Analysis and Computations
Sign discipline carries the day
Convert each traverse course to latitude (ΔN = distance × cos azimuth) and departure (ΔE = distance × sin azimuth). Sum them; the vector sum is the closure error, and linear precision is closure distance divided by total traverse length. Adjust by the compass (Bowditch) rule, which distributes error in proportion to course length, or by the transit rule when angles dominate; use least squares when weights are known.
Area by coordinates: A = ½|Σ(Xᵢ·Yᵢ₊₁ − Xᵢ₊₁·Yᵢ)|. Double meridian distance is the classic alternative and still appears in exam scenarios.
Horizontal curves: the degree of curve has two definitions - arc basis (100 ft of arc) and chord basis (100 ft of chord) - and they give different radii. Know T = R·tan(Δ/2), L = R·Δ in radians, LC = 2R·sin(Δ/2), E = R(sec(Δ/2) − 1), M = R(1 − cos(Δ/2)). Vertical curves are parabolas: K = L/A, and the high or low point lies at distance K·|g₁| from the BVC.
Traps
- Reversing the sign convention for latitudes and departures.
- Using an arc-basis radius for a chord-basis problem.
- Computing curve length in degrees instead of radians.
- Mixing stationing (100-ft stations) with plain footage.
- Reporting area in square feet when the deed is in acres (1 acre = 43,560 ft²).
Worked example
A −2.0% grade meets a +1.6% grade with L = 400 ft. A = |−2.0 − 1.6| = 3.6; K = 400/3.6 = 111.1 ft per percent. The low point is 111.1 × 2.0 = 222.2 ft from the BVC, at station BVC + 2.22 stations.