3 earth atmosphere
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3 earth atmosphere
- 1. Earth Atmosphere SOLO HERMELIN Updated: 08.11.12 1
- 2. Table of Content SOLO 2 Earth Atmosphere
- 4. The Earth Atmosphere might be described as a Thermodynamic Medium in a Gravitational Field and in Hydrostatic Equilibrium set by Solar Radiation. Since Solar Radiation and Atmospheric Reradiation varies diurnally and annually and with latitude and longitude, the Standard Atmosphere is only an approximation. SOLO 4 Earth Atmosphere The purpose of the Standard Atmosphere has been defined by the World Metheorological Organization (WMO). The accepted standards are the COESA (Committee on Extension to the Standard Atmosphere) US Standard Atmosphere 1962, updated by US Standard Atmosphere 1976.
- 5. The basic variables representing the thermodynamics state of the gas are the Density, ρ, Temperature, T and Pressure, p. SOLO 5 Earth Atmosphere The Density, ρ, is defined as the mass, m, per unit volume, v, and has units of kg/m3 . v m v ∆ ∆ = →∆ 0 limρ The Temperature, T, with units in degrees Kelvin ( ͦ K). Is a measure of the average kinetic energy of gas particles. The Pressure, p, exerted by a gas on a solid surface is defined as the rate of change of normal momentum of the gas particles striking per unit area. It has units of N/m2 . Other pressure units are millibar (mbar), Pascal (Pa), millimeter of mercury height (mHg) S f p n S ∆ ∆ = →∆ 0 lim kPamNbar 100/101 25 == ( ) mmHginHgkPamkNmbar 00.7609213.29/325.10125.1013 2 === The Atmospheric Pressure at Sea Level is:
- 6. 6 Earth Atmosphere Physical Foundations of Atmospheric Model The Atmospheric Model contains the values of Density, Temperature and Pressure as function of Altitude. Atmospheric Equilibrium (Barometric) Equation In figure we see an atmospheric element under equilibrium under pressure and gravitational forces ( )[ ] 0=⋅+−+⋅⋅⋅− APdPPHdAg gρ or ( ) gg HdHgPd ⋅⋅=− ρ In addition, we assume the atmosphere to be a thermodynamic fluid. At altitude bellow 100 km we assume the Equation of an Ideal Gas where V – is the volume of the gas N – is the number of moles in the volume V m – the mass of gas in the volume V R* - Universal gas constant TRNVP ⋅⋅=⋅ * V m M m N == ρ& MTRP /* ⋅⋅= ρ
- 7. Earth Atmosphere ( ) mmHginHgkPamkNmbar 00.7609213.29/325.10125.1013 2 ===
- 8. We must make a distinction between: - Kinetic Temperature (T): measures the molecular kinetic energy and for all practical purposes is identical to thermometer measurements at low altitudes. - Molecular Temperature (TM): assumes (not true) that the Molecular Weight at any altitude (M) remains constant and is given by sea-level value (M0) SOLO 8 Earth Atmosphere T M M TM ⋅= 0 To simplify the computation let introduce: - Geopotential Altitude H - Geometric Altitude Hg Newton Gravitational Law implies: ( ) 2 0 + ⋅= gE E g HR R gHg The Barometric Equation is ( ) gg HdHgPd ⋅⋅=− ρ The Geopotential Equation is defined as HdgPd ⋅⋅=− 0ρ This means that g gE E g Hd HR R Hd g g Hd ⋅ + =⋅= 2 0 Integrating we obtain g gE E H HR R H ⋅ + =
- 9. 9 Earth Atmosphere Atmospheric Constants Definition Symbol Value Units Sea-level pressure P0 1.013250 x 105 N/m2 Sea-level temperature T0 288.15 ͦ K Sea-level density ρ0 1.225 kg/m3 Avogadro’s Number Na 6.0220978 x 1023 /kg-mole Universal Gas Constant R* 8.31432 x 103 J/kg-mole -ͦ K Gas constant (air) Ra=R*/M0 287.0 J/kg--ͦ K Adiabatic polytropic constant γ 1.405 Sea-level molecular weight M0 28.96643 Sea-level gravity acceleration g0 9.80665 m/s2 Radius of Earth (Equator) Re 6.3781 x 106 m Thermal Constant β 1.458 x 10-6 Kg/(m-s-ͦ K1/2) Sutherland’s Constant S 110.4 ͦ K Collision diameter σ 3.65 x 10-10 m
- 10. 10 Earth Atmosphere Physical Foundations of Atmospheric Model Atmospheric Equilibrium Equation HdgPd ⋅⋅=− 0ρ At altitude bellow 100 km we assume t6he Equation of an Ideal Gas TRMTRP a MRR a aa ⋅⋅=⋅⋅= = ρρ / * * / Hd TR g P Pd a ⋅=− 0 Combining those two equations we obtain Assume that T = T (H), i.e. function of Geopotential Altitude only. The Standard Model defines the variation of T with altitude based on experimental data. The 1976 Standard Model for altitudes between 0.0 to 86.0 km is divided in 7 layers. In each layer dT/d H = Lapse-rate is constant.
- 11. 11 Earth Atmosphere Layer Index Geopotential Altitude Z, km Geometric Altitude Z; km Molecular Temperature T, ͦ K 0 0.0 0.0 288.150 1 11.0 11.0102 216.650 2 20.0 20.0631 216.650 3 32.0 32.1619 228.650 4 47.0 47.3501 270.650 5 51.0 51.4125 270.650 6 71.0 71.8020 214.650 7 84.8420 86.0 186.946 1976 Standard Atmosphere : Seven-Layer Atmosphere Lapse Rate Lh; ͦ K/km -6.3 0.0 +1.0 +2.8 0.0 -2.8 -2.0
- 12. 12 Earth Atmosphere Physical Foundations of Atmospheric Model • Troposphere (0.0 km to 11.0 km). We have ρ (6.7 km)/ρ (0) = 1/e=0.3679, meaning that 63% of the atmosphere lies below an altitude of 6.7 km. ( ) Hd HLTR g Hd TR g P Pd aa ⋅ ⋅+ =⋅=− 0 00 kmKLHLTT /3.60 −=⋅+= Integrating this equation we obtain ( )∫∫ ⋅ ⋅+ =− H a P P Hd HLTR g P PdS S 0 0 0 1 0 ( ) 0 00 lnln 0 T HLT RL g P P aS S ⋅+ ⋅ ⋅ −= Hence aRL g SS H T L PP ⋅ − ⋅+⋅= 0 0 0 1 and − ⋅= ⋅ 1 0 0 0 g RL S S a P P L T H
- 13. 13 Earth Atmosphere Physical Foundations of Atmospheric Model Hd TR g P Pd Ta ⋅=− * 0 Integrating this equation we obtain ( )T TaS S HH TR g P P T −⋅ ⋅ −= * 0 ln Hence ( )T Ta T HH TR g SS ePP −⋅ ⋅ − ⋅= * 0 and S STTa T P P g TR HH ln 0 * ⋅ ⋅ += ∫∫ =− H HTa P P T S TS Hd TR g P Pd * 0 • Stratosphere Region (HT=11.0 km to 20.0 km). Temperature T = 216.65 ͦ K = TT* is constant (isothermal layer), PST=22632 Pa
- 14. 14 Earth Atmosphere Physical Foundations of Atmospheric Model ( )[ ] Hd HHLTR g Hd TR g P Pd SSTaa ⋅ −⋅+⋅ =⋅=− * 00 ( ) ( ) PaPHPkmKLHHLTT SSSSSST 5474.9,/0.1 * ===−⋅−= Integrating this equation we obtain ( )[ ]∫∫ ⋅ −⋅+ =− H H SSTa P P S S SS Hd HHLTR g P Pd * 0 1 ( )[ ] * * 0 lnln T ST aSSS S T HHLT RL g P P −⋅+ ⋅ ⋅ = Hence ( ) aRL g S T S SSS HH T L PP ⋅ − −⋅+⋅= 0 * 1 and − ⋅+= ⋅ 1 0 * g RL SS S S T S aS P P L T HH Stratosphere Region (HS=20.0 km to 32.0 km).
- 15. 15 Earth Atmosphere 1962 Standard Atmosphere from 86 km to 700 km Layer Index Geometric Altitude km Molecular Temperature K Kinetic Temperature K Molecular Weight Lapse Rate K/km 7 86.0 186.946 186.946 28.9644 +1.6481 8 100.0 210.65 210.02 28.88 +5.0 9 110.0 260.65 257.00 28.56 +10.0 10 120.0 360.65 349.49 28.08 +20.0 11 150.0 960.65 892.79 26.92 +15.0 12 160.0 1110.65 1022.20 26.66 +10.0 13 170.0 1210.65 1103.40 26.49 +7.0 14 190.0 1350.65 1205.40 25.85 +5.0 15 230.0 1550.65 132230 24.70 +4.0 16 300.0 1830.65 1432.10 22.65 +3.3 17 400.0 2160.65 1487.40 19.94 +2.6 18 500.0 2420.65 1506.10 16.84 +1.7 19 600.0 2590.65 1506.10 16.84 +1.1 20 700.0 2700.65 1507.60 16.70
- 16. 16 Earth Atmosphere 1976 Standard Atmosphere from 86 km to 1000 km Geometric Altitude Range: from 86.0 km to 91.0 km (index 7 – 8) 78 /0.0 TT kmK Zd Td = = Geometric Altitude Range: from 91.0 km to 110.0 km (index 8 – 9) 2/12 8 2 8 2/12 8 1 1 − − − − ⋅−= − −⋅+= a ZZ a ZZ a A Zd Td a ZZ ATT C kma KA KTC 9429.19 3232.76 1902.263 −= −= = Geometric Altitude Range: from 110.0 km to 120.0 km (index 9 – 10) ( ) kmK Zd Td ZZLTT Z /0.12 99 += −⋅+= Geometric Altitude Range: from 120.0 km to 1000.0 km (index 10 – 11) ( ) ( ) ( ) ( ) + + ⋅−= + + ⋅−⋅= ⋅−⋅−−= ∞ ∞∞ ZR ZR ZZ kmK ZR ZR TT Zd Td TTTT E E E E 10 10 10 10 10 / exp ξ λ ξλ KT kmR km E 1000 10356766.6 /01875.0 3 = ×= = ∞ λ
- 18. 18 Central Air Data Computer Earth Atmosphere
- 19. References SOLO 19 S. Hermelin, “Air Vehicle in Spherical Earth Atmosphere” Frank J, Regan, Satya M. Anandakrishnan, “Dynamics of Atmospheric Re-Entry”, AIAA Education Series, 1993 R.P.G. Collinson, “Introduction to Avionics”, Chapman & Hall, Inc., 1996, 1997, 1998 Earth Atmosphere John D. Anderson, “Flight”, 4th Ed., McGraw Hill, 2000, Ch. 3, “The Standard Atmosphere”
- 20. 20 SOLO Technion Israeli Institute of Technology 1964 – 1968 BSc EE 1968 – 1971 MSc EE Israeli Air Force 1970 – 1974 RAFAEL Israeli Armament Development Authority 1974 – 2013 Stanford University 1983 – 1986 PhD AA
- 21. 21 Earth Atmosphere Polytropic Process A Polytropic Process is a Thermodynamic Process that is reversible and obeys the relation: where P is the pressure, V is the volume, n the Polytropic Index, and C is a constant. CVP n =⋅ The equation is a valid characterization of a thermodynamic process assuming that the process is quasi-static and the values of the heat capacities, Cp and CV , are almost constant when n is not zero or infinity. (In reality, Cp and CV are actually functions of temperature and pressure, but are nearly constant within small changes of temperature). Polytropic Index Relation Effects n = 0 P V0 =Const Equivalent to an isobaric process (constant pressure) n = 1 P V = N k T (constant) Equivalent to an isothermal process (constant temperature) 1 < n < γ - A quasi-adiabatic process such as internal combustion engine during expansion. Or in vapor compression refrigeration during compression. n = γ - γ = Cp/CV is the adiabatic index, yielding an adiabatic process (no heat transferred) n = ∞ - Equivalent to an isochoric process (constant volume)
- 22. Earth Atmosphere Explanation of the Thermal Gradient in the Atmospheric Layers by the Polytropic Process A Polytropic Process is a Thermodynamic Process that is reversible and obeys the relation: where P is the pressure, V is the volume, n the Polytropic Index, and C is a constant. n n nn C V M CPMCCVP ρ000 = =⇒==⋅ Equation of an Ideal Gas MTRP /* ⋅⋅= ρ Take the Logarithmic Differentiation of those two equations ρ ρd P Pd n =⋅ 1 T Tdd P Pd += ρ ρ By eliminating d ρ/ρ we obtain T Td n n P Pd ⋅ − = 1 We have gggg Hd Td T P n n Hd P T Td n n Hd P P Pd Hd Pd ⋅⋅ − =⋅⋅ − =⋅= 11
- 23. Earth Atmosphere Explanation of the Thermal Gradient in the Atmospheric Layers by the Polytropic Process (continue – 1) ( )g g Hg Hd Pd ⋅=− ρBarometric Equation gg Hd Td T P n n Hd Pd ⋅⋅ − = 1 ( ) * 1 RT MP Hd Pd Hg gg ⋅ ⋅ =⋅−=ρ Molecular Temperature (TM) versus Kinetic Temperature (T) T M M TM ⋅= 0 ( ) * 000 11 R MHg n n Hd Pd P T M M n n Hd Td M M Hd Td g ggg M ⋅ ⋅ − −=⋅⋅⋅ − =⋅= ( ) * 01 R MHg n n Hd Td g g M ⋅ ⋅ − −= This equation gives a relation between dTM/dHg , the Polytropic Exponent n and g (Hg).
- 24. Earth Atmosphere Explanation of the Thermal Gradient in the Atmospheric Layers by the Polytropic Process (continue – 2) ( ) * 01 R MHg n n Hd Td g g M ⋅ ⋅ − −= The Temperature Gradient dTM/dHg , determine the Stability of the Stratification in the Stationary Atmosphere. The Stratification is more stable when the temperature decrease with increasing height become smaller. For dTM/dHg = 0 when n = 1, the Atmosphere is Isothermal and has a very stable stratification. For n = γ = 1.405, the stratification is Adiabatic (Isentropic) with dTM/dHg =-0.98 ͦK per 100 m [-9.8 ͦ K per km]. This stratification is indiferent because an air volume moving upward for a certain distance cools off through expansion at just the same rate as the temperature drops with height. This air volume maintains the temperature of the ambient air and is, therefore, in an indifferent equilibrium at every altitude.
- 25. Earth Atmosphere Explanation of the Thermal Gradient in the Atmospheric Layers by the Polytropic Process (continue – 3) Geopotential Altitude H, km 0,0 11.0 20,0 32.0 47,0 51.0 71.0 84.8520 Thermal Lapse-rate L, ͦK/km -6.5 +0.0 +1.0 +2.8 +0.0 -2.8 -2.0 Polytropic Exponent n 1.2350 1.0000 0.9716 0.9242 1.0000 1.0893 1.0622 Variation of the Polytropic Exponent with Altitude
- 26. Earth Atmosphere Explanation of the Thermal Gradient in the Atmospheric Layers by the Polytropic Process (continue – 4) ( ) * 01 R MHg n n Hd Td g g M ⋅ ⋅ − −= ( )g g Hg Hd Pd ⋅=− ρBarometric Equation Equation of an Ideal Gas MTRP /* ⋅⋅= ρ ( ) M T R HdHg P Pd gg ⋅ ⋅ =− * ( ) ( ) ( ) ( )gM gg M R R gM gg T M M T HTR HdHg HTR HdHgM P Pd M ⋅ ⋅ −= ⋅ ⋅⋅ −= =⋅= 0 * 0 * 0 ( ) gg HdHgHdg ⋅=⋅0 Relation between Geopotential Altitude H, Geometric Altitude Hg. ( ) ( ) ( )gMgM gg HTR Hdg HTR HdHg P Pd ⋅ ⋅ −= ⋅ ⋅ −= 0
- 27. Earth Atmosphere Explanation of the Thermal Gradient in the Atmospheric Layers by the Polytropic Process (continue – 5) Let carry the integration in two cases: ( ) ( ) ( )gMgM gg HTR Hdg HTR HdHg P Pd ⋅ ⋅ −= ⋅ ⋅ −= 0 ( ) ( ) ( ) ( ) mxb HbgRHgRHgHg gEgEgg /10139.3: 1/21/1 7 00 2 0 − − = ⋅−⋅=−⋅≈+⋅= 1. The Non-isothermal layer with LZ:=dT/dHg ≠ 0 2. The Isothermal layer with LZ:=dT/dHg = 0 ( ) ( )∫∫ −+ ⋅⋅− −= g ig iiii H H ggZM gg P P HHLT HdHb R g P Pd 10 ( ) ( ) ( )iZMM i Z Z L T b LR g gg M Z ii ZZLTT ZZ LR bg HH TR L P P ii i i iZ iM iZ i i i −⋅+= −⋅ ⋅ ⋅ ⋅ +−⋅ ⋅ == −⋅+⋅ ⋅ − 0 1 exp1 0 ρ ρ 1 ( ) ( ) ii i MMZi M i ii TTLZZ b TR ZZg P P == −⋅+⋅ ⋅ −⋅ −== &0 2 1exp 0 ρ ρ 2
- 28. Earth Atmosphere
- 29. 29 Layer Level Name Base Geopotential Height h (in km) Base Geometric Height z (in km) Lapse Rate (in °C/km) Base Temperature T (in °C) Base Atmospheric Pressure p (in Pa) 0 Troposphere 0.0 0.0 -6.5 +15.0 101325 1 Tropopause 11.000 11.019 +0.0 -56.5 22632 2 Stratosphere 20.000 20.063 +1.0 -56.5 5474.9 3 Stratosphere 32.000 32.162 +2.8 -44.5 868.02 4 Stratopause 47.000 47.350 +0.0 -2.5 110.91 5 Mesosphere 51.000 51.413 -2.8 -2.5 66.939 6 Mesosphere 71.000 71.802 -2.0 -58.5 3.9564 7 Mesopause 84.852 86.000 — -86.2 0.3734 Earth Atmosphere ICAO_Standard_Atmosphere
- 30. 30 Layer Level Name Base Geopotential Height h (in km) Base Geometric Height z (in km) Lapse Rate (in °C/km) Base Temperature T (in °C) Base Atmospheric Pressure p (in Pa) 0 Troposphere 0.0 0.0 -6.5 +15.0 101325 1 Tropopause 11.000 11.019 +0.0 -56.5 22632 2 Stratosphere 20.000 20.063 +1.0 -56.5 5474.9 3 Stratosphere 32.000 32.162 +2.8 -44.5 868.02 4 Stratopause 47.000 47.350 +0.0 -2.5 110.91 5 Mesosphere 51.000 51.413 -2.8 -2.5 66.939 6 Mesosphere 71.000 71.802 -2.0 -58.5 3.9564 7 Mesopause 84.852 86.000 — -86.2 0.3734 Earth Atmosphere ICAO_Standard_Atmosphere
- 31. 31 Earth Atmosphere There are two different equations for computing pressure at various height regimes below 86 km (or 278,400 feet). The first equation is used when the value of Standard Temperature Lapse Rate is not equal to zero; the second equation is used when standard temperature lapse rate equals zero. where = Static pressure (pascals) = Standard temperature (K) = Standard temperature lapse rate -0.0065 (K/m) in ISA = Height above sea level (meters) = Height at bottom of layer b (meters; e.g., = 11,000 meters) =Universal gas constant for air: 8.31432 N·m /(mol·K) = Gravitational acceleration (9.80665 m/s2 ) = Molar mass of Earth's air (0.0289644 kg/mol) ( ) bLR Mg bbb b b hhLT T PP ⋅ ⋅ −⋅+ ⋅= * 0 ( ) ⋅ −⋅⋅− ⋅= b b b TR hhMg PP * 0 exp Equation 1: Equation 2:
- 32. 32 Earth Atmosphere There are two different equations for computing pressure at various height regimes below 86 km (or 278,400 feet). Subscript b Height above sea level hb Static pressure Standard temperature Tb (K) Temperature lapse rate Lb (m) (ft) (Pascals) (inHg) (K/m) (K/ft) 0 0 0 101325.00 29.92126 288.15 -0.0065 -0.0019812 1 11,000 36,089 22632.10 6.683245 216.65 0.0 0.0 2 20,000 65,617 5474.89 1.616734 216.65 0.001 0.0003048 3 32,000 104,987 868.02 0.2563258 228.65 0.0028 0.00085344 4 47,000 154,199 110.91 0.0327506 270.65 0.0 0.0 5 51,000 167,323 66.94 0.01976704 270.65 -0.0028 -0.00085344 6 71,000 232,940 3.96 0.00116833 214.65 -0.002 -0.0006096
- 35. 35 SOLO Anders Celsius 1701-1744 15.273−= KC THERMODYNAMICS Temperature Scales 1. Fahrenheit 2. Celsius 3. Kelvin 4. Rankine Daniel Gabriel Fahrenheit 1686-1736 Mercury-in-Glass Thermometer 1714 William John Macquorn Rankine (1820-1872) William Thomson Lord Kelvin (1824-1907) Absolute Temperature 1848 KR 5 9 = 67.459−= RF 32 5 9 += CF
- 36. SOLO THERMODYNAMICS Temperature Scales from Celsius to Celsius Fahrenheit [°F] = [°C] × 9 ⁄5 + 32 [°C] = ([°F] − 32) × 5 ⁄9 Kelvin [K] = [°C] + 273.15 [°C] = [K] − 273.15 Rankine [°R] = ([°C] + 273.15) × 9 ⁄5 [°C] = ([°R] − 491.67) × 5 ⁄9 Delisle [°De] = (100 − [°C]) × 3 ⁄2 [°C] = 100 − [°De] × 2 ⁄3 Newton [°N] = [°C] × 33 ⁄100 [°C] = [°N] × 100 ⁄33 Réaumur [°Ré] = [°C] × 4 ⁄5 [°C] = [°Ré] × 5 ⁄4 Rømer [°Rø] = [°C] × 21 ⁄40 + 7.5 [°C] = ([°Rø] − 7.5) × 40 ⁄21
Editor's Notes
- Frank J, Regan, Satya M. Anandakrishnan, “Dynamics of Atmospheric Re-Entry”, AIAA Education Series, 1993
- Frank J, Regan, Satya M. Anandakrishnan, “Dynamics of Atmospheric Re-Entry”, AIAA Education Series, 1993
- Frank J, Regan, Satya M. Anandakrishnan, “Dynamics of Atmospheric Re-Entry”, AIAA Education Series, 1993
- R.P.G. Collinson, “Introduction to Avionics”, Chapman & Hall, Inc., 1996, 1997, 1998 Frank J, Regan, Satya M. Anandakrishnan, “Dynamics of Atmospheric Re-Entry”, AIAA Education Series, 1993
- Frank J, Regan, Satya M. Anandakrishnan, “Dynamics of Atmospheric Re-Entry”, AIAA Education Series, 1993
- R.P.G. Collinson, “Introduction to Avionics”, Chapman & Hall, Inc., 1996, 1997, 1998 Frank J, Regan, Satya M. Anandakrishnan, “Dynamics of Atmospheric Re-Entry”, AIAA Education Series, 1993
- R.P.G. Collinson, “Introduction to Avionics”, Chapman & Hall, Inc., 1996, 1997, 1998 Frank J, Regan, Satya M. Anandakrishnan, “Dynamics of Atmospheric Re-Entry”, AIAA Education Series, 1993
- R.P.G. Collinson, “Introduction to Avionics”, Chapman & Hall, Inc., 1996, 1997, 1998 Frank J, Regan, Satya M. Anandakrishnan, “Dynamics of Atmospheric Re-Entry”, AIAA Education Series, 1993
- Frank J, Regan, Satya M. Anandakrishnan, “Dynamics of Atmospheric Re-Entry”, AIAA Education Series, 1993
- Frank J, Regan, Satya M. Anandakrishnan, “Dynamics of Atmospheric Re-Entry”, AIAA Education Series, 1993
- http://en.wikipedia.org/wiki/Polytropic_process
- Frank J, Regan, Satya M. Anandakrishnan, “Dynamics of Atmospheric Re-Entry”, AIAA Education Series, 1993
- Frank J, Regan, Satya M. Anandakrishnan, “Dynamics of Atmospheric Re-Entry”, AIAA Education Series, 1993
- Frank J, Regan, Satya M. Anandakrishnan, “Dynamics of Atmospheric Re-Entry”, AIAA Education Series, 1993
- Frank J, Regan, Satya M. Anandakrishnan, “Dynamics of Atmospheric Re-Entry”, AIAA Education Series, 1993
- Frank J, Regan, Satya M. Anandakrishnan, “Dynamics of Atmospheric Re-Entry”, AIAA Education Series, 1993
- Frank J, Regan, Satya M. Anandakrishnan, “Dynamics of Atmospheric Re-Entry”, AIAA Education Series, 1993
- http://www.atmo.arizona.edu/students/courselinks/fall12/atmo336/lectures/sec1/structure.html
- http://en.wikipedia.org/wiki/ICAO_Standard_Atmosphere
- http://en.wikipedia.org/wiki/ICAO_Standard_Atmosphere
- http://en.wikipedia.org/wiki/Barometric_formula
- http://en.wikipedia.org/wiki/Barometric_formula
- http://www.hac-panda.co.za/html/environment.html
- John D. Anderson, “Flight”, 4th Ed., McGraw Hill, 2000, pg. 95
- http://en.wikipedia.org/wiki/Temperature