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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. 2. 3. 4.
Tesis adalah hak milik Universiti Tun Hussein Onn Malaysia. Perpustakaan dibenarkan membuat salinan untuk tujuan pengajian sahaja. Perpustakaan dibenarkan membuat salinan tesis ini sebagai bahan pertukaran di antara institusi pengaj ian tinggi. "Sila tandakan (,I)
D
SULIT
D
(Mengandungi maklumat yang berdarjah keselamatan atau kepentingan Malaysia seperti yang termaktub di dalam AKT A RAHSIA RASMI 1972)
TERHAD
(Mengandungi maklumat TERHAD yang telalzdite tukan oleh organisasi/ badan di mana penyelidikan dijalanka
D
TIDAK TERHAD
ck~d~ (TANDATANGAN PENULIS)
;~ h: I ka ?Ie~
Dis
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Ala mat Tctap: 137, KAMPUNG PARIT SRI BAIIROM DARAT, 83100 RENGIT, BATU PAIIAT,JOHOR.
Tarikh:
I'd-
JANUARJ 2009
~
(TANDltr1\GAf PROF. DR.
..P"ENYELIA)
INJLR'~
BIN SEllA YANG (Nama Pcnyclia)
Tarikh:
i'2.
JANUARJ 2009
CATAT AN: * Potong yang tidak berkenaan . •• 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
...................................... ~ .l .................................. .
Signature
.........
Co-Supervisor:
Associate Professor Mohd. Ashraf Othman
Date
......... (.;:?,./ .... .I......... / ..Q.~l ............................... .
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........................................
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
I
II
xxiii
INTRODUCTION
1.1
Overview
1.2
Problem Statement
3
1.3
Objectives of Study
5
1.4
Scope of Study
6
1.5
Research Significance
6
LITERATURE REVIEW
2.1
Overview
8
2.2
Existing Type of Airship
9
2.3
Literature Review
II
2.3.1
2.3.2
Derivation of Equations of Motion
16
2.3.1.1 Generalized Force Equations
20
2.3.1.2 Generalized Moment Equations
21
The Linearized Equations of Motion
23
viii
2.3.3
Drag
24
2.3.4 Approximate Models of the Longitudinal Stability Modes
2.3.5
Approximate Models of the Lateral Stability Modes
2.4 III
Summary
31 34
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
IV
27
Equations of Motion
41
3.6.2 Linearization
42
3.6.3
42
Decoupled Equations of Motion
3.6.4 State Space Form
43
3.6.5
44
Stability in State Space Form
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
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
56
Aerostatics
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 4.4
V
65
Summary
66
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
5.7
5.6.1
Static Equilibrium
74
5.6.2
Longitudinal Stability
76
5.6.3
Directional Stability
78
5.6.4
Lateral Stability
79
Dynamic Stability 5.7.1
80
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 5.8 VI
Summary
89 91
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 6.2.7 6.3
Selected Airship Design
Baseline Specifications
98 100 101 101
6.3.1
Envelope's Geometry
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
xi 6.5.3.3 Lateral (rudder) 6.5.4
Comparison Between Approximate and Actual Stability Modes
116
6.5.5
Response Analysis
117
6.5.6
Airship Simulator
120
Summary
122
CONCLUSION
124
REFERENCES
126
APPENDICES
131
6.6
VII
115
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
III
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
xv
LIST OF SYMBOL
Airship Conceptual Design and Baseline Specification
A
Referencel area (volume) 2/3
a
~
B
Buoyancy
b
Radius of cylinder
C
Coefficient
C
Chord
D
Drag
d
Maximum diameter
E
Endurance
e
Length from chord tip control to chord root control offins.
fl.!
Load or tension per unit width
h
Longitudinal membrane stress
g
Gravitational constant
Hp
Altitude
I
Membrane second moment of area
ISA
International Standard Atmosphere
k
Percentage of pure helium
kD
Percentage of total drag coefficient
length of envelope
Length Gross lift Net lift III
Mass
ME
Maximum bending moment
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
xvii Body altitude f1
Fluid viscosity
P
Density
Subscripts
0
Condition at ISA SL
aero
Aerodynamic
air
Air
m'a
Available
eg
Centre of gravity
eha
Characteristic
er
Cruising
etr
Control
eyl
Cylinder
D
Drag
e
envelope
f
fin
fie
Fin trailing edge
heliulIl -
Helium
int
Internal
lIlax
Maximum
p
Pressure
p
Propeller
req
Required
R
Root
T
Tip
V
Volumetric
xviii Airship Stability
A
State matrix
a
Aerodynam ic
a
Coordinate of centre of gravity
a I. a2, a3
Acceleration at arbitrarily point P relative to the body axes
Adj
Adjoint
B
Input matrix
B
Buoyancy force
b
Buoyancy
b
Coordinate of centre of buoyancy
C
Output matrix
C
Coefficient
c
Distance from centre of buoyancy to thrust
cb
Centre of buoyancy
cg
Centre of gravity
Cl'
Centre of volume
D
Feedfonvard matrix
d
Maximum diameter
d
Thrust coordinate
DCM
Direct cosine matrix
det
Determinant
c
Trim equilibrium
G
Transfer function matrix
g
Gravitational/Gravitational constant
GUI
Graphical User Interface
II
Distance from cb to cg
1
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
xix Lamb's inertia ratio for moment along lateral axis oy Airship's length Distance from cb to cg of horizontal fin Normalised rolling moment J
Apparent product of inertia
L
Rolling moment
Lift
Lift
M
Pitching moment
m
Mass matrix
m
Airship mass
111
Normalised pitching moment
N
Matrix of numerator polynomials
N
Yawing moment
11
Normalised yawing moment
o
Origin of body axes
ox
Body axis
oy
Body axis
oz p
Body axis
p
Roll rate perturbation
power -
Power
q
Pitch rate perturbation
r
Yaw rate perturbation
S
Laplace operator
Ssd
Horizontal! vertical fin area
T
Thrust
T
Time constant
U
Axial velocity
u
Input or control vector
11
Axial velocity perturbation
v
Lateral velocity
Vo
Total velocity
Vol
Volume
Arbitrary chosen point
xx v
Lateral velocity perturbation
w
Airship weight
w
Normal velocity
w
Normal velocity perturbation
x
Axial force
i
Derivative of the state vector with the respect of trim
x
State vector
x
Body axis reference
x
Normalised axial force
y
Lateral force
y
Body axis reference
y
output vector
y
Normalised lateral force
Z
Normal force
z
Body axis reference
z
Normalised normal force
Greek Letter
a
Angle of attack
fJ
Sideslip
/';.
Characteristic polynomial
r5
Control angle
Jill
Incremental mass
e
Pitch attitude
AI
Eigenvalues
Aij
Elements ofDCM
!1
Thrust elevation angle
p
density
¢
Roll attitude
