Prof. dr. ir. Jacco Hoekstra

The standard atmosphere I

Introduction to Aeronautical Engineering

M.T. Salam - CC - BY - SA

Felix Baumgartner October 14th, 2012

38 969 m

Joe Kittinger August 16th , 1960

31 333 m

R. de Pandora - CC - BY - SA Kansir - CC - BY

Why a standard atmosphere?

We need a reference atmosphere for:

– Meaningful aircraft performance specification

– Definition of (pressure) altitude and densities

– Model atmosphere for simulation and analysis

Why a standard atmosphere?

We need a reference atmosphere for:

– Meaningful aircraft performance specification

– Definition of (pressure) altitude and densities

– Model atmosphere for simulation and analysis

What is a standard atmosphere?

As function of altitude we need: – Pressure p [Pa]

– Air density ρ [kg/m3]

– Temperature T [K]

Physically correct, so it obeys:

– Equation of state:

– Pressure increase due to gravity

p RT 287.00 J kgKR

101325 N/m2

Standard atmosphere is a model atmosphere

Real atmosphere International Standard Atmosphere (ISA)

NASA, muffinn - CC - BY

The hydrostatic equation

Describes pressure increase due to the gravity of air.

p + Δp

m∙ g

p

Δ h

Area

A

The hydrostatic equation

Describes pressure increase due to the gravity of air.

dp = - ρ g dh

m∙ g

p

( )

down upF F

mg p p A pA

A h g pA pA pA

h g p

p g h

p + Δp

Δ h

Area

A

The hydrostatic equation

Describes pressure increase due to the gravity of air.

dp = - ρ g dh

m∙ g

p

( )

down upF F

mg p p A pA

A h g pA pA pA

h g p

p g h

p + Δp

Δ h

Area

A

The hydrostatic equation

Describes pressure increase due to the gravity of air.

dp = - ρ g dh

m∙ g

p

( )

down upF F

mg p p A pA

A h g pA pA pA

h g p

p g h

p + Δp

Δ h

Area

A

The hydrostatic equation

Describes pressure increase due to the gravity of air.

dp = - ρ g dh

m∙ g

p

( )

down upF F

mg p p A pA

A h g pA pA pA

h g p

p g h

p + Δp

Δ h

Area

A

The hydrostatic equation

Describes pressure increase due to the gravity of air.

dp = - ρ g dh

m∙ g

p

( )

down upF F

mg p p A pA

A h g pA pA pA

h g p

p g h

p + Δp

Δ h

Area

A

The hydrostatic equation

Describes pressure increase due to the gravity of air.

dp = - ρ g dh

m∙ g

p

( )

down upF F

mg p p A pA

A h g pA pA pA

h g p

p g h

p + Δp

Δ h

Area

A

The hydrostatic equation

Describes pressure increase due to the gravity of air.

dp = - ρ g dh

m∙ g

p

( )

down upF F

mg p p A pA

A h g pA pA pA

h g p

p g h

p + Δp

Δ h

Area

A

The hydrostatic equation

Describes pressure increase due to the gravity of air.

dp = - ρ g dh

m∙ g

p

( )

down upF F

mg p p A pA

A h g pA pA pA

h g p

p g h

p + Δp

Δ h

Area

A

The hydrostatic equation

Describes pressure increase due to the gravity of air.

dp = - ρ g dh

m∙ g

p

( )

down upF F

mg p p A pA

A h g pA pA p A

h g p

p g h

p + Δp

Δ h

Area

A

The hydrostatic equation

Describes pressure increase due to the gravity of air.

dp = - ρ g dh

m∙ g

p

( )

down upF F

mg p p A pA

A h g pA pA p A

A h g p A

p g h

p + Δp

Δ h

Area

A

The hydrostatic equation

Describes pressure increase due to the gravity of air.

dp = - ρ g dh

m∙ g

p

( )

down upF F

mg p p A pA

A h g pA pA p A

A h g p A

p g h

p + Δp

Δ h

Area

A

The hydrostatic equation

Describes pressure increase due to the gravity of air.

dp = - ρ g dh

m∙ g

p

( )

down upF F

mg p p A pA

A h g pA pA p A

h g p

p g h

p + Δp

Δ h

Area

A

The hydrostatic equation

Describes pressure increase due to the gravity of air.

dp = - ρ g dh

m∙ g

p

( )

down upF F

mg p p A pA

A h g pA pA p A

h g p

p g h

p + Δp

Δ h

Area

A

The hydrostatic equation

Describes pressure increase due to the gravity of air.

dp = - ρ g dh

m∙ g

p

( )

down upF F

mg p p A pA

A h g pA pA p A

h g p

p g h

p + Δp

Δ h

Area

A

The hydrostatic equation

Describes pressure increase due to the gravity of air.

dp = - ρ g dh

m∙ g

p

( )

down upF F

mg p p A pA

A h g pA pA p A

h g p

p g h

p + Δp

Δ h

Area

A

How to define a standard atmosphere?

As function of altitude: – Pressure p , air density ρ , temperature T

Physically correct, so it obeys:

– Equation of state:

– Hydrostatic equation:

p RT

101325 N/m2

dp = - ρ g dh

How to define a standard atmosphere?

As function of altitude: – Pressure p , air density ρ , temperature T

Physically correct, so it obeys:

– Equation of state:

– Hydrostatic equation:

p RT

101325 N/m2

dp = - ρ g dh

Define temperature as function of altitude Define start value for pressure

ISA Temperature

profile

0

0

30

101325 Pa

15 C 288.15

1.225

o

p

T K

kgm

Sea level (h = 0 m):

h [km]

T [K]

troposphere

stratosphere

mesosphere

thermosphere

stratopause

tropopause

mesopause

ISA Temperature profile

Level name Base geopotential height [m]

Base temperature [⁰C]

Lapse rate [⁰C/km]

Base atmospheric pressure [Pa]

Troposphere 0 15 -6.5 101,325

Tropopause 11,000 -56.5 0 22,632

Stratosphere 20,000 -56.5 +1.0 5474.9

Stratosphere 32,000 -44.5 +2.8 868.02

Stratopause 47,000 -2.5 0 110.91

Mesosphere 51,000 -2.5 -2.8 66.939

Mesosphere 71,000 -58.5 -2.0 3.9564

Mesopause 84,852 -86.2 - 0.3734

ISA Temperature profile

Level name Base geopotential height [m]

Base temperature [⁰C]

Lapse rate [⁰C/km]

Base atmospheric pressure [Pa]

Troposphere 0 15 -6.5 101,325

Tropopause 11,000 -56.5 0 22,632

Stratosphere 20,000 -56.5 +1.0 5474.9

Stratosphere 32,000 -44.5 +2.8 868.02

Stratopause 47,000 -2.5 0 110.91

Mesosphere 51,000 -2.5 -2.8 66.939

Mesosphere 71,000 -58.5 -2.0 3.9564

Mesopause 84,852 -86.2 - 0.3734

How do we calculate pressure p and density ρ ?

p RT

dp = - ρ g dh

Felix Baumgartner October 14th, 2012

38 969 m

Joe Kittinger August 16th , 1960

31 333 m

R. de Pandora - CC - BY - SA Kansir - CC - BY

The standard atmosphere I

Meteotek08 - CC - BY - SA