ID Land Surveyor cheat sheet

Principles and Practice of Surveying - Core Reference

• Closure in latitude and departure: for a closed traverse, ΣN−ΣS and ΣE−ΣW should each equal zero; linear misclosure = √(Δlat² + Δdep²), and relative precision = misclosure ÷ total perimeter (express as 1:N).

• Compass rule (Bowditch) adjusts latitudes and departures proportionally to leg length: correction per leg = −(total misclosure) × (leg length ÷ perimeter). Transit rule instead distributes corrections proportionally to the latitude/departure magnitudes, not lengths.

• Traverse area by coordinates (shoelace): 2A = Σ[Xᵢ(Yᵢ₊₁ − Yᵢ₋₁)] with consistent axis naming; take absolute value and divide by 2. Double meridian distance (DMD) method: 2A = Σ(DMD × latitude), where DMD of the first leg equals its departure and each subsequent DMD = prior DMD + prior departure + current departure.

• Horizontal curve formulas: T = R·tan(Δ/2); L = R·Δ(rad) = 100·Δ/D (arc definition, D in degrees); LC = 2R·sin(Δ/2); M = R[1 − cos(Δ/2)]; E = R[sec(Δ/2) − 1]; degree of curve D = 5729.578/R (arc definition) or 50/R (chord definition, ft).

• Vertical curve: elevation at any station = BVC elevation + g₁x + [(g₂ − g₁)/2L]x², with x measured from the BVC and grades as decimals; highest/lowest point occurs at x = −g₁L/(g₂ − g₁). K = L/A, where A = |g₂ − g₁| in percent.

• Leveling: differential elevation difference = backsight − foresight; arithmetic check ΣBS − ΣFS = last elevation − first elevation. Curvature and refraction combined correction ≈ 0.0206·M² ft (M in thousands of feet) or 0.0675·K² m (K in km), subtracted from the rod reading.

• Angular closure for an n-sided closed polygon: theoretical sum of interior angles = (n − 2)·180°; compare measured sum to this value before distributing the misclosure equally among angles.

• State plane coordinates: Lambert Conformal Conic for east-west-extending zones (standard parallels, scale exact there, grid factor <1 between them); Transverse Mercator for north-south zones. Ground-to-grid: grid distance = ground distance × elevation factor × scale factor, with elevation factor ≈ R/(R + h).

• Error propagation: for a sum or difference, variances add (σ² = σ₁² + σ₂²); for independent repeated measurements, standard error of the mean = σ/√n. A 95% confidence interval uses roughly 1.96σ (or t for small samples).