AE1101-FlightMech-4

1 Challenge the future

Introduction to Aerospace Engineering

Lecture slides

15-12-2012

Challenge the future

Delft University of Technology

Introduction Aerospace Engineering

Flight Mechanics

Dr. ir. Mark Voskuijl

2 Flight mechanics

7&8. Flight envelope

3 Flight mechanics

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 Flight mechanics

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

5 Flight mechanics

Summary - Jet Force

Drag

Airspeed

Max thrust

1. Max. Endurance 2. Maximum climb

3. Minimum descent (CL / CD)max

Max. Range (CL/CD

2)max

Max. Speed (depends on Tmax)

Min. speed CL,max

Min. rate of descent (T =0) (CL

3 /CD2)max

6 Flight mechanics

Summary – Propeller Aircraft

Power

Power required

Airspeed

Power available

1. Max. Endurance 2. Max. Rate of climb 3. Minimum rate of descent (T= 0) (CL

3 / CD2 )max

1. Max. Range 2. Smallest glide angle (CL/CD)max

Max. Speed (depends on Pamax)

Min. speed CL,max

7 Flight mechanics

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

8 Flight mechanics

Introduction

• So far we considered the aircraft performance at one given

altitude

• How is aircraft performance influenced by altitude effects?

Lockheed U-2: High altitude jet aircraft for weather and radiation research and also reconnaissance missions

Question: How high can this aircraft fly?

9 Flight mechanics

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!!!

10 Flight mechanics

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

11 Flight mechanics

Altitude effects on aerodynamic drag

• Drag (one particular ):

1 2

D DH H

L L

C CD W D W

C C

Consider a constant angle of attack

1

1

2

2

2 1

2 1

H

H L

H

H L

WV

S C

WV

S C

1 1 1 1 2 2

2 1

2 1 12 2 2

, ,

, ,

,,

r H H H H r H H

r H r H

H r H Hr H H H

P D V P VP P

P VP D V

One point on the drag curve corresponds to a particular

D

Pr

V

V

• Airspeed (one particular ):

• Power required (one particular )

One point on the power curve corresponds to a particular

12 Flight mechanics

Altitude effects on aerodynamic drag

For increasing altitude:

• Drag curve shifts to the right

• Power curve shifts up and to the

right

Overview

13 Flight mechanics

Altitude effects on engine thrust

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

Jet aircraft

0.75

0 0

( ) constant

(in troposphere)

T V

T

T

14 Flight mechanics

Altitude effects on power available

• Turboprop airplanes show similar behaviour as turbojet airplanes

• For supercharged piston engines, power available is fairly constant up

to the critical altitude

Propeller aircraft

0.75

,0 0

( ) constant

(in troposphere)

a

a

a

P V

P

P

15 Flight mechanics

Performance diagram How does it change with altitude?

16 Flight mechanics

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

17 Flight mechanics

Minimum airspeed

• Aerodynamic limit (stall)

• Power limit

• Minimum airspeed increases

with altitude!

P

V

Pa, h1

Pr,h2

Pa, h2

Pr, h1

Vmin,h1 Vmin,h2

How does it change with altitude?

18 Flight mechanics

Minimum airspeed As function of altitude

H

Vmin

Stall limit

Power limit

Up to a certain altitude, the minimum airspeed is determined by the stall. At higher altitudes it depends on the engine power

19 Flight mechanics

Maximum airspeed

• Power available shifts down

• Power required shifts up

and to the right

• Depending on the engine

characteristics and altitude,

Vmax will increase or

decrease

P

V

Pa, h1

Pr,h2

Pa, h2

Pr, h1

Vmax,h1

How does it change with altitude?

20 Flight mechanics

Maximum rate of climb

• RCmax decreases with altitude

How does it change with altitude?

P

V

Pa, h1

Pr,h2

a rP P

RCW

21 Flight mechanics

Maximum altitude

22 Flight mechanics

Maximum altitude

Practically it is impossible to reach the theoretical (absolute) ceiling in steady flight

23 Flight mechanics

Story U2

24 Flight mechanics

Performance limits combined

At the theoretical ceiling: Vmin = Vmax = VRCmax = Vmax

25 Flight mechanics

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

26 Flight mechanics

Ved (design diving speed)

• Positive and negative gusts of 25

ft/s must be considered at the

design diving speed

tanU U

V V

Structural aircraft limit

L LL

dC dC UC

d d V

212

LdC UV S

L d Vn nW W

27 Flight mechanics

Ved (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

212

LdC UV S

d VnW

constant

Vd VMO

Safety margin

28 Flight mechanics

Maximum Mach number

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 M = 0.94 Total loss of elevator effectiveness M = 0.98 Normal behavior

Bell X-1

De Havilland Swallow

Sound Barrier

29 Flight mechanics

Maximum Mach number

• Undesirable flying qualities

associated with buffeting effects

0

Troposphere (<11km):

288.15 0.0065

Stratosphere (>11km)

constant

V M a M RT

T T H H

T

H

V

Mmax MMO

Safety margin

Operational limit

30 Flight mechanics

Cabin pressure

• Pressurized cabin

• Maximum pressure differential on

fuselage structure (structural limit)

• Maximum flight altitude

31 Flight mechanics

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

32 Flight mechanics

Flight envelope

• 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

Altitude and airspeed to which aircraft is constrained

33 Flight mechanics

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

34 Flight mechanics

Problem!

How does the pilot know where the stall limit is???

The airspeed indicator solves this problem!

Stall limit is variable with altitude

35 Flight mechanics

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

36 Flight mechanics

Airspeed indication Basic six

37 Flight mechanics

Pneumatic instruments

38 Flight mechanics

Pitot tube / static port

39 Flight mechanics

Airspeed indication

Displacement is measure of pressure difference pt – p = ½ V2 (M<<1)

1 equation 2 unknowns

40 Flight mechanics

Airspeed indication

2 21 102 2

0

e

def

e

V V

V V

Solution: So, the airspeed indicator does not show the true airspeed!

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)

min

,max

2 1 (TAS)

L

WV

S C

,min min

0

(EAS)eV V

,min

0 ,max

2 1 (EAS)e

L

WV

S C

Minimum equivalent airspeed is independent of altitude!

41 Flight mechanics

Altimeter

42 Flight mechanics

Height altitude or level?

43 Flight mechanics

Transition altitude 3000 ft

Sea level

p0 at actual pressure QNH

p0 is set at 1013.25 mbar

44 Flight mechanics

Transition level FL 40

Sea level

p0 at actual pressure QNH

p0 is set at 1013.25 mbar

45 Flight mechanics

Vertical speed indicator

46 Flight mechanics

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

47 Flight mechanics

Example Question Climbing performance of the Beach King Air

Two engine propeller aircraft CD = CD0 + kCL

2 CD0 = 0.02 k = 0.04 W = 60 [kN] S = 28.2 [m2]

Power available can be assumed independent of airspeed Maximum power available at sealevel is 741 kW Aircraft is performing a steady symmetrical climb Question a: What is the maximum rate of climb of this aircraft at sea-level ( = 1.225 [kg/m3] and what is the corresponding airspeed?

Question b: What is the maximum rate of climb at 1000 m ( = 1.1117 [kg/m3]) and the

corresponding airspeed. Explain why your results are different than for question a

0.75

,max,

0

(in troposphere)a a sealevelP P