Surveying Methods and Computations
Surveying methods and computations covers traverse geometry, adjustments, coordinate geometry, leveling, and volumes. The exam rewards clean sign conventions and correct closure logic.
Traverse and adjustment
For each course, latitude = distance × cos(azimuth) and departure = distance × sin(azimuth). A closed traverse should sum to zero; the residual is the linear misclosure, and relative precision = perimeter / linear misclosure. The compass (Bowditch) rule distributes latitude and departure errors in proportion to course length: correction = −total error × (course length / perimeter). Least squares is preferred when redundant observations and weights are available.
Area and volumes
Area by coordinates uses the shoelace formula: 2A = Σ(X_i Y_{i+1} − X_{i+1} Y_i), taken as an absolute value. Average end area volume = L(A₁ + A₂)/2; the prismoidal formula is more accurate for varying sections. Leveling closure compares the sum of backsights and foresights to the known elevation difference; curvature and refraction are corrected for long sights.
Worked example
A four-course traverse has Σlatitude = +0.12 ft, Σdeparture = −0.08 ft, and perimeter = 1,000.00 ft. Linear misclosure = √(0.12² + (−0.08)²) = 0.144 ft; relative precision = 1,000/0.144 ≈ 1:6,900. For a 300.00 ft course, compass-rule latitude correction = −0.12 × (300/1,000) = −0.036 ft; departure correction = +0.08 × 0.3 = +0.024 ft.
Traps
Reversing a correction sign; using the total traverse length instead of the course length; mixing bearings and azimuths in the same formula; forgetting to convert DMS consistently.