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UNIVERSITI TUN HUSSEIN ONN MALAYSIA

BORANG PENGESAHAN STATUS TESIS·

JUDUL: CONCEPTUAL DESIGN OF A SMALL NON-RIGID AIRS"'P WITII

PARTICULAR ATTENTION TO ITS STATIC AND DYNAMIC STABILITY

SESI PENGAJIAN 2008/2009

Saya ______________ A __ Z_IA_N __ B_IN_T_I_H_A_R_I_R_I_(7_8_0_82_7_-0_8_-6_3_8_4) ____________ __

(HURUF BESAR)

menga].,:u membenarkan tesis (PSM/Sarjana/Dslasr Falsafah)* ini disimpan di Perpustakaan dengan syarat-syarat kegunaan seperti berikut :

I. Tesis adalah hak milik Universiti Tun Hussein Onn Malaysia. 2. Perpustakaan dibenarkan membuat salinan untuk tujuan pengajian sahaja. 3. Perpustakaan dibenarkan membuat salinan tesis ini sebagai bahan pertukaran di antara institusi

pengaj ian tinggi. 4. "Sila tandakan (,I)

D D D

SULIT

TERHAD

(Mengandungi maklumat yang berdarjah keselamatan atau kepentingan Malaysia seperti yang termaktub di dalam AKT A RAHSIA RASMI 1972)

(Mengandungi maklumat TERHAD yang telalzdite tukan oleh organisasi/ badan di mana penyelidikan dijalanka

TIDAK TERHAD ;~ h: I Dis ka ?Ie~

ck~d~ ~ ~ (TANDATANGAN PENULIS) (TANDltr1\GAf ..P"ENYELIA)

Ala mat Tctap:

137, KAMPUNG PARIT SRI BAIIROM DARAT, 83100 RENGIT, BATU PAIIAT,JOHOR.

Tarikh: I'd- JANUARJ 2009

CAT A T AN: * Potong yang tidak berkenaan .

PROF. DR. INJLR'~ BIN SEllA YANG (Nama Pcnyclia)

Tarikh: i'2. JANUARJ 2009

•• Jika Tesis ini SULIT atau TERHAD. sila lampirkan surat daripada pihak berkuasa! organisasi berkenaan dengan menyatakan sekali tempoh tesis ini perlu dikelaskan sebagai SULIT atau TERHAD.

Tesis dimaksudkan sebagai tesis bagi Ijazah Doktor Falsafah dan Sarjana secara penyelidikan. atau disertasi bagi pengajian secara kerja kursus dan penyelidikan. atau Laporan Projek Sarjana Muda (PSM).

"We declared that we had read this thesis and according to our opinion, this thesis is

qualified in term of scope and quality for purpose of awarding the

Signature

Supervisor Professor Dr. Ing. Darwin Sebayang

Date \ 2! I / oei ...................................... ~ .l .................................. .

Signature ......... ~ ....................................... . Co-Supervisor: Associate Professor Mohd. Ashraf Othman

Date ......... (.;:?,./ .... .I ......... / .. Q.~l ............................... .

CONCEPTUAL DESIGN OF A SMALL NON-RIGID AIRSHIP WITH

PARTICULAR ATTENTION TO ITS STATIC AND DYNAMIC STABILITY

AZIAN BINTI HARlRI

A thesis submitted in

fulfillment of the requirements for the award of the

Degree of Master of Mechanical Engineering

Faculty of Mechanical and Manufacturing Engineering

Universiti Tun Hussein Onn Malaysia

JANUARY, 2009

II

"I declare that this thesis entitled "Conceptual Design of A Small Non-Rigid

Airship with Particular Attention to Its Static and Dynamic Stability" is the

result of my own research except cited in references. This thesis has not been

accepted for any degree and not concurrently submitted in candidature of any

degree."

Signature ~1W~ ..... v.~.~ .. 'Y .................................................... .

Name Azian Binti !-Iariri

Date ....... \.~ .. j .. ~ ... .!.9..q ...................................... .

iii

To Illy beloved husband,

Hairul Nizat

For always being there when two hands were just not enough.

To Illy precious,

Harish Hallllall & Imrall Hallllall

For neverfailed to put a big slllile on Illy face even on tough day.

IV

ACKNOWLEDGEMENT

In the name of Allah, Most Gracious, Most Merciful.

Alhal1ldulillah, all praise to Allah, the Most Beneficient and the Most

Merciful, who has give me the strength and grace to complete this study succesfully.

I would like to take this opportunity to put on record, my heartfelt thanks and

deep appreciation to Professor Ing. Dr. Darwin Sebayang for his extraordinary

patience, enduring optimism, guidance, invaluable advice and assistance in the

completion of this master thesis.

I would also like to extend my gratitude to co-supervisor Associate Professor

Mohd. AshrafOthman, Mr. Ignatius Agung Wibowo, Mr. Rosman Tukiman and

Captain AI-Amin Said. They have assisted me in giving advices, ideas, and technical

support to this project.

Last but not least, I would like to express my gratitude to my family and

friends and to all who involved directly and indirectly in this study for all the

support, endless encouragement and D'ua. They are truly my inspiration.

v

ABSTRACT

Small size airships are traditionally designed and built based on experience

rather than scientific approaches. Hence, its design approach has only been

discussed in a very limited number of literatures. Thus, with these challenges at

hand, a conceptual design study of airship in Malaysia was done to identify and

explore the basic technology of airship design. This study focused on the conceptual

design, determination of basic specifications and preliminary design of small size

non-rigid airship for monitoring missions in Malaysia. The preliminary design

focused on static stability, dynamic stability and development of a virtual simulator.

The mathematical model of the designed airship for dynamic stability was rederived

based on literatures and is then programmed to Graphical User Interface (GUI) with

the aid of Matlab software. The airship was designed to fulfill the design

specification suitable for monitoring with maximum speed of 40 km/h, cruising

speed of20 km/h, operating altitude of 120 m and able to carry payload of at least of

6 kg. The dimension of 10 m length with maximum diameter of2.3 m was chosen

with a pair of 0.25 hp engines to accomplish the desired specification. The designed

airship was statically stable with trimmed angle of attack of approximately 0.18

degree. Through mathematical model of airship dynamics, following a detailed

procedure including stability considerations, the airship had been analyzed and found

to be dynamically stable with low control power and the time taken for the

longitudinal response of elevator and vectored thrust to become stable was in the

order of approximately 80 seconds while the lateral response of rudder becomes

stable in approximately 30 seconds. The result of this study concluded that the

designed airship fulfilled the design specification for monitoring mission and the

designed airship was statically and dynamically stable during cruising speed. The

virtual simulator also effectively provides a better understanding of the response of

the designed airship through visualization.

vi

ABSTRAK

Kapal udara bersaiz kecil secara tradisinya direkabentuk dan dibina menerusi

pengalaman tanpa pendekatan saintifik. Oleh itu, pendekatan rekabentuknya hanya

dibincangkan dalam bilangan literatur yang amat terhad. Walaupun dengan cabaran

besar yang dihadapi, kajian rekabentuk konsep kapal udara di Malaysia ini dilakukan

bagi mengenalpasti dan meneroka teknologi asas merekabentuk kapal udara. Kajian

ini fokus kepada rekabentuk konsep, penentuan spesifikasi asas dan rekabentuk

permulaan kapal udara untuk misi pengawasan di Malaysia. Rekabentuk permulaan

ini pula fokus kepada kestabilan statik, kestabilan dinamik dan pembangunan

penyelaku maya. Model matematik bagi kestabilan dinamik telah diterbitkan semula

berdasarkan Iiteratur dan diprogramkan ke antaramuka grafik (GUI) dengan bantu an

peri sian Mat/ab. Kapal udara direkabentuk bagi memenuhi spesifikasi misi

pengawasan udara dengan halaju maksimum 40 km/h, halaju menjajap 20 km/h,

altitud kendalian 120 m dan mampu membawa beban bayar sekurang-kurangnya

seberat 6 kg. Dimensi panjang 10m dan diameter maksimum 2.3 m telah dipilih

bersama sepasang enjin berkuasa 0.25 hp bagi mencapai spesifikasi yang

dikehendaki. Kapal udara yang direka bentuk adalah stabil secara statik dengan

sudut serang semasa trim adalah 0.18 darjah. Bagi analisa kestabilan dinamik,

sebuah model matematik dinamik kapal udara dibangunkan. Menerusi model

dinamik ini, yang melalui prosedur yang terperinci termasuk analisa kestabilan,

adalah didapati kapal udara adalah stabil secara dinamik dengan kuasa kawalan yang

rendah dan masa yang diambil untuk sambutan membujur bagi penaik dan tujah

vector menjadi stabil adalah 80 saat manakala bagi sambutan sisi oleh kemudi

menjadi stabil setelah 30 saat. Dapatan kajian ini menyimpulkan kapal udara yang

direkabentuk memenuhi spesifikasi yang dikehendaki untuk pengawasan udara dan

adalah stabil secara statik dan dinamik semasa menjajap. Penyelaku maya yang

dibangunkan juga secara efektif dapat memberikan pemahaman terhadap respon

kapal udara yang lebih baik menerusi visualisasi.

\'11

TABLE OF CONTENTS

CHAPTER TOPIC PAGE

ACKNOWLEDGEMENTS iv

ABSTRACT v

TABLE OF CONTENTS VII

LIST OF TABLES xii

LIST OF FIGURES xiii

LIST OF SYMBOLS xv

LIST OF APPENDICES xxiii

I INTRODUCTION

1.1

1.2

1.3

1.4

1.5

Overview

Problem Statement

Objectives of Study

Scope of Study

Research Significance

3

5

6

6

II LITERATURE REVIEW

2.1

2.2

2.3

Overview

Existing Type of Airship

Literature Review

2.3.1 Derivation of Equations of Motion

8

9

II

16

2.3.1.1 Generalized Force Equations 20

2.3.1.2 Generalized Moment Equations 21

2.3.2 The Linearized Equations of Motion 23

viii

2.3.3 Drag 24

2.3.4 Approximate Models of the Longitudinal

Stability Modes 27

2.3.5 Approximate Models of the Lateral

Stability Modes 31

2.4 Summary 34

III METHODOLOGY

3.1 Overview 35

3.2 Design Requirements 36

3.3 Conceptual Design 37

3.4 Baseline Specifications Determination 38

3.5 Static Stability of Airship 39

3.6 Mathematical Model of Airship Dynamic 40

3.6.1 Equations of Motion 41

3.6.2 Linearization 42

3.6.3 Decoupled Equations of Motion 42

3.6.4 State Space Form 43

3.6.5 Stability in State Space Form 44

3.6.6 Stability Modes Approximation 46

3.6.7 Airship Transfer Function 46

3.6.8 Response 48

3.7 Airship Virtual Simulator 49

3.8 Summary 49

IV AIRSHIP CONCPETUAL DESIGN AND

BASELINE SPECIFICATIONS

4.1 Overview 50

4.2 Conceptual Design 52

4.3 Baseline Specifications Determination 53

4.3.1 Envelope's Geometry 53

4.3.2 Fin's Geometry 54

4.3.3 Aerostatics 56

4.3.4 The Off Standard Atmosphere 56

IX

4.3.5 Lifting Gas 58

4.3.6 Reynolds Number 59

4.3.7 Power 59

4.3.7.1 Power Required 60

4.3.7.2 Thrust Available 60

4.3.8 Maximum Duration 60

4.3.9 Structures 61

4.3.9.1 Bending Moment 61

4.3.9.2 Envelope Pressure 63

4.3.10 Weight Estimation 64

4.3.11 Determination of Centre

of Gravity 65

4.4 Summary 66

V AIRSHIP STABILITY

5.1 Overview 67

5.2 Generalized Body Axes 67

5.3 Rectilinear Flight 69

5.4 Angular Relationships and Motion Variables 70

5.5 Axes Transformation 71

5.6 Static Stability 73

5.6.1 Static Equilibrium 74

5.6.2 Longitudinal Stability 76

5.6.3 Directional Stability 78

5.6.4 Lateral Stability 79

5.7 Dynamic Stability 80

5.7.1 Disturbance Forces and Moments 81

a) Aerodynamic Effects 81

b) Power Effects 83

c) Gravitational and

Buoyancy Effects 84

5.7.2 Linearized Equations of Motion of Airship 86

5.7.3 Decoupled Equations of Motion 87

a) Longitudinal Equations 87

x

b) Lateral Equations 89

5.8 Summary 91

VI RESULT AND DISCUSSION

6.1 Overview 92

6.2 Conceptual Design 92

6.2.1 Mission 93

6.2.2 Product Review 93

6.2.3 Designed Airship Specifications 95

6.2.4 Function of Airship 95

6.2.5 Function Structure of Designed Airship 96

6.2.6 Design Solutions and Evaluations 97

6.2.6.1 Design Solutions 97

6.2.6.2 Evaluation Criteria

and Weight Factor 98

6.2.7 Selected Airship Design 100

6.3 Baseline Specifications 101

6.3.1 Envelope's Geometry 101

6.3.2 Fin's Geometry 102

6.3.3 Gondola's Geometry 103

6.3.4 Aerostatics 104

6.3.5 Drag 105

6.3.6 Thrust 106

6.3.7 Structure 107

6.3.8 Weight Estimation 108

6.3.9 Centre of Gravity 108

6.3.10 Preliminary Dimension 109

6.4 Static Stability 109

6.5 Mathematical Model of Airship Dynamic III

6.5.1 State Space Equation 112

6.5.2 State Space Eigenvalues 113

6.5.3 Transfer Function 114

6.5.3.1 Longitudinal (elevator) 115

6.5.3.2 Longitudinal (thrust) 115

VII

6.6

6.5.3.3 Lateral (rudder)

6.5.4 Comparison Between Approximate

and Actual Stability Modes

6.5.5 Response Analysis

6.5.6 Airship Simulator

Summary

CONCLUSION

REFERENCES

APPENDICES

xi

115

116

117

120

122

124

126

131

xii

LIST OF TABLES

TABLE TABLE PAGE

2.4 Moments and products of inertia 22

2.5 Approximate longitudinal stability modes 30

2.6 Approximate lateral stability modes 33

3.2 Airship's design requirements 37

4.2 Parameters derived from statistical data 55

4.3 Component weight breakdown formulae 64

5.4 Summary of perturbation variables 71

6.1 Product review of commercialized airship 94

6.2 Basic specifications of the designed airship 95

6.5 Morphological chart of airship 98

6.7 Evaluation criteria and weight factor of airship 100

6.12 Gross lift and net lift value according to altitude 104

6.15 Estimated weight 108

6.22 Comparison between exact and approximate solution 116

xiii

LIST OF FIGURES

FIGURE TITLE PAGE

1.1 Airship's basic components 2

2.1 Airship structural categories 10

2.2 Motion referred to generalized body axes 17

2.3 Acceleration terms due to rotary motion 18

3.1 Methodology used in this study 36

3.3 The VDI 2221 model of design process 37

3.4 The conceptual design process used in this study 38

3.5 Baseline specifications determination method 39

3.6 Flow chart of the mathematical model of airship dynamic 41

3.7 Roots on the s-plane 45

3.8 Airship input-output relationship 47

4.1 Schematic view of fin 55

5.1 General configuration body axes for airship 68

5.2 Trimmed steady rectilinear flight 69

5.3 Angular relationship 70

5.5 Inertial axis to body axis transformation 72

5.6 Resolution of velocity through angle of attack and sideslip 73

5.7 System axis transformation 73

5.8 Example of positive, neutral and negative static stability

condition 73

xiv

5.9 Forces and moments acts on the longitudinal direction

during steady trimmed flight 76

5.10 Plot ofM-a for a stable airship 77

5.11 Forces and moments acts on the directional direction 78

5.12 Forces and moments acts on the lateral direction 80

5.13 Steady-state aerodynamic model 82

5.14 Typical propulsion system geometry 83

6.3 Function of airship for aerial monitoring 96

6.4 Sub system of airship 97

6.6 Evaluation criteria method of airship 99

6.8 Selected airship solution 101

6.9 Basic envelope dimension 102

6.10 Fin's dimension 103

6.11 Gondola basic dimension 104

6.13 Power required 106

6.14 Thrust and drag value at various velocities 107

6.16 Preliminary dimension of designed airship 109

6.17 Longitudinal static stability analysis 1 10

6.18 Directional static stability analysis 110

6.19 Lateral static stability analysis I I I

6.20 Eigenvalues s-plane for longitudinal equation 113

6.21 Eigenvalues s-plane for lateral equation 114

6.23 Longitudinal response owing to 1 degree elevator input II8

6.24 Longitudinal response owing to I degree thrust input 118

6.25 Lateral response owing to I degree rudder input 119

6.26 Airship simulator layout 120

6.27 Setting the desired input 121

6.28 Response output 122

LIST OF SYMBOL

Airship Conceptual Design and Baseline Specification

A

a

B

b

C

C

D

d

E

e

fl.!

h g

Hp I

ISA

k

kD

III

ME

Referencel area (volume) 2/3

~ length of envelope

Buoyancy

Radius of cylinder

Coefficient

Chord

Drag

Maximum diameter

Endurance

Length from chord tip control to chord root control offins.

Load or tension per unit width

Longitudinal membrane stress

Gravitational constant

Altitude

Membrane second moment of area

International Standard Atmosphere

Percentage of pure helium

Percentage of total drag coefficient

Length

Gross lift

Net lift

Mass

Maximum bending moment

xv

xvi

N Number

P Power

p Pressure

Q Fuel consumption rate

Re Reynolds number

I' Envelope radius

S Surface area

SL Sea level

T Temperature

Membrane thickness

Thrust - Thrust

U Upstream velocity

u Gust velocity

V Velocity

Va Total speed

VDI Vereb1 Deutscher Ingenieure

Vol Volume

TV Weight

11'e Gross weight with fuel tanks empty

HI Gross weight with fuel tanks full

x x axis coordinate

y y axis coordinate

Greek Letter

ae Angle of attack at trim

fJ Side slip

iJP Total internal pressure

!Jp Differential pressure

17p Propeller efficiency

f1

P

Subscripts

0

aero air

m'a eg

eha er

etr

eyl D

e

f fie heliulIl -int

lIlax p

p

req

R

T

V

Body altitude

Fluid viscosity

Density

Condition at ISA SL

Aerodynamic

Air

Available

Centre of gravity

Characteristic

Cruising

Control

Cylinder

Drag

envelope

fin

Fin trailing edge

Helium

Internal

Maximum

Pressure

Propeller

Required

Root

Tip

Volumetric

xvii

xviii

Airship Stability

A

a

a

a I. a2, a3

Adj

B

B

b

b

C

C

c

cb

cg

Cl'

D

d

d

DCM

det

c

G

g

GUI

II

1

State matrix

Aerodynam ic

Coordinate of centre of gravity

Acceleration at arbitrarily point P relative to the body axes

Adjoint

Input matrix

Buoyancy force

Buoyancy

Coordinate of centre of buoyancy

Output matrix

Coefficient

Distance from centre of buoyancy to thrust

Centre of buoyancy

Centre of gravity

Centre of volume

Feedfonvard matrix

Maximum diameter

Thrust coordinate

Direct cosine matrix

Determinant

Trim equilibrium

Transfer function matrix

Gravitational/Gravitational constant

Graphical User Interface

Distance from cb to cg

Moment of inertia

Identity matrix

Product of inertia

Step magnitude

Lamb's inertia ratio for rotation about lateral axis oy

Lamb's inertia ratio for moment along longitudinal axis ox

J

L

Lift

M

m

m

111

N

N

11

o

ox

oy

oz p

p

power -

q

r

S

Ssd

T

T

U

u

11

v Vo

Vol

Lamb's inertia ratio for moment along lateral axis oy

Airship's length

Distance from cb to cg of horizontal fin

Normalised rolling moment

Apparent product of inertia

Rolling moment

Lift

Pitching moment

Mass matrix

Airship mass

Normalised pitching moment

Matrix of numerator polynomials

Yawing moment

Normalised yawing moment

Origin of body axes

Body axis

Body axis

Body axis

Arbitrary chosen point

Roll rate perturbation

Power

Pitch rate perturbation

Yaw rate perturbation

Laplace operator

Horizontal! vertical fin area

Thrust

Time constant

Axial velocity

Input or control vector

Axial velocity perturbation

Lateral velocity

Total velocity

Volume

xix

v

w w w

x i

x

x

x y

y

y

y

Z

z

z

Greek Letter

a

fJ /';.

r5

Jill

e AI

Aij

!1

p

¢

Lateral velocity perturbation

Airship weight

Normal velocity

Normal velocity perturbation

Axial force

Derivative of the state vector with the respect of trim

State vector

Body axis reference

Normalised axial force

Lateral force

Body axis reference

output vector

Normalised lateral force

Normal force

Body axis reference

Normalised normal force

Angle of attack

Sideslip

Characteristic polynomial

Control angle

Incremental mass

Pitch attitude

Eigenvalues

Elements ofDCM

Thrust elevation angle

density

Roll attitude

xx