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ISA Atmosphere Model

Implement International Standard Atmosphere (ISA)

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  • ISA Atmosphere Model block

Libraries:
Aerospace Blockset / Environment / Atmosphere

Alternative Configurations of ISA Atmosphere Model Block:
Lapse Rate Model

Description

The ISA Atmosphere Model block implements the mathematical representation of the International Standard Atmosphere (ISA) values for ambient temperature, pressure, density, and speed of sound for the input geopotential altitude.

The ISA Atmosphere Model and Lapse Rate Model blocks are alternative configurations of the same block.

The ISA Atmosphere Model block has these implementations:

  • ISA Atmosphere Model — The default ISA model implements the mathematical representation of the ISA values for ambient temperature, pressure, density, and speed of sound for the input geopotential altitude between sea level (0 m) and tropopause (20000 m).

  • Lapse Rate Model — The lapse rate model implements the mathematical representation of the lapse rate atmospheric equations for ambient temperature, pressure, density, and speed of sound for the input geopotential altitude. To convert from the ISA implementation to the Lapse Rate implementation, select the Change atmospheric parameters parameter. You can customize this atmospheric model by specifying atmospheric properties.

To implement the mathematical representation of the ISA values for ambient temperature, pressure, density, and speed of sound for the input geopotential altitude between -5000 m and mesopause (84852 m), select the Use extended ISA model parameter.

The ISA Atmosphere Model block icon displays the input and output port labels in metric units.

Limitations

  • In the default model, the block limits the implementation to the geopotential altitude of 0 m (minimum) and 20000 m (maximum). In the extended model, the limits are -5000 meters (minimum) and 84852 meters (maximum). The limits are inclusive.

  • Density and speed of sound are calculated using a perfect gas relationship.

Ports

Input

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Geopotential height, specified as a scalar or m-by-n array.

Data Types: double

Output

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Temperature, returned as a scalar or m-by-n array, in K.

Data Types: double

Speed of sound, returned as a scalar or m-by-n array, in m/s.

Data Types: double

Air pressure, returned as a scalar or m-by-n array, in Pa.

Data Types: double

Densities, returned as a scalar or an m-by-n array, in kg/m3.

Data Types: double

Kinematic viscosity, returned as a scalar or m-by-n array, in m2/s.

Dependencies

Selecting the Output kinematic and dynamic viscosity check box adds the ν (m2/s) output port.

Data Types: double

Dynamic viscosity, returned as a scalar or m-by-n array, in N s/m2.

Dependencies

Selecting the Output kinematic and dynamic viscosity check box adds the μ (N s/m2) output port.

Data Types: double

Parameters

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Mathematical representation of the International Standard Atmosphere model.

  • To implement the mathematical representation of the ISA values for ambient temperature, pressure, density, and speed of sound for the input geopotential altitude between the sea level and the tropopause, clear this checkbox. For input heights outside the limits, the output values are held constant.

  • To implement the mathematical representation of the ISA values for ambient temperature, pressure, density, and speed of sound for the input geopotential altitude between -5000 meters and the mesopause, select this check box. For input heights outside the limits, the output values are held constant if the out-of-range action input is set as None or Warning.

Dependencies

Selecting this check box removes the Change atmospheric parameters check box.

Programmatic Use

Block Parameter: useExtended
Type: character vector
Values: 'off' | 'on'
Default: 'off'

Sutherland temperature in Kelvin, specified as a scalar.

Dependencies

This optional input is available when the Output kinematic and dynamic viscosity and Change atmospheric parameters are e.

Reference temperature in Kelvin, specified as a scalar.

Dependencies

This optional input is available when the Output kinematic and dynamic viscosity is selected.

Dependencies

This optional input is available when the Output kinematic and dynamic viscosity and Change atmospheric parameters are e.

Reference dynamic viscosity in kilograms per meter second, specified as a scalar.

Dependencies

This optional input is available when the Output kinematic and dynamic viscosity and Change atmospheric parameters are e.

Option to output kinematic and dynamic viscosity.

Dependencies

Selecting this check box:

  • Adds the ν (m2/s) output port.

  • Adds the μ (N s/m2) output port.

Dependencies

If selected simultaneously with the Change atmospheric parameters checkbox, adds the Viscosity parameters tab.

Programmatic Use

Block Parameter: viscosityOut
Type: character vector
Values: 'off' | 'on'
Default: 'off'

Out-of-range block behavior, specified as follows:

ActionDescription
None No action.
Warning

Warning in the Diagnostic Viewer, model simulation continues.

Error

Error in the Diagnostic Viewer, model simulation stops.

Dependencies

To enable this parameter, select Use extended ISA model.

If this parameter is not visible, the default action is None.

Programmatic Use

Block Parameter: action
Type: character vector
Values: 'None' | 'Warning' | 'Error'
Default: 'Warning'

Customize various atmospheric parameters to be different from the ISA values. Selecting this check box converts the block from ISA Atmosphere Model to Lapse Rate Model.

Dependencies

Selecting this check box enables the Atmospheric parameters tab with these parameters:

  • Acceleration due to gravity (m/s^2)

  • Ratio of specific heats

  • Characteristic gas constant (J/Kg/K)

  • Lapse rate (K/m)

  • Height of troposphere (m)

  • Height of tropopause (m)

  • Air density at mean sea level (Kg/m^3)

  • Ambient pressure at mean sea level (N/m^2)

  • Lowest altitude (m)

Selecting in conjunction with Output kinematic and dynamic viscosity enables the Viscosity parameters tab with these parameters:

  • S

  • Tref

  • μref

Selecting this check box removes the Use extended ISA model check box.

Programmatic Use

Block Parameter: custom
Type: character vector
Values: 'off' | 'on'
Default: 'off'

Acceleration from gravity (g). in m/s2, specified as double scalar.

Dependencies

This parameter is enabled when the Change atmospheric parameters check box is selected.

Programmatic Use

Block Parameter: g
Type: character vector
Values: double scalar
Default: 9.80665

Ratio of specific heats γ, specified as a double value.

Dependencies

This parameter is enabled when the Change atmospheric parameters check box is selected.

Programmatic Use

Block Parameter: gamma
Type: character vector
Values: double scalar
Default: 1.4

Characteristic gas constant (R), specified as double scalar, in J/Kg/K.

Dependencies

This parameter is enabled when the Change atmospheric parameters check box is selected.

Programmatic Use

Block Parameter: R
Type: character vector
Values: double scalar
Default: 287.0531

Lapse rate of the troposphere, specified as double scalar, in K/m.

Dependencies

This parameter is enabled when the Change atmospheric parameters check box is selected.

Programmatic Use

Block Parameter: L
Type: character vector
Values: double scalar
Default: 0.0065

Height of the troposphere (range of decreasing temperatures), specified as double scalar, in m.

Dependencies

This parameter is enabled when the Change atmospheric parameters check box is selected.

Programmatic Use

Block Parameter: h_trop
Type: character vector
Values: double scalar
Default: 11000

Height of the tropopause (range of constant temperature), specified as double scalar, in m.

Dependencies

This parameter is enabled when the Change atmospheric parameters check box is selected.

Programmatic Use

Block Parameter: h_strat
Type: character vector
Values: double scalar
Default: 20000

Air density at mean sea level, specified as double scalar, in Kg/m3.

Dependencies

This parameter is enabled when the Change atmospheric parameters check box is selected.

Programmatic Use

Block Parameter: rho0
Type: character vector
Values: double scalar
Default: 1.225

Ambient pressure at mean sea level, specified as double scalar, in N/m2.

Dependencies

This parameter is enabled when the Change atmospheric parameters check box is selected.

Programmatic Use

Block Parameter: P0
Type: character vector
Values: double scalar
Default: 101325

Ambient temperature at mean sea level (T0), specified as double scalar, in K.

Dependencies

This parameter is enabled when the Change atmospheric parameters check box is selected.

Programmatic Use

Block Parameter: K
Type: character vector
Values: double scalar
Default: 101325

Lowest altitude above which temperature and pressure lapse, specified as double scalar, in m. Lowest altitude (m) must be below Height of tropopause.

Dependencies

This parameter is enabled when the Change atmospheric parameters check box is selected.

Programmatic Use

Block Parameter: h0
Type: character vector
Values: double scalar
Default: 0

Alternative Configurations

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The Lapse Rate Model block implements the mathematical representation of the lapse rate atmospheric equations for ambient temperature, pressure, density, and speed of sound for the input geopotential altitude. You can customize this atmospheric model by specifying atmospheric properties.

Libraries:
Aerospace Blockset / Environment / Atmosphere

Algorithms

The dynamic viscosity is computed using [1]:

μ=β•T32T+S

The kinematic viscosity is computed using [1]:

η=μρ

where:

  • β — A constant dependent on the reference temperature and dynamic viscosity.

  • T — Kelvin kinetic temperature.

  • S — Sutherland constant.

  • ρ — Mass density of air.

References

[1] U.S. Standard Atmosphere., Washington, D.C.: U.S. Government Printing Office, 1976.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced before R2006a

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See Also

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