Traverse Misclosure, a Prism-Constant Blunder, and Adjustment Choice
A five-sided boundary traverse closes on two New York State Plane Coordinate points. A total station measured five angles and five distances. The angular misclosure is 22 arc-seconds, while the project specification allows 15 arc-seconds. The linear misclosure is 0.21 ft over a perimeter of 2,860 ft. One leg was observed twice: 412.36 ft and 412.29 ft. The field book shows that for the first distance the prism constant was set to 0 mm, although the prism used is marked -30 mm. The remaining four distances used the -30 mm setting. The boundary is in a suburban area with several property corners marked by magnetic nails and one corner marked by an old stone bound. The client wants a map and a coordinate list suitable for a boundary description.
1. Compute the linear precision ratio and evaluate the traverse against a 1:10,000 relative-accuracy standard.
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The ratio is 0.21 ft divided by 2,860 ft, or about 1:13,619. On its face, that meets a 1:10,000 standard. But the ratio must not be accepted without checking the angular misclosure and the measurement error sources, because a small linear misclosure can result from compensating errors or from an adjustment that hides a blunder. Here the angular misclosure of 22 arc-seconds exceeds the 15 arc-second specification, so the traverse is not acceptable as raw data even though the linear ratio looks good. The repeated distance differs by 0.07 ft, which is larger than the expected reading repeatability and suggests a setting or observation problem. The prism-constant mismatch is a systematic error: 30 mm is about 0.098 ft, so the first leg is likely about 0.10 ft too long. That single error could account for a large part of the 0.21-ft misclosure. Correct or re-observe before judging the traverse.
2. What is the likely source of the misclosure, and what would you do before adjusting the traverse?
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The most likely source is the prism constant on the first leg. A -30 mm prism constant applied incorrectly changes that distance by about 0.098 ft. If the first leg was recorded as 412.36 ft with a 0 mm setting, the corrected value would be approximately 412.26 ft, close to the repeat observation of 412.29 ft. That correction reduces the linear misclosure and may change its direction. The angular misclosure of 22 arc-seconds still requires investigation: check for a transcription error, a wrong angle entered in the field book, a setup or target-centering problem, or an angular blunder at one station. Recompute the traverse with the corrected distance and compare the angular closure. Do not simply distribute the 22 arc-seconds over all angles. If the angular error remains after rechecking, re-observe the suspect station. Only after blunders are eliminated should the traverse be adjusted.
3. Compare compass-rule adjustment with a least-squares adjustment for this traverse, and state how you would report the final coordinates.
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The compass rule is simple and defensible for a conventional traverse with independent random errors: it distributes the linear misclosure in proportion to course length and the angular misclosure equally among angles. It does not use the actual precision of each observation, and it can distort a traverse with a known systematic error or with mixed observation quality. A least-squares adjustment is preferable when the angular and distance observations have different weights, when GNSS and total-station observations are combined, or when the client needs realistic coordinate uncertainties. For this traverse, correct the prism constant and investigate the angular misclosure first; then use least squares if the remaining errors appear random and you have realistic standard deviations. Report the final coordinates, the adjusted distances and bearings, the angular and linear closures before and after correction, the datum and epoch, and the uncertainty. State that the stone bound controls over the magnetic nails if it is an original monument, and disclose any conflicting corner evidence.