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Lapse Rate Model

Implement lapse rate model for atmosphere

Library

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, described below, by specifying atmospheric properties in the block dialog.

The following equations define the troposphere

The following equations define the tropopause (lower stratosphere)

where:

T0Absolute temperature at mean sea level in kelvin (K)
ρ0Air density at mean sea level in kg/m3
P0Static pressure at mean sea level in N/m2
hAltitude in m
htsHeight of the troposphere in m
TAbsolute temperature at altitude h in kelvin (K)
ρAir density at altitude h in kg/m3
PStatic pressure at altitude h in N/m2
aSpeed of sound at altitude h in m/s2
LLapse rate in K/m
RCharacteristic gas constant J/kg-K
γSpecific heat ratio
gAcceleration due to gravity in m/s2

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

Dialog Box

Change atmospheric parameters

When selected, the following atmospheric parameters can be customized to be different from the ISA values.

Acceleration due to gravity

Specify the acceleration due to gravity (g).

Ratio of specific heats

Specify the ratio of specific heats γ.

Characteristic gas constant

Specify the characteristic gas constant (R).

Lapse rate

Specify the lapse rate of the troposphere (L).

Height of troposphere

Specify the upper altitude of the troposphere, a range of decreasing temperature.

Height of tropopause

Specify the upper altitude of the tropopause, a range of constant temperature.

Air density at mean sea level

Specify the air density at sea level (ρ0).

Ambient pressure at mean sea level

Specify the ambient pressure at sea level (P0).

Ambient temperature at mean sea level

Specify the ambient temperature at sea level (T0).

Lowest altitude (m)

Specify the lowest altitude above which temperature and pressure lapse. Lowest altitude (m) must be below Height of tropopause. Default value is 0 m.

Inputs and Outputs

InputDimension TypeDescription

First

 Contains the geopotential height.

OutputDimension TypeDescription

First

 Contains the temperature.

Second

 Contains the speed of sound.

Third

 Contains the air pressure.

Fourth

 Contains the air density.

Assumptions and 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.

Reference

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

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