Surveying Fundamentals and Geodesy
Surveying Fundamentals and Geodesy
This domain tests how positions and heights are referenced to the Earth, how surveys close and adjust, and when plane approximations stop being defensible.
Core rules and concepts
- A geoid is an equipotential surface approximating mean sea level; an ellipsoid is a mathematical reference surface; a geodetic datum fixes the ellipsoid to the Earth in origin, orientation, and scale.
- Orthometric heights are referenced to the geoid; ellipsoidal heights are referenced to the ellipsoid. GNSS yields ellipsoidal height h; orthometric H = h − N, where N is geoid undulation.
- Plane surveying is acceptable over small extents. Curvature and refraction grow with distance; combined correction is approximately 0.0675d² with d in km and correction in metres.
- Networks need redundancy. Angular misclosure is distributed by a stated adjustment model, commonly an equal correction per angle when angles are equally weighted.
Worked example
A leveling line of 2 km shows a 0.30 m discrepancy. If sight lengths are badly unbalanced, curvature and refraction alone can account for about 0.0675 × 2² = 0.27 m, so the field procedure must be corrected rather than the arithmetic fudged. For a five-sided traverse, observed interior angles sum to 540°00′45″; the theoretical sum is (5−2)×180° = 540°. Misclosure is +45″; equal correction is −9″ per angle, giving adjusted angles that sum to 540°.
Traps
- Treating GNSS ellipsoidal heights as orthometric elevations without a geoid model.
- Applying curvature correction without considering balanced sights or the sign convention.
- Using the polygon formula (n−2)×180° with the wrong n or mixing interior and exterior angles.
- Ignoring datum differences when combining old survey control with GNSS-derived coordinates.