RTK Stakeout in State Plane Coordinates: A Uniform 0.31-ft Offset
A 2,400-ft sewer main is being staked from NAD83(2011) State Plane coordinates using RTK GNSS. Project control was published in State Plane, and the combined scale factor at the site is 0.999872. The design engineer provided stake coordinates in a local ground system whose origin coincides with the State Plane control, but the coordinates were not scaled. The party chief entered the design coordinates directly into the RTK rover and set 12 stakes. A total station check from the same control, using ground distances, shows every staked point about 0.31 ft long along the line from the control point, with no random scatter. The crew reran the RTK shot and got the same result. The contractor has already laid out forms for two structures and is asking whether to shift them. Another crew suggests changing the RTK scale factor to 1.000000.
1. What is the likely cause of the uniform 0.31-ft offset, and why is it not a GNSS precision problem?
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The offset is a coordinate-scale problem, not a random GNSS error. The combined factor is 0.999872, so a ground distance must be multiplied by that factor to obtain the State Plane grid distance. Over 2,400 ft the difference is 2,400 x (1 - 0.999872) = 0.307 ft, essentially the observed 0.31 ft. The offset is uniform and along the line from control, which is the signature of a systematic scale difference.
RTK precision is indicated by repeatability, not by agreement with ground distances. Rerunning the shot and getting the same result confirms repeatability but does not test scale. The rover is correctly reporting State Plane coordinates; the error is that ground coordinates were entered as if they were grid coordinates. Changing the RTK scale factor to 1.000000 would not fix the coordinate system and could corrupt other work. The correct approach is to transform the design ground coordinates to grid coordinates by applying the combined factor, or to work in a properly defined ground coordinate system and convert observations consistently.
2. A design point lies 1,200.00 ft from the control point on a bearing of N 45 degrees E in the ground system. Compute the grid coordinate differences that should be entered, assuming the control grid coordinate is known.
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First resolve the ground vector into north and east components. The bearing is N 45 degrees E, so the north component is 1,200.00 cos 45 = 848.528 ft and the east component is 1,200.00 sin 45 = 848.528 ft.
Convert each ground component to grid by multiplying by the combined factor: 848.528 x 0.999872 = 848.419 ft. Therefore the grid coordinate differences from the control point are approximately 848.42 ft north and 848.42 ft east. Add those differences to the control point's State Plane coordinates to obtain the coordinate to enter into the rover.
The check is the inverse: the grid distance is sqrt(848.419^2 + 848.419^2) = 1,199.69 ft, which is 0.31 ft shorter than the 1,200.00-ft ground distance. That matches the field symptom. For a short line this component-by-component scaling is adequate; for a long line or a line crossing a large scale-factor change, the scale factor should be evaluated along the line rather than at one point.
3. What field check would you require before the contractor shifts the forms, and how would you prevent recurrence?
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I would establish at least two control points with published State Plane coordinates and occupy one while checking the other with a total station using ground distances. The inverse between the computed grid coordinates should agree with the measured ground distance after applying the combined factor. I would also check a third point not on the same line to detect rotation or a localization error. Only after the coordinate transformation is verified would I compute the shift for the two structures.
To prevent recurrence, the project should adopt a written coordinate protocol: identify whether each file is ground or grid, state the combined factor and its source, and require a scale check at the start of each stakeout. The designer's coordinates should be transformed once by a responsible person, and the transformed file should be labeled and archived. The rover should not be used with an arbitrary scale factor of 1.000000, because that hides the mismatch rather than resolving it. A final as-staked check by total station on at least one structure is prudent because the forms are already in place and the cost of a wrong shift is high.