Ground Distance, Grid Distance, and a Stakeout Offset
A surveyor uses RTK GNSS to establish two control points on a 22.6-acre parcel near Hagerstown, Maryland. The coordinates are in the Maryland State Plane Coordinate System, NAD83(2011), Lambert Conformal Conic. The combined factor at the site is 0.999952. The two points are also measured with a total station: horizontal ground distance 1,842.36 ft. A 1998 record plat gives the same line as 1,842.10 ft, but the plat does not state whether distances are ground or grid. The surveyor computes grid coordinates from the GNSS observations and stakes a building corner from those coordinates. A later total-station check between the two control points yields 1,842.36 ft ground. The contractor reports that the building is 0.07 ft off the planned offset from the property line. The parcel area computed from ground coordinates is 22.60 acres.
1. Compute the grid distance between the control points and compare it with the 1998 record distance. What can and cannot be concluded?
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Grid distance equals ground distance multiplied by the combined factor: 1,842.36 ft × 0.999952 = 1,842.36 ft − 0.0884 ft = 1,842.27 ft. The record distance is 1,842.10 ft. Compared with the computed grid distance, the record is short by 0.17 ft. Compared with the measured ground distance, the record is short by 0.26 ft. The record is somewhat closer to grid than to ground, but the difference is too large to be explained by rounding alone at this precision. The surveyor cannot conclude that the record is grid merely because it is closer; the plat does not state its basis. The correct next step is to examine the 1998 plat notes, deed basis, and any state-plane statement, and to check whether the line was re-monumented or the record distance was derived from different control. The computed grid distance is the value to use if the project control is grid-based.
2. Compute the grid area from the ground area and assess whether the difference is significant.
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Area scales by the square of the combined factor: grid area = ground area × (0.999952)^2 = 22.60 acres × 0.999904 = 22.5978 acres. The difference is about 0.0022 acre, or 0.0022 × 43,560 = 95.8 square feet. Numerically the difference is small and would not normally change a zoning or lot-area determination by itself, but the surveyor must label the basis. A plat that mixes ground distances, grid coordinates, and acreage without stating the basis creates ambiguity, especially where a minimum lot area or density calculation is close to a threshold. The surveyor should report the area on the same basis as the coordinates and distances shown on the plat, and should note the combined factor or the grid-to-ground relationship if state-plane coordinates are used.
3. Can the combined factor explain the contractor's 0.07-ft offset over a typical building offset? Show the calculation and state the likely conclusion.
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The scale effect over a short building offset is small. For an offset of, say, 150 ft, the grid-ground difference is 150 ft × (1 − 0.999952) = 150 ft × 0.000048 = 0.0072 ft, about 0.007 ft. The reported 0.07-ft discrepancy is roughly ten times larger, so the combined factor does not explain it. Even over a 1,000-ft line, the scale effect is only about 0.048 ft. The surveyor should look for other causes: centering or prism-constant error, an incorrect instrument height or target height, a control-coordinate error, stakeout using grid coordinates with ground distances without conversion, or a difference between the staked line and the property-line offset. An independent check measurement and a review of the stakeout reduction are warranted before the building layout is accepted or adjusted.