Grid Distance, Ground Distance, and a 42-Minute Orientation Difference
A surveyor retraces a 1.5-mile rural boundary in Tippecanoe County. Two NGS monuments with NAD83(2011) Indiana State Plane West zone coordinates serve as control; the map projection scale factor at the site is 0.99998. Mean ground elevation is 700 ft; use R = 20,906,000 ft. A total station set on one control point and oriented on the other measures a horizontal ground distance of 5,280.12 ft between two boundary monuments. The deed calls that line as 80.00 chains (5,280.00 ft). The surveyor reduces the measurement to the state plane and reports a grid distance of 5,279.84 ft, then tells the client the boundary is 0.28 ft short of the deed. The client's fence sits at the deed distance. Separately, because the instrument was oriented on grid north, the field bearings differ from the record bearings by about 42 minutes, and the party chief wants to rotate all field data to match the deed.
1. Compute the elevation factor, combined factor, and grid distance. Was the 0.28-ft difference a boundary discrepancy? Show the reasoning.
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Elevation factor = R/(R+h) = 20,906,000/(20,906,000+700) = 0.9999665. Combined factor = elevation factor x scale factor = 0.9999665 x 0.99998 = 0.9999465. Grid distance = 5,280.12 x 0.9999465 = 5,279.84 ft. The 0.28 ft is the expected projection reduction, not evidence that a monument is misplaced. The deed distance of 5,280.00 ft is a surface distance unless the deed says otherwise and cannot be compared directly with a grid distance. To compare, either convert the deed distance to grid (5,280.00 x 0.9999465 = 5,279.72 ft) or convert the measured grid distance to ground (5,279.84/0.9999465 = 5,280.12 ft). The 0.12-ft difference between the deed and the measured ground distance is within reasonable retracement variation, and the monuments control over the deed distance in any event. Do not report a 'shortage' based on mixed surfaces.
2. Explain the 42-minute bearing difference and the correct use of convergence. What is the proper basis of bearing?
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Grid north and geodetic or true north differ by the convergence angle, which varies with longitude across the state plane zone. If the total station was oriented on grid north, the field bearings are grid bearings; the record bearings may be true, magnetic at the deed date, or an assumed basis. A 42-minute rotation is far too large to be random error and is consistent with convergence plus a different basis of bearing. The relationship is approximately: grid azimuth = geodetic azimuth minus convergence, with the sign depending on the convention and the side of the central meridian. Rotating the field data by the convergence alone is not enough if the deed basis is magnetic. Establish a basis of bearing from a reliable record line or from the state plane coordinates, state it on the plat, and transform all data consistently. Test the rotation on a known line; do not simply 'rotate to match the deed,' because that forces the boundary to the record bearing and can hide an orientation error.
3. How should the surveyor present the distance and orientation on the plat and in the report, and should the fence be moved?
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Report both ground and grid distances, the combined factor, the convergence, the coordinate system and epoch, and the basis of bearing. Identify which distances are record calls and which are measured. Explain that the 0.28 ft is a grid-versus-ground artifact and that the 0.12-ft ground difference is not a basis for moving a monument. The fence is a possession line at the deed distance; if the monuments are original and support a line elsewhere, show the fence and the monument line and explain the conflict. The surveyor does not order the fence moved; that is the owners' or a court's decision. If the fence has been mutually accepted for the statutory period, a boundary agreement may be appropriate. Give the client a clear written explanation so the 0.28-ft figure is not misused in a sale or permit application.