GNSS Grid Versus Ground Coordinates on a Kona Parcel
Your firm is staking a 40-acre parcel in Kona, Hawaii Island, using two control points established by network RTK in Hawaii State Plane Zone 1, NAD83(2011), epoch 2010.0. The published projection scale factor at the site is 0.999966. The average ellipsoid height is 2,100 ft. A total-station traverse between the two control points gives a ground distance of 4,826.34 ft. The GNSS grid coordinate inverse gives 4,825.71 ft. The field crew proposes to set the lot corners directly from the grid coordinates, because “state plane is the legal system.” The client's engineer will build a 1,000-ft driveway along one boundary and wants no more than 0.10 ft of misalignment. You must decide the basis of bearings and distances for stakeout.
1. Compute the combined factor and the expected grid-to-ground difference for the 4,826-ft line. Does the 0.63-ft discrepancy indicate a GNSS blunder?
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The elevation factor is R/(R+h), using R ≈ 20,902,000 ft and h = 2,100 ft: 20,902,000 / (20,902,000 + 2,100) = 0.9998995. Combined factor = 0.999966 × 0.9998995 = 0.9998655. Ground distance = grid distance / combined factor = 4,825.71 / 0.9998655 = 4,826.36 ft. The measured total-station ground distance is 4,826.34 ft, so the difference is only 0.02 ft. The 0.63-ft grid-versus-ground difference is exactly what the projection and elevation factors predict; it is not evidence of a GNSS blunder. The apparent “error” comes from comparing grid distance to ground distance without applying the combined factor. The RTK coordinates and the total-station measurement are consistent once reduced correctly.
2. What is the effect of using grid distances without correction over the 1,000-ft driveway? Is the crew's proposal acceptable?
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Over 1,000 ft, the scale correction is 1,000 × (1 / 0.9998655 − 1) ≈ 0.135 ft. That exceeds the engineer's 0.10-ft tolerance. If the crew sets corners using grid distances directly, the staked line will be short by about 0.13 ft per 1,000 ft, and the error grows with distance. The proposal is therefore not acceptable for construction stakeout at this tolerance. State plane coordinates are suitable for the legal coordinate record and for computations, but the field stakeout must use ground distances or a consistent scaling procedure. The crew could hold grid bearings but scale every distance by dividing by the combined factor, or use a total station with a scale factor applied. The key is to state the basis of bearings and distances on the stakeout plan and to use one consistent system.
3. Recommend the stakeout procedure: which coordinates/bearings to hold, how to handle the combined factor, and what check you would require before setting corners.
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Hold the state plane coordinates of the two control points as the primary record, and compute grid bearings between them. For stakeout, either compute ground distances by dividing grid distances by the site combined factor, or set the instrument to apply the scale factor. Use the grid bearings for azimuths and note that the convergence over a 40-acre parcel is negligible at this precision; if the parcel were larger, I would evaluate convergence explicitly. Before setting corners, require an independent check: occupy one control point, backsight the other, and measure a third known monument or a check point; compare the measured ground distance to the scaled grid distance. Also verify the combined factor with the actual site elevation and northing, not a regional average. Record the method, the combined factor, and the check results on the stakeout notes.