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BASICS OF TRAVERSING H.U. MINING ENGINEERING DEPARTMENT
MAD 256 – SURVEYING BASICS OF TRAVERSING
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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
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Applications of traversing
Establishing coordinates for new points (E,N)known (,d) (,d) (,d) (E,N)new (E,N)new
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Applications of traversing
These new points can then be used as a framework for mapping existing features (E,N)new (E,N)known (E,N)new (E,N)new (E,N)new (,d) (,d)
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Applications of traversing
They can also be used as a basis for setting out new work (E,N)new (E,N)known
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Equipment Traversing requires :
An instrument to measure angles (theodolite) or bearings (magnetic compass) An instrument to measure distances (EDM or tape)
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Measurement sequence C B D A E 232o 168o 60.63 99.92 56o 352o 205o
77.19 129.76 21o A 118o 32.20 303o 48o E
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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
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Calculate internal angles
Point Foresight Azimuth Backsight Internal Angle Adjusted A 21o 118o 97o B 56o 205o 149o C 168o 232o 64o D 352o 120o E 303o 48o 105o =(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 = 56o Azimuth to A = 205o Angle at B = 205o - 56o = 149o
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Calculate angular misclose
Point Foresight Azimuth Backsight Internal Angle Adjusted A 21o 118o 97o B 56o 205o 149o C 168o 232o 64o D 352o 120o E 303o 48o 105o =(n-2)*180 535o Misclose -5o Adjustment -1o
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Calculate adjusted angles
Point Foresight Azimuth Backsight Internal Angle Adjusted A 21o 118o 97o 98o B 56o 205o 149o 150o C 168o 232o 64o 65o D 352o 120o 121o E 303o 48o 105o 106o =(n-2)*180 535o 540o Misclose -5o Adjustment -1o
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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
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Compute adjusted azimuths
Line Forward Azimuth Reverse Azimuth Internal Angle AB 23o 203o 150o BC 53o CD DE EA 53o B 150o D 203o A E
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Compute adjusted azimuths
Line Forward Azimuth Reverse Azimuth Internal Angle AB 23o 203o 150o BC 53o 233o 65o CD 168o DE EA 233o 65o 168o B D 23o A E
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Compute adjusted azimuths
Line Forward Azimuth Reverse Azimuth Internal Angle AB 23o 203o 150o BC 53o 233o 65o CD 168o 348o 121o DE 227o EA 53o 348o B 121o D 23o 227o A E
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Compute adjusted azimuths
Line Forward Azimuth Reverse Azimuth Internal Angle AB 23o 203o 150o BC 53o 233o 65o CD 168o 348o 121o DE 227o 47o 106o EA -59o 301o 53o 168o B D 23o 47o A 106o 301o E
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Compute adjusted azimuths
Line Forward Azimuth Reverse Azimuth Internal Angle AB 23o 203o 150o BC 53o 233o 65o CD 168o 348o 121o DE 227o 47o 106o EA 301o 98o 23o (check) 53o 168o B D 23o 227o 98o A 121o E
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(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
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Vector components Line Azimuth Distance E N AB 23o 77.19 30.16 71.05
BC 53o 99.92 79.80 60.13 CD 168o 60.63 12.61 -59.31 DE 227o 129.76 -94.90 -88.50 EA 301o 32.20 -27.60 16.58 (399.70) (0.07) (-0.05)
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Linear misclose & accuracy
Convert the rectangular misclose components to polar coordinates Accuracy is given by Beware of quadrant when calculating using tan-1
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For the example… Misclose (E, N) Convert to polar (,d) Accuracy
(0.07, -0.05) Convert to polar (,d) = o (2nd quadrant) = o d = 0.09 m Accuracy 1:( / 0.09) = 1:4441
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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
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The example… East misclose 0.07 m North misclose –0.05 m
Side AB m Side BC m Side CD m Side DE m Side EA m Total perimeter m
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Vector components (pre-adjustment)
Side E N dE dN Eadj Nadj 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)
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The adjustment components
Side E N dE dN Eadj Nadj 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 Misc (0.07) (-0.05) (0.070) (-0.050)
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Adjusted vector components
Side E N dE dN 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 DE -94.90 -88.50 0.023 -0.016 EA -27.60 16.58 0.006 -0.004 16.584 Misc (0.07) (-0.05) 0.070 -0.050 (0.000)
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