Introduction to Aerospace Engineering - … · •Ramjet •Rocket •Before we can answer this question we must define what is efficient . Flight mechanics 29 Useful definitions

1 Challenge the future

Introduction to Aerospace Engineering

Lecture slides

15-12-2012

Challenge the future

Delft University of Technology

Flight mechanics

Introduction Aerospace Engineering Flight Mechanics

Dr. Ir. Mark Voskuijl

2 Flight mechanics

1.& 2. Flight Mechanics

3 Flight mechanics

Question

A Boeing 747 runs out of fuel at 10 km altitude

Suddenly all engines stop…

How far will this aircraft be able to glide?

a) 180 [m]

b) 1800 [m]

c) 18000 [m]

d) 180000 [m]

4 Flight mechanics

5 Flight mechanics

Flight mechanics

• What is the performance of a given aircraft; i.e. how far, high,

fast, slow can it fly?

• How long can an aircraft remain airborne following an engine

failure and how far can it glide?

• How is aircraft morphology related to aircraft performance?

Key questions

6 Flight mechanics

Flight Mechanics

The performance of the complete vehicle is analyzed

High altitude Orbits

Launchers

Steep climbs

Gliding flight

Low speed

7 Flight mechanics

Flight Mechanics

Equations of motion

Aerodynamics

Aircraft Structure

Pilot (flying

strategy)

Propulsion system

Atmosphere

8 Flight mechanics

Contents

1. What is Flight mechanics?

2. Practical matters

3. General equations of motion

4. Propulsion

5. Aerodynamics

6. Summary

7. Additional material (background information for AE1100 project)

9 Flight mechanics

Contents

1. What is Flight mechanics?



4. Propulsion

5. Aerodynamics

6. Summary


10 Flight mechanics

Flight mechanics

Hours 1 & 2 : Introduction, general equations of motion

Hours 3 & 4 : Horizontal flight performance

Hours 5 & 6 : Climbing and descending flight

Hours 7 & 8 : Flight envelope

Hours 9 & 10: Example questions and solutions

11 Flight mechanics

What do you need to learn?

• Most important!!! Lecture sheets (blackboard)

• Introduction to flight: paragraphs; 6.1, 6.2, 9.1 9.2, 9.4, 9.6

• Better book to consult for more information: Ruijgrok, “Elements of Airplane Performance” (only 14 euro’s at VSV)

• Practice questions (blackboard)

12 Flight mechanics

Contents

1. What is Flight and Orbital Mechanics?



4. Propulsion

5. Aerodynamics

6. Summary


13 Flight mechanics

Equations of motion

• Newton’s laws

• Coordinate systems

• Assumptions

• Equations of motion

Overview

14 Flight mechanics

Equations of motion Newton’s laws

Newton’s laws only hold with respect to a frame of reference which is in absolute rest. This is called an inertial frame of reference

Coordinate systems translating uniformly to the frame of reference in absolute rest are also inertial frames of reference

A rotating frame of reference is not an inertial frame of reference

15 Flight mechanics

Equations of motion

V

Zb

Ze

Xe

Xb

Xg

Zg

Xa

Za

G: Earth axis system

E: Moving Earth axis system

Coordinate systems

A: Air path axis system

B: Body axis system

Angles: - pitch attitude - angle of attack - flight path angle

16 Flight mechanics

Assumptions

Assumption 1: the earth is flat

2

2

Centrifugal force

e

e

W VC

g R h

C V

W R h g

Valid assumption

2

2

Example

100 [m/s]

6371 [km]

9.80665 [m/s ]

0 [m]

1000.00016

6371000 0 9.80665

(0.016%)

e

V

R

g

h

C

W

17 Flight mechanics

Assumptions

Assumption 2: the earth is non-rotating

18 Flight mechanics

Foucault - story

19 Flight mechanics

Assumptions

Assumption 3: Gravity is constant

1 2

2

M MF

R

(Newton’s law of gravitation)

At maximum altitude for atmospheric flight (60 – 80 km), g is very close to g at sea level

Note: these assumptions are fine for flight mechanics but not for orbital mechanics

20 Flight mechanics

Equations of motion Free Body Diagram - Forces

L

D

W

T V

T

Zb

Ze

Xe

Xb

Xa

Important: • Lift vector perpendicular

to airspeed • Drag parallel to airspeed • Thrust not necessarily in

direction of Xb

21 Flight mechanics

Xa

Equations of motion Kinetic diagram - accelerations

V

Zb

Ze

Xe

dV

dt

dV

dt

Xb

22 Flight mechanics

Equations of motion

// : cos sin

: cos sin

V T

V T

W dVF T D W

g dt

W dF V L W T

g dt

23 Flight mechanics

Contents




4. Propulsion

5. Aerodynamics

6. Summary


24 Flight mechanics

Propulsion

1. Fundamental equations and definitions

2. Propeller or Jet engine?

3. Pure Jet engine

4. Propeller

Overview

25 Flight mechanics

Propulsion

0

0

out in

f j

j

F I I I

T m m V mV

T m V V

Propulsion System

Momentum equation

Force V0 Vj

Fuel is added to the mass flow

Conclusion A force is created by acceleration of mass. Two fundamental options:

1. Give a small amount of mass a large acceleration

2. Give a large amount of mass a small acceleration

Fundamental equations

26 Flight mechanics


• A small acceleration to a large mass:

• A large acceleration to a small mass:

• The mass can be taken from the surrounding

air (airbreathing engine) but it can also be

taken along

27 Flight mechanics


28 Flight mechanics


• Which propulsion type is the best?

• Propeller

• Jet

• Turbofan

• Ramjet

• Rocket

• Before we can answer this question we must define what is efficient

29 Flight mechanics

Useful definitions

• Power Available

• Jet Power

• Thermal Power

• Total efficiency

• Propulsive efficiency

• Thermal efficiency

30 Flight mechanics

Useful definitions

2 1

W F x

W T x x

2 1

WP

t

T x x xP T TV

t t

Power available

Work (energy) Power (energy per second)

V V

x t + t t

T T

aP TV

31 Flight mechanics

Useful definitions

Jet power is defined as the increase in kinetic energy of the flow

Jet power

Propulsion System

Force V0 Vj

Fuel is added to the mass flow

2 21 12 2

j jP mV mV

32 Flight mechanics

Useful definitions

FH

Qg

Thermal power

Thermal power (Q) is the heat energy supplied to the process (burning fuel)

f

in

Q m H

FHQ

g

Q mq

Variables: mf mass flow of fuel [kg/s] F fuel flow [N/s] H heating value [J/kg] (constant) m mass flow of air [kg/s] qin heat per kg air [J/kg]

33 Flight mechanics

Useful definitions

• Total efficiency is defined as the ratio of Power available

(energy for transportation) over Thermal power (fuel required)

• It is also the multiplication of propulsive efficiency and thermal

efficiency

Total Efficiency

atot

jatot j th

j

P

Q

PP

P Q

34 Flight mechanics

Useful definitions

2

1

aj

jj

P

VP

V

Propulsive efficiency

Conclusions: • The jet velocity Vj must be

larger than V in order to create thrust

• Therefore propulsive efficiency must be smaller than 100%!

35 Flight mechanics

Useful definitions

100 [N]

Option 1:

1 200 100 100 [N]

Option 2:

1 300 200 100 [N]

j

T

T m V V

T

T

,1

2 266%

20011

100

jjV

V

Jet or propeller?

• At large airspeeds it becomes more efficient to give a large acceleration to air

• At low airspeeds it is more efficient to give a large amount of air a small acceleration

,2

2 280%

30011

200

jjV

V

36 Flight mechanics

Useful definitions

Jet or propeller?

37 Flight mechanics

Useful definitions

jT m V V

2

1

atot j th

aj

jj

j

th

P

Q

P

VP

V

P

Q

Summary

2 21 12 2

a

j j

P TV

P mV mV

FHQ

g

Thrust Power Efficiency

Try to understand what these equations mean. Then you will be able to derive them. Do not memorize them

38 Flight mechanics

Working principle jet engine

See also, Physics 1 – lecture 7 (Chapter 9 of Cengel & Boles)

39 Flight mechanics

Working principle jet engine

• The compression at the intake depends on the flight velocity (kinetic

energy)

• The compression ratio (p2 / p1) at the intake is relatively low (in the

order of 1 2)

• Compression ratio in the compressor is relatively high (in the order of

30 – 40)

• Jet velocity is very high 0jT m V V

40 Flight mechanics

Propulsive force

Thrust is assumed to be independent of airspeed

Typical analytical assumption – Jet

41 Flight mechanics

Jet engine - simplified

Thrust

Airspeed

For basic flight mechanics applications, thrust of a turbojet can be assumed to be constant with airspeed for a given flight altitude

42 Flight mechanics

Working principle turboprop Schematic

43 Flight mechanics

Working principle turboprop

• Shaft power (Pbr) is provided by gasturbine

• Propeller accelerates air

44 Flight mechanics

Working principle propeller Motion of a propeller blade section

45 Flight mechanics

Working principle turboprop Induced velocity

46 Flight mechanics

Working principle propeller Actuator disk theory – blade element theory

47 Flight mechanics

Working principle propeller

Local velocities at a blade section

48 Flight mechanics

Working principle propeller Variable blade pitch

49 Flight mechanics

Working principle propeller Variable blade pitch

50 Flight mechanics

Propulsive force

Pa is assumed to be constant and independent of airspeed

Typical analytical assumption – Propeller

51 Flight mechanics

Propeller - simplified

Power available

Airspeed

For basic flight mechanics applications, power available of a propeller aircraft can be assumed to be constant with airspeed for a given flight altitude

52 Flight mechanics

Contents



3. General equations of motion and power equation

4. Propulsion

5. Aerodynamics

6. Summary


53 Flight mechanics

Aerodynamics

212

2 1

L

L

L W

C V S W

WV

S C

Lift

max

min

2 1

L

WV

S C

54 Flight mechanics

Aerodynamic forces Drag polar

0

2

LD D

CC C

Ae

55 Flight mechanics

Aerodynamic forces Drag polar

0

2

LD D

CC C

Ae

56 Flight mechanics

Aerodynamic forces Lift – Drag polar

0

2

LD D

CC C

Ae

57 Flight mechanics

0

2

LD D

CC C

Ae

58 Flight mechanics

Aerodynamic forces

Lift

0

2

LD D

CC C

Ae21

2

2

2 1

L

L

L W

C V S W

WC

S V

Drag

So, one part of the drag decreases (!) with airspeed (1/V2) and one part increases with airspeed (V2)

Drag as a function of airspeed

212DD C V S

0

22 21 1

2 2L

D

CD C V S V S

Ae

0

22 21 1

2 22 2 4

4 1 1D

WD C V S V S

S V Ae

0

221

2 212

D

WD C V S

Ae V S

59 Flight mechanics

Aerodynamic forces Drag as a function of airspeed

Aircraft are quite unique in the sense that drag increases when airspeed decreases!

0

0

210 2

2

212

i

D

i

D D D

D C V S

WD

Ae V S

60 Flight mechanics

Aerodynamic forces

• Di predominant factor at low airspeeds

Large S; low wing loading (W/S) required

• D0 predominant factor at high airspeeds

Small parasite drag CD0 and small S; high wing loading (W/S)

Consequences for aircraft design

Very low speed aircraft (bicycle plane) high speed aircraft (F104 Starfighter)

61 Flight mechanics

Contents




4. Propulsion

5. Aerodynamics

6. Summary


62 Flight mechanics

Summary

• You should be able to derive the

equations of motion for 2

dimensional flight

• The thrust (T) of a jet aircraft can be

assumed independent of airspeed

• The power available (Pa) of a

propeller aircraft can be assumed

independent of airspeed

• The complete aircraft aerodynamics

can be represented by 1 equation;

the lift drag polar

// : cos sin

: cos sin

V T

V T

W dVF T D W

g dt

W dF V L W T

g dt

0

2

LD D

CC C

Ae

63 Flight mechanics

Questions

64 Flight mechanics

Contents




4. Propulsion

5. Aerodynamics

6. Summary

7. Additional material (background information for AE1100

project)

65 Flight mechanics

Additional material

Extra information which may be useful for the propeller practical in

the AE1100 project is included in the next couple of sheets. You do

not have to learn this for the exam.

Actuator disk theory

66 Flight mechanics

Working principle turboprop Actuator disk theory

67 Flight mechanics


221 1

0 0 1 02 2 ap V p V V

0jT m V V

132a aV V

Bernoulli

Momentum equation

Actuator disk theory

2 21 1

2 0 0 0 32 2a ap V V p V V

2

2 1T R p p

22 21 10 3 02 2aT R V V V

2 13 0 32a aT R V V V

0 3 0aT m V V V

3aT mV

2

3 0a aT R V V V

68 Flight mechanics


2 2102br jP m V V

22 21

0 0 3 02br a aP R V V V V V

22

0 3br a aP R V V V

Actuator disk theory – propulsive efficiency

This efficiency is a theoretical upper limit Assumptions: - No rotational kinetic energy in slipstream - Axial velocity is uniform over the disk

0 0

0

0

1

1j

abr a

TV V

VP V V

V

2 2

0

2

1 1

jT

R V

Shaft power Pbr may be expressed as the increase in kinetic energy of the air mass flow

69 Flight mechanics


Actuator disk theory – blade element theory

70 Flight mechanics


Actuator disk theory – blade element theory

71 Flight mechanics

Blade element theory How to calculate the thrust and torque of a prop

Step 1: Calculate angle of attack of blade element

Step 2: Calculate Lift and Drag of element

Step 3: Integrate forces over whole blade (thrust and torque)

Step 4: Calculate induced velocity (actuator disk)

Step 0: assume induced velocity is equal to zero

Documents

Introduction to Aerospace Engineering - … · •Ramjet •Rocket •Before we can answer this question we must define what is efficient . Flight mechanics 29 Useful definitions