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Published byHarvey Floyd Modified about 1 year ago

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

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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 ( ,d) (E,N) new (E,N) known

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

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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 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

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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

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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

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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)* o Misclose-5 o Adjustment-1 o

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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)* o 540 o Misclose-5 o Adjustment-1 o

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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

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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

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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

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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

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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

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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

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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 LineAzimuthDistance EE NN AB23 o BC53 o CD168 o DE227 o EA301 o (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) (0.07, -0.05) Convert to polar ( ,d) = o (2 nd 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 : 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

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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 EE NNdEdEdNdN E adj N adj ABAB BC CD DE EA Misc(0.07)(-0.05)

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The adjustment components Side EE NNdEdEdNdN E adj N adj ABAB BC CD DE EA Misc(0.07)(-0.05)(0.070)(-0.050)

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Adjusted vector components Side EE NNdEdEdNdN E adj N adj AB BC CD DE EA Misc(0.07)(-0.05) (0.000)

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