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Local Attraction and Traverse

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 Magnetic ore Underground iron pipes

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Local Attraction and Traverse

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  1. Local Attraction and Traverse

  2. 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 • 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

  3. 5.4 Local attractions • Let Station A be affected by local attraction • Observed bearing of AB = θ1 • Computed angle B = 1800 + θ – ß would not be right. ß B θ θ1 C A Unit 5: Compass traversing & Traverse computation

  4. 5.4 Local attractions • Detection of Local attraction • 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 • First method • Second method

  5. 5.4 Local attractions • First method • 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

  6. 5.4 Local attractions • Second method • 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 = (2n-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.

  7. e1 D E c1 C a1 c2 b2 A B b1 5.5 Traverse, types, compass & chain traversing • Traverse • 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 Unit 5: Compass traversing & Traverse computation

  8. B α γ C θ A Φ ß D E 5.5 Traverse, types, compass & chain traversing • Use of traverse • Locate details, topographic details • Lay out engineering works • Types of Traverse • Open Traverse • Closed Traverse

  9. 250 R B 220 L C A 5.5 Types of traverse • Open traverse • Geometrically don’t close • No geometric verification • Measuring technique must be refined • Use – route survey (road, irrigation, coast line etc..) Unit 5: Compass traversing & Traverse computation

  10. B α γ C θ 250 R A D B Φ 220 L C ß D A Co-ordinate of A &D is already known E 5.5 Types of traverse Contd… • Close traverse • 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..

  11. c2 b2 B B Aa22 + Aa12 - a2a12 c1 b1 cosA = C A 2×Aa2×Aa1 a2 A b1 a1 b2 C c1 D c2 5.5 Methods of traversing • Methods of traversing • Chain traversing (Not chain surveying) • Chain & compass traversing (Compass surveying) • Transit tape traversing (Theodolite Surveying) • Plane-table traversing (Plane Table Surveying) Unit 5: Compass traversing & Traverse computation

  12. B length C A D F E 5.5 Methods of traversing Contd… • Chain & compass traversing (Free or loose needle method) • Bearing measured by compass & distance measured by tape/chain • Bearing is measured independently at each station • Not accurate as transit – tape traversing

  13. 5.5 Methods of traversing Contd… • Transit tape traversing • 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

  14. B length C A D F E 5.5 Methods of traversing Contd… • By observing bearing

  15. F length E A D B C 5.5 Methods of traversing Contd… • By observing interior angle • Always rotate the 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 Unit 5: Compass traversing & Traverse computation

  16. F length E A D B C 5.5 Methods of traversing Contd… • By observing exterior angle • 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

  17. 250 R D B 220 L C A 5.5 Methods of traversing Contd… • By observing deflection angle • Angle made by survey line with prolongation of preceding line • Should be recorded as right ( R ) or left ( L ) accordingly Unit 5: Compass traversing & Traverse computation

  18. 5.5 Locating the details in traverse • By observing angle and distance from one station • By observing angles from two stations

  19. 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

  20. 5.5 Checks in traverse • Checks in closed Traverse • 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

  21. B α α γ B C γ θ C A θ A Φ ß D D E E Φ ß 5.5 Checks in traverse Contd… • Checks for angular error are available • Interior angle, sum of interior angles = (2n-4) right angle, where n is number of traverse side • Exterior angle, sum of exterior angles = (2n+4) right angle, where n is number of traverse side Unit 5: Compass traversing & Traverse computation

  22. B B C θ C A A D E ß 5.5 Checks in traverse Contd… • 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. ß should be = θ + 1800 Unit 5: Compass traversing & Traverse computation

  23. D E E D P C C C Q A B D A B 5.5 Checks in traverse Contd… • Checks in open traverse • No direct check of angular measurement is available • Indirect checks • 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. Unit 5: Compass traversing & Traverse computation E

  24. 5.6 Field work and field book • Field work consists of following steps • Steps • Reconnaissance • Marking and Fixing survey station • First Compass traversing then only detailing • Bearing measurement & distance measurement • Bearing verification should be done if possible • Details measurement • Offsetting • Bearing and distance • Bearings from two points • Bearing from one points and distance from other point Unit 5: Compass traversing & Traverse computation

  25. w1 B w2 C A b1 b2 b4 b3 D E Contd… 5.6 Field work and field book • Field book • Make a sketch of field with all details and traverse in large size Unit 5: Compass traversing & Traverse computation

  26. A (300.000, 300.000) B(295.351, 429.986) LATITUDE AXIS C (138.080, 446.580) E (74.795, 49.239) D (26.879, 353.448) (0,0) DEPARTURE AXIS 5.7 Computation & plotting a traverse • Methods of plotting a traverse • Angle and distance method • Coordinate method Unit 5: Compass traversing & Traverse computation

  27. 5.7 Computation & plotting a traverse Contd… • Angle and distance method • Suitable for small survey • Inferior quality in terms of accuracy of plotting • Different methods under this • By protractor • By the tangent of angle • By the chord of the angle Unit 5: Compass traversing & Traverse computation

  28. 5.7 Computation & plotting a traverse Contd… • By protractor • Ordinary protractor with minimum graduation 10’ or 15’ Unit 5: Compass traversing & Traverse computation

  29. D 5cm×tan600 cm A 600 5cm D B P = b× tanθ θ A B b 5.7 Computation & plotting a traverse Contd… • By the tangent of angle • Trignometrical method • Use the property of right angle triangle, perpendicular =base × tanθ Unit 5: Compass traversing & Traverse computation

  30. D (2×5×sin 450/2)cm D B 450 5cm A θ θ/2 rsinθ/2 θ/2 A B r 5.7 Computation & plotting a traverse Contd… • By the chord of the angle • Geometrical method of laying off an angle Chord r’ = 2rsinθ/2 Unit 5: Compass traversing & Traverse computation

  31. D’ D C C’ E E’ D C E B A’ A B’ e’ B A 5.7 Computation & plotting a traverse Contd… • Coordinate method • Survey station are plotted by their co-ordinates. • Very accurate method of plotting • Closing error is balanced prior to plotting-Biggest advantage Unit 5: Compass traversing & Traverse computation

  32. D = l×sinθ B IV θ I ( +,-) L = l×cosθ l A III II (-,-) (-, +) 5.7 Computation & plotting a traverse Contd… • What is co-ordinates • Latitude • Co-ordinate length parallel to meridian • +ve for northing, -ve for southing • Magnitude = length of line× cos(bearing angle) • Departure • Co-ordinate length perpendicular to meridian • +ve for easting, -ve for westing • Magnitude = length of line× sin(bearing angle) (+,+) Unit 5: Compass traversing & Traverse computation

  33. B θ l A 5.7 Computation & plotting a traverse Contd… • Consecutive co-ordinate • 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 • Latitude co-ordinate of point B = l×cos θ • Departure co-ordinate of point B = l×sin θ Unit 5: Compass traversing & Traverse computation

  34. B C A D 5.7 Computation & plotting a traverse Contd… • Total co-ordinate • 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 • Latitude co-ordinate = (Latitude coordinate of A+ ∑latitude of AB, BC, CD) • Departure co-ordinate = (Departure coordinate of A+ ∑Departure of AB, BC, CD) Unit 5: Compass traversing & Traverse computation

  35. B Dep. AB (-) Dep. BC (-) Lat. AB(+) A Lat. BC(-) Lat. DA(+) D Dep. DA (+) Dep. CD Lat. CD(+) C 5.7 Computation & plotting a traverse Contd… • For a traverse to be closed • Algebric sum of latitude and departure should be zero. Unit 5: Compass traversing & Traverse computation

  36. Dep. BC Dep. AB B Lat. AB A Lat. BC A’ Lat. DA’ D Dep. DA’ C Lat. CD Dep. CD A ∑lat θ A’ ∑dep 5.7 Computation & plotting a traverse Contd… • Real fact is that there is always error • Both angle & distance • Traverse never close • Error of closure can be computed mathematically Closing Error (A’A) =√(∑Lat2+ ∑dep2 ) Bearing of A’A = tan-1∑dep/∑lat Unit 5: Compass traversing & Traverse computation

  37. 5.7 Computation & plotting a traverse Contd… • Error of closure is used to compute the accuracy ratio • 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. Unit 5: Compass traversing & Traverse computation

  38. 5.7 Computation & plotting a traverse Contd… • What to do if the accuracy ratio is unsatisfactory than that required • 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

  39. 5.7 Computation & plotting a traverse Contd… • Balancing the traverse (Traverse adjustment) • Applying the correction to latitude and departure so that algebric sum is zero • Methods • Compass rule (Bowditch) • When both angle and distance are measured with same precision • Transit rule • When angle are measured precisely than the length • Graphical method Unit 5: Compass traversing & Traverse computation

  40. Clat Clat = = ∑L ∑L × × L l Cdep = ∑D × l LT ∑l ∑l Cdep = ∑D × D ∑DT 5.7 Computation & plotting a traverse Contd… Where Clat & Cdep are correction to latitude and departure ∑L = Algebric sum of latitude ∑D = Algebric sum of departure l = length of traverse leg ∑l = Perimeter of traverse • Bowditch rule Where Clat & Cdep are correction to latitude and departure ∑L = Algebric sum of latitude ∑D = Algebric sum of departure L = Latitude of traverse leg LT = Arithmetic sum of Latitude • Transit rule Unit 5: Compass traversing & Traverse computation

  41. a d e c b e’ A B’ C’ D’ E’ A’ 5.7 Computation & plotting a traverse Contd… • Graphical rule • Used for rough survey • Graphical version of bowditch rule without numerical computation • Geometric closure should be satisfied before this. D’ C’ E’ D C E A’ B’ e’ B A Unit 5: Compass traversing & Traverse computation

  42. A B C E D 5.7 Example of coordinate method • Plot the following compass traverse by coordinate method in scale of 1cm = 20 m. Line Length (m) Bearing AB 130.00 S 880 E BC 158.00 S 060 E CD 145.00 S 400 W DE 308.00 N 810 W EA 337.00 N 480 E Unit 5: Compass traversing & Traverse computation

  43. 5.7 Example of coordinate method • Step 1: calculate the latitude & departure coordinate length of survey line and value of closing error P = ∑l = 1078.00 m ∑L= 0.932 ∑D = - 0.536 Closing Error (e) =√ (∑L2+ ∑D2 ) Closing Error (e) = 1.675 m Unit 5: Compass traversing & Traverse computation

  44. Clat(AB) Cdep(AB) = 0.932 × 130 = 0.536 × 130 1078 1078 = - 0.112 = + 0.065 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 Unit 5: Compass traversing & Traverse computation

  45. ∑L= 0 ∑D = 0 5.7 Example of coordinate method • Step 4: Apply the correction worked out (balancing the traverse) Unit 5: Compass traversing & Traverse computation

  46. 5.7 Example of coordinate method • Step 5: Calculate the total coordinate of stations Unit 5: Compass traversing & Traverse computation

  47. 5.7 Example of coordinate method A (300.000, 300.000) B(295.351, 429.986) LATITUDE AXIS C (138.080, 446.580) E (74.795, 49.239) D (26.879, 353.448) (0,0) DEPARTURE AXIS Unit 5: Compass traversing & Traverse computation

  48. 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 Unit 5: Compass traversing & Traverse computation

  49. B C D A E 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” 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

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