Survey Computations, Adjustment, and Data Analysis
What this domain tests
Survey Computations, Adjustment, and Data Analysis tests whether you can reduce observations, distribute error defensibly, and report the quality of the result.
Adjustment principles
- Random errors are treated by least squares; the method minimizes the sum of squared residuals and yields the most probable values.
- Weights are proportional to 1/σ². A distance observed four times with equal precision has four times the weight of a single observation.
- Standard deviation of the mean = σ / √n.
- Error propagation: for independent errors, combined variance = sum of variances.
- Compass (Bowditch) rule distributes northing and easting misclosure proportional to traverse leg length; transit rule distributes proportional to coordinate magnitudes. Neither is a least-squares adjustment.
Traverse and area
- Linear misclosure = √(ΔN² + ΔE²); relative precision = misclosure / perimeter.
- Adjust coordinates, then compute area by the coordinate (shoelace) method: 2A = Σ(Xi Yi+1 − Xi+1 Yi).
Worked example
A closed traverse has perimeter 5,000.00 ft, misclosure in northing +0.080 ft, and in easting −0.060 ft. Linear misclosure = √(0.080² + 0.060²) = 0.100 ft. Relative precision = 0.100 / 5,000.00 = 1:50,000. The compass rule correction to a 500-ft leg is 500/5,000 × (−0.080) = −0.008 ft in northing and +0.006 ft in easting, applied opposite the misclosure.
Traps
Adjusting angles and distances in the wrong order; reporting relative precision as a decimal; distributing misclosure equally instead of by length; and rounding intermediate coordinates before computing area.