Closing a Four-Sided Traverse and Reporting Area
You have coordinates on a closed traverse around a proposed lot: A (N 1000.000, E 1000.000), B (N 1100.000, E 1050.000), C (N 1150.000, E 1150.000), D (N 1050.000, E 1200.000), and the return observation at A is (N 999.980, E 1000.020). The field crew used a total station with an EDM; the perimeter is measured along the four courses. The client wants the area in acres and a statement of relative precision. The county requires coordinates on the NH State Plane coordinate system, but the coordinates above are local assumed. Your technician computed a misclosure of 0.028 ft and an area of 15,000 sq ft by averaging the two coordinate pairs at A. The client asks whether the survey is 'good enough to record' and whether the area should be adjusted.
1. Compute the linear misclosure and relative precision of the traverse. Show the perimeter calculation and state whether the technician's 0.028 ft is correct.
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Using A as the held point, the closing vector is A' - A = (-0.020 N, +0.020 E). Linear misclosure = sqrt((-0.020)^2 + (0.020)^2) = 0.0283 ft. The courses are: AB = sqrt(100^2 + 50^2) = 111.803 ft; BC = sqrt(50^2 + 100^2) = 111.803 ft; CD = sqrt((-100)^2 + 50^2) = 111.803 ft; DA = sqrt((-50)^2 + (-200)^2) = 206.155 ft. Perimeter = 541.565 ft. Relative precision = 541.565 / 0.0283 = 19,100, or 1:19,100. The technician's 0.028 ft is correct to two significant figures, but the precision ratio must use the computed 0.0283 ft and the actual perimeter, not a rounded misclosure.
2. Compute the area by the shoelace method and convert to acres. Does averaging the two A coordinate pairs change the result materially?
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Using coordinates in order A-B-C-D and the shoelace formula, Σ(N_i E_{i+1} - E_i N_{i+1}) = 30,000 sq ft; area = 30,000 / 2 = 15,000 sq ft. In acres: 15,000 / 43,560 = 0.344 acre. Averaging A and A' changes the coordinates by only 0.010 ft in each ordinate; the area change is on the order of a few square feet, far below 0.01 acre. For a record plan, however, I would not silently average a misclosure. I would either hold A and report unadjusted coordinates with the closure, or perform a documented adjustment and show adjusted coordinates and areas. The area should be labeled unadjusted or adjusted accordingly.
3. The client asks whether the survey is good enough to record and whether the area should be adjusted. What is your answer?
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Internal closure of 1:19,100 is better than a common 1:10,000 traverse standard, but relative precision is only an internal-consistency check; it does not prove boundary position or control accuracy. The coordinates are local assumed, not NH State Plane, so they cannot be recorded as State Plane without a documented transformation and control check. The area need not be adjusted for the small misclosure, but the plan must state whether the area is based on unadjusted or adjusted coordinates. Before recording, I would verify the control, datum, units, and boundary evidence; if the plan is a boundary survey, the boundary must be located from monuments and occupation evidence, not from the local traverse alone. I would report the area as 0.344 acre with a note on basis and closure.