Mathematical Principles and Survey Computations
Mathematical Principles and Survey Computations
This domain tests the calculations behind boundary and control work: bearings, coordinates, traverses, areas, curves, and closure. Minnesota questions favor clean computations with a check.
Core rules
- Convert bearings to azimuths consistently; keep quadrant labels correct. Latitude = distance × cos(bearing), departure = distance × sin(bearing).
- Traverse closure is the sum of latitudes and departures. A closed traverse should return to the starting coordinates; misclosure is the vector sum, and precision is misclosure divided by perimeter.
- Area by coordinates uses the shoelace formula: twice the area equals the sum of cross products, taken in order.
- Horizontal curves: arc = RΔ (Δ in radians); chord = 2R sin(Δ/2); tangent = R tan(Δ/2); external = R(sec(Δ/2) − 1).
Worked example
A curve has R = 500.00 ft and Δ = 30°00'00". The arc length is 500 × (30 × π/180) = 261.80 ft. The chord is 2 × 500 × sin 15° = 258.82 ft. The tangent is 500 × tan 15° = 133.97 ft. Reason: the central angle must be in radians for arc length, while chord and tangent use half the central angle. Round only at the end; carrying 0.01 ft early can shift a computed corner.
Traps
Using bearing angle instead of azimuth in latitude/departure; mixing degrees and radians; computing chord with the full central angle; ignoring the sign of a departure; reporting area from unclosed coordinates; treating a ratio of precision as an accuracy standard.