# Heading angle

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

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

## Running according to the marching direction number

- Bring the marching direction number on the compass by turning the compass rose in line with the front sight (direction arrow, line of sight).
- 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.
- Aim over the rear sight and front sight and track down and note a prominent point in the sight line.
- 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 ( ),

Point B has the coordinates ( ).

is positive for latitudes in the northern hemisphere and negative in the southern hemisphere; to the east is positive, to the west is negative.

Then applies to the course angle :

- ,

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

(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 .

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