The 0.098-Foot Ghost
A five-sided closed traverse around a four-lot parcel closes with a linear misclosure of 0.19 ft over a perimeter of 1,610 ft, and an angular misclosure of 8 seconds. The instrument is rated 5 seconds with a 2 mm + 2 ppm EDM. Before accepting the work you check the setup against two monumented baselines: the 100.00-ft baseline reads 100.098 ft, and the 500.00-ft baseline reads 500.098 ft. The instrument's prism constant was left at 0.0 mm; the prism actually in use is stamped '−30 mm.' Pressure and temperature were entered correctly and the same prism was used on every shot. The crew chief wants to 'just average the misclosure around the legs and turn in the plat' so the job can be delivered Friday.
1. Diagnose the source of error from the two baseline checks and quantify the correction.
Read the worked answer
The error is a constant offset, not a scale error.
| Baseline | Measured | Error | Error as ppm of that line |
|---|---|---|---|
| 100.00 ft | 100.098 ft | +0.098 ft | 980 ppm |
| 500.00 ft | 500.098 ft | +0.098 ft | 196 ppm |
If this were a scale (ppm) error, the 500-ft line would show five times the error of the 100-ft line - 0.49 ft, not 0.098 ft. A fixed addition regardless of length is a prism constant error.
0.098 ft x 304.8 mm/ft = 29.9 mm, matching the prism's −30 mm constant entered as 0.0 mm.
Correction: subtract 0.098 ft from every measured distance. Note the offset is worst on short shots - on a 50-ft shot it is 1,960 ppm - which is exactly where cul-de-sac radii and short lot lines get set.
2. Is the angular work acceptable, and does the prism-constant error affect it? State what you check and what you tell the crew chief.
Read the worked answer
Angles are fine and are unaffected.
- Allowable misclosure for a 5-angle polygon: 5" x sqrt(5) = 11.2". Observed 8" is inside that. Balance the angles, then recompute bearings.
- A prism constant changes only the measured distance to the prism, not the horizontal or zenith angle. The angular closure of 8" and the linear closure of 0.19 ft therefore have different causes, which is a useful cross-check: nothing in the angular work needs repair.
- Report the angular closure before balancing and after, so the reviewer can see the work.
To the crew chief: averaging the 0.19-ft misclosure around the legs is the wrong fix. Averaging hides a determinate error you can identify and remove exactly; it also smears a 0.098-ft offset into four legs that were actually measured correctly except for that offset, and it leaves you with no evidence in the file about why.
3. After applying the correction the closure drops to 1:54,000. Do you sign, or re-observe? Justify and list what goes in the file.
Read the worked answer
This one is defensible to accept with documentation, because the error is determinate.
- The correction is 0.098 ft on every leg with a known, physical cause (30 mm prism constant) confirmed on two independent baselines of different length. That is not a fudge factor.
- Verify before signing: re-measure at least one leg between two monuments with the prism constant correctly entered, and confirm it reproduces the corrected value within a few hundredths. If it does not, re-observe the traverse.
- 1:54,000 is well inside a 1:10,000 boundary standard, and the angular closure is inside tolerance, so the geometry is sound.
Into the file: the baseline check sheet with both measured and record values; the instrument serial number, prism constant as set and as stamped; the correction applied and the leg-by-leg before/after distances; the unadjusted and adjusted closure; and a note identifying the source of the original misclosure. If the plat is ever challenged, that record is your defense - an unexplained adjustment of 0.19 ft is not.