## Height

**Description:
**

In outlining the coordinate systems in general use, the elevation or height of a point has been defined as ‘orthometric’ or ‘ellipsoidal’. With the increasing use of satellites in engineering surveys, it is important to understand the different categories. Orthometric height (H) is the one most used in engineering surveys in general terms, it is referred to as height above MSL. Ellipsoidal height and is rarely used in engineering surveys for practical purposes. However, satellite systems define position and height in X, Y and Z coordinates, which for use in local systems are first transformed to φG, λG and h using the equations of Section 8.3.3. The value of h is the ellipsoidal height, which, as it is not related to gravity, is of no practical use, particularly when

**Ellipsoidal and orthometric heights**

dealing with the direction of water flow. It is therefore necessary to transform h to H, the relationship of

However, as ξ is always less then 60, and therefore 0.99999995 < cos ε,≤ 1.0, it can be ignored:

with an error of less than 0.4 mm at the worst worldwide (0.006 mm in the UK).

The term N is referred to as the ‘geoid–ellipsoid separation’or ‘geoid height’and to transform ellipsoidal heights to orthometric, must be known to a high degree of accuracy for the particular reference system in use. In global terms N is known (relative to the WGS84 ellipsoid) to an accuracy of 2–6 m. However, for use in local engineering projects N would need to be known to an accuracy greater than h, in order to provide precise orthometric heights from satellite data.

To this end, many national mapping organizations, such as the Ordnance Survey in Great Britain, have carried out extensive work to produce an accurate model of the geoid and its relationship to the local ellipsoid.