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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