Traversing and Computation
Traversing and Computation
This domain tests traverse layout, bearings, latitudes and departures, closing error, adjustment, and area computation. It rewards careful sign conventions more than memorised shortcuts.
Core rules
- Latitude = L cos θ; departure = L sin θ. North and east are positive; south and west are negative. For a closed traverse, Σlatitude = 0 and Σdeparture = 0 if there is no error.
- Closing error e = sqrt((ΣL)² + (ΣD)²). Its bearing is found from tan θ = ΣD / ΣL, with the quadrant fixed by the signs.
- Bowditch (compass) rule distributes the error in proportion to line length: correction to latitude for a line = -ΣL × (line length / perimeter). Transit rule distributes in proportion to the absolute latitude or departure.
- Coordinates: X (easting) changes by departure, Y (northing) changes by latitude. Area by coordinates uses the shoelace formula: 2A = |Σ(X_i Y_{i+1} - X_{i+1} Y_i)|.
- For a closed polygon, a misclosure within the permissible limit is adjusted; a large misclosure means a field blunder, not a small correction.
Worked example
A three-line traverse has measured legs: AB 100.00 m at 0°, BC 100.00 m at 90°, CA 141.00 m at 225°. Sum latitudes: 100 + 0 - 99.70 = +0.30 m. Sum departures: 0 + 100 - 99.70 = +0.30 m. Closing error = sqrt(0.30² + 0.30²) = 0.424 m. The error bearing is NE (both sums positive), about 45°. The perimeter is 341.00 m; Bowditch corrections would be applied proportionally to each leg.
Traps
Do not use sin for latitude and cos for departure. Do not adjust a traverse before checking for a gross error. Do not ignore the quadrant when finding the error bearing. Area computed from unadjusted coordinates will not close exactly.