Survey Computations, Adjustments, and Error Analysis
What this domain tests
You will be asked to close a traverse, compute a precision ratio, distribute a misclosure, and reason about random versus systematic error.
Core rules
- Random errors combine in quadrature: three segments each ±0.02 ft give ±0.02√3 = ±0.035 ft. Systematic errors add directly.
- Linear misclosure is the vector sum of the latitude and departure residuals: √(ΔN² + ΔE²). Precision ratio = total traverse length divided by the misclosure.
- The compass (Bowditch) rule distributes corrections proportional to course length; the transit rule distributes proportional to the latitude and departure magnitudes. Corrections carry the opposite sign of the misclosure.
- Least squares minimizes the sum of squared residuals, uses redundant observations, and yields residuals and error ellipses; it cannot detect a blunder by itself.
- A small misclosure can hide compensating blunders; closure is a check, not proof of correctness.
Worked example
A five-course traverse has a total length of 3,200.00 ft, with ΔN = +0.08 ft and ΔE = −0.06 ft. Linear misclosure = √(0.08² + 0.06²) = 0.10 ft. Precision = 3,200.00/0.10 = 1:32,000. Under the compass rule, the correction applied to a 640.00 ft course is 0.10 × (640/3,200) = 0.02 ft, split between latitude and departure in proportion to the misclosure components and applied opposite in sign.
Traps that cost marks
- Using the misclosure vector instead of the perimeter in the precision ratio.
- Applying corrections with the same sign as the misclosure.
- Mixing compass-rule and transit-rule distribution in one adjustment.
- Treating a closed traverse as error-free.
- Reporting more decimal places than the observations support.