These notes resulted from discussions with the Survey Computing section of the Ordnance Survey of Great Britain (OSGB) and with the US Defense Mapping Agency (DMA)
Geodetic Datums and WGS 84. The so-called `World Geodetic System 1984', amongst other things, defines an ellipsoid (a three-dimensional ellipse) which is the currently accepted `best fit' for the overall shape of the Earth. When an ellipsoid is fixed at a particular orientation and position with respect to the Earth, it constitutes a so-called `Geodetic Datum'. WGS 84 is one such Geodetic Datum. Conventional surveying and projection techniques are then applied to the appropriate Geodetic Datum in order to produce a map. An ellipsoid itself is therefore insufficient to define a Geodetic Datum, the position and orientation of the ellipsoid to the Earth need to be defined also. The ellipsoid radii for WGS 84 are as follows, noting that the FAI Sphere is 6371 km for the purpose of measurement for FAI purposes:
GPS/SATNAV. GPS uses the WGS 84 Geodetic Datum as its world reference system, although software programmes supplied with the equipment allow other Geodetic Datums (see below) to be used in calculations. GPS works on cartesian co-ordinates based in the normal way on XYZ values. Z values are referenced to the Earth's spin axis, which is approximately the line joining the geographical poles (not exactly because the spin axis both rotates and moves). X values are referenced to a datum meridian, Greenwich. Y values are at right angles to the others.
Mapping. For conversion to a flat surface (ie for mapping), a projection process is applied to a world reference system (Geodetic Datum) with its associated ellipsoid. You may choose such a Datum for an number of reasons. WGS 84 is the latest standard for the whole world but may not an exact fit in a given area. If really precise mapping is needed, information on local real Earth data is needed such as from the geoid:
The Geoid. The geoid is the shape of an assumed earth using a theoretical water surface (ie a surface completely at a theoretical sea level) as it would be without terrain and without external gravity (ie no spin, no tides). A geoid is therefore a smooth surface close to real mean sea level over the whole earth (MSL +20 m - 40 m, the variation depending on gravity effects of mountains, trenches & crustal thickness and density). The exact geoid shape therefore varies with locality. For accurate local mapping, you look at the area that you want to map, and then match the local geoid to a formula which most closely approximates to its shape. For very specific mapping tasks, you may use a formula correct for a small area of the geoid; for the channel tunnel between UK & France, a model accurate for the channel area was used, because of the need for the bores to meet properly in the middle! Centimetres of accuracy mattered in this case.
Projections. The most common projection for mapping to high accuracy (as opposed to general navigation) is the Transverse Mercator (TM), which is particularly suited to maps of N/S areas. For example, the UK OSGB 36 Grid is based on a TM projection with a datum meridian of 2° W. For formulas applying world-wide for TM projections, the definitive work is: Redfearn J C B, Transverse Mercator Formulae; Survey Review 9/69 Pages 318-322; published 1948.
UTM Grid. The Universal Transverse Mercator (UTM) grid is a world-wide system. However, note that the UTM grid also uses 2 conic projections for polar regions. UTM is a projection and does not define an ellipsoid or Geodetic Datum. It uses 60 segments of 6° round the globe; each segment is called a `gore' and identified by a Zone number. Some nations are on the lines between UTM Zones, and for national mapping purposes they use different zoning so as to avoid discontinuities across their maps. For transformations from UTM Grid to Lat & Long, a Geodetic Datum must be defined such as ED 50 or 79 for Europe, OSGB 36 for the UK, WGS 84 etc.
Difference between different geodetic datums. Lats & Longs can differ by several hundred metres for the same point on the earth's surface depending on whether you use WGS 84 or another Geodetic Datum. There are over 240 other Geodetic Datums currently in use, ranging from Antigua 43 to Zanderij (Surinam).
Aviation Applications. FAA (US), CAA (UK), ICAO and other bodies are urgently studying these matters. Eurocontrol has decided to use WGS 84 for ATC aspects. In the future, airfield, runway and approach datums will use WGS 84 figures, to provide world-wide standardisation and to make the use of GPS easier.
Conversions. Conversions between geodetic datums (eg ED 79 to WGS 84) are, in theory, straightforward but need computing. At least 7 parameters set each datum. In 1993, accurate data in Europe was, for the first time, available in WGS 84 form after a long programme of measurement and calculation. For Europe, another geodetic datum is called ETRF 89 (European Terrestrial Reference 89) and is WGS 84 for the European area. ETRF 89 even includes, for the long term, the predicted movement of tectonic plates. Measuring points use interferometer and other measurements of stars in order to obtain highly accurate results. In a similar way, North American Datum 83 (NAD 83) is identical to WGS 84 for the North American area.
Future Mapping. In the future, it is likely that, world wide, map lats/longs and local grids will be re-drawn to the WGS 84 datum instead of the present local Geodetic Datums used now. This will entail new maps, different grid references and slightly different lat/longs from those in use now. Where grid references are concerned, the new WGS 84 grids may deliberately be created with significantly different grid datums compared to present grid systems, in order to reduce ambiguity.
Accuracy of Measurement. Grid co-ordinates are accurate and unambiguous, as long as you state clearly the grid datum used, ie OSGB 36, UTM Grid with its Zone number and Geodetic Datum, or others. However, for a given point on the Earth's surface, there are many different Lats and Longs which can quite correctly be quoted, varying by up to several hundred metres. These depend on the Geodetic Datum used in the conversion. As an example, in the UK, differences in Lat/Long of between 75 and 135 m occur depending on whether the OSGB 36 or WGS 84 Datums are used. Furthermore, if some other datum is set by mistake, the difference can be over 1000 m. These differences have serious implications for precise navigation systems such as approach and landing aids, which is why ICAO and other aviation bodies are urgently addressing the problem.
FAI Measurements. These differences are significant also for FAI measurements for records of distance and speed, and have implications for GPS validation of Turning Points. However, the basic FAI system for distance measurement is not accurate because of the use of an assumed sphere of radius 6371.00 km rather than an ellipsoid, equating to WGS 84 radius only at about 35° latitude. At a latitude of 55°, the difference between the FAI radius and WGS 84 is about 7 km. FAI should consider changing from the sphere to WGS 84. Meanwhile the implications for distance calculations and validation of FAI distances should be noted.
Survey Computing Section (Attn Ian Wilson)
Ordnance Survey
Romsey Road, Maybush
SOUTHAMPTON SO9 4DH
United Kingdom
Last updated by John Leibacher on Sunday, November 5, 1995 at 17:53
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