Standard Parameters
Note that the rotation angles given in the table are in seconds and must be converted to radians before use in the calculation.
| Region | Start datum | Target datum | (Metre) | (Metre) | (Metre) | s (ppm) | rx (Arcsecond) | ry (Arcsecond) | rz (Arcsecond) |
|---|---|---|---|---|---|---|---|---|---|
| Slovenia ETRS89 | D48 | D96 | 409.545 | 72.164 | 486.872 | 17.919665 | −3.085957 | −5.469110 | 11.020289 |
| England, Scotland, Wales | WGS84 | OSGB36 | −446.448 | 125.157 | −542.06 | 20.4894 | −0.1502 | −0.247 | −0.8421 |
| Ireland | WGS84 | Ireland 1965 | −482.53 | 130.596 | −564.557 | −8.15 | 1.042 | 0.214 | 0.631 |
| Germany | WGS84 | DHDN | −591.28 | −81.35 | −396.39 | −9.82 | 1.4770 | −0.0736 | −1.4580 |
| Germany | WGS84 | Bessel 1841 | −582 | −105 | −414 | −8.3 | −1.04 | −0.35 | 3.08 |
| Germany | WGS84 | Krassovski 1940 | −24 | 123 | 94 | −1.1 | −0.02 | 0.26 | 0.13 |
| Austria (BEV) | WGS84 | MGI | −577.326 | −90.129 | −463.920 | −2.423 | 5.137 | 1.474 | 5.297 |
| USA | WGS84 | Clarke 1866 | 8 | −160 | −176 | 0 | 0 | 0 | 0 |
These are standard parameter sets for the 7-parameter transformation (or data transformation) between two ellipsoids. For a transformation in the opposite direction, the signs of all the parameters must be changed. The translations cx, cy, cz are sometimes described as tx, ty, tz, or dx, dy, dz. The rotations x, y, and z are sometimes also described as, and . In the United Kingdom the prime interest is the transformation between the OSGB36 datum used by the Ordnance survey for Grid References on its Landranger and Explorer maps to the WGS84 implementation used by GPS technology. The Gauss–Krüger coordinate system used in Germany normally refers to the Bessel ellipsoid. A further datum of interest was the ED50 datum based on the Hayford ellipsoid. It is used by NATO for military maps and in future for most EU countries.
The earth does not have a perfect ellipsoidal shape, but is described as a geoid. Instead, the geoid of the earth is described by many ellipsoids. Depending upon the actual location, the "locally best aligned ellipsoid" has been used for surveying and mapping purposes. The standard parameter set gives an accuracy of about 7 m for a OSGB36/WGS84 transformation. This is not precise enough for surveying, and the Ordnance Survey supplements these results by using a lookup table of further translations in order to reach 1 cm accuracy.
Read more about this topic: Helmert Transformation
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