1、飞行力学全册配套最完整飞行力学全册配套最完整 精品课件精品课件(英文版）英文版） I Principles of straight and steady level flight 1. Straight and steady level flight Lift Z V Velocity vector X Drag Thrust F Weight mg Thrust balances drag An airplane has : wings to generate lift, engines to balance drag. Lift balances weight 1. Straight an
2、d steady level flight Expressions for lift and drag : Lift : V2 S CzDrag : V2 S Cx V2 is the kinetic pressure, also noted q is the air density (in kg/m3) V is the air velocity (in m/s) S is the wing reference surface (in m2) Cz and Cx are lift and drag coefficients Drag is parallel to the velocity v
3、ector and opposed to velocity (Cx is always positive) Lift is normal to the velocity vector (upwards when Cz is positive) 1. Straight and steady level flight Symmetrical flight Wings leveled (zero bank angle) Zero lateral force (zero sideslip angle) Straight and level flight : velocity vector is hor
4、izontal Lift balances weight Steady flight : Constant speed : thrust balances drag Moment equilibrium is achieved by flight controls deflections 1. Straight and steady level flight V Velocity vector Angle of attack, , is the angle between the velocity vector and the airplane longitudinal reference.
5、Lift and drag coefficients are functions of angle of attack. Angle of attack and pitch attitude Horizontal plane In straight and level flight, the velocity vector is horizontal : angle of attack equals pitch attitude : = Pitch attitude, , is the angle b e t w e e n t h e a i r p l a n e longitudinal
6、 reference and the horizontal plane. Flight controls Thrust levers Aerodynamics PropulsionWeightInertia Moments Ma/G +MF/G = dt d ( I . W W k) ForcesRa +F + gm= dt d (mVk) 1. Straight and steady level flight Flight mechanics equations Flight controls are used to control attitude Forward/aft stick (o
7、r control wheel) controls pitching moment through elevator Left/right Stick (or control wheel) controls rolling moment through ailerons (and spoilers) Rudder pedals control yawing moment through rudder 1. Straight and steady level flight 1. Straight and steady level flight Lift equation mg = V2 S Cz
8、lift balances weight Propulsion equation F = V2 S Cxthrust balances drag To maintain straight and steady level flight : Angle of attack is controlled by elevator deflection in order to maintain lift equilibrium (lift = weight) Thrust is controlled by thrust levers in order to maintain thrust equilib
9、rium Equations for straight and steady level flight 2. Pressure and altitude : the altimeter Note : 1 ft = 0.3048 m Pressure (hPa) 0 20 40 60 80 100 120 2004006008001000 Altitude (X 1000 ft) 0 1013.25 hPa 500 hPa 18300 ft 5600 m 300 hPa 30050 ft 9160 m 100 hPa 53080 ft 16180 m 27ft / hPa 73 ft / hPa
10、 Pressure as a function of geopotential altitude (International Standard Atmosphere) 2. Pressure and altitude : the altimeter Pressure altitude Zp(p) is the altitude corresponding to pressure p in the ISA model. Example :Zp 10 000 ft p = 697 hPa The term Flight level (FL) is also used. Flight Level
11、is the pressure altitude expressed in hundreds of feet. Example : FL 100 means Zp 10 000 ft. At a given pressure altitude, temperature is sometimes expressed as a difference between actual temperature and ISA temperature. Example : At FL 100 (Zp 10 000 ft), ISA temperature is - 5 C (268 K). ISA+15 c
12、onditions means that actual temperature at FL100 is 15 higher than ISA temperature, or +10C (-5+15) 2. Pressure and altitude : the altimeter Static pressure p is measured through static ports. International Standard Atmosphere is used to convert pressure p into pressure altitude Zp(p). Indicated alt
13、itude : Zi = Zp(p) - Zp(pc). The altimeter setting, noted pc, is a pressure value selected by the crew, allowing to ajust to current conditions. Altimeter setting pc Zp(pc) Pressure pPressure altitude Zp(p) 2. Pressure and altitude : the altimeter 1000 hpa 900 hpa 800 hpa 0 2000 ft 4000 ft 6000 ft 0
14、 5 4 3 2 1 6 7 8 9 ALT 1 030hPa 000 4 ft 5 pc Zi Zp(p) Static pressure p Indicated Altitude Zi Indicated altitude : Zi = Zp(p) - Zp(pc) 2. Pressure and altitude : the altimeter Altimeter settings : Standard setting : 1013.25 hPa Indicated altitude is pressure altitude. QFE is the current static pres
15、sure on the airport : On ground, indicated altitude is zero. QNH is defined in order to read airport elevation on ground. Zi (p, QNH) H at low altitudes, But, at higher altitudes, altimeter indication is affected by temperature conditions (in cold conditions, altimeter indication is higher than actu
16、al altitude). 2. Pressure and altitude : the altimeter The real atmosphere may differ from the ISA model : pressure at sea level : usual range from 980 to 1050 hPa, much lower values in cyclones, temperature at sea level, altitude for minimal temperature (tropopause) may be lower than 8 km or higher
17、 than 15 km compared to the 11 km ISA value. Consequences : Difference between pressure altitude Zp and geopotential altitude H may exceed several thousands feet QNH setting corrects the difference between actual pressure at sea level and ISA pressure (1013.25hPa), in ISA temperature conditions, an
18、altimeter set at QNH will indicate actual geopotential altitude But, it is not possible to correct temperature error : in cold air, an altimeter set at QNH will indicate an altitude higher than actual altitude 2. Pressure and altitude : the altimeter Static pressure measurements may be affected by :
19、 Instrument / sensor error Static source position error : influence of airflow around the airplane p = pport - p p1 p2 p Undisturbed flow 2. Pressure and altitude : the altimeter Static source position error calibration methods Airplane aerodynamic field (wake) Cone Pressure transducer Height above
20、ground z (radio altimeter, GPS, ) Pressure and temperature on ground pG, TG Pressure at A/C altitude obtained from z, pG, TG and T (temperature at A/C altitude) 2. Pressure and altitude : the altimeter Applicable at sea level, in ISA conditions, between 1.3 Vs in landing configuration and 1.8 Vs in
21、clean configuration. Note : 30 ft error at sea level is equivalent to 123 ft error at FL400. -90 -60 -30 0 30 60 90 50100150200250300 Indicated Air Speed (kt) Maximum position error (ft) Static source position error FAR/CS 25 requirements 3. True airspeed and indicated airspeed Ground Speed and True
22、 Air Speed True Air Speed, TAS or V, is A/C velocity relative to the air Ground Speed, GS or Vk, is A/C velocity relative to the ground. May be measured by inertial or radio navigation sensors (GPS, DME, etc). Units for speed : 1 kt = 1852 m/h = 0.5144 m/s is the drift angle. d d True Air Speed V Wi
23、nd WGround Speed Vk 3. True airspeed and indicated airspeed At low Mach numbers, Bernoullis equation is valid : pt = p + V2 = p + q q is the Kinetic pressure :q = V2 aerodynamic efforts are proportional to q Static port p Static pressure p (static temperature T) Pitot tube pt Total pressure pt (tota
24、l temperature Tt) Total pressure and static pressure 3. True airspeed and indicated airspeed The principle for indicated airspeed (noted Vi) is to convert p into an airspeed indication : Vi (p) At low speeds, when Bernoullis equation is valid, it is possible to use kinetic pressure definition, with
25、air density ISA value at sea level : p = 0Vi2 Pitot tube Static port p = pt p V2 ptp IAS 3. True airspeed and indicated airspeed Equivalent airspeed (EAS), noted EV, is the airspeed corresponding to a given kinetic pressure at s.l. in ISA conditions : q = V2 = 0 EV2 EV = V Indicated Airspeed (IAS),
26、includes airspeed errors. Calibrated Airspeed (CAS), noted Vc, is the theoretical value, after correction of airspeed errors. At low speeds and low altitudes, Calibrated airspeed (CAS) is very close to Equivalent airspeed :Vc EV 0 3. True airspeed and indicated airspeed Kinetic pressure limitations
27、Structural loads increase with kinetic pressure. Above some value of q, flutter may be encountered. Flutter : instability due to coupling between aerodynamic modes and structural modes. Definition of “placard speeds” (maximum IAS) : Clean configuration : VMO, VNO/VNE (light airplanes) Other speed li
28、mitations : VFE (flaps extended), VLE (landing gear extended), VLO (landing gear operation), etc 3. True airspeed and indicated airspeed IAS kt 20 40 60 80100 120 140 160 Airspeed Indicator (ASI) and IAS limitations (light airplane) VNO VNE VFE VS clean VS flaps extended Maximum IAS flaps extended N
29、ever exceed speed Stall speed flaps retracted Stall speed flaps extended Maximum IAS in turbulence 4. General principles of airplane propulsion Intake Exhaust Mass flow Q Mass flow Qj Engine Fuel flow Qc VVj Thrust : F Qj Vj - QV 4. General principles of airplane propulsion 4. General principles of
30、airplane propulsion For propeller engines and jet engines, fuel flow is small, compared to air mass flow : Qj = Q + Qc Q If jet velocity is parallel to A/C velocity, the net thrust F is : F = Q (Vj - V) 4. General principles of airplane propulsion The engine must communicate to the flow the power Wk
31、 corresponding to the kinetic energy increment : Wk = QVj2 - QV2 The propulsive power is : W = V.F Propulsive efficiency :p = W/Wk = The global efficiency is the product of propulsive and thermal efficiencies. VVj 2V Propulsive efficiency Airflow ramjet scramjet A/C Mach number 1 Jet exhaust velocit
32、y Propeller Propfan Turbofan (high bypass) Turbofan (low bypass) Turbojet Variable cycle turbofan 4. General principles of airplane propulsion 5. Jet propulsion : turbojet and turbofan 5. Jet propulsion : turbojet and turbofan Fuel Compressor Intake Turbine Nozzle Combustion chamber Turbojet operati
33、ng cycle 1. Adiabatic compression Intake F : thrust (N) Cs : SFC (kg/N/h) Order of magnitude for SFC in cruise : 1 kg/daN/h(0.1 kg/N/h) Depends on flight conditions and thrust level (optimum at the bucket) 5. Jet propulsion : turbojet and turbofan Optimum thrust for SFC close to maximum thrust SFC T
34、hrust Idle Thrust Max. Thrust Fu Evolution of Specific Fuel Consumption with thrust level Minimum SFC : bucket 6. Straight and steady level flight performance 6. Straight and steady level flight performance Velocity vector Lift Z V X Drag Thrust F Weight mg G Lift equation mg = V2SCz Propulsion equa
35、tion F = V2SCx 6. Straight and steady level flight performance Lift equation mg = V2 S Cz = 0EV2 S Cz Lift coefficient and speed T r u e a i r s p e e d V = Equivalent Airspeed EV = Stall speed (CAS) under 1 g load factor Vs1g = (CAS EAS at low speed/altitude) SCz mg2 SCz mg2 0 maxSCz mg2 0 Speed an
36、d lift coefficient 6. Straight and level flight performance Thrust required for level flight, Fn Straight level flight at constant speed Propulsion equation F = V2 S Cx Lift equation mg = V2 S Cz Thrust must balance drag in order to maintain constant speed and altitude Fn = V2 S Cx Fn = mg = f is th
37、e lift over drag ratio Cz Cx f mg 6. Straight and steady level flight performance In straight and steady level flight Lift coefficient Cz is function of Equivalent Airspeed and wing loading (mg/S) : Thrust required for level flight depends only on weight and lift over drag ratio f. At low speeds : E
38、V Vc (Equivalent Airspeed Calibrated Airpeed) Lift over drag ratio is a function of lift coefficient (incompressible drag polar) 2 0EV 2 S mg Cz f mg Fn 6. Straight and steady level flight performance Wing loading For a given lift coefficient, when wing loading increases, equivalent airspeed increas
39、es Light single engine piston airplanes m/S 100 kg/m2 Commercial jets m/S 700 kg/m2 6. Straight and steady level flight performance Maximum L/D Induced drag = Zero lift drag Zero lift drag V2 Induced drag 1/V2 V Cz Cx (Cz) Fn = mg Cx/Cz lift equation Drag polar Thrust required Fn True Airspeed V min
40、. Fn Stall Symmetrical drag polar Cx = Cx0 + k Cz2 Incompressible drag polar 6. Straight and steady level flight performance Constant lift coefficient Cz Cx = Cx(Cz) Influence of mass m True Airspeed V, Equivalent Airspeed EV are proportional to m Thrust required, Fnis proportional to m Influence of
41、 air density True Airspeed V is proportional to 1/ Equivalent Airspeed EV is independent from Thrust required Fn is independent from 6. Straight and steady level flight performance Thrust F True Airspeed V Thrust required Fn Max. L/D min. Fn min. Fn/V Min. Cx/Cz Stall Maximum engine thrust Fu idle t
42、hrust ( = 0) Engine thrust for intermediate lever angle Thrust diagram (jet airplane) 6. Straight and steady level flight performance Cz Cx Max L/D Min. Fn Cz1 Stall Czmax Cz3 Min Cx/Cz1/2 Min. Fn/V Drag polar and thrust diagram (jet airplane) Fuel flow (kg/h)Ch = Cs.Fn Cs is the SFC (kg/N/h) Fn is
43、the thrust required for level flight Ch = Cs mg Maximum endurance minimum fuel flow At a given altitude, maximum endurance will be obtained at the speed corresponding to minimum thrust required (best L/D) Assuming constant SFC and incompressible drag polar, at a given lift coefficient, fuel flow doe
44、s not depend on altitude. Cz Cx 7. Endurance and range (jet airplanes) 7. Endurance and range (jet airplanes) Specific range, noted Rs, is the distance flown per unit fuel. Unit for Rs : nm/kg or nm/t. Vk : ground speed in knots Ch : fuel flow in kg/h (or t/h) Still air specific range : Best still a
45、ir specific range obtained when Fn/V is minimal Ch Vk Rs Cs.Fn V Ch V Rs 0)(W 7. Endurance and range (jet airplanes) Thrust F Equivalent Airspeed EV Thrust required Fn Max. L/D min. Fn min. Fn/V Min. Cx/Cz Stall Maximum Endurance Maximum range Cruising speeds VMO 7. Endurance and range (jet airplane
46、s) Speed, altitude and economy Direct operating cost per leg is the addition of: Fixed expenses (ATC fees, etc), Fuel expenses, Time dependant expenses (crew, maintenance, etc). When cruising speed increases : For a given leg (fixed distance), time dependant expenses decrease Airplane productivity i
47、ncreases : it is possible to fly more legs with a given number of airplanes Better customer acceptance Consequence : optimum speed is higher than maxi- range speed. Influence of altitude (or temperature) : when altitude increases air density decreases For a given mass, lift coefficient Cz is a funct
48、ion of equivalent airspeed EV (mg = 0EV2 S Cz) True airspeed increases when altitude increases : (V2 = 0EV2) Under the incompressible drag polar assumption, drag coefficient is function of lift coefficient only : thrust required Fn (EV) does not depend on altitude If SFC is constant, fuel flow does
49、not depend on altitude Specific range increases when altitude increases 7. Endurance and range (jet airplanes) Under the preceding assumptions, cruising altitude must be the higher possible : Higher cruising speed (shorter time per leg) Better specific range (lower fuel burnt per leg) That explains
50、why jet airplanes fly at higher altitudes (when compared to propeller airplanes) But, in real life, we have to take into account two phenomena : SFC decreases when altitude increases (higher Fn/Fu ratio) Drag increases wh e n a lti tu d e i nc r e a s e s (compressibility effects) 7. Endurance and r
