Surveying and Engineering Surveying
This domain tests whether you can close a survey, distribute misclosure with a defensible rule, and state clearly whether the result meets a stated tolerance. Marks are won on closure arithmetic and on knowing which observations control which.
Angular and linear closure
- For a closed polygon of n angles, interior angles sum to (2n − 4) × 90°. Misclosure is distributed equally (or weighted by angle quality) before azimuths are computed.
- Linear misclosure is the vector sum of ΔE and ΔN around the loop; relative misclosure = misclosure ÷ perimeter.
- The Bowditch (compass) rule distributes error in proportion to leg length, assuming random length-dependent error; the transit rule suits angle-dominated error.
Levelling
- Rise/fall: Δh = backsight − foresight. Loop misclosure is distributed in proportion to the number of setups or to line length - never dumped on one line.
- Combined curvature and refraction correction: C&R = 0.0675 D² metres, with D in kilometres. Refraction bends the line of sight downward, so the rod appears higher and the correction is subtracted.
- Reciprocal levelling cancels refraction and curvature over long or steep sights.
Worked example: a five-sided closed traverse measures interior angles summing to 540°00′40″ against a theoretical 540°00′00″. Misclosure +40″; distribute −8″ per angle. After recomputing azimuths and coordinates the loop closes with ΔE = +0.042 m and ΔN = −0.019 m, giving a linear misclosure of 0.046 m over a 780 m perimeter, i.e. about 1:17 000 - inside a 1:10 000 specification. Apply Bowditch corrections proportional to leg length, then re-close.
Traps
- Computing coordinates before applying the angular correction, which makes the linear misclosure meaningless.
- Rounding angles to whole seconds mid-computation.
- Resecting from three points lying near a common circle (the danger circle), giving an ill-conditioned fix.