Introduction to Aerospace Engineering Lecture slides Challenge the future 1
Introduction Aerospace Engineering Flight Mechanics Dr. ir. Mark Voskuijl 15-12-2012 Delft University of Technology Challenge the future
7&8. Flight envelope 2
Contents 1. Summary previous lectures 2. Introduction 3. Altitude effects on performance diagram 4. Performance limits 5. Operational limits 6. Flight envelope 7. Flight instruments 8. Example calculations 3
Contents 1. Summary previous lectures 2. Introduction 3. Altitude effects on performance diagram 4. Performance limits 5. Operational limits 6. Flight envelope 7. Flight instruments 8. Example calculations 4
Summary - Jet Force Max thrust Drag Min. speed C L,max Min. rate of descent (T =0) (C L 3 /C D2 ) max 1. Max. Endurance 2. Maximum climb 3. Minimum descent (C L / C D ) max Max. Range (C L /C D2 ) max Max. Speed (depends on T max) Airspeed 5
Summary Propeller Aircraft Power Power available Power required Min. speed C L,max 1. Max. Endurance 2. Max. Rate of climb 3. Minimum rate of descent (T= 0) (C L 3 / C D 2 ) max 1. Max. Range 2. Smallest glide angle (C L /C D ) max Airspeed Max. Speed (depends on P amax ) 6
Contents 1. Summary previous lectures 2. Introduction 3. Altitude effects on performance diagram 4. Performance limits 5. Operational limits 6. Flight envelope 7. Flight instruments 8. Example calculations 7
Introduction So far we considered the aircraft performance at one given altitude How is aircraft performance influenced by altitude effects? Question: How high can this aircraft fly? Lockheed U-2: High altitude jet aircraft for weather and radiation research and also reconnaissance missions 8
What do you need to learn The lecture sheets are most important!!! Background material: Anderson, Introduction to flight, Par. 6.7, 6.10 Not everything is treated in the book!!! 9
Contents 1. Summary previous lectures 2. Introduction 3. Altitude effects on performance diagram 4. Performance limits 5. Operational limits 6. Flight envelope 7. Flight instruments 8. Example calculations 10
Altitude effects on aerodynamic drag Consider a constant angle of attack Drag (one particular ): CD CD DH W D 1 H W 2 C C L Airspeed (one particular ): L D One point on the drag curve corresponds to a particular V V H H 1 2 W S W S 2 1 C H 1 2 1 C H 2 L L P r One point on the power curve corresponds to a particular V Power required (one particular ) P, D V P, V Pr, H2 Pr, H1 P r, H D 2 H V P 2 H2, V r H H H H r H H 1 1 1 1 2 2 H r H H 2 1 1 V 11
Altitude effects on aerodynamic drag Overview For increasing altitude: Drag curve shifts to the right Power curve shifts up and to the right 12
Altitude effects on engine thrust Jet aircraft Two effects: Air density decreases Temperature decreases (up to tropopause) 1. Performance is limited by maximum turbine temperature. Lower air temperature allows more heat added to the gas 2. Decrease in density reduces mass flow and thus engine thrust TV ( ) constant T T0 0 0.75 (in troposphere) 13
Altitude effects on power available Propeller aircraft Turboprop airplanes show similar behaviour as turbojet airplanes P ( V ) constant a P P a a,0 0 0.75 (in troposphere) For supercharged piston engines, power available is fairly constant up to the critical altitude 14
Performance diagram How does it change with altitude? 15
Contents 1. Summary previous lectures 2. Introduction 3. Altitude effects on performance diagram 4. Performance limits 5. Operational limits 6. Flight envelope 7. Flight instruments 8. Example calculations 16
Minimum airspeed How does it change with altitude? Aerodynamic limit (stall) Power limit P P r,h2 P a, h1 Minimum airspeed increases with altitude! P r, h1 P a, h2 V V min,h1 V min,h2 17
Minimum airspeed As function of altitude H Up to a certain altitude, the minimum airspeed is determined by the stall. At higher altitudes it depends on the engine power Stall limit Power limit V min 18
Maximum airspeed How does it change with altitude? Power available shifts down Power required shifts up and to the right P P a, h1 P r,h2 P r, h1 Depending on the engine characteristics and altitude, V max will increase or decrease P a, h2 V V max,h1 19
Maximum rate of climb How does it change with altitude? P P a W r RC P P a, h1 P r,h2 RC max decreases with altitude V 20
Maximum altitude 21
Maximum altitude Practically it is impossible to reach the theoretical (absolute) ceiling in steady flight 22
Story U2 23
Performance limits combined At the theoretical ceiling: V min = V max = V RCmax = V max 24
Contents 1. Summary previous lectures 2. Introduction 3. Altitude effects on performance diagram 4. Performance limits 5. Operational limits 6. Flight envelope 7. Flight instruments 8. Example calculations 25
V ed (design diving speed) Structural aircraft limit Positive and negative gusts of 25 ft/s must be considered at the design diving speed tan U U V V C n L dc L dc L U d d V dc L U 1 2 V S L 2 n d V W W 26
V ed (design diving speed) Structural aircraft limit The aircraft is designed to withstand a certain load factor n The design diving speed increases with increasing altitude n dc L U 1 2 V S 2 d V W V MO V d Safety margin constant 27
Maximum Mach number Sound Barrier Bell X-1 First supersonic flight Chuck Yeager, 1947 Four rocket engines Thin wings, small aspect ratio M = 0.88 0.90: Buffet / Tuck under Bell X-1 M = 0.94 Total loss of elevator effectiveness M = 0.98 Normal behavior De Havilland Swallow 28
Maximum Mach number Operational limit Undesirable flying qualities associated with buffeting effects V M a M RT Troposphere (<11km): T T H 288.15 0.0065H 0 Stratosphere (>11km) T constant H M MO Safety margin M max V 29
Cabin pressure Pressurized cabin Maximum pressure differential on fuselage structure (structural limit) Maximum flight altitude 30
Contents 1. Summary previous lectures 2. Introduction 3. Altitude effects on performance diagram 4. Performance limits 5. Operational limits 6. Flight envelope 7. Flight instruments 8. Example calculations 31
Flight envelope Altitude and airspeed to which aircraft is constrained Note that these limits are fixed Performance limits can exceed or lie within these boundaries The performance limits depend on the aircraft weight as well 32
TWA Flight 841 1979 New York Minneapolis High altitude holding (39,000 ft) Failure with slat nr. 7 34,000 ft dive in 64 seconds Landing gears deployed 6 g pullup Safe landing 33
Problem! Stall limit is variable with altitude How does the pilot know where the stall limit is??? The airspeed indicator solves this problem! 34
Contents 1. Summary previous lectures 2. Introduction 3. Altitude effects on performance diagram 4. Performance limits 5. Operational limits 6. Flight envelope 7. Flight instruments 8. Example calculations 35
Airspeed indication Basic six 36
Pneumatic instruments 37
Pitot tube / static port 38
Airspeed indication Displacement is measure of pressure difference p t p = ½ V 2 (M<<1) 1 equation 2 unknowns 39
Airspeed indication Solution: V 1 2 1 2 2 2 0 e V e def V V 0 So, the airspeed indicator does not show the true airspeed! V V V min e,min e,min V W 2 1 S C min W S L,max 0 2 1 C (EAS) 0 L,max (TAS) (EAS) Minimum equivalent airspeed is independent of altitude! Note, compressibility effects are neglected for now. This will be explained later. (The basic principle is the same; sea level conditions are assumed by the airspeed indicator) 40
Altimeter 41
Height altitude or level? 42
p 0 is set at 1013.25 mbar Transition altitude 3000 ft Sea level p 0 at actual pressure QNH 43
p 0 is set at 1013.25 mbar Transition level FL 40 p 0 at actual pressure QNH Sea level 44
Vertical speed indicator 45
Contents 1. Summary previous lectures 2. Introduction 3. Altitude effects on performance diagram 4. Performance limits 5. Operational limits 6. Flight envelope 7. Flight instruments 8. Example calculations 46
Example Question Climbing performance of the Beach King Air Two engine propeller aircraft C D = C D0 + kc L 2 C D0 = 0.02 k = 0.04 W = 60 [kn] S = 28.2 [m 2 ] Power available can be assumed independent of airspeed Maximum power available at sealevel is 741 kw Aircraft is performing a steady symmetrical climb Pa Pa,max, sealevel 0 0.75 (in troposphere) Question a: What is the maximum rate of climb of this aircraft at sea-level ( = 1.225 [kg/m 3 ] and what is the corresponding airspeed? Question b: What is the maximum rate of climb at 1000 m ( = 1.1117 [kg/m 3 ]) and the corresponding airspeed. Explain why your results are different than for question a 47