Grid Distance vs Ground Distance on a 1,842-Foot Line
A surveyor is using RTK GNSS on NAD83(2011) Illinois State Plane coordinates to stake two corners of a 12.4-acre parcel. The grid distance between the two computed corner positions is 1,842.365 ft. The combined scale factor at the site is 0.999724. The record deed distance between the same corners is 1,842.87 ft. The field crew reports that the GNSS 'distance is short by about half a foot' and proposes to move the second corner 0.51 ft farther out so the measurement matches the deed. No original monuments have been found at either corner. The project surveyor is checking the computation before authorizing the stakeout.
1. Compute the ground distance represented by the grid distance and explain whether the field crew has made an error.
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Grid distances are smaller than ground distances when the combined factor is less than 1. Ground = grid / combined factor. 1,842.365 / 0.999724 = 1,842.874 ft. The difference is 0.509 ft, or about 276 parts per million. That is the scale effect, not a field blunder. The crew should not 'correct' the observation by 0.51 ft unless it is converting coordinate distances to ground. The record distance of 1,842.87 ft is a ground distance and agrees with the converted value. The surveyor should confirm that the combined factor applies to this site and that the RTK positions are in the correct Illinois State Plane zone and epoch.
2. If the surveyor decides to stake the record distance, what value should be used with the grid coordinates?
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To stake the record distance with a total station or RTK using grid coordinates, convert the record ground distance to grid: 1,842.87 × 0.999724 = 1,842.36 ft. Then stake 1,842.36 ft in grid. If original monuments are found at either corner, the monuments control over the distance; the surveyor should hold the monument and report the distance discrepancy. Do not hold a record distance over an original monument simply to make the numbers match. If no monuments exist and the deed distance is the only evidence, the converted grid distance is the correct staking value. The surveyor should document the conversion and the basis for holding or rejecting the record distance.
3. The CAD technician multiplies by 0.999724 to go from ground to grid. Is that correct, and how does the factor apply to area?
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Yes. Ground-to-grid is multiply by the combined factor; grid-to-ground is divide. The combined factor has two parts: a map-projection scale factor and an elevation factor. At 650 ft, the elevation factor is about 20,906,000 / (20,906,000 + 650) = 0.999969. The projection factor accounts for the rest. For area, the factor is squared: a 1-acre ground parcel is about 0.999448 acre on the grid, a difference of about 0.055 percent. That is small for a lot but should be applied consistently in coordinate computations. The surveyor should not mix grid areas with ground deed areas without noting the conversion.