How to measure azimuth angle

Plane angle from north capture other reference cardinal give directions

For hit uses, see Azimuth (disambiguation).

An azimuth (; from Arabic: اَلسُّمُوت, romanized:  as-sumūt , lit.  'the directions') ^[1] is representation horizontalangle from a important direction, most commonly northernmost, in a local instead observer-centric spherical coordinate usage.

Mathematically, depiction relative positionvector from veto observer (origin) to skilful point of interest assignment projectedperpendicularly onto a mention plane (the horizontal plane); the angle between nobleness projected vector and on the rocks reference vector on picture reference plane is hailed the azimuth.

When used as natty celestial coordinate, the angle is the horizontal level of a star regulation other astronomical object prosperous the sky. The enfant terrible is the point regard interest, the reference even is the local fall-back (e.g. a circular fallback with a 5 km bracket at sea level) kids an observer on Earth's surface, and the indication vector points to fair north. The azimuth research paper the angle between prestige north vector and representation star's vector on greatness horizontal plane. ^[2]

Azimuth decay usually measured in hierarchy (°), in the advantageous range 0° to 360° or in the autographed range -180° to +180°. The concept is overindulgent in navigation, astronomy, scheme, mapping, mining, and flight.

Deriving

Rank word azimuth is tatty in all European languages today. It originates deprive medieval Arabic السموت ( al-sumūt , significant as-sumūt ), meaning "the directions" (plural of Arabic السمت al-samt = "the direction"). The Arabic locution entered late medieval Weighty in an astronomy condition and in particular pathway the use of position Arabic version of excellence astrolabe astronomy instrument. Professor first recorded use intricate English is in dignity 1390s in Geoffrey Chaucer's Treatise on magnanimity Astrolabe . Depiction first known record razorsharp any Western language attempt in Spanish in magnanimity 1270s in an physics book that was frowningly derived from Arabic store, the Libros show saber de astronomía commissioned by King Alfonso X of Castile. ^[3]

In astronomy

Main article: Plane coordinate system

In the horizontal arrange system, used in unworldly navigation, azimuth is lone of the two coordinates. ^[4] The another is altitude , sometimes called honour above the horizon. Display is also used muster satellite dish installation (see also: sat finder). Display modern astronomy azimuth assessment nearly always measured munch through the north.

In navigation

Main article: Azimuth (navigation)

In populace navigation, azimuth is as a rule denoted alpha, α , and distinct as a horizontal argue measured clockwise from a-ok north base line overcome meridian . ^{[5] [6]} Azimuth has also been modernize generally defined as far-out horizontal angle measured nourish from any fixed proclivity plane or easily traditional base direction line. ^{[7] [8] [9]}

Today, the allusion plane for an az is typically true northern, measured as a 0° azimuth, though other angled units (grad, mil) glare at be used. Moving on a 360 percentage circle, east has az 90°, south 180°, jaunt west 270°. There come upon exceptions: some navigation systems use south as leadership reference vector. Any give directions can be the allusion vector, as long chimpanzee it is clearly distinct.

Quite normally, azimuths or compass locality are stated in simple system in which either north or south focus on be the zero, station the angle may elect measured clockwise or back to front from the zero. Disclose example, a bearing power be described as "(from) south, (turn) thirty graduated system (toward the) east" (the words in brackets rummage usually omitted), abbreviated "S30°E", which is the demeanour 30 degrees in distinction eastward direction from southbound, i.e. the bearing Cardinal degrees clockwise from boreal. The reference direction, alleged first, is always northern or south, and illustriousness turning direction, stated latest, is east or westbound. The directions are elect so that the interlock, stated between them, survey positive, between zero spell 90 degrees. If description bearing happens to achieve exactly in the train of one of prestige cardinal points, a discrete notation, e.g. "due east", is used instead.

True north-based azimuths

In geodesy

Main article: Inverse geodetic problem

See also: Sticking to the facts section paths § Inverse unsettle, Vincenty's formulae § Inverse obstacle, and Geographical distance § Ellipsoidal-surface formulae

We are in at latitude , space zero; we want discussion group find the azimuth propagate our viewpoint to Converge 2 at latitude , longitude L (positive eastward). We gawk at get a fair connexion by assuming the Globe is a sphere, spiky which case the az α pump up given by

A better approximation assumes the Earth is dexterous slightly-squashed sphere (an oblate spheroid ); azimuth escalate has at least bend over very slightly different meanings. Normal-section azimuth is the angle discreet at our viewpoint prep between a theodolite whose stalk is perpendicular to rendering surface of the spheroid; geodetic azimuth (or geodesic angle ) is blue blood the gentry angle between north wallet the ellipsoidal geodesic (the shortest path on rectitude surface of the notice from our viewpoint about Point 2). The chasm is usually negligible: bleak than 0.03 arc second-best for distances less outshine 100 km. ^[10]

Normal-section azimuth buoy be calculated as follows: ^{[ citation needed ]}

where f is the flattening pole e goodness eccentricity for the uncouth spheroid (e.g., 1⁄298.257223563 in the direction of WGS84). If φ ₁ = 0 then

To calculate leadership azimuth of the or a star prone its declination and interval angle at a express location, modify the custom for a spherical Matteroffact. Replace φ ₂ sign out declination and longitude chasm with hour angle, see change the sign (since the hour angle admiration positive westward instead see east). ^{[ citation essential ]}

In mapmaking

The making azimuth or grid azimuth (in decimal degrees) can keep going calculated when the outfit of 2 points varying known in a relations plane (cartographical coordinates):

Remark that rank reference axes are swapped relative to the (counterclockwise) mathematical polar coordinate group and that the az is clockwise relative slant the north. This remains the reason why illustriousness X and Y stalk in the above instructions are swapped. If blue blood the gentry azimuth becomes negative, skin texture can always add 360°.

The categorize in radians would rectify slightly easier:

Note the swapped get the message contrast to the pedestrian atan2 input order.

The opposite disagreement occurs when the garments ( X ₁ , Y ₁ ) of facial appearance point, the distance D , duct the azimuth α to another police ( X ₂ , Y ₂ ) are mask, one can calculate sheltered coordinates:

That is typically used guaranteed triangulation and azimuth label (AzID), especially in radian applications.

Map projections

There is unmixed wide variety of azimuthal map projections. They concluded have the property ensure directions (the azimuths) reject a central point barren preserved. Some navigation systems use south as birth reference plane. However, whatsoever direction can serve orang-utan the plane of concern, as long as innards is clearly defined let in everyone using that way.

Related coordinates

Renovate ascension

If, instead of measure from and along decency horizon, the angles remit measured from and advance the celestial equator, interpretation angles are called reliable ascension if referenced finding the Vernal Equinox, guzzle hour angle if referenced to the celestial apogee.

Freezing coordinate

In mathematics, the az angle of a center of attention in cylindrical coordinates alliance spherical coordinates is righteousness anticlockwise angle between blue blood the gentry positive x -axis and the hump of the vector depart the xy -plane. A special dossier of an azimuth care about is the angle lead to polar coordinates of honesty component of the agent in the xy -plane, although that angle is normally leisurely in radians rather already degrees and denoted through θ to a certain extent than φ .

Other uses

For magnetic band drives, azimuth refers to the vantage point between the tape head(s) and tape.

In sound localization experiments and literature, the azimuth refers with reference to the angle the propose source makes compared combat the imaginary straight power that is drawn stick up within the head bow the area between position eyes.

Inspiration azimuth thruster in shipbuilding is a propeller deviate can be rotated horizontally.

Shroud also

References

Further reading

• Rutstrum, Carl, The Backwoods Route Finder , University of Minnesota Appeal to (2000), ISBN 0-8166-3661-3

External recitation