Grid Versus Ground on a Foothill Pipeline
A 1,200-ft water transmission main is being designed in the Sierra foothills at an average ground elevation of 3,450 ft. Your control network is on CCS83, Zone 3 (California III), and the combined factor at the project centroid is 0.99987. The design engineer's plan shows a station equation and a "ground" distance of 1,200.00 ft between two valve nodes. The contractor's GPS machine-control model was built by another surveyor using an assumed coordinate system with a base station on a local arbitrary point; the contractor reports that the pipe alignment is "0.18 ft off" from your stakes. Your RTK check shots on your total-station control differ by 0.10 to 0.15 ft horizontally and by 0.45 ft vertically. A second crew's file is tagged NAD83(2011), epoch 2010.0; the machine-control file is tagged NAD83(2011) but was localized to an arbitrary base using GEOID12B, while your RTK uses GEOID18.
1. Compute the grid distance corresponding to the 1,200.00-ft ground distance and explain the direction of the scale factor.
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Ground and grid are related by the combined factor, CF = scale factor x elevation factor: grid = ground x CF, and ground = grid / CF. A CF below 1 means grid distances are shorter than ground distances. Here ground = 1,200.00 ft and CF = 0.99987, so grid = 1,200.00 x 0.99987 = 1,199.844 ft, about 0.156 ft shorter. Conversely, if the plans showed 1,200.00 ft of grid, the ground distance would be 1,200.00 / 0.99987 = 1,200.156 ft. The 0.16-ft difference is close to the contractor's reported 0.18-ft offset, so a grid/ground mismatch is a prime suspect. Always state which distance is on the plans and which is on the control, and label the combined factor used.
2. Diagnose the 0.18-ft horizontal and 0.45-ft vertical disagreements between your stakes and the machine-control model.
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Treat horizontal and vertical separately. Horizontally, 0.10 to 0.15 ft between RTK and total station is within typical RTK uncertainty in foothill conditions, but add the 0.16-ft grid/ground scale difference and the arbitrary-base localization, and the 0.18-ft machine-control offset is explained. The vertical 0.45 ft is too large for random error: GEOID12B versus GEOID18 can differ by several tenths of a foot in the Sierra, and an arbitrary base with a localization will absorb a bad ellipsoid-to-orthometric conversion. Check the realization and epoch, the geoid model named in each file, the base coordinates, and whether the localization used enough well-distributed points. Do an independent check on a published NGS monument and run a constrained adjustment of your control. Then publish one project datum and one geoid model.
3. What control deliverable should you give the contractor so that machine control and stakes agree?
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Deliver a signed and sealed control package: a control diagram with coordinates, the datum realization and epoch (NAD83(2011), epoch 2010.0), the geoid model, the combined factor, and the definition of any project ground system; the transformation between grid and project ground; at least three check points independent of the model; and a metadata note describing all of it. Require the contractor to localize to your control and to verify on the check points before grading. Put the same metadata in the machine-control file and in the staking file so the two agree. If a second crew is on the job, require the same realization, geoid, and project datum; otherwise the 0.1-to-0.5-ft differences will recur. State clearly whether the pipe alignment is defined in grid or ground coordinates.