# Swiss national coordinates

The Swiss national coordinates ,  abbreviated as CH1903 or  LV03 for "National survey 1903", also referred to as military coordinates or Swiss Grid , belong to a coordinate system that is used in official surveys and on many maps of Switzerland . The Principality of Liechtenstein also uses these coordinates in the older version of the Swiss civil coordinates (Liechtenstein reference system) no longer common in Switzerland today .

CH1903 is based on the Bessel ellipsoid and an oblique, conformal cylinder projection ( Mercator projection ). Due to the small size of Switzerland, a single map projection from the ellipsoid is sufficient . The newer system that is being converted is that of the national surveying 1995 ( LV95 ), in the form of  CHTRS95 ( Swiss Terrestrial Reference System  1995) and  CH1903 + .

## Map projection

The fundamental point for this coordinate system is the former observatory in Bern , where the building for exact sciences of the University of Bern is today. Its coordinates in meters are set at 600,000  /  200,000 in the “military coordinates ” system used today ; In the previously used system of "civil coordinates", the former observatory in Bern formed the origin or zero point with the coordinate values ​​0/0.

The geodetic date is based on the country triangulation from 1903 to 1939 (LV03). The network scale results from the three baselines measured in 1880/81 in Aarberg , Bellinzona and Weinfelden . They can be viewed directly from a large area and are well distributed within the country.

For the projection, the Bessel ellipsoid is first mapped onto a sphere and from this onto a cylinder touching the sphere in the Bern meridian . The circle of contact between the ball and cylinder is a great circle and intersects the Bern meridian at right angles. In this double projection, the cylinder axis does not coincide with the earth's axis, but the axes form an angle that corresponds to the latitude of Bern. From the intersection of the meridian and the great circle, the first coordinate axis (“y-axis”, developed great circle) points in an easterly direction and the second coordinate (“x-axis”, 7 ° 26 ′ east, “Bernese meridian”) points north . In comparison to the mathematical convention , the x and y axes are swapped.

The height mark of the associated leveling is located in a rock in the port basin of Geneva, the Pierre du Niton , with a height of 373.60 m above the Marseille gauge .

### Military coordinates

Adding y = 600 km ( false easting ) and x = 200 km ( false northing ) to the “ civil coordinates” gives the “military coordinates”. The coordinate 0/0 (zero point) of the «military coordinates» is near Bordeaux in France . The starting point and thus also the zero point resulting from it were deliberately chosen so that the error rate when determining and transmitting the coordinates of any point in Switzerland should be as small as possible.

This system fulfills the following requirements:

• The zero point is set so that the whole country is in the first quadrant of the coordinate system. This means that the coordinate values ​​within the country are always positive.
• The whole country lies to the south and east of a line running northeast from the zero point, i.e. in the lower half of the quadrant. This ensures that the value of the y-coordinate (east) within the country is always greater than that of the x-coordinate (north).
• The northernmost and easternmost points of the country are less than 1000 km from the axes, which means that all points in Switzerland have a maximum of six-digit coordinates.

These advantages of the "military coordinates" were also recognized in the official surveying of Switzerland, which is why in 1918 there was a uniform conversion to the "military coordinates".

On the other hand, the cadastral surveying of Liechtenstein stayed with the "civil coordinates". It is not possible to mix up the coordinates in the territory of the principality, so a changeover was not found necessary.

Example coordinates

• Bern y = 600000, x = 200000 (Sidlerstr. 5, 3012 Bern, University of Bern, Exact Sciences; WGS84 : 46.9510827861504654, 7.4386324175389165)
• Rigi y = 679520, x = 212273
• Zurich-Seebach y = 684592, x = 252857
• Vaduz  LI y = 158008, x = 23061 (CH1903: y = 758008, x = 223061)

## application areas

CH1903 is the “official” coordinate system in Switzerland. The Office for Spatial Planning and Surveying, the Federal Statistical Office and many other authorities use CH1903 for georeferencing . The official national map of Switzerland uses the Swiss national coordinates. Emergency services in Liechtenstein and Switzerland also exclusively use this coordinate system. The Swiss national coordinates are also used by the Swiss Army , the Border Guard , Civil Defense , REGA , the cantonal police and other Swiss rescue services. The  EPSG has assigned the code 21781 to the CH1903 system.

The Liechtenstein national survey, and thus the entire surveying and mapping system, still uses the Swiss civil coordinates with reference to Bern.

## Conversion of WGS84 to CH1903

### Calculation bases

The conversion from the ellipsoidal WGS84 coordinates to the Swiss projection coordinates (CH1903) can easily be done using an approximation formula. With the formulas described below, an accuracy of about one meter is possible.

1. Coordinates are converted into sexagesimal seconds. Result: latitude φ and longitude λ.

2. The auxiliary quantities φ 'and λ' are formed from φ and λ. The formulas for this are:

${\ displaystyle \ varphi '= {\ frac {\ varphi -169028.66} {10000}}}$
${\ displaystyle \ lambda '= {\ frac {\ lambda -26782.5} {10000}}}$

3. Finally, the Swiss coordinates ( and in m) are calculated: ${\ displaystyle x}$${\ displaystyle y}$

${\ displaystyle {\ begin {matrix} x & = & 200147.07 \\\ & + & 308807.95 \ cdot \ varphi '\\\ & + & 3745.25 \ cdot \ lambda' ^ {2} \\\ & + & 76 .63 \ cdot \ varphi '^ {2} \\\ & + & 119.79 \ cdot \ varphi' ^ {3} \\\ & - & 194.56 \ cdot \ lambda '^ {2} \ cdot \ varphi' \ end {matrix}}}$
${\ displaystyle {\ begin {matrix} y & = & 600072.37 \\\ & + & 211455.93 \ cdot \ lambda '\\\ & - & 10938.51 \ cdot \ lambda' \ cdot \ varphi '\\\ & - & 0.36 \ cdot \ lambda '\ cdot \ varphi' ^ {2} \\\ & - & 44.54 \ cdot \ lambda '^ {3} \ end {matrix}}}$

### example

Practical example: center of La Chaux-des-Breuleux on

φ = 47 ° 13 '15 "N
λ = 7 ° 1 '41 "E

Conversion into sexagesimal seconds:

φ = ( 47 * 3600) + ( 13 * 60) + 15 = 169995
λ = ( 7 x 3600) + ( 1 x 60) + 41 = 25301

Calculation of the auxiliary variables:

φ ′ = ( 169995 - 169028.66) / 10000 = 0.096634
λ ′ = ( 25301 - 26782.5) / 10000 = −0.14815

Calculation of the meter coordinates:

x = 200147.07 + 308807.95 · φ ′ + 3745.25 · λ′² + 76.63 · φ′² + 119.79 · φ′³ - 194.56 · λ′² · φ ′
x = 230071
y = 600072.37 + 211455.93 · λ ′ - 10938.51 · λ ′ · φ ′ - 0.36 · λ ′ · φ′² - 44.54 · λ′³
y = 568902

The national coordinates of La Chaux-des-Breuleux are therefore 568'902 / 230'071.

### Liechtenstein

These values ​​for Bern (600,000 / 200,000) must be added to the Liechtenstein national survey coordinates. The high value (x-coordinate, always smaller than 100,000) is only given in five digits, both coordinates in meters.

Example Vaduz :

Liechtenstein reference system: 158008/23061
158008 + 600000 = 758008
23061 + 200000 = 223061
Swiss military coordinates: 758'008 / 223'061

## Land survey 1995

The national survey LV95 introduced two new reference systems, which should replace the historical system based on national triangulation. The EPSG code for this is 2056:

• CHTRS95 ( Swiss Terrestrial Reference System 1995 ) is based closely on the European reference system ETRS89 . The frame of reference is defined in such a way that both systems are identical at the time .${\ displaystyle t_ {0} = 1993.0}$
• The local reference system CH1903 + uses the same ellipsoid as CH1903 ( Bessel 1841 ). The aim was to match the existing system as closely as possible. However, the projected coordinates are given an additional offset of 2,000 km or 1,000 km for clear differentiation. This means that the projection center in the old Bern observatory has the coordinates 2,600,000 m / 1,200,000 m. The fundamental point was moved to Zimmerwald , however, as the old fundamental point can no longer be used today.

To convert from CH1903 + to CH1903, the local distortions of the over 100 year old system must be simulated. With the help of a transformation data set, the corrections of up to 1.6 m can be calculated according to a clearly defined algorithm.

### Timeframe of the changeover

Approx. The conversion to the new frame of reference began in 2005. According to the Geoinformation Ordinance, Art. 53, the data of the official surveying must be transferred from CH1903 / LV03 to CH1903 + / LV95 by the end of 2016 (reference data) or end of 2020 (other geographic reference data) at the latest . Liechtenstein will also take part in this change.

### Example coordinates

Measuring point ETRS89 CH1903 CH1903 +
Zimmerwald 7 ° 27'54.983506 "E. 46 ° 52'37.540562 "N. y = 602,030.680 x = 191,775.030 E = 2,602,030.740 N = 1,191,775.030
Bern 7 ° 26'19.076715 "E. 46 ° 57'3.897982 "N. y = 600,000,000 x = 200,000,000 E = 2,600,000,000 N = 1,200,000,000
Pledges 9 ° 47'3.697723 "E. 47 ° 30'55.172797 "N. y = 776,668.105 x = 265,372.681 E = 2,776,668.590 N = 1,265,372.250
Monte Generoso 9 ° 1'16.389053 "E. 45 ° 55'45.438020 "N. y = 722,758.810 x = 87,649.670 E = 2,722,759.060 N = 1,087,648.190
Source: Swisstopo

## literature

• Gubler et al .: Eidgenössische Landestopographie 1976 and 1984. 1996.

GIS and tools:

## Individual evidence

1. not to be confused with Swissgrid , the Swiss transmission system operator
2. Thomas Dähler: The Swiss coordinate zero point near Bordeaux In: Schweizerische Bauzeitung. Volume 93, Issue 14, 1975 ( e-periodica.ch E-Periodica, PDF; 2.4 MB).
3. a b c Liechtenstein national survey: General ( Memento of November 13, 2009 in the Internet Archive )
4. Art. 53 Transitional Provisions SR 510.620 Ordinance on Geoinformation
5. cms.geo.admin.ch (PDF), swisstopo.admin.ch