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TOPIC 5

TOPIC 5. TRAVERSING. MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my. Stationing. Stations are dimensions measured along a baseline. The beginning point is described as 0+00. A point 100 ft(m) from the beginning is 1+00.

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TOPIC 5

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  1. TOPIC 5 TRAVERSING MS SITI KAMARIAH MD SA’AT LECTURER SCHOOL OF BIOPROCESS ENGINEERING sitikamariah@unimap.edu.my

  2. Stationing • Stations are dimensions measured along a baseline. • The beginning point is described as 0+00. • A point 100 ft(m) from the beginning is 1+00. • A point 565.98 ft(m) from the beginning is 5+65.98. • Points measured before the beginning station are 0-50, -1+00, etc.

  3. Baseline Stations and Offset Distances

  4. Overview • In this lecture we will cover : • Rectangular and polar coordinates • Definition of a traverse • Applications of traversing • Equipment and field procedures • Reduction and adjustment of data

  5. North Point B NB (EB,NB) N=NB-NA NA Point A E=EB-EA (EA,NA) East EB EA Rectangular coordinates

  6. North Point B  Point A East Polar coordinates d  ~ whole-circle bearing d ~ distance

  7. Whole circle bearings North 0o Bearing are measured clockwise from NORTH and must lie in the range 0o   360o 4th quadrant 1st quadrant West 270o East 90o 3rd quadrant 2nd quadrant South 180o

  8. d d N N   E E Coordinate conversions Polar to rectangular Rectangular to polar

  9. What is a traverse? • Control survey • A series of established stations tied together by angle and distance. • The angles are measured using theodolites/total station, while distances can be measured using total stations, steel tapes or EDM.

  10. A closed traverse A traverse between known points What is a traverse? • A polygon of 2D (or 3D) vectors • Sides are expressed as either polar coordinates (,d) or as rectangular coordinate differences (E,N) • A traverse must either close on itself • Or be measured between points with known rectangular coordinates

  11. Types of Traverses • Open Traverse using deflection angles. • Closed traverse using interior angles.

  12. Open Traverse

  13. Closed Traverse

  14. (E,N)known (E,N)known (,d) (,d) (,d) Applications of traversing • Establishing coordinates for new points (E,N)new (E,N)new

  15. (E,N)known (E,N)new (E,N)known (E,N)new (E,N)new (,d) (,d) (,d) (,d) (,d) (,d) (E,N)new (E,N)new Applications of traversing • These new points can then be used as a framework for mapping existing features

  16. (E,N)known (E,N)known (E,N)new (E,N)new Applications of traversing • They can also be used as a basis for setting out new work

  17. Equipment • Traversing requires : • An instrument to measure angles (theodolite) or bearings (magnetic compass) • An instrument to measure distances (EDM or tape)

  18. Computation of Latitudes and Departures • Latitude-north/south rectangular component of line (North +;South -) Latitude (ΔY) = distance(H) cos α • Departure-east/west rectangular component of line (East +;West -) Departure (ΔX) = distance(H) sin α Where: α = bearing or azimuth of the traverse course H = the horizontal distance of the traverse course

  19. Location of a Point

  20. Closure of Latitudes and Departures

  21. Latitude / Departure Computations

  22. Measurement sequence C 232o 168o 60.63 99.92 56o B 352o 205o D 232o 77.19 129.76 21o A 32.20 118o 303o 48o E

  23. Computation sequence • Calculate angular (bearing/azimuth) misclose • Adjust angular (bearing/azimuth) misclose • Calculate adjusted bearings • Reduce distances for slope etc… • Compute (E, N) for each traverse line • Calculate linear misclose • Calculate accuracy • Adjust linear misclose.

  24. Calculate internal angles • At each point : • Measure foresight bearing • Measure backsight bearing • Calculate internal angle (back-fore) • For example, at B : • Bearing to C = 56o • Bearing to A = 205o • Angle at B = 205o - 56o = 149o

  25. Calculate angular misclose

  26. Calculate adjusted angles

  27. Compute adjusted bearings • Adopt a starting bearing • Then, working clockwise around the traverse : • Calculate reverse bearing to backsight (forward bearing 180o) • Subtract (clockwise) internal adjusted angle • Gives bearing of foresight • For example (bearing of line BC) • Adopt bearing of AB 23o • Reverse bearing BA (=23o+180o) 203o • Internal adjusted angle at B 150o • Forward bearing BC (=203o-150o) 53o

  28. Compute adjusted bearings C 53o B 150o D 203o A E

  29. Compute adjusted bearings C 233o 65o 168o B D 23o A E

  30. Compute adjusted bearings C 53o 348o B 121o D 23o 227o A E

  31. Compute adjusted bearings C 53o 168o B D 23o 47o A 106o 301o E

  32. Compute adjusted bearings C 53o 168o B D 23o 227o 98o A 121o E

  33. (E,N) for each line • The rectangular components for each line are computed from the polar coordinates (,d) • Note that these formulae apply regardless of the quadrant so long as whole circle bearings are used

  34. Vector components

  35. Closure Error and Closure Correction

  36. Compass Rule – distributes the errors in lat/dep. C lat AB= AB Σ lat P C dep AB = AB Σ dep P Where: C lat AB = correction in latitude AB ∑ lat = error of closure in latitude AB = distance AB P = perimeter of traverse Where: C dep AB = correction in departure AB ∑ lat = error of closure in departure AB = distance AB P = perimeter of traverse

  37. Linear misclose & accuracy • Convert the rectangular misclose components to polar coordinates • Accuracy is given by Beware of quadrant when calculating  using tan-1

  38. N + + • positive okay • negative add 360o +  E +  • negative add 180o • positive add 180o   Quadrants and tan function

  39. For the example… • Misclose (E, N) • (0.07, -0.05) • Convert to polar (,d) •  = -54.46o (2nd quadrant) = 125.53o • d = 0.09 m • Accuracy • 1:(399.70 / 0.09) = 1:4441

  40. Bowditch adjustment • The adjustment to the easting component of any traverse side is given by : Eadj = Emisc * side length/total perimeter • The adjustment to the northing component of any traverse side is given by : Nadj = Nmisc * side length/total perimeter

  41. The example… • East misclose 0.07 m • North misclose –0.05 m • Side AB 77.19 m • Side BC 99.92 m • Side CD 60.63 m • Side DE 129.76 m • Side EA 32.20 m • Total perimeter 399.70 m

  42. Vector components (pre-adjustment)

  43. The adjustment components

  44. Adjusted vector components

  45. Summary of initial traverse computation • Balance the angle • Compute the bearing or azimuth • Compute the latitude and departure, the linear error of closure, and the precision ratio of the traverse

  46. THANK YOU

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