Category A B1 B2 B3 Level 1 2 3 M o d u l e 0 8-0 1 B a s i c A e r o d y n a m i c s P h y s i c s o f t h e A t m o s p h e r e 08-01- 1
Category A B1 B2 B3 Level 1 2 3 T a b l e o f c o n t e n t s INTERNATIONAL STANDARD ATMOSPHERE (ISA), APPLICATION TO AERODYNAMICS... 3 1. PROPERTIES OF THE STANDARD ATMOSPHERE:... 4 1.1. Parameters:... 4 1.2. Standard values at see level Z = 0 km:... 5 1.3. Table of the standard atmosphere:... 5 2. APPLICATION TO AIRCRAFT AERODYNAMICS:... 8 2.1. Density ():... 8 2.2. Static pressure P:... 9 2.3. Temperature (T):... 11 2.4. Airflow and dynamic pressure:... 13 08-01- 2
Category A B1 B2 B3 Level 1 2 3 INTERNATIONAL STANDARD ATMOSPHERE (ISA), APPLICATION TO AERODYNAMICS The atmosphere is the natural elements in which the aircraft operates. From the surface of the ground towards higher altitudes, the atmosphere is composed of several layers. 08-01- 3
Category A B1 B2 B3 Level 1 2 3 1. PROPERTIES OF THE STANDARD ATMOSPHERE: The characteristics of the atmosphere, basically, influence the behavior of the aircraft. The pressure, the density as well as the temperature decrease with altitude. 1.1. Parameters: The atmosphere can be represented by physical models. These theories link together atmospheric variables such as density, pressure and temperature. Density () in kilograms per cubic meter (Kg/m 3 ) Pressure (P) in pascals (Pa) Temperature (T) in Kelvin (K) 08-01- 4
Category A B1 B2 B3 Level 1 2 3 1.2. Standard values at see level Z = 0 km): The aerodynamic behavior of the aircraft depends on the state of the air, which varies according to the altitude. Moreover, at a given altitude, the state of the air varies according to the place and climate conditions. The average values retained by the I.C.A.O (International Civil Aviation Organization) for the standard atmosphere at sea level are: 0 = 1,2256 Kg/m3 P 0 = 101325 Pa T 0 = 288,15 K 1.3. Table of the standard atmosphere: ALTITUDE DENSITY PRESSURE TEMPERATURE Z in km in kg / m 3 P in pascals T in Kelvin T in Celsius 0 1.2256 101325 288.15 15 1 1.1109 89876 281.65 8.5 2 1.1060 79486 275.15 2 3 0.9189 70097 268.65-4.5 4 0.8187 61631 262.15-11 5 0.7354 54008 255.65-17.5 6 0.6589 47150 249.15-24 7 0.5893 41048 242.65-30.5 8 0.5246 35583 236.15-37 08-01- 5
Category A B1 B2 B3 Level 1 2 3 9 0.4657 30717 229.65-43.5 10 0.4118 26420 223.15-50 11 0.3638 22604 216.65-56.5 12 0.3098 19317 216.65-56.5 13 0.2647 16492 216.65-56.5 14 0.2255 14088 216.65-56.5 15 0.1932 12038 216.65-56.5 16 0.1647 10272 216.65-56.5 17 0.1402 08780 216.65-56.5 18 0.1196 07495 216.65-56.5 19 0.1020 06397 216.65-56.5 20 0.0873 05465 216.65-56.5 22 0.0637 03797 216.65-56.5 24 0.0461 02704 216.65-56.5 25 0.0397 02401 216.65-56.5 08-01- 6
Category A B1 B2 B3 Level 1 2 3 The table of the standard parameters is prepared by the International Civil Aviation Organization (ICAO). The following formulae allow us to calculate to an approximate value. For an altitude ranging between 0 and 11 km: ρ = ρ Z 0 20 - Z 20 + Z in kg/m3 (kilogram per cubic meter) 31 - Z P = P Z 0 31 + Z 2 in Pa (pascal) T = T - 6,5 Z in K (Kelvin) Z 0 For an altitude ranging between 11 and 25 km: ρ =ρ Z 11 26 - Z - 11 26 + Z - 11 2 in kg/m 3 (kilogram per cubic meter) 26 - Z - 11 P = P Z 11 26 + Z - 11 2 in Pa (ascals) T Z = T 11 = 216,5 K = const 08-01- 7
Category A B1 B2 B3 Level 1 2 3 2. APPLICATION TO AIRCRAFT AERODYNAMICS: Let us observe the 3 principal parameters which define the state of the air at rest. 2.1. Density (): Density tells us how much of a substance occupies a given volume. M (kg) ρ (kg.m 3 ) = V (m 3 ) Density of air is the ratio of a mass of air to its volume. 08-01- 8
Category A B1 B2 B3 Level 1 2 3 Consider a mass of air in a cylinder closed by a piston. By applying a force to this same piston we generate a decrease in volume and the density of air increase. 2.2. Static pressure P: We previously saw that the weight of the atmosphere which superimposes a volume of air exerts a force on the latter. Let us consider a tiny cube inside a volume of air. It is noted that on the face of this cube, the surrounding air exerts a force F towards the cube and perpendicular to this face. The origin of this force is thus the weight of the air located at the top of the cube. Thus, the face of surface S is subjected to a pressure F/S. This value of pressure is identical on all the faces and does not change. It is therefore an intrinsic value at the center of this cube. The value attached to this point is the static pressure (Ps): it is Σ of the forces that the surrounding air exerts at a point 08-01- 9
Category A B1 B2 B3 Level 1 2 3 F (N) P (Pa) = S (m 2 ) Torricelli experiment shows that, at sea level, the atmospheric pressure H is: F ρghs P = 1 atm. = = 0 = ρgh S S 3 3 13.6 (10 kg/m ) (9.81N/kg) (0.76m) S S P = 1.014 105 Pa = 1.014 bar 0 It is said that the static pressure or ambient is an absolute pressure in opposition to pressures known as differential which are of different type (example: dynamic pressure). Laplace s equation provides information on the variation of static pressure according to the variation of altitude: 08-01- 10
Category A B1 B2 B3 Level 1 2 3 When the altitude increases, this equation indicates that the pressure decreases especially when is bigger. It is thus observed that this decrease will be larger at low altitudes than at high altitudes. It clearly appears that the higher we go in the atmosphere, the more the weight of the airstream located above the measuring point decreases. 2.3. Temperature (T): The temperature is expressed in degrees Celsius (C). When it is read on a thermometer the zero corresponds to the melting point of ice and the hundred scale to boiling point of water. The absolute temperature is the temperature in degree Celsius plus 273, it is expressed in Kelvin (K). From 0 to 11 Km of altitude, the temperature falls by 6.5 every 1000 m. In standard temperature at 11 Km of altitude the temperature is 56.5C, absolute temperature 216.5 K, which will remain constant up to 25 Km of altitude. 08-01- 11
Category A B1 B2 B3 Level 1 2 3 We have just described the three parameters which define the state of the air at rest. It is important to remember the law of the ideal gases, in which the pressure, the volume and the temperature are directly related. R is the the constant of ideal gases. For one mole of ideal gas, R = 8.31 J.K -1 PV = RT 08-01- 12
Category A B1 B2 B3 Level 1 2 3 2.4. Airflow and dynamic pressure: Relation between the state of the air and speed: By considering the elements which we previously described a new parameter is introduced essential to aerodynamic study: speed. We will not be interested with air at rest but with the flow of air compared to a body submerged in airflow. In a flow considered incompressible, along the flow of molecules, when speed varies, the pressure acts in the opposite direction. Bernoulli s equation in incompressible fluid: 08-01- 13
Category A B1 B2 B3 Level 1 2 3 1 2 P s + 2.ρ.V = const Let us start from this equation, and observe in a tube of fluid flow, the displacement of a point having values of pressure and speed. Like the points, the quantity 1 2 P s + 2.ρ.V remains fixed. This is the major reason why aircraft can fly. The presence of a wing in a flow and its shape will vary the air speed around the wing. Change of speed will give rise to variations of pressure which will generate aerodynamic force known as lift. 08-01- 14