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BASICS OF TRAVERSING

H.U. MINING ENGINEERING DEPARTMENT MAD 256 – SURVEYING. BASICS OF TRAVERSING. A closed traverse. A traverse between known points. What is a traverse?. A polygon of 2D (or 3D) vectors

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BASICS OF TRAVERSING

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  1. H.U. MINING ENGINEERING DEPARTMENT MAD 256 – SURVEYING BASICS OF TRAVERSING

  2. 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

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

  4. (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

  5. (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

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

  7. 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

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

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

  10. Calculate angular misclose

  11. Calculate adjusted angles

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

  13. Compute adjusted azimuths C 53o B 150o D 203o A E

  14. Compute adjusted azimuths C 233o 65o 168o B D 23o A E

  15. Compute adjusted azimuths C 53o 348o B 121o D 23o 227o A E

  16. Compute adjusted azimuths C 53o 168o B D 23o 47o A 106o 301o E

  17. Compute adjusted azimuths C 53o 168o B D 23o 227o 98o A 121o E

  18. (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

  19. Vector components

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

  21. 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

  22. 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

  23. 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

  24. Vector components (pre-adjustment)

  25. The adjustment components

  26. Adjusted vector components

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