Introduction to Aerospace Engineering

Transcription

1 Introduction to Aerospace Engineering Lecture slides Challenge the future 1

2 Introduction Aerospace Engineering Flight Mechanics Dr. ir. Mark Voskuijl Delft University of Technology Challenge the future

3 7&8. Flight envelope 2

4 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

5 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

6 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

7 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

8 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

9 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

10 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

11 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

12 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 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 H r H H V 11

13 Altitude effects on aerodynamic drag Overview For increasing altitude: Drag curve shifts to the right Power curve shifts up and to the right 12

14 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 T (in troposphere) 13

15 Altitude effects on power available Propeller aircraft Turboprop airplanes show similar behaviour as turbojet airplanes P ( V ) constant a P P a a, (in troposphere) For supercharged piston engines, power available is fairly constant up to the critical altitude 14

16 Performance diagram How does it change with altitude? 15

17 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

18 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

19 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

20 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

21 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

22 Maximum altitude 21

23 Maximum altitude Practically it is impossible to reach the theoretical (absolute) ceiling in steady flight 22

24 Story U2 23

25 Performance limits combined At the theoretical ceiling: V min = V max = V RCmax = V max 24

26 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

27 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

28 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

29 Maximum Mach number Sound Barrier Bell X-1 First supersonic flight Chuck Yeager, 1947 Four rocket engines Thin wings, small aspect ratio M = : Buffet / Tuck under Bell X-1 M = 0.94 Total loss of elevator effectiveness M = 0.98 Normal behavior De Havilland Swallow 28

30 Maximum Mach number Operational limit Undesirable flying qualities associated with buffeting effects V M a M RT Troposphere (<11km): T T H H 0 Stratosphere (>11km) T constant H M MO Safety margin M max V 29

31 Cabin pressure Pressurized cabin Maximum pressure differential on fuselage structure (structural limit) Maximum flight altitude 30

32 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

33 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

34 TWA Flight 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

35 Problem! Stall limit is variable with altitude How does the pilot know where the stall limit is??? The airspeed indicator solves this problem! 34

36 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

37 Airspeed indication Basic six 36

38 Pneumatic instruments 37

39 Pitot tube / static port 38

40 Airspeed indication Displacement is measure of pressure difference p t p = ½ V 2 (M<<1) 1 equation 2 unknowns 39

41 Airspeed indication Solution: V 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 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

42 Altimeter 41

43 Height altitude or level? 42

44 p 0 is set at mbar Transition altitude 3000 ft Sea level p 0 at actual pressure QNH 43

45 p 0 is set at mbar Transition level FL 40 p 0 at actual pressure QNH Sea level 44

46 Vertical speed indicator 45

47 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

48 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 (in troposphere) Question a: What is the maximum rate of climb of this aircraft at sea-level ( = [kg/m 3 ] and what is the corresponding airspeed? Question b: What is the maximum rate of climb at 1000 m ( = [kg/m 3 ]) and the corresponding airspeed. Explain why your results are different than for question a 47