Surveying Calculations and Adjustments
Traverse computation
Latitude = distance × cos(bearing); departure = distance × sin(bearing). North and east are positive. Sum the latitudes and departures around a closed traverse to get the misclosure; linear precision is closure divided into the perimeter, expressed as 1:N. The compass (Bowditch) rule distributes the latitude and departure errors in proportion to the length of each course; the transit rule distributes in proportion to the magnitude of the latitude or departure. Least squares distributes by the actual precision of each observation - the correct answer whenever a question specifies differing weights or standard deviations.
Angles and coordinates
Sum of interior angles of a closed polygon = (n − 2) × 180°. Angle misclosure is distributed equally unless weights are given. Area by coordinates uses the double-meridian-distance or the shoelace formula; double-meridian distances also compute area and check the adjustment.
Curves and levels
For a circular curve: T = R tan(Δ/2), L = RΔ(radians), and D = 5729.58/R for degree of curve by arc definition. A level loop misclosure is adjusted in proportion to distance run between benchmarks.
Worked example
A closed loop of course lengths 300, 400, and 500 ft has a closure of 0.060 ft. Precision = 0.060/1200 = 1/20,000. The compass rule correction applied to the 300-ft course is 0.060 × (300/1200) = 0.015 ft, split into latitude and departure components.