6.2 Geodesy, Earth Models, and Coordinate Systems
Key Takeaways
- Geodesy provides the earth models and reference systems behind latitude, longitude, ellipsoid height, and projected coordinates.
- Surveyors distinguish the physical earth, geoid, reference ellipsoid, geodetic coordinates, and map projection plane.
- FS questions commonly test conceptual differences rather than advanced geodetic derivations.
Geodesy Concepts Behind Survey Coordinates
Geodesy is the science of measuring and representing the earth. Surveyors use geodesy whenever work extends beyond a small local plane, uses GNSS, references a datum, or reports State Plane coordinates. FS questions do not require you to derive geodetic formulas from first principles, but they do require you to know which surface, coordinate type, and height system are being used.
The physical earth is irregular. Surveying simplifies it with reference surfaces. The geoid is an equipotential gravity surface often associated with mean sea level in a broad conceptual sense. It is not a simple mathematical shape. The reference ellipsoid is a smooth mathematical model used for geodetic latitude, longitude, and ellipsoid height. A map projection then transforms ellipsoidal positions to a flat grid.
| Surface or system | What it represents | Why it matters |
|---|---|---|
| Physical ground | Actual terrain where measurements occur | Construction, monuments, and occupation exist here |
| Geoid | Gravity-related reference surface | Basis for orthometric heights through geoid models |
| Ellipsoid | Smooth mathematical earth model | Basis for geodetic latitude, longitude, and ellipsoid height |
| Projection plane or grid | Flat coordinate representation | Basis for mapping, COGO, and State Plane coordinates |
| Local assumed plane | Project-specific coordinate frame | Useful for small sites but not automatically geodetic |
Latitude and longitude are angular coordinates on an ellipsoid or datum. Latitude measures north-south position relative to the equator. Longitude measures east-west position relative to a reference meridian. Ellipsoid height is measured along the ellipsoid normal, not along the direction of gravity. Orthometric height, used for many elevations, is related to the geoid and gravity field.
A key FS distinction is that GNSS commonly produces geodetic coordinates and ellipsoid heights in a defined reference frame. Project plans and benchmarks may use projected coordinates and orthometric heights. The surveyor must transform or convert between systems carefully. Reporting a GNSS ellipsoid height as a benchmark elevation without applying an appropriate geoid model would be a conceptual error.
Geometric geodesy deals with shapes, reference ellipsoids, coordinates, and positions. Physical geodesy deals with gravity, the geoid, and height systems. Both matter in surveying because horizontal position and elevation are tied to different reference concepts. The exam may ask why two points with similar ellipsoid heights can have different orthometric elevations, or why a geoid model is needed.
Coordinate systems can be local, geodetic, projected, or engineering based. A local site coordinate system may be convenient for construction but may not match State Plane coordinates. A projected coordinate system provides northing and easting on a grid. A geodetic coordinate system provides latitude and longitude. A vertical datum provides a basis for elevations. Mixing them without labels causes errors.
Scale is another geodetic issue. Distances measured on the ground differ from distances on the ellipsoid and distances on a projection grid. Elevation factor and grid scale factor help relate ground and grid distances. For a small property survey, the difference may be minor. For control networks, long routes, or precise layout, it can be significant.
For FS study, memorize the relationships rather than isolated terms. Ground observations are reduced to horizontal or vertical quantities. GNSS positions are tied to a datum and ellipsoid. Heights may need a geoid model. Projected coordinates are created by a projection. Construction may require ground distances. If an answer ignores these distinctions, it is likely wrong.
Which surface is a smooth mathematical model used for geodetic latitude, longitude, and ellipsoid height?
Why is a geoid model commonly needed with GNSS-derived heights?
Which coordinate type uses angular values?