A Traverse That Closes Too Well in One Direction
You are surveying a four-sided lot with a 7-second total station and an EDM whose prism constant you believe is set correctly. The field data close as follows: perimeter 1,624.97 ft; angular misclosure +0 degrees 00 minutes 16 seconds over four angles; linear misclosure 0.21 ft, composed of 0.14 ft in northing and 0.16 ft in easterly, i.e. about 1:7,700. The measured distances are 512.36, 300.12, 512.41, and 300.08 ft. Surveys of record from the 1970s show the lot as a near-perfect rectangle of 512.3 by 300.1 ft. The lender's closing instructions require relative precision of 1:10,000 or better. Your notes show ambient temperature was recorded for the first two setups but not for the last two, and the same prism and same instrument were used throughout.
1. Evaluate the angular and linear misclosure against the equipment and state whether the traverse satisfies the lender's 1:10,000 requirement.
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Angular. A reasonable allowable for four angles observed with a 7-second instrument is about 7 seconds times the square root of 4, or 14 seconds. The observed 16 seconds exceeds that, so at face value the angles fail and should be reobserved with more repetitions before any adjustment is accepted.
Linear. 0.21 ft over 1,624.97 ft is 1 part in 7,738 - below the required 1:10,000. The traverse does not meet the stated requirement as observed.
Important distinction. Relative precision is a statement about internal consistency; it is not accuracy, and it says nothing about whether the surveyor held the right monuments. A traverse can close 1:20,000 and still be wrong if the control was wrong. Conversely, the honest answer here is: the survey fails the standard as observed, and the response is to find out why, not to round 7,738 up to 10,000. If the lot corners are found monuments, the monuments control the boundary and the traverse is only a check - but the surveyor still may not represent the survey as meeting a 1:10,000 standard it does not meet.
2. The misclosure vector is nearly parallel to the long sides of the lot. What does that pattern suggest, and what checks would you make before adjusting anything?
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A misclosure aligned with one direction is the signature of a systematic error, not random scatter. Random error from a 7-second instrument and ordinary EDM precision would scatter; it would not line up with the long walls.
The prime suspects, in order:
- Reflector/prism constant. A constant offset applies to every leg and accumulates. Errors of 15 to 30 mm (0.05 to 0.10 ft) per leg are common when the wrong constant or a mismatched prism is used, and would produce exactly a directional closure. Check the constant against a calibrated baseline with the exact prism used.
- Scale/reduction error. If any part of the data was reduced to grid with a combined factor while the record is on a ground basis, distances scale proportionally - about 130 ppm here, consistent with the observed misclosure.
- Atmospheric correction. Temperature was recorded for only two setups and never entered; a 20 degree Fahrenheit error is roughly 10 ppm, too small alone but it corrupts the diagnosis.
- Setup error. Plumb/centering offsets at the two middle setups, or a tripod leg kicked between backsight and foresight.
Recommended checks: re-measure one leg with a second instrument and a different prism; run a known baseline; re-reduce with measured temperature and pressure; re-observe the angles with additional repetitions and both faces. Only after the blunder hunt fails do you adjust.
3. Assume the checks reveal nothing and the data are as good as they will get. How do you adjust, and what do you state on the plat and in the report?
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If no blunder is found, the residual is random and within a defensible tolerance for the work - but not within the lender's stated 1:10,000. Adjust by the compass (Bowditch) rule, distributing the northing and easting misclosures in proportion to distance, state the method used, and confirm the adjusted figure closes exactly. Prefer to hold the found monuments and adjust only between them; the monument positions are the accurate part of the survey, and the traverse is subordinate to them.
Report the survey's actual relative precision as computed, not as desired. If the closing instructions demand 1:10,000, the correct professional response is either to reobserve until the network genuinely meets it, or to notify the client and lender in writing that the delivered survey does not meet that criterion and why. What you may not do is adopt a more favorable number, silently discard the closing instructions, or bury the misclosure. Also note on the plat the basis of bearings, the distances shown (ground), and whether any distances are record versus measured.