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

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Presentation on theme: "BASICS OF TRAVERSING H.U. MINING ENGINEERING DEPARTMENT MAD 256 – SURVEYING."— Presentation transcript:

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

2 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 A closed traverse A traverse between known points

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

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

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

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

8 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

9 Calculate internal angles Point Foresight Azimuth Backsight Azimuth Internal Angle Adjusted Angle A21 o 118 o 97 o B56 o 205 o 149 o C168 o 232 o 64 o D232 o 352 o 120 o E303 o 48 o 105 o  =(n-2)*180 Misclose Adjustment At each point : Measure foresight azimuth Meaure backsight azimuth Calculate internal angle (back-fore) For example, at B : Azimuth to C = 56 o Azimuth to A = 205 o Angle at B = 205 o - 56 o = 149 o

10 Calculate angular misclose Point Foresight Azimuth Backsight Azimuth Internal Angle Adjusted Angle A21 o 118 o 97 o B56 o 205 o 149 o C168 o 232 o 64 o D232 o 352 o 120 o E303 o 48 o 105 o  =(n-2)*180 535 o Misclose-5 o Adjustment-1 o

11 Calculate adjusted angles Point Foresight Azimuth Backsight Azimuth Internal Angle Adjusted Angle A21 o 118 o 97 o 98 o B56 o 205 o 149 o 150 o C168 o 232 o 64 o 65 o D232 o 352 o 120 o 121 o E303 o 48 o 105 o 106 o  =(n-2)*180 535 o 540 o Misclose-5 o Adjustment-1 o

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

13 Compute adjusted azimuths Line Forward Azimuth Reverse Azimuth Internal Angle AB23 o 203 o 150 o BC53 o CD DE EA AB 203 o 53 o A B C D E 150 o

14 Compute adjusted azimuths Line Forward Azimuth Reverse Azimuth Internal Angle AB23 o 203 o 150 o BC53 o 233 o 65 o CD168 o DE EA AB 23 o 233 o 168 o A B C D E 65 o

15 Compute adjusted azimuths Line Forward Azimuth Reverse Azimuth Internal Angle AB23 o 203 o 150 o BC53 o 233 o 65 o CD168 o 348 o 121 o DE227 o EA AB 23 o 53 o 348 o 227 o A B C D E 121 o

16 Compute adjusted azimuths Line Forward Azimuth Reverse Azimuth Internal Angle AB23 o 203 o 150 o BC53 o 233 o 65 o CD168 o 348 o 121 o DE227 o 47 o 106 o EA -59 o 301 o AB 23 o 53 o 168 o 47 o 301 o A B C D E 106 o

17 Compute adjusted azimuths Line Forward Azimuth Reverse Azimuth Internal Angle AB23 o 203 o 150 o BC53 o 233 o 65 o CD168 o 348 o 121 o DE227 o 47 o 106 o EA301 o 121 o 98 o AB23 o (check) 23 o 53 o 168 o 227 o 121 o A B C D E 98 o

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 LineAzimuthDistance EE NN AB23 o 77.1930.1671.05 BC53 o 99.9279.8060.13 CD168 o 60.6312.61-59.31 DE227 o 129.76-94.90-88.50 EA301 o 32.20-27.6016.58  (399.70)(0.07)(-0.05)

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)  = -54.46 o (2 nd quadrant) = 125.53 o 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 :  E adj =  E misc * side length/total perimeter The adjustment to the northing component of any traverse side is given by :  N adj =  N misc * 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) Side EE NNdEdEdNdN  E adj  N adj ABAB30.1671.05 BC79.8060.13 CD12.61-59.31 DE-94.90-88.50 EA-27.6016.58 Misc(0.07)(-0.05)

25 The adjustment components Side EE NNdEdEdNdN  E adj  N adj ABAB30.1671.050.014-0.010 BC79.8060.130.016-0.012 CD12.61-59.310.011-0.008 DE-94.90-88.500.023-0.016 EA-27.6016.580.006-0.004 Misc(0.07)(-0.05)(0.070)(-0.050)

26 Adjusted vector components Side EE NNdEdEdNdN  E adj  N adj AB30.1671.050.014-0.01030.14671.060 BC79.8060.130.016-0.01279.78460.142 CD12.61-59.310.011-0.00812.599-59.302 DE-94.90-88.500.023-0.016-94.923-88.484 EA-27.6016.580.006-0.004-27.60616.584 Misc(0.07)(-0.05)0.070-0.050(0.000)


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