Lapse Rate Model

Implement lapse rate model for atmosphere

  • Library:
  • Aerospace Blockset / Environment / Atmosphere

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

The ISA Atmosphere Model and Lapse Rate Model blocks are identical blocks. When configured for ISA Atmosphere Model, the block implements ISA values. When configured for Lapse Rate Model, the block implements the mathematical representation of lapse rate atmospheric equations.

The Lapse Rate Model block icon displays the input and output 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

Parameters

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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 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)

Programmatic Use

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

Acceleration from gravity (g). in m/s2, specified as real, 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: real, 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: real, double scalar
Default: 1.4

Characteristic gas constant (R), specified as real, 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: real, double scalar
Default: 287.0531

Lapse rate of the troposphere, specified as real, 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: real, double scalar
Default: 0.0065

Height of the troposphere (range of decreasing temperatures), specified as real, 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: real, double scalar
Default: 11000

Height of the tropopause (range of constant temperature), specified as real, 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: real, double scalar
Default: 20000

Air density at mean sea level, specified as real, 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: real, double scalar
Default: 1.225

Ambient pressure at mean sea level, specified as real, 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: real, double scalar
Default: 101325

Ambient temperature at mean sea level (T0), specified as real, 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: real, double scalar
Default: 101325

Lowest altitude above which temperature and pressure lapse, specified as real, 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: real, double scalar
Default: 0

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.

Introduced before R2006a