Direction angle

Definition of the direction angle

Direction angle (usually denoted by) is a term used in mathematics and geodesy for the angle between the north direction ( grid north ) and a straight line or line . The directional angle of a line from point to point is given from the parallel to the north-facing x-axis through the point to the right, i.e. clockwise. ${\displaystyle t}$ ${\displaystyle A}$ ${\displaystyle E}$ ${\displaystyle A}$

In navigation , the direction angle is referred to as the course angle , compass angle or march number. It means the same size.

calculation

Common spellings for the direction angle are or . The index denotes the starting point or position and the second index the end or destination point. ${\displaystyle t_{A}^{E}}$ ${\displaystyle t_{A,E}}$ ${\displaystyle A}$ ${\displaystyle E}$

For the direction angle in a geodetic coordinate system , i.e. H. with geodetically positive or mathematically negative direction of rotation , the following relationship applies:

${\displaystyle \tan t_{A}^{E}={\frac {y_{E}-y_{A}}{x_{E}-x_{A}}}={\frac {\Delta y}{\Delta x}}.}$

When calculating polar coordinates from Cartesian coordinates, the quadrant in which the direction angle lies must be taken into account. The function is suitable for this : ${\displaystyle \operatorname {arctan} }$

${\displaystyle t_{A}^{E}=\operatorname {arctan} {y_{E}-y_{A} \over x_{E}-x_{A}}=\operatorname {arctan} {\Delta y \over \Delta x}}$