Measurement and Computations
These items test whether you know what the instrument actually measures, how error accumulates, and how observations become a defensible coordinate. Expect traverse closure, level-loop adjustment, error propagation and precision statements.
Instruments and error
- Total stations measure angles and slope distances. EDM error is a constant (prism/instrument offset) plus a scale term in ppm; at short ranges the constant dominates.
- Systematic errors - collimation, prism constant, temperature, refraction, projection scale - can be modeled and corrected. Random errors shrink as 1/√n. Blunders must be found, never averaged away.
- Accuracy is closeness to truth; precision is repeatability. A tight traverse run from a wrong starting azimuth is precise and wrong.
Traverse reduction
Compute latitudes (d·cos bearing) and departures (d·sin bearing). Misclosure = √(ΔN² + ΔE²); relative precision = perimeter ÷ misclosure, stated as 1:N. The compass (Bowditch) rule distributes misclosure in proportion to line length; least squares weights observations by their quality. For a closed polygon of n sides, the sum of interior angles equals (n − 2)·180°.
Worked example
A five-sided closed traverse gives Σdepartures = +0.062 ft and Σlatitudes = −0.058 ft, perimeter 1,650.00 ft. Linear misclosure = √(0.062² + 0.058²) = √(0.003844 + 0.003364) = √0.007208 = 0.085 ft. Relative precision = 1,650.00 ÷ 0.085 = 1:19,400. Under the compass rule, a 250.00-ft line receives a departure correction of 250/1650 × (−0.062) = −0.0094 ft and a latitude correction of 250/1650 × (+0.058) = +0.0088 ft.
Traps
- Applying corrections with the same sign as the misclosure instead of opposing it.
- Comparing a precision figure to a standard without checking the survey class and whether the standard applies to the traverse or the final coordinates.
- Mixing grid and ground distances before computing closure.
- Averaging observations that contain a blunder, which smears the error through every coordinate.