[{"data":1,"prerenderedAt":2008},["ShallowReactive",2],{"blog-\u002Fblog\u002Finverted-sights-underground-and-overhead-levelling":3,"blog-surround-\u002Fblog\u002Finverted-sights-underground-and-overhead-levelling":1997},{"id":4,"title":5,"author":6,"body":7,"category":1965,"description":1966,"extension":1967,"image":1968,"meta":1969,"navigation":1989,"path":1990,"publishedAt":1991,"readTime":1992,"seo":1993,"sitemap":1994,"stem":1995,"__hash__":1996},"blog\u002Fblog\u002F15.inverted-sights-underground-and-overhead-levelling.md","Inverted Sights: Levelling Techniques for Overheads and Soffits","Surveyiiing Expert",{"type":8,"value":9,"toc":1940},"minimark",[10,15,29,33,40,44,53,57,62,431,435,796,800,842,846,855,988,1267,1271,1678,1682,1708,1712,1769,1773,1921,1925,1928,1932],[11,12,14],"h2",{"id":13},"overview","Overview",[16,17,18,19,23,24,28],"p",{},"Surveyors often need to determine the elevation of points that cannot be stood upon, such as the underside of a bridge (soffit), the roof of a tunnel, or the ceiling of a building. This is achieved using ",[20,21,22],"strong",{},"Inverted Sights",", where the levelling staff is held upside-down with its base against the overhead point ",[25,26,27],"span",{},"40",".",[11,30,32],{"id":31},"why-this-matters","Why This Matters",[16,34,35,36,39],{},"Precise clearance measurements are critical for safety. For instance, determining the minimum vertical clearance between a motorway surface and an overpass requires measuring levels on both the road and the bridge soffit ",[25,37,38],{},"41, 42",". Mistakes in these calculations can lead to structural damage or vehicle collisions.",[11,41,43],{"id":42},"theory","Theory",[16,45,46,47,50,51,28],{},"When a staff is inverted, the graduations increase downwards from the point of contact. To maintain mathematical consistency in levelling books, inverted staff readings are treated as ",[20,48,49],{},"negative quantities"," ",[25,52,27],{},[11,54,56],{"id":55},"mathematical-principles","Mathematical Principles",[58,59,61],"h3",{"id":60},"height-of-collimation-hpc-method","Height of Collimation (HPC) Method",[16,63,64,65,111,112,155,156,194,195,306,50,429,28],{},"If the staff is held inverted at point ",[25,66,69,91],{"className":67},[68],"katex",[25,70,73],{"className":71},[72],"katex-mathml",[74,75,77],"math",{"xmlns":76},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[78,79,80,87],"semantics",{},[81,82,83],"mrow",{},[84,85,86],"mi",{},"B",[88,89,86],"annotation",{"encoding":90},"application\u002Fx-tex",[25,92,96],{"className":93,"ariaHidden":95},[94],"katex-html","true",[25,97,100,105],{"className":98},[99],"base",[25,101],{"className":102,"style":104},[103],"strut","height:0.6833em;",[25,106,86],{"className":107,"style":110},[108,109],"mord","mathnormal","margin-right:0.0502em;"," and the reading is ",[25,113,115,135],{"className":114},[68],[25,116,118],{"className":117},[72],[74,119,120],{"xmlns":76},[78,121,122,132],{},[81,123,124,128],{},[125,126,127],"mn",{},"3.0",[129,130,131],"mtext",{}," m",[88,133,134],{"encoding":90},"3.0\\text{ m}",[25,136,138],{"className":137,"ariaHidden":95},[94],[25,139,141,145,148],{"className":140},[99],[25,142],{"className":143,"style":144},[103],"height:0.6444em;",[25,146,127],{"className":147},[108],[25,149,152],{"className":150},[108,151],"text",[25,153,131],{"className":154},[108],", and the height of the line of sight (HPC) is ",[25,157,159,176],{"className":158},[68],[25,160,162],{"className":161},[72],[74,163,164],{"xmlns":76},[78,165,166,173],{},[81,167,168,171],{},[125,169,170],{},"62.0",[129,172,131],{},[88,174,175],{"encoding":90},"62.0\\text{ m}",[25,177,179],{"className":178,"ariaHidden":95},[94],[25,180,182,185,188],{"className":181},[99],[25,183],{"className":184,"style":144},[103],[25,186,170],{"className":187},[108],[25,189,191],{"className":190},[108,151],[25,192,131],{"className":193},[108],":\n",[25,196,198,233],{"className":197},[68],[25,199,201],{"className":200},[72],[74,202,203],{"xmlns":76},[78,204,205,230],{},[81,206,207,210,214,217,220,224,227],{},[129,208,209],{},"Level of Point B",[211,212,213],"mo",{},"=",[129,215,216],{},"HPC",[211,218,219],{},"−",[211,221,223],{"stretchy":222},"false","(",[129,225,226],{},"Reading",[211,228,229],{"stretchy":222},")",[88,231,232],{"encoding":90},"\\text{Level of Point B} = \\text{HPC} - (\\text{Reading})",[25,234,236,261,285],{"className":235,"ariaHidden":95},[94],[25,237,239,243,249,254,258],{"className":238},[99],[25,240],{"className":241,"style":242},[103],"height:0.6944em;",[25,244,246],{"className":245},[108,151],[25,247,209],{"className":248},[108],[25,250],{"className":251,"style":253},[252],"mspace","margin-right:0.2778em;",[25,255,213],{"className":256},[257],"mrel",[25,259],{"className":260,"style":253},[252],[25,262,264,268,274,278,282],{"className":263},[99],[25,265],{"className":266,"style":267},[103],"height:0.7667em;vertical-align:-0.0833em;",[25,269,271],{"className":270},[108,151],[25,272,216],{"className":273},[108],[25,275],{"className":276,"style":277},[252],"margin-right:0.2222em;",[25,279,219],{"className":280},[281],"mbin",[25,283],{"className":284,"style":277},[252],[25,286,288,292,296,302],{"className":287},[99],[25,289],{"className":290,"style":291},[103],"height:1em;vertical-align:-0.25em;",[25,293,223],{"className":294},[295],"mopen",[25,297,299],{"className":298},[108,151],[25,300,226],{"className":301},[108],[25,303,229],{"className":304},[305],"mclose",[25,307,309,344],{"className":308},[68],[25,310,312],{"className":311},[72],[74,313,314],{"xmlns":76},[78,315,316,341],{},[81,317,318,320,322,324,326,328,330,332,334,336,339],{},[129,319,209],{},[211,321,213],{},[125,323,170],{},[211,325,219],{},[211,327,223],{"stretchy":222},[211,329,219],{},[125,331,127],{},[211,333,229],{"stretchy":222},[211,335,213],{},[125,337,338],{},"65.0",[129,340,131],{},[88,342,343],{"encoding":90},"\\text{Level of Point B} = 62.0 - (-3.0) = 65.0\\text{ m}",[25,345,347,368,387,414],{"className":346,"ariaHidden":95},[94],[25,348,350,353,359,362,365],{"className":349},[99],[25,351],{"className":352,"style":242},[103],[25,354,356],{"className":355},[108,151],[25,357,209],{"className":358},[108],[25,360],{"className":361,"style":253},[252],[25,363,213],{"className":364},[257],[25,366],{"className":367,"style":253},[252],[25,369,371,375,378,381,384],{"className":370},[99],[25,372],{"className":373,"style":374},[103],"height:0.7278em;vertical-align:-0.0833em;",[25,376,170],{"className":377},[108],[25,379],{"className":380,"style":277},[252],[25,382,219],{"className":383},[281],[25,385],{"className":386,"style":277},[252],[25,388,390,393,396,399,402,405,408,411],{"className":389},[99],[25,391],{"className":392,"style":291},[103],[25,394,223],{"className":395},[295],[25,397,219],{"className":398},[108],[25,400,127],{"className":401},[108],[25,403,229],{"className":404},[305],[25,406],{"className":407,"style":253},[252],[25,409,213],{"className":410},[257],[25,412],{"className":413,"style":253},[252],[25,415,417,420,423],{"className":416},[99],[25,418],{"className":419,"style":144},[103],[25,421,338],{"className":422},[108],[25,424,426],{"className":425},[108,151],[25,427,131],{"className":428},[108],[25,430,27],{},[58,432,434],{"id":433},"rise-and-fall-method","Rise and Fall Method",[16,436,437,438,467,468,506,507,467,535,577,578,664,50,793,28],{},"The same logic applies. If you move from a standard staff reading at ",[25,439,441,455],{"className":440},[68],[25,442,444],{"className":443},[72],[74,445,446],{"xmlns":76},[78,447,448,453],{},[81,449,450],{},[84,451,452],{},"A",[88,454,452],{"encoding":90},[25,456,458],{"className":457,"ariaHidden":95},[94],[25,459,461,464],{"className":460},[99],[25,462],{"className":463,"style":104},[103],[25,465,452],{"className":466},[108,109]," (",[25,469,471,488],{"className":470},[68],[25,472,474],{"className":473},[72],[74,475,476],{"xmlns":76},[78,477,478,485],{},[81,479,480,483],{},[125,481,482],{},"2.0",[129,484,131],{},[88,486,487],{"encoding":90},"2.0\\text{ m}",[25,489,491],{"className":490,"ariaHidden":95},[94],[25,492,494,497,500],{"className":493},[99],[25,495],{"className":496,"style":144},[103],[25,498,482],{"className":499},[108],[25,501,503],{"className":502},[108,151],[25,504,131],{"className":505},[108],") to an inverted reading at ",[25,508,510,523],{"className":509},[68],[25,511,513],{"className":512},[72],[74,514,515],{"xmlns":76},[78,516,517,521],{},[81,518,519],{},[84,520,86],{},[88,522,86],{"encoding":90},[25,524,526],{"className":525,"ariaHidden":95},[94],[25,527,529,532],{"className":528},[99],[25,530],{"className":531,"style":104},[103],[25,533,86],{"className":534,"style":110},[108,109],[25,536,538,556],{"className":537},[68],[25,539,541],{"className":540},[72],[74,542,543],{"xmlns":76},[78,544,545,553],{},[81,546,547,549,551],{},[211,548,219],{},[125,550,127],{},[129,552,131],{},[88,554,555],{"encoding":90},"-3.0\\text{ m}",[25,557,559],{"className":558,"ariaHidden":95},[94],[25,560,562,565,568,571],{"className":561},[99],[25,563],{"className":564,"style":374},[103],[25,566,219],{"className":567},[108],[25,569,127],{"className":570},[108],[25,572,574],{"className":573},[108,151],[25,575,131],{"className":576},[108],"):\n",[25,579,581,606],{"className":580},[68],[25,582,584],{"className":583},[72],[74,585,586],{"xmlns":76},[78,587,588,603],{},[81,589,590,593,595,598,600],{},[129,591,592],{},"Difference",[211,594,213],{},[129,596,597],{},"Reading A",[211,599,219],{},[129,601,602],{},"Reading B",[88,604,605],{"encoding":90},"\\text{Difference} = \\text{Reading A} - \\text{Reading B}",[25,607,609,630,652],{"className":608,"ariaHidden":95},[94],[25,610,612,615,621,624,627],{"className":611},[99],[25,613],{"className":614,"style":242},[103],[25,616,618],{"className":617},[108,151],[25,619,592],{"className":620},[108],[25,622],{"className":623,"style":253},[252],[25,625,213],{"className":626},[257],[25,628],{"className":629,"style":253},[252],[25,631,633,637,643,646,649],{"className":632},[99],[25,634],{"className":635,"style":636},[103],"height:0.8889em;vertical-align:-0.1944em;",[25,638,640],{"className":639},[108,151],[25,641,597],{"className":642},[108],[25,644],{"className":645,"style":277},[252],[25,647,219],{"className":648},[281],[25,650],{"className":651,"style":277},[252],[25,653,655,658],{"className":654},[99],[25,656],{"className":657,"style":636},[103],[25,659,661],{"className":660},[108,151],[25,662,602],{"className":663},[108],[25,665,667,706],{"className":666},[68],[25,668,670],{"className":669},[72],[74,671,672],{"xmlns":76},[78,673,674,703],{},[81,675,676,678,680,682,684,686,688,690,692,694,697,700],{},[129,677,592],{},[211,679,213],{},[125,681,482],{},[211,683,219],{},[211,685,223],{"stretchy":222},[211,687,219],{},[125,689,127],{},[211,691,229],{"stretchy":222},[211,693,213],{},[211,695,696],{},"+",[125,698,699],{},"5.0",[129,701,702],{}," (a Rise)",[88,704,705],{"encoding":90},"\\text{Difference} = 2.0 - (-3.0) = +5.0\\text{ (a Rise)}",[25,707,709,730,748,775],{"className":708,"ariaHidden":95},[94],[25,710,712,715,721,724,727],{"className":711},[99],[25,713],{"className":714,"style":242},[103],[25,716,718],{"className":717},[108,151],[25,719,592],{"className":720},[108],[25,722],{"className":723,"style":253},[252],[25,725,213],{"className":726},[257],[25,728],{"className":729,"style":253},[252],[25,731,733,736,739,742,745],{"className":732},[99],[25,734],{"className":735,"style":374},[103],[25,737,482],{"className":738},[108],[25,740],{"className":741,"style":277},[252],[25,743,219],{"className":744},[281],[25,746],{"className":747,"style":277},[252],[25,749,751,754,757,760,763,766,769,772],{"className":750},[99],[25,752],{"className":753,"style":291},[103],[25,755,223],{"className":756},[295],[25,758,219],{"className":759},[108],[25,761,127],{"className":762},[108],[25,764,229],{"className":765},[305],[25,767],{"className":768,"style":253},[252],[25,770,213],{"className":771},[257],[25,773],{"className":774,"style":253},[252],[25,776,778,781,784,787],{"className":777},[99],[25,779],{"className":780,"style":291},[103],[25,782,696],{"className":783},[108],[25,785,699],{"className":786},[108],[25,788,790],{"className":789},[108,151],[25,791,702],{"className":792},[108],[25,794,795],{},"43",[11,797,799],{"id":798},"field-workflow","Field Workflow",[801,802,803,807,812,816,821,825,833,837],"steps",{},[58,804,806],{"id":805},"establish-a-benchmark","Establish a Benchmark",[16,808,809,810,28],{},"Take a standard Backsight (BS) to a known Bench Mark (BM) to establish the instrument's Height of Collimation (HPC) ",[25,811,27],{},[58,813,815],{"id":814},"positioning-the-staff","Positioning the Staff",[16,817,818,819,28],{},"Hold the base of the staff against the underside of the overhead structure. Ensure the staff is held vertically using a circular bubble or by gently \"waving\" the staff to find the minimum reading ",[25,820,38],{},[58,822,824],{"id":823},"reading-and-booking","Reading and Booking",[16,826,827,828,50,831,28],{},"Note the reading and enter it into the \"Intermediate Sight\" (IS) or \"Foresight\" (FS) column of the levelling book, clearly marking it with a ",[20,829,830],{},"negative sign",[25,832,795],{},[58,834,836],{"id":835},"calculations","Calculations",[16,838,839,840,28],{},"Proceed with reductions (HPC or Rise & Fall) treating the negative values algebraically ",[25,841,795],{},[11,843,845],{"id":844},"step-by-step-example","Step-by-Step Example",[16,847,848,851,852,28],{},[20,849,850],{},"Problem:"," Find the clearance between a road and a bridge soffit ",[25,853,854],{},"40, 44",[856,857,858,901,942],"ul",{},[859,860,861,862,900],"li",{},"HPC = ",[25,863,865,882],{"className":864},[68],[25,866,868],{"className":867},[72],[74,869,870],{"xmlns":76},[78,871,872,879],{},[81,873,874,877],{},[125,875,876],{},"224.981",[129,878,131],{},[88,880,881],{"encoding":90},"224.981\\text{ m}",[25,883,885],{"className":884,"ariaHidden":95},[94],[25,886,888,891,894],{"className":887},[99],[25,889],{"className":890,"style":144},[103],[25,892,876],{"className":893},[108],[25,895,897],{"className":896},[108,151],[25,898,131],{"className":899},[108]," (calculated from road BM).",[859,902,903,904,28],{},"Standard reading on road crown = ",[25,905,907,924],{"className":906},[68],[25,908,910],{"className":909},[72],[74,911,912],{"xmlns":76},[78,913,914,921],{},[81,915,916,919],{},[125,917,918],{},"0.981",[129,920,131],{},[88,922,923],{"encoding":90},"0.981\\text{ m}",[25,925,927],{"className":926,"ariaHidden":95},[94],[25,928,930,933,936],{"className":929},[99],[25,931],{"className":932,"style":144},[103],[25,934,918],{"className":935},[108],[25,937,939],{"className":938},[108,151],[25,940,131],{"className":941},[108],[859,943,944,945,28],{},"Inverted reading on bridge soffit = ",[25,946,948,967],{"className":947},[68],[25,949,951],{"className":950},[72],[74,952,953],{"xmlns":76},[78,954,955,964],{},[81,956,957,959,962],{},[211,958,219],{},[125,960,961],{},"4.566",[129,963,131],{},[88,965,966],{"encoding":90},"-4.566\\text{ m}",[25,968,970],{"className":969,"ariaHidden":95},[94],[25,971,973,976,979,982],{"className":972},[99],[25,974],{"className":975,"style":374},[103],[25,977,219],{"className":978},[108],[25,980,961],{"className":981},[108],[25,983,985],{"className":984},[108,151],[25,986,131],{"className":987},[108],[989,990,991,1078,1180],"ol",{},[859,992,993,50,996,28],{},[20,994,995],{},"Level of Road Crown:",[25,997,999,1024],{"className":998},[68],[25,1000,1002],{"className":1001},[72],[74,1003,1004],{"xmlns":76},[78,1005,1006,1021],{},[81,1007,1008,1010,1012,1014,1016,1019],{},[125,1009,876],{},[211,1011,219],{},[125,1013,918],{},[211,1015,213],{},[125,1017,1018],{},"224.000",[129,1020,131],{},[88,1022,1023],{"encoding":90},"224.981 - 0.981 = 224.000\\text{ m}",[25,1025,1027,1045,1063],{"className":1026,"ariaHidden":95},[94],[25,1028,1030,1033,1036,1039,1042],{"className":1029},[99],[25,1031],{"className":1032,"style":374},[103],[25,1034,876],{"className":1035},[108],[25,1037],{"className":1038,"style":277},[252],[25,1040,219],{"className":1041},[281],[25,1043],{"className":1044,"style":277},[252],[25,1046,1048,1051,1054,1057,1060],{"className":1047},[99],[25,1049],{"className":1050,"style":144},[103],[25,1052,918],{"className":1053},[108],[25,1055],{"className":1056,"style":253},[252],[25,1058,213],{"className":1059},[257],[25,1061],{"className":1062,"style":253},[252],[25,1064,1066,1069,1072],{"className":1065},[99],[25,1067],{"className":1068,"style":144},[103],[25,1070,1018],{"className":1071},[108],[25,1073,1075],{"className":1074},[108,151],[25,1076,131],{"className":1077},[108],[859,1079,1080,50,1083,28],{},[20,1081,1082],{},"Level of Bridge Soffit:",[25,1084,1086,1117],{"className":1085},[68],[25,1087,1089],{"className":1088},[72],[74,1090,1091],{"xmlns":76},[78,1092,1093,1114],{},[81,1094,1095,1097,1099,1101,1103,1105,1107,1109,1112],{},[125,1096,876],{},[211,1098,219],{},[211,1100,223],{"stretchy":222},[211,1102,219],{},[125,1104,961],{},[211,1106,229],{"stretchy":222},[211,1108,213],{},[125,1110,1111],{},"229.547",[129,1113,131],{},[88,1115,1116],{"encoding":90},"224.981 - (-4.566) = 229.547\\text{ m}",[25,1118,1120,1138,1165],{"className":1119,"ariaHidden":95},[94],[25,1121,1123,1126,1129,1132,1135],{"className":1122},[99],[25,1124],{"className":1125,"style":374},[103],[25,1127,876],{"className":1128},[108],[25,1130],{"className":1131,"style":277},[252],[25,1133,219],{"className":1134},[281],[25,1136],{"className":1137,"style":277},[252],[25,1139,1141,1144,1147,1150,1153,1156,1159,1162],{"className":1140},[99],[25,1142],{"className":1143,"style":291},[103],[25,1145,223],{"className":1146},[295],[25,1148,219],{"className":1149},[108],[25,1151,961],{"className":1152},[108],[25,1154,229],{"className":1155},[305],[25,1157],{"className":1158,"style":253},[252],[25,1160,213],{"className":1161},[257],[25,1163],{"className":1164,"style":253},[252],[25,1166,1168,1171,1174],{"className":1167},[99],[25,1169],{"className":1170,"style":144},[103],[25,1172,1111],{"className":1173},[108],[25,1175,1177],{"className":1176},[108,151],[25,1178,131],{"className":1179},[108],[859,1181,1182,50,1185,28],{},[20,1183,1184],{},"Vertical Clearance:",[25,1186,1188,1213],{"className":1187},[68],[25,1189,1191],{"className":1190},[72],[74,1192,1193],{"xmlns":76},[78,1194,1195,1210],{},[81,1196,1197,1199,1201,1203,1205,1208],{},[125,1198,1111],{},[211,1200,219],{},[125,1202,1018],{},[211,1204,213],{},[125,1206,1207],{},"5.547",[129,1209,131],{},[88,1211,1212],{"encoding":90},"229.547 - 224.000 = 5.547\\text{ m}",[25,1214,1216,1234,1252],{"className":1215,"ariaHidden":95},[94],[25,1217,1219,1222,1225,1228,1231],{"className":1218},[99],[25,1220],{"className":1221,"style":374},[103],[25,1223,1111],{"className":1224},[108],[25,1226],{"className":1227,"style":277},[252],[25,1229,219],{"className":1230},[281],[25,1232],{"className":1233,"style":277},[252],[25,1235,1237,1240,1243,1246,1249],{"className":1236},[99],[25,1238],{"className":1239,"style":144},[103],[25,1241,1018],{"className":1242},[108],[25,1244],{"className":1245,"style":253},[252],[25,1247,213],{"className":1248},[257],[25,1250],{"className":1251,"style":253},[252],[25,1253,1255,1258,1261],{"className":1254},[99],[25,1256],{"className":1257,"style":144},[103],[25,1259,1207],{"className":1260},[108],[25,1262,1264],{"className":1263},[108,151],[25,1265,131],{"className":1266},[108],[11,1268,1270],{"id":1269},"formula-breakdown-arithmetical-checks","Formula Breakdown: Arithmetical Checks",[16,1272,1273,1274,1462,1463,50,1676,28],{},"In the HPC method, the standard check for Intermediate Sights (IS) must be adjusted for inverted sights:\n",[25,1275,1277,1333],{"className":1276},[68],[25,1278,1280],{"className":1279},[72],[74,1281,1282],{"xmlns":76},[78,1283,1284,1330],{},[81,1285,1286,1289,1292,1294,1297,1299,1301,1303,1306,1309,1311,1314,1316,1318,1320,1323,1325,1328],{},[211,1287,1288],{},"∑",[129,1290,1291],{},"RL (except 1st)",[211,1293,213],{},[211,1295,1296],{"stretchy":222},"[",[211,1298,1288],{},[211,1300,223],{"stretchy":222},[129,1302,216],{},[211,1304,1305],{},"×",[84,1307,1308],{},"n",[211,1310,229],{"stretchy":222},[211,1312,1313],{"stretchy":222},"]",[211,1315,219],{},[211,1317,1288],{},[211,1319,223],{"stretchy":222},[129,1321,1322],{},"IS",[211,1324,696],{},[129,1326,1327],{},"FS",[211,1329,229],{"stretchy":222},[88,1331,1332],{"encoding":90},"\\sum \\text{RL (except 1st)} = [\\sum (\\text{HPC} \\times n)] - \\sum (\\text{IS} + \\text{FS})",[25,1334,1336,1368,1398,1420,1447],{"className":1335,"ariaHidden":95},[94],[25,1337,1339,1342,1349,1353,1359,1362,1365],{"className":1338},[99],[25,1340],{"className":1341,"style":291},[103],[25,1343,1288],{"className":1344,"style":1348},[1345,1346,1347],"mop","op-symbol","small-op","position:relative;top:0em;",[25,1350],{"className":1351,"style":1352},[252],"margin-right:0.1667em;",[25,1354,1356],{"className":1355},[108,151],[25,1357,1291],{"className":1358},[108],[25,1360],{"className":1361,"style":253},[252],[25,1363,213],{"className":1364},[257],[25,1366],{"className":1367,"style":253},[252],[25,1369,1371,1374,1377,1380,1383,1389,1392,1395],{"className":1370},[99],[25,1372],{"className":1373,"style":291},[103],[25,1375,1296],{"className":1376},[295],[25,1378,1288],{"className":1379,"style":1348},[1345,1346,1347],[25,1381,223],{"className":1382},[295],[25,1384,1386],{"className":1385},[108,151],[25,1387,216],{"className":1388},[108],[25,1390],{"className":1391,"style":277},[252],[25,1393,1305],{"className":1394},[281],[25,1396],{"className":1397,"style":277},[252],[25,1399,1401,1404,1407,1411,1414,1417],{"className":1400},[99],[25,1402],{"className":1403,"style":291},[103],[25,1405,1308],{"className":1406},[108,109],[25,1408,1410],{"className":1409},[305],")]",[25,1412],{"className":1413,"style":277},[252],[25,1415,219],{"className":1416},[281],[25,1418],{"className":1419,"style":277},[252],[25,1421,1423,1426,1429,1432,1438,1441,1444],{"className":1422},[99],[25,1424],{"className":1425,"style":291},[103],[25,1427,1288],{"className":1428,"style":1348},[1345,1346,1347],[25,1430,223],{"className":1431},[295],[25,1433,1435],{"className":1434},[108,151],[25,1436,1322],{"className":1437},[108],[25,1439],{"className":1440,"style":277},[252],[25,1442,696],{"className":1443},[281],[25,1445],{"className":1446,"style":277},[252],[25,1448,1450,1453,1459],{"className":1449},[99],[25,1451],{"className":1452,"style":291},[103],[25,1454,1456],{"className":1455},[108,151],[25,1457,1327],{"className":1458},[108],[25,1460,229],{"className":1461},[305],"\nWhen performing this sum, use the actual negative values for the IS entries. For example:\n",[25,1464,1466,1530],{"className":1465},[68],[25,1467,1469],{"className":1468},[72],[74,1470,1471],{"xmlns":76},[78,1472,1473,1527],{},[81,1474,1475,1478,1480,1482,1484,1486,1488,1491,1493,1495,1498,1501,1503,1505,1507,1509,1511,1514,1516,1518,1521,1523,1525],{},[125,1476,1477],{},"362.0",[211,1479,213],{},[211,1481,1296],{"stretchy":222},[211,1483,223],{"stretchy":222},[125,1485,170],{},[211,1487,1305],{},[125,1489,1490],{},"3",[211,1492,229],{"stretchy":222},[211,1494,696],{},[211,1496,1497],{},"…",[129,1499,1500],{}," ",[211,1502,1313],{"stretchy":222},[211,1504,219],{},[211,1506,1296],{"stretchy":222},[211,1508,223],{"stretchy":222},[211,1510,219],{},[125,1512,1513],{},"7.0",[211,1515,229],{"stretchy":222},[211,1517,696],{},[125,1519,1520],{},"2.5",[211,1522,1313],{"stretchy":222},[211,1524,213],{},[125,1526,1477],{},[88,1528,1529],{"encoding":90},"362.0 = [ (62.0 \\times 3) + \\dots ] - [ (-7.0) + 2.5 ] = 362.0",[25,1531,1533,1551,1573,1594,1619,1646,1667],{"className":1532,"ariaHidden":95},[94],[25,1534,1536,1539,1542,1545,1548],{"className":1535},[99],[25,1537],{"className":1538,"style":144},[103],[25,1540,1477],{"className":1541},[108],[25,1543],{"className":1544,"style":253},[252],[25,1546,213],{"className":1547},[257],[25,1549],{"className":1550,"style":253},[252],[25,1552,1554,1557,1561,1564,1567,1570],{"className":1553},[99],[25,1555],{"className":1556,"style":291},[103],[25,1558,1560],{"className":1559},[295],"[(",[25,1562,170],{"className":1563},[108],[25,1565],{"className":1566,"style":277},[252],[25,1568,1305],{"className":1569},[281],[25,1571],{"className":1572,"style":277},[252],[25,1574,1576,1579,1582,1585,1588,1591],{"className":1575},[99],[25,1577],{"className":1578,"style":291},[103],[25,1580,1490],{"className":1581},[108],[25,1583,229],{"className":1584},[305],[25,1586],{"className":1587,"style":277},[252],[25,1589,696],{"className":1590},[281],[25,1592],{"className":1593,"style":277},[252],[25,1595,1597,1600,1604,1607,1610,1613,1616],{"className":1596},[99],[25,1598],{"className":1599,"style":291},[103],[25,1601,1497],{"className":1602},[1603],"minner",[25,1605],{"className":1606,"style":1352},[252],[25,1608,1313],{"className":1609},[305],[25,1611],{"className":1612,"style":277},[252],[25,1614,219],{"className":1615},[281],[25,1617],{"className":1618,"style":277},[252],[25,1620,1622,1625,1628,1631,1634,1637,1640,1643],{"className":1621},[99],[25,1623],{"className":1624,"style":291},[103],[25,1626,1560],{"className":1627},[295],[25,1629,219],{"className":1630},[108],[25,1632,1513],{"className":1633},[108],[25,1635,229],{"className":1636},[305],[25,1638],{"className":1639,"style":277},[252],[25,1641,696],{"className":1642},[281],[25,1644],{"className":1645,"style":277},[252],[25,1647,1649,1652,1655,1658,1661,1664],{"className":1648},[99],[25,1650],{"className":1651,"style":291},[103],[25,1653,1520],{"className":1654},[108],[25,1656,1313],{"className":1657},[305],[25,1659],{"className":1660,"style":253},[252],[25,1662,213],{"className":1663},[257],[25,1665],{"className":1666,"style":253},[252],[25,1668,1670,1673],{"className":1669},[99],[25,1671],{"className":1672,"style":144},[103],[25,1674,1477],{"className":1675},[108],[25,1677,795],{},[11,1679,1681],{"id":1680},"practical-tips","Practical Tips",[856,1683,1684,1693,1699],{},[859,1685,1686,1689,1690,28],{},[20,1687,1688],{},"Inverted Boning Rods:"," In tunnel work, gradients can be controlled using inverted boning rods suspended from the roof ",[25,1691,1692],{},"45",[859,1694,1695,1698],{},[20,1696,1697],{},"Staff Stability:"," Ensure the staff is firmly pressed against the structure. Any gap between the base of the staff and the soffit will result in an incorrectly high level (too much clearance).",[859,1700,1701,1704,1705,28],{},[20,1702,1703],{},"Digital Levels:"," Modern digital levels often have an \"Invert\" program that automatically handles the sign conversion ",[25,1706,1707],{},"46",[11,1709,1711],{"id":1710},"common-mistakes","Common Mistakes",[856,1713,1714,1720],{},[859,1715,1716,1719],{},[20,1717,1718],{},"Mixing Signs:"," Forgetting the negative sign in the booking stage is the most common cause of massive errors (often equal to twice the staff reading).",[859,1721,1722,1725,1726,1765,1766,28],{},[20,1723,1724],{},"Staff Graduation Joint:"," If using a telescopic staff, ensure the sections are fully locked. A small gap at a joint (e.g., ",[25,1727,1729,1747],{"className":1728},[68],[25,1730,1732],{"className":1731},[72],[74,1733,1734],{"xmlns":76},[78,1735,1736,1744],{},[81,1737,1738,1741],{},[125,1739,1740],{},"12",[129,1742,1743],{}," mm",[88,1745,1746],{"encoding":90},"12\\text{ mm}",[25,1748,1750],{"className":1749,"ariaHidden":95},[94],[25,1751,1753,1756,1759],{"className":1752},[99],[25,1754],{"className":1755,"style":144},[103],[25,1757,1740],{"className":1758},[108],[25,1760,1762],{"className":1761},[108,151],[25,1763,1743],{"className":1764},[108],") will ruin the level ",[25,1767,1768],{},"47",[11,1770,1772],{"id":1771},"faq","FAQ",[1774,1775,1776,1785,1793],"accordion",{},[1777,1778,1780],"accordion-item",{"label":1779},"Can I use inverted sights with a digital level?",[16,1781,1782,1783,28],{},"Yes. Most digital levels include a setting to 'Invert' the staff reading, allowing for automatic data reduction ",[25,1784,1707],{},[1777,1786,1788],{"label":1787},"Is the Rise and Fall method better for inverted sights?",[16,1789,1790,1791,28],{},"The Rise and Fall method is recommended because it provides a complete arithmetical check on every observation, whereas the HPC method has a more cumbersome check for intermediate sights ",[25,1792,795],{},[1777,1794,1796],{"label":1795},"What if the staff is not held vertical?",[16,1797,1798,1799,1873,1874,1917,1918,28],{},"If the staff is leaning (e.g., at ",[25,1800,1802,1823],{"className":1801},[68],[25,1803,1805],{"className":1804},[72],[74,1806,1807],{"xmlns":76},[78,1808,1809,1820],{},[81,1810,1811],{},[1812,1813,1814,1817],"msup",{},[125,1815,1816],{},"5",[211,1818,1819],{},"∘",[88,1821,1822],{"encoding":90},"5^\\circ",[25,1824,1826],{"className":1825,"ariaHidden":95},[94],[25,1827,1829,1833],{"className":1828},[99],[25,1830],{"className":1831,"style":1832},[103],"height:0.6741em;",[25,1834,1836,1839],{"className":1835},[108],[25,1837,1816],{"className":1838},[108],[25,1840,1843],{"className":1841},[1842],"msupsub",[25,1844,1847],{"className":1845},[1846],"vlist-t",[25,1848,1851],{"className":1849},[1850],"vlist-r",[25,1852,1855],{"className":1853,"style":1832},[1854],"vlist",[25,1856,1858,1863],{"style":1857},"top:-3.063em;margin-right:0.05em;",[25,1859],{"className":1860,"style":1862},[1861],"pstrut","height:2.7em;",[25,1864,1870],{"className":1865},[1866,1867,1868,1869],"sizing","reset-size6","size3","mtight",[25,1871,1819],{"className":1872},[281,1869],"), the reading must be corrected by multiplying by ",[25,1875,1877,1898],{"className":1876},[68],[25,1878,1880],{"className":1879},[72],[74,1881,1882],{"xmlns":76},[78,1883,1884,1895],{},[81,1885,1886,1889,1892],{},[84,1887,1888],{},"cos",[211,1890,1891],{},"⁡",[84,1893,1894],{},"θ",[88,1896,1897],{"encoding":90},"\\cos \\theta",[25,1899,1901],{"className":1900,"ariaHidden":95},[94],[25,1902,1904,1907,1910,1913],{"className":1903},[99],[25,1905],{"className":1906,"style":242},[103],[25,1908,1888],{"className":1909},[1345],[25,1911],{"className":1912,"style":1352},[252],[25,1914,1894],{"className":1915,"style":1916},[108,109],"margin-right:0.0278em;",". An inclined staff always produces a reading that is too high ",[25,1919,1920],{},"41",[11,1922,1924],{"id":1923},"conclusion","Conclusion",[16,1926,1927],{},"Inverted sights are a simple yet powerful modification of the standard levelling procedure. By treating overhead readings as negative quantities, the surveyor can seamlessly integrate clearance and structural elevations into any site control network.",[11,1929,1931],{"id":1930},"references","References",[16,1933,1934,1935,1939],{},"Schofield, W. (2001). ",[1936,1937,1938],"em",{},"Engineering Surveying",". 5th ed. Butterworth-Heinemann.",{"title":1941,"searchDepth":1942,"depth":1942,"links":1943},"",2,[1944,1945,1946,1947,1952,1958,1959,1960,1961,1962,1963,1964],{"id":13,"depth":1942,"text":14},{"id":31,"depth":1942,"text":32},{"id":42,"depth":1942,"text":43},{"id":55,"depth":1942,"text":56,"children":1948},[1949,1951],{"id":60,"depth":1950,"text":61},3,{"id":433,"depth":1950,"text":434},{"id":798,"depth":1942,"text":799,"children":1953},[1954,1955,1956,1957],{"id":805,"depth":1950,"text":806},{"id":814,"depth":1950,"text":815},{"id":823,"depth":1950,"text":824},{"id":835,"depth":1950,"text":836},{"id":844,"depth":1942,"text":845},{"id":1269,"depth":1942,"text":1270},{"id":1680,"depth":1942,"text":1681},{"id":1710,"depth":1942,"text":1711},{"id":1771,"depth":1942,"text":1772},{"id":1923,"depth":1942,"text":1924},{"id":1930,"depth":1942,"text":1931},"Vertical Control","A technical guide to performing precise levelling on the underside of structures, tunnels, and bridges using inverted staff techniques.","md","\u002Fimages\u002Finverted-sights.jpg",{"authorCredentials":1970,"commentCount":1971,"tags":1972,"relatedTools":1977,"relatedArticles":1981,"sources":1984},"LS",0,[1973,22,1974,1975,1976],"Levelling","Tunnels","Bridges","Construction",[1978,1979,1980],"Levelling Staff","Automatic Level","Digital Level",[1982,1983],"precise-levelling-techniques","road-vertical-curves",[1985],{"title":1986,"type":1987,"note":1988},"Engineering Surveying (Fifth Edition)","Book","Primary source for inverted sight booking and arithmetic checks.",true,"\u002Fblog\u002Finverted-sights-underground-and-overhead-levelling","2024-04-03",15,{"title":5,"description":1966},{"loc":1990},"blog\u002F15.inverted-sights-underground-and-overhead-levelling","7IwqHIg0gTVOXf3d_kyrkooFKZhRykrytAS6h3Ek3G4",[1998,2003],{"title":1999,"path":2000,"stem":2001,"description":2002,"children":-1},"Scale Factors & MSL Reduction: Correcting Grid to Ground","\u002Fblog\u002Fscale-factors-and-distance-reduction","blog\u002F14.scale-factors-and-distance-reduction","A technical guide to reducing measured distances to the ellipsoid and applying scale factors for National Grid consistency.",{"title":2004,"path":2005,"stem":2006,"description":2007,"children":-1},"Weighted Observations: Using Statistical Reliability to Find the MPV","\u002Fblog\u002Fweighted-observations-mpv","blog\u002F16.weighted-observations-mpv","A technical guide to applying weights to surveying measurements to determine the Most Probable Value (MPV) and assess indices of precision.",1783851950494]