Azimuth
lastmod 2019-11-29created 2019-11-293 edits
An azimuth (meridian angle) is an angle measured in a spherical coordinate system. It is computed by projecting the vector from an observer at the origin to the target perpendicularly onto a reference plane, and taking the angle that this projection makes with a reference vector lying on the reference plane. The reference vector can be true north, grid north, magnetic north, and so on.[1]
One example of an azimuth is measuring the position of a star. Here the star is the target, the reference plane is given by the horizon or sea level, and the reference vector points north. The azimuth is given as the angle between north and the star projected perpendicularly onto the horizontal plane.
Azimuths are usually expressed in degrees (°). Azimuths have practical applications in navigation, astronomy, engineering, mapping, and gunnery.
Navigation
In general navigation today, the reference for azimuth is true north, expressed as 0°, and other units (grads, mils) can also be used. In any case, an azimuth cannot exceed the largest angle in a circle. In a 360° circle, this is 359 degrees 59 minutes 59 seconds (359° 59' 59").
For example, moving clockwise in a 360° circle, facing east gives an azimuth of 90°, south 180°, and west 270°. However, exceptions exist. Some navigation systems use south as the reference. Any direction can serve as the reference, as long as it is clearly defined for everyone using that system.
Azimuth relative to true north
The angle measured clockwise from the north of the meridian is called the true azimuth.
| From north | |||
| N | 0° or 360° | | S | 180° |
| NNE | 22.5° | | SSW | 202.5° |
| NE | 45° | | SW | 225° |
| ENE | 67.5° | | WSW | 247.5° |
| E | 90° | | W | 270° |
| ESE | 112.5° | | WNW | 292.5° |
| SE | 135° | | NW | 315° |
| SSE | 157.5° | | NNW | 337.5° |
Calculating azimuth
We want to find the azimuth when standing at a point with latitude \(\phi_1\) and longitude 0, looking toward a point with latitude \(\phi_2\) and longitude L (east is positive). We can get a reasonable approximation by assuming the Earth is a sphere, in which case the azimuth \(\alpha\) is:
\[ \tan \alpha = \frac{\sin L}{(\cos \phi_1)(\tan \phi_2)- (\sin\phi_1)(\cos L)} \]