Local Attraction and Traverse 5 4 Error in

Local Attraction and Traverse

5. 4 Error in compass survey (Local attraction & observational error) Local attraction is the influence that prevents magnetic needle pointing to magnetic north pole Unavoidable substance that affect are Ø Ø Magnetic ore Underground iron pipes High voltage transmission line Electric pole etc. Influence caused by avoidable magnetic substance doesn’t come under local attraction such as instrument, watch wrist, key etc 2

5. 4 Local attractions Let Station A be affected by local attraction Observed bearing of AB = θ 1 Computed angle B = 1800 + θ – ß would not be right. ß B θ 1 θ A Unit 5: Compass traversing & Traverse computation C 3

5. 4 Local attractions Detection of Local attraction Ø Ø By observing the both bearings of line (F. B. & B. B. ) and noting the difference (1800 in case of W. C. B. & equal magnitude in case of R. B. ) We confirm the local attraction only if the difference is not due to observational errors. If detected, that has to be eliminated Two methods of elimination Ø Ø First method Second method 4

5. 4 Local attractions First method Ø Ø Ø Difference of B. B. & F. B. of each lines of traverse is checked to not if they differ by correctly or not. The one having correct difference means that bearing measured in those stations are free from local attraction Correction are accordingly applied to rest of station. If none of the lines have correct difference between F. B. & B. B. , the one with minimum error is balanced and repeat the similar procedure. Diagram is good friend again to solve the numerical problem. Pls. go through the numerical examples of your text book. Unit 5: Compass traversing & Traverse computation 5

5. 4 Local attractions Second method Ø Ø Based on the fact that the interior angle measured on the affected station is right. All the interior angles are measured Check of interior angle – sum of interior angles = (2 n-4) right angle, where n is number of traverse side Errors are distributed and bearing of lines are calculated with the corrected angles from the lines with unaffected station. Pls. go through the numerical examples of your text book. 6

5. 5 Traverse, types, compass & chain traversing Traverse Ø Ø Ø A control survey that consists of series of established stations tied together by angle and distance Angles measured by compass/transits/ theodolites Distances measured by tape/EDM/Stadia/Subtense bar D e 1 E c 1 a 1 A Unit 5: Compass traversing & Traverse computation b 2 B b 1 C c 2 7

5. 5 Traverse, types, compass & chain traversing Use of traverse Ø Ø Locate details, topographic details Lay out engineering works Types of Traverse Ø Ø Open Traverse Closed Traverse B α A γ θ ß Φ C D E 8

5. 5 Types of traverse Open traverse Ø Ø Geometrically don’t close No geometric verification Measuring technique must be refined Use – route survey (road, irrigation, coast line etc. . ) B 250 R C 220 L A Unit 5: Compass traversing & Traverse computation 9

5. 5 Types of traverse Contd… Close traverse Ø Ø Geometrically close (begins and close at same point)-loop traverse Start from the points of known position and ends to the point of known position – may not geometrically close – connecting traverse Can be geometrically verified Use – boundary survey, lake survey, forest survey etc. . B α A θ ß E B γ C Φ D A 250 R D 220 L C Co-ordinate of A &D is already known 10

5. 5 Methods of traversing Ø Ø Chain traversing (Not chain surveying) Chain & compass traversing (Compass surveying) Transit tape traversing (Theodolite Surveying) Plane-table traversing (Plane Table Surveying) B cos. A = Aa 22 + Aa 12 - a 2 a 12 2×Aa 1 a 2 c 2 b 2 A b 1 a 1 c 1 D b 2 C c 2 Unit 5: Compass traversing & Traverse computation b 1 A B c 1 C 11

5. 5 Methods of traversing Contd… Chain & compass traversing (Free or loose needle method) Ø Ø Ø Bearing measured by compass & distance measured by tape/chain Bearing is measured independently at each station Not accurate as transit – tape traversing B len gth C A D F E 12

5. 5 Methods of traversing Contd… Transit tape traversing Ø Ø Ø Traversing can be done in many ways by transit or theodolite By observing bearing By observing interior angle By observing exterior angle By observing deflection angle Unit 5: Compass traversing & Traverse computation 13

5. 5 Methods of traversing Contd… By observing bearing B len gth C A D F E 14

5. 5 Methods of traversing Contd… By observing interior angle Ø Ø Ø Always rotate theodolite to clockwise direction as the graduation of cirle increaes to clockwise Progress of work in anticlockwise direction measures directly interior angle Bearing of one line must be measured if the traverse is to plot by coordinate method F E A D B Unit 5: Compass traversing & Traverse computation len gth C 15

5. 5 Methods of traversing Contd… By observing exterior angle Ø Ø Progress of work in clockwise direction measures directly exterior angle Bearing of one line must be measured if the traverse is to plot by coordinate method F len gth E A D B C 16

5. 5 Methods of traversing Contd… By observing deflection angle Ø Ø Angle made by survey line with prolongation of preceding line Should be recorded as right ( R ) or left ( L ) accordingly B 250 R A Unit 5: Compass traversing & Traverse computation C 220 L D 17

5. 5 Locating the details in traverse By observing angle and distance from one station By observing angles from two stations 18

5. 5 Locating the details in traverse By observing distance from one station and angle from one station By observing distances from two points on traverse line Unit 5: Compass traversing & Traverse computation 19

5. 5 Checks in traverse Checks in closed Traverse Ø Ø Errors in traverse is contributed by both angle and distance measurement Checks are available for angle measurement but There is no check for distance measurement For precise survey, distance is measured twice, reverse direction second time Unit 5: Compass traversing & Traverse computation 20

5. 5 Checks in traverse Contd… Checks for angular error are available Ø Ø Interior angle, sum of interior angles = (2 n-4) right angle, where n is number of traverse side Exterior angle, sum of exterior angles = (2 n+4) right angle, where n is number of traverse side B α A α γ θ ß Φ B C θ D E C A E D Φ ß Unit 5: Compass traversing & Traverse computation 21 γ

5. 5 Checks in traverse Contd… Ø Ø Deflection angle – algebric sum of the deflection angle should be 00 or 3600. Bearing – The fore bearing of the last line should be equal to its back bearing ± 1800 measured at the initial station. B B A C C θ A D ß should be = θ + Unit 5: Compass traversing & Traverse computation 1800 ß E 22

5. 5 Checks in traverse Contd… Checks in open traverse Ø Ø No direct check of angular measurement is available Indirect checks v v Measure the bearing of line AD from A and bearing of DA from D Take the bearing to prominent points P & Q from consecutive station and check in plotting. D E P C C C A E D A B Unit 5: Compass traversing & Traverse computation E B Q D 23

5. 6 Field work and field book Field work consists of following steps Steps Ø Ø Reconnaissance Marking and Fixing survey station First Compass traversing then only detailing Bearing measurement & distance measurement v Ø Bearing verification should be done if possible Details measurement v v Offsetting Bearing and distance Bearings from two points Bearing from one points and distance from other point Unit 5: Compass traversing & Traverse computation 24

Contd… 5. 6 Field work and field book Line Field book Ø Make a sketch of field with all details and traverse in large size w 1 B w 2 A C b 1 b 4 E b 2 b 3 D Unit 5: Compass traversing & Traverse computation Bearing Distance Remarks AB AE BA BC CB CD DC DE ED EA Line Bearing Distance Remarks Bw 1 Cw 2 Db 3 Eb 4 Eb 1 25

5. 7 Computation & plotting a traverse Methods of plotting a traverse Ø LATITUDE AXIS Ø Angle and distance method Coordinate method (0, 0) A (300. 000, 300. 000) B(295. 351, 429. 986) C (138. 080, 446. 580) E (74. 795, 49. 239) D (26. 879, 353. 448) DEPARTURE AXIS Unit 5: Compass traversing & Traverse computation 26

5. 7 Computation & plotting Contd… a traverse Angle and distance method Ø Ø Ø Suitable for small survey Inferior quality in terms of accuracy of plotting Different methods under this v v v By protractor By the tangent of angle By the chord of the angle Unit 5: Compass traversing & Traverse computation 27

5. 7 Computation & plotting Contd… a traverse By protractor Ø Ordinary protractor with minimum graduation 10’ or 15’ Unit 5: Compass traversing & Traverse computation 28

5. 7 Computation & plotting Contd… a traverse By the tangent of angle Ø Ø Trignometrical method Use the property of right angle triangle, perpendicular =base × tanθ D 0 0 600 A 6 an m ×t m 5 c 5 c cm D B P = b× tanθ A θ b B Unit 5: Compass traversing & Traverse computation 29

5. 7 Computation & plotting Contd… a traverse By the chord of the angle Ø Geometrical method of laying off an angle D (2× 5×sin 450/2)cm D B 450 5 c A m Chord r’ = 2 rsinθ/2 θ A Unit 5: Compass traversing & Traverse computation θ/2 rsinθ/2 B r 30

5. 7 Computation & plotting Contd… a traverse Coordinate method Survey station are plotted by their co-ordinates. Very accurate method of plotting Closing error is balanced prior to plotting-Biggest advantage Ø Ø Ø D D’ E’ E A’ B’ e’ A E C’ C D C A B B Unit 5: Compass traversing & Traverse computation 31

5. 7 Computation & plotting Contd… a traverse What is co-ordinates Ø Latitude Co-ordinate length parallel to meridian v +ve for northing, -ve for southing v Magnitude = length of line× cos(bearing angle) Departure IV v v Co-ordinate length perpendicular to meridian +ve for easting, -ve for westing v Magnitude = length of line× sin(bearing angle) v Unit 5: Compass traversing & Traverse computation θ ( +, -) l B I L = l×cosθ Ø D = l×sinθ (+, +) A III II (-, -) (-, +) 32

5. 7 Computation & plotting Contd… a traverse Consecutive co-ordinate Ø Ø Ø Co-ordinate of points with reference to preceding point Equals to latitude or departure of line joining the preceding point and point under consideration If length and bearing of line AB is l and θ, then consecutive co-ordinates (latitude, departure) is given by v v Latitude co-ordinate of point B = l×cos θ Departure co-ordinate of point B = l×sin θ B θ l A Unit 5: Compass traversing & Traverse computation 33

5. 7 Computation & plotting Contd… a traverse Total co-ordinate Ø Ø Co-ordinate of points with reference to common origin Equals to algebric sum of latitudes or departures of lines between the origin and the point The origin is chosen such that two reference axis pass through most westerly If A is assumed to be origin, total co-ordinates (latitude, departure) of point D is given by v v Latitude co-ordinate = (Latitude coordinate of A+ ∑latitude of AB, BC, CD) Departure co-ordinate = (Departure coordinate of A+ ∑Departure of AB, BC, CD) B C A D Unit 5: Compass traversing & Traverse computation 34

5. 7 Computation & plotting Contd… a traverse For a traverse to be closed Algebric sum of latitude and departure should be zero. B Dep. AB (-) Lat. BC(-) Dep. BC (-) Lat. DA(+) A Dep. CD Unit 5: Compass traversing & Traverse computation Dep. DA (+) Lat. CD(+) D C Lat. AB(+) Ø 35

Ø A A’ D C Dep. CD Lat. DA’ Ø Both angle & distance Traverse never close Error of closure can be computed mathematically B Dep. DA’ Lat. CD Ø Dep. AB Lat. BC Real fact is that there is always error Dep. BC Lat. AB 5. 7 Computation & plotting Contd… a traverse A Closing Error (A’A) =√(∑Lat 2+ ∑dep 2 ) Bearing of A’A = tan-1 ∑dep/∑lat Unit 5: Compass traversing & Traverse computation θ A’ ∑lat ∑dep 36

5. 7 Computation & plotting Contd… a traverse Error of closure is used to compute the accuracy ratio Ø Ø Ø Accuracy ratio = e/P, where P is perimeter of traverse This fraction is expressed so that numerator is 1 and denominator is rounded to closest of 100 units. This ratio determines the permissible value of error. S. N. Types of traverse Permissible value of total linear error of closure 4 5 Minor theodolite traverse for detailing Compass traverse 1 in 3, 000 1 in 300 to 1 in 600 Unit 5: Compass traversing & Traverse computation 37

5. 7 Computation & plotting Contd… a traverse What to do if the accuracy ratio is unsatisfactory than that required Ø Ø Ø Double check all computation Double check all field book entries Compute the bearing of error of closure Check any traverse leg with similar bearing (± 50) Remeasure the sides of traverse beginning with a course having a similar bearing to the error of closure Unit 5: Compass traversing & Traverse computation 38

5. 7 Computation & plotting Contd… a traverse Balancing the traverse (Traverse adjustment) Ø Applying the correction to latitude and departure so that algebric sum is zero Methods Ø Compass rule (Bowditch) v Ø Transit rule v Ø When both angle and distance are measured with same precision When angle are measured precisely than the length Graphical method Unit 5: Compass traversing & Traverse computation 39

5. 7 Computation & plotting Contd… a traverse Where Clat & Cdep are correction to latitude and departure Bowditch rule Clat = ∑L × l Cdep = ∑D × l ∑l ∑l ∑L = Algebric sum of latitude ∑D = Algebric sum of departure l = length of traverse leg ∑l = Perimeter of traverse Where Clat & Cdep are correction to latitude and departure Transit rule Clat = ∑L × L LT ∑L = Algebric sum of latitude Cdep = ∑D × D ∑DT ∑D = Algebric sum of departure L = Latitude of traverse leg LT = Arithmetic sum of Latitude Unit 5: Compass traversing & Traverse computation 40

5. 7 Computation & plotting Contd… a traverse D’ Graphical rule Ø Ø Ø Used for rough survey Graphical version of bowditch rule without numerical computation Geometric closure should be satisfied before this. A Unit 5: Compass traversing & Traverse computation E’ C’ C D E A’ B’ e’ A b c B’ C’ d B a e e’ D’ E’ A’ 41

5. 7 Example of coordinate method Plot the following compass traverse by coordinate method in scale of 1 cm = 20 m. Line AB BC CD DE EA Length (m) 130. 00 158. 00 145. 00 308. 00 337. 00 Bearing S 880 E S 060 E S 400 W N 810 W N 480 E A B C E D Unit 5: Compass traversing & Traverse computation 42

5. 7 Example of coordinate method Step 1: calculate the latitude & departure coordinate length of survey line and value of closing error Line Bearing Length (m) Latitude co ordinate Departure Coordinate AB BC CD DE EA S 880 E S 060 E S 400 W N 810 W N 480 E 130. 00 158. 00 145. 00 308. 00 337. 00 -4. 537 -157. 134 -111. 076 48. 182 225. 497 129. 921 16. 515 -93. 204 -304. 208 250. 440 P = ∑l = 1078. 00 m ∑L= 0. 932 ∑D = - 0. 536 Closing Error (e) =√ (∑L 2+ ∑D 2 ) Closing Error (e) = 1. 675 m Unit 5: Compass traversing & Traverse computation 43

5. 7 Example of coordinate method Step 2: calculate the ratio of error of closure and total perimeter of traverse (Precision) Precision = e/P = 1. 675/1078 = 1/643 which is okey with reference to permissible value (1 in 300 to 1 in 600) Step 3: Calculate the correction for the latitude and departure by Bowditch’s method Clat(AB) = 0. 932× 130 1078 = - 0. 112 Unit 5: Compass traversing & Traverse computation Cdep(AB) = 0. 536 × 130 1078 = + 0. 065 44

5. 7 Example of coordinate method Step 4: Apply the correction worked out (balancing the traverse) Line Latitude coordinate Departure coordinate Correction Corrected to Latitude Departure co ordinate Coordinate AB -4. 537 BC -157. 134 CD -111. 076 DE 48. 182 EA 225. 497 129. 921 16. 515 -93. 204 -304. 208 250. 440 -0. 112 -0. 137 -0. 125 -0. 226 -0. 291 Unit 5: Compass traversing & Traverse computation +0. 065 +0. 079 +0. 072 +0. 153 +0. 168 - 4. 649 - 157. 271 - 111. 201 + 47. 916 +225. 206 +129. 986 + 16. 594 - 93. 132 - 304. 055 + 250. 608 ∑L= 0 ∑D = 0 45

5. 7 Example of coordinate method Step 5: Calculate the total coordinate of stations Line Corrected Latitude co ordinate Corrected Departure Coordinate Stations Total Latitude Coordinate Total Departure Coordinate B 300. 000 (assumed) 295. 351 300. 000 (assumed) 429. 986 C 138. 080 446. 580 D 26. 879 353. 448 E 74. 795 49. 239 A 300. 000 (CHECK) 300. 00(CHECK) A AB BC CD DE EA - 4. 649 - 157. 271 - 111. 201 + 47. 916 + 225. 206 +129. 986 + 16. 594 - 93. 132 -304. 055 + 250. 608 Unit 5: Compass traversing & Traverse computation 46

5. 7 Example of coordinate method LATITUDE AXIS A (300. 000, 300. 000) B(295. 351, 429. 986) C (138. 080, 446. 580) E (74. 795, 49. 239) (0, 0) D (26. 879, 353. 448) DEPARTURE AXIS Unit 5: Compass traversing & Traverse computation 47

Degree of accuracy in traversing The angular error of closure in traverse is expressed as equal to C√N Where C varies from 15” to 1’ and N is the number of angle measured S. N. Types of traverse Angular error of closure Total linear error of closure 1 2 3 First order traverse for horizontal control Second order traverse for horizontal control Third order traverse for survey of important boundaries Minor theodolite traverse for detailing Compass traverse 6”√N 15”√N 30”√N 1 in 25, 000 1 in 10, 000 1 in 5, 000 1’N 15’√N 1 in 3, 000 1 in 300 to 1 in 600 4 5 Unit 5: Compass traversing & Traverse computation 48

5. 7 Tutorial Plot the traverse by co-ordinate method, where observed data are as follows Interior angles A = 1010 24’ 12” B = 1490 13’ 12” C = 800 58’ 42” D = 1160 19’ 12” E = 920 04’ 42” B C D A E Side length AB = 401. 58’, BC = 382. 20’, CD = 368. 28’ DE = 579. 03’, EA = 350. 10’ Bearing of side AB = N 510 22’ 00” E (Allowable precision is 1/3000) Unit 5: Compass traversing & Traverse computation 49