Fly-levelling misclosure before setting out a floor level
On a 1.2 km fly-levelling run from a permanent bench-mark A to a second bench-mark C near a site office, the level was set up twice. The book reads: backsight on A = 1.585, foresight on change point B = 2.410; then, after moving the instrument, backsight on B = 1.870 and foresight on C = 1.245. The published reduced level of A is 100.000 m and of C is 99.815 m. The work was done on a hot afternoon, the staff was held on a soft shoulder at B, and the assistant admits he did not check the bubble before the second backsight. The firm's specification allows a closing error of 8√n mm for n instrument setups. A mason is waiting to set the finished floor level of an extension at 101.000 m; there is no other bench-mark within 3 km and a re-run would take half a day.
1. Reduce the levels and apply the two arithmetical checks. Then compute the closing error and decide whether the run meets the specification.
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Reduction
- Height of instrument, setup 1 = 100.000 + 1.585 = 101.585
- RL of B = 101.585 − 2.410 = 99.175
- Height of instrument, setup 2 = 99.175 + 1.870 = 101.045
- RL of C = 101.045 − 1.245 = 99.800
Check 1 - backsight and foresight sums
ΣBS = 1.585 + 1.870 = 3.455; ΣFS = 2.410 + 1.245 = 3.655. ΣBS − ΣFS = −0.200. Last RL − first RL = 99.800 − 100.000 = −0.200. ✔
Check 2 - rise and fall
A to B: 1.585 − 2.410 = −0.825 (fall). B to C: 1.870 − 1.245 = +0.625 (rise). Net = −0.200, which equals the difference of the end RLs. ✔
So the arithmetic is correct; a wrong arithmetic entry would have broken one of these checks.
Closing error
Observed RL of C = 99.800, published RL = 99.815, so the misclosure = −0.015 m = 15 mm (the run finished low).
Permissible error = 8√n = 8 × √2 = 11.3 mm.
Since 15 mm exceeds 11.3 mm, the run fails the specification and cannot be booked as a transfer of the bench-mark as it stands.
2. Given the time pressure, what would you do next? Explain the likely cause of the error, state whether you would accept and distribute the misclosure, and if so give the corrected RL of B.
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Diagnosis first. The sign of the misclosure (run finishing low) fits the stated field fault. A staff standing on soft ground at B settles while the foresight is being read: the foresight is read too large, so the computed RL of B - and everything after it - is too low. Failure to check the bubble before the second backsight adds a collimation error that grows with distance.
Decision. The correct professional answer is to re-observe rather than accept blindly. The cheapest re-run is not the whole line: reset the instrument halfway between B and C, hold the staff on a firm peg or a steel plate at B, and repeat only the second setup, then re-check the closing error. Fifteen millimetres is roughly three times a normal floor-level setting tolerance (about ±5 mm), and the error is systematic, not random, so distributing it does not make the benchmark trustworthy.
If the engineer decides to accept (for example, for preliminary earthwork only, never for a finished floor), distribute the misclosure in proportion to the number of setups, with the sign opposite to the error: 15 mm / 2 = 7.5 mm per setup.
- Corrected RL of B = 99.175 + 0.008 = 99.183 m
- Corrected RL of C = 99.800 + 0.015 = 99.815 m, which now agrees with the published value.
Whichever route is taken, the correction and its justification must be recorded in the level book, with a note that B was a soft-ground change point.
3. Using the properly closed bench-mark C, describe how the 101.000 m floor level would be set out and checked, with a worked staff reading.
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Setting out procedure
- Set up the level between bench-mark C and the extension, on firm ground, roughly equidistant from both so that any collimation error cancels.
- Take a backsight on C (RL 99.815) and compute the height of instrument. If the backsight reads 1.420, HI = 99.815 + 1.420 = 101.235 m.
- Required staff reading for the floor level = HI − required RL = 101.235 − 101.000 = 0.235 m.
- Drive a peg near the corner, hold the staff on it, and drive the peg until the staff reads exactly 0.235; mark the peg top as the finished floor level. Repeat at all corners so the whole floor is set from one HI.
- Check: re-read the staff on C at the end of the operation; the HI must be unchanged. Transfer the level to a painted temporary bench-mark on a column or gate pillar at, say, 101.500, so that the level can be recovered after the instrument is moved.
Practical cautions. Use a firm, stable change point; check the bubble before and after every reading; keep the staff vertical (use a staff level or wave it to find the minimum reading); avoid long sights on a hot afternoon because refraction bends the line of sight; do the two-peg test on the instrument before starting. Note in the field book that the level was set from a corrected bench-mark and that the original fly run closed 15 mm outside specification.