Kentucky Single Zone and a Traverse That Does Not Meet Contract
A surveyor measures a line between two property monuments at ground elevation 620 ft in Kentucky Single Zone (KY1600). The ground distance is 5,280.00 ft. The project's combined scale factor is computed as 0.99991. A closed traverse around the parcel has a departure misclosure of +0.24 ft and a latitude misclosure of -0.14 ft over a total traverse length of 4,200 ft. The surveyor's contract requires a relative accuracy of 1:20,000, while the local planning commission accepts plats at 1:10,000. The angular closure is 18 seconds for eight angles. The surveyor wants to apply the compass rule and submit the plat because the planning commission standard is met. The client is scheduled to close in three days.
1. Compute the grid distance for the 5,280.00-ft ground line and show the relation between ground and grid.
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Grid distance = ground distance × combined factor. Here grid = 5,280.00 ft × 0.99991 = 5,279.52 ft. The combined factor is the product of the map projection scale factor and the elevation factor; it is less than 1 because the project is above the ellipsoid and the projection scale is slightly under unity at that location. The grid distance is about 0.48 ft shorter than the ground distance, which is significant at the 0.10-ft level but not unusual for state plane work. The surveyor should state the combined factor, the elevation used, and the zone in the report. If the deed distance is 80.00 chains (5,280.00 ft) on the ground, the surveyor should not hold 5,280.00 ft on the grid; the grid coordinate difference should be 5,279.52 ft, with the ground-to-grid reduction documented.
2. Compute the traverse precision and decide whether the contract standard is met.
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Linear misclosure = sqrt(0.24² + 0.14²) = sqrt(0.0576 + 0.0196) = sqrt(0.0772) = 0.278 ft. Relative precision = 4,200 / 0.278 = about 1:15,100. The contract requires 1:20,000, so the traverse does not meet the contract standard. It does meet the planning commission's 1:10,000 minimum, but that is not the governing standard for the surveyor's professional obligation to the client. The angular closure of 18 seconds for eight angles is about 6.4 seconds per angle, which is not obviously a blunder, but the linear misclosure is too large for the contract. Meeting a regulatory minimum does not excuse failing the contractual accuracy requirement.
3. Should the surveyor apply the compass rule and submit, or take another action? Explain the reasoning.
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The surveyor should not simply adjust and submit as though the contract were met. The compass rule distributes misclosure proportionally to line length and assumes random error; it does not create accuracy. Before adjusting, the surveyor should check for systematic error or a blunder: recheck the control coordinates, the instrument and prism constants, the temperature and pressure corrections, and the angular closure. If the error is random and the adjusted coordinates are only for a plat that must meet 1:10,000, the surveyor might use the adjustment for that limited purpose, but the surveyor should disclose that the contract's 1:20,000 standard was not achieved. The better professional action is to reobserve the traverse or strengthen it with additional measurements, then adjust. The client's three-day closing does not justify certifying a survey that does not meet the contracted accuracy.