RTK, Grid Distance, and the 0.56-Foot Misclosure
An Ohio surveyor is establishing control for a 3,200-ft boundary line in Adams County. Network RTK yields 12 fixed solutions with horizontal precision of 0.02 ft, but two points in deep woods remain in float. A total-station traverse between the fixed points measures 3,200.18 ft on the ground. The GPS grid distance between the same points is 3,199.62 ft. The site elevation is about 950 ft above the ellipsoid, and the project is in the Ohio South State Plane zone. A CAD technician uses the grid distance to compute lot corner coordinates and stakes the line; the line closes 0.56 ft short at the far end. The client wants to know why the line does not close and whether the float points can be used. The surveyor also needs to decide how to document the basis of bearings.
1. Explain the source of the 0.56-ft difference and the correct way to convert between grid and ground.
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The difference is a scale effect, not a blunder. State Plane coordinates are grid values; ground distances at elevation are longer than grid distances. The combined factor is the product of the elevation factor and the map scale factor. Here grid divided by ground is 3,199.62 / 3,200.18 = 0.999825. The elevation factor is approximately R / (R + h) = 20,906,000 / (20,906,950) = 0.999955, so the map scale factor is about 0.999870. The 0.56-ft difference is almost exactly the scale correction. To convert grid to ground, divide the grid distance by the combined factor, or establish a local ground coordinate system and apply it consistently. Using grid distances directly for ground stakeout shortened the line by 0.56 ft and caused the misclosure.
2. What should the surveyor do about the two float points?
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The float points should not be used as control. A float solution has not resolved the integer ambiguities, so its coordinates can be meters off even when the displayed precision looks small. The surveyor should occupy the fixed points with a total station and traverse to the float locations, use static GPS with longer occupations, or establish control from an independent source. The float points can be used only as checks after fixed control is established. The surveyor should also run a closed traverse or redundant ties so a single bad point cannot propagate. If the boundary depends on those corners, the surveyor must show the control quality and not let a float position become a boundary monument.
3. What documentation and accuracy checks are needed before staking the boundary?
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Document the coordinate system, epoch, geoid model, projection and zone, combined factor, and whether coordinates are grid or ground. Include a control diagram showing fixed points, checks, and ties to published control or other reliable monuments. Report the traverse closure and the residuals at checkpoints. Verify scale and rotation by measuring between two independent control points and comparing ground and grid values. Keep boundary monuments tied to the control so the basis of bearings is clear. Before staking, confirm that the CAD file uses the same units and factor as the field work. If grid and ground are mixed, the error will appear as a systematic misclosure rather than a random one.