# Belong to Swiss

national coordinates Swiss national coordinates (also called “military coordinates”, “CH1903”) to a coordinate system, which is used during the official measurement and on many maps of Switzerland. CH1093 is based on the Bessel 1841 ellipsoid. There Switzerland quite, can a simple map projection (named Swissgrid) from that is small to ellipsoids be made.

## map projection

the starting point for thisCoordinate system is the former observatory in Berne, in whose place today Institut for accurate science of the University of Berne is. Its coordinates are fixed on 600 ' 000 m/200 ' 000 m. From this point the y axle point to the east (false easting) and the x axis to the north (false northing).

The coordinate 0/0 (zero point) lies in close proximity to Bordeaux in France. The starting point and thus also the zero point with Bordeaux, following from it, became consciously in such a wayselected that the error rate should be as small as possible during the regulation and transmission of the coordinates of any point of Switzerland. In addition required it the following defaults:

• The zero point is to be specified in such a way that itself the whole country in the first quadrant of the coordinate systemfinds. Thus the Koordiatenwerte is always positive within the country.
• The whole country is appropriate south and east for a line arranged from the zero point after northeast, thus in the lower half of the quadrant. Thus it is reached that the value of the Y-coordinatewithin the country is ever larger than that the x-coordinate.
• The southernmost and the westernmost point of the country at least in each case 100 km are appropriate far away from the axes of coordinates, at the same time may the northernmost and the easternmost point for at the most 999 km of thatAxles far away its. Thus all points of Switzerland point uniformly six-digit coordinate values to (when measurement in meters).
• Finally the Y-coordinate of the westernmost point is specified in such a way that their value is larger than that the x-coordinate of the northernmost point. Thus is for each coordinate value already due to its size clearly whether it concerns the x or y-value. If a coordinate value is appropriate below 400 ' 000, it acts within the country around the x-value, over it is it the y-value.

Example coordinates:
Rigi y=679520, x=212273
Zurich sea-brook y=684592, x=252857

## conversion WGS84 on CH1903

### design fundamentals

the conversion of the ellipsoidischen WGS84 - coordinates on Swiss projection coordinates (CH1903) can be easily managed by means of a Näherungsformel. With the formulas described belowan accuracy of approximately a meter is possible.

1. Coordinates are converted into Sexagesimalsekunden. Result: Width φ and the length λ.

2. The auxiliary variables are formed φ' and λ' out φ and λ. The formulas in addition are:

[itex] \ phi'= \ frac {\ phi-169028.66} {10000}< /math>

[itex] \ lambda'= \ frac {\ lambda-26782.5} {10000}< /math>

3. Finally Swiss become coordinates ([itex] x< /math> and [itex] y< /math> in m) computes:

[itex] \ begin {matrix} x&=& 200147,07 \ \ \

&+& 308807,95 \ cdot \ phi' \ \ \ &+& 3745,25 \ cdot \ lambda'^2 \ \ \ &+& 76,63 \ cdot \ phi'^2 \ \ \ &+& 119,79 \ cdot \ phi'^3\ \ \ &-& 194,56 \ cdot \ lambda'^2 \ cdot \ phi'

\ end {to matrix}< /math>

[itex] \ begin {matrix} y&=& 600072,37 \ \ \

&+& 211455,93 \ cdot \ lambda' \ \ \&-& 10938,51 \ cdot \ lambda' \ cdot \ phi' \ \ \&-& 0,36 \ cdot \ lambda' \ \ phi'^2 cdot \ \ \&-& 44,54 \ cdot \ lambda'^3 \ end {to matrix}< /math>

### example

practical example: Center of La Chaux the Breuleux on

φ = 47° 13 ' 15 " N
λ = 7° 1 ' 41 " E

transformation in Sexagesimalsekunden:

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

computation of the auxiliary variables:

φ' = (169995 - 169028,66)/10000 = 0,096634
λ' = (25301 - 26782,5)/10000 = -0,14815

computation 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 the Breuleux is therefore 568 ' 902/230 ' 071.

### pseudo code

input var gradL, minuteL, sekundeL inputs #Längskoordinaten var gradB, minuteB,sekundeB outputs #Breitenkoordinaten var x, y var p, l p = (((gradB * 3600) + (minuteB * 60) + sekundeB) - 169028,66)/10000 l = (((gradL * 3600) + (minuteL * 60) + sekundeL) - 26782,5)/10000 x= 200147,07 + 308807,95 * p + 3745,25 * l^2 + 76,63 * p^2 - 194,56 * l^2 * p + 119,79 * p^3 y = 600072,37 + 211455,93 * l - 10938,51 * l * p - 0,36 *l * p^2 - to 44,54 * l^3