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Every student of aerodynamics and flight mechanics is introduced to an atmosphere table, which allows one to determine the temperature, pressure, and density at any altitude. If you don't happen to have such a table handy, you may want to look at a sample atmosphere table in US units or SI units. The equations used are those adopted 15 October 1976 by the United States Committee on Extension to the Standard Atmosphere (COESA), representing 29 U.S. scientific and engineering organizations. The values selected in 1976 are slight modifications of those adopted in 1962. The equations and parameters used are documented in a book entitled U.S. Standard Atmosphere, 1976 published by the U.S. Government Printing Office, Washington, D.C. A summary of the definition of the 1976 atmosphere is on another page.

The equations defining the 1976 Standard Atmosphere are coded for inclusion in your own aeronautical studies. The program is supplied in several different programming languages: Fortran, Pascal(Delphi), Visual Basic, C, C++, Fortran77, IDL, Python and QBasic.

The fundamental procedure is a subroutine called Atmosphere that accepts altitude as an input argument and returns non-dimensional values of temperature, pressure, and density which are ratios of the quantity at altitude to that at sea-level. The equations are taken directly from the NASA publication. Since the definition of the international standard is given in SI units, the altitude is supplied in kilometers. The standard atmosphere is defined as a set of layers and the routine determines which layer contains the specified altitude. The desired layer is found by binary search. The temperature is then computed by interpolation. Then the pressure is computed from the hydrostatic equations and the density follows from the perfect gas law. As an example of the code on the CD-ROM, you may download the source code of the Fortran version of Atmosphere.

In order to check the operation of the subroutine, a program called Tables is included that computes and prints a formatted page of data showing the atmospheric quantities at various altitudes. Since nearly every introductory aerodynamics textbook contains such a table, you may question the value of producing yet another one. By going through this exercise, you will have these routines in your standard computational toolbox. When you are studying a new vehicle concept or flight procedure, you can concentrate on your idea and not on validating your atmosphere calculations.

The routine Atmosphere implements the first seven layers of the atmosphere, as defined in the 1976 standard. This defines the atmosphere from sea level to 86 kilometers (282,000 ft.) altitude. For heights above 86 kilometers, see the Upper Atmosphere page.

As a practical matter, almost all flight takes place in the first two layers and they are commonly referred to as the troposphere and the stratosphere. The routine Atmosphere which does the very elegant binary search through the layers will usually use the first or second. An alternate routine called SimpleAtmosphere is included in this package which is only correct to 20 km, but is much simpler because it only makes one test for altitude. The table generating program has been modified to make a second table of the lower atmosphere.

You may read the page describing the hydrostatic equations. XHTML+MathML, 12KB or PDF, 69KB.

For more information, go to the National Space Science Data Center (NSSDC) description of the 1976 atmosphere.

You may also be interested in Non-standard Atmospheres. Starting in January 2005, I included non-standard atmosphere subroutines on the CD-ROM.

As an example of using this subroutine, I have written a program that computes the trajectory of a baseball. This may help you answer important questions such as whether a baseball travels further in Denver than at sea level.

PDAS home > Contents > Standard Atmosphere
Public Domain Aeronautical Software (PDAS)