Precise-Levelling Field Practice — four short questions: 18-Geom-B3 Networks and Precise Engineering Surveys, December 2018, Q7

Question 7: Precise-Levelling Field Practice — four short questions (12 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(1) Equal foresight and backsight distances. Balancing the two sight lengths cancels three systematic errors at each set-up. Collimation error (line of sight not truly horizontal) produces a reading error proportional to sight distance; equal distances make the backsight and foresight errors equal, so they cancel in the difference $\text{BS}-\text{FS}$. The same balancing cancels the Earth-curvature effect and, because refraction is (over short, equal, symmetric sights) nearly the same on both, most of the atmospheric-refraction effect as well. Thus a residual instrument mis-collimation does not accumulate.

(2) Line of sight kept above 0.5 m. The air layer within roughly half a metre of the ground has strong, unstable vertical temperature gradients (especially over sun-heated surfaces), causing large and erratic refraction and shimmer that bend the line of sight and blur the staff graduations. Keeping the sight above 0.5 m avoids this turbulent near-ground layer, greatly reducing refraction error and improving pointing.

(3) Even number of set-ups. Precise levelling staves carry a small staff index (zero) error — the graduation zero not coinciding exactly with the staff base — and levelling is run with a pair of staves alternating as backsight and foresight. With an even number of set-ups each staff serves equally often as backsight and as foresight, so its index error enters with both signs and cancels in the summed height difference. (An even count also returns the two staves to their starting roles, and pairs them so any staff-to-staff constant difference cancels.)

(4) Reducing vertical refraction in trigonometric levelling. Use reciprocal (simultaneous) trigonometric levelling: observe the zenith (or vertical) angles at both ends of the line at the same instant, and mean the two height differences. Because the ray curvature due to refraction is essentially equal and of opposite sign as seen from the two ends, simultaneous reciprocal observation cancels the bulk of the refraction (and the Earth-curvature) effect. Observing simultaneously is important because refraction changes with time; if not simultaneous, observe quickly around midday when the gradient is most stable.

Concept & Theory

Topic. Systematic-error cancellation in precise geometric and trigonometric levelling.

Key relations. Combined curvature–refraction correction $\approx 0.0675\,D^2$ (m, $D$ in km); collimation error $\propto$ sight distance $\Rightarrow$ cancels for balanced sights; reciprocal mean $\Delta h=\tfrac12(\Delta h_{AB}-\Delta h_{BA})$.

Why this works. Each practice targets a specific systematic error and arranges the geometry (equal distances, symmetric roles, reciprocal observation) so that error enters twice with opposite sign and cancels in the sum or mean — the same “reversal” principle as two-face angle observation.

Common pitfall. Thinking balanced sights remove random errors — they remove systematic ones; random staff-reading error is still reduced only by repetition. Also assuming refraction is constant — it is not, which is why reciprocal observations must be simultaneous.

Source. Wolf & Ghilani §5 (levelling), §19 (precise levelling); Canadian vertical control to CGVD2013.

Question 7 of 12: Precise-Levelling Field Practice — four short questions

Question 7: Precise-Levelling Field Practice — four short questions (12 marks)