The atmosphere, aerodynamic and airplane nomenclatures

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Aircraft Stability and Control – Atmosphere, Airplane Nomenclatures The Atmosphere, Aerodynamic and Airplane Nomenclatures Ngô Khánh Hiếu 1 Aircraft Stability and Control – Atmosphere, Airplane Nomenclatures Basic definitions (1/8) Pressure: - Is the normal force per unit area acting on the fluid. - Static pressure is the pressure of the air above the elevation being considered. - to distinguish it from the total and dynamic pressures, the actual pressure of the fluid, which is associated not with its motion but with its state, is often referred to as the static pressure, but where the term pressure alone is used it refers to this static pressure. - Bernoulli’s equation for incompressible fluids: 1 ρV 2 + p = pT 2 p : “free-stream pressure”, static pressure - Standard atmospheric pressure at sea-level is defined as the pressure that can support a column of mercury 760 mm in length. So, its value is 1.01325 105 N/m2 (or 2116.22 Ib/ft2). - The ratio of the pressure P at altitude to sealevel standard pressure Po is: δ= - The equation of state: P = ρ RT where: R = 287 J/kgoK - Many pressure gages indicate the difference between the absolute pressure and the atmospheric pressure existing at the gage (gage presssure). pT: total pressure (Stagnation pressure) Ngô Khánh Hiếu P P0 2 Aircraft Stability and Control – Atmosphere, Airplane Nomenclatures Basic definitions (2/8) Temperature: - Is an abstract concept but can be thought of as a measure of the motion of molecular particles within a substance. - The temperatures are measured using the absolute Kelvin or Rankin scales. 9 TF = TC + 32 5 TK = TC + 273.15 = TR = TF + 459.67 5 ( TF + 459.67 ) 9 - The temperature of atmosphere varies significantly with altitude. The ratio of ambient temperature at altitude, T, to a sea-level standard value, To, is denoted by : θ= Ngô Khánh Hiếu T T0 The altitude (h) used in ISA standard atmosphere is “Geopotential altitudes” (not “Geometric altitudes”). hgeometric = hgeopotential Rearth Rearth − hgeopotential However, the difference between these two altitudes at 30 km is about 0.5%. 3 Aircraft Stability and Control – Atmosphere, Airplane Nomenclatures Basic definitions (3/8) Density: Variation of density with temperature for water (ref. Wikipedia) Mass ρ= Unit volume From the equation of state, it can be seen that the density of a gas is directly proportional to the pressure and inversely proportional to the absolute temperature. For vehicles that are flying at approximately 100 m/s or less, the density of the air flowing past the vehicle is assumed constant. Variation of density with temperature for air (ref. Wikipedia) The ratio of ambient air density ( ) to standard sea-level air density ( o) is given by : σ= Ngô Khánh Hiếu ρ ρ0 4 Aircraft Stability and Control – Atmosphere, Airplane Nomenclatures Basic definitions (4/8) Viscosity: - Viscosity can be thought of as the internal friction of a fluid. - In all real fluids, a shearing deformation is accompanied by a shearing stress. The shearing stress is proportional to the rate of shearing deformation. The constant of proportionality is called the coefficient of viscosity ( , kg/m.s). τ =µ υ= - Kinematic viscosity: u y - The unit of kinematic viscosity is stokes. 1 stokes = 100 centistokes = 0.00001 m2/s 1 centistokes = 1 mm2/s : Dynamic viscosity - For temperatures below 3000 K, the dynamic viscosity of air is independent of pressure. So, it can be calculated by the Sutherland’s equation: � T 2 � −6 � µ = 1.458 10 � �T + 110.4 � � � 3 Ngô Khánh Hiếu µ ρ (ref. Wikipedia) 5 Aircraft Stability and Control – Atmosphere, Airplane Nomenclatures Basic definitions (5/8) Mach number: M= V a - The speed of sound is established by the properties of the fluid. For a perfect gas: a = γ RT - The aerodynamic characteristics of an airplane depend on the flow regime around the airplane. As the flight Mach number is increased, the flow around the airplane can be completely subsonic, a mixture of subsonic and supersonic flow or completely supersonic. - The flight Mach number is used to classify the various flow regimes. An approximate classification of the flow regimes follows: Incompressible subsonic flow 0 < M < 0.3 Compressible subsonic flow 0.3 < M < 0.8 Transonic flow 0.8 < M < 1.2 Supersonic flow 1.2 < M < 5.0 Hypersonic flow 5.0 < M Ngô Khánh Hiếu 6 Aircraft Stability and Control – Atmosphere, Airplane Nomenclatures Basic definitions (6/8) Pressure variation in a static fluid medium: If fluid particles are either all at rest or all moving with the same velocity, the fluid is said to be a static medium. Since there is no relative motion between adjacent layers of the fluids, there are no shear forces. The only forces acting on the surface of the fluid elements are pressure forces. - Consider the small fluid element whose center is defined by the coordinates x, y, z. dP gdz = − �P � RT - For air, the earth’s mean atmosphere temperature decreases almost linearly with z up to an altitude of nearly 11000 m. We obtain: g / RB � Bz � P = Po � 1− � T � o � 5.26 � Bz � = Po � 1− � T � o � where: B = 0.0065 K/m; To = 288.15 K Ngô Khánh Hiếu 7 Aircraft Stability and Control – Atmosphere, Airplane Nomenclatures Basic definitions (7/8) The standard atmosphere: The basis for establishing a standard atmosphere is a defined variation of temperature with altitude. In reality, variations would exist from one location on the earth to another and over seasons at a given location. A standard atmosphere is a valuable tool that provides engineers with a standard when conducting analyses and performance comparisons of different aircraft design. Ngô Khánh Hiếu 8 Aircraft Stability and Control – Atmosphere, Airplane Nomenclatures Basic definitions (8/8) Bernoulli’s equation for a compressible fluid: P = c.ρ γ - If the flow can be assumed to be isentropic, 2 2 2 dP VdV = − − g� dz � � ρ 1 1 1 γ P 1 2 + V + gz = constant γ −1 ρ 2 - For perfect gas, a 2 = γ RT = γ . P ρ 1 � � �2 � 2 �P0 � � V = a� � − 1� � � � � � γ −1� �P � � � � � γ −1 γ γ −1 γ P0: stagnation pressure 1 � � �2 � V 2 �P0 � � M = =� � − 1� � � � � a � γ −1� �P � � � � � Ngô Khánh Hiếu These two equations can be used with M<1 9 Aircraft Stability and Control – Atmosphere, Airplane Nomenclatures The atmosphere (1/2) - Troposphere: h θ= 11000 m T B = 1+ h T0 T0 P −g δ = = θ BR P0 − ( 1+ g ρ BR ) σ= =θ ρ0 - Troposphere: 11000 m h 20000 m θ = θ1 δ = δ1.e −( h − h1 ) g RT1 �δ1 � −( h − h1 ) g RT1 σ =� � .e θ1 � � Ngô Khánh Hiếu 10
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