Control Surveys and Adjustments
This domain tests traverse design, misclosure analysis, and adjustment. You must be able to judge whether a network meets a specification and then distribute error defensibly, whether by compass rule or least squares.
Closure and precision
- Angular misclosure is the difference between the measured sum and the geometric sum. Specifications often express the allowable as a√n, where a is the instrument's rated accuracy and n is the number of angles.
- Linear misclosure is the vector sum of latitude and departure errors. Precision ratio = total traverse length / linear misclosure, expressed as 1:N.
- Level loops are checked by misclosure against a limit usually proportional to the square root of the loop length in kilometers or miles.
Adjustment methods
- The compass (Bowditch) rule distributes latitude and departure errors in proportion to leg length; it is appropriate when errors are random and lengths are similar in quality.
- The transit rule distributes errors in proportion to the latitude and departure magnitudes.
- Least squares uses a stochastic model with weights proportional to 1/σ². It yields residuals, a reference variance, error ellipses, and a chi-square test of the adjustment. It also supports blunder detection.
- Redundancy is what allows a chi-square test and residual checks; a minimally constrained network gives little evidence of blunders.
Worked example
A closed traverse has total length 2,400.00 ft, with misclosure components ΔN = +0.18 ft and ΔE = -0.24 ft. Linear misclosure = √(0.18² + 0.24²) = 0.30 ft. Precision = 2,400 / 0.30 = 1:8,000, which passes a 1:5,000 specification but fails 1:10,000. Under the compass rule, a 600.00-ft leg receives a northing correction of -0.18 × (600/2,400) = -0.045 ft and an easting correction of +0.24 × (600/2,400) = +0.060 ft.
Traps that cost marks
- Applying corrections with the wrong sign.
- Presenting adjusted coordinates as if they were measured values.
- Adjusting a traverse that contains a blunder or a systematic error.
- Using unweighted least squares when observations have very different precisions.
- Quoting a precision ratio without stating the total length.