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A Curve Stakeout That Is 'Close Enough for a County Road'

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A Curve Stakeout That Is 'Close Enough for a County Road'

A county road project in Lyon County specifies a 500.00-foot-radius horizontal curve, delta = 48 degrees 00 minutes 00 seconds right, PI at station 143+27.50, with centerline stakes at 100-foot arcs from the PC. Your party chief sets the instrument on the PC, backsights the PI, zeros the circle and turns deflection angles. The contractor's inspector later occupies the PC, sights the stake near station 145+00, and finds it out of position. Her measured chord from the PC to that stake is 384.60 feet, against the 384.91 feet tabulated on the stakeout sheet. The party chief says the instrument was 'calibrated in March,' the prism constant is 'whatever it came with,' and the work is 'close enough for a county road.' The project tolerance for centerline stakes is plus or minus 0.05 foot. Grading has stopped and the inspector wants an answer today.

1. Compute T, L, the PC and PT stations, and the deflection angle and chord from the PC to station 145+00. Is the 0.31-foot discrepancy acceptable?

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Geometry:

  • T = R tan(delta/2) = 500.00 x tan 24 degrees = 500.00 x 0.445229 = 222.61 ft
  • PC = 143+27.50 - 222.61 = 141+04.89
  • L = R x delta(rad) = 500.00 x 0.837758 = 418.88 ft
  • PT = 141+04.89 + 418.88 = 145+23.77

Stake at 145+00:

  • Arc from PC = 145+00.00 - 141+04.89 = 395.11 ft
  • Deflection = arc/(2R) = 395.11/1,000 = 0.39511 rad = 22.638 degrees = 22 degrees 38 minutes 17 seconds
  • Chord = 2R sin(deflection) = 1,000 x sin 22.638 degrees = 384.91 ft

Verdict: the inspector measured 384.60 ft; the tabulated chord is 384.91 ft. The 0.31-ft error is six times the plus or minus 0.05-ft tolerance, so the stake is rejected. Note also that a pure angular blunder barely changes a chord's length; a chord that is short by 0.31 ft points toward a distance or instrument-position problem, not simply a mis-turned angle.

2. List the checks you would run, in a defensible order, to isolate the cause, and state what each result would tell you.

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  1. Sheet arithmetic. Recompute the curve data and the tabulated chord from the design R and delta. If the sheet is wrong, everything downstream is wrong.
  2. PC position. Measure PC to PI and compare with T = 222.61 ft; measure PC to PT and compare with 2R sin(delta/2) = 406.74 ft. Agreement confirms the setup point and the curve's overall size.
  3. Circle and backsight. With the instrument still on the PC, turn from the PI to the suspect stake and compare the angle with 180 degrees - 22 degrees 38 minutes 17 seconds. A mismatch of more than roughly a minute is a blunder, not instrument noise.
  4. EDM calibration. Measure a known baseline or the distance between two control points with the prism actually in use. A constant offset appearing on every distance points to the prism constant (0 versus -30 mm is 0.098 ft) or an incorrect atmospheric/scale setting.
  5. Settings audit. Confirm prism constant, temperature and pressure entries, scale factor, and whether the instrument was reading the correct face. Any single check that explains 0.31 ft consistently across the curve identifies the cause; several small contributors do not add up to this size of error.

3. The party chief proposes to re-stake only the bad point with the same setup. Explain why that is wrong and what you direct instead.

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If the error comes from the setup, the backsight, or a distance-setting problem, it is systematic: it grows with distance from the PC and affects every stake on the curve. Re-staking one point from the same instrument position simply reproduces the same error at that point and leaves the other stakes wrong.

What to direct:

  • Shut down the stakeout until the cause is identified.
  • Verify the instrument and prism on an independent known baseline or between control points, and correct any constant or atmospheric setting.
  • Re-establish the setup on the PC, carefully re-zero on the PI, and confirm the PC-PI and PC-PT distances before turning any deflection.
  • Re-stake the entire curve from the corrected setup, including the PT, and have the inspector check an independent chord or angle that was not used to set the stakes.

Document the failure, the cause, the correction, and the re-staked values in the project file. Curve stakeouts are produced from one setup, so a systematic error is not a single-point fix.