Bessel ellipsoid

The Bessel ellipsoid (or Bessel 1841) is an important reference ellipsoid of geodesy. It is currently used by several national surveys of Europe and on other continents, but will be replaced in the next decades by modern ellipsoids of satellite geodesy.

The Bessel ellipsoid was derived 1841 by Friedrich Wilhelm Bessel, based on several meridian arcs and other data of continental geodetic networks of Europe, Russia and the British Survey of India.

It is based on 10 meridional arcs and 38 precise measurements of the astro-geographic latitude and longitude (see also Astro geodesy). The dimensions of the ellipsoid axes were defined — corresponding to the former calculation methods — by logarithms.

The data (Bessel and GPS ellipsoid)

The Bessel ellipsoid fits especially well to the geoid curvature of Europe and Eurasia. Therefore it is optimal for National survey networks in these regions, despite of the fact that its axes are about 700 m shorter than that of the mean Earth ellipsoid derived by satellites.

Below the two axes "a", "b" and the flattening "f = (a-b)/a". As for comparison, the data of the modern "World Geodetic System" WGS84 are shown, which is mainly used for modern surveys and the GPS system.

* Bessel ellipsoid 1841 (defined by log "a" and "f"):
** a = 6.377.397,155 m
** f = 1 / 299,1528153513233 (0,003342 773154 ­± 0,000005)
** b = 6.356.078,963 m.

* Earth ellipsoid WGS84 (defined directly by "a" and "f"):
** a = 6.378.137,0 m"'
** f = 1 / 298,257223563
** b = 6.356.752,30 m"'.

Bessel ellipsoid and the National surveys

The ellipsoid data published by Bessel (1841) were the best and most modern data of the Earth's figure. They were used by almost all national surveys; just some surveys in Asia switched to the Clarke ellipsoid of 1880. After the forecome of geophysical reduction techniques, later many projects used the Hayford ellipsoid of 1910 which was adopted 1924 by the IAG as International ellipsoid 1924, or other newer ellipsoid data. All of them are influenced, too, by geophysical effects like vertical deflection, mean continental and rock density or the distribution of network data. Therefore every reference ellipsoid deviates from worldwide data (e.g. of satellite geodesy) like the pioneer work of Bessel.

In 1950 about 50% of the European triangulation networks and about 20% of other continents were based on the Bessel ellipsoid. In the following decades the American states switched mainly to the Hayford ellipsoid 1908 ("internat. Ell. 1924"). Additionally is was used for the European unification project ED50 which was sponsored by the USA after World War II, while Russia forced its satellite states in Eastern Europe to use the Krassowski ellipsoid of about 1940.

Up to now, the Bessel ellipsoid is the geodetic system e.g. for Germany, for Austria or for Czech Republic. Partly also in the successive states of Yugoslavia and some Asian countries (e.g. Sumatra & Borneo, Belitung) or Okinawa (Japan); in Africa e.g. Eritrea and Namibia.

See also

* Geodesy, WGS 72, WGS84
* Gauss-Krüger coordinate system, Helmert transform
* [http://www.geoima.de/software/easy/e_ellinfo.html worldwide Ellipsoids (website in german)]
* [http://www.gpsy.com/gpsinfo/geotoutm/index.html Conversion of Longitude and Latitude degrees into UTM coordinates]