The Prism Constant and the Wooded Traverse
You are running a closed traverse around a 12-acre wooded parcel in the Missouri Ozarks. There are six setups with a total station rated at 1-inch accuracy and a 360-degree prism. The instrument's prism constant is set to 0.0 mm, but the prism is marked -30 mm. You observe 1,850 ft of perimeter; angular misclosure is 18 seconds and linear misclosure is 0.16 ft. A separate 400.00-ft baseline measured with a calibrated steel tape reads 400.02 ft; the total station reads 399.90 ft. The field book shows temperature 31 degrees F, pressure 30.10 inHg, and the instrument was last checked six months ago. The client needs a plat for a boundary line adjustment and wants to know whether the traverse is acceptable.
1. Analyze the misclosures and identify the likely systematic error.
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The baseline check is the key: 399.90 ft versus 400.02 ft is 0.12 ft short over 400 ft, or about 300 parts per million. A -30 mm prism constant is 0.030 m, or about 0.098 ft per distance. The sign and magnitude match the total station reading short because the instrument constant was set to 0.0 mm. Every observed distance is therefore short by roughly 0.10 ft, which produces a scale error in the traverse. The 18-second angular misclosure is small and not the primary problem; temperature and pressure corrections at 31 degrees F are much smaller than the prism error. I would correct the prism constant, recheck the 400-ft baseline, and reobserve the traverse. I would not simply adjust the computed coordinates, because that would bury a systematic instrument error in the adjustment.
2. What closure standard would you apply, and can the traverse be adjusted?
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The applicable standard depends on the purpose of the survey and the Missouri minimum standards, but a boundary traverse should generally close much better than 1:5,000 after systematic errors are removed. The uncorrected 0.16 ft over 1,850 ft is about 1:11,500, which looks acceptable numerically but is contaminated by a scale error; closure ratio alone can hide a systematic problem. After correcting the prism constant, I would recompute the angular and linear misclosure. If the corrected traverse meets the standard, I would adjust it by a consistent method, such as compass rule or least squares, and document the adjustment. If it does not meet the standard, I would reobserve the questionable setups rather than force a closure.
3. What would you report to the client and what field records should support the plat?
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I would report the baseline failure, the prism-constant error, the corrective action, and the final closure. The client should know that the first observations were rejected, not silently adjusted. The field records should include the baseline check, instrument calibration date, prism constant, temperature and pressure, field notes, sketch of the traverse, angular and linear misclosure, adjustment method, and final coordinates. I would also note any setups with poor visibility or short sights. This record protects the plat and demonstrates that the surveyor identified and corrected a systematic error rather than accepting a misleadingly good closure ratio.