Grid north

Astronomical azimuths refer to geographic, more precisely astronomical, north, geodetic, however, to grid north. The difference in Gauss-Krüger coordinates is a few degrees and is referred to as meridian  convergence γ.

As a grid north in which is Geodesy and mapping a reference direction defined, parallel to the grating lines of a geodetic coordinate system runs.

At the reference meridian of the grid , grid north usually points to the geographic north pole of the earth , i.e. in the geographic north direction ( geographic north ). At locations away from the reference meridian, the grid lines with a constant right or east value do not point to geographic north, but to grid north. The deviation between geographic north and grid north is called meridian convergence .

The meridian images in a geodetic or cartographic representation of the earth do not have to be straight lines, but can also be curved . Strictly speaking, the statement that north is always up on a map is therefore incorrect .

Meridian stripe systems

A grid in the Gauß-Krüger coordinate system with a line spacing of 50 km is placed over a map of Germany.
The red lines mark the central meridians, the blue lines the edges of the meridian strips

The most important of these coordinate systems laid out in north-south strips are the Gauß-Krüger and the UTM coordinate system . The central axis of these 300 to 500 km wide meridian strips, the reference, middle or central meridian , is oriented precisely to the north , but to the east and west of it the parallels to it (viewed in the geodetic figure) are taken as the reference direction . They are named Latternord .

The choice of such meridian strips for the calculation of surveying networks is related to the impossibility of mapping a doubly curved surface like the earth ellipsoid into the plane without distortion . A vivid picture of this is the strip-shaped peeling of an orange : the tips meet in the "poles", but the edges tear when spreading out into the plane of the tabletop.

In order to keep these natural distortions for land surveying and cartography to a minimum, only meridian strips with an extension of 3 ° or 6 °  difference in length are used , which means 120 or 60 strip systems over the entire earth. Most large-scale topographic maps are created in these coordinate systems and all boundary points and buildings are located for official purposes.

Grid north in Gauß-Krüger and UTM

Each individual strip has its central or middle meridian as the "zero direction" (for Germany, for example, 6 ° or 12 ° east of Greenwich , for Austria 28 °, 31 ° or  34 ° east of Ferro ). The directions within each strip now all relate to this reference meridian; they deviate from geographic north by approximately the following angle:

${\displaystyle \gamma \approx \Delta \lambda \cdot \sin \varphi }$

With

• the difference between a point and the reference meridian in terms of longitude ${\displaystyle \Delta \lambda }$
• the latitude of the point. ${\displaystyle \varphi }$

The angle is called meridian convergence and, with its dependence on geographical latitude, expresses the meridians moving closer together when one approaches one of the poles. It can reach half the width of the strip, i.e. H. in Central Europe ± 1.5 ° or ± 3 °. ${\displaystyle \gamma }$

Unlike the above Approximation formula requires the exact calculation of ellipsoidal series expansions for the solution of elliptic integrals , but there are many freely available computer programs for this.

literature

• Bernhard Heck: Calculation methods and evaluation models for land surveying , 3rd edition, Wichmann-Verlag, Karlsruhe 2003