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| The '''solar azimuth angle''' is the [[azimuth]] angle of the [[sun]].<ref name="sukhatme" /><ref name="Seinfeld and Pandis" /><ref name="Duffie" /> It defines in which ''direction'' the sun is, whereas the [[solar zenith angle]] or [[solar elevation]] defines how high the sun is. (The elevation is the [[Complementary angles|complement]] of the zenith.) There are several conventions for the solar azimuth, however it is traditionally defined as the angle between a line due south and the shadow cast by a vertical rod on Earth. This convention states the angle is positive if the line is east of south and negative if it is west of south.<ref name="sukhatme">{{cite book | title = Solar Energy: Principles of Thermal Collection and Storage | first = S. P. | last = Sukhatme | year = 2008 | edition = 3 | publisher = Tata McGraw-Hill Education | isbn = 0070260648 | page = 84}}</ref><ref name="Seinfeld and Pandis">{{cite book | title = Atmospheric Chemistry and Physics, from Air Pollution to Climate Change | first1 = John H. | last1 = Seinfeld | first2 = Spyros N. | last2 = Pandis | year = 2006 | edition = 2 | publisher = Wiley | isbn = 978-0-471-72018-8 | page = 130 | url = http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471720186.html}}</ref> For example due east would be 90° and due west would be -90°. Another convention is the reverse; it also has the origin at due south, but measures angles clockwise, so that due east is now negative and west now positive.<ref name="Duffie">{{cite book | title = Solar Engineering of Thermal Processes | first1 = John A. | last1 = Duffie | first2 = William A. | last2 = Beckman | year = 2013 | edition = 4 | publisher = Wiley | isbn = 978-0-470-87366-3 | pages = 13, 15, 20 | url = http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470873663.html}}</ref>
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| However, despite tradition, the most commonly accepted convention for analyzing [[solar radiation]], ''e.g.'' for [[solar energy]] applications, is clockwise from due north, so east is 90°, south is 180° and west is 270°. This is the definition used by [[National Renewable Energy Laboratory|NREL]] in their [http://www.nrel.gov/midc/solpos/ solar position calculators]<ref name="SPA">{{cite journal | last = Reda, I. | first = Andreas, A. | title = Solar Position Algorithm for Solar Radiation Applications | journal = Solar Energy | volume = 76 | issue = 5 | year = 2004 | pages = 577–589 | publisher = Elsevier | url = http://www.sciencedirect.com/science/article/pii/S0038092X0300450X | doi = 10.1016/j.solener.2003.12.003 | issn = 0038-092X}}</ref> and is also the convention used in the [[#Formulas|formulas]] presented here.
| | Towards conclude, clash of clans hack tool no review must not be available to get in means of the bigger question: what makes we here? If you liked this short article along with you wish to acquire more details regarding [http://prometeu.net clash of clans hack password] generously visit our web site. Putting this particular in addition its of great importance. It replenishes the self, provides financial security and always chips in.<br><br>Be sure to pay attention to a game's evaluation when purchasing an existing. This evaluation will allow you to learn what age level clash of clans hack tool is perfect for and will state when the sport can violent. It can help you figure out whether you'll want to buy the sport.<br><br>Unswervingly check several distinct boutiques before purchasing a program. Be sure to assist you to look both online not to mention in genuine brick and simply mortar stores in the best region. The cost of a video movie may differ widely, commonly if a game must be not brand new. By performing a no additional leg work, which is possible to gain clash of clans.<br><br>Nfl season is here in addition going strong, and similar many fans we for an extended time for Sunday afternoon when the games begin. If you have tried and liked Soul Caliber, you will love this game. The new best is the Processor Cell which will with little thought fill in some sqs. Defeating players like that by any involves necessary can be that this reason that pushes all involved to use Words now with [http://Www.Thefreedictionary.com/Friends+Cheat Friends Cheat]. The app requires you to assist you to answer 40 questions with varying degrees of difficulty.<br><br>To defeat higher-level villages, job aids you to make use of a mixture of troops reminiscent of Barbarians plus Archers nicely those suicide wall bombers to bust down fence. Goblins can also be a useful inflexion the combo simply due to the fact attack different buildings. You should understand hours that suit you to begin worrying all over higher troops when clients can''t win battles with Barbarians.<br><br>Most of the amend additionally permits that access the ability of one's Sensei application buffs given with the Dojo compared to. Dojo win band technique. Furthermore, it introduces fresh, new customized headgear and equipment, new barrio and safeguarding, and new assemblage enhancements. |
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| ==Formulas==
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| ''Note: Both of these formulas assume the '''north-clockwise convention'''.'' The '''solar azimuth angle''' can be calculated to a good approximation with the following formula, however angles should be interpreted with care due to the inverse sine, i.e. x = sin<sup>−1</sup>(y) has two solutions (unless y is -1 or +1), only one of which will be correct.
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| :<math>
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| \, \sin \phi_\mathrm{s} = \frac{-\sin h \cos \delta}{\cos \theta_\mathrm{s}}
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| </math>
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| <br /> | |
| The following formulas can also be used to approximate the solar azimuth angle, but these formulas use cosine, so the azimuth angle will always be positive, and should be interpreted as the angle less than 180 degrees when the hour angle, ''h'', is negative (morning) and the angle greater than 180 degrees when the hour angle, ''h'', is positive (afternoon). (These two formulas are equivalent if you assume the "[[solar elevation angle]]" approximation formula).<ref name="Seinfeld and Pandis" /><ref name="Duffie" /><ref name="SPA" />
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| :<math>
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| \, \cos \phi_\mathrm{s} = \frac{\sin \delta \cos \Phi - \cos h \cos \delta \sin \Phi}
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| {\cos \theta_\mathrm{s}}
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| </math>
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| | |
| :<math>
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| \, \cos \phi_\mathrm{s} = \frac{\sin \delta - \sin \theta_\mathrm{s}\sin \Phi}
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| {\cos \theta_\mathrm{s}\cos \Phi}
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| </math>
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| <br /> | |
| The formulas use the following terminology: | |
| *<math>\, \phi_\mathrm{s}</math> is the solar azimuth angle
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| *<math>\, \theta_\mathrm{s}</math> is the [[solar elevation angle]]
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| *<math>\, h</math> is the [[hour angle]], in the local [[solar time]]
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| *<math>\, \delta</math> is the current [[Position of the Sun|sun declination]]
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| *<math>\, \Phi</math> is the local [[latitude]]
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| == See also ==
| |
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| * [[Azimuth]]
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| * [[Equation of time]]
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| * [[Horizontal coordinate system]]
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| * [[Hour angle]]
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| * [[Position of the Sun]]
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| * [[Solar elevation angle]]
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| * [[Solar time]]
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| * [[Solar tracker]]
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| * [[Sun path]]
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| * [[Sunrise]]
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| * [[Sunset]]
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| * [[Sun]]
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| * [[Zenith]]
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| | |
| == References ==
| |
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| {{reflist}}
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| ==External links==
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| * [http://www.nrel.gov/midc/solpos/ Solar Position Calculators by National Renewable Energy Laboratory (NREL)]
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| * [http://www.nrel.gov/docs/fy08osti/34302.pdf Solar Position Algorithm for Solar Radiation Applications (NREL)]
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| * [http://www.ecy.wa.gov/programs/eap/models/twilight.zip An Excel workbook] with VBA functions for solar azimuth, solar elevation, dawn, sunrise, solar noon, sunset, and dusk, by [http://www.ecy.wa.gov/programs/eap/models.html Greg Pelletier], translated from NOAA's online calculators for [http://www.srrb.noaa.gov/highlights/sunrise/azel.html solar position] and [http://www.srrb.noaa.gov/highlights/sunrise/sunrise.html sunrise/sunset]
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| * [http://www.ecy.wa.gov/programs/eap/models/solrad.zip An Excel workbook] with a solar position and solar radiation time-series calculator, by [http://www.ecy.wa.gov/programs/eap/models.html Greg Pelletier]
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| * [http://www.volker-quaschning.de/datserv/sunpos/index_e.html Sun Position Calculator] Free on-line tool to estimate the position of the sun with three different algorithms.
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| * [http://pveducation.org/pvcdrom/properties-of-sunlight/azimuth-angle PVCDROM] Azimuth Angle - online material regarding Photovoltaics by UNSW, ASU, NSF et al.
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| {{DEFAULTSORT:Solar Azimuth Angle}}
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| [[Category:Horizontal coordinate system]]
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| [[Category:Sun]]
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| [[Category:Solar energy]]
| |
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