Aeronautics 1110x 2a-slides

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Aeronautics 1110x 2a-slides

Aeronautics 1110x 2a-slides

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  • 1. Prof. dr. ir. Jacco Hoekstra The standard atmosphere I Introduction to Aeronautical Engineering M.T. Salam - CC - BY - SA
  • 2. 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
  • 3. 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
  • 4. 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
  • 5. 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
  • 6. Standard atmosphere is a model atmosphere Real atmosphere International Standard Atmosphere (ISA) NASA, muffinn - CC - BY
  • 7. The hydrostatic equation Describes pressure increase due to the gravity of air. p + Δp m∙ g p Δ h Area A
  • 8. 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
  • 9. 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
  • 10. 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
  • 11. 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
  • 12. 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
  • 13. 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
  • 14. 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
  • 15. 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
  • 16. 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
  • 17. 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
  • 18. 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
  • 19. 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
  • 20. 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
  • 21. 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
  • 22. 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
  • 23. 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
  • 24. 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
  • 25. ISA Temperature profile 0 0 30 101325 Pa 15 C 288.15 1.225 o p T K kg m      Sea level (h = 0 m): h [km] T [K] troposphere stratosphere mesosphere thermosphere stratopause tropopause mesopause
  • 26. 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
  • 27. 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
  • 28. How do we calculate pressure p and density ρ ? p RT dp = - ρ g dh
  • 29. 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
  • 30. The standard atmosphere I Meteotek08 - CC - BY - SA