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Traverse Calculations and Coordinate Systems

Geology and Surveying 70380 (Part B - Surveying). Traverse Calculations and Coordinate Systems. Objectives. Calculate rectangular coordinates from bearings and distances Calculate bearing and distance between points with known rectangular coordinates

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Traverse Calculations and Coordinate Systems

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  1. Geology and Surveying 70380 (Part B - Surveying) Traverse Calculations and Coordinate Systems

  2. Objectives • Calculate rectangular coordinates from bearings and distances • Calculate bearing and distance between points with known rectangular coordinates • Calculate misclose bearing and distance in a traverse figure • Adjust field traverse data to match existing plan information

  3. r N q E Polar and Rectangular Coordinates N Origin

  4. Eastings and Northings N Departure = DE r DN Latitude = DN q Origin DE

  5. Latitudes and Departures DE = E2 – E1DN = N2 – N1 = l Sinq = l Cosq N 2 Latitude (L) = DN DN q r 1 DE Origin Departure (D) = DE

  6. Brg C A T S Brg = 180° - q Bearings and Distances From 1 to 2 DE = E2 – E1DN = N2 – N1 = l Sinq = l Cosq N 1 l DN q 2 DE

  7. N N +DE Bearing = 45° +DN q -DN Bearing = 135° q N +DE N C A q -DE Bearing 315° +DN T S -DE Bearing = 225° -DN q Quadrant Calculations

  8. Example 1 E 600.000 N 1000.000 From 1 to 2 DE = 649.222 – 600.000 = 49.222 DN = 901.899 – 1000.000 = -98.101 N Brg l DN q 2 E 649.222 N 901.899 DE Bearing 1  2 = 180° - 26°38’42” = 153°21’18”

  9. Coordinate Calculations

  10. DN DE Computation of Closes 2 3 1 Closed Traverse 5

  11. Coordinates N Bearing 1  2 = 35°00’00” Distance (l) = 164.385 2 DN = Latitude (L) l q 1 DE = Departure (D) DE = D = l Sinq = 164.385 Sin35° = +94.287 DN = L = l Cosq = 164.385 Cos35° = +134.656

  12. 35°00’00” 164.385 +94.287 +134.656 89°00’00” 125.816 +125.797 +2.196 135°00’00” 247.503 +175.011 -175.011 224°00’00” 207.617 -144.223 -149.347 335°00’00” 137.834 -58.251 +124.920 288°00’00” 202.534 -192.621 +62.586 S = 0.000 0.000 This traverse has a zero misclose Example Traverse Calcs q l D L

  13. Example with Misclose

  14. Example with Misclose

  15. 94.287 134.656 220.084 136.852 395.095 -38.159 250.872 -187.506 192.621 -62.586 Coordinates from Traverse Line q l L (DN) D (DE) Easting Northing Stn 0 0 1 E2 = E1 + DE N2 = N1 + DN 1  2 35°00’00” 164.385 +134.656 +94.287 2 2  3 89°00’00” 125.816 +2.196 +125.797 3 3  4 135°00’00” 247.503 -175.011 +175.011 4 4  5 224°00’00” 207.617 -149.347 -144.223 5 5  6 335°00’00” 137.834 +124.920 -58.251 6 6  1 288°00’00” 202.534 +62.586 -192.621 0 0 1 S = 0.000 0.000 E5 = E4 + DE N5 = N4 + DN E3 = E2 + DE N3 = N2 + DN E6 = E5 + DE N6 = N5 + DN E4 = E3 + DE N4 = N3 + DN E1 = E6 + DE N1 = N6 + DN

  16. Practical Application See example in study book

  17. Summary We have seen how to: • Calculate rectangular coordinates from bearings and distances • Calculate bearing and distance between points with known rectangular coordinates • Calculate misclose bearing and distance in a traverse figure • Adjust field traverse data to match existing plan information

  18. Self Study • Read Module 20 • Do self assessment Questions

  19. Questions?

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