The course angle (also direction angle , in Switzerland azimuth or artillery promille or English azimuth ) is a term from navigation and describes the angle between north direction and target direction. It is always given starting from north in a clockwise direction . For example, if you move directly to the east, the course angle is 90 ° or 1600 lines . The specific numerical value of the course angle depends on the angle unit used, e.g. B. Example degree , graduation , line .

If 100 lines are used as the angle unit (90 ° then corresponds to 16 units), the course angle is also called the march number , march direction number or compass number , etc. Ä.

## Finding a heading number with the compass from the map

1. The compass edge applied at the line from start to finish.
2. Turn the compass rose so that its north-south line coincides with the map north / grid north .
3. Read off the direction of march on the front sight (direction arrow, line of sight).

## Running according to the marching direction number

1. Bring the marching direction number on the compass by turning the compass rose in line with the front sight (direction arrow, line of sight).
2. Hold the compass level at eye level and adjust the mirror so that the needle can be checked. Align the needle with the north marking.
3. Aim over the rear sight and front sight and track down and note a prominent point in the sight line.
4. Walk in the direction of the prominent point in the area.

## calculation

The course angle can be calculated if the start and destination are known. The course angle is calculated with the help of the side cosine law from spherical trigonometry .

Point A has the coordinates ( ), ${\ displaystyle \, \ varphi _ {A}, \ lambda _ {A}}$

Point B has the coordinates ( ). ${\ displaystyle \, \ varphi _ {B}, \ lambda _ {B}}$

${\ displaystyle \, \ varphi}$is positive for latitudes in the northern hemisphere and negative in the southern hemisphere; to the east is positive, to the west is negative. ${\ displaystyle \, \ lambda}$

Then applies to the course angle : ${\ displaystyle \, \ omega}$

${\ displaystyle \ cos \ omega = {\ frac {\ sin \ varphi _ {B} - \ sin \ varphi _ {A} \ cdot \ cos e} {\ cos \ varphi _ {A} \ cdot \ sin e} }}$,

with the restriction that only an angle in the range 0 °… 180 ° is calculated. There is no distinction in which quadrant the course lies.

Where is the spherical distance on the unit sphere between A and B, which results from ${\ displaystyle e}$

${\ displaystyle \ operatorname {arc} e = {\ frac {{\ text {Length of the orthodromes from}} \ A \ {\ text {to}} \ B} {\ text {Earth's radius}}}}$

(To calculate the orthodromic length, see here .)

When it is the spherical distance e on the unit sphere, expressed in radians, see Spherical geometry, distance . ${\ displaystyle \ operatorname {arc} e}$

If the starting point, the course angle and the route length are known, the target coordinates can also be calculated with this formula.