en>Eric Kvaalen: Γ(s) is infinite, not zero, at non-positive integers.

2014-08-20T11:31:31Z

Γ(s) is infinite, not zero, at non-positive integers.

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	~~[[Image:Density Altitude.png\|thumb\|right\|375px\|Density Altitude Computation Chart]]~~

	'''Density altitude''' is the [[altitude]] relative to the standard atmosphere conditions ([[International Standard Atmosphere\|ISA]]) at which the [[density of air\|air density]] would be equal to the indicated air density at the place of observation. In other words, density altitude is air density given as a height [[above mean sea level]]. "Density altitude" can also be considered to be the [[pressure altitude]] adjusted for non-standard temperature.

	~~Both an increase in [[temperature]], decrease in [[atmospheric pressure]], and, to a much lesser degree, increase in [[humidity]] will cause an increase in density altitude. In hot~~ and ~~humid conditions, the density altitude at a particular location may be significantly higher than the true altitude.~~

	In aviation the density altitude is used to assess the aircraft's aerodynamic performance under certain weather conditions. The lift generated by the aircraft's airfoils and the relation between indicated and true airspeed are also subject to air density changes. Furthermore, the power delivered by the aircraft's engine is affected by the air density and air composition.

	~~==Aircraft safety==~~
	~~Air density is perhaps the single most important factor affecting aircraft performance. It has a direct bearing on:<ref~~ name~~="A">AOPA Flight Training, Volume 19, Number 4; April 2007; Aircraft Owners and Pilots Association; ISSN 1047-6415</ref>~~
	* The [[Lift (force)\|lift]] generated by the wings — reduction in air density reduces the wing's lift.
	* The efficiency of the propeller or rotor — which for a propeller (effectively an [[airfoil]]) behaves similarly to lift on wings.
	* The power output of the engine — power output depends on oxygen intake, so the engine output is ~~reduced as the equivalent "dry air" density decreases and produces even less power as moisture displaces oxygen in more humid conditions.~~

	Aircraft taking off from a "[[hot and high]]" airport such as the [[Mariscal Sucre International Airport\|Quito Airport]] or [[Mexico City International Airport\|Mexico City]] are at a significant [[aerodynamic]] disadvantage. The following effects result from a density altitude which is higher than the actual physical altitude:<ref name="A" />
	* The aircraft will accelerate slower on takeoff as a result of reduced power production.
	* The aircraft will need to achieve a higher true airspeed to attain the same lift - this implies both a longer takeoff roll and a higher true airspeed which must be maintained when airborne to avoid [[stall (flight)\|stalling]].
	* The aircraft will climb slower as the result of reduced power production and lift.

	Due to these performance issues, a plane's takeoff weight may need to be lowered or takeoffs may need to be scheduled for cooler times of the day. Wind direction and [[runway]] slope may need to be taken into account.

	~~==Calculation==~~
	~~Density altitude can be calculated from atmospheric pressure and temperature (assuming dry air).~~

	~~:<math>~~
	~~\mathrm{DA} = \frac{T_\text{SL}}{\gamma} \left[1-\left(\frac{P/P_{SL}}{\mathrm{T}/T_{SL}}\right)^\frac{\Gamma R}{gM-\Gamma R}\right]~~
	~~</math>~~

	~~where~~

	~~: <math>\mathrm{DA}=</math> density altitude in feet~~
	~~: <math>P=</math> atmospheric (static) pressure~~
	~~: <math>P_{SL}=</math> standard sea level atmospheric pressure (1013.25 hPa [[International Standard Atmosphere\|ISA]] or 29.92126 inHg [[U.S._Standard_Atmosphere\|US]]))~~
	~~: <math>\mathrm{T}=</math> [[Outside air temperature\|true (static) air temperature]] in [[kelvin]]s (K) [add 273.15 to the Celsius (°C)] figure~~
	~~: <math>T_{SL}=</math> [[International Standard Atmosphere\|ISA]] standard sea level air temperature in [[kelvin]]s (K) (288.15 K)~~
	~~: <math>\gamma=</math> lapse rate (0.0019812 K/ft)~~
	~~: <math>\Gamma=</math> lapse rate (0.0065 K/m)~~
	~~: <math>R=</math> gas constant (8.31432 J/mol·K)~~
	~~: <math>g=</math> gravity (9.80665 m/s²)~~
	~~: <math>M=</math> molar mass of dry air (0~~.~~0289644 kg/mol)~~


	~~'''''National Weather Service Equation'''''~~

	~~The [[National Weather Service]] uses the following dry-air approximation of the above equation~~ in ~~their standards.~~

	~~:<math>~~
	~~\mathrm{DA} = 145442.16 \left[1-\left~~(~~\frac{17.326 P}{459.67+T}\right~~)~~^{0~~.~~235}\right]~~
	~~</math>~~

	~~where~~

	~~: <math>\mathrm{DA}=</math> density altitude in feet~~
	~~: <math>P=</math> Is the station pressure (atmospheric static pressure) in [[inches of mercury]] (inHg)~~
	: <~~math~~>T=<~~/math~~> ~~T is the station temperature (atmospheric temperature) in Fahrenheit (F)~~

	~~Note that the NWS standard specifies that the density altitude should be rounded~~ to ~~the nearest 100 feet.~~

	~~'''Easy formula~~ to ~~calculate ''density altitude'' from ''pressure altitude'''''~~

	~~This is an easier formula to calculate (with great approximation) ''density altitude'' from ''pressure altitude''~~ ..~~and ''International Standard Atmosphere temperature deviation''~~

	~~:'''Density altitude in feet''' = pressure altitude in feet + 118~~.~~8 x (OAT - ISA_temperature)~~

	~~Where:~~

	~~:OAT = [~~[~~Outside air temperature]] in °C~~
	~~:ISA_temperature = 15 °C - 1.98ºC / 1000ft x PA~~
	~~considering that temperature drops at the rate of 1.98 °C each 1000 ft of altitude until the Tropopause (36000ft), usually rounded to 2ºC~~

	~~Or simply:~~

	~~DA=PA+118.8([PA/500]+OAT-15)~~

	~~Or even simpler~~

	~~DA=1.24 PA + 118.8 OAT - 1782~~

	~~where DA=density altitude and PA=pressure altitude where PA=Hgt+30(1013-QNH)~~

	~~== Notes ==~~
	~~<!--See~~ http://~~en.wikipedia.org/wiki/Wikipedia:Footnotes for an explanation of how to generate~~
	~~footnotes using the <ref(erences/)> tags-->~~
	~~{{Reflist}}~~

	~~==References==~~
	~~{{refbegin}}~~
	*{{cite book \|id= AFM 51-40 / NAVAIR 00-~~80V-49\| date=1 December 1989 \| title=Air Navigation \| chapter= \| editor= \| others= \| pages= \| publisher=Departments of the Air Force and Navy \| url= \| authorlink= }}~~
	*{{cite web \| title=Air Density and Density Altitude \| url=http://wahiduddin.~~net~~/~~calc~~/~~density_altitude.htm \| accessdate=9 January 2006 }}~~
	* Advisory Circular AC 61-~~23C, ''Pilot's Handbook of Aeronautical Knowledge'', U.S. [[Federal Aviation Administration]], Revised 1997~~
	* http://www.tpub.com/content/aerographer/14269/css/14269_74.htm
	~~{{refend}}~~

	~~{{USGovernment\|sourceURL=[http://www.faa.gov/library/manuals/aviation/ Pilot's Handbook of Aeronautical Knowledge]}}~~

	~~==See also==~~
	*[[Outside air temperature]]
	*[[Barometric formula]]
	*[[List of longest runways]]

	~~==External links==~~
	*[http://www.pilotoutlook.com/calculators/density-~~altitude~~-~~calculator Density Altitude Calculator]~~
	*[http://www.experimentalaircraft.info/flight-planning/aircraft-performance-3.php Density Altitude influence on aircraft performance]
	*[http://www.newbyte.co.il/calc.html ~~Newbyte Atmospheric Calculator], [http://market.android.com/details?id=appinventor.ai_barkan86.AtmosCalculatorFree Android Version]~~

	~~{{DEFAULTSORT:Density Altitude}}~~
	~~[[Category:Altitudes in aviation]]~~
	~~[[Category:Atmospheric thermodynamics]~~]

en>Spectral sequence: /* Relations to other L-functions */ ratio holomorphic, cite Martinet

2013-05-25T20:32:12Z

Relations to other L-functions: ratio holomorphic, cite Martinet

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en>Headbomb: /* References */Various citation cleanup + AWB fixes using AWB (8062)

2012-07-30T20:24:31Z

References: Various citation cleanup + AWB fixes using AWB (8062)

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Dedekind zeta function - Revision history

en>Eric Kvaalen: Γ(s) is infinite, not zero, at non-positive integers.

en>Spectral sequence: /* Relations to other L-functions */ ratio holomorphic, cite Martinet

en>Headbomb: /* References */Various citation cleanup + AWB fixes using AWB (8062)