Geodetic and Control Surveying
The geodetic domain tests datum literacy, Michigan's State Plane system, GNSS and control procedures, and the computations that convert between ground, ellipsoid, and grid.
Datums and the Michigan Coordinate System
Michigan's statutory coordinate system (Act 9 of 1964, as amended) uses the Lambert Conformal Conic projection in three zones: Michigan North (FIPS 2111), Central (2112), and South (2113), now referenced to NAD83(2011). Coordinates are for reference and do not alter property rights. Bearings, distances, and areas change when you move from ground to grid.
Scale, elevation, and combined factors
Grid distance = ground distance × combined factor, where combined factor = elevation factor × projection (scale) factor. Elevation factor ≈ R ÷ (R + h), with h taken as ellipsoid height (orthometric height plus geoid separation, for example GEOID18). State Plane scale factors are below 1.0 in Michigan and vary across a zone, so one factor per survey is an approximation.
Control practice
Tie to published NGS or state CORS monuments, run closed loops, and examine residuals before holding published coordinates. GNSS yields ellipsoid heights, which must be converted to orthometric elevations before comparison with bench marks.
Worked example
Ground distance 1,000.000 ft; elevation factor 0.999962; scale factor 0.999900. Combined factor = 0.999862. Grid distance = 1,000.000 × 0.999862 = 999.862 ft. To go from grid back to ground, divide by the combined factor; never multiply.
Traps
Applying the factor in the wrong direction; mixing NAD27 and NAD83 coordinates in one adjustment; treating an ellipsoid height as an elevation; forgetting convergence when converting grid bearings to true bearings.