Survey Computations and Coordinate Systems
This domain tests the arithmetic and coordinate logic behind boundary and control work. Expect inverse computations, traverse adjustment, and grid-to-ground conversions.
Traverse computations
Convert bearings to azimuths, compute latitudes and departures, sum them, and determine linear closure. Angular closure is compared with the allowable based on the instrument and number of angles. A compass rule distributes latitude and departure errors in proportion to line length; a transit rule distributes by latitude and departure magnitude. State the adjustment rule used.
Coordinate systems
Geodetic coordinates are transformed to State Plane grid coordinates through a projection. Grid distance differs from ground distance by the combined factor, approximately grid scale factor × elevation factor. To convert grid distance to ground distance, divide by the combined factor; to convert ground to grid, multiply by it. Kentucky uses one State Plane zone, a Lambert Conformal Conic projection on NAD83. Grid convergence affects azimuths and must be applied when relating grid bearings to astronomic or ground bearings.
Worked example
Point A is N 1,000.000, E 2,000.000; point B is N 1,500.000, E 2,400.000. ΔN = +500.000, ΔE = +400.000. Distance = √(500² + 400²) = 640.312 feet. Bearing = arctan(400 ÷ 500) = 38.6598°, or N 38°39′35″ E. The reasoning is to compute the inverse in the correct quadrant and report bearing and distance consistently.
Traps
Using ground distance as grid distance, applying the combined factor upside down, ignoring quadrant, mixing feet and meters, and omitting convergence are common errors.