3. Geodetic Datums and Coordinate Systems
Geodetic Datums and Coordinate Systems
This domain tests datum realisation, coordinate transformations, map projections and grid computations. You must distinguish a datum from a projection and know how scale factor and convergence enter survey coordinates.
Core rules
- A datum includes an ellipsoid, origin, orientation and realisation (a set of stations with coordinates).
- Sri Lanka has used the Kandawala datum and later the SLD99 geocentric datum; mixing them without transformation corrupts coordinates.
- A map projection converts ellipsoidal coordinates to grid coordinates; the Transverse Mercator is common for national grids.
- Grid scale factor k varies with distance from the central meridian; grid convergence is the angle between grid north and true north.
- A Helmert 7-parameter transformation includes three translations, three rotations and a scale factor; it is approximate and epoch-dependent.
Worked example
For a Transverse Mercator projection with central scale factor k0 = 0.9996, estimate k at 200 km from the central meridian. Use k is approximately k0(1 + x^2/(2R^2)). With R = 6371 km, x^2/(2R^2) = 40,000/(2 x 40.59 x 10^6) is approximately 0.000493. Then k is approximately 0.9996 x 1.000493 = 1.00009. A ground distance of 1,000.000 m becomes about 1,000.093 m on the grid.
Traps
Calling WGS84 a projection; using grid distance as ground distance; ignoring convergence in azimuth; applying a transformation in the wrong direction; assuming one transformation suits all epochs.