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

The standard atmosphere I Introduction to Aeronautical Engineering Prof. dr. ir. Jacco Hoekstra M.T. Salam - CC - BY - SA

Felix Baumgartner Joe Kittinger August 16 th , 1960 October 14 th , 2012 31 333 m 38 969 m R. de Pandora - CC - BY - SA Kansir - CC - BY

Why a standard atmosphere? We need a reference atmosphere for: – Meaningful aircraft performance spec ification – 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 spec ification – 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/m 3 ] – Temperature T [K] Physically correct, so it obeys:   – Equation of state: R  p RT 287.00 J kgK – Pressure increase due to gravity 101325 N/m 2

Standard atmosphere is a model atmosphere International Standard Atmosphere Real atmosphere (ISA) NASA, muffinn - CC - BY

The hydrostatic equation Describes pressure increase due to the gravity of air. p + Δ p Area A m ∙ g Δ h p

The hydrostatic equation Describes pressure increase due to the gravity of air.    F F p + Δ p down up Area     mg ( p p A ) pA A         A h g pA pA pA m ∙ g      Δ h h g p       p g h p dp = - ρ g dh

The hydrostatic equation Describes pressure increase due to the gravity of air.    F F p + Δ p down up Area     mg ( p p A ) pA A         A h g pA pA pA m ∙ g      Δ h h g p       p g h p dp = - ρ g dh

The hydrostatic equation Describes pressure increase due to the gravity of air.    F F p + Δ p down up Area     mg ( p p A ) pA A         A h g pA pA pA m ∙ g      Δ h h g p       p g h p dp = - ρ g dh

The hydrostatic equation Describes pressure increase due to the gravity of air.    F F p + Δ p down up Area     mg ( p p A ) pA A         A h g pA pA pA m ∙ g      Δ h h g p       p g h p dp = - ρ g dh

The hydrostatic equation Describes pressure increase due to the gravity of air.    F F p + Δ p down up Area     mg ( p p A ) pA A         A h g pA pA pA m ∙ g      Δ h h g p       p g h p dp = - ρ g dh

The hydrostatic equation Describes pressure increase due to the gravity of air.    F F p + Δ p down up Area     mg ( p p A ) pA A         A h g pA pA pA m ∙ g      Δ h h g p       p g h p dp = - ρ g dh

The hydrostatic equation Describes pressure increase due to the gravity of air.    F F p + Δ p down up Area     mg ( p p A ) pA A         A h g pA pA pA m ∙ g      Δ h h g p       p g h p dp = - ρ g dh

The hydrostatic equation Describes pressure increase due to the gravity of air.    F F p + Δ p down up Area     mg ( p p A ) pA A         A h g pA pA pA m ∙ g      Δ h h g p       p g h p dp = - ρ g dh

The hydrostatic equation Describes pressure increase due to the gravity of air.    F F p + Δ p down up Area     mg ( p p A ) pA A         A h g pA pA p A m ∙ g      Δ h h g p       p g h p dp = - ρ g dh

The hydrostatic equation Describes pressure increase due to the gravity of air.    F F p + Δ p down up Area     mg ( p p A ) pA A         A h g pA pA p A m ∙ g       Δ h A h g p A       p g h p dp = - ρ g dh

The hydrostatic equation Describes pressure increase due to the gravity of air.    F F p + Δ p down up Area     mg ( p p A ) pA A         A h g pA pA p A m ∙ g       Δ h A h g p A       p g h p dp = - ρ g dh

The hydrostatic equation Describes pressure increase due to the gravity of air.    F F p + Δ p down up Area     mg ( p p A ) pA A         A h g pA pA p A m ∙ g      Δ h h g p       p g h p dp = - ρ g dh

The hydrostatic equation Describes pressure increase due to the gravity of air.    F F p + Δ p down up Area     mg ( p p A ) pA A         A h g pA pA p A m ∙ g      Δ h h g p       p g h p dp = - ρ g dh

The hydrostatic equation Describes pressure increase due to the gravity of air.    F F p + Δ p down up Area     mg ( p p A ) pA A         A h g pA pA p A m ∙ g      Δ h h g p       p g h p dp = - ρ g dh

The hydrostatic equation Describes pressure increase due to the gravity of air.    F F p + Δ p down up Area     mg ( p p A ) pA A         A h g pA pA p A m ∙ g      Δ h h g p       p g h p 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: p RT dp = - ρ g dh – Hydrostatic equation: 101325 N/m 2

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: p RT dp = - ρ g dh – Hydrostatic equation: Define temperature as function of altitude 101325 N/m 2 Define start value for pressure

thermosphere ISA mesopause Temperature profile mesosphere h [km] stratopause Sea level (h = 0 m):  p 101325 Pa stratosphere 0   o T 15 C 288.15 K 0 tropopause kg   1.225 troposphere 3 0 m T [K]

ISA Temperature profile Level name Base geopotential Base Lapse rate Base atmospheric height [m] temperature [⁰C] [⁰C/km] 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 Base Lapse rate Base atmospheric height [m] temperature [⁰C] [⁰C/km] 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 Joe Kittinger August 16 th , 1960 October 14 th , 2012 31 333 m 38 969 m R. de Pandora - CC - BY - SA Kansir - CC - BY

The standard atmosphere I Meteotek08 - CC - BY - SA