View source for U.S. Standard Atmosphere

{{Short description|Static atmospheric model}}
{{distinguish|International Standard Atmosphere}}
{{Comparison_US_standard_atmosphere_1962.svg}}
The '''U.S. Standard Atmosphere''' is a [[static atmospheric model]] of how the [[pressure]], [[temperature]], [[density]], and [[viscosity]] of the [[Earth's atmosphere]] change over a wide range of [[altitude]]s or [[elevation]]s. The model, based on an existing international standard, was first published in 1958 by the U.S. Committee on Extension to the Standard Atmosphere, and was updated in 1962, 1966, and 1976. It is largely consistent in methodology with the [[International Standard Atmosphere]], differing mainly in the assumed temperature distribution at higher altitudes.
[[Image:Atmospheric composition Langley.svg|thumb|250px|Visualization of composition by volume of Earth's atmosphere. Water vapor is not included, as this is highly variable. Each tiny cube (such as the one representing krypton) has one millionth of the volume of the entire block. Data is from [http://www.nasa.gov/centers/langley/pdf/245893main_MeteorologyTeacherRes-Ch2.r4.pdf NASA Langley].]]

==Methodology==

The USSA [[mathematical model]] divides the atmosphere into layers with an assumed linear distribution of [[absolute temperature]] ''T'' against [[geopotential altitude]] ''h''.<ref name="Graham Gyatt">Gyatt, Graham (2006-01-14): [http://nebula.wsimg.com/ab321c1edd4fa69eaa94b5e8e769b113?AccessKeyId=AF1D67CEBF3A194F66A3&disposition=0&alloworigin=1 "The Standard Atmosphere"]. A mathematical model of the 1976 U.S. Standard Atmosphere.</ref> The other two values (pressure ''P'' and density ''ρ'') are computed by [[simultaneous equations model|simultaneously solving the equations]] resulting from:
* the [[vertical pressure variation]], which relates pressure, density and geopotential altitude (using a standard pressure of {{convert|101325|Pa|psi|sigfig=5}} at [[sea level|mean sea level]] as a [[boundary value problem|boundary condition]]):
:: <math>\frac{dP}{dh} = - \rho g </math>, and
* the [[ideal gas law]] in [[mole (unit)|molar]] form, which relates pressure, density, and temperature:
:: <math>\ P = \rho R_{\rm specific}T </math>
at each geopotential altitude, where ''g'' is the [[Standard_gravity|standard acceleration of gravity]], and ''R''<sub>specific</sub> is the [[Gas constant#Specific gas constant|specific gas constant]] for dry air.

Air density must be calculated in order to solve for the pressure, and is used in calculating [[dynamic pressure]] for moving vehicles. [[Viscosity#Dynamic (shear) viscosity|Dynamic viscosity]] is an empirical function of temperature, and [[Viscosity#Kinematic viscosity|kinematic viscosity]] is calculated by dividing dynamic viscosity by the density.

Thus the standard consists of a tabulation of values at various altitudes, plus some formulas by which those values were derived.

To allow modeling [[list of places on land with elevations below sea level|conditions below mean sea level]], the troposphere is actually extended to {{convert|-2000|ft|m|sp=us}}, where the temperature is {{convert|66.1|F|C}}, pressure is {{convert|15.79|psi|Pa}}, and density is {{convert|1.2985|kg/m3|lb/ft3|sp=us|disp=flip}}.

==1962 version==
The basic assumptions made for the 1962 version were:<ref name="isbn0-8493-0252-8">{{cite book |author=Tuve, George Lewis |author2=Bolz, Ray E. |title=CRC handbook of tables for applied engineering science |publisher=[[CRC Press]] |location=Boca Raton |date=1973 |isbn=0-8493-0252-8 |url-access=registration |url=https://archive.org/details/crchandbookoftab0000unse_y0b1 }}</ref>

*air is a clean, dry, [[perfect gas]] mixture ([[heat capacity|''c''{{sub|p}}/''c''{{sub|v}}]] = 1.40)
*[[molecular weight]] to 90&nbsp;km of 28.9644 (C-12 scale)
*principal sea-level constituents are assumed to be (in mole percent):
** [[Nitrogen|N<sub>2</sub>]] – 78.084%
** [[Oxygen|O<sub>2</sub>]] – 20.9476%
** [[Argon|Ar]] – 0.934%
** [[Carbon dioxide|CO<sub>2</sub>]] – 0.0314%
** [[Neon|Ne]] – 0.001818%
** [[Helium|He]] – 0.000524%
** [[Methane|CH<sub>4</sub>]] – 0.0002%.
*assigned mean conditions at [[sea level]] are as follows :
**[[Pressure|''P'']] = 14.696 [[Pounds per square inch|psi]] = 2116.22&nbsp;psf = 101325&nbsp;Pa = 760 mm Hg = 29.92&nbsp;[[Inch of mercury|inHg]] = 0.1013250&nbsp;MN/m<sup>2</sup>
**[[Temperature|''T'']] = 59&nbsp;°F = 518.67&nbsp;°R = 15&nbsp;°C = 288.15&nbsp;K
**[[Density|''ρ'']] = 0.0764734 lb/(cu ft) = 1.225 0&nbsp;kg/m<sup>3</sup>
**[[Earth's gravity|''g'']] = 32.174 1&nbsp;ft/s<sup>2</sup> = 9.80665&nbsp;m/s<sup>2</sup>
**[[Gas_constant#U.S._Standard_Atmosphere|''R<sup>*</sup>'']] = 1545.31&nbsp;ft⋅lb/(lbmol⋅°R) = 8.31432&nbsp;J/(mol⋅K).

The [[Federal Aviation Regulations]] define '''Standard Atmosphere''' in {{CodeFedReg |14|1|1|}} by reference to the U.S. Standard Atmosphere, 1962 (Geopotential altitude tables).

==1976 version==

This is the most recent version and differs from previous versions only above 51&nbsp;km:

{| class="wikitable"
|-
! rowspan="2"|Subscript ''b''
! colspan="2"|Geopotential<br/> height above MSL<ref name="USA 1962">U.S. Standard Atmosphere, 1962, U.S. Government Printing Office, Washington, D.C., 1962, https://www.ngdc.noaa.gov/stp/space-weather/online-publications/miscellaneous/us-standard-atmosphere-1976/us-standard-atmosphere_st76-1562_noaa.pdf</ref>
! colspan="2"|Static pressure
! rowspan="2"|Standard<br/> temperature<br/> (K)
! colspan="2"|Temperature<br/> lapse rate
|-
! (m) !! (ft) !! (Pa) !! (inHg) !! (K/m) !! (K/ft)
|-
| align="center" |0
| align="center" |0
| align="center" |0
| align="center" |101325
| align="center" |29.92126
| align="center" |288.15
| align="center" | −0.0065
| align="center" | −0.001981
|-
| align="center" |1
| align="center" |11,000
| align="center" |36,089
| align="center" |22632.1
| align="center" |6.683245
| align="center" |216.65
| align="center" |0.0
| align="center" |0.0
|-
| align="center" |2
| align="center" |20,000
| align="center" |65,617
| align="center" |5474.89
| align="center" |1.616734
| align="center" |216.65
| align="center" |0.001
| align="center" |0.0003048
|-
| align="center" |3
| align="center" |32,000
| align="center" |104,987
| align="center" |868.019
| align="center" |0.2563258
| align="center" |228.65
| align="center" |0.0028
| align="center" |0.0008534
|-
| align="center" |4
| align="center" |47,000
| align="center" |154,199
| align="center" |110.906
| align="center" |0.0327506
| align="center" |270.65
| align="center" |0.0
| align="center" |0.0
|-
| align="center" |5
| align="center" |51,000
| align="center" |167,323
| align="center" |66.9389
| align="center" |0.01976704
| align="center" |270.65
| align="center" | −0.0028
| align="center" | −0.0008534
|-
| align="center" |6
| align="center" |71,000
| align="center" |232,940
| align="center" |3.95642
| align="center" |0.00116833
| align="center" |214.65
| align="center" | −0.002
| align="center" | −0.0006096
|-
| align="center" |7
| align="center" |84,852
| align="center" |278,385
|
|
| align="center" |186.946
|
|
|}

[[Image:Us standard atmosphere model.png]]

==See also==
*[[Atmospheric models]]
*[[NRLMSISE-00]]
*[[Barometric formula]]
*[[Standard temperature and pressure]]

==References==

{{Reflist}}

==Documents==
* U.S. Extension to the ICAO Standard Atmosphere, U.S. Government Printing Office, Washington, D.C., 1958.
* U.S. Standard Atmosphere, 1962, U.S. Government Printing Office, Washington, D.C., 1962. [https://ntrs.nasa.gov/api/citations/19630003300/downloads/19630003300.pdf]
* U.S. Standard Atmosphere Supplements, 1966, U.S. Government Printing Office, Washington, D.C., 1966.
* [https://ntrs.nasa.gov/api/citations/19770009539/downloads/19770009539.pdf?attachment=true U.S. Standard Atmosphere], 1976, U.S. Government Printing Office, Washington, D.C., 1976 (Linked file is 17 MB).

==External links==
{{Commonscat}}
*[https://web.archive.org/web/20060513194709/http://modelweb.gsfc.nasa.gov/atmos/us_standard.html NASA GSFC ModelWeb]
*[http://nebula.wsimg.com/ab321c1edd4fa69eaa94b5e8e769b113?AccessKeyId=AF1D67CEBF3A194F66A3&amp;disposition=0&amp;alloworigin=1 A mathematical model of the 1976 U.S. Standard Atmosphere]
*[http://www.digitaldutch.com/atmoscalc/ Online 1976 US Standard Atmosphere calculator and table generator]
*[http://www.luizmonteiro.com/StdAtm.aspx Calculate 28 properties of 1976 Standard Atmosphere]

[[Category:Atmosphere of Earth]]
[[Category:Atmospheric thermodynamics]]