Traverse That Missed 1:10,000 by a Factor of Two
You are running a 6-point closed traverse to provide control for a plat. Eight legs total 1,850 ft; the total station, prisms, and tribrachs were calibrated last month. Conditions: air temperature 96 °F, station pressure 29.10 inHg; the instrument sat in a closed truck between setups; one backsight is only 38 ft while the longest sight is 512 ft. Reduction gives angular closure of 14" (allowable 30") and linear misclosure components of ΔE = +0.38 ft and ΔN = +0.18 ft, i.e. a misclosure bearing of N 25° E. Leg CD bears N 26° E and measures 315.08 ft. The figure's centroid lies bearing S 25° W of the closing station. The prism constant was left at 0 mm; the prism is marked −30 mm. One rodperson read distances off the display and called them to the recorder. The plat standard is 1:10,000.
1. Compute the closure ratio and allowable misclosure, then use the misclosure direction and the listed conditions to identify which are capable of producing this error and which are not.
Read the worked answer
Precision check. Misclosure = √(0.38² + 0.18²) = 0.42 ft. Ratio = 0.42 / 1,850 = 1:4,400, against a required 1:10,000, i.e. allowable 1,850/10,000 = 0.185 ft. The traverse fails by more than 2×. Required action is to find the cause, not to adjust harder.
Rule the small stuff out with numbers.
- Temperature: 96 °F vs 68 °F reference = 15.6 °C; roughly 1 ppm/°C → about 16 ppm → 16 × 10⁻⁶ × 1,850 ft ≈ 0.03 ft. Too small.
- Pressure: a 1 inHg error is roughly 3 ppm; even a gross entry error of 1 inHg is ≈ 0.006 ft over this loop. Too small.
- Prism constant: 30 mm = 0.098 ft per distance. This is an additive error applied to every leg in nearly the same way; in a closed figure the sum of e·(unit vectors) tends to cancel, so it cannot generate 0.42 ft of loop closure. It does shift every point by about 0.1 ft radially and will corrupt stakeout and any radial check - fix it, but do not blame it for the closure.
Test the two survivors.
- Systematic scale error (atmosphere, projection, wrong units): misclosure from a scale error points radially at the figure's centroid, which N 25° E matches. But the required scale error is 0.42 ft / (distance from centroid to closing station, ≈ 780 ft) ≈ 540 ppm. No atmospheric or projection effect reaches 540 ppm. Rejected as the cause.
- Distance blunder on one leg: a blunder in a leg produces misclosure parallel to the blundered leg, with magnitude equal to the blunder. Misclosure bears N 25° E; leg CD bears N 26° E and is 315.08 ft. A 0.42 ft error on a 315 ft leg is 1:750 - exactly the size of a mis-called or mis-recorded reading. This is the leading hypothesis.
2. Design the minimum field work that would confirm or refute the diagnosis, and state the instrument/procedure fixes you would make before re-observing.
Read the worked answer
Confirmation (minimum work, no full re-traverse):
- Re-measure CD only, in both directions, from the existing occupied stations - if the direct and reverse distances differ from 315.08 ft by about 0.4 ft and agree with each other, the original call is the blunder.
- Recompute the traverse closing on the corrected CD and inspect the new misclosure; it should collapse to well under 0.185 ft.
- Check the station recoveries at C and D (disturbed stakes, tribrach forced-centering, optical plummet) - a blunder also appears if the instrument was set over the wrong point.
Fixes before re-observing:
- Enter the correct prism constant (−30 mm) and confirm it in the instrument's records screen; verify the display units.
- Enter temperature and pressure at the instrument (or enable the correct atmospheric correction), and re-enter them when conditions change; the truck-cab heat soak is a hint that the entered values were stale.
- Eliminate the record-by-call chain: log distances internally or read them off the display at the instrument.
- Fix the sight-length asymmetry. The 38 ft backsight matters through orientation, not distance: a 20" pointing error at 38 ft is fine, but any residual orientation error is then carried through 500 ft legs (20" ≈ 0.05 ft at 500 ft). Occupy with a longer backsight or use multiple rounds and check the horizontal collimation.
- Check centering: 0.005 ft of centering error on a 38 ft shot is 130 ppm on that leg.
3. Coordinates from this traverse were already sent to the design engineer with a note that they were "preliminary." What do you do now, and what do you not do?
Read the worked answer
- Do not adjust the 0.42 ft away. Least-squares adjustment distributes random error; it smears a blunder across every station, so a "closed" traverse would carry a silent 0.1–0.3 ft distortion in all the coordinates - worse than an honest failure, because no one downstream can see it.
- Send a written hold/retraction identifying which coordinates are affected, the size of the discrepancy, and the new date. "Preliminary" reduces but does not eliminate reliance; a telephone call is not documentation.
- Re-observe CD, re-reduce from the raw field data, and re-adjust from the corrected observation set, then reissue with a revision number, a note of the change, and the final closure ratio.
- Document the instrument settings (prism constant, atmospheric entries) on the field file - this is what demonstrates the standard of care if the engineer's design was affected.
- Keep the original raw data and the failed reduction in the file; do not overwrite them.