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Lapse Rate Model

Implement lapse rate model for atmosphere

  • Lapse Rate Model block

Libraries:
Aerospace Blockset / Environment / Atmosphere

Alternative Configurations of Lapse Rate Model Block:
ISA Atmosphere Model

Description

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.

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

The Lapse Rate Model block has these implementations:

  • 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. You can customize this atmospheric model by specifying atmospheric properties.

  • ISA Atmosphere Model — The 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). To convert from the Lapse Rate implementation to the ISA implementation, clear the Change atmospheric parameters parameter.

The Lapse Rate Model block icon displays the input and output port labels in metric units.

Limitations

  • Below the geopotential altitude of 0 km and above the geopotential altitude of the tropopause, temperature and pressure values are held.

  • 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 array.

Data Types: double

Output

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Temperature, returned as a scalar or array, in K.

Data Types: double

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

Data Types: double

Air pressure, returned as a scalar or array, in Pa.

Data Types: double

Air density, returned as scalar or 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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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'

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

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 ISA Atmosphere Model block 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).

Libraries:
Aerospace Blockset / Environment / Atmosphere

Algorithms

These equations define the troposphere:

T=T0LhP=P0(TT0)gLRρ=ρ0(TT0)gLR1a=γRT

These equations define the tropopause (lower stratosphere):

T=T0LhtsP=P0(TT0)gLRegRT(htsh)ρ=ρ0(TT0)gLR1egRT(htsh)a=γRT

where:

T 0

Absolute temperature at mean sea level in kelvin (K)

ρ 0

Air density at mean sea level in kg/m 3

P 0

Static pressure at mean sea level in N/m 2

h

Altitude in m

hts

Height of the troposphere in m

T

Absolute temperature at altitude h in kelvin (K)

ρ

Air density at altitude h in kg/m 3

P

Static pressure at altitude h in N/m 2

a

Speed of sound at altitude h in m/s 2

L

Lapse rate in K/m

R

Characteristic gas constant J/kg-K

γ

Specific heat ratio

g

Acceleration due to gravity in m/s 2

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