Grid Coordinates, Ground Distances, and a Rotation You Cannot Skip
You are laying out a 22-lot residential plat in the Mississippi East state plane zone. Your control was observed by network RTK and reduced to the grid using a combined factor of 0.999872. Two found boundary monuments, which you intend to hold for the basis of bearings, have grid coordinates yielding a grid azimuth of N 88 degrees 47 minutes 52 seconds E and a grid spacing of 1,247.318 ft. The 1908 deed between those same two monuments calls N 88 degrees 42 minutes 30 seconds E, a distance of 1,247.47 ft. Lot areas must be shown to 0.001 acre. The project engineer, working from your raw grid coordinate list, has already computed lot areas and set two lot corners with a stakeout routine directly from those coordinates.
1. Compute the ground distance between the monuments and the rotation you must apply, and explain which distance appears on the plat.
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Ground distance = grid distance divided by the combined factor: 1,247.318 / 0.999872 = 1,247.478 ft, i.e. 1,247.48 ft. That agrees with the 1908 record call of 1,247.47 ft to within 0.01 ft, which is a strong confirmation that the record is on a ground basis and that the grid spacing must not be shown as a boundary distance.
Rotation = record azimuth minus grid azimuth: 88 degrees 42 minutes 30 seconds minus 88 degrees 47 minutes 52 seconds = minus 0 degrees 05 minutes 22 seconds. Every grid-derived bearing gets that rotation applied before it becomes a record bearing.
What goes on the plat: the ground (surface) dimensions, not the grid dimensions. Bearings are stated on the record basis, referenced to the line between the two held monuments. If you choose to also show state plane coordinates, label them as a separate coordinate annotation, state the zone, datum and realization, epoch, and combined factor, and add a note that the coordinates are for reference and are not to be used to establish boundaries.
Note also that the 5 minute 22 second difference is not purely a convergence value - you cannot assume the 1908 surveyor used true north. What you are actually doing is holding his bearing and rotating everything else to it.
2. Quantify the error created by the engineer's stakeout from raw grid coordinates at a lot corner 250 ft from control, and describe the consequences.
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Two errors act together:
Rotation. 0 degrees 05 minutes 22 seconds equals about 0.001561 radians. At 250 ft from the control the transverse offset is 250 times 0.001561, or roughly 0.39 ft, swinging counterclockwise from the intended position.
Scale. The combined factor differs from unity by about 128 ppm, so 250 ft is under-measured by about 0.032 ft - small by comparison but in the same problem.
Combined, the staked corner is roughly 0.4 ft from where the ground-basis survey places it. That is enough to put a corner on the wrong side of a setback line, inside a drainage easement, or off the frontage dimension by more than the plat's stated precision. On a 60-ft lot frontage, 0.4 ft is a measurable lot width deficiency that can trigger a zoning variance the developer did not budget for.
The corrected response: recompute the lot geometry in ground/record basis, notify the engineer in writing of the discrepancy and the cause, and restake the two corners before any construction stakeout or concrete is placed. Document the notification and the restake. Do not simply adjust your plat to match the field stakes - the coordinates were the error, and the monuments and record basis still control.
3. What must the plat itself state about basis of bearings, distances, coordinates, and closure?
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A defensible plat in this situation carries, at minimum:
- Basis of bearings, stated explicitly: bearings are referenced to the record line between monument A and monument B, held as N 88 degrees 42 minutes 30 seconds E, with the monuments described and their positions shown.
- Distance basis: whether distances and areas shown are surface/ground or grid, and, if state plane is annotated, the zone, datum and realization, epoch, geoid model, and the combined factor applied.
- A coordinate disclaimer if coordinates are shown at all, stating that they are for reference and locational purposes and are not to be used to establish or reestablish boundary positions.
- Closure/relative precision statement for the boundary traverse and for the control, computed honestly.
- Monument list and legend: what was found, what was set, and which were held.
- Curve data and area tabulation computed to the precision shown, with areas labeled as to basis.
Also include a note on any rotation applied between grid and record basis, since a future surveyor retracing your plat needs to reproduce your sequence. A plat that shows coordinates without stating the basis invites exactly the stakeout error the engineer just made.