Office Track - Level II Work Elements
The Office track at Level II tests computation and drafting: coordinate geometry, traverse adjustment, area, horizontal curves, field-data reduction, and the units and rounding that decide whether a plat closes.
Coordinates
Forward: ΔN = d·cos(Az), ΔE = d·sin(Az). Inverse: distance = √(ΔN² + ΔE²), azimuth = arctan(ΔE/ΔN) resolved into the correct quadrant. Bearings are quadrant angles; azimuths run 0–360° clockwise from north.
Adjustment
The compass (Bowditch) rule distributes the closure in proportion to course length; the transit rule uses the size of each latitude and departure. Adjust before computing final coordinates, area, or curve data.
Area
Use the coordinate (shoelace) method or double meridian distances, carry the signs, and close back to the first station. A sign flip doubles the error instead of cancelling it.
Curves
Arc definition: D = 5729.57795/R in feet. T = R·tan(Δ/2), L = 100Δ/D, long chord = 2R·sin(Δ/2), external = R·(sec(Δ/2) − 1).
Units
US survey foot = 1200/3937 m; international foot = 0.3048 m. The difference is about 2 ppm and matters on state plane coordinates.
Worked example. From N 5000.00, E 5000.00 to N 5100.00, E 5150.00: ΔN = +100.00, ΔE = +150.00. Distance = √(100² + 150²) = √32,500 = 180.28. Azimuth = arctan(150/100) = 56.3099° = 56°18'36"; both differences are positive, so the bearing is in the northeast quadrant, N 56°18'36" E. Entering easting first is the commonest blunder - most software wants (N, E, Z).
Traps. A bearing written where an azimuth is required; 360° booked as 0°; rounding mid-calculation; compass and transit rules swapped; a scale factor applied to the wrong side of a grid-to-ground conversion; a deflection angle used as Δ.