The standard atmosphere I Introduction to Aeronautical Engineering - - PowerPoint PPT Presentation

• 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 kgK R 

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 up

F 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 up

F 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 up

F 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 up

F 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 up

F 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 up

F 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 up

F 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 up

F 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 up

F 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 up

F 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 up

F 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 up

F 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 up

F 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 up

F 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 up

F 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

3

101325 Pa 15 C 288.15 1.225

• p

T K kg m      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 15

• 6.5

101,325 Tropopause 11,000

• 56.5

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

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 15

• 6.5

101,325 Tropopause 11,000

• 56.5

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

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