Surveying Mathematics and Measurement Analysis
Surveying Mathematics and Measurement Analysis
This domain tests computation: coordinate geometry, traverse closure, area, adjustments, and basic statistical evaluation. Items reward clean sign conventions and correct unit conversions.
Core methods
- Latitude = distance × cos(bearing/azimuth); departure = distance × sin(bearing/azimuth). Sum latitudes and departures to obtain closure.
- Linear misclosure = √(Σlatitude² + Σdeparture²). Relative precision = total traverse length ÷ linear misclosure, expressed as 1:N.
- Area by coordinates uses the double-meridian formula or the shoelace formula; keep units consistent. 1 acre = 43,560 ft².
- Apply an adjustment consistently: compass rule distributes latitude and departure corrections in proportion to course length; the transit rule distributes by coordinate magnitude. Never adjust before checking closure.
Worked example
A closed traverse has total length 2,500.00 ft, Σlatitude = +0.12 ft, and Σdeparture = -0.16 ft. Linear misclosure = √(0.12² + (-0.16)²) = √(0.0144 + 0.0256) = √0.0400 = 0.20 ft. Relative precision = 2,500.00 ÷ 0.20 = 12,500, so the closure is 1:12,500. For compass rule, the latitude correction for a 500.00-ft course is -0.12 × (500.00/2,500.00) = -0.024 ft; the departure correction is +0.16 × (500/2,500) = +0.032 ft. Apply corrections with signs opposite the misclosure.
Traps
Sign errors in latitudes/departures; mixing DMS and decimal degrees; using slope distance in a coordinate calculation; dividing misclosure by the wrong length; and converting area before checking square units.