The azimuth is the angle formed between a reference direction (in this example north) and aline from the observer to a point of interest projected on the same plane as the reference direction orthogonal to thezenith.
The wordazimuth is used in all European languages today. It originates from medieval Arabicالسموت (al-sumūt, pronouncedas-sumūt), meaning "the directions" (plural of Arabicالسمتal-samt = "the direction"). The Arabic word entered late medieval Latin in an astronomy context and in particular in the use of the Arabic version of theastrolabe astronomy instrument. Its first recorded use in English is in the 1390s inGeoffrey Chaucer'sA Treatise on the Astrolabe. The first known record in any Western language is in Spanish in the 1270s in an astronomy book that was largely derived from Arabic sources, theLibros del saber de astronomía commissioned byKing Alfonso X of Castile.[3]
Azimuth marker, Mount Allen (Sandstone Peak), southern California, US
In land navigation, azimuth is usually denotedalpha,α, and defined as a horizontal angle measuredclockwise from a north base line ormeridian.[5][6]Azimuth has also been more generally defined as a horizontal angle measured clockwise from any fixed reference plane or easily established base direction line.[7][8][9]
Today, the reference plane for an azimuth is typicallytrue north, measured as a 0° azimuth, though other angular units (grad,mil) can be used. Moving clockwise on a 360 degree circle, east has azimuth 90°, south 180°, and west 270°. There are exceptions: some navigation systems use south as the reference vector. Any direction can be the reference vector, as long as it is clearly defined.
Quite commonly, azimuths or compass bearings are stated in a system in which either north or south can be the zero, and the angle may be measured clockwise or anticlockwise from the zero. For example, a bearing might be described as "(from) south, (turn) thirty degrees (toward the) east" (the words in brackets are usually omitted), abbreviated "S30°E", which is the bearing 30 degrees in the eastward direction from south, i.e. the bearing 150 degrees clockwise from north. The reference direction, stated first, is always north or south, and the turning direction, stated last, is east or west. The directions are chosen so that the angle, stated between them, is positive, between zero and 90 degrees. If the bearing happens to be exactly in the direction of one of thecardinal points, a different notation, e.g. "due east", is used instead.
We are standing at latitude, longitude zero; we want to find the azimuth from our viewpoint to Point 2 at latitude, longitudeL (positive eastward). We can get a fair approximation by assuming the Earth is a sphere, in which case the azimuthα is given by
A better approximation assumes the Earth is a slightly-squashed sphere (anoblate spheroid);azimuth then has at least two very slightly different meanings.Normal-section azimuth is the angle measured at our viewpoint by atheodolite whose axis is perpendicular to the surface of the spheroid;geodetic azimuth (orgeodesic azimuth) is the angle between north and theellipsoidal geodesic (the shortest path on the surface of the spheroid from our viewpoint to Point 2). The difference is usually negligible: less than 0.03 arc second for distances less than 100 km.[10]
Normal-section azimuth can be calculated as follows:[citation needed]
wheref is the flattening ande the eccentricity for the chosen spheroid (e.g.,1⁄298.257223563 forWGS84).Ifφ1 = 0 then
To calculate the azimuth of the Sun or a star given itsdeclination andhour angle at a specific location, modify the formula for a spherical Earth. Replaceφ2 with declination and longitude difference with hour angle, and change the sign (since the hour angle is positive westward instead of east).[citation needed]
A standard Brunton Geocompass, commonly used by geologists and surveyors to measure azimuth
Thecartographical azimuth orgrid azimuth (in decimal degrees) can be calculated when the coordinates of 2 points are known in a flat plane (cartographical coordinates):
Remark that the reference axes are swapped relative to the (counterclockwise) mathematicalpolar coordinate system and that the azimuth is clockwise relative to the north.This is the reason why the X and Y axis in the above formula are swapped.If the azimuth becomes negative, one can always add 360°.
Note the swapped in contrast to the normalatan2 input order.
The opposite problem occurs when the coordinates (X1,Y1) of one point, the distanceD, and the azimuthα to another point (X2,Y2) are known, one can calculate its coordinates:
This is typically used intriangulation and azimuth identification (AzID), especially inradar applications.
There is a wide variety ofazimuthal 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. However, any direction can serve as the plane of reference, as long as it is clearly defined for everyone using that system.
Comparison of some azimuthal projections centred on 90° N at the same scale, ordered by projection altitude in Earth radii.(click for detail)
If, instead of measuring from and along the horizon, the angles are measured from and along thecelestial equator, the angles are calledright ascension if referenced to the Vernal Equinox, or hour angle if referenced to thecelestial meridian.
In mathematics, the azimuth angle of a point incylindrical coordinates orspherical coordinates is the anticlockwiseangle between the positivex-axis and the projection of thevector onto thexy-plane. A special case of an azimuth angle is the angle inpolar coordinates of the component of the vector in thexy-plane, although this angle is normally measured inradians rather than degrees and denoted byθ rather thanφ.
Formagnetic tape drives,azimuth refers to the angle between the tape head(s) and tape.
Insound localization experiments and literature, theazimuth 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.
