Misclosure at 1:10,700 on an 18-Leg Road Traverse
You are checking a 6.2 km, 18-leg closed traverse run with a 5 second total station for a rural road design in Kaduna State. The traverse closes on two control pillars. Angular misclosure is 52 seconds against an allowable of 2 minutes 07 seconds for 18 angles at 30 seconds times the square root of n. Linear misclosure is 0.58 m, a ratio of 1:10,700, which passes the firm's 1:5,000 detail specification but fails its 1:15,000 control specification. The misclosure vector points almost exactly along the traverse direction. A 350 m baseline measured with the same instrument between two pillars differs from its published value by 31 mm. The prism constant is set to 0 in the instrument, but the prisms are marked minus 30 mm. Field temperature was 36 degrees Celsius and pressure 1008 hPa; no atmospheric correction was entered. The design team wants the digital terrain model tomorrow.
1. Before any adjustment, decide whether the 0.58 m misclosure is random or systematic. Show the check arithmetic and say what it implies.
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The misclosure is systematic, and the arithmetic shows it.
Prism additive constant: the instrument is set to 0 mm while the prisms are marked minus 30 mm, so every measured distance is wrong by 30 mm. Average leg length is 6200 divided by 18, about 344 m, giving a scale error of 0.030 divided by 344, which is 87 parts per million. Over 6.2 km that is 0.54 m. The observed linear misclosure is 0.58 m, so the prism error alone accounts for roughly 93 per cent of it.
Corroboration: the 350 m baseline is 31 mm out, which is 89 parts per million, essentially the same ratio from an independent measurement. The misclosure vector also lies along the traverse direction, which is exactly what a scale error produces; random error would give a direction unrelated to the route.
The angular work is sound, 52 seconds against an allowable 2 minutes 07 seconds, so the problem is entirely in the distances. The missing atmospheric correction at 36 degrees Celsius adds a few further parts per million, small but not zero and worth applying once the main error is corrected.
2. The designer wants the DTM tomorrow. Do you apply Bowditch and deliver, or do something else? Justify the choice.
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Do not apply Bowditch and deliver.
Bowditch, or the compass rule, distributes misclosure in proportion to leg length on the assumption that the error is random and accumulative. A scale error is not random; it is itself proportional to distance. Applying Bowditch would spread it in proportion to distance, which means the traverse would close perfectly while every coordinate along the route is pulled toward the closure. The network would look right and be wrong in the middle, which is the worst of both outcomes for a road design.
Correct path: the raw observations should still be in the instrument or the field book. Apply the correct prism constant and the atmospheric correction, then recompute the coordinates from scratch. Recompute the misclosure; if it falls to a value consistent with the angular work, the residual random component can then be adjusted, and the result checked against the 350 m baseline before release.
If raw data are lost, the prism correction can be applied to the stored slope distances provided the correction and its basis are documented, but re-observe a sample of legs including the longest as verification. If the recomputed misclosure still fails 1:15,000, re-observation of the whole traverse is mandatory and no adjustment is defensible.
3. What do you tell the design team, and what do you record so this does not recur?
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To the design team: state plainly that the DTM is held for 24 to 48 hours because the control traverse failed the control specification for a known, correctable reason, and give the numbers. A designer who receives a grid without knowing the control status will use it for earthworks volumes and longitudinal grades, and a systematic half-metre shift in plan position does not reveal itself until construction. Give them the expected re-issue date and the provisional status of anything issued in the meantime.
Record in the survey report and file metadata: instrument and prism serial numbers, prism constant as set and as marked on the prisms, atmospheric settings and correction applied, date and time of observation, angular and linear misclosure before and after correction, the baseline check result, the adjustment method used, and the accuracy statement supported by the post-correction closure.
Fix the cause: put a prism constant check and a baseline check on the pre-survey checklist, and confirm the EDM calibration certificate is current. The professional issue here is not the 30 mm; it is releasing a product whose stated accuracy cannot be supported by the evidence in the file.