A Traverse That Closes in Distance but Not in Scale
Your firm is running a closed-loop traverse around a 40-acre parcel. There are 12 stations and a total traverse length of 8,400 ft. The 5-second total station and tribrachs were calibrated six months ago. The field book shows an angular misclosure of +18" and a linear misclosure of 0.42 ft, with a note that the crew entered the atmospheric correction using 29.92 inHg and 68 degrees F, the instrument's default, although the site is at 5,000 ft elevation and the day's actual pressure was 25.6 inHg at 92 degrees F. The crew also used a new prism with a manufacturer's constant of 0 mm, and the instrument's prism constant is set to 0 mm. A check baseline measured with an independent calibrated EDM differs from your traverse distances by about 0.33 ft over the full 8,400 ft, and the difference per 100 ft is essentially constant at 0.004 ft, a proportional difference.
1. Is the angular misclosure acceptable for a 5-second instrument over 12 angles?
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With 12 angles, a 5-second instrument, and a common standard of 5" times the square root of n, the allowable misclosure is 5" x sqrt(12), about 17.3". An 18" misclosure is marginally over that. It is not alarming by itself; some standards use 1.5 or 2 times the nominal accuracy, and 18" would pass. The pattern matters. The angles close near the limit while the distances show a systematic proportional error, so the angular work is probably usable and the distance error is the real problem. Check centering and targeting, instrument leveling, and refraction. If you need a tighter closure, reobserve the angles with forced centering rather than distributing 18" and moving on.
2. What is the likely cause of the proportional linear misclosure, and how do you test it?
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A constant proportional difference is a scale error, not a prism-constant error. A prism constant would add the same number of feet to every distance regardless of length; here the difference grows with distance, about 0.004 ft per 100 ft, or roughly 40 ppm over 8,400 ft. The field note explains it: the crew entered 29.92 inHg, the sea-level default, instead of the actual 25.6 inHg at 5,000 ft. At roughly 9 ppm per inch of mercury, 4.3 inHg gives about 39 ppm, which matches the observed 0.33 ft. Temperature (68 degrees entered versus 92 degrees actual) adds a smaller error. The prism constant is set to 0 mm and the prism is 0 mm, so that is not the source. Test by measuring the calibrated baseline with the correct atmospheric values; the residual should collapse.
3. What do you do with the fieldwork and how do you document it?
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Do not paper over it. The best practice is to reobserve the distances with the correct pressure and temperature, or apply the instrument's ppm correction computed from the actual conditions, then rerun the adjustment. Check the correction against the calibrated baseline. If the baseline agrees after correction, the traverse can be salvaged, but document exactly what was applied and why. If you cannot demonstrate the correction, reject the fieldwork and reobserve. For the deliverable, report the basis of bearings, the adjustment method, the misclosure before and after adjustment, and the atmospheric values used. A 40-ppm error is 0.33 ft in 8,400 ft, enough to matter for boundary and construction, so it must be corrected rather than accepted.