures and latitudes (coordinate increments):",[15,207,208],{},[35,209,211,263],{"className":210},[38],[35,212,214],{"className":213},[42],[44,215,216],{"xmlns":46},[48,217,218,260],{},[51,219,220,224,227,231,233,236,239,241,245,247,249,251,253,256,258],{},[54,221,223],{"mathvariant":222},"normal","Δ",[54,225,226],{},"E",[228,229,230],"mo",{},"=",[54,232,187],{},[54,234,235],{},"sin",[228,237,238],{},"⁡",[54,240,154],{},[242,243],"mspace",{"width":244},"2em",[54,246,223],{"mathvariant":222},[54,248,56],{},[228,250,230],{},[54,252,187],{},[54,254,255],{},"cos",[228,257,238],{},[54,259,154],{},[58,261,262],{"encoding":60},"\\Delta E = D \\sin\\theta \\qquad \\Delta N = D \\cos\\theta",[35,264,266,290,332],{"className":265,"ariaHidden":65},[64],[35,267,269,272,275,279,283,287],{"className":268},[69],[35,270],{"className":271,"style":74},[73],[35,273,223],{"className":274},[78],[35,276,226],{"className":277,"style":278},[78,79],"margin-right:0.0576em;",[35,280],{"className":281,"style":282},[242],"margin-right:0.2778em;",[35,284,230],{"className":285},[286],"mrel",[35,288],{"className":289,"style":282},[242],[35,291,293,296,299,303,307,310,313,317,320,323,326,329],{"className":292},[69],[35,294],{"className":295,"style":167},[73],[35,297,187],{"className":298,"style":171},[78,79],[35,300],{"className":301,"style":302},[242],"margin-right:0.1667em;",[35,304,235],{"className":305},[306],"mop",[35,308],{"className":309,"style":302},[242],[35,311,154],{"className":312,"style":171},[78,79],[35,314],{"className":315,"style":316},[242],"margin-right:2em;",[35,318,223],{"className":319},[78],[35,321,56],{"className":322,"style":80},[78,79],[35,324],{"className":325,"style":282},[242],[35,327,230],{"className":328},[286],[35,330],{"className":331,"style":282},[242],[35,333,335,338,341,344,347,350],{"className":334},[69],[35,336],{"className":337,"style":167},[73],[35,339,187],{"className":340,"style":171},[78,79],[35,342],{"className":343,"style":302},[242],[35,345,255],{"className":346},[306],[35,348],{"className":349,"style":302},[242],[35,351,154],{"className":352,"style":171},[78,79],[15,354,355,356,114],{},"For a perfect ",[107,357,358],{},"closed loop",[15,360,361],{},[35,362,364,401],{"className":363},[38],[35,365,367],{"className":366},[42],[44,368,369],{"xmlns":46},[48,370,371,398],{},[51,372,373,376,378,380,382,386,388,390,392,394,396],{},[228,374,375],{},"∑",[54,377,223],{"mathvariant":222},[54,379,226],{},[228,381,230],{},[383,384,385],"mn",{},"0",[242,387],{"width":244},[228,389,375],{},[54,391,223],{"mathvariant":222},[54,393,56],{},[228,395,230],{},[383,397,385],{},[58,399,400],{"encoding":60},"\\sum \\Delta E = 0 \\qquad \\sum \\Delta N = 0",[35,402,404,435,471],{"className":403,"ariaHidden":65},[64],[35,405,407,411,417,420,423,426,429,432],{"className":406},[69],[35,408],{"className":409,"style":410},[73],"height:1em;vertical-align:-0.25em;",[35,412,375],{"className":413,"style":416},[306,414,415],"op-symbol","small-op","position:relative;top:0em;",[35,418],{"className":419,"style":302},[242],[35,421,223],{"className":422},[78],[35,424,226],{"className":425,"style":278},[78,79],[35,427],{"className":428,"style":282},[242],[35,430,230],{"className":431},[286],[35,433],{"className":434,"style":282},[242],[35,436,438,441,444,447,450,453,456,459,462,465,468],{"className":437},[69],[35,439],{"className":440,"style":410},[73],[35,442,385],{"className":443},[78],[35,445],{"className":446,"style":316},[242],[35,448],{"className":449,"style":302},[242],[35,451,375],{"className":452,"style":416},[306,414,415],[35,454],{"className":455,"style":302},[242],[35,457,223],{"className":458},[78],[35,460,56],{"className":461,"style":80},[78,79],[35,463],{"className":464,"style":282},[242],[35,466,230],{"className":467},[286],[35,469],{"className":470,"style":282},[242],[35,472,474,478],{"className":473},[69],[35,475],{"className":476,"style":477},[73],"height:0.6444em;",[35,479,385],{"className":480},[78],[15,482,483,484,487,488,517,518,114],{},"For a ",[107,485,486],{},"closed link"," from station ",[35,489,491,505],{"className":490},[38],[35,492,494],{"className":493},[42],[44,495,496],{"xmlns":46},[48,497,498,503],{},[51,499,500],{},[54,501,502],{},"S",[58,504,502],{"encoding":60},[35,506,508],{"className":507,"ariaHidden":65},[64],[35,509,511,514],{"className":510},[69],[35,512],{"className":513,"style":74},[73],[35,515,502],{"className":516,"style":278},[78,79]," to ",[35,519,521,534],{"className":520},[38],[35,522,524],{"className":523},[42],[44,525,526],{"xmlns":46},[48,527,528,532],{},[51,529,530],{},[54,531,226],{},[58,533,226],{"encoding":60},[35,535,537],{"className":536,"ariaHidden":65},[64],[35,538,540,543],{"className":539},[69],[35,541],{"className":542,"style":74},[73],[35,544,226],{"className":545,"style":278},[78,79],[15,547,548],{},[35,549,551,614],{"className":550},[38],[35,552,554],{"className":553},[42],[44,555,556],{"xmlns":46},[48,557,558,611],{},[51,559,560,562,564,566,568,577,580,587,589,591,593,595,597,603,605],{},[228,561,375],{},[54,563,223],{"mathvariant":222},[54,565,226],{},[228,567,230],{},[569,570,571,573],"msub",{},[54,572,226],{},[574,575,576],"mtext",{},"end",[228,578,579],{},"−",[569,581,582,584],{},[54,583,226],{},[574,585,586],{},"start",[242,588],{"width":244},[228,590,375],{},[54,592,223],{"mathvariant":222},[54,594,56],{},[228,596,230],{},[569,598,599,601],{},[54,600,56],{},[574,602,576],{},[228,604,579],{},[569,606,607,609],{},[54,608,56],{},[574,610,586],{},[58,612,613],{"encoding":60},"\\sum \\Delta E = E_{\\text{end}} - E_{\\text{start}} \\qquad \\sum \\Delta N = N_{\\text{end}} - N_{\\text{start}}",[35,615,617,644,725,805,867],{"className":616,"ariaHidden":65},[64],[35,618,620,623,626,629,632,635,638,641],{"className":619},[69],[35,621],{"className":622,"style":410},[73],[35,624,375],{"className":625,"style":416},[306,414,415],[35,627],{"className":628,"style":302},[242],[35,630,223],{"className":631},[78],[35,633,226],{"className":634,"style":278},[78,79],[35,636],{"className":637,"style":282},[242],[35,639,230],{"className":640},[286],[35,642],{"className":643,"style":282},[242],[35,645,647,651,714,718,722],{"className":646},[69],[35,648],{"className":649,"style":650},[73],"height:0.8333em;vertical-align:-0.15em;",[35,652,654,657],{"className":653},[78],[35,655,226],{"className":656,"style":278},[78,79],[35,658,661],{"className":659},[660],"msupsub",[35,662,666,705],{"className":663},[664,665],"vlist-t","vlist-t2",[35,667,670,700],{"className":668},[669],"vlist-r",[35,671,675],{"className":672,"style":674},[673],"vlist","height:0.3361em;",[35,676,678,683],{"style":677},"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;",[35,679],{"className":680,"style":682},[681],"pstrut","height:2.7em;",[35,684,690],{"className":685},[686,687,688,689],"sizing","reset-size6","size3","mtight",[35,691,693],{"className":692},[78,689],[35,694,697],{"className":695},[78,696,689],"text",[35,698,576],{"className":699},[78,689],[35,701,704],{"className":702},[703],"vlist-s","​",[35,706,708],{"className":707},[669],[35,709,712],{"className":710,"style":711},[673],"height:0.15em;",[35,713],{},[35,715],{"className":716,"style":717},[242],"margin-right:0.2222em;",[35,719,579],{"className":720},[721],"mbin",[35,723],{"className":724,"style":717},[242],[35,726,728,731,778,781,784,787,790,793,796,799,802],{"className":727},[69],[35,729],{"className":730,"style":410},[73],[35,732,734,737],{"className":733},[78],[35,735,226],{"className":736,"style":278},[78,79],[35,738,740],{"className":739},[660],[35,741,743,770],{"className":742},[664,665],[35,744,746,767],{"className":745},[669],[35,747,750],{"className":748,"style":749},[673],"height:0.2806em;",[35,751,752,755],{"style":677},[35,753],{"className":754,"style":682},[681],[35,756,758],{"className":757},[686,687,688,689],[35,759,761],{"className":760},[78,689],[35,762,764],{"className":763},[78,696,689],[35,765,586],{"className":766},[78,689],[35,768,704],{"className":769},[703],[35,771,773],{"className":772},[669],[35,774,776],{"className":775,"style":711},[673],[35,777],{},[35,779],{"className":780,"style":316},[242],[35,782],{"className":783,"style":302},[242],[35,785,375],{"className":786,"style":416},[306,414,415],[35,788],{"className":789,"style":302},[242],[35,791,223],{"className":792},[78],[35,794,56],{"className":795,"style":80},[78,79],[35,797],{"className":798,"style":282},[242],[35,800,230],{"className":801},[286],[35,803],{"className":804,"style":282},[242],[35,806,808,811,858,861,864],{"className":807},[69],[35,809],{"className":810,"style":650},[73],[35,812,814,817],{"className":813},[78],[35,815,56],{"className":816,"style":80},[78,79],[35,818,820],{"className":819},[660],[35,821,823,850],{"className":822},[664,665],[35,824,826,847],{"className":825},[669],[35,827,829],{"className":828,"style":674},[673],[35,830,832,835],{"style":831},"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;",[35,833],{"className":834,"style":682},[681],[35,836,838],{"className":837},[686,687,688,689],[35,839,841],{"className":840},[78,689],[35,842,844],{"className":843},[78,696,689],[35,845,576],{"className":846},[78,689],[35,848,704],{"className":849},[703],[35,851,853],{"className":852},[669],[35,854,856],{"className":855,"style":711},[673],[35,857],{},[35,859],{"className":860,"style":717},[242],[35,862,579],{"className":863},[721],[35,865],{"className":866,"style":717},[242],[35,868,870,873],{"className":869},[69],[35,871],{"className":872,"style":650},[73],[35,874,876,879],{"className":875},[78],[35,877,56],{"className":878,"style":80},[78,79],[35,880,882],{"className":881},[660],[35,883,885,911],{"className":884},[664,665],[35,886,888,908],{"className":887},[669],[35,889,891],{"className":890,"style":749},[673],[35,892,893,896],{"style":831},[35,894],{"className":895,"style":682},[681],[35,897,899],{"className":898},[686,687,688,689],[35,900,902],{"className":901},[78,689],[35,903,905],{"className":904},[78,696,689],[35,906,586],{"className":907},[78,689],[35,909,704],{"className":910},[703],[35,912,914],{"className":913},[669],[35,915,917],{"className":916,"style":711},[673],[35,918],{},[15,920,921],{},"Raw field sums rarely hit these targets. Misclosure components:",[15,923,924],{},[35,925,927,987],{"className":926},[38],[35,928,930],{"className":929},[42],[44,931,932],{"xmlns":46},[48,933,934,984],{},[51,935,936,943,945,947,949,951,953,956,958,960,962,968,970,972,974,976,978,980,982],{},[569,937,938,941],{},[54,939,940],{},"e",[54,942,226],{},[228,944,230],{},[228,946,375],{},[54,948,223],{"mathvariant":222},[54,950,226],{},[228,952,579],{},[574,954,955],{},"target ",[54,957,223],{"mathvariant":222},[54,959,226],{},[242,961],{"width":244},[569,963,964,966],{},[54,965,940],{},[54,967,56],{},[228,969,230],{},[228,971,375],{},[54,973,223],{"mathvariant":222},[54,975,56],{},[228,977,579],{},[574,979,955],{},[54,981,223],{"mathvariant":222},[54,983,56],{},[58,985,986],{"encoding":60},"e_E = \\sum \\Delta E - \\text{target } \\Delta E \\qquad e_N = \\sum \\Delta N - \\text{target } \\Delta N",[35,988,990,1048,1075,1146,1173],{"className":989,"ariaHidden":65},[64],[35,991,993,997,1039,1042,1045],{"className":992},[69],[35,994],{"className":995,"style":996},[73],"height:0.5806em;vertical-align:-0.15em;",[35,998,1000,1003],{"className":999},[78],[35,1001,940],{"className":1002},[78,79],[35,1004,1006],{"className":1005},[660],[35,1007,1009,1031],{"className":1008},[664,665],[35,1010,1012,1028],{"className":1011},[669],[35,1013,1016],{"className":1014,"style":1015},[673],"height:0.3283em;",[35,1017,1019,1022],{"style":1018},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[35,1020],{"className":1021,"style":682},[681],[35,1023,1025],{"className":1024},[686,687,688,689],[35,1026,226],{"className":1027,"style":278},[78,79,689],[35,1029,704],{"className":1030},[703],[35,1032,1034],{"className":1033},[669],[35,1035,1037],{"className":1036,"style":711},[673],[35,1038],{},[35,1040],{"className":1041,"style":282},[242],[35,1043,230],{"className":1044},[286],[35,1046],{"className":1047,"style":282},[242],[35,1049,1051,1054,1057,1060,1063,1066,1069,1072],{"className":1050},[69],[35,1052],{"className":1053,"style":410},[73],[35,1055,375],{"className":1056,"style":416},[306,414,415],[35,1058],{"className":1059,"style":302},[242],[35,1061,223],{"className":1062},[78],[35,1064,226],{"className":1065,"style":278},[78,79],[35,1067],{"className":1068,"style":717},[242],[35,1070,579],{"className":1071},[721],[35,1073],{"className":1074,"style":717},[242],[35,1076,1078,1082,1088,1091,1094,1097,1137,1140,1143],{"className":1077},[69],[35,1079],{"className":1080,"style":1081},[73],"height:0.8778em;vertical-align:-0.1944em;",[35,1083,1085],{"className":1084},[78,696],[35,1086,955],{"className":1087},[78],[35,1089,223],{"className":1090},[78],[35,1092,226],{"className":1093,"style":278},[78,79],[35,1095],{"className":1096,"style":316},[242],[35,1098,1100,1103],{"className":1099},[78],[35,1101,940],{"className":1102},[78,79],[35,1104,1106],{"className":1105},[660],[35,1107,1109,1129],{"className":1108},[664,665],[35,1110,1112,1126],{"className":1111},[669],[35,1113,1115],{"className":1114,"style":1015},[673],[35,1116,1117,1120],{"style":1018},[35,1118],{"className":1119,"style":682},[681],[35,1121,1123],{"className":1122},[686,687,688,689],[35,1124,56],{"className":1125,"style":80},[78,79,689],[35,1127,704],{"className":1128},[703],[35,1130,1132],{"className":1131},[669],[35,1133,1135],{"className":1134,"style":711},[673],[35,1136],{},[35,1138],{"className":1139,"style":282},[242],[35,1141,230],{"className":1142},[286],[35,1144],{"className":1145,"style":282},[242],[35,1147,1149,1152,1155,1158,1161,1164,1167,1170],{"className":1148},[69],[35,1150],{"className":1151,"style":410},[73],[35,1153,375],{"className":1154,"style":416},[306,414,415],[35,1156],{"className":1157,"style":302},[242],[35,1159,223],{"className":1160},[78],[35,1162,56],{"className":1163,"style":80},[78,79],[35,1165],{"className":1166,"style":717},[242],[35,1168,579],{"className":1169},[721],[35,1171],{"className":1172,"style":717},[242],[35,1174,1176,1179,1185,1188],{"className":1175},[69],[35,1177],{"className":1178,"style":1081},[73],[35,1180,1182],{"className":1181},[78,696],[35,1183,955],{"className":1184},[78],[35,1186,223],{"className":1187},[78],[35,1189,56],{"className":1190,"style":80},[78,79],[15,1192,1193],{},"Linear misclosure:",[15,1195,1196],{},[35,1197,1199,1241],{"className":1198},[38],[35,1200,1202],{"className":1201},[42],[44,1203,1204],{"xmlns":46},[48,1205,1206,1238],{},[51,1207,1208,1210,1212],{},[54,1209,940],{},[228,1211,230],{},[1213,1214,1215],"msqrt",{},[51,1216,1217,1227,1230],{},[1218,1219,1220,1222,1224],"msubsup",{},[54,1221,940],{},[54,1223,226],{},[383,1225,1226],{},"2",[228,1228,1229],{},"+",[1218,1231,1232,1234,1236],{},[54,1233,940],{},[54,1235,56],{},[383,1237,1226],{},[58,1239,1240],{"encoding":60},"e = \\sqrt{e_E^2 + 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0 400000 1296","xMinYMin slice",[1432,1433],"path",{"d":1434},"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z",[35,1436,704],{"className":1437},[703],[35,1439,1441],{"className":1440},[669],[35,1442,1445],{"className":1443,"style":1444},[673],"height:0.3038em;",[35,1446],{},[15,1448,1449],{},"Misclosure azimuth:",[15,1451,1452],{},[35,1453,1455,1500],{"className":1454},[38],[35,1456,1458],{"className":1457},[42],[44,1459,1460],{"xmlns":46},[48,1461,1462,1497],{},[51,1463,1464,1470,1472,1475,1479,1485,1488,1494],{},[569,1465,1466,1468],{},[54,1467,154],{},[54,1469,940],{},[228,1471,230],{},[574,1473,1474],{},"atan2",[228,1476,1478],{"stretchy":1477},"false","(",[569,1480,1481,1483],{},[54,1482,940],{},[54,1484,226],{},[228,1486,1487],{"separator":65},",",[569,1489,1490,1492],{},[54,1491,940],{},[54,1493,56],{},[228,1495,1496],{"stretchy":1477},")",[58,1498,1499],{"encoding":60},"\\theta_e = \\text{atan2}(e_E, e_N)",[35,1501,1503,1561],{"className":1502,"ariaHidden":65},[64],[35,1504,1506,1510,1552,1555,1558],{"className":1505},[69],[35,1507],{"className":1508,"style":1509},[73],"height:0.8444em;vertical-align:-0.15em;",[35,1511,1513,1516],{"className":1512},[78],[35,1514,154],{"className":1515,"style":171},[78,79],[35,1517,1519],{"className":1518},[660],[35,1520,1522,1544],{"className":1521},[664,665],[35,1523,1525,1541],{"className":1524},[669],[35,1526,1529],{"className":1527,"style":1528},[673],"height:0.1514em;",[35,1530,1532,1535],{"style":1531},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[35,1533],{"className":1534,"style":682},[681],[35,1536,1538],{"className":1537},[686,687,688,689],[35,1539,940],{"className":1540},[78,79,689],[35,1542,704],{"className":1543},[703],[35,1545,1547],{"className":1546},[669],[35,1548,1550],{"className":1549,"style":711},[673],[35,1551],{},[35,1553],{"className":1554,"style":282},[242],[35,1556,230],{"className":1557},[286],[35,1559],{"className":1560,"style":282},[242],[35,1562,1564,1567,1573,1577,1617,1621,1624,1664],{"className":1563},[69],[35,1565],{"className":1566,"style":410},[73],[35,1568,1570],{"className":1569},[78,696],[35,1571,1474],{"className":1572},[78],[35,1574,1478],{"className":1575},[1576],"mopen",[35,1578,1580,1583],{"className":1579},[78],[35,1581,940],{"className":1582},[78,79],[35,1584,1586],{"className":1585},[660],[35,1587,1589,1609],{"className":1588},[664,665],[35,1590,1592,1606],{"className":1591},[669],[35,1593,1595],{"className":1594,"style":1015},[673],[35,1596,1597,1600],{"style":1018},[35,1598],{"className":1599,"style":682},[681],[35,1601,1603],{"className":1602},[686,687,688,689],[35,1604,226],{"className":1605,"style":278},[78,79,689],[35,1607,704],{"className":1608},[703],[35,1610,1612],{"className":1611},[669],[35,1613,1615],{"className":1614,"style":711},[673],[35,1616],{},[35,1618,1487],{"className":1619},[1620],"mpunct",[35,1622],{"className":1623,"style":302},[242],[35,1625,1627,1630],{"className":1626},[78],[35,1628,940],{"className":1629},[78,79],[35,1631,1633],{"className":1632},[660],[35,1634,1636,1656],{"className":1635},[664,665],[35,1637,1639,1653],{"className":1638},[669],[35,1640,1642],{"className":1641,"style":1015},[673],[35,1643,1644,1647],{"style":1018},[35,1645],{"className":1646,"style":682},[681],[35,1648,1650],{"className":1649},[686,687,688,689],[35,1651,56],{"className":1652,"style":80},[78,79,689],[35,1654,704],{"className":1655},[703],[35,1657,1659],{"className":1658},[669],[35,1660,1662],{"className":1661,"style":711},[673],[35,1663],{},[35,1665,1496],{"className":1666},[1667],"mclose",[15,1669,27,1670,1672,1673,1701,1702,81],{},[29,1671,32],{"href":31}," assumes a closed loop (target misclosure ",[35,1674,1676,1689],{"className":1675},[38],[35,1677,1679],{"className":1678},[42],[44,1680,1681],{"xmlns":46},[48,1682,1683,1687],{},[51,1684,1685],{},[383,1686,385],{},[58,1688,385],{"encoding":60},[35,1690,1692],{"className":1691,"ariaHidden":65},[64],[35,1693,1695,1698],{"className":1694},[69],[35,1696],{"className":1697,"style":477},[73],[35,1699,385],{"className":1700},[78],", ",[35,1703,1705,1718],{"className":1704},[38],[35,1706,1708],{"className":1707},[42],[44,1709,1710],{"xmlns":46},[48,1711,1712,1716],{},[51,1713,1714],{},[383,1715,385],{},[58,1717,385],{"encoding":60},[35,1719,1721],{"className":1720,"ariaHidden":65},[64],[35,1722,1724,1727],{"className":1723},[69],[35,1725],{"className":1726,"style":477},[73],[35,1728,385],{"className":1729},[78],[10,1731,1733],{"id":1732},"misclosure-and-relative-precision","Misclosure and Relative Precision",[15,1735,1736,1737,1765],{},"Absolute misclosure ",[35,1738,1740,1753],{"className":1739},[38],[35,1741,1743],{"className":1742},[42],[44,1744,1745],{"xmlns":46},[48,1746,1747,1751],{},[51,1748,1749],{},[54,1750,940],{},[58,1752,940],{"encoding":60},[35,1754,1756],{"className":1755,"ariaHidden":65},[64],[35,1757,1759,1762],{"className":1758},[69],[35,1760],{"className":1761,"style":1250},[73],[35,1763,940],{"className":1764},[78,79]," must be judged against traverse size. Relative precision normalizes quality:",[15,1767,1768],{},[35,1769,1771,1823],{"className":1770},[38],[35,1772,1774],{"className":1773},[42],[44,1775,1776],{"xmlns":46},[48,1777,1778,1820],{},[51,1779,1780,1783,1785,1787,1794,1796,1799,1801,1808,1810,1812,1814],{},[54,1781,1782],{},"P",[228,1784,230],{},[228,1786,375],{},[569,1788,1789,1791],{},[54,1790,187],{},[54,1792,1793],{},"i",[242,1795],{"width":244},[574,1797,1798],{},"Relative precision",[228,1800,230],{},[1802,1803,1804,1806],"mfrac",{},[54,1805,940],{},[54,1807,1782],{},[242,1809],{"width":244},[54,1811,56],{},[228,1813,230],{},[1802,1815,1816,1818],{},[54,1817,1782],{},[54,1819,940],{},[58,1821,1822],{"encoding":60},"P = \\sum D_i \\qquad \\text{Relative precision} = \\frac{e}{P} \\qquad N = \\frac{P}{e}",[35,1824,1826,1845,1916,2015],{"className":1825,"ariaHidden":65},[64],[35,1827,1829,1832,1836,1839,1842],{"className":1828},[69],[35,1830],{"className":1831,"style":74},[73],[35,1833,1782],{"className":1834,"style":1835},[78,79],"margin-right:0.1389em;",[35,1837],{"className":1838,"style":282},[242],[35,1840,230],{"className":1841},[286],[35,1843],{"className":1844,"style":282},[242],[35,1846,1848,1851,1854,1857,1898,1901,1907,1910,1913],{"className":1847},[69],[35,1849],{"className":1850,"style":410},[73],[35,1852,375],{"className":1853,"style":416},[306,414,415],[35,1855],{"className":1856,"style":302},[242],[35,1858,1860,1863],{"className":1859},[78],[35,1861,187],{"className":1862,"style":171},[78,79],[35,1864,1866],{"className":1865},[660],[35,1867,1869,1890],{"className":1868},[664,665],[35,1870,1872,1887],{"className":1871},[669],[35,1873,1876],{"className":1874,"style":1875},[673],"height:0.3117em;",[35,1877,1878,1881],{"style":1531},[35,1879],{"className":1880,"style":682},[681],[35,1882,1884],{"className":1883},[686,687,688,689],[35,1885,1793],{"className":1886},[78,79,689],[35,1888,704],{"className":1889},[703],[35,1891,1893],{"className":1892},[669],[35,1894,1896],{"className":1895,"style":711},[673],[35,1897],{},[35,1899],{"className":1900,"style":316},[242],[35,1902,1904],{"className":1903},[78,696],[35,1905,1798],{"className":1906},[78],[35,1908],{"className":1909,"style":282},[242],[35,1911,230],{"className":1912},[286],[35,1914],{"className":1915,"style":282},[242],[35,1917,1919,1923,2000,2003,2006,2009,2012],{"className":1918},[69],[35,1920],{"className":1921,"style":1922},[73],"height:1.0404em;vertical-align:-0.345em;",[35,1924,1926,1930,1997],{"className":1925},[78],[35,1927],{"className":1928},[1576,1929],"nulldelimiter",[35,1931,1933],{"className":1932},[1802],[35,1934,1936,1988],{"className":1935},[664,665],[35,1937,1939,1985],{"className":1938},[669],[35,1940,1943,1959,1970],{"className":1941,"style":1942},[673],"height:0.6954em;",[35,1944,1946,1950],{"style":1945},"top:-2.655em;",[35,1947],{"className":1948,"style":1949},[681],"height:3em;",[35,1951,1953],{"className":1952},[686,687,688,689],[35,1954,1956],{"className":1955},[78,689],[35,1957,1782],{"className":1958,"style":1835},[78,79,689],[35,1960,1962,1965],{"style":1961},"top:-3.23em;",[35,1963],{"className":1964,"style":1949},[681],[35,1966],{"className":1967,"style":1969},[1968],"frac-line","border-bottom-width:0.04em;",[35,1971,1973,1976],{"style":1972},"top:-3.394em;",[35,1974],{"className":1975,"style":1949},[681],[35,1977,1979],{"className":1978},[686,687,688,689],[35,1980,1982],{"className":1981},[78,689],[35,1983,940],{"className":1984},[78,79,689],[35,1986,704],{"className":1987},[703],[35,1989,1991],{"className":1990},[669],[35,1992,1995],{"className":1993,"style":1994},[673],"height:0.345em;",[35,1996],{},[35,1998],{"className":1999},[1667,1929],[35,2001],{"className":2002,"style":316},[242],[35,2004,56],{"className":2005,"style":80},[78,79],[35,2007],{"className":2008,"style":282},[242],[35,2010,230],{"className":2011},[286],[35,2013],{"className":2014,"style":282},[242],[35,2016,2018,2022],{"className":2017},[69],[35,2019],{"className":2020,"style":2021},[73],"height:1.2173em;vertical-align:-0.345em;",[35,2023,2025,2028,2088],{"className":2024},[78],[35,2026],{"className":2027},[1576,1929],[35,2029,2031],{"className":2030},[1802],[35,2032,2034,2080],{"className":2033},[664,665],[35,2035,2037,2077],{"className":2036},[669],[35,2038,2041,2055,2063],{"className":2039,"style":2040},[673],"height:0.8723em;",[35,2042,2043,2046],{"style":1945},[35,2044],{"className":2045,"style":1949},[681],[35,2047,2049],{"className":2048},[686,687,688,689],[35,2050,2052],{"className":2051},[78,689],[35,2053,940],{"className":2054},[78,79,689],[35,2056,2057,2060],{"style":1961},[35,2058],{"className":2059,"style":1949},[681],[35,2061],{"className":2062,"style":1969},[1968],[35,2064,2065,2068],{"style":1972},[35,2066],{"className":2067,"style":1949},[681],[35,2069,2071],{"className":2070},[686,687,688,689],[35,2072,2074],{"className":2073},[78,689],[35,2075,1782],{"className":2076,"style":1835},[78,79,689],[35,2078,704],{"className":2079},[703],[35,2081,2083],{"className":2082},[669],[35,2084,2086],{"className":2085,"style":1994},[673],[35,2087],{},[35,2089],{"className":2090},[1667,1929],[15,2092,2093,2094,2125,2126,2154],{},"Formatted as ",[107,2095,2096,2097],{},"1 : ",[35,2098,2100,2113],{"className":2099},[38],[35,2101,2103],{"className":2102},[42],[44,2104,2105],{"xmlns":46},[48,2106,2107,2111],{},[51,2108,2109],{},[54,2110,56],{},[58,2112,56],{"encoding":60},[35,2114,2116],{"className":2115,"ariaHidden":65},[64],[35,2117,2119,2122],{"className":2118},[69],[35,2120],{"className":2121,"style":74},[73],[35,2123,56],{"className":2124,"style":80},[78,79]," — one unit of error per ",[35,2127,2129,2142],{"className":2128},[38],[35,2130,2132],{"className":2131},[42],[44,2133,2134],{"xmlns":46},[48,2135,2136,2140],{},[51,2137,2138],{},[54,2139,56],{},[58,2141,56],{"encoding":60},[35,2143,2145],{"className":2144,"ariaHidden":65},[64],[35,2146,2148,2151],{"className":2147},[69],[35,2149],{"className":2150,"style":74},[73],[35,2152,56],{"className":2153,"style":80},[78,79]," units measured. Example: 1 : 10,000 means ~1 m error per 10 km surveyed.",[15,2156,2157,2158,2186],{},"Relative precision indicates observation consistency, not absolute positional accuracy at every point. High 1 : ",[35,2159,2161,2174],{"className":2160},[38],[35,2162,2164],{"className":2163},[42],[44,2165,2166],{"xmlns":46},[48,2167,2168,2172],{},[51,2169,2170],{},[54,2171,56],{},[58,2173,56],{"encoding":60},[35,2175,2177],{"className":2176,"ariaHidden":65},[64],[35,2178,2180,2183],{"className":2179},[69],[35,2181],{"className":2182,"style":74},[73],[35,2184,56],{"className":2185,"style":80},[78,79]," can still hide systematic orientation or scale errors (uncalibrated EDM, wrong starting azimuth).",[10,2188,2190],{"id":2189},"is-the-traverse-acceptable","Is the Traverse Acceptable?",[15,2192,2193],{},"Before adjustment, compare relative precision to project specifications. Adjusting a traverse that fails tolerance only spreads bad data through the network.",[2195,2196,2197,2213],"table",{},[2198,2199,2200],"thead",{},[2201,2202,2203,2207,2210],"tr",{},[2204,2205,2206],"th",{},"Survey order \u002F class",[2204,2208,2209],{},"Minimum relative precision",[2204,2211,2212],{},"Typical applications",[2214,2215,2216,2228,2239,2250,2261],"tbody",{},[2201,2217,2218,2222,2225],{},[2219,2220,2221],"td",{},"First-order",[2219,2223,2224],{},"1 : 100,000",[2219,2226,2227],{},"National geodetic control, deformation monitoring",[2201,2229,2230,2233,2236],{},[2219,2231,2232],{},"Second-order, Class I",[2219,2234,2235],{},"1 : 50,000",[2219,2237,2238],{},"Major infrastructure, municipal control",[2201,2240,2241,2244,2247],{},[2219,2242,2243],{},"Second-order, Class II",[2219,2245,2246],{},"1 : 20,000",[2219,2248,2249],{},"Engineering control, construction baselines",[2201,2251,2252,2255,2258],{},[2219,2253,2254],{},"Third-order, Class I",[2219,2256,2257],{},"1 : 10,000",[2219,2259,2260],{},"Local layout, suburban boundaries, topo control",[2201,2262,2263,2266,2269],{},[2219,2264,2265],{},"Third-order, Class II",[2219,2267,2268],{},"1 : 5,000",[2219,2270,2271],{},"Rural boundaries, preliminary route surveys",[15,2273,2274,2275,2278,2279,2308],{},"Closed loops also require ",[107,2276,2277],{},"angular closure",". For ",[35,2280,2282,2296],{"className":2281},[38],[35,2283,2285],{"className":2284},[42],[44,2286,2287],{"xmlns":46},[48,2288,2289,2294],{},[51,2290,2291],{},[54,2292,2293],{},"n",[58,2295,2293],{"encoding":60},[35,2297,2299],{"className":2298,"ariaHidden":65},[64],[35,2300,2302,2305],{"className":2301},[69],[35,2303],{"className":2304,"style":1250},[73],[35,2306,2293],{"className":2307},[78,79]," sides:",[15,2310,2311],{},[35,2312,2314,2350],{"className":2313},[38],[35,2315,2317],{"className":2316},[42],[44,2318,2319],{"xmlns":46},[48,2320,2321,2347],{},[51,2322,2323,2326,2328,2330,2332,2334,2336,2338,2341,2344],{},[574,2324,2325],{},"Theoretical sum",[228,2327,230],{},[228,2329,1478],{"stretchy":1477},[54,2331,2293],{},[228,2333,579],{},[383,2335,1226],{},[228,2337,1496],{"stretchy":1477},[228,2339,2340],{},"⋅",[383,2342,2343],{},"180",[54,2345,2346],{"mathvariant":222},"°",[58,2348,2349],{"encoding":60},"\\text{Theoretical sum} = (n - 2) \\cdot 180°",[35,2351,2353,2374,2395,2416],{"className":2352,"ariaHidden":65},[64],[35,2354,2356,2359,2365,2368,2371],{"className":2355},[69],[35,2357],{"className":2358,"style":167},[73],[35,2360,2362],{"className":2361},[78,696],[35,2363,2325],{"className":2364},[78],[35,2366],{"className":2367,"style":282},[242],[35,2369,230],{"className":2370},[286],[35,2372],{"className":2373,"style":282},[242],[35,2375,2377,2380,2383,2386,2389,2392],{"className":2376},[69],[35,2378],{"className":2379,"style":410},[73],[35,2381,1478],{"className":2382},[1576],[35,2384,2293],{"className":2385},[78,79],[35,2387],{"className":2388,"style":717},[242],[35,2390,579],{"className":2391},[721],[35,2393],{"className":2394,"style":717},[242],[35,2396,2398,2401,2404,2407,2410,2413],{"className":2397},[69],[35,2399],{"className":2400,"style":410},[73],[35,2402,1226],{"className":2403},[78],[35,2405,1496],{"className":2406},[1667],[35,2408],{"className":2409,"style":717},[242],[35,2411,2340],{"className":2412},[721],[35,2414],{"className":2415,"style":717},[242],[35,2417,2419,2422],{"className":2418},[69],[35,2420],{"className":2421,"style":167},[73],[35,2423,2425],{"className":2424},[78],"180°",[15,2427,2428,2429,2544,2545,2573],{},"Angular misclosure must not exceed ",[35,2430,2432,2456],{"className":2431},[38],[35,2433,2435],{"className":2434},[42],[44,2436,2437],{"xmlns":46},[48,2438,2439,2453],{},[51,2440,2441,2444,2446,2449],{},[54,2442,2443],{},"c",[228,2445,230],{},[54,2447,2448],{},"k",[1213,2450,2451],{},[54,2452,2293],{},[58,2454,2455],{"encoding":60},"c = k\\sqrt{n}",[35,2457,2459,2477],{"className":2458,"ariaHidden":65},[64],[35,2460,2462,2465,2468,2471,2474],{"className":2461},[69],[35,2463],{"className":2464,"style":1250},[73],[35,2466,2443],{"className":2467},[78,79],[35,2469],{"className":2470,"style":282},[242],[35,2472,230],{"className":2473},[286],[35,2475],{"className":2476,"style":282},[242],[35,2478,2480,2484,2488],{"className":2479},[69],[35,2481],{"className":2482,"style":2483},[73],"height:1.04em;vertical-align:-0.2397em;",[35,2485,2448],{"className":2486,"style":2487},[78,79],"margin-right:0.0315em;",[35,2489,2491],{"className":2490},[78,1273],[35,2492,2494,2535],{"className":2493},[664,665],[35,2495,2497,2532],{"className":2496},[669],[35,2498,2501,2515],{"className":2499,"style":2500},[673],"height:0.8003em;",[35,2502,2505,2508],{"className":2503,"style":2504},[1287],"top:-3em;",[35,2506],{"className":2507,"style":1949},[681],[35,2509,2512],{"className":2510,"style":2511},[78],"padding-left:0.833em;",[35,2513,2293],{"className":2514},[78,79],[35,2516,2518,2521],{"style":2517},"top:-2.7603em;",[35,2519],{"className":2520,"style":1949},[681],[35,2522,2525],{"className":2523,"style":2524},[1421],"min-width:0.853em;height:1.08em;",[1424,2526,2529],{"xmlns":1426,"width":1427,"height":2527,"viewBox":2528,"preserveAspectRatio":1430},"1.08em","0 0 400000 1080",[1432,2530],{"d":2531},"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",[35,2533,704],{"className":2534},[703],[35,2536,2538],{"className":2537},[669],[35,2539,2542],{"className":2540,"style":2541},[673],"height:0.2397em;",[35,2543],{}," ( ",[35,2546,2548,2561],{"className":2547},[38],[35,2549,2551],{"className":2550},[42],[44,2552,2553],{"xmlns":46},[48,2554,2555,2559],{},[51,2556,2557],{},[54,2558,2448],{},[58,2560,2448],{"encoding":60},[35,2562,2564],{"className":2563,"ariaHidden":65},[64],[35,2565,2567,2570],{"className":2566},[69],[35,2568],{"className":2569,"style":167},[73],[35,2571,2448],{"className":2572,"style":2487},[78,79]," in seconds, instrument-dependent). Balance within tolerance before computing preliminary azimuths; reject and re-observe if over limit.",[10,2575,2577],{"id":2576},"why-adjustment-is-mathematically-necessary","Why Adjustment is Mathematically Necessary",[15,2579,2580],{},"Even at 1 : 25,000, unadjusted coordinates are inconsistent — the closing station gets two positions. That causes CAD\u002FGIS gaps, stakeout disagreements between legs, and boundary geometry that does not close legally.",[15,2582,2583],{},"Adjustment distributes random error across legs so one consistent coordinate set exists per station. Systematic errors should be removed by calibration and field procedure first.",[10,2585,2587],{"id":2586},"bowditch-compass-rule-adjustment","Bowditch (Compass Rule) Adjustment",[15,2589,27,2590,2593,2594,2597,2598,2601],{},[107,2591,2592],{},"Bowditch"," or ",[107,2595,2596],{},"compass rule"," (Bowditch \u002F Adrain, c. 1808) suits traverses where angles and distances have comparable relative precision. Corrections to each leg are ",[107,2599,2600],{},"proportional to leg length"," relative to total perimeter.",[15,2603,2604,2605,2634,2635,2705,2706,114],{},"For leg ",[35,2606,2608,2621],{"className":2607},[38],[35,2609,2611],{"className":2610},[42],[44,2612,2613],{"xmlns":46},[48,2614,2615,2619],{},[51,2616,2617],{},[54,2618,1793],{},[58,2620,1793],{"encoding":60},[35,2622,2624],{"className":2623,"ariaHidden":65},[64],[35,2625,2627,2631],{"className":2626},[69],[35,2628],{"className":2629,"style":2630},[73],"height:0.6595em;",[35,2632,1793],{"className":2633},[78,79]," with distance ",[35,2636,2638,2656],{"className":2637},[38],[35,2639,2641],{"className":2640},[42],[44,2642,2643],{"xmlns":46},[48,2644,2645,2653],{},[51,2646,2647],{},[569,2648,2649,2651],{},[54,2650,187],{},[54,2652,1793],{},[58,2654,2655],{"encoding":60},"D_i",[35,2657,2659],{"className":2658,"ariaHidden":65},[64],[35,2660,2662,2665],{"className":2661},[69],[35,2663],{"className":2664,"style":650},[73],[35,2666,2668,2671],{"className":2667},[78],[35,2669,187],{"className":2670,"style":171},[78,79],[35,2672,2674],{"className":2673},[660],[35,2675,2677,2697],{"className":2676},[664,665],[35,2678,2680,2694],{"className":2679},[669],[35,2681,2683],{"className":2682,"style":1875},[673],[35,2684,2685,2688],{"style":1531},[35,2686],{"className":2687,"style":682},[681],[35,2689,2691],{"className":2690},[686,687,688,689],[35,2692,1793],{"className":2693},[78,79,689],[35,2695,704],{"className":2696},[703],[35,2698,2700],{"className":2699},[669],[35,2701,2703],{"className":2702,"style":711},[673],[35,2704],{}," and perimeter ",[35,2707,2709,2722],{"className":2708},[38],[35,2710,2712],{"className":2711},[42],[44,2713,2714],{"xmlns":46},[48,2715,2716,2720],{},[51,2717,2718],{},[54,2719,1782],{},[58,2721,1782],{"encoding":60},[35,2723,2725],{"className":2724,"ariaHidden":65},[64],[35,2726,2728,2731],{"className":2727},[69],[35,2729],{"className":2730,"style":74},[73],[35,2732,1782],{"className":2733,"style":1835},[78,79],[15,2735,2736],{},[35,2737,2739,2822],{"className":2738},[38],[35,2740,2742],{"className":2741},[42],[44,2743,2744],{"xmlns":46},[48,2745,2746,2819],{},[51,2747,2748,2761,2763,2765,2771,2773,2783,2785,2797,2799,2801,2807,2809],{},[569,2749,2750,2753],{},[54,2751,2752],{},"C",[51,2754,2755,2757,2759],{},[54,2756,226],{},[228,2758,1487],{"separator":65},[54,2760,1793],{},[228,2762,230],{},[228,2764,579],{},[569,2766,2767,2769],{},[54,2768,940],{},[54,2770,226],{},[228,2772,2340],{},[1802,2774,2775,2781],{},[569,2776,2777,2779],{},[54,2778,187],{},[54,2780,1793],{},[54,2782,1782],{},[242,2784],{"width":244},[569,2786,2787,2789],{},[54,2788,2752],{},[51,2790,2791,2793,2795],{},[54,2792,56],{},[228,2794,1487],{"separator":65},[54,2796,1793],{},[228,2798,230],{},[228,2800,579],{},[569,2802,2803,2805],{},[54,2804,940],{},[54,2806,56],{},[228,2808,2340],{},[1802,2810,2811,2817],{},[569,2812,2813,2815],{},[54,2814,187],{},[54,2816,1793],{},[54,2818,1782],{},[58,2820,2821],{"encoding":60},"C_{E,i} = -e_E \\cdot \\frac{D_i}{P} \\qquad C_{N,i} = -e_N \\cdot 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components:",[15,3306,3307],{},[35,3308,3310,3414],{"className":3309},[38],[35,3311,3313],{"className":3312},[42],[44,3314,3315],{"xmlns":46},[48,3316,3317,3411],{},[51,3318,3319,3321,3334,3336,3338,3351,3353,3365,3367,3369,3381,3383,3385,3397,3399],{},[54,3320,223],{"mathvariant":222},[569,3322,3323,3325],{},[54,3324,226],{},[51,3326,3327,3329,3331],{},[54,3328,1793],{},[228,3330,1487],{"separator":65},[574,3332,3333],{},"adj",[228,3335,230],{},[54,3337,223],{"mathvariant":222},[569,3339,3340,3342],{},[54,3341,226],{},[51,3343,3344,3346,3348],{},[54,3345,1793],{},[228,3347,1487],{"separator":65},[574,3349,3350],{},"raw",[228,3352,1229],{},[569,3354,3355,3357],{},[54,3356,2752],{},[51,3358,3359,3361,3363],{},[54,3360,226],{},[228,3362,1487],{"separator":65},[54,3364,1793],{},[242,3366],{"width":244},[54,3368,223],{"mathvariant":222},[569,3370,3371,3373],{},[54,3372,56],{},[51,3374,3375,3377,3379],{},[54,3376,1793],{},[228,3378,1487],{"separator":65},[574,3380,3333],{},[228,3382,230],{},[54,3384,223],{"mathvariant":222},[569,3386,3387,3389],{},[54,3388,56],{},[51,3390,3391,3393,3395],{},[54,3392,1793],{},[228,3394,1487],{"separator":65},[574,3396,3350],{},[228,3398,1229],{},[569,3400,3401,3403],{},[54,3402,2752],{},[51,3404,3405,3407,3409],{},[54,3406,56],{},[228,3408,1487],{"separator":65},[54,3410,1793],{},[58,3412,3413],{"encoding":60},"\\Delta E_{i,\\text{adj}} = \\Delta E_{i,\\text{raw}} + C_{E,i} \\qquad \\Delta N_{i,\\text{adj}} = \\Delta N_{i,\\text{raw}} + C_{N,i}",[35,3415,3417,3487,3557,3679,3749],{"className":3416,"ariaHidden":65},[64],[35,3418,3420,3423,3426,3478,3481,3484],{"className":3419},[69],[35,3421],{"className":3422,"style":2831},[73],[35,3424,223],{"className":3425},[78],[35,3427,3429,3432],{"className":3428},[78],[35,3430,226],{"className":3431,"style":278},[78,79],[35,3433,3435],{"className":3434},[660],[35,3436,3438,3470],{"className":3437},[664,665],[35,3439,3441,3467],{"className":3440},[669],[35,3442,3444],{"className":3443,"style":674},[673],[35,3445,3446,3449],{"style":677},[35,3447],{"className":3448,"style":682},[681],[35,3450,3452],{"className":3451},[686,687,688,689],[35,3453,3455,3458,3461],{"className":3454},[78,689],[35,3456,1793],{"className":3457},[78,79,689],[35,3459,1487],{"className":3460},[1620,689],[35,3462,3464],{"className":3463},[78,696,689],[35,3465,3333],{"className":3466},[78,689],[35,3468,704],{"className":3469},[703],[35,3471,3473],{"className":3472},[669],[35,3474,3476],{"className":3475,"style":2881},[673],[35,3477],{},[35,3479],{"className":3480,"style":282},[242],[35,3482,230],{"className":3483},[286],[35,3485],{"className":3486,"style":282},[242],[35,3488,3490,3493,3496,3548,3551,3554],{"className":3489},[69],[35,3491],{"className":3492,"style":2831},[73],[35,3494,223],{"className":3495},[78],[35,3497,3499,3502],{"className":3498},[78],[35,3500,226],{"className":3501,"style":278},[78,79],[35,3503,3505],{"className":3504},[660],[35,3506,3508,3540],{"className":3507},[664,665],[35,3509,3511,3537],{"className":3510},[669],[35,3512,3514],{"className":3513,"style":1875},[673],[35,3515,3516,3519],{"style":677},[35,3517],{"className":3518,"style":682},[681],[35,3520,3522],{"className":3521},[686,687,688,689],[35,3523,3525,3528,3531],{"className":3524},[78,689],[35,3526,1793],{"className":3527},[78,79,689],[35,3529,1487],{"className":3530},[1620,689],[35,3532,3534],{"className":3533},[78,696,689],[35,3535,3350],{"className":3536},[78,689],[35,3538,704],{"className":3539},[703],[35,3541,3543],{"className":3542},[669],[35,3544,3546],{"className":3545,"style":2881},[673],[35,3547],{},[35,3549],{"className":3550,"style":717},[242],[35,3552,1229],{"className":3553},[721],[35,3555],{"className":3556,"style":717},[242],[35,3558,3560,3563,3612,3615,3618,3670,3673,3676],{"className":3559},[69],[35,3561],{"className":3562,"style":2831},[73],[35,3564,3566,3569],{"className":3565},[78],[35,3567,2752],{"className":3568,"style":2838},[78,79],[35,3570,3572],{"className":3571},[660],[35,3573,3575,3604],{"className":3574},[664,665],[35,3576,3578,3601],{"className":3577},[669],[35,3579,3581],{"className":3580,"style":1015},[673],[35,3582,3583,3586],{"style":2853},[35,3584],{"className":3585,"style":682},[681],[35,3587,3589],{"className":3588},[686,687,688,689],[35,3590,3592,3595,3598],{"className":3591},[78,689],[35,3593,226],{"className":3594,"style":278},[78,79,689],[35,3596,1487],{"className":3597},[1620,689],[35,3599,1793],{"className":3600},[78,79,689],[35,3602,704],{"className":3603},[703],[35,3605,3607],{"className":3606},[669],[35,3608,3610],{"className":3609,"style":2881},[673],[35,3611],{},[35,3613],{"className":3614,"style":316},[242],[35,3616,223],{"className":3617},[78],[35,3619,3621,3624],{"className":3620},[78],[35,3622,56],{"className":3623,"style":80},[78,79],[35,3625,3627],{"className":3626},[660],[35,3628,3630,3662],{"className":3629},[664,665],[35,3631,3633,3659],{"className":3632},[669],[35,3634,3636],{"className":3635,"style":674},[673],[35,3637,3638,3641],{"style":831},[35,3639],{"className":3640,"style":682},[681],[35,3642,3644],{"className":3643},[686,687,688,689],[35,3645,3647,3650,3653],{"className":3646},[78,689],[35,3648,1793],{"className":3649},[78,79,689],[35,3651,1487],{"className":3652},[1620,689],[35,3654,3656],{"className":3655},[78,696,689],[35,3657,3333],{"className":3658},[78,689],[35,3660,704],{"className":3661},[703],[35,3663,3665],{"className":3664},[669],[35,3666,3668],{"className":3667,"style":2881},[673],[35,3669],{},[35,3671],{"className":3672,"style":282},[242],[35,3674,230],{"className":3675},[286],[35,3677],{"className":3678,"style":282},[242],[35,3680,3682,3685,3688,3740,3743,3746],{"className":3681},[69],[35,3683],{"className":3684,"style":2831},[73],[35,3686,223],{"className":3687},[78],[35,3689,3691,3694],{"className":3690},[78],[35,3692,56],{"className":3693,"style":80},[78,79],[35,3695,3697],{"className":3696},[660],[35,3698,3700,3732],{"className":3699},[664,665],[35,3701,3703,3729],{"className":3702},[669],[35,3704,3706],{"className":3705,"style":1875},[673],[35,3707,3708,3711],{"style":831},[35,3709],{"className":3710,"style":682},[681],[35,3712,3714],{"className":3713},[686,687,688,689],[35,3715,3717,3720,3723],{"className":3716},[78,689],[35,3718,1793],{"className":3719},[78,79,689],[35,3721,1487],{"className":3722},[1620,689],[35,3724,3726],{"className":3725},[78,696,689],[35,3727,3350],{"className":3728},[78,689],[35,3730,704],{"className":3731},[703],[35,3733,3735],{"className":3734},[669],[35,3736,3738],{"className":3737,"style":2881},[673],[35,3739],{},[35,3741],{"className":3742,"style":717},[242],[35,3744,1229],{"className":3745},[721],[35,3747],{"className":3748,"style":717},[242],[35,3750,3752,3755],{"className":3751},[69],[35,3753],{"className":3754,"style":2831},[73],[35,3756,3758,3761],{"className":3757},[78],[35,3759,2752],{"className":3760,"style":2838},[78,79],[35,3762,3764],{"className":3763},[660],[35,3765,3767,3796],{"className":3766},[664,665],[35,3768,3770,3793],{"className":3769},[669],[35,3771,3773],{"className":3772,"style":1015},[673],[35,3774,3775,3778],{"style":2853},[35,3776],{"className":3777,"style":682},[681],[35,3779,3781],{"className":3780},[686,687,688,689],[35,3782,3784,3787,3790],{"className":3783},[78,689],[35,3785,56],{"className":3786,"style":80},[78,79,689],[35,3788,1487],{"className":3789},[1620,689],[35,3791,1793],{"className":3792},[78,79,689],[35,3794,704],{"className":3795},[703],[35,3797,3799],{"className":3798},[669],[35,3800,3802],{"className":3801,"style":2881},[673],[35,3803],{},[15,3805,3806,3807,3909,3910,4011],{},"Then ",[35,3808,3810,3838],{"className":3809},[38],[35,3811,3813],{"className":3812},[42],[44,3814,3815],{"xmlns":46},[48,3816,3817,3835],{},[51,3818,3819,3821,3823],{},[228,3820,375],{},[54,3822,223],{"mathvariant":222},[569,3824,3825,3827],{},[54,3826,226],{},[51,3828,3829,3831,3833],{},[54,3830,1793],{},[228,3832,1487],{"separator":65},[574,3834,3333],{},[58,3836,3837],{"encoding":60},"\\sum \\Delta E_{i,\\text{adj}}",[35,3839,3841],{"className":3840,"ariaHidden":65},[64],[35,3842,3844,3848,3851,3854,3857],{"className":3843},[69],[35,3845],{"className":3846,"style":3847},[73],"height:1.0361em;vertical-align:-0.2861em;",[35,3849,375],{"className":3850,"style":416},[306,414,415],[35,3852],{"className":3853,"style":302},[242],[35,3855,223],{"className":3856},[78],[35,3858,3860,3863],{"className":3859},[78],[35,3861,226],{"className":3862,"style":278},[78,79],[35,3864,3866],{"className":3865},[660],[35,3867,3869,3901],{"className":3868},[664,665],[35,3870,3872,3898],{"className":3871},[669],[35,3873,3875],{"className":3874,"style":674},[673],[35,3876,3877,3880],{"style":677},[35,3878],{"className":3879,"style":682},[681],[35,3881,3883],{"className":3882},[686,687,688,689],[35,3884,3886,3889,3892],{"className":3885},[78,689],[35,3887,1793],{"className":3888},[78,79,689],[35,3890,1487],{"className":3891},[1620,689],[35,3893,3895],{"className":3894},[78,696,689],[35,3896,3333],{"className":3897},[78,689],[35,3899,704],{"className":3900},[703],[35,3902,3904],{"className":3903},[669],[35,3905,3907],{"className":3906,"style":2881},[673],[35,3908],{}," and ",[35,3911,3913,3941],{"className":3912},[38],[35,3914,3916],{"className":3915},[42],[44,3917,3918],{"xmlns":46},[48,3919,3920,3938],{},[51,3921,3922,3924,3926],{},[228,3923,375],{},[54,3925,223],{"mathvariant":222},[569,3927,3928,3930],{},[54,3929,56],{},[51,3931,3932,3934,3936],{},[54,3933,1793],{},[228,3935,1487],{"separator":65},[574,3937,3333],{},[58,3939,3940],{"encoding":60},"\\sum \\Delta N_{i,\\text{adj}}",[35,3942,3944],{"className":3943,"ariaHidden":65},[64],[35,3945,3947,3950,3953,3956,3959],{"className":3946},[69],[35,3948],{"className":3949,"style":3847},[73],[35,3951,375],{"className":3952,"style":416},[306,414,415],[35,3954],{"className":3955,"style":302},[242],[35,3957,223],{"className":3958},[78],[35,3960,3962,3965],{"className":3961},[78],[35,3963,56],{"className":3964,"style":80},[78,79],[35,3966,3968],{"className":3967},[660],[35,3969,3971,4003],{"className":3970},[664,665],[35,3972,3974,4000],{"className":3973},[669],[35,3975,3977],{"className":3976,"style":674},[673],[35,3978,3979,3982],{"style":831},[35,3980],{"className":3981,"style":682},[681],[35,3983,3985],{"className":3984},[686,687,688,689],[35,3986,3988,3991,3994],{"className":3987},[78,689],[35,3989,1793],{"className":3990},[78,79,689],[35,3992,1487],{"className":3993},[1620,689],[35,3995,3997],{"className":3996},[78,696,689],[35,3998,3333],{"className":3999},[78,689],[35,4001,704],{"className":4002},[703],[35,4004,4006],{"className":4005},[669],[35,4007,4009],{"className":4008,"style":2881},[673],[35,4010],{}," match targets. Progressive coordinates:",[15,4013,4014],{},[35,4015,4017,4104],{"className":4016},[38],[35,4018,4020],{"className":4019},[42],[44,4021,4022],{"xmlns":46},[48,4023,4024,4101],{},[51,4025,4026,4039,4041,4047,4049,4051,4063,4065,4077,4079,4085,4087,4089],{},[569,4027,4028,4030],{},[54,4029,226],{},[51,4031,4032,4034,4036],{},[54,4033,1793],{},[228,4035,1229],{},[383,4037,4038],{},"1",[228,4040,230],{},[569,4042,4043,4045],{},[54,4044,226],{},[54,4046,1793],{},[228,4048,1229],{},[54,4050,223],{"mathvariant":222},[569,4052,4053,4055],{},[54,4054,226],{},[51,4056,4057,4059,4061],{},[54,4058,1793],{},[228,4060,1487],{"separator":65},[574,4062,3333],{},[242,4064],{"width":244},[569,4066,4067,4069],{},[54,4068,56],{},[51,4070,4071,4073,4075],{},[54,4072,1793],{},[228,4074,1229],{},[383,4076,4038],{},[228,4078,230],{},[569,4080,4081,4083],{},[54,4082,56],{},[54,4084,1793],{},[228,4086,1229],{},[54,4088,223],{"mathvariant":222},[569,4090,4091,4093],{},[54,4092,56],{},[51,4094,4095,4097,4099],{},[54,4096,1793],{},[228,4098,1487],{"separator":65},[574,4100,3333],{},[58,4102,4103],{"encoding":60},"E_{i+1} = E_i + \\Delta E_{i,\\text{adj}} \\qquad N_{i+1} = N_i + \\Delta N_{i,\\text{adj}}",[35,4105,4107,4173,4228,4350,4405],{"className":4106,"ariaHidden":65},[64],[35,4108,4110,4114,4164,4167,4170],{"className":4109},[69],[35,4111],{"className":4112,"style":4113},[73],"height:0.8917em;vertical-align:-0.2083em;",[35,4115,4117,4120],{"className":4116},[78],[35,4118,226],{"className":4119,"style":278},[78,79],[35,4121,4123],{"className":4122},[660],[35,4124,4126,4155],{"className":4125},[664,665],[35,4127,4129,4152],{"className":4128},[669],[35,4130,4132],{"className":4131,"style":1875},[673],[35,4133,4134,4137],{"style":677},[35,4135],{"className":4136,"style":682},[681],[35,4138,4140],{"className":4139},[686,687,688,689],[35,4141,4143,4146,4149],{"className":4142},[78,689],[35,4144,1793],{"className":4145},[78,79,689],[35,4147,1229],{"className":4148},[721,689],[35,4150,4038],{"className":4151},[78,689],[35,4153,704],{"className":4154},[703],[35,4156,4158],{"className":4157},[669],[35,4159,4162],{"className":4160,"style":4161},[673],"height:0.2083em;",[35,4163],{},[35,4165],{"className":4166,"style":282},[242],[35,4168,230],{"className":4169},[286],[35,4171],{"className":4172,"style":282},[242],[35,4174,4176,4179,4219,4222,4225],{"className":4175},[69],[35,4177],{"className":4178,"style":650},[73],[35,4180,4182,4185],{"className":4181},[78],[35,4183,226],{"className":4184,"style":278},[78,79],[35,4186,4188],{"className":4187},[660],[35,4189,4191,4211],{"className":4190},[664,665],[35,4192,4194,4208],{"className":4193},[669],[35,4195,4197],{"className":4196,"style":1875},[673],[35,4198,4199,4202],{"style":677},[35,4200],{"className":4201,"style":682},[681],[35,4203,4205],{"className":4204},[686,687,688,689],[35,4206,1793],{"className":4207},[78,79,689],[35,4209,704],{"className":4210},[703],[35,4212,4214],{"className":4213},[669],[35,4215,4217],{"className":4216,"style":711},[673],[35,4218],{},[35,4220],{"className":4221,"style":717},[242],[35,4223,1229],{"className":4224},[721],[35,4226],{"className":4227,"style":717},[242],[35,4229,4231,4234,4237,4289,4292,4341,4344,4347],{"className":4230},[69],[35,4232],{"className":4233,"style":2831},[73],[35,4235,223],{"className":4236},[78],[35,4238,4240,4243],{"className":4239},[78],[35,4241,226],{"className":4242,"style":278},[78,79],[35,4244,4246],{"className":4245},[660],[35,4247,4249,4281],{"className":4248},[664,665],[35,4250,4252,4278],{"className":4251},[669],[35,4253,4255],{"className":4254,"style":674},[673],[35,4256,4257,4260],{"style":677},[35,4258],{"className":4259,"style":682},[681],[35,4261,4263],{"className":4262},[686,687,688,689],[35,4264,4266,4269,4272],{"className":4265},[78,689],[35,4267,1793],{"className":4268},[78,79,689],[35,4270,1487],{"className":4271},[1620,689],[35,4273,4275],{"className":4274},[78,696,689],[35,4276,3333],{"className":4277},[78,689],[35,4279,704],{"className":4280},[703],[35,4282,4284],{"className":4283},[669],[35,4285,4287],{"className":4286,"style":2881},[673],[35,4288],{},[35,4290],{"className":4291,"style":316},[242],[35,4293,4295,4298],{"className":4294},[78],[35,4296,56],{"className":4297,"style":80},[78,79],[35,4299,4301],{"className":4300},[660],[35,4302,4304,4333],{"className":4303},[664,665],[35,4305,4307,4330],{"className":4306},[669],[35,4308,4310],{"className":4309,"style":1875},[673],[35,4311,4312,4315],{"style":831},[35,4313],{"className":4314,"style":682},[681],[35,4316,4318],{"className":4317},[686,687,688,689],[35,4319,4321,4324,4327],{"className":4320},[78,689],[35,4322,1793],{"className":4323},[78,79,689],[35,4325,1229],{"className":4326},[721,689],[35,4328,4038],{"className":4329},[78,689],[35,4331,704],{"className":4332},[703],[35,4334,4336],{"className":4335},[669],[35,4337,4339],{"className":4338,"style":4161},[673],[35,4340],{},[35,4342],{"className":4343,"style":282},[242],[35,4345,230],{"className":4346},[286],[35,4348],{"className":4349,"style":282},[242],[35,4351,4353,4356,4396,4399,4402],{"className":4352},[69],[35,4354],{"className":4355,"style":650},[73],[35,4357,4359,4362],{"className":4358},[78],[35,4360,56],{"className":4361,"style":80},[78,79],[35,4363,4365],{"className":4364},[660],[35,4366,4368,4388],{"className":4367},[664,665],[35,4369,4371,4385],{"className":4370},[669],[35,4372,4374],{"className":4373,"style":1875},[673],[35,4375,4376,4379],{"style":831},[35,4377],{"className":4378,"style":682},[681],[35,4380,4382],{"className":4381},[686,687,688,689],[35,4383,1793],{"className":4384},[78,79,689],[35,4386,704],{"className":4387},[703],[35,4389,4391],{"className":4390},[669],[35,4392,4394],{"className":4393,"style":711},[673],[35,4395],{},[35,4397],{"className":4398,"style":717},[242],[35,4400,1229],{"className":4401},[721],[35,4403],{"className":4404,"style":717},[242],[35,4406,4408,4411,4414],{"className":4407},[69],[35,4409],{"className":4410,"style":2831},[73],[35,4412,223],{"className":4413},[78],[35,4415,4417,4420],{"className":4416},[78],[35,4418,56],{"className":4419,"style":80},[78,79],[35,4421,4423],{"className":4422},[660],[35,4424,4426,4458],{"className":4425},[664,665],[35,4427,4429,4455],{"className":4428},[669],[35,4430,4432],{"className":4431,"style":674},[673],[35,4433,4434,4437],{"style":831},[35,4435],{"className":4436,"style":682},[681],[35,4438,4440],{"className":4439},[686,687,688,689],[35,4441,4443,4446,4449],{"className":4442},[78,689],[35,4444,1793],{"className":4445},[78,79,689],[35,4447,1487],{"className":4448},[1620,689],[35,4450,4452],{"className":4451},[78,696,689],[35,4453,3333],{"className":4454},[78,689],[35,4456,704],{"className":4457},[703],[35,4459,4461],{"className":4460},[669],[35,4462,4464],{"className":4463,"style":2881},[673],[35,4465],{},[15,4467,4468],{},"Back-calculate adjusted distance and azimuth:",[15,4470,4471],{},[35,4472,4474,4538],{"className":4473},[38],[35,4475,4477],{"className":4476},[42],[44,4478,4479],{"xmlns":46},[48,4480,4481,4535],{},[51,4482,4483,4495,4497],{},[569,4484,4485,4487],{},[54,4486,187],{},[51,4488,4489,4491,4493],{},[54,4490,1793],{},[228,4492,1487],{"separator":65},[574,4494,3333],{},[228,4496,230],{},[1213,4498,4499],{},[51,4500,4501,4503,4517,4519,4521],{},[54,4502,223],{"mathvariant":222},[1218,4504,4505,4507,4515],{},[54,4506,226],{},[51,4508,4509,4511,4513],{},[54,4510,1793],{},[228,4512,1487],{"separator":65},[574,4514,3333],{},[383,4516,1226],{},[228,4518,1229],{},[54,4520,223],{"mathvariant":222},[1218,4522,4523,4525,4533],{},[54,4524,56],{},[51,4526,4527,4529,4531],{},[54,4528,1793],{},[228,4530,1487],{"separator":65},[574,4532,3333],{},[383,4534,1226],{},[58,4536,4537],{"encoding":60},"D_{i,\\text{adj}} = \\sqrt{\\Delta E_{i,\\text{adj}}^2 + \\Delta N_{i,\\text{adj}}^2}",[35,4539,4541,4608],{"className":4540,"ariaHidden":65},[64],[35,4542,4544,4547,4599,4602,4605],{"className":4543},[69],[35,4545],{"className":4546,"style":2831},[73],[35,4548,4550,4553],{"className":4549},[78],[35,4551,187],{"className":4552,"style":171},[78,79],[35,4554,4556],{"className":4555},[660],[35,4557,4559,4591],{"className":4558},[664,665],[35,4560,4562,4588],{"className":4561},[669],[35,4563,4565],{"className":4564,"style":674},[673],[35,4566,4567,4570],{"style":1531},[35,4568],{"className":4569,"style":682},[681],[35,4571,4573],{"className":4572},[686,687,688,689],[35,4574,4576,4579,4582],{"className":4575},[78,689],[35,4577,1793],{"className":4578},[78,79,689],[35,4580,1487],{"className":4581},[1620,689],[35,4583,4585],{"className":4584},[78,696,689],[35,4586,3333],{"className":4587},[78,689],[35,4589,704],{"className":4590},[703],[35,4592,4594],{"className":4593},[669],[35,4595,4597],{"className":4596,"style":2881},[673],[35,4598],{},[35,4600],{"className":4601,"style":282},[242],[35,4603,230],{"className":4604},[286],[35,4606],{"className":4607,"style":282},[242],[35,4609,4611,4615],{"className":4610},[69],[35,4612],{"className":4613,"style":4614},[73],"height:1.84em;vertical-align:-0.6758em;",[35,4616,4618],{"className":4617},[78,1273],[35,4619,4621,4803],{"className":4620},[664,665],[35,4622,4624,4800],{"className":4623},[669],[35,4625,4628,4783],{"className":4626,"style":4627},[673],"height:1.1642em;",[35,4629,4632,4636],{"className":4630,"style":4631},[1287],"top:-3.8em;",[35,4633],{"className":4634,"style":4635},[681],"height:3.8em;",[35,4637,4639,4642,4707,4710,4713,4716,4719],{"className":4638,"style":1296},[78],[35,4640,223],{"className":4641},[78],[35,4643,4645,4648],{"className":4644},[78],[35,4646,226],{"className":4647,"style":278},[78,79],[35,4649,4651],{"className":4650},[660],[35,4652,4654,4698],{"className":4653},[664,665],[35,4655,4657,4695],{"className":4656},[669],[35,4658,4660,4684],{"className":4659,"style":1315},[673],[35,4661,4663,4666],{"style":4662},"top:-2.3987em;margin-left:-0.0576em;margin-right:0.05em;",[35,4664],{"className":4665,"style":682},[681],[35,4667,4669],{"className":4668},[686,687,688,689],[35,4670,4672,4675,4678],{"className":4671},[78,689],[35,4673,1793],{"className":4674},[78,79,689],[35,4676,1487],{"className":4677},[1620,689],[35,4679,4681],{"className":4680},[78,696,689],[35,4682,3333],{"className":4683},[78,689],[35,4685,4686,4689],{"style":1330},[35,4687],{"className":4688,"style":682},[681],[35,4690,4692],{"className":4691},[686,687,688,689],[35,4693,1226],{"className":4694},[78,689],[35,4696,704],{"className":4697},[703],[35,4699,4701],{"className":4700},[669],[35,4702,4705],{"className":4703,"style":4704},[673],"height:0.4374em;",[35,4706],{},[35,4708],{"className":4709,"style":717},[242],[35,4711,1229],{"className":4712},[721],[35,4714],{"className":4715,"style":717},[242],[35,4717,223],{"className":4718},[78],[35,4720,4722,4725],{"className":4721},[78],[35,4723,56],{"className":4724,"style":80},[78,79],[35,4726,4728],{"className":4727},[660],[35,4729,4731,4775],{"className":4730},[664,665],[35,4732,4734,4772],{"className":4733},[669],[35,4735,4737,4761],{"className":4736,"style":1315},[673],[35,4738,4740,4743],{"style":4739},"top:-2.3987em;margin-left:-0.109em;margin-right:0.05em;",[35,4741],{"className":4742,"style":682},[681],[35,4744,4746],{"className":4745},[686,687,688,689],[35,4747,4749,4752,4755],{"className":4748},[78,689],[35,4750,1793],{"className":4751},[78,79,689],[35,4753,1487],{"className":4754},[1620,689],[35,4756,4758],{"className":4757},[78,696,689],[35,4759,3333],{"className":4760},[78,689],[35,4762,4763,4766],{"style":1330},[35,4764],{"className":4765,"style":682},[681],[35,4767,4769],{"className":4768},[686,687,688,689],[35,4770,1226],{"className":4771},[78,689],[35,4773,704],{"className":4774},[703],[35,4776,4778],{"className":4777},[669],[35,4779,4781],{"className":4780,"style":4704},[673],[35,4782],{},[35,4784,4786,4789],{"style":4785},"top:-3.1242em;",[35,4787],{"className":4788,"style":4635},[681],[35,4790,4793],{"className":4791,"style":4792},[1421],"min-width:1.02em;height:1.88em;",[1424,4794,4797],{"xmlns":1426,"width":1427,"height":4795,"viewBox":4796,"preserveAspectRatio":1430},"1.88em","0 0 400000 1944",[1432,4798],{"d":4799},"M983 90\nl0 -0\nc4,-6.7,10,-10,18,-10 H400000v40\nH1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7\ns-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744\nc-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30\nc26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722\nc56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5\nc53.7,-170.3,84.5,-266.8,92.5,-289.5z\nM1001 80h400000v40h-400000z",[35,4801,704],{"className":4802},[703],[35,4804,4806],{"className":4805},[669],[35,4807,4810],{"className":4808,"style":4809},[673],"height:0.6758em;",[35,4811],{},[15,4813,4814],{},[35,4815,4817,4879],{"className":4816},[38],[35,4818,4820],{"className":4819},[42],[44,4821,4822],{"xmlns":46},[48,4823,4824,4876],{},[51,4825,4826,4838,4840,4842,4844,4846,4858,4860,4862,4874],{},[569,4827,4828,4830],{},[54,4829,154],{},[51,4831,4832,4834,4836],{},[54,4833,1793],{},[228,4835,1487],{"separator":65},[574,4837,3333],{},[228,4839,230],{},[574,4841,1474],{},[228,4843,1478],{"stretchy":1477},[54,4845,223],{"mathvariant":222},[569,4847,4848,4850],{},[54,4849,226],{},[51,4851,4852,4854,4856],{},[54,4853,1793],{},[228,4855,1487],{"separator":65},[574,4857,3333],{},[228,4859,1487],{"separator":65},[54,4861,223],{"mathvariant":222},[569,4863,4864,4866],{},[54,4865,56],{},[51,4867,4868,4870,4872],{},[54,4869,1793],{},[228,4871,1487],{"separator":65},[574,4873,3333],{},[228,4875,1496],{"stretchy":1477},[58,4877,4878],{"encoding":60},"\\theta_{i,\\text{adj}} = \\text{atan2}(\\Delta E_{i,\\text{adj}}, \\Delta N_{i,\\text{adj}})",[35,4880,4882,4950],{"className":4881,"ariaHidden":65},[64],[35,4883,4885,4889,4941,4944,4947],{"className":4884},[69],[35,4886],{"className":4887,"style":4888},[73],"height:0.9805em;vertical-align:-0.2861em;",[35,4890,4892,4895],{"className":4891},[78],[35,4893,154],{"className":4894,"style":171},[78,79],[35,4896,4898],{"className":4897},[660],[35,4899,4901,4933],{"className":4900},[664,665],[35,4902,4904,4930],{"className":4903},[669],[35,4905,4907],{"className":4906,"style":674},[673],[35,4908,4909,4912],{"style":1531},[35,4910],{"className":4911,"style":682},[681],[35,4913,4915],{"className":4914},[686,687,688,689],[35,4916,4918,4921,4924],{"className":4917},[78,689],[35,4919,1793],{"className":4920},[78,79,689],[35,4922,1487],{"className":4923},[1620,689],[35,4925,4927],{"className":4926},[78,696,689],[35,4928,3333],{"className":4929},[78,689],[35,4931,704],{"className":4932},[703],[35,4934,4936],{"className":4935},[669],[35,4937,4939],{"className":4938,"style":2881},[673],[35,4940],{},[35,4942],{"className":4943,"style":282},[242],[35,4945,230],{"className":4946},[286],[35,4948],{"className":4949,"style":282},[242],[35,4951,4953,4956,4962,4965,4968,5020,5023,5026,5029,5081],{"className":4952},[69],[35,4954],{"className":4955,"style":3847},[73],[35,4957,4959],{"className":4958},[78,696],[35,4960,1474],{"className":4961},[78],[35,4963,1478],{"className":4964},[1576],[35,4966,223],{"className":4967},[78],[35,4969,4971,4974],{"className":4970},[78],[35,4972,226],{"className":4973,"style":278},[78,79],[35,4975,4977],{"className":4976},[660],[35,4978,4980,5012],{"className":4979},[664,665],[35,4981,4983,5009],{"className":4982},[669],[35,4984,4986],{"className":4985,"style":674},[673],[35,4987,4988,4991],{"style":677},[35,4989],{"className":4990,"style":682},[681],[35,4992,4994],{"className":4993},[686,687,688,689],[35,4995,4997,5000,5003],{"className":4996},[78,689],[35,4998,1793],{"className":4999},[78,79,689],[35,5001,1487],{"className":5002},[1620,689],[35,5004,5006],{"className":5005},[78,696,689],[35,5007,3333],{"className":5008},[78,689],[35,5010,704],{"className":5011},[703],[35,5013,5015],{"className":5014},[669],[35,5016,5018],{"className":5017,"style":2881},[673],[35,5019],{},[35,5021,1487],{"className":5022},[1620],[35,5024],{"className":5025,"style":302},[242],[35,5027,223],{"className":5028},[78],[35,5030,5032,5035],{"className":5031},[78],[35,5033,56],{"className":5034,"style":80},[78,79],[35,5036,5038],{"className":5037},[660],[35,5039,5041,5073],{"className":5040},[664,665],[35,5042,5044,5070],{"className":5043},[669],[35,5045,5047],{"className":5046,"style":674},[673],[35,5048,5049,5052],{"style":831},[35,5050],{"className":5051,"style":682},[681],[35,5053,5055],{"className":5054},[686,687,688,689],[35,5056,5058,5061,5064],{"className":5057},[78,689],[35,5059,1793],{"className":5060},[78,79,689],[35,5062,1487],{"className":5063},[1620,689],[35,5065,5067],{"className":5066},[78,696,689],[35,5068,3333],{"className":5069},[78,689],[35,5071,704],{"className":5072},[703],[35,5074,5076],{"className":5075},[669],[35,5077,5079],{"className":5078,"style":2881},[673],[35,5080],{},[35,5082,1496],{"className":5083},[1667],[15,5085,5086,5087,202],{},"Run the full workflow in the ",[29,5088,87],{"href":86},[10,5090,5092],{"id":5091},"worked-example-4-leg-closed-loop","Worked Example: 4-Leg Closed Loop",[15,5094,5095,5096,5099,5100,5193,5194,5287],{},"Control station ",[107,5097,5098],{},"A",": ",[35,5101,5103,5126],{"className":5102},[38],[35,5104,5106],{"className":5105},[42],[44,5107,5108],{"xmlns":46},[48,5109,5110,5123],{},[51,5111,5112,5118,5120],{},[569,5113,5114,5116],{},[54,5115,226],{},[54,5117,5098],{},[228,5119,230],{},[383,5121,5122],{},"1000.0000",[58,5124,5125],{"encoding":60},"E_A = 1000.0000",[35,5127,5129,5184],{"className":5128,"ariaHidden":65},[64],[35,5130,5132,5135,5175,5178,5181],{"className":5131},[69],[35,5133],{"className":5134,"style":650},[73],[35,5136,5138,5141],{"className":5137},[78],[35,5139,226],{"className":5140,"style":278},[78,79],[35,5142,5144],{"className":5143},[660],[35,5145,5147,5167],{"className":5146},[664,665],[35,5148,5150,5164],{"className":5149},[669],[35,5151,5153],{"className":5152,"style":1015},[673],[35,5154,5155,5158],{"style":677},[35,5156],{"className":5157,"style":682},[681],[35,5159,5161],{"className":5160},[686,687,688,689],[35,5162,5098],{"className":5163},[78,79,689],[35,5165,704],{"className":5166},[703],[35,5168,5170],{"className":5169},[669],[35,5171,5173],{"className":5172,"style":711},[673],[35,5174],{},[35,5176],{"className":5177,"style":282},[242],[35,5179,230],{"className":5180},[286],[35,5182],{"className":5183,"style":282},[242],[35,5185,5187,5190],{"className":5186},[69],[35,5188],{"className":5189,"style":477},[73],[35,5191,5122],{"className":5192},[78]," m, ",[35,5195,5197,5220],{"className":5196},[38],[35,5198,5200],{"className":5199},[42],[44,5201,5202],{"xmlns":46},[48,5203,5204,5217],{},[51,5205,5206,5212,5214],{},[569,5207,5208,5210],{},[54,5209,56],{},[54,5211,5098],{},[228,5213,230],{},[383,5215,5216],{},"5000.0000",[58,5218,5219],{"encoding":60},"N_A = 5000.0000",[35,5221,5223,5278],{"className":5222,"ariaHidden":65},[64],[35,5224,5226,5229,5269,5272,5275],{"className":5225},[69],[35,5227],{"className":5228,"style":650},[73],[35,5230,5232,5235],{"className":5231},[78],[35,5233,56],{"className":5234,"style":80},[78,79],[35,5236,5238],{"className":5237},[660],[35,5239,5241,5261],{"className":5240},[664,665],[35,5242,5244,5258],{"className":5243},[669],[35,5245,5247],{"className":5246,"style":1015},[673],[35,5248,5249,5252],{"style":831},[35,5250],{"className":5251,"style":682},[681],[35,5253,5255],{"className":5254},[686,687,688,689],[35,5256,5098],{"className":5257},[78,79,689],[35,5259,704],{"className":5260},[703],[35,5262,5264],{"className":5263},[669],[35,5265,5267],{"className":5266,"style":711},[673],[35,5268],{},[35,5270],{"className":5271,"style":282},[242],[35,5273,230],{"className":5274},[286],[35,5276],{"className":5277,"style":282},[242],[35,5279,5281,5284],{"className":5280},[69],[35,5282],{"className":5283,"style":477},[73],[35,5285,5216],{"className":5286},[78]," m.",[5289,5290,5292],"h3",{"id":5291},"raw-field-observations","Raw field observations",[2195,5294,5295,5308],{},[2198,5296,5297],{},[2201,5298,5299,5302,5305],{},[2204,5300,5301],{},"Leg",[2204,5303,5304],{},"Azimuth (°)",[2204,5306,5307],{},"Distance (m)",[2214,5309,5310,5321,5332,5343],{},[2201,5311,5312,5315,5318],{},[2219,5313,5314],{},"AB",[2219,5316,5317],{},"45.000",[2219,5319,5320],{},"120.00",[2201,5322,5323,5326,5329],{},[2219,5324,5325],{},"BC",[2219,5327,5328],{},"135.000",[2219,5330,5331],{},"150.00",[2201,5333,5334,5337,5340],{},[2219,5335,5336],{},"CD",[2219,5338,5339],{},"225.000",[2219,5341,5342],{},"110.00",[2201,5344,5345,5348,5351],{},[2219,5346,5347],{},"DA",[2219,5349,5350],{},"311.170",[2219,5352,5353],{},"150.30",[5289,5355,5357],{"id":5356},"step-1-raw-components","Step 1: Raw components",[2195,5359,5360,5439],{},[2198,5361,5362],{},[2201,5363,5364,5366,5403],{},[2204,5365,5301],{},[2204,5367,5368,5402],{},[35,5369,5371,5387],{"className":5370},[38],[35,5372,5374],{"className":5373},[42],[44,5375,5376],{"xmlns":46},[48,5377,5378,5384],{},[51,5379,5380,5382],{},[54,5381,223],{"mathvariant":222},[54,5383,226],{},[58,5385,5386],{"encoding":60},"\\Delta E",[35,5388,5390],{"className":5389,"ariaHidden":65},[64],[35,5391,5393,5396,5399],{"className":5392},[69],[35,5394],{"className":5395,"style":74},[73],[35,5397,223],{"className":5398},[78],[35,5400,226],{"className":5401,"style":278},[78,79]," (m)",[2204,5404,5405,5402],{},[35,5406,5408,5424],{"className":5407},[38],[35,5409,5411],{"className":5410},[42],[44,5412,5413],{"xmlns":46},[48,5414,5415,5421],{},[51,5416,5417,5419],{},[54,5418,223],{"mathvariant":222},[54,5420,56],{},[58,5422,5423],{"encoding":60},"\\Delta N",[35,5425,5427],{"className":5426,"ariaHidden":65},[64],[35,5428,5430,5433,5436],{"className":5429},[69],[35,5431],{"className":5432,"style":74},[73],[35,5434,223],{"className":5435},[78],[35,5437,56],{"className":5438,"style":80},[78,79],[2214,5440,5441,5450,5460,5469],{},[2201,5442,5443,5445,5448],{},[2219,5444,5314],{},[2219,5446,5447],{},"84.8528",[2219,5449,5447],{},[2201,5451,5452,5454,5457],{},[2219,5453,5325],{},[2219,5455,5456],{},"106.0660",[2219,5458,5459],{},"−106.0660",[2201,5461,5462,5464,5467],{},[2219,5463,5336],{},[2219,5465,5466],{},"−77.7817",[2219,5468,5466],{},[2201,5470,5471,5473,5476],{},[2219,5472,5347],{},[2219,5474,5475],{},"−113.1398",[2219,5477,5478],{},"98.9418",[5289,5480,5482],{"id":5481},"step-2-misclosure-and-precision","Step 2: Misclosure and precision",[22,5484,5485,5540,5739,5793],{},[25,5486,5487,5539],{},[35,5488,5490,5509],{"className":5489},[38],[35,5491,5493],{"className":5492},[42],[44,5494,5495],{"xmlns":46},[48,5496,5497,5506],{},[51,5498,5499,5501,5503],{},[54,5500,1782],{},[228,5502,230],{},[383,5504,5505],{},"530.30",[58,5507,5508],{"encoding":60},"P = 530.30",[35,5510,5512,5530],{"className":5511,"ariaHidden":65},[64],[35,5513,5515,5518,5521,5524,5527],{"className":5514},[69],[35,5516],{"className":5517,"style":74},[73],[35,5519,1782],{"className":5520,"style":1835},[78,79],[35,5522],{"className":5523,"style":282},[242],[35,5525,230],{"className":5526},[286],[35,5528],{"className":5529,"style":282},[242],[35,5531,5533,5536],{"className":5532},[69],[35,5534],{"className":5535,"style":477},[73],[35,5537,5505],{"className":5538},[78]," m",[25,5541,5542,5193,5641,5539],{},[35,5543,5545,5570],{"className":5544},[38],[35,5546,5548],{"className":5547},[42],[44,5549,5550],{"xmlns":46},[48,5551,5552,5567],{},[51,5553,5554,5560,5562,5564],{},[569,5555,5556,5558],{},[54,5557,940],{},[54,5559,226],{},[228,5561,230],{},[228,5563,579],{},[383,5565,5566],{},"0.0027",[58,5568,5569],{"encoding":60},"e_E = -0.0027",[35,5571,5573,5628],{"className":5572,"ariaHidden":65},[64],[35,5574,5576,5579,5619,5622,5625],{"className":5575},[69],[35,5577],{"className":5578,"style":996},[73],[35,5580,5582,5585],{"className":5581},[78],[35,5583,940],{"className":5584},[78,79],[35,5586,5588],{"className":5587},[660],[35,5589,5591,5611],{"className":5590},[664,665],[35,5592,5594,5608],{"className":5593},[669],[35,5595,5597],{"className":5596,"style":1015},[673],[35,5598,5599,5602],{"style":1018},[35,5600],{"className":5601,"style":682},[681],[35,5603,5605],{"className":5604},[686,687,688,689],[35,5606,226],{"className":5607,"style":278},[78,79,689],[35,5609,704],{"className":5610},[703],[35,5612,5614],{"className":5613},[669],[35,5615,5617],{"className":5616,"style":711},[673],[35,5618],{},[35,5620],{"className":5621,"style":282},[242],[35,5623,230],{"className":5624},[286],[35,5626],{"className":5627,"style":282},[242],[35,5629,5631,5635,5638],{"className":5630},[69],[35,5632],{"className":5633,"style":5634},[73],"height:0.7278em;vertical-align:-0.0833em;",[35,5636,579],{"className":5637},[78],[35,5639,5566],{"className":5640},[78],[35,5642,5644,5669],{"className":5643},[38],[35,5645,5647],{"className":5646},[42],[44,5648,5649],{"xmlns":46},[48,5650,5651,5666],{},[51,5652,5653,5659,5661,5663],{},[569,5654,5655,5657],{},[54,5656,940],{},[54,5658,56],{},[228,5660,230],{},[228,5662,579],{},[383,5664,5665],{},"0.0531",[58,5667,5668],{"encoding":60},"e_N = -0.0531",[35,5670,5672,5727],{"className":5671,"ariaHidden":65},[64],[35,5673,5675,5678,5718,5721,5724],{"className":5674},[69],[35,5676],{"className":5677,"style":996},[73],[35,5679,5681,5684],{"className":5680},[78],[35,5682,940],{"className":5683},[78,79],[35,5685,5687],{"className":5686},[660],[35,5688,5690,5710],{"className":5689},[664,665],[35,5691,5693,5707],{"className":5692},[669],[35,5694,5696],{"className":5695,"style":1015},[673],[35,5697,5698,5701],{"style":1018},[35,5699],{"className":5700,"style":682},[681],[35,5702,5704],{"className":5703},[686,687,688,689],[35,5705,56],{"className":5706,"style":80},[78,79,689],[35,5708,704],{"className":5709},[703],[35,5711,5713],{"className":5712},[669],[35,5714,5716],{"className":5715,"style":711},[673],[35,5717],{},[35,5719],{"className":5720,"style":282},[242],[35,5722,230],{"className":5723},[286],[35,5725],{"className":5726,"style":282},[242],[35,5728,5730,5733,5736],{"className":5729},[69],[35,5731],{"className":5732,"style":5634},[73],[35,5734,579],{"className":5735},[78],[35,5737,5665],{"className":5738},[78],[25,5740,5741,5539],{},[35,5742,5744,5763],{"className":5743},[38],[35,5745,5747],{"className":5746},[42],[44,5748,5749],{"xmlns":46},[48,5750,5751,5760],{},[51,5752,5753,5755,5757],{},[54,5754,940],{},[228,5756,230],{},[383,5758,5759],{},"0.0532",[58,5761,5762],{"encoding":60},"e = 0.0532",[35,5764,5766,5784],{"className":5765,"ariaHidden":65},[64],[35,5767,5769,5772,5775,5778,5781],{"className":5768},[69],[35,5770],{"className":5771,"style":1250},[73],[35,5773,940],{"className":5774},[78,79],[35,5776],{"className":5777,"style":282},[242],[35,5779,230],{"className":5780},[286],[35,5782],{"className":5783,"style":282},[242],[35,5785,5787,5790],{"className":5786},[69],[35,5788],{"className":5789,"style":477},[73],[35,5791,5759],{"className":5792},[78],[25,5794,5795,5796,5827,5828,5831],{},"Relative precision ",[35,5797,5799,5814],{"className":5798},[38],[35,5800,5802],{"className":5801},[42],[44,5803,5804],{"xmlns":46},[48,5805,5806,5811],{},[51,5807,5808],{},[228,5809,5810],{},"≈",[58,5812,5813],{"encoding":60},"\\approx",[35,5815,5817],{"className":5816,"ariaHidden":65},[64],[35,5818,5820,5824],{"className":5819},[69],[35,5821],{"className":5822,"style":5823},[73],"height:0.4831em;",[35,5825,5810],{"className":5826},[286]," ",[107,5829,5830],{},"1 : 9,965"," (acceptable for urban design control)",[5289,5833,5835],{"id":5834},"step-3-bowditch-corrections","Step 3: Bowditch corrections",[15,5837,5838,5839,5873,5874,5908],{},"Corrections oppose misclosure (",[35,5840,5842,5858],{"className":5841},[38],[35,5843,5845],{"className":5844},[42],[44,5846,5847],{"xmlns":46},[48,5848,5849,5855],{},[51,5850,5851,5853],{},[228,5852,1229],{},[383,5854,5566],{},[58,5856,5857],{"encoding":60},"+0.0027",[35,5859,5861],{"className":5860,"ariaHidden":65},[64],[35,5862,5864,5867,5870],{"className":5863},[69],[35,5865],{"className":5866,"style":5634},[73],[35,5868,1229],{"className":5869},[78],[35,5871,5566],{"className":5872},[78]," m easting, ",[35,5875,5877,5893],{"className":5876},[38],[35,5878,5880],{"className":5879},[42],[44,5881,5882],{"xmlns":46},[48,5883,5884,5890],{},[51,5885,5886,5888],{},[228,5887,1229],{},[383,5889,5665],{},[58,5891,5892],{"encoding":60},"+0.0531",[35,5894,5896],{"className":5895,"ariaHidden":65},[64],[35,5897,5899,5902,5905],{"className":5898},[69],[35,5900],{"className":5901,"style":5634},[73],[35,5903,1229],{"className":5904},[78],[35,5906,5665],{"className":5907},[78]," m northing total):",[2195,5910,5911,6061],{},[2198,5912,5913],{},[2201,5914,5915,5917,5989],{},[2204,5916,5301],{},[2204,5918,5919,5402],{},[35,5920,5922,5940],{"className":5921},[38],[35,5923,5925],{"className":5924},[42],[44,5926,5927],{"xmlns":46},[48,5928,5929,5937],{},[51,5930,5931],{},[569,5932,5933,5935],{},[54,5934,2752],{},[54,5936,226],{},[58,5938,5939],{"encoding":60},"C_E",[35,5941,5943],{"className":5942,"ariaHidden":65},[64],[35,5944,5946,5949],{"className":5945},[69],[35,5947],{"className":5948,"style":650},[73],[35,5950,5952,5955],{"className":5951},[78],[35,5953,2752],{"className":5954,"style":2838},[78,79],[35,5956,5958],{"className":5957},[660],[35,5959,5961,5981],{"className":5960},[664,665],[35,5962,5964,5978],{"className":5963},[669],[35,5965,5967],{"className":5966,"style":1015},[673],[35,5968,5969,5972],{"style":2853},[35,5970],{"className":5971,"style":682},[681],[35,5973,5975],{"className":5974},[686,687,688,689],[35,5976,226],{"className":5977,"style":278},[78,79,689],[35,5979,704],{"className":5980},[703],[35,5982,5984],{"className":5983},[669],[35,5985,5987],{"className":5986,"style":711},[673],[35,5988],{},[2204,5990,5991,5402],{},[35,5992,5994,6012],{"className":5993},[38],[35,5995,5997],{"className":5996},[42],[44,5998,5999],{"xmlns":46},[48,6000,6001,6009],{},[51,6002,6003],{},[569,6004,6005,6007],{},[54,6006,2752],{},[54,6008,56],{},[58,6010,6011],{"encoding":60},"C_N",[35,6013,6015],{"className":6014,"ariaHidden":65},[64],[35,6016,6018,6021],{"className":6017},[69],[35,6019],{"className":6020,"style":650},[73],[35,6022,6024,6027],{"className":6023},[78],[35,6025,2752],{"className":6026,"style":2838},[78,79],[35,6028,6030],{"className":6029},[660],[35,6031,6033,6053],{"className":6032},[664,665],[35,6034,6036,6050],{"className":6035},[669],[35,6037,6039],{"className":6038,"style":1015},[673],[35,6040,6041,6044],{"style":2853},[35,6042],{"className":6043,"style":682},[681],[35,6045,6047],{"className":6046},[686,687,688,689],[35,6048,56],{"className":6049,"style":80},[78,79,689],[35,6051,704],{"className":6052},[703],[35,6054,6056],{"className":6055},[669],[35,6057,6059],{"className":6058,"style":711},[673],[35,6060],{},[2214,6062,6063,6073,6083,6092],{},[2201,6064,6065,6067,6070],{},[2219,6066,5314],{},[2219,6068,6069],{},"+0.0006",[2219,6071,6072],{},"+0.0120",[2201,6074,6075,6077,6080],{},[2219,6076,5325],{},[2219,6078,6079],{},"+0.0008",[2219,6081,6082],{},"+0.0150",[2201,6084,6085,6087,6089],{},[2219,6086,5336],{},[2219,6088,6069],{},[2219,6090,6091],{},"+0.0110",[2201,6093,6094,6096,6099],{},[2219,6095,5347],{},[2219,6097,6098],{},"+0.0007",[2219,6100,6101],{},"+0.0151",[5289,6103,6105],{"id":6104},"step-4-adjusted-coordinates","Step 4: Adjusted coordinates",[2195,6107,6108,6121],{},[2198,6109,6110],{},[2201,6111,6112,6115,6118],{},[2204,6113,6114],{},"Station",[2204,6116,6117],{},"Easting (m)",[2204,6119,6120],{},"Northing (m)",[2214,6122,6123,6131,6142,6152,6162],{},[2201,6124,6125,6127,6129],{},[2219,6126,5098],{},[2219,6128,5122],{},[2219,6130,5216],{},[2201,6132,6133,6136,6139],{},[2219,6134,6135],{},"B",[2219,6137,6138],{},"1084.8534",[2219,6140,6141],{},"5084.8648",[2201,6143,6144,6146,6149],{},[2219,6145,2752],{},[2219,6147,6148],{},"1190.9202",[2219,6150,6151],{},"4978.8138",[2201,6153,6154,6156,6159],{},[2219,6155,187],{},[2219,6157,6158],{},"1113.1391",[2219,6160,6161],{},"4901.0431",[2201,6163,6164,6167,6169],{},[2219,6165,6166],{},"A (closed)",[2219,6168,5122],{},[2219,6170,5216],{},[5289,6172,6174],{"id":6173},"step-5-adjusted-azimuths-and-distances","Step 5: Adjusted azimuths and distances",[2195,6176,6177,6189],{},[2198,6178,6179],{},[2201,6180,6181,6183,6186],{},[2204,6182,5301],{},[2204,6184,6185],{},"Adj. azimuth (°)",[2204,6187,6188],{},"Adj. distance (m)",[2214,6190,6191,6201,6211,6221],{},[2201,6192,6193,6195,6198],{},[2219,6194,5314],{},[2219,6196,6197],{},"44.996",[2219,6199,6200],{},"120.009",[2201,6202,6203,6205,6208],{},[2219,6204,5325],{},[2219,6206,6207],{},"134.996",[2219,6209,6210],{},"149.990",[2201,6212,6213,6215,6218],{},[2219,6214,5336],{},[2219,6216,6217],{},"225.004",[2219,6219,6220],{},"109.992",[2201,6222,6223,6225,6228],{},[2219,6224,5347],{},[2219,6226,6227],{},"311.175",[2219,6229,6230],{},"150.309",[5289,6232,6234],{"id":6233},"field-book-summary","Field book summary",[2195,6236,6237,6583],{},[2198,6238,6239],{},[2201,6240,6241,6243,6245,6248,6279,6314,6349,6385,6420,6456,6491,6494,6524],{},[2204,6242,6114],{},[2204,6244,5301],{},[2204,6246,6247],{},"Raw θ (°)",[2204,6249,6250,6251,5402],{},"Raw ",[35,6252,6254,6267],{"className":6253},[38],[35,6255,6257],{"className":6256},[42],[44,6258,6259],{"xmlns":46},[48,6260,6261,6265],{},[51,6262,6263],{},[54,6264,187],{},[58,6266,187],{"encoding":60},[35,6268,6270],{"className":6269,"ariaHidden":65},[64],[35,6271,6273,6276],{"className":6272},[69],[35,6274],{"className":6275,"style":74},[73],[35,6277,187],{"className":6278,"style":171},[78,79],[2204,6280,6250,6281],{},[35,6282,6284,6299],{"className":6283},[38],[35,6285,6287],{"className":6286},[42],[44,6288,6289],{"xmlns":46},[48,6290,6291,6297],{},[51,6292,6293,6295],{},[54,6294,223],{"mathvariant":222},[54,6296,226],{},[58,6298,5386],{"encoding":60},[35,6300,6302],{"className":6301,"ariaHidden":65},[64],[35,6303,6305,6308,6311],{"className":6304},[69],[35,6306],{"className":6307,"style":74},[73],[35,6309,223],{"className":6310},[78],[35,6312,226],{"className":6313,"style":278},[78,79],[2204,6315,6250,6316],{},[35,6317,6319,6334],{"className":6318},[38],[35,6320,6322],{"className":6321},[42],[44,6323,6324],{"xmlns":46},[48,6325,6326,6332],{},[51,6327,6328,6330],{},[54,6329,223],{"mathvariant":222},[54,6331,56],{},[58,6333,5423],{"encoding":60},[35,6335,6337],{"className":6336,"ariaHidden":65},[64],[35,6338,6340,6343,6346],{"className":6339},[69],[35,6341],{"className":6342,"style":74},[73],[35,6344,223],{"className":6345},[78],[35,6347,56],{"className":6348,"style":80},[78,79],[2204,6350,6351,6352],{},"Corr ",[35,6353,6355,6370],{"className":6354},[38],[35,6356,6358],{"className":6357},[42],[44,6359,6360],{"xmlns":46},[48,6361,6362,6368],{},[51,6363,6364,6366],{},[54,6365,223],{"mathvariant":222},[54,6367,226],{},[58,6369,5386],{"encoding":60},[35,6371,6373],{"className":6372,"ariaHidden":65},[64],[35,6374,6376,6379,6382],{"className":6375},[69],[35,6377],{"className":6378,"style":74},[73],[35,6380,223],{"className":6381},[78],[35,6383,226],{"className":6384,"style":278},[78,79],[2204,6386,6351,6387],{},[35,6388,6390,6405],{"className":6389},[38],[35,6391,6393],{"className":6392},[42],[44,6394,6395],{"xmlns":46},[48,6396,6397,6403],{},[51,6398,6399,6401],{},[54,6400,223],{"mathvariant":222},[54,6402,56],{},[58,6404,5423],{"encoding":60},[35,6406,6408],{"className":6407,"ariaHidden":65},[64],[35,6409,6411,6414,6417],{"className":6410},[69],[35,6412],{"className":6413,"style":74},[73],[35,6415,223],{"className":6416},[78],[35,6418,56],{"className":6419,"style":80},[78,79],[2204,6421,6422,6423],{},"Adj ",[35,6424,6426,6441],{"className":6425},[38],[35,6427,6429],{"className":6428},[42],[44,6430,6431],{"xmlns":46},[48,6432,6433,6439],{},[51,6434,6435,6437],{},[54,6436,223],{"mathvariant":222},[54,6438,226],{},[58,6440,5386],{"encoding":60},[35,6442,6444],{"className":6443,"ariaHidden":65},[64],[35,6445,6447,6450,6453],{"className":6446},[69],[35,6448],{"className":6449,"style":74},[73],[35,6451,223],{"className":6452},[78],[35,6454,226],{"className":6455,"style":278},[78,79],[2204,6457,6422,6458],{},[35,6459,6461,6476],{"className":6460},[38],[35,6462,6464],{"className":6463},[42],[44,6465,6466],{"xmlns":46},[48,6467,6468,6474],{},[51,6469,6470,6472],{},[54,6471,223],{"mathvariant":222},[54,6473,56],{},[58,6475,5423],{"encoding":60},[35,6477,6479],{"className":6478,"ariaHidden":65},[64],[35,6480,6482,6485,6488],{"className":6481},[69],[35,6483],{"className":6484,"style":74},[73],[35,6486,223],{"className":6487},[78],[35,6489,56],{"className":6490,"style":80},[78,79],[2204,6492,6493],{},"Adj θ (°)",[2204,6495,6422,6496,5402],{},[35,6497,6499,6512],{"className":6498},[38],[35,6500,6502],{"className":6501},[42],[44,6503,6504],{"xmlns":46},[48,6505,6506,6510],{},[51,6507,6508],{},[54,6509,187],{},[58,6511,187],{"encoding":60},[35,6513,6515],{"className":6514,"ariaHidden":65},[64],[35,6516,6518,6521],{"className":6517},[69],[35,6519],{"className":6520,"style":74},[73],[35,6522,187],{"className":6523,"style":171},[78,79],[2204,6525,6526,6527,1701,6555,1496],{},"Coordinates 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5000.0000",[2201,6615,6616,6618,6620,6622,6624,6626,6628,6631,6634,6637,6640,6642,6644],{},[2219,6617],{},[2219,6619,5314],{},[2219,6621,5317],{},[2219,6623,5320],{},[2219,6625,5447],{},[2219,6627,5447],{},[2219,6629,6630],{},"0.0006",[2219,6632,6633],{},"0.0120",[2219,6635,6636],{},"84.8534",[2219,6638,6639],{},"84.8648",[2219,6641,6197],{},[2219,6643,6200],{},[2219,6645],{},[2201,6647,6648,6650,6652,6654,6656,6658,6660,6662,6664,6666,6668,6670,6672],{},[2219,6649,6135],{},[2219,6651],{},[2219,6653],{},[2219,6655],{},[2219,6657],{},[2219,6659],{},[2219,6661],{},[2219,6663],{},[2219,6665],{},[2219,6667],{},[2219,6669],{},[2219,6671],{},[2219,6673,6674],{},"1084.8534, 5084.8648",[2201,6676,6677,6679,6681,6683,6685,6687,6689,6692,6695,6698,6701,6703,6705],{},[2219,6678],{},[2219,6680,5325],{},[2219,6682,5328],{},[2219,6684,5331],{},[2219,6686,5456],{},[2219,6688,5459],{},[2219,6690,6691],{},"0.0008",[2219,6693,6694],{},"0.0150",[2219,6696,6697],{},"106.0668",[2219,6699,6700],{},"−106.0510",[2219,6702,6207],{},[2219,6704,6210],{},[2219,6706],{},[2201,6708,6709,6711,6713,6715,6717,6719,6721,6723,6725,6727,6729,6731,6733],{},[2219,6710,2752],{},[2219,6712],{},[2219,6714],{},[2219,6716],{},[2219,6718],{},[2219,6720],{},[2219,6722],{},[2219,6724],{},[2219,6726],{},[2219,6728],{},[2219,6730],{},[2219,6732],{},[2219,6734,6735],{},"1190.9202, 4978.8138",[2201,6737,6738,6740,6742,6744,6746,6748,6750,6752,6755,6758,6761,6763,6765],{},[2219,6739],{},[2219,6741,5336],{},[2219,6743,5339],{},[2219,6745,5342],{},[2219,6747,5466],{},[2219,6749,5466],{},[2219,6751,6630],{},[2219,6753,6754],{},"0.0110",[2219,6756,6757],{},"−77.7811",[2219,6759,6760],{},"−77.7707",[2219,6762,6217],{},[2219,6764,6220],{},[2219,6766],{},[2201,6768,6769,6771,6773,6775,6777,6779,6781,6783,6785,6787,6789,6791,6793],{},[2219,6770,187],{},[2219,6772],{},[2219,6774],{},[2219,6776],{},[2219,6778],{},[2219,6780],{},[2219,6782],{},[2219,6784],{},[2219,6786],{},[2219,6788],{},[2219,6790],{},[2219,6792],{},[2219,6794,6795],{},"1113.1391, 4901.0431",[2201,6797,6798,6800,6802,6804,6806,6808,6810,6813,6816,6819,6822,6824,6826],{},[2219,6799],{},[2219,6801,5347],{},[2219,6803,5350],{},[2219,6805,5353],{},[2219,6807,5475],{},[2219,6809,5478],{},[2219,6811,6812],{},"0.0007",[2219,6814,6815],{},"0.0151",[2219,6817,6818],{},"−113.1391",[2219,6820,6821],{},"98.9569",[2219,6823,6227],{},[2219,6825,6230],{},[2219,6827],{},[2201,6829,6830,6832,6834,6836,6838,6840,6842,6844,6846,6848,6850,6852,6854],{},[2219,6831,5098],{},[2219,6833],{},[2219,6835],{},[2219,6837],{},[2219,6839],{},[2219,6841],{},[2219,6843],{},[2219,6845],{},[2219,6847],{},[2219,6849],{},[2219,6851],{},[2219,6853],{},[2219,6855,6613],{},[2201,6857,6858,6863,6865,6867,6869,6872,6875,6877,6879,6882,6884,6886,6888],{},[2219,6859,6860],{},[107,6861,6862],{},"Sum",[2219,6864],{},[2219,6866],{},[2219,6868,5505],{},[2219,6870,6871],{},"−0.0027",[2219,6873,6874],{},"−0.0531",[2219,6876,5566],{},[2219,6878,5665],{},[2219,6880,6881],{},"0.0000",[2219,6883,6881],{},[2219,6885],{},[2219,6887],{},[2219,6889],{},[10,6891,6893],{"id":6892},"bowditch-vs-least-squares","Bowditch vs. Least Squares",[15,6895,6896,6897,6900],{},"Bowditch is empirical and suited to a single loop or link. ",[107,6898,6899],{},"Least squares"," minimizes weighted observation residuals, handles redundant interconnected networks, and yields error ellipses — the geodetic standard for complex control.",[2195,6902,6903,6918],{},[2198,6904,6905],{},[2201,6906,6907,6910,6913,6916],{},[2204,6908,6909],{},"Feature",[2204,6911,6912],{},"Bowditch (compass)",[2204,6914,6915],{},"Transit rule",[2204,6917,6899],{},[2214,6919,6920,7018,7032,7045,7058],{},[2201,6921,6922,6925,6928,7015],{},[2219,6923,6924],{},"Basis",[2219,6926,6927],{},"Empirical; ∝ leg length",[2219,6929,6930,6931,1701,6974],{},"Empirical; ∝ ",[35,6932,6934,6955],{"className":6933},[38],[35,6935,6937],{"className":6936},[42],[44,6938,6939],{"xmlns":46},[48,6940,6941,6952],{},[51,6942,6943,6946,6948,6950],{},[54,6944,6945],{"mathvariant":222},"∥",[54,6947,223],{"mathvariant":222},[54,6949,226],{},[54,6951,6945],{"mathvariant":222},[58,6953,6954],{"encoding":60},"\\|\\Delta E\\|",[35,6956,6958],{"className":6957,"ariaHidden":65},[64],[35,6959,6961,6964,6968,6971],{"className":6960},[69],[35,6962],{"className":6963,"style":410},[73],[35,6965,6967],{"className":6966},[78],"∥Δ",[35,6969,226],{"className":6970,"style":278},[78,79],[35,6972,6945],{"className":6973},[78],[35,6975,6977,6997],{"className":6976},[38],[35,6978,6980],{"className":6979},[42],[44,6981,6982],{"xmlns":46},[48,6983,6984,6994],{},[51,6985,6986,6988,6990,6992],{},[54,6987,6945],{"mathvariant":222},[54,6989,223],{"mathvariant":222},[54,6991,56],{},[54,6993,6945],{"mathvariant":222},[58,6995,6996],{"encoding":60},"\\|\\Delta N\\|",[35,6998,7000],{"className":6999,"ariaHidden":65},[64],[35,7001,7003,7006,7009,7012],{"className":7002},[69],[35,7004],{"className":7005,"style":410},[73],[35,7007,6967],{"className":7008},[78],[35,7010,56],{"className":7011,"style":80},[78,79],[35,7013,6945],{"className":7014},[78],[2219,7016,7017],{},"Statistical optimization",[2201,7019,7020,7023,7026,7029],{},[2219,7021,7022],{},"Angle vs. distance",[2219,7024,7025],{},"Assumes comparable precision",[2219,7027,7028],{},"Assumes angles more precise",[2219,7030,7031],{},"Custom weights",[2201,7033,7034,7037,7040,7042],{},[2219,7035,7036],{},"Topology",[2219,7038,7039],{},"Single loop\u002Flink",[2219,7041,7039],{},[2219,7043,7044],{},"Arbitrary networks",[2201,7046,7047,7050,7053,7055],{},[2219,7048,7049],{},"Uncertainty",[2219,7051,7052],{},"Relative precision only",[2219,7054,7052],{},[2219,7056,7057],{},"Error ellipses",[2201,7059,7060,7063,7066,7069],{},[2219,7061,7062],{},"Limitations",[2219,7064,7065],{},"No redundancy metrics",[2219,7067,7068],{},"Weak theoretical basis",[2219,7070,7071],{},"Requires software",[15,7073,7074],{},"Bowditch remains appropriate for most local engineering, topo, and construction traverses.",[10,7076,7078],{"id":7077},"common-errors","Common Errors",[5289,7080,7082],{"id":7081},"wrong-sign-on-corrections","Wrong sign on corrections",[15,7084,7085,7305,7306,7376,7377,7380],{},[35,7086,7088,7137],{"className":7087},[38],[35,7089,7091],{"className":7090},[42],[44,7092,7093],{"xmlns":46},[48,7094,7095,7134],{},[51,7096,7097,7109,7111,7113,7119,7121,7127,7130,7132],{},[569,7098,7099,7101],{},[54,7100,2752],{},[51,7102,7103,7105,7107],{},[54,7104,226],{},[228,7106,1487],{"separator":65},[54,7108,1793],{},[228,7110,230],{},[228,7112,579],{},[569,7114,7115,7117],{},[54,7116,940],{},[54,7118,226],{},[228,7120,1478],{"stretchy":1477},[569,7122,7123,7125],{},[54,7124,187],{},[54,7126,1793],{},[54,7128,7129],{"mathvariant":222},"\u002F",[54,7131,1782],{},[228,7133,1496],{"stretchy":1477},[58,7135,7136],{"encoding":60},"C_{E,i} = -e_E (D_i\u002FP)",[35,7138,7140,7204],{"className":7139,"ariaHidden":65},[64],[35,7141,7143,7146,7195,7198,7201],{"className":7142},[69],[35,7144],{"className":7145,"style":2831},[73],[35,7147,7149,7152],{"className":7148},[78],[35,7150,2752],{"className":7151,"style":2838},[78,79],[35,7153,7155],{"className":7154},[660],[35,7156,7158,7187],{"className":7157},[664,665],[35,7159,7161,7184],{"className":7160},[669],[35,7162,7164],{"className":7163,"style":1015},[673],[35,7165,7166,7169],{"style":2853},[35,7167],{"className":7168,"style":682},[681],[35,7170,7172],{"className":7171},[686,687,688,689],[35,7173,7175,7178,7181],{"className":7174},[78,689],[35,7176,226],{"className":7177,"style":278},[78,79,689],[35,7179,1487],{"className":7180},[1620,689],[35,7182,1793],{"className":7183},[78,79,689],[35,7185,704],{"className":7186},[703],[35,7188,7190],{"className":7189},[669],[35,7191,7193],{"className":7192,"style":2881},[673],[35,7194],{},[35,7196],{"className":7197,"style":282},[242],[35,7199,230],{"className":7200},[286],[35,7202],{"className":7203,"style":282},[242],[35,7205,7207,7210,7213,7253,7256,7296,7299,7302],{"className":7206},[69],[35,7208],{"className":7209,"style":410},[73],[35,7211,579],{"className":7212},[78],[35,7214,7216,7219],{"className":7215},[78],[35,7217,940],{"className":7218},[78,79],[35,7220,7222],{"className":7221},[660],[35,7223,7225,7245],{"className":7224},[664,665],[35,7226,7228,7242],{"className":7227},[669],[35,7229,7231],{"className":7230,"style":1015},[673],[35,7232,7233,7236],{"style":1018},[35,7234],{"className":7235,"style":682},[681],[35,7237,7239],{"className":7238},[686,687,688,689],[35,7240,226],{"className":7241,"style":278},[78,79,689],[35,7243,704],{"className":7244},[703],[35,7246,7248],{"className":7247},[669],[35,7249,7251],{"className":7250,"style":711},[673],[35,7252],{},[35,7254,1478],{"className":7255},[1576],[35,7257,7259,7262],{"className":7258},[78],[35,7260,187],{"className":7261,"style":171},[78,79],[35,7263,7265],{"className":7264},[660],[35,7266,7268,7288],{"className":7267},[664,665],[35,7269,7271,7285],{"className":7270},[669],[35,7272,7274],{"className":7273,"style":1875},[673],[35,7275,7276,7279],{"style":1531},[35,7277],{"className":7278,"style":682},[681],[35,7280,7282],{"className":7281},[686,687,688,689],[35,7283,1793],{"className":7284},[78,79,689],[35,7286,704],{"className":7287},[703],[35,7289,7291],{"className":7290},[669],[35,7292,7294],{"className":7293,"style":711},[673],[35,7295],{},[35,7297,7129],{"className":7298},[78],[35,7300,1782],{"className":7301,"style":1835},[78,79],[35,7303,1496],{"className":7304},[1667],". Negative ",[35,7307,7309,7327],{"className":7308},[38],[35,7310,7312],{"className":7311},[42],[44,7313,7314],{"xmlns":46},[48,7315,7316,7324],{},[51,7317,7318],{},[569,7319,7320,7322],{},[54,7321,940],{},[54,7323,226],{},[58,7325,7326],{"encoding":60},"e_E",[35,7328,7330],{"className":7329,"ariaHidden":65},[64],[35,7331,7333,7336],{"className":7332},[69],[35,7334],{"className":7335,"style":996},[73],[35,7337,7339,7342],{"className":7338},[78],[35,7340,940],{"className":7341},[78,79],[35,7343,7345],{"className":7344},[660],[35,7346,7348,7368],{"className":7347},[664,665],[35,7349,7351,7365],{"className":7350},[669],[35,7352,7354],{"className":7353,"style":1015},[673],[35,7355,7356,7359],{"style":1018},[35,7357],{"className":7358,"style":682},[681],[35,7360,7362],{"className":7361},[686,687,688,689],[35,7363,226],{"className":7364,"style":278},[78,79,689],[35,7366,704],{"className":7367},[703],[35,7369,7371],{"className":7370},[669],[35,7372,7374],{"className":7373,"style":711},[673],[35,7375],{}," requires ",[107,7378,7379],{},"positive"," departure corrections. Same-sign corrections double the error.",[5289,7382,7384],{"id":7383},"balancing-angles-before-checking-linear-misclosure","Balancing angles before checking linear misclosure",[15,7386,7387,7388,1701,7421,7454],{},"Angular balancing can mask distance blunders. Compute raw ",[35,7389,7391,7406],{"className":7390},[38],[35,7392,7394],{"className":7393},[42],[44,7395,7396],{"xmlns":46},[48,7397,7398,7404],{},[51,7399,7400,7402],{},[54,7401,223],{"mathvariant":222},[54,7403,226],{},[58,7405,5386],{"encoding":60},[35,7407,7409],{"className":7408,"ariaHidden":65},[64],[35,7410,7412,7415,7418],{"className":7411},[69],[35,7413],{"className":7414,"style":74},[73],[35,7416,223],{"className":7417},[78],[35,7419,226],{"className":7420,"style":278},[78,79],[35,7422,7424,7439],{"className":7423},[38],[35,7425,7427],{"className":7426},[42],[44,7428,7429],{"xmlns":46},[48,7430,7431,7437],{},[51,7432,7433,7435],{},[54,7434,223],{"mathvariant":222},[54,7436,56],{},[58,7438,5423],{"encoding":60},[35,7440,7442],{"className":7441,"ariaHidden":65},[64],[35,7443,7445,7448,7451],{"className":7444},[69],[35,7446],{"className":7447,"style":74},[73],[35,7449,223],{"className":7450},[78],[35,7452,56],{"className":7453,"style":80},[78,79]," first to detect field book errors.",[5289,7456,7458],{"id":7457},"using-slope-distances","Using slope distances",[15,7460,7461],{},"Apply horizontal reduction before traverse math; raw slope distances distort perimeter and misclosure.",[5289,7463,7465],{"id":7464},"uncorrected-field-errors","Uncorrected field errors",[15,7467,7468],{},"Temperature, tension, sag, meteorological EDM corrections, and similar systematic effects propagate through every leg.",[10,7470,7472],{"id":7471},"next-steps","Next Steps",[116,7474,7475,7509,7515],{},[25,7476,7477,7478,7480,7481,202],{},"Enter raw azimuths and horizontal distances in the ",[29,7479,32],{"href":31}," — check misclosure and 1 : ",[35,7482,7484,7497],{"className":7483},[38],[35,7485,7487],{"className":7486},[42],[44,7488,7489],{"xmlns":46},[48,7490,7491,7495],{},[51,7492,7493],{},[54,7494,56],{},[58,7496,56],{"encoding":60},[35,7498,7500],{"className":7499,"ariaHidden":65},[64],[35,7501,7503,7506],{"className":7502},[69],[35,7504],{"className":7505,"style":74},[73],[35,7507,56],{"className":7508,"style":80},[78,79],[25,7510,7511,7512,7514],{},"If within tolerance, run the ",[29,7513,87],{"href":86}," for balanced coordinates and adjusted legs.",[25,7516,7517,7518,7520],{},"Use the ",[29,7519,94],{"href":93}," for auxiliary grid conversions.",{"title":7522,"searchDepth":7523,"depth":7523,"links":7524},"",2,[7525,7526,7527,7528,7529,7530,7531,7532,7542,7543,7549],{"id":12,"depth":7523,"text":13},{"id":98,"depth":7523,"text":99},{"id":135,"depth":7523,"text":136},{"id":1732,"depth":7523,"text":1733},{"id":2189,"depth":7523,"text":2190},{"id":2576,"depth":7523,"text":2577},{"id":2586,"depth":7523,"text":2587},{"id":5091,"depth":7523,"text":5092,"children":7533},[7534,7536,7537,7538,7539,7540,7541],{"id":5291,"depth":7535,"text":5292},3,{"id":5356,"depth":7535,"text":5357},{"id":5481,"depth":7535,"text":5482},{"id":5834,"depth":7535,"text":5835},{"id":6104,"depth":7535,"text":6105},{"id":6173,"depth":7535,"text":6174},{"id":6233,"depth":7535,"text":6234},{"id":6892,"depth":7523,"text":6893},{"id":7077,"depth":7523,"text":7078,"children":7544},[7545,7546,7547,7548],{"id":7081,"depth":7535,"text":7082},{"id":7383,"depth":7535,"text":7384},{"id":7457,"depth":7535,"text":7458},{"id":7464,"depth":7535,"text":7465},{"id":7471,"depth":7523,"text":7472},"tools","Closed traverses — departures and latitudes, linear misclosure, relative precision, Bowditch compass-rule adjustment, and a full worked example.","md",{},true,"\u002Flearn\u002Ftools\u002Ftraverse-and-bowditch",{"title":5,"description":7551},{"loc":7555},"learn\u002Ftools\u002Ftraverse-and-bowditch","xdCsOQhvo7gOGwN8WTT6GA6Qxn2zrIQt-e5wqZOWMa4",[7561,7566],{"title":7562,"path":7563,"stem":7564,"description":7565,"category":7550,"children":-1},"Bearing & Distance","\u002Flearn\u002Ftools\u002Fbearing-distance","learn\u002Ftools\u002Fbearing-distance","Coordinate geometry for plane surveying — azimuth and quadrant bearings, polar ↔ rectangular conversion, worked examples, and common errors.",{"title":7567,"path":7568,"stem":7569,"description":7570,"category":7550,"children":-1},"Tienstra Resection","\u002Flearn\u002Ftools\u002Ftienstra-resection","learn\u002Ftools\u002Ftienstra-resection","Three-point angular resection — Tienstra barycentric method, danger circle, field practice, worked example, and verification.",1783851946349]