Azimuth

An Azimuth is the angle from a reference vector in a reference plane to a second vector in the same plane, pointing toward, (but not necessarily meeting), something of interest. For example, with the sea as your reference plane, the azimuth of the Sun might be the angle between due North and the point on the horizon the Sun is currently over. An imaginary line drawn along the surface of the sea might point in the direction of the Sun, but would obviously never meet it.

Azimuth is usually measured in degrees (°). The concept is used in many practical applications including navigation, astronomy, mapping, mining and artillery. The word azimuth is derived from the Arabic word السمت ('as-simt'), which means direction, referring to the ways or directions a person faces.

Navigation

In land navigation, an azimuth is defined as a horizontal angle measured clockwise from a north base line or meridian. Azimuth has also been more generally defined as a horizontal angle measured clockwise from any fixed reference plane or easily established base direction line.

Today, the reference plane for an azimuth in a general navigational context is typically true north, measured as a 0° azimuth, though other angular units (grad, mil) can also be employed. In any event, the azimuth cannot exceed the highest number of units in a circle - for a 360° circle, this is 359 degrees, 59 minutes, 59 seconds (359° 59' 59").

For example, moving clockwise on a 360° degree circle, a point due east would have an azimuth of 90°, south 180°, and west 270°. However, there are exceptions: some navigation systems use geographic south as the reference plane. Any direction can potentially serve as the plane of reference, as long as it is clearly defined for everyone using that system.

True north-based azimuths

From North
North	0° or 360°	South	180°
North-Northeast	22.5°	South-Southwest	202.5°
Northeast	45°	Southwest	225°
East-Northeast	67.5°	West-Southwest	247.5°
East	90°	West	270°
East-Southeast	112.5°	West-Northwest	292.5°
Southeast	135°	Northwest	315°
South-Southeast	157.5°	North-Northwest	337.5°

Mapping

There are a wide variety of azimuthal map projections. They all have the property that directions (the azimuths) from a central point are preserved. Some navigation systems use south as the reference plane as in the Philippine practice. However, any direction can serve as the plane of reference, as long as it is clearly defined for everyone using that system.

Astronomy

Used in celestial navigation, an azimuth is the direction of a celestial body from the observer. In astronomy, an azimuth is sometimes referred to as a bearing. In modern astronomy azimuth is nearly always measured from the north. In former times, it was common to refer to azimuth from the south, as it was then zero at the same time the hour angle of a star was zero. This assumes, however, that the star (upper) culminates in the south, which is only true for most stars in the Northern Hemisphere.

Other uses

The term azimuth is also used in context with military artillery coordination. In artillery laying, an azimuth is defined as the direction of fire.

An azimuth in aerial navigation is defined as the direction of flight, as taken from the location of the aircraft.

In mining operations, an azimuth or meridian angle is any angle measured clockwise from any meridian or horizontal plane of reference.

In tape and cassette tape-deck machines, an azimuth refers to the angle between the tape head(s) and tape. For magnetic tape drives, azimuth refers to the angle between the tape head(s) and tape.

In sound localization experiments and literature, the azimuth refers to the angle the sound source makes compared to the imaginary straight line that is drawn from within the head through the area between the eyes.

An azimuth thruster in shipbuilding is a propeller that can be rotated horizontally.

Other systems

Right Ascension

If instead of measuring from and along the horizon the angles are measured from and along the celestial equator, the angles are called right ascension if referenced to the Vernal Equinox, or hour angle if referenced to the Prime Meridian.

Horizontal coordinate

In the horizontal coordinate system, used in celestial navigation and satellite dish installation, azimuth is one of the two coordinates. The other is altitude, sometimes called elevation above the horizon. See also: Sat finder.

Polar coordinate

In three-dimensional polar coordinate systems, including cylindrical coordinates and spherical coordinates, the azimuth of a point is the angle between the positive x-axis and the projection of the vector onto the xy-plane (the component of the vector in the xy-plane). In cylindrical coordinates, theta, $\theta$, is almost universally used to represent the azimuth in mathematical applications, whereas physical applications may denote the azimuth using the symbol phi, $\phi$. Although there are several conventions in spherical coordinates, the azimuth is usually denoted by either theta, $\theta$, or phi, $\phi$.

See also

• Panning (camera)
• Altitude (astronomy)
• Azimuthal quantum number
• Inclination
• Longitude
• Magnetic declination
• Zenith
• Sound Localization

References

• Rutstrum, Carl, The Wilderness Route Finder, University of Minnesota Press (2000), ISBN 0816636613
• U.S. Army, Advanced Map and Aerial Photograph Reading, FM 21-26, Headquarters, War Department, Washington, D.C. (17 September 1941)
• U.S. Army, Advanced Map and Aerial Photograph Reading, FM 21-26, Headquarters, War Department, Washington, D.C. (23 December 1944)
• U.S. Army, Map Reading and Land Navigation, FM 21-26, Headquarters, Dept. of the Army, Washington, D.C. (7 May 1993)