The U.S. Standard Atmosphere is a static atmospheric model of how the

pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...

temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...

density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...

, and

viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...

of the

Earth's atmosphere The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing fo ...

change over a wide range of

altitude Altitude or height (also sometimes known as depth) is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context ...

s or

elevation The elevation of a geographic location is its height above or below a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface (see Geodetic datum § Ver ...

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 The International Standard Atmosphere (ISA) is a static atmospheric model of how the pressure, temperature, density, and viscosity of the Earth's atmosphere change over a wide range of altitudes or elevations. It has been established to provide a ...

, differing mainly in the assumed temperature distribution at higher altitudes.

Methodology

The USSA mathematical model divides the atmosphere into layers with an assumed linear distribution of

absolute temperature Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics. Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic w ...

''T'' against geopotential altitude ''h''.Gyatt, Graham (2006-01-14)
"The Standard Atmosphere"
A mathematical model of the 1976 U.S. Standard Atmosphere. The other two values (pressure ''P'' and density ''ρ'') are computed by simultaneously solving the equations resulting from: * the

vertical pressure variation Vertical pressure variation is the variation in pressure as a function of elevation. Depending on the fluid in question and the context being referred to, it may also vary significantly in dimensions perpendicular to elevation as well, and these var ...

, which relates pressure, density and geopotential altitude (using a standard pressure of at

mean sea level There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set. For a data set, the '' ari ...

as a

boundary condition In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to th ...

): ::

\frac = - \rho g

, and * the

ideal gas law The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stat ...

in molar form, which relates pressure, density, and temperature: ::

\ P = \rho R_T

at each geopotential altitude, where ''g'' is the standard acceleration of gravity, and ''R''_specific is the

specific gas constant The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per ...

for dry air. Air density must be calculated in order to solve for the pressure, and is used in calculating

dynamic pressure In fluid dynamics, dynamic pressure (denoted by or and sometimes called velocity pressure) is the quantity defined by:Clancy, L.J., ''Aerodynamics'', Section 3.5 :q = \frac\rho\, u^2 where (in SI units): * is the dynamic pressure in pascals ( ...

for moving vehicles. Dynamic viscosity is an empirical function of temperature, and

kinematic viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the int ...

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 conditions below mean sea level, the troposphere is actually extended to , where the temperature is , pressure is , and density is .

1962 version

The basic assumptions made for the 1962 version were: *air is a clean, dry,

perfect gas In physics and engineering, a perfect gas is a theoretical gas model that differs from real gases in specific ways that makes certain calculations easier to handle. In all perfect gas models, intermolecular forces are neglected. This means that one ...

mixture ( ''c''/''c'' = 1.40) *

molecular weight A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...

to 90 km of 28.9644 (C-12 scale) *principal sea-level constituents are assumed to be (in mole percent): ** N₂ – 78.084% ** O₂ – 20.9476% ** Ar – 0.934% ** CO₂ – 0.0314% ** Ne – 0.001818% ** He – 0.000524% ** CH₄ – 0.0002%. *assigned mean conditions at

sea level Mean sea level (MSL, often shortened to sea level) is an average surface level of one or more among Earth's coastal bodies of water from which heights such as elevation may be measured. The global MSL is a type of vertical datuma standardise ...

are as follows : ** ''P'' = 14.696

psi Psi, PSI or Ψ may refer to: Alphabetic letters * Psi (Greek) (Ψ, ψ), the 23rd letter of the Greek alphabet * Psi (Cyrillic) (Ѱ, ѱ), letter of the early Cyrillic alphabet, adopted from Greek Arts and entertainment * "Psi" as an abbreviatio ...

= 2116.22 psf = 101325 Pa = 29.92 inHg = 0.1013250 MN/m² ** ''T'' = 59 °F = 518.67 °R = 15 °C = 288.15 K ** ''ρ'' = 0.0764734 lb/(cu ft) = 1.225 0 kg/m³ ** ''g'' = 32.174 1 ft/s² = 9.80665 m/s² ** ''R^*'' = 1545.31 ft⋅lb/(lbmol⋅°R) = 8.31432 J/(mol⋅K).

1976 version

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

References

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. * U.S. Standard Atmosphere Supplements, 1966, U.S. Government Printing Office, Washington, D.C., 1966.
U.S. Standard Atmosphere
1976, U.S. Government Printing Office, Washington, D.C., 1976 (Linked file is 17 MB).

External links