Geodesy and Geodetic Surveying
Reference surfaces and heights
Geodesy supplies the framework on which all surveys hang. The ellipsoid is a mathematical model (GRS80 for NAD83); the geoid is an equipotential surface approximating mean sea level. Heights relate by h = H + N, where h is ellipsoid height (GNSS-derived), H is orthometric height (what a level run produces), and N is the geoid undulation from a model such as GEOID18. Mixing h and H is a classic exam trap, and N varies with location - it is not a constant.
Datums and horizontal coordinates
NAD27 and NAD83 differ by hundreds of meters; a position cannot be shifted between them by a simple offset. WGS84 and ITRF are close to NAD83 but not identical. State Plane Coordinates divide states into zones with a defined projection and a scale factor that is exactly 1.0 only along the standard parallels (or the central meridian in a transverse Mercator). UTM uses 6° zones with a central-meridian scale factor of 0.9996.
Grid versus ground
Grid distance = ground distance × combined factor, where combined factor = scale factor × elevation factor, and elevation factor ≈ R/(R + h) using mean radius and average elevation above the ellipsoid. Grid azimuth differs from geodetic azimuth by the convergence angle. Sign errors here - applying the factor the wrong way, or adding instead of subtracting convergence - are a favorite distractor.
Worked example
Ground distance 1,000.000 ft, scale factor 0.99992, elevation factor 0.99997: combined factor = 0.99989, so grid distance = 999.890 ft.