Gauss–Krüger coordinate system

The Gauss -Krüger coordinate system is a Cartesian coordinate system, which allows sufficiently small areas of the earth with metric coordinates ( Easting and Northing ) Compliant ( conformal ) to locate. There is a conformal transverse cylinder Figure (transverse Mercator).

Origin

The system was developed by Carl Friedrich Gauss and published by Johann Heinrich Louis Krüger and is mainly used in German-speaking countries. From 1935 to 2010, the Gaussian krügersche system in Germany was used as a basis for the representation of the triangulation results, later followed by the Netherlands, Sweden and South Africa. Much earlier, however, the military used the Gaussian triangle mesh. The Osnabrück country was taken from 1834 to 1847, the Emsland 1853-1860 and East Friesland in 1866, the same year took over the Prussian General Staff, the trigonometric, topographic and cartographic Arbeiten.Sehr many detailed topographic maps, especially large and medium-scale, build on the Gauss -Krüger coordinate system.

Construction

The grid of geographic coordinates is divided into 3 ° wide meridian strip ( a division into 6 ° will also be used). Each meridian strip changes from North to the South Pole in parallel with its so-called central meridian. The central meridians adjacent meridian strip are thus apart 3 ° (or 6 °).

Each meridian strip receives a code number (only for the Gauss -Krüger meridian system with 3 ° - strip ). This is derived from the number of degrees of the central meridian (0 °, 3 °, 6 °, ...).

Code = {0 °, 3 °, 6 °, ..., 351 °, 354 °, 357 ° } / 3 °.

Alternatively, in Eastern Europe and Asia, a numbering system is used, the zone 1 is also the central meridian assigns 3 ° east longitude, but uses zones with 6 ° of latitude, so that the central meridian of the Gauss - Kruger zone 21 then located at 123 ° east longitude. The eastern areas of Siberia are thus in zones 31 and 32 at the middle meridians 177 ° and 171 ° west longitude.

The meridian is mapped onto a cylinder angle preserving ( conformal), whose axis lies in the equatorial plane and whose radius is equal to the meridian radius of curvature of the reference ellipsoid. The cylinder touches as the earth's shape along the central meridian. The origin of the coordinate system is the intersection of the central meridian and the equator. The counts from the origin of a coordinate positive to the east ( easting ), the other coordinate positive to grid north ( northing ). You read the easting and northing values ​​as in any Cartesian coordinate system from, ie parallel to the axes and not to the now arcuate lines of longitude and latitude lines. For the right value is often the letter Y and used for the high value of the letter X.

The easting and northing values ​​are given in the SI unit meters. Thus, the high value indicates the distance from the equator to the central meridian isometrically mapped to Ordinatenfußpunkt and the right value, the (distorted ) distance from the central meridian on to the point. In order to avoid negative values ​​in the legal values ​​, a constant value of 500,000 m to this value when Gauss - Kruger meridian system added ( from the Austrian Federal Reporting Network ( BMN ) - depending on the reference meridian - the values ​​of 150,000 m ( strip M28 ), 450,000 m ( strips M31 ) or 750,000 m ( strip M34 ) added).

The right value is above written the code number of the central meridian; So on the seventh position of the decimal point. At the mention of coordinates these are usually listed in order Easting and Northing.

Example: The parade ground in Mannheim has the following coordinates

• Geographically (WGS84 ): 49 ° 29 ' 13.6 " N / 8 ° 27' 58.6 " E
• Gauss - Krüger: Easting 3461404 meters, Northing 5483498 m

From the law of value is given by the code number " 3" shows that 9 ° East is used as the reference meridian. 461404 there is less than 500,000, it can be seen that the position of the reference meridian is west.

Each system has according to a decision of the Working Committee of the Surveying Authorities of the States of the Federal Republic of Germany ( AdV ) from 1966 to both sides an area of ​​1 ° 40 ', so that two adjacent systems with a 20 length minutes ( on average approximately 23 km) wide strip cover. In this overlap area, the coordinates in each meridian, and the coordinates of the adjacent meridian strip are specified for each point. This is geodetic measurements and calculations to a certain extent also on the meridian edge addition possible without having to change the strip.

Unlike UTM

The UTM coordinates and the Gauss- Kruger meridian system use up to a scale factor, the same imaging equations (transverse cylindrical conformal mapping ) to the surface of the earth ellipsoid Verebnung.

The main difference is that the Gauss -Krüger meridian system in Germany (as well as in Austria and other states) the Bessel or Krasovsky ellipsoid underlie and 3 ° wide meridian strips are used, while UTM coordinates on the WGS84 - or the GRS80 ellipsoid and also use 6 ° wide meridian strip. With increasing strip width take at this compliant picture style the track distortions to the outer edge of the strip towards significantly. To compensate for the result of the wider meridian stronger linear and angular distortion at the zone edges of a scale factor of 0.9996 shall be placed at UTM. The central meridian is represented thus reduced by a factor of 0.9996 (40 cm / km). With increasing distance from the central meridian east or west, this shortening decreased due to the increasing image distortion within the zone. At about 180 km distance, the length distortion disappears. In the Gauss -Krüger coordinates are omitted because of only 3 ° wide stripes on such a scale factor because the maximum distortion is still within its practical relevance accuracy.

Structural differences between the two systems exist in the different approaches to naming the strip and the coordinates. Since the UTM system was originally introduced as a reporting system for the U.S. military, the appointment at UTM is planquadrat oriented. The coordinate values ​​of the UTM system should be to distinguish from those of the Gauss -Krüger system ( easting and northing value ) best with the East and North, and East and North value, respectively.

In Germany currently a transition occurs from the Gauss -Krüger coordinates ( Potsdam- date, Bessel / Krasovsky ellipsoid ) to the UTM system with reference to the ETRS89 ( system) with the GRS80 ellipsoid.

Use in Germany

In the German cartography and geodesy is used ( in parts also the Krasovsky ellipsoid ) reference ellipsoid as the Bessel ellipsoid.

The spatial definition of the Bessel ellipsoid to the earth system - the storage of the ellipsoid in the center of mass of the earth and its orientation relative to the Earth's rotation axis - was for the then Prussia with the help of the central point Rauenberg in Berlin. After its destruction, the central point of the network has been transferred to the computationally Helmertturm in Potsdam, therefore, the geodetic datum of this system is often mistakenly referred to as the Potsdam Datum (see: Geodetic datum ). This Rauenberg date is also the basis of the German main triangle mesh ( DHDN ).

In the GDR the Krasovsky ellipsoid was used as a basis as in the Soviet Union. It still finds its application in Mecklenburg- Vorpommern and Saxony- Anhalt.

In official Surveying ( Land Surveying ) is currently being switched from Gauss-Krueger - coordinates on the UTM coordinates.

As an internationally standardized designation used by OGC, the EPSG ( European Petroleum Survey Group ). For the meridian strip used in Germany or in the territory of the former German Empire following designations apply:

• 31466 for the meridian with the digit 2
• 31467 for the meridian with the digit 3
• 31468 for the meridian with the code 4
• 31469 for the meridian with the code 5

There is currently still a number of spatial data services with false IDs ( 31492-31495 ) or old identifiers ( 31462-31465 ). It should be noted that the systems differ with old and new identifier in the sequence of coordinate values ​​( Easting, Northing [ old ] or northing, easting [ new] ).

Use in Russia

Generally, however, other ellipsoids may be used. In Russia is how to use such as the Gauss -Krüger projection using the Krasovsky ellipsoid.

Use in Austria

In Austria, the date is used for Austria, the Austrian Federal signaling network based on a shifted Bessel ellipsoid. Increasingly, the UTM coordinate system is applied to the authorities and other organizations, while the army modeled on NATO also uses the MGRS system.

In practice, the Gauss -Krüger coordinate system is used predominantly. Accordingly, in civil engineering, hydraulic engineering, and the like Gauss-Krueger - coordinates are used for example in CAD systems as a reference ( eg the so-called world coordinate system of the CAD software AutoCAD). The coordinate system of the CAD software ( eg world coordinates of AutoCAD) then corresponds to the Gauss -Krüger coordinate system.

The Finnish YKJ coordinates

The published from 1970 to 2005 topographic maps (or produced until 2003 nautical maps) Finland use the country's unique YKJ coordinate system ( yhtenäiskoordinaattijärjestelmä ).

The system with two seven -digit numbers at the location with an accuracy of one meter ( easting and northing ). It refers to the 27 eastern longitude with a shift east (false easting ) of 3,500,000 meters and a scale factor of 1 As the geodetic datum reference ellipsoid is used from 1924 Hayford.

The YKJ coordinate system is currently being replaced by EUREF -FIN, the national implementation of ETRS89.