iii
Dedicated
To my parents who are no more in this world
and
ACKNOWLEDGEMENT
I would like to express my sincere gratitude to my supervisor, Assoc. Prof. Dr. Adi Maimun Bin Hj. Abdul Malik, for his encouragement, proper and valuable guidance, and critic views. I am also grateful to my co-supervisor Assoc. Prof. Dr. Omar Bin Yaakob for his valuable advice, guidance, and encouragement. I am especially grateful to the IRPA, Ministry of Science, and Technology, Malaysia for giving the financial support for this study.
I would like to thank to the following individuals:
All the Marine laboratory staff, for the assistance during the experimental part of the study, especially to Mr. Rahman for his effort to put the bilge keel in the model.
Enck. Ahmad Fuad Bin Sabki for arranging the boat for full scale trial. Ng Chee Wei, for providing the information and data of the wave buoy.
All of my fellow colleagues in the Marine Technology Laboratory, Ahmad Nasirudin, Ahmad Fitriadhy, Andi Harris Mahmud, and Dony Setyawan.
v
ABSTRACT
ABSTRAK
vii
TABLE OF CONTENTS
CHAPTER TITLE PAGE
TITLE PAGE i DECLARATION OF ORIGINALITY ii DEDICATION iii ACKNOWLEDGEMENT iv ABSTRACT v ABSTRAK vi
TABLE OF CONTENTS vii
LIST OF FIGURES xii
LIST OF TABLES xvii
NOMENCLATURES xviii
LIST OF APPENDICES xxii
1 INTRODUCTION 1 1.1 Background 1 1.2 Research Objective 2 1.3 Scope of Research 3 1.4 Research Outline 3 2 LITERATURE REVIEW 5 2.1 General 5
2.4.1 Numerical Approach 8
2.4.1.1 Frequency Domain Method 9
2.4.1.2 The Panel Method 12
2.4.1.3 Navier Stokes Method 12
2.4.1.4 Time Domain Simulation Method 12 2.4.2 Experimental Approach 16 2.4.3 Full Scale Approach 17
2.4.3.1 Measurement of Wave 18
2.4.3.2 Concept of Wave Spectra 22 2.4.3.3 Response Amplitude Operator 23 2.4.4 Characteristics of Small Vessel in Dynamic
Situation 24
2.5 Seakeeping Criteria 25
2.6 Summary of the Literature Review 27
3 RESEARCH APPROACHES 29
3.1 General 29
3.2 Basic Steps in Predicting Ship Response
In Waves 29
3.3 Time Domain Simulation Approach 30
3.4 Experimental Approach 33
3.5 Full Scale Approach 33
3.6 Encountering Wave Spectra 35
3.7 Concluding Remarks 36 4 MATHEMATICAL MODELLING 37 4.1 General 37 4.2 Mathematical Model 37 4.3 Components of Forces 38 4.4 Coordinate Systems 39 4.5 Equations of Motions 40
4.6 Treatment of Forces and Moments 42
ix 4.8 Computational Procedures 47 4.9 Concluding Remarks 48 5 SIMULATION PROGRAM 49 5.1 General 49 5.2 Mathematical Modelling 49
5.3 Components of the Simulation Program 50
5.3.1 Source Code Files 50
5.3.2 Executable Files 50
5.3.3 Input Files 50
5.3.4 Output Files 53
5.4 Running the Program 54
5.5 Results from the Simulation in Regular Waves 54 5.6 Analysis of the Output from Simulation in Regular
Waves 57
5.7 Results from the Simulation in Irregular Waves 60 5.8 Analysis of the Output from Simulation in
Irregular Waves 62
5.9 Discussion of the Results 64
5.10 Concluding Remarks 64
6 EXPERIMENTAL APPROACH 65
6.1 General 65
6.2 Model Preparation 65
6.3 Roll Decay Test 66
6.4 Experimental Setup for Roll Decay Test 67 6.5 Roll Decay Test Analysis 67 6.6 Roll Decay Analysis Result 69
6.7 Seakeeping Experiment 70
6.8 Experimental Set-up for Regular and Irregular
Wave Test 71
6.9 Scaling Law 72
6.11 Output of the Regular Wave Test 72 6.12 Analysis of the Output of Regular Wave Test 76 6.13 Output of the Irregular Wave Test 79 6.14 Analysis of the Output of Irregular Wave Test 81 6.15 Discussion about the Results from Experiment 83
6.16 Concluding Remarks 84
7 FULL SCALE SEA TRIALS 85
7.1 General 85
7.2 Components of Full Scale Trial 86 7.2.1 Measurement of Sea Wave 86 7.2.2 Results from the Wave Buoy 87 7.2.3 Measurement of Vessel Response 90 7.3 Detail of the Measurement 92
7.4 Results from the VMMS 93
7.5 Analysis of the Results from Full Scale
Measurement 99
7.6 Discussion of the Results of the Full Scale Trial 104
7.7 Concluding Remarks 106
8 COMPARISON AND VALIDATION OF RESULTS 107
8.1 General 107
8.2 Comparison of Wave Spectra 107
8.3 Comparison of the RAO 109
8.4 Comparison of the Responses 111
8.5 Validation of the RAO 113
8.6 Discussion about the Comparison 115
8.7 Concluding Remarks 116
9 DISCUSSION, CONCLUSION & FUTURE WORKS 117
9.1 General 117
9.2 Discussion 117
xi
9.2.2 Model Experiment 118
9.2.3 Full Scale Sea Trial 119
9.3 Conclusion 119
9.4 Future Works 120
9.4.1 Simulation Program 121
9.4.2 Hydrodynamic Coefficients 121
9.4.3 Full Scale Sea Trials 122
LIST OF FIGURES
FIGURE NO. TITLE PAGE
3.1 Mechanism to convert time domain to frequency domain 34 3.2 Time history of random wave 34
3.3 Different ship heading s 35
4.1 Co-ordinate systems 40
5.1 Calculated non dimensional added mass and
damping coefficients 51 5.2 A35 and A53 as obtained by Seakeeper 52 5.3 B35 and B53 as obtained by Seakeeper 52 5.4 GZ curve for the vessel TRF 1010 53 5.5 Time history of wave at LW= 85.32m, TW= 7.39s,
HW= 1.70m (Head Sea) 54
5.6 Time history of heave response at LW= 85.32m,
TW= 7.39s, HW= 1.70m (Head Sea) 55
5.7 Time history of pitch response at LW= 85.32m,
TW= 7.39s, HW= 1.70m (Head Sea) 55
5.8 Time history of wave response at LW= 47.4m,
TW= 5.50s, HW= 0.948m (Following Sea) 55
5.9 Time history of heave response at LW= 47.4m,
TW= 5.50s, HW= 0.948m (Following Sea) 56
5.10 Time history of Pitch response at LW= 47.4m,
TW= 5.50s, HW= 0.948m (Following Sea) 56
5.11 Time history of wave at LW= 47.4m, TW= 5.50s,
HW= 0.948m (Beam Sea) 56
xiii
TW= 5.50s, HW= 0.948m (Beam Sea) 57
5.13 Heave RAO in head sea from simulation 58 5.14 Pitch RAO in head sea from simulation 58 5.15 Heave RAO in following sea from simulation 59 5.16 Pitch RAO in following sea from simulation 59 5.17 Roll RAO in beam sea from simulation 60 5.18 Time history of wave input to the simulation 61 5.19 Time history of heave response from simulation 61 5.20 Time history of roll response from simulation 61 5.21 Time history of pitch response from simulation 62 5.22 Heave spectra from simulation in irregular wave 63 5.23 Roll spectra from simulation in irregular wave 63 5.24 Pitch spectra from simulation in irregular wave 63 6.1 Sample of roll decay results 69 6.2 Wave result for LW= 3.80m, HW= 0.7599m,
TW= 1.55s, VM= 0.6726m/s (Head Sea) 73
6.3 Heave result for LW= 3.80m, HW= 0.7599m,
TW= 1.55s, VM= 0.6726m/s (Head Sea) 73
6.4 Pitch result for LW= 3.80m, HW= 0.7599m,
TW= 1.55s, VM= 0.6726m/s (Head Sea) 74
6.5 Wave result for LW= 6.132m, HW= 0.06132m,
TW= 1.98s, VM= 0.9180m/s (Following Sea) 74
6.6 Heave result for LW= 6.132m, HW= 0.06132m,
TW= 1.98s, VM= 0.9180m/s (Following Sea) 74
6.7 Pitch result for LW= 6.132m, HW= 0.06132m,
TW= 1.98s, VM= 0.9180m/s (Following Sea) 75
6.8 Wave results for LW=2.23m, HW= .0466m, TW= 1.19s
VM= 0.00 m/sec (Beam Sea) 75
6.9 Roll response for LW=2.23m, HW= .0466m, TW= 1.19s
VM= 0 m/sec (Beam Sea) 75
6.14 Pitch RAO from following sea in regular wave 78 6.15: Roll RAO from beam sea in regular wave 79
6.16 Time history of irregular wave 79
6.17 Time history of irregular heave 80 6.18 Time history of irregular Pitch 80 6.19 Time history of irregular Roll 80 6.20 Heave spectra in head sea from irregular experiment 81 6.21 Heave RAO in head sea from irregular experiment 81 6.22 Pitch spectra in head sea from irregular experiment 82 6.23 Pitch RAO in head sea from irregular experiment 82 6.24 Roll spectra in beam sea from irregular experiment 82 6.25 Roll RAO in beam sea from irregular experiment 83 7.1 Wave spectra during head sea trial 87 7.2 Wave spectra during following sea trial 88 7.3 Wave spectra during bow quartering sea trial 88 7.4 Wave spectra during beam sea trial 88 7.5 Wave spectra during stern quartering sea trial 89 7.6 Averaged wave spectra of the whole duration 89
7.7 Typical Installation of VMMS 90
7.8 Flow of data processing and analyzing 91
7.9 Front panel window of VMMS 91
7.10 Data processing window of VMMS 91
7.11 Data analysis window of VMMS 92
xv
7.23 Pitch spectra in head sea trial 97 7.24 Pitch spectra in following sea trial 97 7.25 Pitch spectra in bow quartering sea trial 98 7.26 Pitch spectra in beam sea trial 98 7.27 Pitch spectra in stern quartering sea trial 98 7.28 Heave RAO in head sea trial 99 7.29 Heave RAO in following sea trial 100 7.30 Heave RAO in bow quartering sea trial 100
7.31 Heave RAO in beam sea trial 100
7.32 Heave RAO in stern quartering sea trial 101 7.33 Roll RAO in head sea trial 101 7.34 Roll RAO in following sea trial 101 7.35 Roll RAO in bow quartering sea trial 102
7.36 Roll RAO in beam sea trial 102
7.37 Roll RAO in stern quartering sea trial 102 7.38 Pitch RAO in head sea trial 103 7.39 Pitch RAO in following sea trial 103 7.40 Pitch RAO in bow quartering sea trial 103
7.41 Pitch RAO in beam sea trial 104
7.42 Pitch RAO in stern quartering sea trial 104
8.1 The comparison of wave spectra 109
8.2 Comparison of heave RAO 110
8.3 Comparison of pitch RAO 110
8.4 Comparison of roll RAO 111
8.5 Comparison of heave response 112
8.6 Comparison of pitch response 112
8.7 Comparison of roll response 113
A.1 Co-ordinate System 133
D.1 Profile (Starboard) 157
D.2 Profile (Port) 157
D.3 Lines plan of profile 158
D.4 Lines plan of half breadth 158
E.2 Slice view of the wave buoy 162
E.3 Wave buoy arrangement 162
E.4 Front view and main dimension of wave buoy 163
F.1 Random sea surface 164
F.2 Wave buoy floating at random sea 164 F.3 Full scale photograph of the boat TRF1010 165 F.4 Preparation for the full scale trial 165
F.5 Operation of the VMMS 166
F.6 Instrumentation of VMMS 166
F.7 Model taking for the test 167
xvii
LIST OF TABLES
TABLE NO. TITLE PAGE
2.1 The typical geometry of fishing vessel 6 2.2 Types of fishing boats in Malaysia 7
2.3 Sea-state codes 20
2.4 Typical personnel performance of warships 27 6.1 Summary of results for roll decay test of TRF1010 69 7.1 HS and TZ from the wave spectral moment 89
7.2 Location and other measurement detail 93 8.1 The RMS values and HS calculated from the spectra 109
8.2 The RMS values of the motion 113
8.3 Validation of the natural frequency with theoretical 115 D.1 Principal particulars of TRF1010 (Full Scale) 159
D.2 Bilge keel specification 159
D.3 Principal particulars of TRF1010 (Model) 160
D.4 Sample test protocol 160
NOMENCLATURES
Vessel and Environmental Parameters
LOA - Length Overall in meter
LBP - Length between perpendiculars in meter
LWL - Length of waterline in meter
B - Breadth in meter D - Depth in meter
T - Draught in meter CB - Block coefficient
CWP - Waterplane area coefficients
CM - Midship area coefficients
KG - Vertical distance of the centre of gravity from the keel GMT - Transverse Metacentric height
VS - Forward speed of the vessel in m/sec
Δ - Vessel displacement in Tonne
κ - Wave number
TW - Wave period in seconds
LW - Wave length in meter
VW - Wave celerity
HS, H1/3 - Significant wave height in meter
ζ - Distance from still water free surface
W
ζ - Wave profile DW - Water depth
TZ - Average zero crossing periods in seconds
TR - Natural roll period
xix
Tm - Modal Period in seconds
ω - Wave frequency in rad/sec ( )
R e
S ω - Spectral density for response in m2.s/rad
( )e
Sζ ω - Encounter wave spectral density in m2.s/rad S
ω - Mean frequency RMS - Root mean square value
yy
K - Radius of gyration about y axis AWP - Waterplane area coefficient
'
xx
I - Moment of inertia about x axis Hω - Wave height in meter
ξ - Wave elevation in meter RAO - Response Amplitude Operator
) (ω
ζ
S - Wave spectral density in m2.s/rad
) (ω
Z
S - Spectral density for heave motion m2.s/rad )
(ω
φ
S - Spectral density for roll motion in deg2.s/rad
) (ω
θ
S - Spectral density for pitch motion in deg2.s/rad e
ω - Encounter frequency in rad/sec γ - Peak enhancement factor
Ω - Peak frequency in the wave spectra α - Philips constant
xx
K - Radius of gyration about x axis in m v
I - Virtual mass moment of inertia in tonnes.m2 n
ω - Natural frequency in rad/sec
d
ω - Damped frequency in rad/sec
d
T - Damped period in sec p
ω - Peak frequency in rad/sec
z
ω - Zero crossing frequency in rad/sec
θ
ω - Natural period for pitching in rad/sec
φ
Co-ordinate Systems
Gxyz - Body co-ordinate system about centre of gravity
OWξηζ - Wave co-ordinate system about still water surface amidships
φ,θ, ψ - Euler angles (roll, pitch, and yaw respectively) max
φ - Roll response
3
φ - Roll amplitude at time t3
1
φ - Roll amplitude at time t1
κ - Non dimensional damping factor
Λ - Tuning factor φ μ - Magnification factor γ - Damping ratio n a - Added mass Equations of Motion m - Mass of body
Ix, Iy, Iz - Principal mass moments of inertia about the x, y and z
axes respectively
u, v, w - Linear velocities along the respective x, y and z axes p, q, r - Angular velocities along the respective x, y and z axes Fx, Fy, Fz - Force acting in x, y and z direction respectively
K, M, N - Moment acting about x, y, z axes respectively
Forces and Moments
p - Pressure acting on the wetted surface
ρ - Density of water
xxi
S - Wetted surface area of vessel ∇ - Under water volume of vessel ω - Frequency of excitation
nj - Outward unit normal vector in the jth mode of motion
φ - Time dependent velocity potential φI - Incident wave potential
φD - Diffracted wave potential
φRj - Generated wave potential due to motions of the body in the jth direction
Hydrodynamic Coefficients
mj - Mass or mass moment of inertia of body in the jth direction (j =
1,2,…,6)
Ajj - Hydrodynamic reaction in phase with acceleration (added
mass) in the jth direction (j = 1,2,…,6)
Bjj - Hydrodynamic reaction in phase with velocity (damping) in
the jth direction (j = 1,2,…,6)
LIST OF APPENDICES
APPENDIX TITLE PAGE
A Transformation Matrix 128
B Treatment of Forces and Moments 135
C Input-Output of Simulation Program 142
D Boat and Model 152
E Wave Buoy 156
CHAPTER 1
INTRODUCTION
1.1 Background
Fishing vessel is one of the traditional vessels in Malaysia as well as all over the world. A large number of the population depends on these fishing vessels for catching fish to fulfil their livelihood. On the other hand these fishing vessels are providing the people of all over the world with essential nutrition to survive. Most of their operational life they are more likely to operate in deep sea and to sustain harsh weather. Sometimes it is very difficult for them to overcome such weather. Such harsh weather can cause excessive motions, which can degrade the performance; the operation of crew on board, even it can be the cause for the capsizing of the vessel.
Study has been showed that most of the fishing vessels in Malaysia are built traditionally. Except in some modern shipyards in Malaysia, master-builders normally use their intuitive experience and directly implement their designs into the building process without the use of plans or sophisticated calculations (Yaakob, O., 1998). Although the method is simple, quick and tested, since it is based on age-old tradition of trial and error. As a consequence these fishing boats may experience critical situation in severe weather condition.
instance, February 23, 1991, in which a fishing boat capsized in rough seas while ferrying about 20 tourists back from Pulau Kepas was one of the most obvious case.
The frequently happened sea accidents had led to the consideration of analyzing the motion and improving safety at sea and many actions have been taken to remain the sea worthiness of ships at sea. Among them seakeeping analysis was one of the practices to ensure that a ship would always safe in sailing. Nowadays seakeeping analysis has become more and more common practice in the ship design process.
The seakeeping is critical for small vessel like fishing vessel. This is due to her size and mission. The small vessel tends to experience excessive motion than others. The main reason is her underwater hull shape. Throughout this period, numerous methods have been incorporated to evaluate the ship seakeeping. Nowadays naval architect has some numerical tools to study the seakeeping behaviour of a ship design, but these tools have to be used carefully, as most of them are limited due to the theoretical assumptions made (Arribas, P. and Fernandez, C., 2005).
1.2 Research Objective
The objectives of the present research are described as follows:
i. To choose the closest theoretical wave spectra for Malaysian water by comparing the wave spectra obtained from wave buoy and theoretical calculation.
ii. To predict the motion of the vessel based on the local sea environment iii. To compare the response spectra obtained from full scale
3
1.3 Scope of Research
The scope of research in the field of seakeeping is very wide. Only the motion related seakeeping will be studied here in this research.
i. Through this research closest theoretical wave spectra can be chosen for the purpose of floating structure design in Malaysia.
ii. The simulation program can be applied to find the response amplitude operator (RAO) of the vessel.
iii. The experimental results can be used to verify the output of the simulation program.
iv. Full scale test results can provide the real motion of the vessel in waves. v. The combined results from the three different methods can be applied to
obtain more realistic behaviour of the vessel in waves.
1.4 Research Outline
This study starts with the critical review of the importance of the study of the prediction of seakeeping for fishing vessel. Then it concentrates on the problem of an existing Malaysian fishing vessel. Then it describes the way to find out the procedure to predict seakeeping performance of a vessel. There are several methods to find out the seakeeping performance of fishing vessel. Here three different approaches have been adopted to find the seakeeping behavior of fishing vessel.
The model testing was carried out to find the Response Amplitude Operator (RAO) of the vessel for different ship heading and sea conditions. These RAOs is used to obtain the motion response of the vessel in different ship heading. The roll decay tests were also conducted to obtain the natural rolling period. From the roll decay test the KG of the vessel was also obtained. This determined KG is used to validate the KG of the full scale vessel for a certain loading condition.
In the simulation part, a six-degrees-of-freedom mathematical model is adopted to the simulation program. The main effort of this model is based on the accurate computation in time domain of the motion of the vessel. Whilst, the dynamic term in the equation of motion is estimated by using the frequency dependent coefficient, which can be obtained through the published literatures. Finally the response amplitude operator can be obtained by the computed motion for different wave condition.
CHAPTER 2
LITERATURE REVIEW
2.1 General
Generally seakeeping means finding the motion and related things of a vessel in a certain sea-state. In other words it describes the behaviour of the vessel in a seaway. Investigation of ship seakeeping is very important to all ship designers, ship operators and regulatory bodies, because it is a major design requirement and also the key factor in ensuring the safety of ship including human life and goods. In order to guarantee the ship’s good seakeeping performance and safety, it is important to predict the ship’s motions and wave loads within sufficient engineering accuracy (Shan et al., 2004). According to Sarioz and Narli, (1995) the overall performance of ships depends on the seakeeping performance in specified sea areas where the vessel is designed to operate.
2.2 Review of the Characteristics of Fishing Vessel
The fishing vessels have a number of special features which distinguish them from other types of ships. The features are based on their hull geometry and intended mission. Based on the hull geometry the fishing vessel has the following characteristics:
- The fishing vessels are small compared with other types of vessels. - They have low L/B ratio.
- They have low freeboard, which enable more effective fishing. - They are designed to have shallow draught.
- In relation to the length and height of waves being encountered they are considered small.
Table 2.1: The typical geometry of fishing vessel (Yaakob, O. 1998)
Parameter Typical Range
Length breadth ratio 2.8 to 5.8 Breadth draught ratio 1.5 to 4.0 Midship area coefficient 0.44 to 0.88 LCB %L (-aft) -12.0 to +3.5
7
2.3 Review of the Fishing Vessel of Malaysia
In Malaysia the fishing boats are classified in two categories, namely, traditional and modern. Also they can be classified according to the size like small boats, medium sized boats, and large sized boats. In 1986, there were 40,000 fishing boats operated by nearly 110,000 fishermen in Malaysia to supply 725,000 tons of fish per year. The quantity of types of fishing fleets during the time is shown as follows:
Table 2.2: Types of fishing boats in Malaysia (Chen, 1986) Types of Fishing Boats in 1986
Trawlers 5766 boats
Purse seiners 1671 boats
Gill net 18759 boats
Hook & Liners 4519 boats Others (Lift net, Trap etc.) 9285 boats
During that time most of the fishing boats are small in size (below 70 GRT). Size of offshore trawlers of 15 tons and 25 tons are very common while trawlers up to 100 tons are very few. Purse seiners are generally bigger boats which ranging from 25 to 70 tons.
Radar, Global Positioning System (GPS), wireless, fish finder like echo sounder and sonar, etc.
2.4 Review of the Method for Studying Ship Motion (Seakeeping)
For the assessment of seakeeping two things are necessary. First of all the wave conditions of the sea area to which the assessment is related and how the total energy of the wave system is distributed with respect to frequency and then the response of the ship in waves covering the necessary frequency band. These responses are normally defines by the appropriate Response Amplitude Operator (RAO) in the form of response per unit wave height. The analysis of the seakeeping performance of any ship design depends on good theoretical predictions validated by model experiments and full scale trials (Fein, et al., 1980). For a new type of ship the dependence of experimental data is vital to build confidence in the analytical tool and to gain insight into the hydrodynamic phenomena unique to that ship type.
Throughout this period, numerous methods have been followed to evaluate the ship seakeeping. Nowadays the naval architect has some numerical tools to study the seakeeping behaviour of a design, but these tools have to be used carefully, as most of them are limited due to the theoretical assumptions made (Arribas, and Fernandez, 2005). Basically the most remarkable methods employed on investigating ship seakeeping are (i) Numerical Approach (ii) Model Experimental Approach; and (iii) Full Scale Measurement Approach. Those methods will briefly be reviewed as below
2.4.1 Numerical Approach
9
numerical approach can be splitted into two main parts namely, Frequency Domain and Time Domain. Both methods are widely used for finding the ship motion indicators in a seaway.
Since ship motion and sea load experiments are extremely expensive and time consuming, it is not usually feasible to perform these experiments for individual ship designs. Therefore the papers of St. Denis and Pierson have further emphasized the importance of the development of theoretical and numerical methods for predicting the regular wave responses (Salvesen et al., 1970).
2.4.1.1 Frequency Domain Method
Today, frequency domain analysis is widely used for preliminary calculations of hydrodynamic forces and vessel Response Amplitude Operator (RAO). In this method all the motion and force coefficient are calculated as a function of frequency these are generally computed in frequency domain (Clauss, 2005). Most of the frequency domain methods use so called strip theory. For the study of ship motion strip theory is most widely used for its speed and robustness. The strip theory for heave and pitch motions in head waves of Korvin-Krouvosky and Jacobs (1957) was the first motion theory suitable for numerical computations which had adequate accuracy for engineering applications. This theory was later extended by Jacobs (1958) to include the wave induced vertical shear forces and bending moments for a ship in regular head waves.
the coefficients in the equations of motion do not satisfy the symmetry relation ship proved by Timman and Newman (1962).
After that period new strip theories for heave and pitch motions in head waves has been derived independently by several authors Tasai and Takaki (1969) and Borodai and Netsvetayev (1969). All of these new strip theories have identical forward speed terms satisfying the Timman and Newman symmetry relationships.
It should be mentioned that Ogilvie and Tuck (1969) have derived a completely new strip theory for head sea by using slender body theory. Unfortunately there are some integral terms in their theory which have not yet been evaluated; thus their theory cannot be fully utilized or judged at that time.
For the sway, roll and yaw motions and for the horizontal wave induced loads there exist few computational methods. Tasai (1967) has derived a strip theory for the sway-yaw-roll motions, but this theory is only applicable for the zero forward speed. However the forward speed terms in their equations of motion did not satisfy Timman and Newman (1962) symmetry relationship and their theory lacks many of the forward speed terms included in the theory presented herein. Furthermore comparisons between experiment and the theory of Grim and Schenzle exist only for the zero forward speed.
11
Many of the early methods of studying ship motion were limited to zero forward speed, head sea, or motion in the vertical plane only. There are many forms of the strip theory. The principal differences between the various implementations of strip theory are due to the correction of forward speed. During 1969 and 70s several papers were published by different groups working independently which introduced more general form of the theory. The method described by Salvesen et al. (1970) has been proven to be the most widely accepted method. This method includes prediction of heave, pitch, sway, roll, and yaw as well as wave induced loads for a ship at constant speed at an arbitrary heading in regular waves. Vessel response in a general random sea can be predicted from the regular wave results using the principle of superposition described by Denis and Pierson (1953).
There are three main stages to compute ship response using strip theory. First the ship is divided into a number of sections or strips. Then two dimensional hydrodynamic coefficients (added mass, damping, and restoring) are calculated for each section. These values are then integrated along the length of the vessel to obtain the hydrodynamic coefficients of the vessel.
There are two methods to find the hydrodynamic forces acting on the ship, namely; Conformal mapping, and Frank Close-Fit method. Various methods have been proposed for Conformal Mapping such as those of Lewis, (1929) and Ursell, (1949). The method of Frank, (1967) is perhaps the most commonly used methods.
2.4.1.2 The Panel Method
For large volume of vessels or structures, the assumptions of strip theory are not applicable. So another method for computing the wave structure interaction is required. The three dimensional panel methods address this issue by solving the wave radiation potential over a set of three dimensional panels. Panel method can be based on Green functions method (Chang, (1977), Inglis and Price, (1981), Chen et al, 2000). The panel method can also be based on Rankine Source method (Bertram, 1997, 1998). The most significant advantage of panel method is the ability to handle complex, high volume geometric forms. However the numerical solutions are much more complex and time consuming and in general the motion predictions are not much improved (Fonseca et al. 2001).
2.4.1.3 The Navier-Stokes Method
Another method called Navier-Stokes method uses Computational Fluid Dynamics to calculate ship response. However it has generally been accepted as referring to specially those methods, which involve the solution of some forms of the Navier-Stokes equation. The main important thing to this method is that it includes the viscous effect. All the significant features of the flow around a body including those attributed to radiation, diffraction, mass forces, and viscosity are accounted for. This approach should then provide a very accurate prediction of vessel forces and motions in a seaway (Rixmann, 2001).
2.4.1.4 Time Domain Simulation Method
13
technology and its availability. However, as computer technology has advanced, the time simulation approach gained more ground. Today, very fast computers encourage most of the research activities to utilize simulation techniques.
Time domain method for solving ship motion is basically described as linear and non-linear method. The comparison of linear and nonlinear computations shows that nonlinearities have a considerable influence on the results, particularly in predicting the instantaneous location of the hull in relation to waves. Although results from those linearized calculations have produced excellent agreement with experiments for some problems, very poor agreements were found in others.
Inconsistency in the results, believed to be caused by the exclusion of nonlinearities, led researchers to include higher-order terms in the boundary conditions. The higher-order theories are significantly more complex due to the presence of the higher-order derivatives in the free-surface boundary conditions. Higher-order theories produce reasonable results for some problems but the methods are difficult to apply to a wide variety of problems. The shortcomings of perturbation expansion methods have led to the next logical step of solving the fully nonlinear problem.
The greatest contribution of time simulation is that non-linear effects can be included in the study. The instantaneous changes in the underwater volume of a vessel was proven to be very important on vessel motions and included in the calculations. Time simulation also showed that hydrostatic coupling, especially between roll and heave, is very strong. This was further improved when the effects of the instantaneous wave profile were included by De Kat, and Paulling, (1989). This approach which provides non-linear restoring/excitation force has gained some ground for head and following waves but not for beam waves (Denise, 1982).
well established such as time dependent hydrodynamic coefficients and forces. De Kat and Paulling tried to introduce time dependence on hydrodynamic coefficients so that different frequencies can be employed during the time simulation (Umeda et al., 2000). It is quite likely that as time simulation attracts more researchers and computers become faster these problems will be solved gradually.
The motion analysis in time domain was first reported by Cummins (1962), and Ogilvie (1964). The aim of the time domain simulation approach is to relate the vessel safety to the vessel motion. Previously, this concept was hard to be followed because it involves many complicated computation procedures. However, with the advancement of computer technology, this study becomes easier and it has attracted many researchers to follow this concept such as Paulling et al. (1975), Hamamoto and Akiyoshi (1988), de Kat and Paulling (1989) and Umeda et al. (2000). Under this concept, the equations of motions, which are made up by three translation components: surge, sway and heave, and three rotational components: roll, pitch, and yaw are solved simultaneously by utilizing numerical integration procedure.
Another successful motion analysis in time domain was developed by Maimun (1993). His time domain simulation program can treat regular and irregular wave to find the motion of vessel. Although the program was mainly developed for prediction the motion in astern seas it can be used to predict the motion in any direction. The program has several options. This simulation program can predict the motion of a vessel successfully.
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A comparative study on the time-domain analysis of non-linear ship motions and loads was conducted by Watanabe and Soares (1999). The comparison of non-linear time-domain simulation programs from different organizations. A benchmark study has been performed by comparing the predictions of different non-linear time-domain codes applied to study the vertical wave-induced bending moment in a containership in waves of different steepness. Their comparative study gives good results for lower wave height region.
Method of time-domain computation of large amplitude 3D ship motions with forward speed was reported by Sen (2002). The computation method described here is transient Green function. Comparison of linear and nonlinear computations show that nonlinearities have a considerable influence on the results, particularly in predicting the instantaneous location of the hull in relation to the wave.
Wu and Hermundstad (2002) reported a time-domain simulation of wave-induced nonlinear motions and loads and its applications in ship design. In this paper a new approach for calculating the long-term probability of exceeding in the nonlinear responses is also described. Like others they also conducted experiment in the tank to validate their results. They obtained good results.
In 2003, time domain simulation of symmetric ship motion in waves was reported by Ballard, et al. (2003). They presented a mathematical model for predicting heave and pitch motion in regular waves where the memory effect has been included. They included non-linear incident wave and restoring force/moment contributions in their study. They calculated heave, pitch RAO in regular waves which shows good agreement. They also compared their result with experimental output.
The well-known strip theory proposed by Salvesen et al. (1970) is the method frequently used to solve this problem. But, it should be noted that this theory is developed for vessel motion in small amplitude and viscous effect is neglected.
2.4.2 Experimental Approach by Model Ship
The experimental approach is the most reliable method to evaluate vessel seakeeping. The main advantage of the model testing is that the ship needs not to be built before they can be operated in the sea. By model testing the performance of the ship can be assessed at the design stage. In model testing, suitable measurements are generally easier to accomplish than at full scale. To obtain the RAO in regular wave the experimental approach is the best approach, because the wave can be controlled in the regular wave test. The real behavior of the model ship can be obtained from this approach.
According to Aanesland and Stansberg (1995) experimental approach is quite sufficient for head and following sea. But for the beam sea it is really difficult to predict because in the beam sea condition the model need to be run in zero speed due to the breadth of the towing tank. The main reason is due to the ability of experiment to show the real situation in a particular condition. As shown by Grochowalski (1989) and Yamakoshi et al. (1982) the experimental approach is very useful and could be applied to simulate the problem of vessel stability in dynamic situation.
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Aanesland and Stansberg (1995) reported experimental seakeeping test results. They reported that the experimental result have better agreement with each other than with the numerical computations. Used separately or in combination experiment and computations may give realistic information about the ships that have been modeled. From their work they suggested to use several transient waves consisting of different frequency bands in order to get more completely RAO curves.
2.4.3 Full Scale Approach
Full scale seakeeping trials are made to confirm the seakeeping performance of a new vessel and to collect data for design purpose and for evaluating the accuracy of numerical predictions and model tests (Rantanen et al., 1995). The use of full scale trial is not confined to seakeeping trials only but may also be used when the tasks of the vessel requires reliable assessment of ship motion and sea-state. The full scale approach relates to the motion analysis as the real world situation.
Another full scale trial for the measurement of encountered waves and ship motions has been reported by Rantanen et al., (1995). They used the onboard wave measurement system as using wave buoy to measure the wave is difficult for a moving ship. Their system (wave radar) gave the output as vertical relative velocity instead of the motion. Their system showed prominent accuracy in full scale seakeeping trial.
2.4.3.1 The Measurement of Wave
There are two types of sea waves found in nature. Wind waves and swell. Wind blows for a long distant and the waves are created due to these wind. Swell are the waves that generated at the long distance and propagated thousands of kilometres and they are no more dependent on the wind. Wind-excited seaway can be approximated with good accuracy as the superposition of many elementary waves of different wave lengths and propagation directions.
The attempt to measure wave in the ocean is not new. For long period researchers have been trying to get the characteristics of the sea wave. To get the characteristics of wave it is necessary to know the characteristics of regular wave, although the regular waves are seldom found in nature. Hence their characteristics are very important for naval architects. However such waves do not occur in real ocean environment they can provide the way how to treat the irregular waves which are normally found in nature. In reality, waves are three-dimensional in nature and different components travel in different directions. Measurements of waves are difficult and thus spectra are made for “uni-directional” waves and corrected for three dimensional natures.
Bhattacharya, (1978) mentioned the importance of wave measurement in his book. He mentioned that the wave measurements in an actual seaway are necessary for the interpretation of full scale test results. Hashizume et al. (1989) reported results of a full scale measurement of ship motion in a severe sea together with an estimated wave energy spectrum. The non linearity of the motion was studied by means of time domain simulation based on the estimated wave energy spectra and the results were in good agreement with the measured motion. The characteristics of
wave parameters necessary for the design and operation of marine structure can be obtained from wave data analysis (Mynett and Keuning, 1990).
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and wave scattering. But the comparison of the wave energy spectra with the original one did not yield satisfactory agreement. Just after three months in December 1992 they presented a further developed method based on the so called “Baysian Model” with which better results were obtained. The idea to estimate a sea condition by means of onboard measurements of wave induced ship motions has been around for a long time (Hua and Palmquist, 1995).
Important progress in collecting full scale data has been made by the introduction of shipborne wave recorder (Tucker, 1956). The major advantage of using shipborne wave height sensor includes measurements of seaway parameters in seas too severe to launch a buoy reduced trial down time associated with buoy launch and recovery and an increase in collection time of seaway data available at zero speed as well as underway (Martin and Dipper, 1997). There were several research projects since 1970s with the purpose to develop methods for wave estimation by measuring the ship motions in an actual seaway.
Someys et al. (1987) developed an onboard-based surveillance system where the estimation of sea state was carried out by the full-scale measurements of the ship motion in waves. Hashizume et al., (1989) reported results of full-scale measurements of ship motions in a severe sea together with an estimated wave energy spectrum. To predict the performance of a ship in waves it is necessary to obtain the wave characteristics first. There are several ways to represent a seaway and the most famous method is the spectra representation. Many researchers have contributed in this area.
There is no alternative to establish a standard spectra in which the vessel is designed to operate. Several attempts have been taken in the last few years to find out the wave spectra for Malaysian water. Remarkable one was the measurement carried out by a research vessel Unipertama- VII on 1st March 2003 in east coast of Peninsular Malaysia (Yaakob et al., 2003). Another few attempts were taken for Full Scale Measurement on 2001 in the straits of Malacca near Kukup using the shipboard wave radar and near Pulau Sibu in South China Sea using CMST wave recorder respectively (Yaakob and Maimun, 2001). But these measurements did not put much emphasis on the RAO of the vessel. Normally the waves are measured to obtain one dimensional wave spectra but sometimes two dimensional wave spectra (directional) is also important in certain cases (Bhattacharya, 1978).
a. Visual Observation
The wave data can be assessed by the visual observation. This can be done by incorporating sea-state code. In 1970 the World Meteorological Organisation (WMO) agreed the standard sea state code is as shown in the Table 2.3 below. Each sea state code corresponds to a range of significant wave height and there is no indication of period.
Table 2.3: Sea-state codes
Sea State Code Significant Wave Height (m) Description
Range Mean 0 0 0 Calm (glassy) 1 0 - 0.1 0.05 Calm (rippled) 2 0.1 – 0.5 0.3 Smooth (Wavelets) 3 0.5 – 1.25 0.875 Slight 4 1.25 – 2.5 1.875 Moderate 5 2.5 – 4.0 3.25 Rough 6 4.0 – 6.0 5.0 Very Rough 7 6.0 – 9.0 7.5 High 8 9.0 – 14.0 11.5 Very High
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b. Wave Atlases
A very comprehensive atlas based on over 55 million observations from ships on passage between 1854 and 1984 was published as “Global Wave Statistics” by Hogben et al. (1986). This superseded the earlier work by Hogben and Lumb (1967). The new atlas covers virtually the entire globe and gives the probabilities of occurrence of significant wave height and zero crossing periods for all the sea area.
c. Satellite Altimeter
The concept of a satellite radar altimeter was established by an instrument carried on SKYLAB in 1973. It was not until March 1985 that another altimeter was launched in the US Navy’s satellite called Geosat. The European Space Agency’s (ERS-1) was launched in July 1991 and its still working. These altimeters measure the significant wave height with certain accuracy. According to Cater (1995) the design accuracy of HS specified to date for satellite radar altimeter has been 0.5 rms
or 10% of HS whichever is higher; and the 1 s values transmitted from satellite have
generally achieved this accuracy.
The satellite altimeter uses microwave radar pulse that is sent from the orbiting satellite, bounces off the earth’s surface and returns to the orbiting spacecraft to measure the wave height of sea at a certain location and time. The travel time of this pulse (the time it takes to get to the surface of the Earth and return to the satellite) is then recorded. The significant wave height is presumed from the stand up characteristic of a pulse waveform reflected from the sea surface on that occasion. The wave data measured by one of the satellite called TOPEX is available free online given by Jet Propulsion Laboratory at http://podaac.jpl.nasa.gov/topex
d. Neural Networking
wave heights closely agree with the measured wave heights. Their study shows that the wave forecasting can be efficiently carried out using neural networks.
2.4.3.2 The Concept of Wave Spectra
The wave spectra consider primarily is the short term local description of the ocean under stationary conditions in terms of significant wave height and average wave period. The concept of the spectra was first proposed by St. Dennis and Pierson in 1953. Several different spectra have been presented to represent a given sea-state. Therefore for a proper definition of ships operational environment ship designers need many representative wave spectra for different trade routes, with probability measures of the condition they represent. For that purpose a large number of sea–state observations have been collected by several authors and some atlases now exists.
Usually the wave amplitude can be represented as a function of time. From the representation the period of the wave can easily be distinguished. But this method is suitable for regular wave. For irregular wave where there is no definite shape of the wave amplitude then the spectral representation bears a good agreement. An irregular wave pattern can be generated if a large number of sinusoidal waves of different wavelengths and heights are superimposed on each other (Bhattacharya, 1978). The wave can be represented as spectra. These spectra are based on the frequency.
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Marks, (1967) reported in 1967 that during the full scale measurements onboard a hydrofoil boat, determined long crested wave energy spectra using measured pitch, heave, and relative motion at the bow. Webster and Dillingham, (1981) introduced a numerical model for estimation of wave energy spectra of short crested waves through ship motion measurement of surge, sway, heave, roll, pitch, and yaw at zero speed.
After that many oceanographer have proposed a number of empirical formula to describe the seaway as a function of wind speed (Bishop and Price, 1979). Those of Neumann, Darbyshire, the British Towing Tank Panel, and others have now been superseded by the Pierson-Moskowitz spectrum. This was obtained from the analysis of extensive wave data relating to fully developed sea conditions in North Atlantic Ocean. Some spectra developed for fully developed sea and some developed for partially developed sea.
2.4.3.3 The Response Amplitude Operator (RAO)
The RAO is like a filter function, which takes the wave as input, and gives the motion as output. RAO depends on the geometry of the ship hull and load conditions of the vessel as well as its speed and direction with respect to wave (Perez and Blanke, 2000). The accuracy of the RAO depends very much upon the directional distribution of wave energy since wave direction is estimated visually and the measured spectrum contains all the wave energy from different directions. The more long crested the waves are the better is the RAO estimate (Rantanen. et al., 1995). The RAO can be obtained from full scale trial although it is not an ideal approach because of problems associated with the wave measurements and determination of directionality aspects of the seaway (Fein et al., 1980).
2.4.4 Characteristics of Small Vessel in Dynamic Situation
The stability of small vessel is considered as a complex matter compared to the large vessel. The main reason is due to the size, specific mission and design of small vessel is totally different from large vessel. In the study of Nickum, (1978), he discussed the U.S. Coast Guard criteria and IMCO criteria of the seagoing vessel. He concluded that there was no problem had been found on the existing stability criteria as a guideline to evaluate vessel stability of large vessel. But, for vessel under 100m such as coastal freighters, coastal bulk carriers, fishing vessels, towing vessels, yachts and research vessels usually suffered the most part of casualties even it had satisfied the stability requirement. To solve this problem, the same type of vessel should be complied under the criteria, which is developed for vessel having similar characteristics.
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criteria proposed by IMCO, but he still emphasized that the stability instruction given by the regulatory body should be strictly followed by the operators to avoid casualty.
Morall, (1979) conducted capsizing experiment on small fishing boat models in various seas states and made a conclusion that the IMO criteria for stability were rather inadequate. He indicated that dependency on GM alone to define vessel stability is not enough. Then, he recommended more emphasis should be given on determining the maximum value and position of the maximum righting moment on the stability curves as well as the minimum value of the angle of vanishing stability. His findings were similar to the problem faced by many offshore supply vessels in United States, (Bovet, 1973). Casualty records showed that the dependency on GM alone in defining safe stability criteria has led to a number of vessels being lost.
Based on the analysis of vessel lost of small fishing vessel during 1965-1984 in north China inshore water, Huang et al (1995) found that many affected vessels are well designed to meet the requirement of the stability criteria. The findings indicated that, the main reason of this problem is due to the current stability criteria are simple. Those are based on the statical equilibrium between heeling and righting moment.
Obviously, many studies showed that the existing regulations are not enough for defining safe stability of small vessel in dynamic situations (effect of wind and wave). The main reason is due to small vessel having small reserve buoyancy and more susceptible to large motions as compared to large vessel. Hence, a critical look on the stability of small vessel should be carried out. It is recommended that the new stability criteria not only cover the possible problem arising in dynamic situation but also practical to be referred by the vessel designer and operator.
2.5 Seakeeping Criteria
seakeeping performance requirements. According to Khalil and Moazzem (1986) performance data for fishing vessel in Malaysia is important for improving their design. The seakeeping performance of fishing vessel is related to some critical values of motion related variables (Aanesland and Stansberg, 1995). The seakeeping performance assessment is usually criteria based. To define seakeeping criteria it is necessary to account for two aspects; the ability of the ship to physically carry out her mission and the working condition on board which must ensure that some comfort standard is met. A third aspect may be important for special type of missions which is the survival capacity in heavy weather (Fonseca et al., 2001)
No specific reference have been found in the literature concerning fishing vessel but the governing criteria may be considered as deck wetness, slamming, significant roll, pitch, and vertical accelerations. Basic seakeeping criteria will typically include ship motion and ship motion related phenomena as well as addressing seaway-induced loads and dynamic stability. In general, mission effectiveness will degrade with increasing motions in a seaway.
According to the ITTC Seakeeping committee (2005) the motion response criteria are those formulated on the basis of ship motions predicted by seakeeping computer programs or measured by experiments and/or full-scale trials. These include, Root Mean Square (RMS) roll, pitch and yaw angles, RMS vertical and lateral displacements, RMS vertical velocity as well as RMS longitudinal, lateral and vertical accelerations. All these criteria refer to whole ship responses which are not, in general, very sensitive to the prediction method applied, i.e. whether predicted by means of one of the strip method programs, other programs, or measured by tests.
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(2004) in their paper have given the typical performance criteria for personnel performance in a warship are listed bellow:
Table 2.4: Typical personnel performance for warships (Sarioz and Narli, 2004)
Application Motion Limit Location
General Vertical acceleration 0.4g Bridge
Lateral Acceleration 0.2g Bridge
Specific Task MSI 20% of Personnel Task Location
MII 1/min Task Location
(Note: MII is Motion Induced Interruption)
Usually the Seakeeping performance procedure is based upon the probability of exceeding specified ship motions in a sea environment particular to the vessels mission.
2.6 Summary of the Literature Review
the three methods would be a stronger performance prediction for fishing vessel operating in Malaysian Water.
CHAPTER 3
RESEARCH APPROACH
3.1 General
This chapter put emphasis on the different approaches which has been used to predict the motion and Response Amplitude Operator (RAO) of the vessel which is vital to analyze the seakeeping performance. The approaches that are used in this research are
1. Simulation Approach
2. Model Experiment Approach 3. Full Scale Approach
In the simulation part, investigation of large amplitude of motion and wave has been discussed. In the experimental approach part the detail of the model testing has been presented. Also the principle for calculating RAO from regular wave test has been presented. In the full scale part the principle of establishing wave spectra from time series wave data and the motion spectra and hence the RAO is presented.
3.2 Basic Steps in Predicting Ship Response in Waves (Seakeeping)
i. Choose suitable wave spectra. The spectra may be suitable theoretical spectra or may be the measured spectra.
ii. Calculate the encountering frequency ωe as a function of wave frequency ω , vessel speed V and the heading angle of the vesselS μ so that.
2 cos S e V g ω μ ω = ±ω
iii. Calculate the encounter spectra as following:
( ) ( )
e e d d S S ω ω ω ω ζ = ×iv. Obtain the RAO as
Parameter Input Wave sponse Re Vessel RAO=
v. Obtain the Response spectra as
( )
( )
2 RAO SSR ωe = ζ ωe ×
The estimation of vessel response can be obtained from full scale sea trial by motion monitoring system (VMMS), numerical calculation, and model experiment in towing tank. The wave input parameter is the wave spectra that can be obtained from the time series wave data that obtained from wave buoy. The different approaches for predicting the motion as described below:
3.3 Time Domain Simulation Approach
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Investigation of the behaviour of the vessel in different conditions would certainly help to provide a better understanding of the motion of the vessel. In order to take into account non-linearity changes in excitation forces, response of the vessel in time is a need to adopt in simulation modelling.
Time domain with small steps in time gives a very clear understanding what is happening. The simulation process starts from the beginning when the vessels motion (heave, pitch, roll, sway, yaw, surge, sway) is taken as zero as the initial condition. As time increases the vessel poses motion due to the excitation forces. At each time step the vessel motion can be examined in detail. The simulation process continues until the total allotted time for the simulation reached.
Regarding the motion of the vessel when the simulation runs in head or following sea the most significant motion is taken as heave and pitch. The most important effect of heave motion is the non-linear coupling between roll and heave due to changes in restoring forces and moment. This occurs due to the significant changes on the instantaneous underwater volume of the vessel which becomes more vital in the case of large amplitudes motion.
In the case of beam seas, pitching is usually small and thus it can be ignored. Due to the reasons explained above the equation of motion following non-linear coupled system of equations is used for the calculation of surge, sway, heave, roll, pith and yaw motions together with instantaneous sinkage and trim.
• Wave Excitation Forces
Waves may be considered as regular or irregular, but in this research regular waves are taken into account in the investigations undertaken. The wave excitation forces and moments can be separated into two: Firstly, the Froude-Krylov forces and moments which are caused by the undisturbed incident wave when it passes through the vessel, assuming that the vessel is not there; secondly, the diffraction forces and moments which are caused by the hydrodynamic disturbance due to the presence of the vessel. Wave excitation forces and moments are calculated by using a two dimensional method using integral equation.
• Hydrodynamic Coefficients
The hydrodynamic coefficients such as radiation force are very important in estimating vessel motions by theoretical and experimental methods. The theoretical method used in this research to estimate the hydrodynamic coefficients like added mass and damping is based on two dimensional linear potential theories and thus it does not include viscous effect. The sectional added mass and damping are integrated along the vessel to obtain the total coefficients of a vessel.
• Restoring Forces
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3.4 Model Experiment Approach
In the experimental approach the first part deals with the roll decay test. The roll decay test is performed to check the natural period of the ship and also to confirm the KG of the ship. In another way it can be said that the roll decay test is the validation of the loading of the vessel. The second part deals with the seakeeping experiment in different heading conditions. Regular wave was used for the seakeeping test. From the seakeeping experiment the ship motion and corresponding wave are measured and from them the RAO can be calculated. The experimental approach gives the following information:
i. Roll decay test to find the natural period of roll ii. Roll decay test determines the KG of the vessel
iii. Seakeeping test to obtain the RAO of the vessel in regular waves in different heading conditions and speeds.
iv. Seakeeping test to obtain the RAO following the Pierson-Moskowitz spectra in irregular wave.
The detail formulation to calculate the natural frequency of ship and hence the KG of the vessel has been provided in Chapter 6. The RAO obtained from experiment in different heading condition will be combined with the measured wave spectra to get the response spectra for different motions. These motion spectra include heave, pitch, and roll. These response spectra are based on the experiment.
3.5 Full Scale Approach
wave buoy and the measurement of vessel motion by Vessel Motion Monitoring System (VMMS).
The wave buoy measures the wave amplitude in time domain. This is an irregular wave pattern as shown in Figure 3.2. But by the linear theory of superposition it is assumed that this irregular wave is composed of many sinusoidal waves. Each wave has its own wave length and wave period. The principle can be described as in the following Figure 3.1:
Figure 3.1: Mechanism to convert time domain to frequency domain
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3.6 Encountering Wave Spectra
The wave buoy is not advancing at the same speed of the ship. So the frequency of wave it experiences can be said as wave frequency. But when a ship advances at a certain speed it experiences a wave of different frequency as the wave buoy experiences. For example, when the ship moves in the head sea she experiences higher frequency and when moves to following sea the observed frequency become less. The virtual frequency that the ship experiences in different heading angle is called the Encountering Frequency (ωe). Fig.3.3 showed the different ship headings.
Figure 3.3: Different ship headings
If the ship advances at V m/s and the heading of the ship relative to wave is
μ, and the wave frequency is denoted by ω then the encounter frequency (ωe) is given by the following expression:
If the wave spectra is denoted by Sς(ω) then the spectra encountered by the
vessel is given by the following expression:
g V S Sζ ωe ωζ ω μ cos 2 1 ) ( ) ( − = (3.4)
So there is a need to convert the wave spectra obtained from the wave buoy and relate it to the response spectra which is based on encounter frequency to get the RAO of the vessel in real condition. This has been illustrated in detail in the Chapter 7.
3.7 Concluding Remarks
In this chapter different approach adopted for finding motion and hence the RAO has been discussed. After getting the RAO from all three approaches they were compared to each other. The comparison has been shown in Chapter 8. Also the RAO obtained from simulation and experiment in regular waves will be used to find the motion response spectra using the principle of superposition. From these response spectra the root mean square (RMS) values will be calculated which would be used to assess the seakeeping performance of the vessel in Malaysian water.
CHAPTER 4
MATHEMATICAL MODELLING
4.1 General
Technique of simulating the large amplitude motion is presented in this chapter. The theory behind the time domain simulation program is explained here. This chapter also explains the forces and moments calculated by the program and the method used to solve the equations of motions.
4.2 Mathematical Model
Utilising time domain simulation approach to describe the motion of a ship in following and quartering seas have been done previously by many researchers like Paulling et al. (1975), Kastner (1982), Hamamoto et al. (1988) and de Kat and Paulling (1989). This method becomes popular mostly due to the capability of this technique to solve many non-linear terms arising in the equations of motion. Up to now, this method is still the important technique to predict the dynamic behaviour of a ship in waves.
hydrostatic component derives from the wave, accurate computation of the Froude-Krylov forces up to free surface is important in the simulation. For the hydrodynamic forces such as inertia and damping forces are calculated directly using the empirical formulas. This study assumed that the simulation procedure might not lead to serious error on the simulation result especially for the case where the frequency of encounter is low.
4.3 Component of Forces
The forces involved in the equation of motion are divided into excitation forces and reaction forces. Usually, excitation forces of a vessel are a component derived directly either from wave or wind force. In responses to the excitation forces, the vessel produces reaction forces (radiation forces). The following is the description of radiation forces (inertia forces, damping forces and restoring forces) and excitation forces (Froude-Krylov forces and diffraction forces) in the simulation program.
The radiation forces are defined as the force resulting from the radiation of the wave away from a vessel that forced the vessel to oscillate in calm water, Lewis (1988). The solution of the radiation forces is usually related to the determination of the added mass and damping coefficient. The added mass term is part of the hydrodynamic force due to the motion in phase of acceleration. The damping term is part of the hydrodynamic force due to the motion in phase of velocity. Various techniques have been developed to compute the terms of added mass and damping. The well-known Frank-Close-Fit method, which applies strip theory, is the most common method to calculate the added mass and damping coefficient, Atlar (1982). In the simulation, the hydrodynamic coefficients are predicted by using Frank-Close– Fit method.
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the case of the vessel moving in large amplitude and taking the coupling effect. Therefore, in this program, restoring force is calculated by integrating underwater volume up to still water in each time step and also takes into account the coupling effect between the motions.
The Froude-Krylov force is defined as the force result form the integration of the incident wave over the wetted surface of the vessel, where it is imagined that the pressure is undisturbed by the presence of the vessel, de Kat and Paulling (1989). In this study, interest is given on the vessel travelling in astern seas condition. Therefore, Froude-Krylov force is considered to play an important role in the total excitation force. It is calculated non-linearly by integrating of pressure in the undisturbed wave system up to the instantaneous wetted surface.
The diffraction forces are defined as the force caused by the diffraction of the incident wave due to the presence of the vessel. Diffraction force can be calculated by solving the diffracted wave potential. There are numerous methods to determine the diffracted wave potential including pure strip theory, slender body theory, and three dimensional sink-source methods. However, for the condition where the wavelength of the incident wave is large and the encounter frequency is low, the diffraction force is usually neglected in the wave excitation force. As indicated by Barrie (1985), including of diffraction effect might add to the accuracy of the simulation result, but without it did not lead to serious error on the simulation result.
4.4 Co-ordinate Systems
In deriving the basic equations of motions, two co-ordinate systems are utilised to describe the motions of a vessel, namely vessel co-ordinate system and wave co-ordinate system. The co-ordinate systems of this program are showed in Figure 4.1. G y z x O ξ ζ η
Gxyz : Vessel co-ordinate system about centre of gravity (G). Oξηζ : Wave co-ordinate system about still water surface amidships.
Figure 4.1: Co-ordinate systems
To describe the motion of the ship at the vessel co-ordinate system, a simple relationship between the vessel co-ordinate system and the wave co-ordinate system is necessary. Firstly, the velocity vectors in the vessel co-ordinate system have to transform to the wave co-ordinate system to obtain Eulerian angles of the vessel orientation with respect to still water surface. Secondly, forces due to the wave excitation are calculated by referring to the wave co-ordinate system. Lastly, the forces are transformed to the vessel co-ordinate system before the equations of motion can be solved. The detail of transformation between the two co-ordinate systems is shown in Appendix A.
4.5 Equations of Motions
