Traverse Misclosure Around a Downtown Block
Your firm runs a closed traverse around a city block in downtown DC to establish control for a facade survey. The traverse has eight courses totaling 3,240 ft. The angular misclosure is 14 seconds, and the linear misclosure is 0.16 ft. The field crew used a 2-second total station and forced centering, with backsight checks at each setup. The project specification requires a relative precision of at least 1:10,000 for boundary control and 1:20,000 for monitoring. A second, independent check between two traverse stations gives a distance difference of 0.04 ft. The traverse closes on a known NGS benchmark pair. The client asks whether the traverse is 'good enough' to set property corners, and whether you should use the compass rule or a least-squares adjustment. One station is on a sidewalk that may have been disturbed by utility work.
1. Compute the relative precision and evaluate the traverse against both specifications. Does the angular misclosure raise a concern?
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Linear relative precision is 0.16 ft / 3,240 ft = 1/20,250, or about 49 ppm. That meets the 1:10,000 boundary specification and just meets the 1:20,000 monitoring specification. The angular misclosure is 14 seconds for eight angles. For a 2-second instrument, the expected misclosure is roughly 2"√8 ≈ 5.7", so 14" is about 2.5 times the expected value. It is not necessarily a failure, but it suggests a setup or pointing problem-especially at the station on the disturbed sidewalk. Check the backsight checks and the angle residuals before accepting the traverse. A traverse that meets linear precision can still have a systematic angular error that distorts the shape.
2. Compass rule or least squares? How would you handle the suspect station?
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Use least squares if the project justifies it and if you need residuals to evaluate the suspect station. The compass rule distributes misclosure by course length and assumes random error; it will hide a systematic error at one station. Least squares with weights based on instrument specifications and redundant observations lets you test the station and detect a disturbed point. If the suspect station has a large residual, re-observe it or exclude it from the adjustment and re-run. For a boundary control traverse, a compass rule may be acceptable when the misclosure is small and random, but you must document the method. Do not use a simple adjustment to mask a bad setup.
3. The independent check differs by 0.04 ft. Is that consistent with the traverse precision, and what do you report?
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The independent check difference of 0.04 ft is consistent with a traverse whose linear misclosure is 0.16 ft and whose relative precision is about 1:20,000. The check is a separate measure of the same line, so it should be compared using the same distance basis-grid or ground. If the check line is 500 ft, 0.04 ft is 1:12,500, which is weaker than the traverse; if it is 1,000 ft, it is 1:25,000. Determine the check line length and compute its relative precision before judging. Report the adjusted coordinates, the adjustment method, the misclosure, the check result, and a note that the sidewalk station was re-observed. Do not report more precision than the data support.