State Plane, Ground Distance, and a Pipeline Control Network in Williams County
You are establishing horizontal control for a 4.5-mile produced-water pipeline in Williams County. You observe static GNSS sessions on three new monuments and process them relative to a North Dakota continuously operating reference station in NAD83(2011), epoch 2010.00. The project lies in the North Dakota North State Plane zone. At the east end, a 3,000.000-ft ground baseline yields a grid distance of 2,999.12 ft; at the west end, a similar baseline yields 2,999.38 ft. The site elevation ranges from 2,050 to 2,180 ft. The pipeline contractor will stake valves and bends using a total station from your control. The client's GIS consultant wants the control in "North Dakota State Plane, NAD83" for a web map. A county reviewer asks why the grid coordinates do not close to the ground distances by exactly 3,000.00 ft.
1. Compute the combined scale factor at each end of the project and explain the difference between grid distance and ground distance.
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Combined scale factor is grid distance divided by ground distance.
East end: 2,999.12/3,000.000 = 0.9997067.
West end: 2,999.38/3,000.000 = 0.9997933.
The difference is 0.0000866, or 86.6 parts per million. Over 3,000 ft that is 0.26 ft between the two ends for the same ground distance; over the full 4.5 miles (23,760 ft) it is about 2.06 ft. That is why a single project-wide factor can create a significant misclosure.
The combined factor has two parts. The elevation factor accounts for the project being above the ellipsoid: approximately 1 − H/R, where H is ellipsoid height and R is the Earth radius. At about 2,100 ft, the elevation factor is roughly 0.99990. The map projection scale factor accounts for the distortion of the State Plane Lambert Conformal Conic projection. The product of the two gives the combined factor. Grid distance is the distance on the projection; ground distance is the horizontal distance at the project elevation. Because the combined factor is less than 1 here, grid distances are shorter than ground distances.
2. Recommend which coordinates the contractor should use for stakeout and which the GIS consultant should use. Explain the consequences of using the wrong one.
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For construction stakeout, the contractor should use either a project ground coordinate system or State Plane coordinates with an explicit scale factor applied. A practical approach is to define a project coordinate system at the centroid of the pipeline, compute one combined factor there, and use it consistently for all stakeout computations. Alternatively, keep State Plane coordinates but require the field crew to convert grid distances to ground distances before setting valves and bends.
If the contractor stakes directly from grid coordinates without applying the factor, every measured ground distance will be short by about 0.0002 to 0.0003 times the distance. At 3,000 ft that is 0.7 to 0.9 ft; over 4.5 miles it can exceed 6 ft. That is enough to miss a valve tie or create a bend conflict.
For the GIS consultant, State Plane is appropriate because the web map is a statewide, projection-based product. The GIS data should carry the zone, units, datum realization, and epoch. The GIS consultant should not mix ground coordinates into a State Plane layer without a documented transformation, because the layer will not align with county parcels, roads, or other State Plane data.
3. What coordinate metadata would you deliver with the control, and why does the phrase "NAD83" alone create a problem?
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I would deliver: datum realization NAD83(2011), epoch 2010.00, North Dakota North State Plane zone, units in U.S. survey feet, the geoid model used for any orthometric heights, the projection and combined scale factors at the project ends and centroid, the CORS used, the observation dates and session lengths, the adjustment software and report, and the horizontal and vertical accuracies.
"NAD83" alone is ambiguous. NAD83 has multiple realizations, including NAD83(1986), HARN, CORS96, and 2011, and coordinates differ between them by decimeters to meters depending on location. A coordinate without a realization and epoch can be misused in a boundary or construction record. The reviewer also needs to know that the grid-to-ground difference is expected and documented, not a blunder. Delivering the metadata prevents another surveyor or GIS user from treating a grid coordinate as a ground coordinate and creating a false misclosure.