azimuth - wikipedia, the free encyclopedia.pdf

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10/13/13 3:56 PMAzimuth - Wikipedia, the free encyclopedia

Page 1 of 5http://en.wikipedia.org/wiki/Azimuth

The azimuth is the angle formed between a reference

direction (North) and a line from the observer to a point of

interest projected on the same plane as the reference

direction.

AzimuthFrom Wikipedia, the free encyclopedia

An azimuth ( i/zm/; from Arabic !"#$

as-samt, meaning "a way, a part, or quarter"[1])

is an angular measurement in a sphericalcoordinate system. The vector from an observer

(origin) to a point of interest is projected

perpendicularly onto a reference plane; the angle

between the projected vector and a reference

vector on the reference plane is called the

azimuth.

An example is the position of a star in the sky.

The star is the point of interest, the reference

plane is the horizon or the surface of the sea, andthe reference vector points north. The azimuth is

the angle between the north vector and the

perpendicular projection of the star down onto

the horizon.[2]

Azimuth is usually measured in degrees (). The

concept is used in navigation, astronomy,

engineering, mapping, mining and artillery.

Contents

1 Navigation1.1 True north-based azimuths

2 Calculating azimuth3 Mapping4 Astronomy

5 Other systems5.1 Right ascension5.2 Horizontal coordinate5.3 Polar coordinate

6 Other uses of the term7 See also8 Notes9 References

10 External links

Navigation
http://en.wikipedia.org/wiki/File:Azimuth-Altitude_schematic.svghttp://en.wikipedia.org/wiki/File:Azimuth-Altitude_schematic.svghttp://en.wikipedia.org/wiki/Azimuth#External_linkshttp://en.wikipedia.org/wiki/Azimuth#Referenceshttp://en.wikipedia.org/wiki/Azimuth#Noteshttp://en.wikipedia.org/wiki/Azimuth#See_alsohttp://en.wikipedia.org/wiki/Azimuth#Other_uses_of_the_termhttp://en.wikipedia.org/wiki/Azimuth#Polar_coordinatehttp://en.wikipedia.org/wiki/Azimuth#Astronomyhttp://en.wikipedia.org/wiki/Azimuth#Mappinghttp://en.wikipedia.org/wiki/Azimuth#Calculating_azimuthhttp://en.wikipedia.org/wiki/Azimuth#Navigationhttp://en.wikipedia.org/wiki/Azimuth#True_north-based_azimuthshttp://en.wikipedia.org/wiki/Engineeringhttp://en.wikipedia.org/wiki/Maphttp://en.wikipedia.org/wiki/Artilleryhttp://en.wikipedia.org/wiki/Navigationhttp://en.wikipedia.org/wiki/Astrometryhttp://en.wikipedia.org/wiki/Perpendicularhttp://en.wikipedia.org/wiki/Origin_(mathematics)http://en.wikipedia.org/wiki/Spherical_coordinate_systemhttp://en.wikipedia.org/wiki/Vector_spacehttp://en.wikipedia.org/wiki/Spherical_coordinate_systemhttp://en.wikipedia.org/wiki/Spherical_coordinate_systemhttp://upload.wikimedia.org/wikipedia/commons/c/c4/En-us-azimuth.ogghttp://en.wikipedia.org/wiki/Help:IPA_for_Englishhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Arabic_languagehttp://en.wikipedia.org/wiki/Azimuth#External_linkshttp://en.wikipedia.org/wiki/Azimuth#Referenceshttp://en.wikipedia.org/wiki/Azimuth#Noteshttp://en.wikipedia.org/wiki/Azimuth#See_alsohttp://en.wikipedia.org/wiki/Azimuth#Other_uses_of_the_termhttp://en.wikipedia.org/wiki/Azimuth#Polar_coordinatehttp://en.wikipedia.org/wiki/Azimuth#Horizontal_coordinatehttp://en.wikipedia.org/wiki/Azimuth#Right_ascensionhttp://en.wikipedia.org/wiki/Azimuth#Other_systemshttp://en.wikipedia.org/wiki/Azimuth#Astronomyhttp://en.wikipedia.org/wiki/Azimuth#Mappinghttp://en.wikipedia.org/wiki/Azimuth#Calculating_azimuthhttp://en.wikipedia.org/wiki/Azimuth#True_north-based_azimuthshttp://en.wikipedia.org/wiki/Azimuth#Navigationhttp://en.wikipedia.org/wiki/Artilleryhttp://en.wikipedia.org/wiki/Maphttp://en.wikipedia.org/wiki/Engineeringhttp://en.wikipedia.org/wiki/Astrometryhttp://en.wikipedia.org/wiki/Navigationhttp://en.wikipedia.org/wiki/Degree_(angle)http://en.wikipedia.org/wiki/Azimuth#cite_note-2http://en.wikipedia.org/wiki/Northhttp://en.wikipedia.org/wiki/Seahttp://en.wikipedia.org/wiki/Horizonhttp://en.wikipedia.org/wiki/Starhttp://en.wikipedia.org/wiki/Plane_(mathematics)http://en.wikipedia.org/wiki/Perpendicularhttp://en.wikipedia.org/wiki/Projection_(mathematics)http://en.wikipedia.org/wiki/Origin_(mathematics)http://en.wikipedia.org/wiki/Vector_spacehttp://en.wikipedia.org/wiki/Spherical_coordinate_systemhttp://en.wikipedia.org/wiki/Angle#Measuring_angleshttp://en.wikipedia.org/wiki/Azimuth#cite_note-1http://en.wikipedia.org/wiki/Arabic_languagehttp://en.wikipedia.org/wiki/Help:IPA_for_Englishhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Help:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Help:IPA_for_Englishhttp://en.wikipedia.org/wiki/File:En-us-azimuth.ogghttp://upload.wikimedia.org/wikipedia/commons/c/c4/En-us-azimuth.ogghttp://en.wikipedia.org/wiki/File:Azimuth-Altitude_schematic.svg


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In land navigation, azimuth is usually denoted alpha, , and defined as a horizontal angle measured

clockwise from a north base line or meridian.[3][4]Azimuth has also been more generally defined as a

horizontal angle measured clockwise from any fixed reference plane or easily established base direction

line.[5][6][7]

Today the reference plane for an azimuth is typically true 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, south180, and west 270. There are exceptions: some navigation systems use south as the reference plane. Any

direction can be the plane of reference, 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 "S30E", 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 directionof one of the cardinal points, a different notation, e.g. "due east", is used instead.

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

Calculating azimuth

We are standing at latitude , longitude zero; we want to find the azimuth from our viewpoint to Point 2 at

latitude , longitude L (positive eastward). We can get a fair approximation by assuming the Earth is a

sphere, in which case the azimuth is given by

A better approximation assumes the Earth is a slightly-squashed sphere (a spheroid); "azimuth" then has at

least two very slightly different meanings. "Normal-section azimuth" is the angle measured at our viewpoint

by a theodolite whose axis is perpendicular to the surface of the spheroid; "geodetic azimuth" is the anglebetween north and the geodesic that is, the shortest path on the surface of the spheroid from our viewpoint
http://en.wikipedia.org/wiki/Cardinal_pointhttp://en.wikipedia.org/wiki/Angular_milhttp://en.wikipedia.org/wiki/Grad_(angle)http://en.wikipedia.org/wiki/True_northhttp://en.wikipedia.org/wiki/Azimuth#cite_note-7http://en.wikipedia.org/wiki/Azimuth#cite_note-6http://en.wikipedia.org/wiki/Azimuth#cite_note-5http://en.wikipedia.org/wiki/Azimuth#cite_note-4http://en.wikipedia.org/wiki/Azimuth#cite_note-3http://en.wikipedia.org/wiki/Meridian_(geography)http://en.wikipedia.org/wiki/Clockwise_and_counterclockwisehttp://en.wikipedia.org/wiki/Alpha


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to Point 2. The difference is usually unmeasurably small; if Point 2 is not more than 100 km away the

difference will not exceed 0.03 arc second.

Various websites will calculate geodetic azimuth e.g. GeoScience Australia site

(http://www.ga.gov.au/geodesy/datums/vincenty_inverse.jsp). Formulas for calculating geodetic azimuth are

linked in the distance article.

Normal-section azimuth is simpler to calculate; Bomford says Cunningham's formula is exact for anydistance. If is the flattening for the chosen spheroid (e.g. 1/298.257223563 for WGS84) then

If = 0 then

To calculate the azimuth of the sun or a star given its declination and hour angle at our location, we modify

the formula for a spherical earth. Replace with declination and longitude difference with hour angle, and

change the sign (since hour angle is positive westward instead of east).

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.

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.[8] In

astronomy, an azimuth is sometimes referred to as a bearing. In modern astronomy azimuth is nearly alwaysmeasured from the north. (The article on coordinate systems, for example, uses a convention measuring

from the south.) In former times, it was common to refer to azimuth from the south, as it was then zero at the
http://en.wikipedia.org/wiki/Celestial_coordinate_systemhttp://en.wikipedia.org/wiki/Astronomyhttp://en.wikipedia.org/wiki/Bearing_(navigation)http://en.wikipedia.org/wiki/Azimuth#cite_note-8http://en.wikipedia.org/wiki/Map_projection#Azimuthal_.28projections_onto_a_plane.29http://en.wikipedia.org/wiki/World_Geodetic_Systemhttp://en.wikipedia.org/wiki/Geographical_distance#Ellipsoidal-surface_formulaehttp://www.ga.gov.au/geodesy/datums/vincenty_inverse.jsp


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A standard Brunton Geo compass,

used commonly by geologists and

surveyors to measure azimuth

same time that the hour angle of a star was zero. This assumes,

however, that the star (upper) culminates in the south, which is only

true if the star's declination is less than (i.e. further south than) the

observer's latitude.

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 celestial 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 mathematics the azimuth angle of a point in cylindrical coordinates or spherical coordinates is the

anticlockwise angle between the positive x-axis and the projection of the vector onto the xy-plane. The angle

is the same as an angle in polar coordinates of the component of the vector in the xy-plane and is normally

measured in radians rather than degrees. As well as measuring the angle differently, in mathematicalapplications theta, , is very often used to represent the azimuth rather than the symbol phi .

Other uses of the term

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.

See also

Altitude (astronomy)Azimuthal quantum number

Bearing (navigation)Course (navigation)

InclinationLongitude

Magnetic declination
http://en.wikipedia.org/wiki/Magnetic_declinationhttp://en.wikipedia.org/wiki/Longitudehttp://en.wikipedia.org/wiki/Inclinationhttp://en.wikipedia.org/wiki/Course_(navigation)http://en.wikipedia.org/wiki/Bearing_(navigation)http://en.wikipedia.org/wiki/Azimuthal_quantum_numberhttp://en.wikipedia.org/wiki/Altitude_(astronomy)http://en.wikipedia.org/wiki/Propellerhttp://en.wikipedia.org/wiki/Shipbuildinghttp://en.wikipedia.org/wiki/Azimuth_thrusterhttp://en.wikipedia.org/wiki/Sound_localizationhttp://en.wikipedia.org/wiki/Tape_drivehttp://en.wikipedia.org/wiki/Phi_(letter)http://en.wikipedia.org/wiki/Thetahttp://en.wikipedia.org/wiki/Radianhttp://en.wikipedia.org/wiki/Polar_coordinateshttp://en.wikipedia.org/wiki/Plane_(mathematics)http://en.wikipedia.org/wiki/Vector_(geometry)http://en.wikipedia.org/wiki/Anglehttp://en.wikipedia.org/wiki/Spherical_coordinate_systemhttp://en.wikipedia.org/wiki/Cylindrical_coordinate_systemhttp://en.wikipedia.org/wiki/Sat_finderhttp://en.wikipedia.org/wiki/Altitude_(astronomy)http://en.wikipedia.org/wiki/Coordinate_systemhttp://en.wikipedia.org/wiki/Satellite_dishhttp://en.wikipedia.org/wiki/Celestial_navigationhttp://en.wikipedia.org/wiki/Horizontal_coordinate_systemhttp://en.wikipedia.org/wiki/Celestial_meridianhttp://en.wikipedia.org/wiki/Right_ascensionhttp://en.wikipedia.org/wiki/Celestial_equatorhttp://en.wikipedia.org/wiki/Latitudehttp://en.wikipedia.org/wiki/Declinationhttp://en.wikipedia.org/wiki/Culminationhttp://en.wikipedia.org/wiki/Starhttp://en.wikipedia.org/wiki/Hour_anglehttp://en.wikipedia.org/wiki/Compasshttp://en.wikipedia.org/wiki/File:Brunton.JPG


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Panning (camera)Solar azimuth angleSound Localization

Zenith

Notes

1. ^ Charles Knight.Arts and sciences: or, Fourth division of "The English encyclopedia", Volume 1. Bradbury, Evans

& Co. p. 772.

2. ^ http://dictionary.reference.com/browse/azimuth

3. ^ U.S. Army,Map Reading and Land Navigation, FM 2126, Headquarters, Dept. of the Army, Washington, D.C.

(7 May 1993), ch. 6, p. 2

4. ^ U.S. Army,Map Reading and Land Navigation, FM 2126, Headquarters, Dept. of the Army, Washington, D.C.

(28 March 1956), ch. 3, p. 63

5. ^ U.S. Army, ch. 6 p. 2

6. ^ U.S. Army,Advanced Map and Aerial Photograph Reading, Headquarters, War Department, Washington, D.C.

(17 September 1941), pp. 2425

7. ^ U.S. Army,Advanced Map and Aerial Photograph Reading, Headquarters, War Department, Washington, D.C.(23 December 1944), p. 15

8. ^ Rutstrum, Carl, The Wilderness Route Finder, University of Minnesota Press (2000), ISBN 0-8166-3661-3, p. 194

References

Rutstrum, Carl, The Wilderness Route Finder, University of Minnesota Press (2000), ISBN 0-8166-3661-3U.S. Army,Advanced Map and Aerial Photograph Reading, FM 2126, Headquarters, WarDepartment, Washington, D.C. (17 September 1941)

U.S. Army,Advanced Map and Aerial Photograph Reading, FM 2126, Headquarters, WarDepartment, Washington, D.C. (23 December 1944)U.S. Army,Map Reading and Land Navigation, FM 2126, Headquarters, Dept. of the Army,

Washington, D.C. (7 May 1993)

External links

Chisholm, Hugh, ed. (1911). "Azimuth".Encyclopdia Britannica (11th ed.). Cambridge

University Press"Azimuth". Collier's New Encyclopedia. 1921.

Retrieved from "http://en.wikipedia.org/w/index.php?title=Azimuth&oldid=574654130"

Categories: Angle Astronomy Navigation Celestial coordinate system

This page was last modified on 26 September 2013 at 20:43.

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