Traverse Closure After an EDM Prism-Constant Error
A four-person crew closes a five-sided traverse around a proposed 5.6-acre commercial parcel in Anne Arundel County. The total station and EDM were checked that morning, but the same prism was carried over from a previous job. The closed traverse has five angles and five distances; total traverse length is 2,480.00 ft. Office reduction gives a linear misclosure of 0.21 ft and an angular misclosure of +38 seconds (sum of interior angles versus the theoretical sum). The firm's QA manual requires relative precision of at least 1:10,000 and angular closure no worse than 15 seconds times the square root of the number of angles. The party chief notes that the prism constant was left at 0 mm, while the prism certificate states +30 mm. The instrument's atmospheric correction was set for standard temperature and pressure, but the field temperature was 96°F.
1. Compute the relative precision and compare both closures with the firm's criteria. Should the traverse be adjusted now?
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Relative precision is the linear misclosure divided into the total traverse length: 0.21 ft / 2,480.00 ft = 0.00008468, or about 1:11,800. That passes the firm's 1:10,000 linear criterion. The angular criterion is 15" × √5 = 15" × 2.236 = 33.5". The observed angular misclosure of 38" exceeds 33.5", so the traverse fails the angular criterion even though the linear precision passes. The correct decision is not to adjust yet. Adjustment distributes random error; it cannot remove a systematic instrument or procedure error. A traverse that passes one criterion and fails another is a warning that something in the observation process is inconsistent, and the field data should be examined before coordinates are forced to close.
2. Evaluate the prism-constant and atmospheric-correction issues. How large is the prism effect, and why is it more serious than a random error of the same size?
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The prism-constant error is systematic. A +30 mm prism constant means the true correction is +0.030 m, or about 0.0984 ft, per distance. With the instrument set to 0 mm, each reported distance is short by approximately 0.098 ft. Over five legs, the cumulative path-length effect is roughly 0.49 ft, although the closure vector will not equal that simple sum because the legs run in different directions. Even so, a per-leg bias of nearly 0.1 ft is large enough to dominate a 0.21-ft closure. The atmospheric setting adds a smaller bias: field temperature is 28°F above standard, about 15.6°C, and an approximate 1 ppm/°C error gives roughly 15.6 ppm. Over 2,480 ft that is about 0.039 ft. The prism error is more serious because every distance is shifted in the same sense; it does not average out with more observations. The angular misclosure is separate and points to pointing, setup, or instrument-leveling issues, not the EDM.
3. State the corrective procedure before any coordinate adjustment, including what to do if reobservation is not possible.
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First, correct the instrument setup: enter the certified prism constant (+30 mm) and the actual temperature and pressure. Check the prism mounting, the tribrach and optical plummet, and the instrument leveling. Reobserve the five distances and, if the angular closure remains excessive, reobserve the angles with forced centering or a different instrument. Recompute the closures. If the corrected observations meet both criteria, adjust the traverse by an accepted method, such as compass rule or least squares, and document the adjustment. If reobservation is impossible, apply the known prism correction mathematically to each measured distance, apply the atmospheric correction, and recompute. Do not treat the corrected data as free of error until the recomputed closures meet the criteria. If they still fail, reobserve or use an independent control check rather than sealing a plat based on uncorrected data.