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Atmosphere Models

flow_state includes standard atmosphere models to compute pressure, temperature, and density at a given altitude.

For usage examples, see Examples and Config Files.

Overview

Model Function/Class Altitude Range Lat/Season Reference
USSA76 ussa76() 0–86 km No 1
CIRA86 CIRA86() 0–120 km Yes 2

US Standard Atmosphere 1976 (USSA76)

The default model 1. Defines a single reference atmosphere independent of latitude and season.

  • Valid from 0 to 86 km (geometric altitude)
  • Piecewise linear temperature profile with defined lapse rates
  • Assumes hydrostatic equilibrium and ideal gas

Layer Structure

Layer Base Altitude Base Temp Lapse Rate
Troposphere 0 km 288.15 K -6.5 K/km
Tropopause 11 km 216.65 K 0 K/km
Stratosphere 1 20 km 216.65 K +1.0 K/km
Stratosphere 2 32 km 228.65 K +2.8 K/km
Stratopause 47 km 270.65 K 0 K/km
Mesosphere 1 51 km 270.65 K -2.8 K/km
Mesosphere 2 71 km 214.65 K -2.0 K/km

Equations

For gradient layers (\(\lambda \neq 0\)):

\[ T = T_b + \lambda (h - h_b) \]
\[ p = p_b \left( \frac{T}{T_b} \right)^{-g_0 / (\lambda R)} \]

For isothermal layers (\(\lambda = 0\)):

\[ p = p_b \exp\left( -\frac{g_0 (h - h_b)}{R T_b} \right) \]

where \(g_0 = 9.80665\) m/s² is standard gravity and \(R = 287.05\) J/(kg·K).

COSPAR International Reference Atmosphere (CIRA86)

Latitude and season-dependent model 2.

  • Valid from 0 to 120 km altitude
  • Tabulated data interpolated for latitude (0–80°N, 10° increments) and month (1–12)
  • More accurate for high-altitude and polar/equatorial trajectories

Parameters:

Parameter Range Description
latitude 0–80° Degrees North (10° increments)
month 1–12 Month of year (January = 1)

When to Use Which

USSA76 is sufficient for:

  • Most CFD applications in the lower atmosphere (< 50 km)
  • General-purpose calculations
  • When latitude/season effects are negligible

CIRA86 is preferred when:

  • Operating at high altitudes (> 50 km)
  • Latitude effects matter (polar vs. equatorial trajectories)
  • Seasonal variations are important

References

  1. NOAA, NASA, and USAF. U.s. standard atmosphere, 1976. Technical Report NOAA-S/T 76-1562, National Oceanic and Atmospheric Administration, 1976. URL: https://www.ngdc.noaa.gov/stp/space-weather/online-publications/miscellaneous/us-standard-atmosphere-1976/us-standard-atmosphere_st76-1562_noaa.pdf. ↩↩

  2. D. Rees, J. J. Barnett, and K. Labitzke. COSPAR international reference atmosphere: 1986. Part II: middle atmosphere models. Advances in Space Research, 1990. URL: https://doi.org/10.1016/0273-1177(90)90386-E, doi:10.1016/0273-1177(90)90386-E. ↩↩