Grid vs. Ground in a GNSS Boundary Survey
You are preparing a boundary survey in Northeast DC and tying it to the Maryland State Plane Coordinate System (NAD83). Two NGS monuments give grid coordinates. The inverse between the monuments yields a grid distance of 1,245.872 ft. Using a total station, you measure the same line as 1,245.960 ft on the ground. The average ellipsoid height along the line is 250 ft, and the grid scale factor at the project location is 0.999941. The client's lender requires coordinates and distances to 0.01 ft, and the contractor will use the coordinates to lay out a new foundation. A junior technician asks why the two distances do not match and suggests simply using the total-station distance on the plat. You also have a third NGS monument that yields a grid closure of 0.03 ft. The project lies about 4 miles from the state plane central meridian.
1. Compute the combined factor and show whether the total-station distance and the grid distance are consistent. State the result to six decimal places.
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The elevation factor is R/(R+h), using R = 20,906,000 ft and h = 250 ft: 20,906,000 / (20,906,000 + 250) = 0.99998804. The combined factor is the product of the grid scale factor and the elevation factor: 0.999941 × 0.99998804 = 0.999929. Applying the combined factor to the total-station ground distance gives the predicted grid distance: 1,245.960 × 0.999929 = 1,245.8715 ft, which rounds to 1,245.872 ft. That matches the grid inverse. The apparent 0.088-ft difference is exactly the combined-factor effect, not a blunder. The two measurements are consistent when compared on the same basis.
2. What should you report to the contractor for layout: grid coordinates, ground coordinates, or a local coordinate system? Explain the risk and how to avoid a 0.09-ft systematic offset.
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Report grid coordinates for record and a clearly labeled local ground system for layout, or report grid coordinates with the combined factor and a written requirement that the contractor reduce all ground measurements to grid. The risk is that if the contractor sets up on grid coordinates and measures ground distances with a total station or tape, every line will be off by about 71 ppm-0.09 ft on this 1,246-ft line, which exceeds the 0.01-ft tolerance. The error is systematic and grows with distance. A low-distortion local system can be created by multiplying the grid coordinates by 1/0.999929 = 1.000071, but the basis and units must be stated on the plan. Never mix grid and ground values on the same sheet without labeling. Also provide a control diagram and a check point so the contractor can verify the factor.
3. The third monument closure is 0.03 ft. Is that acceptable for a boundary survey in DC? What would you do before accepting the coordinates?
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0.03 ft is about 24 ppm over 1,246 ft and is generally acceptable for boundary control, but closure alone does not prove correctness. Check the third monument's stability, its published coordinates, and whether the closure is a loop or a simple check. Examine the RTK residuals, PDOP, and whether the same base station and projection were used. If the third monument is disturbed or its coordinate is suspect, do not force the network to fit it. Run a least-squares adjustment with realistic weights and inspect residuals; re-observe if any residual exceeds about 0.05 ft. Report the closure and the adjustment method. For a boundary survey, the relative accuracy between adjacent corners matters more than absolute grid accuracy.