air_density documentation

air_density computes density from the baromometric forumula for a US Standard Atmosphere.

See also air_pressure.

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rho = air_density(h)


rho = air_density(h) returns the atmospheric density rho in kg/m^3 corresponding to the heights h in geometric meters above sea level.


The US Standard Atmosphere formula is valid to 86 km above sea level, so let's look at air density from sea level to 85 km:

h = 0:85e3;

rho = air_density(h);

axis tight
box off
ylabel 'height above sea level (km)'
xlabel 'density (kg m^{-3})'

The formula uses a piecewise function that calculates an equation based on different constants for different layers of the atmosphere. The bases of those layers are at 0, 11, 20, 32, 47, 51, and 71 km above sea level. For context, we can plot those layer bases as horizontal lines using hline:

LayerBases = [0 11 20 32 47 51 71];


Pro tip: For some applictions it may be helpful to display the x axis on a log scale. To do that, we could have plotted the data with semilogx instead of using the plot function above, or we can change the x scale to log like this:


Curious about the relationship between atmospheric density and atmospheric pressure? Compare with air_pressure:

p = air_pressure(h);

axis tight
box off
xlabel 'pressure (kPa)'
ylabel 'density (kg m^{-3})'

Author Info

This function is part of the Climate Data Toolbox for Matlab. The function and supporting documentation were written by Chad A. Greene of the University of Texas at Austin.