# BASICS OF TRAVERSING H.U. MINING ENGINEERING DEPARTMENT

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(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 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)

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

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

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 m Side BC m Side CD m Side DE m Side EA m Total perimeter m

Side E N dE dN 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)