H U MINING ENGINEERING DEPARTMENT MAD 256 SURVEYING

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

What is a traverse? • A polygon of 2 D (or 3 D) 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 A closed traverse A traverse between known points

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

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

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

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

Measurement sequence C o 2 o 168 32 60. 63 o 205 o 352 B o 56 . 92 9 9 o 77. 19 2 23 21 o 9. 2 1 . 20 o 8 11 32 A 30 o o 3 E 48 76 D

Computation sequence 1. Calculate angular misclose 2. Adjust angular misclose 3. Calculate adjusted bearings 4. Reduce distances for slope etc… 5. Compute ( E, N) for each traverse line 6. Calculate linear misclose 7. Calculate accuracy 8. Adjust linear misclose

Calculate internal angles Point Foresight Backsight Azimuth Internal Angle A 21 o 118 o 97 o B 56 o 205 o 149 o C 168 o D 232 o E 303 o =(n-2)*180 Misclose Adjustment Adjusted Angle o o 232 64 At each point : • o. Measure foresight azimuth 352 120 o • Meaure backsight azimuth o • o Calculate 105 internal angle (back-fore) 48 For example, at B : • Azimuth to C = 56 o • Azimuth to A = 205 o • Angle at B = 205 o - 56 o = 149 o

Calculate angular misclose Point Foresight Backsight Azimuth Internal Angle A 21 o 118 o 97 o B 56 o 205 o 149 o C 168 o 232 o 64 o D 232 o 352 o 120 o E 303 o 48 o 105 o =(n-2)*180 535 o Misclose -5 o Adjustment -1 o Adjusted Angle

Calculate adjusted angles Point Foresight Backsight Azimuth Internal Angle Adjusted Angle A 21 o 118 o 97 o 98 o B 56 o 205 o 149 o 150 o C 168 o 232 o 64 o 65 o D 232 o 352 o 120 o 121 o E 303 o 48 o 105 o 106 o 535 o 540 o =(n-2)*180 Misclose -5 o Adjustment -1 o

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

Compute adjusted azimuths C o 53 B 203 o 150 o D Line Forward Azimuth Reverse Azimuth Internal Angle AB 23 o 203 o 150 o BC 53 o CD DE EA A E AB

Compute adjusted azimuths C o D 23 o Forward Azimuth Reverse Azimuth Internal Angle AB 23 o 203 o 150 o BC 53 o 233 o 65 o CD 168 o o B 65 o 168 2 33 Line DE EA A E AB

Compute adjusted azimuths C o Forward Azimuth Reverse Azimuth Internal Angle AB 23 o 203 o 150 o BC 53 o 233 o 65 o CD 168 o 348 o 121 o DE 227 o o 121 o 23 o B 348 53 Line o 7 22 D EA A E AB

Compute adjusted azimuths C o B 23 o D o 47 A 106 o o 1 30 E Forward Azimuth Reverse Azimuth Internal Angle AB 23 o 203 o 150 o BC 53 o 233 o 65 o CD 168 o 348 o 121 o DE 227 o 47 o 106 o o 168 53 Line EA AB -59 o 301 o

Compute adjusted azimuths C o B 23 o D o 98 o A o 1 12 E Forward Azimuth Reverse Azimuth Internal Angle AB 23 o 203 o 150 o BC 53 o 233 o 65 o CD 168 o 348 o 121 o DE 227 o 47 o 106 o EA 301 o 121 o 98 o AB 23 o (check) o 168 53 Line 7 22

( 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

Vector components Line Azimuth Distance E N AB 23 o 77. 19 30. 16 71. 05 BC 53 o 99. 92 79. 80 60. 13 CD 168 o 60. 63 12. 61 -59. 31 DE 227 o 129. 76 -94. 90 -88. 50 EA 301 o 32. 20 -27. 60 16. 58 (399. 70) (0. 07) (-0. 05)

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

For the example… • Misclose ( E, N) n (0. 07, -0. 05) • Convert to polar ( , d) n n = -54. 46 o (2 nd quadrant) = 125. 53 o d = 0. 09 m • Accuracy n 1: (399. 70 / 0. 09) = 1: 4441

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

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

Vector components Side E N AB 30. 16 71. 05 BC 79. 80 60. 13 CD 12. 61 -59. 31 DE -94. 90 -88. 50 EA -27. 60 16. 58 Misc (0. 07) (-0. 05) d E (pre-adjustment) d N Eadj Nadj

The adjustment components Side E N d E AB 30. 16 71. 05 0. 014 -0. 010 BC 79. 80 60. 13 0. 016 -0. 012 CD 12. 61 -59. 31 0. 011 -0. 008 DE -94. 90 -88. 50 0. 023 -0. 016 EA -27. 60 16. 58 0. 006 -0. 004 (-0. 05) (0. 070) (-0. 050) Misc (0. 07) d N Eadj Nadj

Adjusted vector components Side E N d E d N Eadj Nadj AB 30. 16 71. 05 0. 014 -0. 010 30. 146 71. 060 BC 79. 80 60. 13 0. 016 -0. 012 79. 784 60. 142 CD 12. 61 -59. 31 0. 011 -0. 008 12. 599 -59. 302 DE -94. 90 -88. 50 0. 023 -0. 016 -94. 923 -88. 484 EA -27. 60 16. 58 0. 006 -0. 004 -27. 606 16. 584 (-0. 05) 0. 070 -0. 050 Misc (0. 07) (0. 000)