Geodesy and Geodetic Surveying
The three surfaces
Geodetic work rests on distinguishing the topographic surface, the geoid (an equipotential surface approximating mean sea level, continued under the continents) and the reference ellipsoid. Ellipsoidal height h relates to orthometric height H through h = H + N, where N is the geoid undulation. Candidates must know the datums used in the Philippines: PRS92 uses the Clarke 1866 ellipsoid but is a geocentric, ITRF-aligned datum; Luzon 1911 used the same ellipsoid in a non-geocentric, locally fitting orientation; WGS84 uses GRS80. Datum transformation uses a 7-parameter Helmert (three translations, three rotations, scale) or the Molodensky formulas.
Coordinates, projections and scale
Geodetic latitude, longitude and height convert to ECEF X, Y, Z and back. For plane coordinates the Philippines uses UTM (Transverse Mercator, k0 = 0.9996, false easting 500 000 m), with Zone 50 (central meridian 117 deg E) and Zone 51 (123 deg E). Grid distance relates to ground distance through the combined factor: CF = scale factor x elevation factor, the elevation factor being approximately R/(R + H). Grid azimuth = geodetic azimuth minus the convergence.
Traps
Reversing the sign of N, omitting the elevation factor, confusing geodetic with geocentric latitude, and forgetting that spherical excess e = Area/R squared, in radians, is needed for large geodetic triangles.
Worked example. A line has grid length 1 000.000 m at 200 m elevation with scale factor 0.999 65 and R = 6 371 000 m. Elevation factor = 6 371 000 / 6 371 200 = 0.999 968 6. CF = 0.999 618 6. Ground distance = 1 000.000 / 0.999 618 6 = 1 000.382 m.