Survey Computations and Adjustments
Survey Computations and Adjustments
The PS exam checks whether you can close a traverse, adjust it correctly, compute coordinates and areas, and solve curves. Expect compass rule, area by coordinates, and horizontal/vertical curve formulas.
Traverse closure and relative precision
Sum latitudes and departures; linear misclosure = √[(ΣLat)² + (ΣDep)²]. Relative precision = misclosure ÷ perimeter, expressed as 1:N. A common boundary standard is 1:10,000 or better. The compass (Bowditch) rule distributes latitude and departure errors proportionally to line length: correction per line = −(misclosure component) × (line length ÷ perimeter).
Area by coordinates
Use the shoelace formula: 2A = Σ(Xi Yi+1 − Xi+1 Yi). Take the absolute value and divide by 2.
Curves
Horizontal curve: T = R tan(Δ/2); L = RΔ (Δ in radians); M = R[1/cos(Δ/2) − 1]. Vertical curve: elevation at distance x from BVC = BVC elevation + g1x + [(g2 − g1)/(2L)]x².
Worked example
A closed traverse has ΣLat = +0.08 ft, ΣDep = −0.09 ft, perimeter = 1,200.00 ft. Misclosure = √(0.08² + 0.09²) = 0.120 ft. Relative precision = 0.120/1,200 = 1/10,000, or 1:10,000. For a 300-ft line, compass-rule latitude correction = −0.08 × (300/1200) = −0.020 ft. Apply the opposite sign to the error.
Traps
- Using transit rule when compass rule is specified.
- Mixing bearings and azimuths in departures.
- Sign errors in the shoelace formula.
- Using degrees instead of radians in arc length.
- Forgetting that vertical-curve K = L/|g2 − g1|.