Lapse Rate Model

Implement lapse rate model for atmosphere

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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h (m) — Geopotential height
scalar | array

Geopotential height, specified as a scalar or array.

Data Types: double

Output

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T (K) — Temperature
scalar | array

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

Data Types: double

a (m/s) — Speed of sound
scalar | array

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

Data Types: double

P (Pa) — Air pressure
scalar | array

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

Data Types: double

ρ (kg/m³) — Air density
scalar | array

Air density, returned as scalar or array, in kg/m³.

Data Types: double

ν (m²/s) — Kinematic viscosity
scalar | m-by-n array

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

μ (N s/m²) — Dynamic viscosity
scalar | m-by-n array

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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S — Sutherland temperature
110.4 K (default) | scalar

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.

T_ref — Reference temperature
273.15 K (default) | scalar

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.

μ_ref — Reference dynamic viscosity
1.716e-5 kg/ms (default) | scalar

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.

Output kinematic and dynamic viscosity — Option to output kinematic and dynamic viscosity
`off` (default) | `on`

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'

Change atmospheric parameters — Customize parameters
`off` (default) | `on`

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
T_ref
μ_ref

Programmatic Use

Block Parameter: custom

Type: character vector

Values: 'off' | 'on'

Default: 'off'

Acceleration due to gravity (m/s^2) — Acceleration
`9.80665` (default) | scalar

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 — Ratio of heats
`1.4` (default) | scalar

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 (J/Kg/K) — Gas constant
`287.0531` (default) | scalar

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 (K/m) — Lapse rate
`0.0065` (default) | scalar

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 troposphere (m) — Troposphere height
`11000` (default) | scalar

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 tropopause (m) — Tropopause height
`20000` (default) | scalar

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 (Kg/m^3) — Air density
`1.225` (default) | scalar

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 (N/m^2) — Ambient pressure
`101325` (default) | scalar

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 (K) — Ambient temperature
`288.15` (default) | scalar

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 (m) — Lowest altitude
`0` (default) | scalar

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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ISA Atmosphere Model — Implement International Standard Atmosphere (ISA)

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:

$\begin{matrix} T = T_{0} - L h \\ P = P_{0} {(\frac{T}{T_{0}})}^{\frac{g}{L R}} \\ ρ = ρ_{0} {(\frac{T}{T_{0}})}^{\frac{g}{L R} - 1} \\ a = \sqrt{γ R T} \end{matrix}$

These equations define the tropopause (lower stratosphere):

$\begin{matrix} T = T_{0} - L h t s \\ P = P_{0} {(\frac{T}{T_{0}})}^{\frac{g}{L R}} e^{\frac{g}{R T}}^{^{(h t s - h)}} \\ ρ = ρ_{0} {(\frac{T}{T_{0}})}^{\frac{g}{L R} - 1} e^{\frac{g}{R T}}^{^{(h t s - h)}} \\ a = \sqrt{γ R T} \end{matrix}$

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

Lapse Rate Model

Description

Limitations

Ports

Input

h (m) — Geopotential height scalar | array

Output

T (K) — Temperature scalar | array

a (m/s) — Speed of sound scalar | array

P (Pa) — Air pressure scalar | array

ρ (kg/m3) — Air density scalar | array

ν (m2/s) — Kinematic viscosity scalar | m-by-n array

Dependencies

μ (N s/m2) — Dynamic viscosity scalar | m-by-n array

Dependencies

Parameters

S — Sutherland temperature 110.4 K (default) | scalar

Dependencies

Tref — Reference temperature 273.15 K (default) | scalar

Dependencies

Dependencies

μref — Reference dynamic viscosity 1.716e-5 kg/ms (default) | scalar

Dependencies

Output kinematic and dynamic viscosity — Option to output kinematic and dynamic viscosity off (default) | on

Dependencies

Dependencies

Programmatic Use

Change atmospheric parameters — Customize parameters off (default) | on

Dependencies

Programmatic Use

Acceleration due to gravity (m/s^2) — Acceleration 9.80665 (default) | scalar

Dependencies

Programmatic Use

Ratio of specific heats — Ratio of heats 1.4 (default) | scalar

Dependencies

Programmatic Use

Characteristic gas constant (J/Kg/K) — Gas constant 287.0531 (default) | scalar

Dependencies

Programmatic Use

Lapse rate (K/m) — Lapse rate 0.0065 (default) | scalar

Dependencies

Programmatic Use

Height of troposphere (m) — Troposphere height 11000 (default) | scalar

Dependencies

Programmatic Use

Height of tropopause (m) — Tropopause height 20000 (default) | scalar

Dependencies

Programmatic Use

Air density at mean sea level (Kg/m^3) — Air density 1.225 (default) | scalar

Dependencies

Programmatic Use

Ambient pressure at mean sea level (N/m^2) — Ambient pressure 101325 (default) | scalar

Dependencies

Programmatic Use

Ambient temperature at mean sea level (K) — Ambient temperature 288.15 (default) | scalar

Dependencies

Programmatic Use

Lowest altitude (m) — Lowest altitude 0 (default) | scalar

Dependencies

Programmatic Use

Alternative Configurations

ISA Atmosphere Model — Implement International Standard Atmosphere (ISA)

Algorithms

References

Extended Capabilities

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

Version History

See Also

h (m) — Geopotential height
scalar | array

T (K) — Temperature
scalar | array

a (m/s) — Speed of sound
scalar | array

P (Pa) — Air pressure
scalar | array

ρ (kg/m³) — Air density
scalar | array

ν (m²/s) — Kinematic viscosity
scalar | m-by-n array

μ (N s/m²) — Dynamic viscosity
scalar | m-by-n array

S — Sutherland temperature
110.4 K (default) | scalar

T_ref — Reference temperature
273.15 K (default) | scalar

μ_ref — Reference dynamic viscosity
1.716e-5 kg/ms (default) | scalar

Output kinematic and dynamic viscosity — Option to output kinematic and dynamic viscosity
`off` (default) | `on`

Change atmospheric parameters — Customize parameters
`off` (default) | `on`

Acceleration due to gravity (m/s^2) — Acceleration
`9.80665` (default) | scalar

Ratio of specific heats — Ratio of heats
`1.4` (default) | scalar

Characteristic gas constant (J/Kg/K) — Gas constant
`287.0531` (default) | scalar

Lapse rate (K/m) — Lapse rate
`0.0065` (default) | scalar

Height of troposphere (m) — Troposphere height
`11000` (default) | scalar

Height of tropopause (m) — Tropopause height
`20000` (default) | scalar

Air density at mean sea level (Kg/m^3) — Air density
`1.225` (default) | scalar

Ambient pressure at mean sea level (N/m^2) — Ambient pressure
`101325` (default) | scalar

Ambient temperature at mean sea level (K) — Ambient temperature
`288.15` (default) | scalar

Lowest altitude (m) — Lowest altitude
`0` (default) | scalar

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