the development of a fixed wing aircraft analysis and ... · bagi ciri-ciri aerodinamik, potongan...

iii

THE DEVELOPMENT OF A FIXED WING AIRCRAFT ANALYSIS AND

DESIGN FLIGHT DYNAMIC SOFTWARE

AHMAD ESHTIWEY AHMAD ALAIAN

A thesis submitted in 18 / 02 / 2016

fulfillment of the requirement for the award of the

Doctor of Philosophy in Mechanical and Manufacturing Engineering

Faculty of Mechanical and Manufacturing Engineering

Universiti Tun Hussien Onn Malaysia

JANUARY 2016

v

ACKNOWLEDGEMENT

This research thesis was made possible through the enormous help and great support

from everyone, including: my father, mother, wife, teachers and family. I would like

to dedicate my acknowledgment of gratitude toward the following significant

advisors and contributors:

First and foremost, I would like to thank Ir. Dr. Bambang Basuno for his endless

support and encouragement. He kindly read my paper and offered invaluable detailed

advices on grammar, organization, and the theme of the thesis.

Second, I would like to thank Assoc Prof. Dr. Zamri Bin Omar who read my thesis

and he provided me with valuable feedbacks and advice. In addition I would like to

thank all the other professors who have taught me about Mechanical Engineering and

Manufacturing in general and Aeronautics department in particular and helped me to

gain my doctoral degree.

Finally, I would like to sincerely thank my parents, wife, daughters, brothers, sisters,

friends, and colleagues who provided me with enormous support throughout my

journey. The product of this research work would not be possible without all of them.

vi

ABSTRACT

The present work focused on the development of computer software for flight

dynamic analysis and controlling the behavior of a fixed-wing aircraft. For a given

aircraft geometry, mass and inertia properties, and flight conditions, the software was

designed in such a way to start the estimation of aerodynamic characteristics,

trimmed flight, stability analysis through linearized approach as well as non-

linearized, and finally the control design of the flying behavior by using PID

controller method. The estimation of aerodynamic characteristics used the semi-

empirical aerodynamic method as used by Roskam. The trimmed flight conditions

were solved through trimmed flight equations iteratively. The linearized form of

flight dynamic equations in longitudinal as well as in lateral direction were solved

using the transfer function approach and state-space method. Whilst, non-linear flight

dynamic equations were solved using the Simulink. Three different PID controller

designs were developed to control the aircraft to follow a particular flight behavior.

The developed computer code was written in MATLAB programming language and

grouped into several modules. The validation results were carried out by comparing

the results of each module to other results available in the literature. The developed

computer code was applied to the case of five aircraft. They were named Cessna 182,

Cessna 310, Piper Cherokee PA 28-162, Learjet 24, and Cessna 620. The first three

aircraft were propeller piston engine aircraft. The fourth aircraft was a jet engine

aircraft while the fifth aircraft represented a turboprop aircraft. The flight dynamics

behavior motion which consisted of 22 flight variables were obtained by solving the

governing equation of flight after the aerodynamic characteristics data were

established and the trimmed fight conditions were solved. A particular flight variable

can be set up to have a particular behavior that follows the movement of the control

surface operations. Various control surface movements were simulated to ensure the

vii

designed PID controller was really providing a particular flight behavior. Through

the implementation of five types of aircraft models, the developed computer code

represents a useful tool for flight dynamic analysis and control design for a fixed-

wing aircraft.

viii

ABSTRAK

Kajian ini memfokuskan pembangunan perisian komputer untuk menganalisis

dinamik penerbangan dan kawalan tingkah laku pesawat bersayap tetap. Perisian

bagi sesuatu pesawat direka berdasarkan geometri, sifat seperti jisim dan inersia, dan

keadaan penerbangan. Perisian tersebut digunakan untuk membuat anggaran awal

bagi ciri-ciri aerodinamik, potongan sayap pesawat, analisis kestabilan melalui

pendekatan linear dan juga tak linear, disusuli dengan kawalan reka bentuk perilaku

penerbangan dengan menggunakan kaedah pengawal PID. Penganggaran ciri

aerodinamik dibuat dengan menggunakan kaedah aerodinamik separa empirikal

sebagaimana yang diguna pakai oleh Roskam. Keadaan potongan sayap pesawat

diselesaikan melalui persamaan potongan sayap pesawat secara lelaran. Persamaan

dinamik penerbangan berbentuk linear dalam arah membujur dan juga sisi

diselesaikan dengan menggunakan pendekatan fungsi pemindahan dan kaedah ruang

keadaan. Seterusnya, persamaan dinamik penerbangan tak linear diselesaikan dengan

menggunakan Simulink. Tiga buah reka bentuk pengawal PID yang berbeza

dibangunkan untuk mengawal pesawat supaya mengikut tingkah laku penerbangan

tertentu. Kod komputer yang dibangunkan ditulis dalam bahasa pengaturcaraan

MATLAB dan dikumpulkan dalam beberapa modul. Keputusan pengesahan

dijalankan dengan membandingkan keputusan setiap modul dengan keputusan yang

terdapat dalam kajian terdahulu. Kod komputer yang dibangunkan kemudiannya

diaplikasikan pada lima kes pesawat. Model pesawat tersebut dikenali sebagai

Cessna 182, Cessna 310, Piper Cherokee PA 28-162 , Learjet 24 dan Cessna 620.

Tiga pesawat pertama yang disenaraikan merupakan pesawat berenjin omboh

bebaling. Pesawat keempat merupakan pesawat berenjin jet, manakala pesawat

kelima mewakili pesawat berenjin turboprop. Tingkah laku gerakan dinamik

penerbangan yang terdiri daripada 22 pemboleh ubah penerbangan diperoleh dengan

ix

menyelesaikan persamaan penentu penerbangan setelah data berkenaan ciri

aerodinamik dibangunkan dan keadaan potongan sayap pesawat diselesaikan.

Pemboleh ubah penerbangan tertentu boleh ditetapkan dengan tingkah laku tertentu

mengikut pergerakan operasi permukaan kawalan. Pelbagai pergerakan permukaan

kawalan disimulasikan untuk memastikan pengawal PID yang direka benar-benar

menepati tingkah laku penerbangan tertentu. Melalui pelaksanaan lima jenis model

pesawat, kod komputer yang dibangunkan menjadi alat yang berguna untuk

menganalisis dinamik penerbangan dan reka bentuk kawalan bagi pesawat bersayap

tetap.

x

CONTENTS

TITLE iii

ACKNOWLEDGEMENTS v

ABSTRACT vi

CONTENTS x

LIST OF FIGURES xiv

LIST OF TABLES xxii

LIST OF SYMBOLS xxv

LIST OF APPENDIXES xxvii

CHAPTER 1 INTRODUCTION 1

1.1 Background of study 1

1.2 Problem statement 4

1.3 Objectives 5

1.4 Scope of work 6

1.5 Research methodology 9

1.6 The results of the research work 9

1.7 Organization of the thesis 10

CHAPTER 2 LITERATURE REVIEW 12

2.1 Aircraft flight dynamics 12

2.2 The governing equation of flight motions 15

2.3 Simplified forms of the governing equation of

flight motion 25

2.3.1 Simplified longitudinal direction

form of equations 26

2.3.2 Simplified lateral-direction form of

xi

equations 29

2.4 The trim condition governing equation 30

2.5 Flying and handing qualities 33

2.5.1 Longitudinal flying qualities 34

2.5.1.1 Static response 34

2.5.1.2 Phugoid response 34

2.5.1.3 Short period response 34

2.5.2 Lateral flying qualities 35

2.5.2.1 Rolling motion 35

2.5.2.2 Spiral stability 36

2.5.2.3 Lateral directional oscillations-Dutch

roll

37

2.6 Compression between linear and non-linear

equation

37

2.7 An overview of the solution of the

governing equation for flight motion

38

2.7.1 Euler’s method 40

2.7.2 The second order Runge-Kutta method 41

2.7.3 The fourth order Runge-Kutta method 41

2.7.4 Adams-Bashforth method of order

three

41

2.8 An overview on the manner of controlling

the aircraft movement

42

2.9 Aircraft controller design 44

2.10 The flight dynamics software 46

2.11 The flight dynamics software development in

the past

48

CHAPTER 3 METHODOLOGY 51

3.1 Introduction 51

3.2 The aerodynamics characteristics estimation 52

3.3 The aircraft dimensional stability and control

derivatives

57

3.4 The method of solving the equation of flight

xii

motion 59

3.4.1 The solution of flight motion based on

state-space approach

59

3.4.2 The solution of flight motion based on

transfer functions approach

62

3.5 The classical PID control design estimation 70

3.5.1 The basic idea of the control system

design

72

3.5.2 The technique in developing PID

controller

76

3.6 Non-linear simulation aircraft behaviour 80

CHAPTER 4 RESULTS AND DISCUSSION 82

4.1 Introduction 82

4.2 Longitudinal and lateral directional dynamic

stability behaviours

82

4.2.1 Input data 85

4.2.2 The output and the results of the

longitudinal and lateral directional

dynamic stability behaviours

88

4.2.2.1 The stability derivatives of longitudinal

and lateral directions

88

4.2.2.2 The solution for flight motion 89

4.2.3 Time history and stability behavior of

aircrafts

97

4.2.3.1 Time history or stability behavior in the

longitudinal direction

100

4.2.3.2 Time history and stability behavior in

the lateral direction

111

4.3 Controller design 138

4.3.1 The results of Cessna 182 controller

design

140

4.3.1.1 The longitudinal direction controller

design

140

xiii

4.3.1.2 The lateral direction controller design 142

4.3.2 Time history of Cessna 182 aircraft 152

4.3.2.1 Time history of pitch angle controller 153

4.3.2.2 Time history of roll angle controller 158

4.3.2.3 Time history of yaw angle controller 168

4.4 The non-linear simulation aircraft behaviour 182

4.4.1 The geometry and the overall

performance data of Piper Cherokee PA

28-161 Warrior

182

4.4.2 The evaluation of the aerodynamics

characteristics of the Piper Cherokee

PA 28-161

188

4.4.3 The Simulink diagram for the Piper

Cherokee PA 28-161

191

4.4.4 The estimation of flight dynamics

behavior with Simulink

194

4.4.5 Comparison between non-linear and

linear models

209

4.5 Summary 214

CHAPTER 5 CONCLUSION AND FUTURE WORK 217

5.1 Introduction 217

5.2 Conclusion 217

5.3 Contribution and the novelty of research 218

5.4 Future work 219

REFERENCES 221

APPENDIX 231

xiv

LIST OF FIGURES

1.1 The automatic and the manual flight control loops 3

1.2 Flight dynamics analysis and design procedure 7

2.1 The locations of the origin of the coordinate systems 16

2.2 The orientation of body axis, stability axis, and wind

axis

18

2.3 Body axis coordinate system 18

2.4a Definitions of aerodynamic forces, thrust, and

acceleration gravitation in body axis coordinate

19

2.4b Definitions of moments, linear, and angular velocity

in body axis coordinate system

19

2.5 Flowchart for non-linear simulation steps 40

2.6 The conventional aircraft 43

2.7 Unity feedback system 45

3.1 A simplified body diagram of the mass, spring and

damper

73

3.2 The block diagram of the vehicle as an open loop

system

73

3.3 The displacement response of mass, spring and

damper as an open loop system due to a unit step

function

74

3.4 The control system with a unity feedback 75

3.5 The displacement response of mass, spring and

damper as a closed-loop system due to a unit step

function

75

3.6 A closed loop system of the dynamic vehicle’s

xv

equation and PID controller 77

3.7 The step response of Method I controller approach 78

3.8 The step response of Method II controller approach 79

3.9 The step response of PID SISO controller approach 79

4.1 Two types of propeller driven aircrafts 84

4.2 Two types of turbo driven aircrafts 84

4.3 MATLAB start menu for the direction analysis 84

4.4 MATLAB start menu for the aircraft model analysis 85

4.5a MATLAB start menu for longitudinal direction 99

4.5b MATLAB start menu to select the lateral effect

control surfaces

99

4.6a Longitudinal direction responses following elevator

single doublet impulse maneuvers of Cessna 182

100

4.6b Longitudinal direction responses following elevator


101

4.6c Longitudinal direction responses following elevator

single doublet impulse maneuvers of Learjet 24

101

4.6d Longitudinal direction responses following elevator


102


multiple doublets impulse maneuvers of Cessna 182

103



104


multiple doublets impulse maneuvers of Learjet 24

105



105


single doublet maneuvers of Cessna 182

106



106


single doublet maneuvers of Learjet 24

107

xvi



107


multiple doublets maneuvers of Cessna 182

108



108


multiple doublets maneuvers of Learjet 24

109



109

4.10a Lateral direction responses following aileron single

duplet impulse maneuvers of Cessna 182

112

4.10b Lateral direction responses following aileron single


112

4.10c Lateral direction responses following aileron single

duplet impulse maneuvers of Learjet 24

113

4.10d Lateral direction responses following aileron single


113

4.11a Figure 4.11a: Lateral direction responses following

aileron multiple doublets impulse maneuvers of

Cessna 180

115

4.11b Lateral direction responses following aileron multiple

doublets impulse maneuvers of Cessna 310

115

4.11c Lateral direction responses following aileron multiple

doublets impulse maneuvers of Learjet 24

116

4.11d Lateral direction responses following aileron multiple

doublets impulse maneuvers of Cessna 620

116

4.12a Lateral direction responses following aileron single

doublet maneuvers of Cessna 182

117

4.12b Lateral direction responses following aileron single


117

4.12c Lateral direction responses following aileron single

doublet maneuvers of Learjet 24

118

xvii

4.12d Lateral direction responses following aileron single


118

4.13a Lateral direction responses following aileron multiple

doublets maneuvers of Cessna 182

119

4.13b Lateral direction responses following aileron multiple


119

4.13c Lateral direction responses following aileron multiple

doublets maneuvers of Learjet 24

120

4.13d Lateral direction responses following aileron multiple


120

4.14a Lateral stability behavior of Cessna 182 following

rudder single duplet impulse maneuvers

123

4.14b Lateral stability behavior of Cessna 310 following


123

4.14c Lateral stability behavior of Learjet 24 following


124

4.14d Lateral stability behavior of Cessna 620 following


124


rudder multiple doublets impulse maneuvers

125



125



126



126


rudder single doublet maneuvers

127



127



128


xviii

rudder single doublet maneuvers 128


rudder multiple doublets maneuvers

129



129



130

4.17d Lateral stability behavior of Cessna 620 aircraft

following rudder multiple doublets maneuvers

130

4.18 The aircraft elevator deflection as pulse 132

4.19a Aircraft velocity stability behavior of four aircraft

models following the elevator deflection

133

4.19b Angle of attack stability behavior of four aircraft

models following the elevator deflection

133

4.19c Pitch angle stability behavior of four aircraft models

following the elevator deflection

134

4.20a Side slip angle stability behavior of four aircraft

models following the aileron deflection

135

4.20b Roll angle stability behavior of four aircraft models

following the aileron deflection

135

4.20c Yaw angle stability behavior of four aircraft models

following the aileron deflection

136

4.21a Side slip angle stability behavior of four aircraft

models following the rudder deflection

136

4.21b Roll angle stability behavior of four aircraft models

following the rudder deflection

137

4.21c Yaw angle stability behavior of four aircraft models

following the rudder deflection

137

4.22 The elevator step response from method I and method

II controller approach

141

4.23 The elevator step response from SISO controller

approach

141

4.24 The aileron step response from method I control

xix

design approach 143

4. 25 The aileron step response with method II control

design approach

144

4. 26 The aileron step response from SISO control design

approach

144

4. 27 The rudder step response from method I control

design approach

146

4. 28 The rudder step response from method II control

design approach

146

4. 29 The rudder step response from SISO control design

approach

146

4.30 The aileron step response from method I control

design approach

148

4. 31 The aileron step response from method II control

design approach

148

4. 32 The aileron step response from SISO control design

approach

149

4. 33 The rudder step response from method I control

design approach

150

4. 34 The rudder step response from method II control

design approach

151

4. 35 The rudder step response from SISO control design

approach

151

4. 36 The various manners of the elevator defection 153

4. 37 Pitch angle behaviors due to the elevator of single

doublet impulse

154

4. 38 Pitch angle controller behavior due to multiple

doublet impulses

155

4. 39 Pitch angle controller behavior due to elevator single

doublet

157

4. 40 Pitch angle controller behavior due to elevator

multiple doublets

158

4.41 The aileron control surfaces deflection 159

xx

4.42 The rudder control surfaces deflection 159

4.43 The stability behavior for Cessna 182 before and after

applying the control design approach (Aileron)

160


applying the control design approach (Rudder)

161



162



163



164



165



166



167



169



170



171



172



173



174



175



176

xxi

4.59 The elevator control surface setting at -2.0 degree 177

4.60 The roll angle response with aileron set at -2.0o 178

4.61 The roll angle response with rudder set at -2.0o 179

4.62 The yaw angle response with aileron set at -2.0o 180

4.63 The yaw angle response with rudder set at -2.0o 181

4.64 Three side views drawing of Piper Cherokee PA 28-

161 aircraft

183

4.65 Aircraft simulation with steady state winds 191

4.66 The velocity in x-direction u as function of time at a

trimmed flight condition.

197

4.67 The angle of attack as function of time at a trimmed

flight condition.

197

4.68 The velocity in x-direction (u) as function of time 198

4.69 The velocity in y-direction (v) as function of time 200

4.70 The velocity in z-direction (w) as function of time 201

4.71 The pitch angle θ as function of time 202

4.72 The yaw angle ψ as function of time 203

4.73 The roll angle ϕ as function of time 204

4.74 Angle of attack α as function of time 205

4.75 Side slip angle β as function of time 207

4.76 Flight bath angle γ as function of time 208

4.77 The angle of attack α comparison 209

4.78 The sideslip angle β comparison 210

4.79 Pitch angle comparison 211

4.80 The yaw angle ψ comparison 212

4.81 The roll angle ϕ comparison 213

xxii

LIST OF TABLES

2.1 The definitions of notations in describing forces,

moment, and velocity components

20

2.2 Phugoid mode flying qualities 34

2.3 Short period mode damping ratio specification 35

2.4 Short period mode damping ratio specification 35

2.5 Bank angle specification 36

2.6 Spiral mode stability specification 37

2.7 Dutch roll mode specification 37

3.1 The required aerodynamics characteristics in solving

flight dynamic equation

53

3.2 The Geometry and the basic aerodynamic data needed

in estimation of the aircraft aerodynamic

characteristics

54

3.3 Longitudinal dimensional stability and control

derivatives

58

3.4 Lateral dimensional stability and control derivatives 58

3.5 The values of the gains 79

4.1 Aircraft geometric data 85

4.2 Aircraft flight condition data 86

4.3 Aircraft mass and inertia data 86

4.4 Aircraft longitudinal steady state input data 86

4.5 Aircraft stability derivative data 86

4.6 Aircraft control derivatives data 86

4.7 The longitudinal direction stability derivative

calculations

88

xxiii

4.8 The lateral direction stability derivatives calculations 89

4.9 Setting up matrix A for longitudinal direction 90

4.10 Setting up matrix B for longitudinal direction 90

4.11 Setting up matrix C for longitudinal direction 91

4.12 Setting up matrix A for lateral direction 92

4.13 Setting up matrix B for lateral direction 92

4.14 Setting up matrix E for lateral direction 94

4.15 Longitudinal direction transfer function in terms of u 95

4.16 Longitudinal direction transfer function in terms of α 95

4.17 The longitudinal transfer function in terms of 96

4.18 Lateral direction transfer function in terms of β 96

4.19 Lateral direction transfer function in terms of ϕ 96

4.20 Lateral direction transfer function in terms of ψ 97

4.21 The maximum and minimum values of α, U, and θ

related to the elevator maneuvers

110

4.22 The expected time to reach the steady state behavior

related to the elevator maneuvers (Sec)

110

4.23 The maximum and minimum values of β, ϕ, and ψ

with aileron maneuver

121


related to the aileron maneuvers (Sec)

121

4.25 The maximum and minimum values of changes in β,

ϕ, and ψ with rudder maneuver

131


related to the rudder maneuvers (Sec)

131

4.27 Gains value of the controller design approaches 142

4.28 Pitch angle controller transfer functions 142

4.29 The values of the gain 145

4.30 Roll angle controller transfer function due to the

aileron maneuvers

145


4.32 Roll angle controller transfer function due to the

rudder maneuvers

147

xxiv


4.34 Yaw angle controller transfer function due to the

aileron maneuvers

150


4.36 Yaw angle controller transfer function due to the

rudder maneuvers

152

4.37 The geometry and the aerodynamic data of Piper

Cherokee PA 28-161 Warrior aircraft

183

4.38 The aircraft geometry and the aerodynamic data 185

4.39 The mass and the moment of inertia Piper Cherokee

28-161 aircraft

189

4.40 The aircraft solution at trim condition 189

4.41 The solution of the aircraft aerodynamics characters 189

4.42 MATLAB flight parameter outputs 192

4.43 The variable state parameters 193

4.44 The scenarios of control surfaces and the engine thrust

during the aircraft in flight

194

4.45 The control surfaces and the engine thrust setting at

trim condition

195

4.46 The behavior of the flight parameters 195

4.47 Responses of the three controller design approaches 215

xxv

LIST OF SYMBOLS

U - X-direction trim velocity

V - Y-direction trim velocity

W - Z-direction trim velocity

u - Velocity in X-direction

v - Velocity in Y-direction

- Total velocity

w - Velocity in Z-direction

- Pitch angle

Ψ - Yaw angle

ϕ - Roll angle

α - Angle of attack

β - Side slip angle

γ - Flight path angle.

p - Roll rate

q - Pitch rate

r - Yaw rate

L - Rolling moment

M - Pitching moment

N - Yawing moment

Ixx - Moment of inertia about X-axis

Iyy - Moment of inertia about Y-axis

Izz - Moment of inertia about Z-axis

T - Thrust

Cx - The aircraft axial force coefficient

CY - The aircraft side force coefficient

xxvi

Cz - The aircraft normal force coefficient

C - The aircraft rolling moment coefficient

Cm - The aircraft pitching moment coefficient

Cn - The aircraft yawing moment coefficient

N - The engine rotational speed in radian

Ixe - The engine moment of inertia of the rotating mass

- The dynamic pressure is equal to

C.G - Aircraft’s center of gravity

S - The wing area reference

- Horizontal tail area

- Wing incidence angle

- The wing span.

- The air density

CL - Aircraft lift coefficient

CD - Aircraft drag coefficient

- Aircraft mass

CY - Aircraft side force coefficient

- Total velocity

- Elevator deflection angle

- Aileron deflection angle

- Rudder deflection angle

- Aircraft engine thrust

- Time

CA - Axial force coefficient

CN - Normal force coefficient

- Wing twist angle

- Distance in X-direction

- Distance in y-direction

- Flight altitude

- Aircraft fuselage average width

M - Mach number

xxvii

LIST OF APPENDIXES

APPENDIX TITLE PAGE

A The aerodynamic characteristics estimation 231

B Examples of how the figures are being

implemented in the software

285

C List of publications during the research work 289

CHAPTER 1

INTRODUCTION

1.1 Background of study

The system that is used to control the aircraft when flying is called flight control

system (FCS) [1]. The flight control system (FCS) deflects the aircraft control

surface to control the aircraft. This system can be operated in different manners; the

first controls the aircraft, which can be done by human [2], while the second is

controlled by computer (AFCS), which is easier, faster and more efficient [3].

In the early days, in order to give the necessary control surface deflections to control

the aircraft, the flight control system (FCS) had been operated mechanical by using

cables and pulleys [4]. However, the new technologies have brought with them the

fly-by-wire [5]. In this system, electrical signals are sent to the control surfaces to

make the required control surface deflections. The signals are sent to the aircraft

control surface by using a computer (FC/FCC) [1].

Moreover, there are several advantages in applying the automatic flight control

system, such as: i) the computer has higher reaction velocity compared to the pilot,

ii) it is not subject to concentration loss and fatigue, and iii) the computer can more

accurately detect the state the aircraft is in (computers can handle huge amounts of

data better and also need not read any small indicator to identify, for example, the

2

velocity or the height of the aircraft). However, there is a downside to the (AFCS); it

is only designed for a certain flight envelope. It means, when the aircraft is outside

the flight envelope, the system cannot operate the aircraft anymore. Besides, the

Automatic flight control system can be categorized into four different types based

on the level of difficulty of the task [1].

(a) (AFCS) as the trimmed flight-holding system.

(b) (AFCS) as the stability augmentation system.

(c) (AFCS) as the command augmentation system.

(d) (AFCS) as the stability maker and command optimization.

The basic elements in the control information loop are the plant (the

controlled system) and the controller. For an aircraft, the controlled system

consists of control apparatus, control surface, and the aircraft. Meanwhile, the

controller part consists of three subsystems, namely: i) aircraft motion sensor, ii)

aircraft motion information processor and iii) control command generator. Figure 1.1

shows the functional diagram of the manual and the automatic control system

for an aircraft. The diagram shows that the primary interface between the

controlled and controller systems can be divided into two parts: i) front-end

interface, which is the aircraft sensory system and ii) back-end interface, which is

the control command generator [1] [6].

3

Figure 1.1: The automatic and the manual flight control loops [1]

Apart from that, the flight control system of an aircraft FCS generally consists of

three important parts. These three parts are: i) the stability augmentation system SAS

that augments the stability of the aircraft. This is done by using the control surfaces

to make the aircraft more stable. A good example of a part of the SAS is the phugoid

damper (similarly, the yaw damper). A phugoid damper uses the elevator to reduce

the effects of the phugoid: it damps it. The SAS is always on when the aircraft is

flying. Without it, the aircraft is less stable or possibly even unstable, ii) the control

augmentation system CAS is a helpful tool for the pilot to control the aircraft. For

example, the pilot can tell the CAS to keep the current heading. The CAS then

follows this command. With this, the pilot does not continually have to compensate

Controller motion Aircraft motion

HUMAN CONTROLLER

AUTOMATIC CONTROLLER

Command generator Information processor Motion sensor

Pilot’s hands, feet

voices Pilot’s brain Cockpit display,

window view, pilot’s

eyes and ears

Actuator FCC RLG, Aces, Pilot

Command generator Information processor Fluids dynamics/

inertial sensors

4

for heading changes himself, and iii) finally, the automatic control system takes

things one step further. It automatically controls the aircraft. It does this by

calculating (for example) the roll angles of the aircraft that are required to stay on a

given flight path. It then makes sure that these roll angles are achieved. In this way,

the airplane is controlled automatically.

There are important differences between the above three systems. First, the SAS is

always on, while the other two systems are only on when the pilot needs them.

Second, there is the matter of reversibility. In the CAS and the automatic control, the

pilot feels the actions that are performed by the computer. In other words, when the

computer decides to move a control panel, the stick / pedals of the pilot move along.

This makes these systems reversible. The SAS, on the other hand, is not reversible:

the pilot does not receive any feedback. The reason for this is simple. If the pilot

receives feedback [7], he would only feel the annoying vibrations. This is of course

undesirable. Therefore, in order to develop such flight control system, the knowledge

of flight dynamic behavior of the aircraft is required [8] [9]. This aircraft flight

dynamic behavior can be determined by solving the governing equation of flight

motion [10] [11]. The aerodynamics forces and the moment act as the input to the

governing equation of flight motion that enables the evaluation of the flight

dynamics behavior to be done at various control surfaces settings. Besides, with the

solution of flight dynamics equation, one can design an appropriate controller, if the

aircraft is decided to have a particular flight behavior.

1.2 Problem statement

The flight dynamics behavior of most aircrafts can be controlled through control

surfaces and engine thrust. With the presence of pilot in the cockpit, the movement

of the aircraft is completely under the control of the pilot. Besides, a pilot can operate

the control surface or adjust the engine thrust in order to keep the aircraft flying as

expected at any time. Nonetheless, unfortunately, the way an aircraft behaves

depends on the flight conditions. On top of that, the flight condition is strongly

influenced by its atmospheric environment. As a result, the work load of the pilot is

increased if the atmospherics environments always change. Hence, the aircraft flight

control system has been introduced to reduce the work load of the pilot in controlling

5

the aircraft movement. Basically, the behavior of the aircraft can be identified and

controlled if all flight variables related to the flight behavior are evaluated in respect

to time. Strictly speaking, 21 flight variables are available to describe the flight

behavior of an aircraft during flight [12]. These 21 flight variables are the three

components of velocity at trim (U, V, W), the three components at any instance flight

(u, v, w), the three aptitude angles (, Ψ, ϕ), the three angle of velocity vectors with

respect to the body axis coordinate system (α, β, γ), the aircraft position with respect

to the inertia reference (x, y, z), while the other six parameters are related to the

derivatives quantities in translational motion and rotational motion [13]. These flight

variables are all related to each other through a number of equations known as the

governing equations of flight motion and they belong to the class of non-linear time-

varying ordinary differential equation. Hence, the ability to solve the governing

equations of flight motion is important since it offers the capability to analyze the

flight dynamics behavior for any given type of aircraft. Therefore, the combination

with the control theory offers the possibility to define the behavior of an aircraft

during flight.

1.3 Objectives

The purpose of the present study is to develop the computer code for allowing user to

carry out flight dynamic analysis and flight control design. The input data for the

developed computer code are: i) the aircraft geometries, ii) mass and moments of

inertia properties of the aircraft and iii) flight conditions data. Hence, the present

work involves:

(a) The development of estimation for the primary aerodynamic characteristics

and the aerodynamic derivatives.

(b) The development of the procedure for solving trimmed flight.

(c) The development of the manners of solving aircraft flight motion in

longitudinal and lateral directions in their linear as well as in their nonlinear

form.

(d) The capability to be used as a controller design to allow the aircraft to have a

particular flight behavior with a PID controller.

6

1.4 Scope of work

The present work focused on the development of computer code for the flight

dynamic analysis and flight controller design of the fixed wing flying vehicle. Such

work will involve three scope of works namely i) aerodynamic characteristic

estimation, ii) the solution of flight dynamic equation of motion and iii) flight

controller design. These three scopes of works are carried out sequentially as shown

in the flow diagram as shown Figure 1.2 and can be explained as follows

(a) The first scope of aerodynamics characteristics will concern with the

aerodynamic estimation by use a semi empirical aerodynamics estimation

follows the method adopted from DATCOM [14], Ref [15] and Ref [16].

(b) The second scope concerned with deriving the governing equation of flight

motion in general form, trimmed flight, and their linearized form in

longitudinal, lateral and directional flight direction. In this scope of work will

involve in manner how to solve the trimmed flight equation, longitudinal

flight equation, lateral and directional flight equation and the nonlinear flight

equation by use of Simulink.

(c) The third scope related in the manner how to control flight behavior through

the operation of the three control surfaces (elevator, aileron and rudder) and

the engine thrust by use of PID controller scheme.

(d) The scope of work as stated in a, b and c will be converted into computer

code written in MATLAB programming language.

The developed software as stated in d was applied to five fixed-wing subsonic

aircraft models, namely are: Cessna 182 [17], Cessna 310 [18], Piper Cherokee 28-

161 [19], Learjet 24 [20] and Cessna 620 aircrafts [21]. The first three aircrafts

belonged to the class of propeller piston engine aircraft, while the last two aircrafts

were a turbojet and a turboprop engine type of aircraft respectively.

7

Software Required

Input Data

Mass and Moments of Inertia

Aircraft mass. Moment of inertia z-axis.

Moment of inertia x-axis. Moment of inertia xz-axis.

Moment of inertia y-axis.

Estimates Primary Aerodynamic Characteristics

CLo, Cmo, CLα,Cmα

, CLq, Cmq, CLα , Cmα

, Cyβ, Clβ, Cnβ , Cyp, ClP, Cnp,

Cyr, Clr, Cnr, CLδE, CmδE

, CyδA , ClδA

, CnδA, CyδR

, CnδR, ClδR

.

Perform believability

Coefficient Typically Coefficient Typically Coefficient Typically

Weight + Ixx + Izz +

Mass + Iyy + Ixz +

Ac of gravity 32.2 Wing span + Wing area +

Mean chord + CDmin 0.02 to 0.03 CDmin(point)

0.0

CLo 0.0 to 0.50 CLα 3.0 to 6.0 CLδ𝐸 0.3 to 0.9

CLα 1.0 to 8.0 CLq 4.0 to 10.0 Cyβ -0.3 to -1.0

CyδA <5.0 % of CyδR

CyδR 0.1 to 0.2 Cyp 0.0 to - 0.3

Cyr 0 .2 to 0.5 Clβ - 0.09 to - 0.30 ClδA 0.05 to 0.2

ClδR 0.0 to 0.02 ClP - 0.30 to - 0.6 Clr 0.07 to 0.20

Cmo - 0.056358 Cmα

- CmδE - 1.0 to – 2.0

Cmα – 3.0 to – 15.0 Cmq

- 11 to – 30 Cnβ 0.06 to 0.2

CnδA <10 % of CnδR

CnδR -0.06 to -0.12 Cnp -0.02 to -0.2

Cnr - 0.09 to -0.4

Yes

Start

Given Aircraft Configurations

Wing Surface Area. Mean Aerodynamic chord.

Wing Span. Other Geometric data.

Given Aircraft Flight Conditions

Flight altitude. True airspeed.

Mach number. Dynamic pressure.

Location of CG in % MAC. Steady-state angle of attack.

No

Dimensional Stability and Control Derivatives

Xu, Xα, XTu , XδE , Mα,, Mu, MTα, MTu

, Mα , Mq, MδE, Zu, Zα, Zα , Zq, ZδE,

Lβ, Lp, Lr, LδA, LδR, Nβ, NTβ, Np, Nr, NδA, NδR, Yβ, Yp, Yr, YδA, YδR.

Aero

dy

na

mic

Evalu

ati

on

s

8

Figure 1.2: Flight dynamics analysis and design procedure

Con

trol

Des

ign

Controller Flight Dynamics Behavior

Roll

Control

Yaw

Control

Pitch

Control

END

Method

I

Method

II

Simulink

Approach

State Space

Approach Transfer Function

Approach

Check via Routh - Hurwitz

Non-Linear Simulation Linear Simulation

Continued

Longitudinal Analysis

Lateral Analysis

Both

Yes

No

Transfer Function and

State-Space Approach

Comparison.

Linear and Non-Linear

Simulation Comparison.

Flight Dynamics Behavior

PID

SISO Control

Design

Control Design

PID

Conventional

Control Design

Fli

gh

t D

yn

amic

Eval

uat

ion

s

Trim Flight Analysis

Estimate trim lift coefficient. Estimate trim drag coefficient.

Estimate trim angle of attack. Estimate the trim angle of elevator.

Estimate the engine thrust at trim. Estimate the pitching moment

coefficient at trim.

9

1.5 Research methodology

In order to develop the capability in evaluating the flight dynamics in aircraft

behavior and the ability to design a controllable flight behavior upon a particular

flight variable, the proposed research methodology comprised of the following items:

(i) Literature research.

(ii) Procurement and commissioning of language program software.

(iii) Collecting aircraft geometry data and estimating the aerodynamic

characteristics needed in the equation of aircraft flight motion.

(iv) Solving the governing equation at trimmed flight condition.

(v) Solving the governing equation of flight motion in their linearized form.

(vi) Solving the governing equation of flight motion in non-linear aircraft model

by using a Simulink

(vii) Controller design under longitudinal flight mode.

(viii) Controller design under lateral and directional flight modes.

The validation of each scope work in view of aerodynamics estimation are carried by

comparing their result with the result provided by Ref [15] and [16], while in the

relationship with the solution of equation of the flight motion are validated with the

result provided by Ref [22]. In the control design with result adopted from Ref [23].

1.6 The results of the research work

The output of this research work had been in the form of software, which allows one

to evaluate the flight dynamic behavior and the controlling flight behavior for a

particular flight parameter. The software possessed the following capabilities:

(a) For a given aircraft configuration and flight condition, the software produced

primary and derivatives aerodynamics characteristics.

(b) In addition to the given mass and the moment of inertia, the software

produced the trimmed flight condition.

(c) Beginning with trim condition, the software evaluated the longitudinal and

the lateral – directional aircraft behavior based on linear flight equation.

10

(d) Beginning with trim condition, the software evaluated all flight parameters

that described the overall flight behavior by solving the non-linear governing

equation of the flight motion.

(e) For a particular flight parameter, the software had been able to be used as a

design tool for longitudinal or lateral–directional flight motion.

Considering the capabilities of the developed computer code as listed above, this

software may very useful in the development of the Unmanned Aerial Vehicle

(UAV) systems which currently had been attracted by almost all countries around

the World to have them. This system can be developed from the Remotely Controller

Aircraft (R.C Aircraft) in which such kind aircraft models are easily obtained in the

market.

1.7 Organization of the thesis

This thesis is divided into five chapters. The first chapter describes the introduction

chapter, including the problem statement, purpose objectives, scope of work, the

research methodology, the results of the research work and the organization of the

thesis.

The second chapter provides the literature review; this chapter is divided into eleven

sections. The first and second sections discuss the aircraft flight dynamics in general

and its governing equation of flight motion. The third section discusses the simplified

forms of the governing equation of flight motion in the form of equation known as

longitudinal equation and lateral-directional equation. The fourth section discusses

the governing equation of flight motion at trim condition. The fifth section

discusses the flying and handing quantities in view of longitudinal motion as

well as in the lateral-directional motion. The comparison between linear and

non-linear equation is discussed in the sixth section. Meanwhile, the seventh

section provides an overview in manner of the governing equation of flight

motion to be solved numerically by the use of numerical integration methods. The

eighth section describes an overview on controlling the aircraft movement

through the control surfaces that are used to influence the aircraft motions. The

ninth section discusses the aircraft control design and it reviews the PID

controller design. Finally, the last two sections discuss the flight dynamic

11

software; the tenth section describes the flight dynamic software in general and

the section eleven provides the examples of flight dynamic software that had

been developed in the past.

Chapter three of the present thesis describes how the flight equations of motions are

solved and the manner of controlling the aircraft movement. Hence, this chapter

includes the reviews on the research methodology that will be carried out,

aerodynamic characteristics estimations, and also the manner of the dimensional

stability and control derivatives to be determined. In addition to this, the solution of

flight motion based on transfer function, state space formulation and the three PID

controller design methods are discussed. Besides that, the non-linear aircraft

simulations are also presented in this chapter.

The results and discussions are presented in chapter four. It starts from describing the

aircrafts geometry, flight condition and mass and moments of inertia data of the

aircraft under investigation. This chapter is divided into three sections. The first

section is related to the longitudinal and lateral directional dynamic stability analysis

with or without control surfaces in operation. Here, for the given aircraft data, one

can evaluate how the flight variables such as aircraft speed u, angle of attack α, pitch

angle θ, change with respect to time in corresponding to the longitudinal motion.

Flight variables are in terms of the side slip angle β, the Euler roll angle ϕ and the

Euler yaw angle ψ with respect to time in relation with lateral motion. These various

flight variables are evaluated for different aircraft models. The second section

discusses the controller design. It reviews the PID controller design applied to a light

propeller aircraft model Cessna 182. The third section discusses the implementation

of the non-linear aircraft simulation developed by using Matlab Simulink. The

nonlinear aircraft simulation is applied to a propeller aircraft Piper Cherokee PA 28-

162. The last chapter which is chapter five provides conclusions and

recommendations for future research and references. This thesis is also accompanied

with three appendixes, A, B and C. Appendix A contains the manner of how

aerodynamics characteristics can be estimated based on the geometry data of the

aircraft. Appendix B describes the examples of how to implement the semi-empirical

aerodynamics method into the Matlab software. Appendix C describes the list of

publication that had been published during the time that the research work was

conducted.

CHAPTER 2

LITERATURE REVIEW

2.1 Aircraft flight dynamics

Flight dynamics is a branch of basic science of aeronautics that studies the flight

behaviors of the aircraft during the flight in an atmosphere. This field, which is

studied together with aerodynamics, aircraft structure and propulsion, plays an

important role in the activities of designing a new aircraft [24]. The flight dynamics,

as well as aerodynamics, represents a larger field of study. As a result, this field of

study is normally split into 5 fields, as suggested by Hull [25]. They are i) trajectory

analysis (performance), ii) stability and control, iii) aircraft sizing, iv) simulation and

v) flight testing. Besides, Etkin [26] provides some examples of the main type of

flight dynamics problems that occur in engineering practices, which are:

(a) Calculation of quantities performance, such as maximum flight speed, flight

altitude, flight endurance, fuel consumption, takeoff, and landing distance.

(b) Calculation trajectories, such as lunch, reentry, orbit, and landing.

(c) Stability of motion.

(d) Response of the vehicle due to control activation and due to propulsive

change.

(e) Response to atmospheric turbulence and how to control it.

13

(f) Aero elastic oscillation (flutter).

(g) Assessment of human–pilot/machine combination (handling qualities).

Considering the types of problems mentioned above, the first two types of the

problems can be categories as flight performance analysis. The scope of work

involved in this analysis is quite a formidable task, as asserted by Ojha [27] that a

performance analysis needs to be carried out for almost all phases of a flight, starting

from takeoff, climb, cruise, turn, descent, and finally landing. In each phase of a

flight, the aircraft may experience engine failure, so the aircraft flies at an unpowered

flight or at a gliding flight condition. In addition to this, the performance analysis

depends on the type of propulsive unit used with the specific types of aircraft.

On top of that, referring to the phases of aircraft flight at takes off, the speed of the

aircraft is quite low and in order to leave the ground, the aircraft has to be set in such

manner to generate lift greater than its weight. In cruise, the aircraft operates at a

constant speed and constant lift. Finally, when the aircraft lands, it needs to reduce its

speed without losing too much lift. Hence, the issue for control of the aircraft is how,

at a given speed, the incidence angle can be maintained. At take-off or landing, in

order to change the incidence of the wing, the aircraft will be rotated in nose up or

nose down. The aircraft control, in this respect, will study how the pilot can fix the

relationship between speed and incidence without increasing or losing too much lift.

In other cases, when an aircraft is in a cruise flight, in which the aircraft is at constant

speed and incidence while the control surfaces are kept at a fixed setting, here, the

aircraft stability needs to be identified in order to evaluate how an aircraft responds

to small disturbances in flight, as well as how it can be designed so that it can remain

at a fixed incidence and speed without overworking the pilot. Basically, there are

various improvements in other areas involved in designing a new aircraft; whether in

the point of aerodynamics, aircraft structure or propulsion system, as well as avionic

and aircraft systems. Compared to other transportation vehicles, aircraft has been

known as a product of high technology and cost, and also highly competitive

amongst the aircraft manufacturer industry. Although the aircraft manufacturer is

currently dominated by the European and the USA, their revenue is formidable. The

total commercial aircraft industry revenue for 1997 was approximately $ 60.0 billion,

of which $ 40.0 billion was attributable to U.S producers. As a result, the U.S aircraft

manufacturers contributed among the largest net exports to U.S governments, with

trade surpluses averaging about $ 25.0 billion annually over the early 1990s [28]. In

14

overall, the aerospace industry, which includes military aircrafts and missiles, based

on the results of market survey conducted by Boeing aircraft, manufacturer provides

the revenue for aerospace industry from 2010 to 2020 at an amount of $ 3.60 trillion

or yearly at around $ 180 billion [29]. Besides, the driving force in utilizing the flight

dynamics knowledge may come from the development of aircraft for fulfilling the

military purposes. Moreover, the ability to fly at a high angle of attack or at a higher

speed and better maneuverability solve a lot of issues related to flight dynamics. In

the past, building an aircraft with good stability characteristics that usually ensure

good flying qualities can only be achieved with good aerodynamic design.

Furthermore, in line with the development of automatic flight control systems

(AFCS), provision of good flying qualities is no longer a guaranteed product in good

aerodynamic design and good stability characteristics. This suggests that the study

pertaining to flight dynamics should be presented in a new format; from conventional

flight dynamics study to modern flight dynamics study. In this format, the modern

flight dynamics is concerned not only with the dynamics, stability, and control of the

basic airframe, but also with, sometimes, the complex interaction between airframe

and flight control system. At present, the modern flight dynamists tend to be

concerned with the wider issues of flying and handling qualities rather than with the

traditional, as well as more limited issues of stability and control. As a result, the

modern flight dynamics, as suggested by Cook [30], involves the work of:

(a) The establishment of a suitable mathematical framework for the problem, the

development of the equations of motion, the solution of the equations of

motion, investigation of response to controls, and the general interpretation of

dynamic behavior.

(b) Reviewing on contemporary flying qualities requirements, as well as their

evaluation and interpretation in the context of stability and control

characteristics.

(c) The development of the feedback control if an aircraft has unacceptable

flying qualities.

Therefore, the present work shared the scope of work suggested by Cook [30], as

mentioned above. Besides, the interest in dealing with problems concerning flight

dynamics; whether the problem in hand is related to the solution of flight

performance or flight stability, as well as control or flight simulation, they share

similar starting points as they start from the governing equation of flight motion.

15

Hence, further difference among of them in imposing the assumptions, which of

course will give a different form of governing equation of motion and how the

governing equation of the corresponding equation should be solved, had been looked

into. Thus, the governing equation of flight motion is presented in the following sub

chapter and in sequence manner, followed by the simplification of the governing

equation of flight motion, for the flight dynamics problem to be treatable.

2.2 The governing equation of flight motions

In flight, an aircraft can move in six degrees of freedom. The movement of the

aircraft can take in three translational and three rotational movements. In order to

understand the aircraft flight behavior, as well as to control the aircraft movement,

one has to derive the governing equation of flight motion. This governing equation

can reflect the possibility to determine the aircraft position, orientation, velocity,

acceleration, forces, and moment acting on the flying vehicle. Unfortunately, all

those quantities cannot be presented by just using a single coordinate system, as one

needs to use more than coordinate systems. Moreover, specifying the position and the

vehicle orientation requires one to define an inertial frame of coordinate system,

while for the forces and the moments that act on the vehicle may be referred to the

axis system attached to the flying vehicle. Strictly speaking, two coordinate systems

need to be defined in formulating the governing equation of flight motion, and they

are: i) the inertial coordinate reference system, and ii) the coordinate body fixed axis

reference system. The inertial coordinate system is defined as a system coordinate, in

which the Newton’s second law is applied [31].

In respect that the rotation of the Earth is relatively slow compared to the problems

involving the dynamics of aircraft, the Earth can be selected as the inertial coordinate

system of reference. Here, the selected coordinate system must be orthogonal and

right-handed [32]. Basically, defining the inertial coordinate system on the Earth can

be done in various manners; here, one can place the origin of the coordinate system

at anywhere on the Earth. Let the coordinate system be denoted by the symbol (F)

with a subscript intended to mnemonic the name of the corresponding coordinate

system. If it is so, (FI) reflects the coordinate system of inertial frame. Meanwhile,

the origin of the inertial coordinate system is denoted by symbol (OI) with the axes of

16

the system labeled as (x, y, and z) and the companion with an appropriate subscript

(I), they become (xI, yI, and zI). The unit vectors, along with x, y, and z, are denoted

as (i, j, and k) respectively. Besides, with the earth being selected as the place of an

inertial coordinate system, it had been identified that three models of the inertial

coordinate system are commonly used in solving the flight dynamic problems, which

are:

(a) The Earth-centered reference frame, (FEC), as shown in Figure 2.1a.

(b) The Earth-fixed reference frame, (FE), as shown in Figure 2.1b.

(c) The local-horizontal reference frame, (FH), as shown in Figure 2.1c.

(a) (b)

(c)

Figure 2.1: The locations of the origin of the coordinate systems [33]

17

Figures 2.1a, b, and c illustrate the placements of their origin of the coordinate

systems for the above three types of inertial coordinate systems.

If one chooses one of those three reference frames as its inertial coordinate axis

system, one has to be consistently used in the whole process of solving the flight

dynamics problems. However, it had been identified that most of the flying vehicles

in the atmospheres, as far as the flight speed below the hypersonic speed, a local

horizontal reference frame is preferred [34].

Meanwhile, the second coordinate system, besides the inertial coordinate system, is a

body fixed axis reference system. This coordinate system, assigned to have the origin

and the axes of the coordinate system, is fixed with respect to the geometry of the

aircraft. Here, three types of body fixed coordinate systems can be applied, and they

are:

(a) Body axis fixed coordinate systems.

(b) Stability axis fixed coordinate systems.

(c) Wind axis fixed coordinate systems.

These three coordinate systems are used in the aircraft’s center of gravity (C.G) as its

origin, and in defining the y and the z axes, they share the same orientation. Their

difference occurs in terms of defining the orientation of the x-axis, as depicted in

Figure 2.2. The x-axis of body axis fixed coordinate system normally coincides or is

parallel to the axis of fuselage. Meanwhile, the x-axis of stability axis fixed

coordinate is parallel with a line drawn to indicate that the present aptitude of aircraft

makes an angle of attack α to the incoming air velocity, whereas the x-axis of wind

fixed coordinate system has direction parallel to wind vector velocity defined with

respect to the x-axis of body axis fixed coordinate system. The choice of which one

will be used depends on the problem of flight dynamics that will be solved.

18

Figure 2.2: The orientation of body axis, stability axis, and wind axis [34]

In respect to the inertial frame of reference, the orientation of body axis coordinate

system is shown in Figure 2.3. In addition, forces and moments, as well as the

definitions of linear and angular velocities on the body axis are shown in Figure 2.4.

Figure 2.3: Body axis coordinate system [33]

19

(a) (b)

Figure 2.4a: Definitions of aerodynamic forces, thrust and acceleration gravitation in

body axis coordinate system [34]

Figure 2.4b: Definitions of moments, linear, and angular velocity in body axis

coordinate system [33]

The definitions of notations that appear in the above figures are explained in Table

2.1.

20

Table 2.1: The definitions of notations in describing forces, moment, and velocity

components [34]

NO DEFINITION ROLL AXIS xb PITCH AXIS yb YAW AXIS zb

1 Angular rate p q r

2 Velocity components u v w

3 Aerodynamic force components X Y Z

4 Aerodynamics moment components L M N

5 Moment of inertia about each axis Ixx Iyy Izz

6 Product of inertia Iyz Ixz Ixy

7 Engine thrust T ….. …..

Basically, the governing equation of flight motion can be broken down into two

groups [31]. The first group is the governing equation of flight motion derived from

the implementation of the Newton’s second law to the aircraft. Meanwhile, the

second group of equations is developed based on the kinematic relationship between

the inertial axis reference systems and the body fixed reference system [35].

As mentioned previously, the inertial coordinate system is employed to specify the

aircraft position, orientation, velocity, and the aircraft acceleration. In other words,

this inertial coordinate system allows one to apply the Newton’s second law to the

aircraft. If the aircraft mass is denoted as (m); the aircraft with respect to the inertial

reference system moves in varying directions based on the vector velocity , and

the forces acting on the aircraft ( ), hence, the Newton’s second law states that for

the given force ( ), there is equal time rate of change in its linear momentum .

Meanwhile, if represents the external moment applied on the aircraft, the

moment will be equal to the time rate of angular momentum . These two

statements can be written mathematically as:

(2.1a)

(2.1b)

The vector velocity represents the vector velocity of the aircraft center of gravity

measured with respect to the inertial reference frame, and the angular velocity vector

is denoted as . If the inertial reference axis is denoted as (XYZ) coordinate

system, while for the body fixed reference frame is denoted in small letter as (xyz),

21

hence the term

|

can be written in terms of

|

by using the

following relation:

|

|

| | (2.2a)

In a similar manner, the rate change of angular momentum, which was previously

written with respect to inertial coordinate system, then completely can be written

with respect to the body fixed coordinate in the following relation.

|

|

| | (2.2b)

Equation 2.2 is substituted to Equation 2.1; which gives the representation of the

Newton’s second law in body fixed reference frame as:

|

|

| | (2.3a)

|

|

| | (2.3b)

If the vector unit of the body axis system (xyz) for x-axis is denoted by , y-axis is

denoted by , and z-axis is denoted with its unit vector , and hence, the two

vectors, velocity ( and angular velocity ( , can be equated as:

(2.4a)

(2.4b)

The externally applied aerodynamic forces , and moments that act on the

aircraft are primarily due to airflow condition and their control surface deflections. In

a similar manner with vector velocity and vector angular velocity , this

applied force and moment , as well as angular momentum ( , can be broken

down into vector components along the longitudinal (x), the lateral (y), and the

vertical axis (z) of the body fixed reference frame. Besides, the force components in

the longitudinal, lateral, and vertical axes are denoted as (Fx), (Fy), and (Fz)

respectively. During application, the moment is denoted in terms of its

component as (L), (M), and (N). On the other hand, the vector angular momentum

associated with their components in body fixed reference is denoted as (Hx),

(Hy), and (Hz). Hence, the forces and the moments, as stated in Equations 2.1a and

2.1b, are written in the form of scalar notation as:

(2.5a)

22

(2.5b)

(2.5c)

(2.6a)

(2.6b)

(2.6c)

The vector angular momentum , in conjunction with the vector angular

velocity , can be written as:

[

] (2.7)

In assuming that the aircraft mass (m) is a constant and by substituting Equation 2.7

into Equations 2.5 and 2.4, one can write these two equations in scalar form as:

(2.8a)

(2.8b)

(2.8c)

( )

(2.9a)

(2.9b)

( )

(2.9c)

The left hand side of the above equations represents the external forces and moments.

These forces and moments are due to aerodynamic forces, aircraft weight, and engine

thrust, which can be written in the following forms:

(2.10a)

(2.10b)

(2.10c)

As for the moments, they can be written as in the following:

(2.11a)

(2.11b)

(2.11c)

23

The definitions of notations that appear in the right hand side of Equations 2.10 and

2.11 are given in the list of symbols.

In other forms, the force equations (Equation 2.10) can be written as:

(2.12a)

(2.12b)

(2.12c)

Meanwhile, the momentum Equations (Equation 2.11) can be written as:

( )

(2.13a)

(2.13b)

( )

(2.13c)

Furthermore, in a relationship between a body axis fixed coordinate system and the

Earth-fixed reference frame, the rotational velocity with respect to the body axis

fixed coordinate system is described by the variables (r, p, and q), while the Earth

fixed coordinate system is described by ( , , and ). The relationship between

these two triples is shown in [31]:

[ ] [

] [

] (2.14)

The above relationship indicates that if the body axis fixed coordinate system is

placed parallel to the Earth fixed coordinate system, which means (θ = 0.0 and ϕ =

0.0), one will obtain ( , and ). Hence, they show the angular rate of

the vehicle to the inertial frame of reference. Besides, the above equation (Equation

2.14) can be solved to represent how the aptitude of the flying vehicle changes with

the inertial frame of reference by inversing that equation and provides the result as:

[

] [

] [ ] (2.15)

Meanwhile, the aircraft position with respect to the inertial reference frame at any

instant results in:

24

[

]

[

] [ ] (2.16)

Equation 2.12 to Equation 2.16 represents the governing equation of aircraft flight

motion. These equations contain 12 state variables, which are sufficient in describing

the flight behavior of the aircraft.

In addition to these 12 state variables, one may add three other state variables: i) the

total velocity (V), ii) the angle of attack α, and iii) the side slip angle β. These three

state variables can be derived from the component velocities (u, v, and w) as depicted

in the following:

√ (2.17a)

(

) (2.17b)

(

) (2.17c)

If one applies the first derivative with respect to time into these three above

equations, one can obtain:

(2.18a)

(2.18b)

( )

√ (2.18c)

If , and , which are defined by Equation 2.12, are substituted into the above

equations, the results are:

(2.19a)

(2.19b)

(2.19c)

With the definitions of (Fx, Fy, and Fz), as given by Equation 2.10 into Equation 2.19,

one obtains the state variables (V, α and β) as:

(2.20a)

221

REFERENCES

1. Jenie, Said D., and Agus Budiyono. "Automatic Flight Control System-

Classical approach and modern control perspective." Indonesia: Department

of Aeronautics and Astronautics-ITB 2006.

2. Pratt, Roger. Flight control systems: practical issues in design and

implementation. No. 57. Iet, 2000.

3. Kuo, Benjamin C. Automatic control systems. Prentice Hall PTR, 1981.

4. Pearsall, Jr Earle S. and Richolt Robert. "Aircraft control system." U.S. Patent

No. 2,389,274. 20 Nov. 1945.

5. Collinson, R. P. G. "Fly-by-wire flight control." Introduction to Avionics

Systems. Springer Netherlands, 2011. 179-253.

6. McLean, Donald. "Automatic flight control systems (Book)." Englewood

Cliffs, NJ, Prentice Hall, 1990, 606 (1990).

7. Franklin, Gene F., J. David Powell, & Abbas Emami-Naeini. "Feedback

Control of Dynamics Systems." Prentice Hall Inc. 2006.

8. McRuer, Duane T., Dunstan Graham, and Irving Ashkenas. Aircraft dynamics

and automatic control. Princeton University Press, 2014.

9. Cook, Michael V. Flight dynamics principles: a linear systems approach to

aircraft stability and control. Butterworth-Heinemann, 2012.

10. Babister, Arthur William. Aircraft Dynamic Stability and Response:

Pergamon International Library of Science, Technology, Engineering and

Social Studies. Elsevier, 2013.

11. Blakelock, John H. Automatic control of aircraft and missiles. John Wiley &

Sons, 1991.

12. Filippone, Antonio. Flight performance of fixed and rotary wing aircraft.

Elsevier, 2006.

222

13. Stevens, Brian L., and Frank L. Lewis. Aircraft control and simulation. John

Wiley & Sons, 2003.

14. Blake, William B. Missile Datcom: User's Manual-1997 FORTRAN 90

Revision. No. AFRL-VA-WP-TR-1998-3009. AIR FORCE RESEARCH

LAB WRIGHT-PATTERSON AFB OH AIR VEHICLES DIRECTORATE,

1998.

15. Roskam, Jan. Airplane Design: Part 2-Preliminary Configuration Design and

Integration of the Propulsion System. DARcorporation, 1985

16. Roskam, Jan. "Airplane Design: Part I-VIII." DARcorporation, Lawrence, KS

2006

17. Steuernagle, J., K. Roy, and S. Ells. "Cessna 182 Skylane Safety

Highlights."AOPA Air Safety Foundation, Marylan, 2001.

18. DAVID, FRED R., and NANCY MARLOW. "CESSNA AIRCRAFT

CORPORATION." Journal of management case studies 1986: 33.

19. Plans, Model Airplane, et al. "The current top posts." Archives of top posts.

2013.

20. Goritschnig, Guenther, et al. "The Evolution of Civil Aircraft Design at

Bombardier: An Historical Perspective." CASI Conference Proceedings.

2003.

21. Field, H. "EUROPE'S AIR TAXIS." Flight International 115.3647 1979.

22. Marcello Napolitano, Aircraft dynamics: From modeling to Simulation, 2012.

23. Lie, Karen. "Cruise Control System in Vehicle." Michigan: Calvin College.

1982

24. Stengel, Robert F. Flight dynamics. Princeton University Press, 2015.

25. Hull, David G. "Fundamentals of Airplane Flight Mechanics." 2007.

26. Etkin, Bernard. "Dynamics of Atmospheric Flight, John Wiley and

Sons." Inc, New York, London, Sydney 1972.

27. Ojha, S.K.: Flight Performance of Aircraft, AIAA, Inc. Washington, DC,

USA, 1995.

28. Benkard, C. Lanier. "A dynamic analysis of the market for wide-bodied

commercial aircraft." The Review of Economic Studies 71.3 2004: 581-611.

29. Airplanes, Boeing Commercial. "Current Market Outlook: 2010-

2029." Seattle, USA, 2010.

223

30. Cook, Michael V. Flight dynamics principles: a linear systems approach to

aircraft stability and control. Butterworth-Heinemann, 2012.

31. Nelson, Robert C. Flight stability and automatic control. Vol. 2.

WCB/McGraw Hill, 1998.

32. Pamadi, Bandu N. Performance, stability, dynamics, and control of airplanes.

Aiaa, 2004.

33. Durham, Wayne. Aircraft Flight Dynamics and Control. John Wiley & Sons,

2013.

34. Roskam, Jan. Airplane Flight Dynamics and Automatic Flight Controls. DAR

Corporation, 1995.

35. Etkin, Bernard. Dynamics of atmospheric flight. Courier Corporation, 2012.

36. Maine, Richard E., and Kenneth W. Iliff. "Application of parameter

estimation to aircraft stability and control." NASA RP-1168 .1986.

37. Bryan, George Hartley. Stability in aviation: an introduction to dynamical

stability as applied to the motions of aeroplanes. Macmillan and Co., limited,

1911.

38. Roskam, Jan, and William A. Anemaat. General aviation aircraft design

methodology in a PC environment. No. 965520. SAE Technical Paper, 1996.

39. Russell, J. Performance and stability of aircraft. Butterworth-Heinemann,

1996.

40. Pamadi, Bandu N. Performance, stability, dynamics, and control of airplanes.

Aiaa, 2004.

41. McLean, Marie. California Women: Activities Guide, Kindergarten through

Grade Twelve. Publications Sales, California State Department of Education,

PO Box 271, Sacramento, CA 95802-0271, 1988.

42. Faghihi, F., and K. Hadad. "Numerical solutions of coupled differential

equations and initial values using Maple software." Applied Mathematics and

Computation 155.2 (2004): 563-572.

43. Chandrasekaran, S., and A. K. Jain. "Dynamic behaviour of square and

triangular offshore tension leg platforms under regular wave loads." Ocean

Engineering 29.3, 2002: 279-313.

44. Golafshani, A. A., M. R. Tabeshpour, and M. S. Seif. "First order

perturbation solution for axial vibration of tension leg platforms." Scientia

Iranica 14.5, 2007: 414-423.

224

45. Garza, Frederico R., and Eugene A. Morelli. "A collection of nonlinear

aircraft simulations in matlab." NASA Langley Research Center, Technical

Report NASA/TM 212145, 2003.

46. Etkin, Bernard, and Lloyd Duff Reid. Dynamics of Flight: Stability and

Control. Vol. 3. New York: Wiley, 1996.

47. Dustman, Larry L. "Transmitter extension apparatus for manipulating model

vehicles." U.S. Patent No. 4,386,914. 7 Jun. 1983.

48. Wassily W. Leontief, Faye Duchin (2004). World Wide Military Last Update:

January 6th

, 2008: from: http://www.worldwide-military.com

49. Fischel, Eduard. "Aileron control for airplanes." U.S. Patent No. 2,137,974.

22 Nov. 1938.

50. Plan, NASA Strategic. "National Aeronautics and Space

Administration."Washington, DC, February , 1995.

51. "Aircraft elevator construction." U.S. Patent 2,430,793, issued November 11,

1947.

52. Fahey, James Charles. The Ships and Aircraft of the US Fleet. Naval Institute

Press, 1958.

53. Carl, Udo. "Drive control for a vertical rudder of an aircraft." U.S. Patent No.

4,759,515. 26 Jul. 1988.

54. Lin, Ching-Fang. "Aircraft rudder command system." U.S. Patent No.

5,170,969. 15 Dec. 1992.

55. Burcham, Frank W., and Charles Gordon Fullerton. Controlling Crippled

Aircraft--with Throttles. National Aeronautics and Space Administration,

Ames Research Center, Dryden Flight Research Facility, 1991.

56. Robbins, Richard E., and Robert D. Simpson. "Method and apparatus for

aircraft pitch and thrust axes control." U.S. Patent No. 4,471,439. 11 Sep.

1984.

57. Miller, Robert A. "Current status of thermal barrier coatings—an

overview."Surface and Coatings Technology 30.1 1987: 1-11.

58. Burcham, Frank W., et al. "Engines-only flight control system." U.S. Patent

No. 5,330,131. 19 Jul. 1994.

59. Robinson, Michael R., and Richard P. Ouellette. "Multi axis thrust vectoring

for turbo fan engines." U.S. Patent No. 5,706,649. 13 Jan. 1998.

https://www.google.com.my/search?tbo=p&tbm=bks&q=inauthor:%22Wassily+W.+Leontief%22

https://www.google.com.my/search?tbo=p&tbm=bks&q=inauthor:%22Faye+Duchin%22

http://www.worldwide-military.com/

225

60. Young, Harvey R. "Power management system." U.S. Patent No. 4,488,851.

18 Dec. 1984.

61. Ang, Kiam Heong, Gregory Chong, and Yun Li. "PID Control System

Analysis, Design, and Technology." Control Systems Technology, IEEE

Transactions on13.4, 2005: 559-576.

62. Åström, Karl Johan, and Tore Hägglund. Advanced PID control. ISA-The

Instrumentation, Systems, and Automation Society; Research Triangle Park,

NC 27709, 2006.

63. Kiong, Tan Kok, et al. "Modern Designs." Advances in PID Control. Springer

London, 1999. 35-97.

64. Smetana, Frederick O., Delbert Clyde Summey, and W. Donald

Johnson.Riding and Handling Qualities of Light Aircraft: A Review and

Analysis. National Aeronautics and Space Administration, 1972.

65. Smetana, F. O., "Aircraft Performance, Stability and Control," Aircraft

Designs, Inc., Monterey, CA, 1988.

66. Smetana, F. O., "Aircraft Performance, Stability and Control," Aircraft

Designs, Inc., Monterey, CA, 2000.

67. Smetana, F. O., Summey, D. C., and Johnson, W. D., "Point and Path

Performance of Light Aircraft—A Review and Analysis," NASA CR 2272,

June 1973.

68. Fink, R. D., and D. E. Hoak. "USAF stability and control DATCOM." Air

Force Flight Dynamics Laboratory, Wright-Patterson AFB, Ohio ,1975.

69. Williams, John E., and Steven R. Vukelich. The USAF stability and control

digital dATCOM. Volume I. Users manual. MCDONNELL DOUGLAS

ASTRONAUTICS CO ST LOUIS MO, 1979.

70. Jelinski, Z., and P. B. Moranda. "Software reliability research, Statistical

Computer Performance Evaluation, W. Freiberger (ed.), 465–484." 1972.

71. Sukert, Alan N. "Empirical validation of three software error prediction

models."Reliability, IEEE Transactions on 28.3 (1979): 199-205.

72. Maskew, Brian. "Program VSAERO theory document." NASA CR-4023 ,

1987.

73. Nathman, James K., and J. O. E. L. Frank. "Application of VSAERO to

Internal Flows." AIAA paper 872415. 1987.

226

74. Carmichael, Ralph L., and Larry L. Erickson. "PAN AIR-A higher order

panel method for predicting subsonic or supersonic linear potential flows

about arbitrary configurations." .1981.

75. Fluent, I. N. C. "Fluent 6.3 Users Guide." Fluent documentation. 2006.

76. Kohnke, Peter, ed. ANSYS theory reference. Ansys, 1999.

77. Manual, ANSYS User’S. "Swanson Analysis Systems." Inc., Volumes I, II,

III, IV, Revision 5. 1994.

78. Strash, Daniel J., and D. M. Tidd. "MGAERO User's Manual." Analytical

Methods Inc., Redmond, WA . 1994.

79. Bassi, Francesco, et al. "Discontinuous Galerkin solution of the Reynolds-

averaged Navier–Stokes, turbulence model equations." Computers &

Fluids 34.4 , 2005: 507-540.

80. Fan Zhang, et al. AutoCAD VBA secondary development guidance (Example

through) (with CD-ROM). Tsinghua University Press Limited, 2006.

81. Earle, James H., and Denise Olsen. Engineering Design Graphics: AutoCAD

Release 14. Addison-Wesley Longman Publishing Co., Inc., 1998.

82. Perry, Alexander R. "The flightgear flight simulator." Proceedings of the

USENIX Annual Technical Conference. 2004.

83. Berndt, J. S. "JSBSim, an open source platform independent flight dynamics

model in C++." JSBSim Reference Manual v1. 0 . 2011.

84. Furth, Peter G., et al. Using archived AVL-APC data to improve transit

performance and management. No. Project H-28. 2006.

85. Lutz, Mark. Programming python. Vol. 8. O'Reilly, 1996.

86. Abzug, Malcolm J. Computational flight dynamics. Aiaa, 1998.

87. Smetana, Frederick O, Delbert Clyde Summey, and W. Donald Johnson.

Riding and Handling Qualities of Light Aircraft: A Review and Analysis.

National Aeronautics and Space Administration, 1972.

88. Stevens, Brian L., and Frank L. Lewis. Aircraft control and simulation. John

Wiley & Sons, 2003.

89. Nelson, Robert C. Flight stability and automatic control. Vol. 2.

WCB/McGraw Hill, 1998.

90. Stengel, Robert F. "Aircraft Flight Dynamics (MAE 331) Fall 2012."

91. Ishak, Iskandar Shah, et al. "Estimation of Aerodynamic Characteristics of a

Light Aircraft." Jurnal Mekanikal 22 , 2006: 64-74.

227

92. Jameson, Antony. "Computational aerodynamics for aircraft design." Science

(Washington) 245.4916, 1989: 361-371.

93. Hirsch, Charles. Numerical Computation of Internal and External Flows: The

Fundamentals of Computational Fluid Dynamics: The Fundamentals of

Computational Fluid Dynamics. Vol. 1. Butterworth-Heinemann, 2007.

94. Blazek, Jiri. Computational Fluid Dynamics: Principles and

Applications:(Book with accompanying CD). Elsevier, 2005.

95. Neacsu, Catalin-Adrian, Mariana Ivanescu, & Ion Tabacu. "Brief Introduction

to Fluent."2005.

96. Choudary, R. B. Introduction to Ansys 10.0. IK International Pvt. Ltd., 2009.

97. Redmond, W. A. "D. Almosnino Analytical Methods, Inc." 1994.

98. Knapp, Matthew, and David Lednicer. "MGAERO validation using KC-135

flight and tunnel data." AIAA Pap 4021, 2000.

99. Williams, John E., and Steven R. Vukelich. The USAF Stability and Control

Digital DATCOM. Volume I. User’s Manual. MCDONNELL DOUGLAS

ASTRONAUTICS CO ST LOUIS MO, 1979.

100. Jan Roskam Method For Estimating Stability and Control Derivative of

Conventional Subsonic Airplaanes. Lawrence, Kansas,1979.

101. Desing, Aerospace Vehicle. "A99936937 ALU-994263”, 2014.

102. Murman, Earll M., R. John Hansman, and John-Paul Clarke. "Aircraft System

and Product Development: Teaching the Conceptual Phase." 39th AIAA

Aerospace Sciences Meeting. 2001.

103. Roskam, Jan. "Airplane Design Part VI: Preliminary Calculation of

Aerodynamic Thrust And Power Characteristics Author: 2000: 550.

104. Jan Roskam, Airplane Flight Dynamic and Automatic Flight Control. Part II.

United states of America; 2003.

105. Cook, Michael V. Flight Dynamics Principles: a Linear Systems Approach to

Aircraft Stability and Control. Butterworth-Heinemann, 2012.

106. Han, Song-Chol, and Hong-Xing Li. "Invertible incline matrices and

Cramer's rule over inclines." Linear algebra and its applications 389, 2004:

121-138.

107. Torenbeek, Egbert. Synthesis of subsonic airplane design: an introduction to

the preliminary design of subsonic general aviation and transport aircraft,

228

with emphasis on layout, aerodynamic design, propulsion and performance.

Springer Science & Business Media, 2013.

108. Hale, Francis J. "Introduction to aircraft performance, selection and

design."JOHN WILEY & SONS, INC., 605 THIRD AVE. NEW YORK, NY

10158, USA, 1984, 416 ,1984.

109. Boyd, Stephen P., and Craig H. Barratt. Linear controller design: limits of

performance. Englewood Cliffs, NJ: Prentice Hall, 1991.

110. Franklin, Gene F., J. David Powell, and Michael L. Workman. Digital

Control of Dynamic Systems. Vol. 3. Menlo Park: Addison-Wesley, 1998.

111. Ang, Kiam Heong, Gregory Chong, and Yun Li. "PID control system

analysis, design, and technology." Control Systems Technology, IEEE

Transactions on13.4, 2005: 559-576.

112. Boyd, Stephen, C. Baratt, and Stephen Norman. "Linear controller design:

Limits of performance via convex optimization." Proceedings of the

IEEE 78.3 ,1990: 529-574.

113. Wang, Liuping. Model predictive control system design and implementation

using MATLAB®. Springer Science & Business Media, 2009.

114. Moore, Holly. MATLAB for Engineers. Prentice Hall Press, 2014.

115. Xue, Dingyu, YangQuan Chen, and Derek P. Atherton. Linear Feedback

Control: Analysis and Design with MATLAB. Vol. 14. Siam, 2007.

116. Wolovich, William A. Automatic control systems: basic analysis and design.

USA: Saunders College Publishing, 1994.

117. Abu-Khalaf, Murad, Rong Chen, and Arkadiy Turevskiy. "PID Control

Design Made Easy." Matlab Digest (2009).

118. Johnson, Michael A., and Mohammad H. Moradi. PID control. Springer-

Verlag London Limited, 2005.

119. Åström, Karl Johan, and Tore Hägglund. Advanced PID control. ISA-The

Instrumentation, Systems, and Automation Society; Research Triangle Park,

NC 27709, 2006.

120. Lie, Karen. "Cruise Control System in Vehicle." Michigan: Calvin College;

1982.

121. Rivera, Daniel E., Manfred Morari, and Sigurd Skogestad. "Internal model

control: PID controller design." Industrial & engineering chemistry process

design and development 25.1, 1986: 252-265.

229

122. Ong, Chee-Mun. Dynamic Simulation of Electric Machinery: Using

MATLAB/SIMULINK. Vol. 5. Upper Saddle River, NJ: Prentice Hall PTR,

1998.

123. Messner, Bill, Dawn Tilbury, and Asst. Prof Rick Hill. "Control Tutorials for

MATLAB and Simulink." 1999.

124. Prof. Dr. Ottmar Beucher. University of Applied Sciences Karlsruhe.

Germany. National Chung Hsing University, Taichung. Summer 2013.

125. Bobál, V., and P. Chalupa. "Self-tuning controllers Simulink library."

Department of Control Theory, Tomas Bata University in Zlin,

Mostni 5139.760 . 2002.

126. Jadlovská, Slávka, and Ján Sarnovský. "An Extended Simulink Library for

Modeling and Control of Inverted Pendula Systems." Proc. of the Int. Conf.

Technical Computing Prague. 2011.

127. Lee, C. W., and A. W. D. Miller. "Trials with devices for atomising

insecticides by exhaust gases from a Cessna 182 aircraft

engine." Miscellaneous report/Tropical pesticides research institute ( 496

(1965).

128. Brock, John C., et al. "Initial results from a test of the NASA EAARL lidar in

the Tampa Bay region." 2002: 89-98.

129. January (2010). Airliners Net. From: http://www.airliners.net/photo/Lear-Jet-

24/1640473/L/.

130. Harry Clements (2012). Air Facts. From: http://airfactsjournal.com /Cessna -

620 -the-stillborn-prodigy/.

131. Hobo (2014). Pilots America. From: http: // web2 .airmail. net/ jperkins/Piper

/ Piper_SEL_03.htm

132. January (2010). Airliners Net. From: http://www.airliners.net/aircraft-

data/stats.main?id=304

133. Glenn C. Stephen (1971). Airplane Flight Manual. From: http://canberra-

aeroclub.com.au/cac/documents/aircraft/vh-ohr/vh-ohr_pilot_operating_

handbook__2014-12-30.pdf.

134. Thomas Noack (2003). Plane spotters Net. From: http:// ww.flugzeuginfo.net

/acdata_php/acdata_pa28_en.php.

http://www.airliners.net/photo/Lear-Jet-24/1640473/L/

http://www.airliners.net/photo/Lear-Jet-24/1640473/L/

http://airfactsjournal.com/

http://www.airliners.net/aircraft-data/stats.main?id=304

http://www.airliners.net/aircraft-data/stats.main?id=304

http://canberra-aeroclub.com.au/cac/documents/aircraft/vh-ohr/vh-ohr_pilot_operating_%20handbook__2014-12-30.pdf



230

135. Schafer, Patricia D. "A Manual of Cherokee Herbal Remedies: History,

Information, Identification, Medicinal Healing." 1993.

136. Lent, Craig S. Learning to Program with MATLAB: Building GUI Tools:

Building GUI Tools. Wiley Global Education, 2013.

137. Marchand, Patrick, and O. Thomas Holland. Graphics and GUIs with

MATLAB. Chapman & Hall/CRC, 2003.

138. Holland, O. Thomas, and Patrick Marchand. Graphics and GUIs with

MATLAB. CRC Press; 2002.

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