PRACTICAL SHIP WEATHER ROUTEING FOR

LIQUEFIED NATURAL GAS CARRIERS

MOHD AZUWAN BIN AHMAD

UNIVERSITI TEKNOLOGI MALAYSIA

PRACTICAL SHIP WEATHER ROUTEING FOR

LIQUEFIED NATURAL GAS CARRIERS

MOHD AZUWAN BIN AHMAD

A thesis submitted in fulfilment of the

requirements for the award of the degree of

Master of Engineering (Marine Technology)

Faculty of Mechanical Engineering

Universiti Teknologi Malaysia

JANUARY 2014

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To Maira and Ozil

iv

ACKNOWLEDGEMENT

Alhamdulillah, I have had tremendous fun doing this research as a part-time

student. Much of its content has slowly accumulated over the course of my career in

managing shipbuilding projects in Korea and China, where I have encountered, learnt

and understood many of the technical and commercial contents discussed and

dissected in the following chapters. By having mentioned that, I must thank several

people for their advice and support over the past years. My research supervisor, Ir.

Dr. Faizul Amri Adnan, has provided positive critic and guidance, as has panel for

group supervision from Universiti Teknologi Malaysia lead by Professor Dr. Roslan

Abdul Rahman. I am also hugely indebted to my colleagues in MISC Berhad for

their helpful comments, courage and persistence in getting me to complete the

research. I would also like to thank many hundreds of seafarers, whom I have never

had the chance to know them personally, for their continuous and collective effort in

recording, keeping and managing ship’s noon reports. I wish to thank my family,

especially my wife, Nurhani Basharuddin and my parents for their unflagging

support and encouragement in everything I do. Last but not least, I wish to thank

Vice President of Group Technical Services Department of MISC Berhad, Mr.

Nordin Mat Yusoff and his management team for the opportunity and financial

support for this study.

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ABSTRACT

The research developed a realistic model which encompasses the ship

routeing process, weather prediction methods, ship environment interaction and route

optimization algorithm. The optimization models were constructed for Tenaga Class

Liquefied Natural Gas Carriers (LNGC) using minimum time, minimum fuel

consumption or combination of both as objective functions. The ship service

performance data which was derived from the analysis of actual records of her past

voyages are incorporated in the ship routeing algorithm. The data has enabled a good

comparison between simulations and actual results. Ship routeing simulation based

on two methods i.e. standard route and simplified shortest path algorithm was

performed and the outcomes have demonstrated the economic and safety benefits.

The results indicate that potential cost saving is high likely and optimum benefit is

not fully acquired by the current standard route practice. Ship routeing may generate

savings in terms of both time and fuel consumption. Furthermore, it was found that a

shorter distance route is not necessarily an optimal solution. The optimal solution

arise from the consideration of all aspects i.e. dynamic weather changes, voyage

optimization, model constraints and objective function.

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ABSTRAK

Kajian ini membina model realistik yang merangkumi proses penghalaan

kapal, kaedah ramalan cuaca, kekangan model, interaksi kapal-persekitaran dan

algoritma laluan optimum. Model optimum telah dibina untuk Kapal Pengangkut Gas

Asli Cecair (LNGC) daripada Kelas Tenaga dengan pengunaan masa atau minyak

yang minimum, atau kedua-duanya sebagai fungsi objektif. Data prestasi servis

terbitan daripada analisis rekod-rekod sebenar perlayaran yang lampau adalah

digabungkan bersama algoritma penghalaan kapal. Data ini telah membolehkan

perbandingan yang baik diantara simulasi dan keputusan sebenar. Simulasi

penghalaan kapal berdasarkan dua kaedah iaitu laluan standard dan algoritma laluan

terpendek dipermudah telah dilakukan dan kebaikan ekonomi dan keselamatan telah

dihasilkan. Keputusan menunjukkan bahawa potensi untuk menjimatkan kos adalah

berkebarangkalian tinggi dan faedah teroptimum tidak dapat terhasil daripada praktis

laluan standard semasa. Hasil daripada penghalaan kapal mungkin menghasilkan

penjimatan untuk masa dan pengunaan minyak. Tambahan lagi, laluan berjarak

pendek tidak semestinya adalah laluan optimum. Penyelesaian optimum hendaklah

dihasilkan daripada pertimbangan semua aspek iaitu perubahan dinamik cuaca,

perlayaran yang dioptimumkan, model kekangan dan fungsi objektif.

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TABLE OF CONTENTS

CHAPTER TITLE PAGE

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENT iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF TABLES xii

LIST OF FIGURES xiv

LIST OF SYMBOL xvii

LIST OF APPENDICES xx

1 INTRODUCTION 1

1.1 Background and Problem Statement 1

1.2 Objectives of Research 4

1.3 Scopes of Research 5

1.4 Significance of Research 7

2 LITERATURE REVIEW 9

2.1 Introduction 9

2.2 Historical Background and

Development in Ship Routeing 10

2.3 Ship Routeing as an Optimization Solution 14

2.4 Meteorological Problem in Ship Routeing 17

2.5 Ship Performance Analysis in Ship Routeing 19

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2.5.1 Speed Correction 20

2.5.2 Speed Loss in Actual Seas 22

2.6 System and Model Constraint in Ship Routeing 23

2.6.1 Environmentally Induced Constraints 23

2.6.2 Ship Control Constraints 23

2.7 Ship Routeing as Mathematical and

Computational Problems 28

2.8 The Need for Realistic Ship Routeing Approach 31

3 RESEARCH METHODOLOGY 34

3.1 Introduction 34

3.2 Proposal on Realistic Approach for an Optimal

Ship Routeing 37

3.3 Implementation to Real Problem:

Case Study of Tenaga Class 43

3.4 Optimization Algorithm for Decision Making 51

4 PREDICTION OF SHIP PERFORMANCE 52

4.1 Introduction 52

4.2 Ship Resistance in a Seaway 54

4.2.1 Calm Water Resistance, calmR 55

4.2.2 Added Resistance Due to

Appendage, appendageR 57

4.2.3 Added Resistance, addedR 58

4.2.3.1 Wind Resistance, windR 59

4.2.3.2 Added Resistance Due

to Waves, AWR 60

4.2.3.3 Effect of Hull and Propeller

Surface Roughness, roughR 62

4.2.3.4 Resistance Change Due to Loading

Conditions (Draft and Trim), loadR 65

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4.2.3.5 Added Resistance Due to Steering,

Yaw Effect and Drift Effect, steerR 66

4.2.3.6 Effect of Ocean Current, currentR 67

4.2.3.7 Effect of Temperature and Salt

Content, seaR 69

4.2.3.8 Effect of Shallow Water, shallowR 69

4.3 Added Resistance and Speed Loss 70

4.3.1 Empirical and Approximate Formulation 71

4.4 Ship Propulsion and Efficiencies 76

4.4.1 Ship Efficiencies 78

4.4.1.1 Relative Rotative Efficiency, Rη 78

4.4.1.2Hull Efficiency, Hη 79

5 SHIP SERVICE PERFORMANCE IN ACTUAL SEAS 80

5.1 Introduction 80

5.1.1 Vessel 81

5.2 Analysis 1: Route Tracking 83

5.3 Analysis II: Weather Observation Record 83

5.4 Analysis III: Speed Profile 90

5.5 Analysis IV: Open Propeller Efficiency and

Propeller Coefficients 91

5.6 Analysis V: Ship Performance Curves 92

5.6.1 Speed Trial Curve and Calm Water Resistance 93

5.6.2 Speed Trial Curve and Lower Case (1st Curve) 96

5.6.3 Speed Loss Comparison 96

5.6.4 Added Resistance at Head Sea 99

5.6.5 Added Resistance Comparison 101

5.7 Analysis VI: Service Margins and Limits 102

5.8 Analysis VII: Hull and Propeller Fouling 104

5.8.1 Power Increment and Speed Loss Due to Fouling 107

5.8.2 Power Penalty: Comparison with Bowden and

Davison (1974) and Commercial Coating Product 109

5.8.3 Percentage Power Increase over Fuel Consumption 111

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5.9 Analysis VIII: Effect of Ocean Current 112

5.10 Analysis IX: Fuel Consumption 114

5.11 Analysis X: Seakeeeping and Ship Motions 117

5.12 Analysis XI: Loading Conditions 118

5.13 Analysis XII: Ship Performance Curve 119

6 SHIP ROUTEING – CASE STUDIES 128

6.1 Introduction 128

6.2 Case Study 1: Standard Route 129

6.2.1 Development of Standard Routes 130

6.2.2 Simulation Results 133

6.2.2.1 Optimization Based on Index 137

6.2.2.2 Optimization Based on Fuel Consumption 139

6.2.2.3 Optimization Based on Duration 140

6.2.2.4 Route Best Practice (R1) 141

6.2.2.5 Route Best Practice (R2) 142

6.2.2.6 Route Best Practice (All Routes) 143

6.2.2.7 Route Best Practice (R1 vs. R2) 144

6.3 Case Study 2: Simplified Shortest Path Algorithm (SSPA) 146

6.3.1 Introduction to SSPA 146

6.3.2 Simulation of SSPA – Constant Power 148

6.4 Validation by Comparison 153

7 DISCUSSIONS 156

7.1 Introduction

7.1.1 Discussion I: Trend of Fouling Effects 156

7.1.2 Discussion II: Accuracy of Weather Information

and its Effect 159

7.1.3 Discussion III: Fuel Consumption Curve 161

7.1.4 Discussion IV: Comparison between Standard

Routes 162

7.1.5 Discussion V: Optimal Ship Routeing and Best

Practices 164

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7.1.6 Discussion VI: Optimal Ship Routeing and Best

Practices 166

7.1.7 Discussion VII: On the Accuracy, Uncertainty

and Reliability 168

7.1.8 Discussion VIII: Benefits of Ship Service

Performance Analysis 169

8 CONCLUSIONS AND RECOMMENDATIONS 170

8.1 Summary 170

8.2 Recommendations for Future Works 172

8.3 Concluding Remarks 173

REFERENCES 174

APPENDICES

APPENDIX A 183

APPENDIX B 184

APPENDIX C 186

APPENDIX D 196

APPENDIX E 197

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LIST OF TABLES

FIGURE TITLE PAGE

2.1 Seakeeping and Motion Constraints 26

2.2 Route Optimization Algorithms/Methods 30

2.3 Ship Routeing in Summary 31

4.1 Comparison between Empirical and

Approximation Methods 73-75

5.1 Main Particulars of Tenaga Class 82

5.2 Beaufort scale of Wind 84

5.3 Monthly Wave Heading Occurrence (%) 88

5.4 Comparison of Resistance and Thrust

(Calm Water and Speed Trial) 95

5.5 Comparison of Resistance and Thrust

(1st Curve and Speed Trial) 96

5.6 Speed Loss Comparison 97

5.7 Power and Engine Speed Limit 104

5.8 Power Increment Due to Fouling 108

5.9 Speed Loss Due to Fouling 109

5.10 Calculation of Power Penalty 109

5.11 Summary on Validation Calculations 122

5.12 Speed Curves and Corresponding Beaufort scale 127

6.1 Detail of Check Points 131

6.2 Detail of Sub-Routes 131

6.3 Detail of Routes (Standard and Alternative) 132

6.4 Sample of Ship Routeing Results for January 134-136

6.5 Definition of X-Axis 138

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6.6 January (R1) Best Practice 141

6.7 January (R2) Best Practice 142

6.8 January Optimum Route (All Routes) 143

6.9 November Optimum Route (All Routes) 144

6.10 January Optimum Route – Contant Speed (R1 vs. R2) 145

6.11 January Optimum Route – Contant Power (R1 vs. R2) 145

6.12 Result Comparisons (Case A, B and C) 152

6.13 Comparison between Actual Voyage and

Ship Routeing Calculation (Complete Voyage) – Speed Based 154

6.14 Comparison between Actual Voyage and

Ship Routeing Calculation (Complete Voyage) – Duration Based 154

6.15 Comparison between Actual Data and

Ship Routeing Calculation (Daily Case) 155

7.1 Ship Routeing Results for January (R1) 162

7.2 Ship Routeing Results (R1 and R2) 163

7.3 Ship Routeing Results (R2 and R8) 164

7.4 Ship Routeing Results (Case A, B, C and R1) 164

7.5 Ship Routeing Results (Case A, Alternatives and Random) 167

7.6 Benefits of Ship Service Performance Analysis 169

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LIST OF FIGURES

FIGURE TITLE PAGE

2.1 Engine Load Diagram 24

2.2 Power Curve and Seakeeping Constraint 28

2.3 Construction of First and Second isochrones 29

3.1 Research Work Flow 36

3.2 General Approach for an Optimal Ship Routeing 39

3.3 Realistic Approach for an Optimal Ship Routeing

(Iteration Process) 40

3.4 Concept of Weather Zones and Route Constructions 41

3.5 Weather Zone Division and Approximation Ship Tracking 41

3.6 LNG Carriers’ Route Tracking 45

3.7 LNG Carriers’ Monthly Route Tracking in Weather Zone

E22 46

3.8 Ship Speed Prediction Algorithm for Route Simulation 47

3.9 Algorithm for Realistic Ship Routeing 49-50

4.1 Component of Ship Resistance in Calm Water, calmR 56

4.2 Ship Resistance Evaluation Methods 57

4.3 Resistance Due to Steering, steerR 66

4.4 Vector Summation for Speed, Heading and Current 68

4.5 Speed Loss Curve 72

4.6 Energy Flow of a Ship in Operation 76

4.7 Scheme of Speed Calculation 77

5.1 Division of Sea Zones 85

5.2 Sample of Scatter Diagram (Zone E22) 86

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5.3 Comparison of Significant Wave Height in Zone E22 89

5.4 Comparison of Mean Wind Speed in Zone E16 89

5.5 Speed Profile for Laden Case 90

5.6 Engine Output Profile for Laden Case 91

5.7 Example of Propeller Program Result Output 92

5.8 Calm Water Resistance 93

5.9 Ship Performance Curve (Power vs. Speed in Head Sea) 94

5.10 Speed Loss Percentage (%) 98

5.11 Transfer Function of Added Resistance 100

5.12 Transfer Function of Added Resistance 100

5.13 Added Resistance Comparison (High Curve) 101

5.14 Added Resistance Comparison (Head and Bow Quartering) 102

5.15 Powering Margin of NCR Power 102

5.16 Effect of Hull and Propeller Fouling over Time 105

5.17 Effect of Fouling over Years 107

5.18 Statement of Power Increment and Speed Loss 107

5.19 Survey of Hull Roughness 110

5.20 Effect of Coatings on Hull Roughness 111

5.21 Typical AF Paint Performance Curve 112

5.22 Occurrence of Current in Bintulu-Tokyo Bay Route 112

5.23 Sample of Ocean Current Data Analysis (Zone E19) 114

5.24 Average Specific Fuel Oil Consumption (SFOC) 115

5.25 Effect of Dry-Docking on Average Fuel Consumption 115

5.26 Daily Fuel Oil Consumption Curve 115

5.27 Power vs. RPM for Ballast Head Case 117

5.28 RPM vs. Speed (Head Sea) 123

5.29 Power vs. RPM (Head Sea) 124

5.30 Ship Performance Curve (Power vs. Speed in Head Sea) 125

6.1 Illustrations of Check Points and Standard Routes 132

6.2 Optimization Based on Index (January – All Routes) 137

6.3 Optimization Based on Index (June – All Routes) 137

6.4 Optimization Based on Index (January – R1 vs. R2) 138

6.5 Optimization Based on FOC (January – R1 vs. R2) 139

6.6 Optimization Based on Duration (January – R1 vs. R2) 140

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6.7 Sample of Simplified Algorithm 147

6.8 Ship Routeing Simulation for Case A 149

6.9 Ship Routeing Simulation for Case B 150

6.10 Ship Routeing Simulation for Case C 150

6.11 Optimized Route by Cases (Case A, B and C) 151

6.12 Illustration of Optimized Routes (Case A, B and C) 151

6.13 Comparison between Case 1 (Standard – Red) and

Case 2 (Case-by-Case – Green) 152

7.1 Effect of Hull and Propeller Fouling 158

7.2 Sample of Hull Roughness Readings 158

7.3 Comparison of Monthly Mean Wind Speed in Zone E13W 160

7.4 Comparison of Daily Mean Wind Speed in Zone E13W 160

7.5 Comparison of Daily Fuel Consumption Curve 162

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LIST OF SYMBOLS

PC Trial allowance

∆ Displacement

β Model scale

SV Vessel’s speed through water

totalR Total ship resistance

calmR Calm water resistance

addedR Added resistance

windR Resistance increase due to wind

AWR Resistance increase due to waves

roughR Resistance increase due to hull and propeller roughness

loadR Resistance change due to loading conditions

steerR Resistance increase due to steering, yaw and drift effects

currentR Resistance increase due to ocean current

seaR Resistance change due to temperature and salt content effect

shallowR Resistance change due to shallow water effect

wR Wave-making resistance

fR Frictional resistance

R∆ , FC∆ Added resistance coefficient

airρ Density of air

windV Relative wind speed

windC Wind coefficient

xviii

projectedA Lateral and/or longi. projected windage

ρ Density of seawater

)( ewS Wave spectral value

ξ Regular wave amplitude

w Circular frequency

R∆ Added frictional resistance

S Ship wetted surface

CV Current drift speed

rqdV Required speed over ground (SOG)

Cµ Encounter angle to stream on required trajectory

Tη Total efficiency

EP Effective power

BP Brake power of engine (power output)

Hη Hull efficiency

Bη Propeller efficiency behind hull, is defined by ROB ηηη ×=

Sη Shaft efficiency, taken as 0.98

Rη Relative Rotative Efficiency

t Thrust deduction factor

w Mean wake fraction

Oη Open propeller efficiencies

J , TK and QK Propeller coefficients

WT Wave period

H Wave height

λ Wave length

SWH Significant Wave Height

AHR Average Hull Roughness

nB , BN or BF Beaufort Number or Beaufort scale

FOC Fuel Consumption

g Gravity

LBP Length between perpendicular

xix

LNG Liquefied Natural Gas

LNGC Liquefied Natural Gas Carrier

KPI Key Performance Indicator

IMO International Maritime Organization

NMRI National Maritime Research Institute

OBO Carrier Ore-Bulk-Oil Carrier

BSRA British Ship Research Association

BOG Boil-Off Gas

NBOG Natural Boil-Off Gas

NM Nautical Miles

JIT Just-in-Time

GHG Greenhouse Gas

SSPA Simplified Shortest Path Algorithm

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LIST OF APPENDICES

APPENDIX TITLE PAGE

A The decomposition of total resistance on

displacement type of ships 183

B Sample of Scatter Diagram 184

C Ship Performance Curves 186

D Sample Screen Shot 196

E Sample Ship Routeing Simulation Results 197

CHAPTER 1

INTRODUCTION

1.1 Background and Problem Statement

Challenging world of shipping trade’s today is in the context of time, cost,

safety and seaworthy. The conundrum is become more complex given by the

following factors:

1. Rising bunker fuel cost

2. More focus on the environmental impacts from ship emissions

3. Higher demands on the ship delivery reliability

4. Fierce competition in sea logistic markets

5. Greater awareness on the ship energy efficiency

6. Development of “green ship”

All of those factors are paramount importance and are the key performance

indicators that control and determine the reliability, operability, safety, seaworthy,

profitability, viability, efficiency, survivability and the future of shipping industry

itself.

2

Whilst law makers are actively formulate and regulate rule-based

environmental protection laws and human safety in ship design and operation; and

ship designers around the world are now driven by the effort to optimize the

efficiency and design of a ship at early stage of ship design process, ship owner or

ship operator has to deal with most part of its; that is responsible to take and maintain

appropriate and effective measures during ship operation. The measures taken are to

ensure that the ship is operating at her optimal conditions i.e. meeting the business

schedule within reasonable cost and in safest condition. In this regard, one of the

recommended, recognised and proven measures is known as ship weather routeing.

By definition, ship routeing is a process in finding an optimum track for a

particular ocean transit by incorporating and anticipating weather conditions and

vessels characteristics in response. The optimization process will lead to cost-driven,

energy-driven, time-driven, safety-driven, seaworthy-driven voyage or combination

of these factors. When a merchant ship is on trading passage from terminal A to

terminal B, she is on the mission to arrive in timely and costly manner, in which,

safety and seaworthy are the constraints, and human is the decision maker. Through

this process, ship routeing is also known as optimum routeing.

As defined by Bowditch (1826), ship weather routeing develops an optimum

track for ocean voyages based on forecasts of weather, sea conditions, and a ship’s

individual characteristics for a particular transit. Within specified limits of weather

and sea conditions, the term optimum is used to mean maximum safety and crew

comfort, minimum fuel consumption, minimum time underway, or any desired

combination of these factors.

The complete ocean trading model consists of several successive stages

where each stage is dependent on the preceding stage. The reliability of sea

transportation mainly depends on the ability of the ship to perform it given task in

specified trading areas within specified timeline. For that reason, the environmental

3

conditions during transport and how the vessel reacts towards environment change

could affect overall reliability of delivery (Grin et al., 2005).

International Maritime Organization (IMO) through Resolution A.528 (13)

adopted on 17 November 1983 has since recommended and recognized ship routeing

practice and it’s contribution towards safety and economy benefit of ship operations,

crew and cargoes. The recommendation was resulted from the awareness on the

damage and total ship loss directly or indirectly caused by the meteorological and

oceanographic factors. It was also, however, highlighted that the final decision

regarding the ship’s navigation rests always with the master.

IMO has then established the minimum standards for ship routeing services

through circulation of MSC/Circ. 1063 on 19 December 2002, in following the new

evidence and conclusion from the Derbyshire case. The OBO carrier, Derbyshire,

was lost off Okinawa in 1980 despite having being supplied with weather routeing

advice. It was concluded that the information provided to the master was insufficient

to assist him in effectively avoiding the worst weather associated with the Orchid

typhoon. This regulation also safeguards the master’s right to deviate from advice

given that might conflict with his/her professional judgement.

At present, in commercial operations, shipmaster shows a natural tendency to

go for minimum passage time and minimum damage to ship and cargo at the earlier

part of voyage. To ensure to arrive on time with minimum fuel consumption at the

later part of the voyage would be the overall goal. Just-in-time arrival contributes to

cost savings. The lesser fuel is consumed, the more environmental friendly the

voyage has become. Similar kind of practice was reported by Hagiwara (1989) and

Bottner (2007).

On the other practice, it was made clear by past evidence indicated that early

concept of ship routeing was based on two different strategies i.e. route selection

4

based on expected weather pattern rather than follow the seasonal route or based on

seasonally recommended routes. These were reported by Chen (1978) and Bowditch

(1826). Both ways proved beneficial and successful to a certain degree. It is however,

the safety and economic benefits are obviously recognized and confirmed through

out centuries.

There are different set of priorities in ship routeing problem. For instance, for

cruise or passenger ship, passenger safety and comfort consistent with arriving on

schedule are the main requirements. Merchant ships with important cargoes may pay

little attention to crew comfort as long as schedule is met without jeopardising safety

of ship and her crew (Motte, 1981).

In this research, more attention and flexibility is given to the economy and

performance integrity of ship routeing i.e. flexibility in meeting schedule in costly

manner with safety and seaworthiness aspects are the constraints. The research will

also provide clear understanding and guideline on time, cost, safety and

seaworthiness from which interrelation and benefits that can be drawn from them.

The proposed approach can also be utilised with no or little modification to any other

type of vessels in any sea zones for any particular purposes.

1.2 Objective of Research

The objective of this research is to determine a practical approach for an

optimal ship weather routeing for Liquefied Natural Gas Carriers through utilisation

of ship service performance analysis.

5

1.3 Scopes of Research

The current research is focusing on the ship routeing based on ship

performance analysis in actual seas. Followings are the scopes of research, as listed

and summarised in sequence working orders:

1. Collect, manage and analyse daily LNG carriers’ onboard voyage data and

observation (Noon Report).

2. Analyse and establish ship service performance in actual seas based on past

voyage data recorded by LNG carriers.

3. Perform ship routeing for LNG carriers for laden case for Bintulu-Tokyo Bay

sea passage by utilising the ship service performance.

4. The objective of ship routeing shall be based on total fuel consumption and

passage duration. The result is validated against the actual past voyage of

LNG carriers.

In ship routeing procedures, other than ship performance prediction, there are

three (3) other elements required to produce more accurate and optimum results i.e.

weather (including sea conditions) prediction models, system or model constraints

and optimization algorithms. Those processes, with an exception of optimization

algorithms, are intentionally being excluded from the research. Those elements will

be discussed on its principle and also be implemented on “As If” basis. The

justifications for these exemptions are provided as follows:

1. “As If” basis is considered and applied for the research. It means as if the

ship routeing is made prior to the actual voyage had taken place on the past.

Weather information and actual route will be based on the actual records. The

main purpose of the inverse calculation is to generate more realistic scenarios

for a fair comparison and validation. This is considered as the best method to

prove the accuracy of the results.

2. Since the actual voyage had successfully taken place, it is being considered

that the model constraint i.e. technical, safety, engine and seaworthiness

6

constraints were fully met during the entire voyage duration. The same

principle is applied for the validation process since both validation and actual

voyage are using the same routes.

3. Previous researches have shown that optimization algorithms will produce an

optimum route as opposed to other route selections. Similarly, adoption any

of these algorithms will also produce similar effect i.e. a better route as

compared to the standard route taken by vessel during her past voyages. None

of these established algorithms will be included in the current research, but

few theoretical routes will be created in addition to the standard routes.

Comparison between routes will be made to prove the objectives of ship

routeing. In addition, simplified algorithm will be introduced to demonstrate

the ship routeing process in simple yet realistic way.

4. Previous researchers have comprehensively studied those three (3) aspects.

Their proposals or methods can be incorporated and integrated as add-on into

this proposal without affecting the fundamental of this research.

5. Research gap is found in the ship performance analysis part. As discuss in

item 3, most ship routeing methods relied on ship performance predictions or

empirical formulae. It is well known that prediction or empirical methods

have its own limitation and lower accuracy in some cases.

6. The case study is limited to LNG carrier operating on laden voyage from

Bintulu (loading terminal) to Tokyo Bay (unloading terminal). But the

proposed method shall valid for other cases, with no or little modification

needed.

7. Implementation of “As If” validation concept will prove that the propose ship

routeing is realistic and practical. This will be discussed in details in

subsequence chapters.

7

1.4 Significance of Research

The significance of this research can be categorised into four (4) different

stages i.e. voyage planning, in-service performance monitoring, post-voyage analysis

and design improvement.

At first stage, obviously, ship routeing is also a strategic voyage planning and

part of voyage optimization scheme. Clear benefits that can be obtained from these

pre-voyage planning activities include potential of fuel savings, improvement of

schedule reliability and integrity, and improvement in safety and seaworthiness

aspect during ship operation. Furthermore, a thoughtful voyage planning will reduce

green house gas emissions, provide protection of marine environment and reduce risk

of damage or accident at seas. IMO through resolution A.893 (21) “Guidelines for

Voyage Planning” adopted on 25 November 1999 and MSC.1/Circ. 1228 “Revised

Guidance to the Master for Avoiding Dangerous Situations in Adverse Weather and

Sea Conditions” on January 2007 has echoed similar objectives.

Secondly, throughout the ship routeing process especially on the ship

performance analysis part, performance monitoring of in-service vessels can be made

systematically and effectively. Ship’s officers can now have analysis tools that can

be used in order for them, not only to monitor, but also to decide on any changes

needed during voyage. This is especially needed when prevailing weather is different

from the anticipated or forecasted data. An evaluation by Li (2006) has also

confirmed that engagement of ship routeing services will help in resolving any claim

dispute as related to charter party agreement.

Similarly, post-voyage analysis can be made by fleet managers or concerned

parties. Performance comparison between fleet, mostly between sister vessels, can be

measured and analysed. Comparison between different propellers, anti-fouling paints,

service speeds, voyage route selections and ship’s draughts, to name a few examples,

8

can be analysed and concluded. In addition, paint maker or equipment manufacturer

can learn on how well their products or equipments responded or performed in actual

operation environments. On separate note, it is also been proved that collections of

wind data from ship’s daily reports provide important and accurate weather

information for specified sea areas.

Finally, all of the above will provide invaluable lesson, reference and input

for a better future ship design. Design for service can be derived from the lesson of

ship routeing process. For instance, through the ship performance analysis, designers

can now have a clear picture on how the ship is performing in actual seas and it

relation with operational efficiency. Therefore, anticipate service margin during ship

design and new building stage can be accurately estimated. Another example, ship

owner and ship charterer can determine the effective ship speed or fuel consumption

of charter party contract beforehand and this will provide competitive edge benefits

for both parties.

174

REFERENCES

Aalbers, A. B., and C. J. G. van Dongen. Weather Routing: Uncertainties and the

Effect of Decision Support Systems.

Aas-Hansen, M. (2010). Monitoring of hull condition of ships. Master dissertation,

Norwegian University of Science and Technology.

Aertssen, G. (1969). Service Performance and Trials at sea. 12th International

Towing Tank Conference (Vol. 25).

Aertssen, G. And Van Sluys, M. F. (1972). Service Performance and Seakeeping

Trials on Large Container, Transaction RINA, Vol. 114.

Aertssen, G. (1975). The Effect of Weather on Two Classes of Container Ships in the

North Atlantic. The Naval Architect.

Allsopp, T., Mason, A., and Philpott, A. (2000, January). Optimal Sailing Routes

with Uncertain Weather. Proceedings of The 35th Annual Conference of the

Operational Research Society of New Zealand. pp. 65-74.

Altosole, M., Borlenghi, M., Capasso, M. and Figari, M. (2007). Computer-based

design tool for a fuel efficient-low emissions marine propulsion plant. ICMRT

Proceedings.

Andersen, P., Borrod, A.S. and Blanchot, H. (2005). Evaluation of the Service

Performance of Ships. Marine Technology (42): pp. 177-183.

Aribas, F.P. (2006). Some Methods to Obtain the Added Resistance of a Ship

Advancing in Waves. Ocean Engineering, 34. pp. 946-955.

Avgouleas, K. (2008). Optimal Ship Routing. Master of Science, Massachusetts

Institute of Technology, Cambridge, MA.

Babbedge, N.H. (1975). Ship Speed Analysis, Master Thesis. Plymouth Polytechnic.

UK.

Baree, M.S, Inoue, Y. And Islam, M.R (2006). An Investigation of Added Resistance

of Ships in Oblique Seas. Transactions of the Hong Kong Institution of

Engineers, Vol.13, Number 2.

175

Bazari, Z. (2007). Ship energy performance benchmarking/rating: methodology and

application. Proceedings of IMarEST-Part A-Journal of Marine Engineering

and Technology, A9, 11-18.

Bijlsma, S. J. (1975). On Minimal-Time Ship Routing. Doctoral dissertation, Delft

University of Technology. Netherlands.

Bijlsma, S. J. (2008). Minimal Time Route Computation for Ships with Pre-Specified

Voyage Fuel Consumption. Journal of Navigation, 61(4), pp. 723.

Bijlsma, S. J. (2010). Optimal Ship Routing with Ocean Current Included. Journal of

Navigation, 63(03), pp. 565-568.

Bleick, W. E., and Faulkner, F. D. (1965). Minimal-Time Ship Routing. Journal of

Applied Meteorology, 4, pp. 217-221.

Blendermann, W. (2004). Ships May Encounter High Wind Loads – A Statistical

Assessment. Proceedings of the Institution of Mechanical Engineers, Part M:

Journal of Engineering for the Maritime Environment, 218(1), pp. 1-10.

Blok, J.J (1993), Resistance Increase of a Ship in Waves. Master Thesis. Delft

University.

Boese, P., (1970). Eine einfache methode zur berechnung der winderstansershohung

eines schiffes im seegang. Shiffstechnik 17 (86).

Bottner, C.U. (2007). Weather Routing for Ships in Degraded Condition.

International Symposium on Safety, Security and Environmental Protection.

National Technical University of Athens, Athens.

Bowden, B.S. and Davison, N.J. (1974). Resistance Increments due to Hull

Roughness Associated with Form Factor Extrapolation Methods. NMI Ship

TM 3800, January.

Bowditch, N (1826). American Practical Navigator, Publication No. 9 (1995

Edition). US Government Printing Office.

British Standard Institution (2002). ISO 15016:2002 - Ships and Marine Technology

- Guidelines for the Assessment of Speed and Power Performance by Analysis

of Speed Trial Data. London. British Standard Institution.

Bruce, A. E., Gadler, D. J., Nakamoto, K. M., and Cobleigh, K. (2011). U.S. Patent

No. 7,949,465. Washington, DC: U.S. Patent and Trademark Office.

Calvert, S. (1990). Optimal weather routing procedures for vessels on oceanic

voyages. Doctoral dissertation, Institute of Marine Studies, Polytechnic South

West, UK.

176

Chen, H.T. (1978). A Dynamic Program for Minimum Cost Ship Routing Under

Uncertainty. Doctor Philosophy, MIT, Cambridge, MA.

Chen, H., Cardone, V., and Lacey, P. (1998). Use of operation support information

technology to increase ship safety and efficiency. SNAME Transactions, 106,

pp. 105-127.

Chen, H. (2002), Weather Routing: A New Approach. Safety at Sea.

Chryssostomidis, C. (1972). Seakeeping Considerations in a Total Design

Methodology. Ninth Symposium on Naval Hydrodynamics. Paris.

Claessens, E. J., Pinkster, H. J. M., and Dallinga, R. P. (2005). On the Use of a

Wind-Wave Model in the Prediction of Operational Performance of Marine

Structures. International shipbuilding progress, 52(4), pp. 297-323.

Cox, A. T., and Cardone, V. J. (2002). 20 Years of Operational Forecasting at

Oceanweather. 7th International Workshop on Wave Hindcasting and

Forecasting October. pp. 21-25.

Dallinga, R., Daalen, E. V., Grin, R., and Willemstein, T. (2004). Scenario

simulations in design for service. Proc. of 9th Symposium of Practical Design

of Ships and Other Floating Structures (PRADS2004), Vol. 2, pp. 604-611.

De Jong, H. J., and Fransen, H. P. (1977). NSMB Trial Allowances 1976.

International Shipbuilding Progress, 24.

Delitala, A. M., Gallino, S., Villa, L., Lagouvardos, K., and Drago, A. (2010).

Weather Routing in Long-Distance Mediterranean Routes. Theoretical and

applied climatology, 102(1), pp. 125-137.

De Wit, C. (1969). Mathematical Treatment of Optimal Ocean Ship Routeing.

Journal of Engineering Mathematics, 3(1), pp. 80-80.

Dinham-Peren, T. A., and Dand, I. W. (2010). THE NEED FOR FULL SCALE

MEASUREMENTS. RINA Conference, William Froude Conference:

Advances in Theoretical and Applied Hydrodynamics-Past and Future,

Portsmouth, UK.

Dolinskaya, I.S., Kotinis, M., Parsons, M.G., Smith, R.L. (2008). Optimal Short-

Range Routing of Vessels in a Seaway. Journal of Ship Research (53:3): pp.

121-129.

Faltinsen, O. M. (1990). Sea Loads on Ships and Offshore Structures. Cambridge

Ocean Technology Series, Cambridge University Press.

177

Frankel, F. G. and Chen, H. T. (1980). Optimisation of Ship Routeing, Technical

Report no. NMRC-KP-189.

Fujii, H, and Takahashi, T. (1975). Experimental Study on the Resistance Increase of

a Ship in Regular Oblique Waves. Proceeding 14th ITTC.

Fujiwara, T., Ueno, M., and Ikeda, Y. (2006). Cruising Performance of a Large

Passenger Ship in Heavy Sea. Proceedings of the Sixteenth. pp. 304-311.

Gerritsma, J., Beukelman, W., 1972. Analysis of the resistance increase in waves of a

fast cargo ship. International Shipbuilding Progress 19 (217).

Grin R., Wilde, J. de and Doorn, J. van (2005). Assessment of LNG Transport

Chains Using Weather –Based Voyage Simulations. Transactions-Society of

Naval Architects and Marine Engineers (113): pp. 534-545.

Haddara, M. R., and Guedes Soares, C. (1999). Wind Loads on Marine Structures.

Marine structures, 12(3), pp. 199-209.

Hagiwara, H. (1989). Weather Routeing of (Sail Assisted) Motor Vessel. Doctor

Philosophy, University of Delft, Netherlands.

Haltiner, G. J., Hamilton, H. D., and Árnason, G. (1962). Minimal-Time Ship

Routing. Journal of Applied Meteorology, 1, pp. 1-7.

Haltiner, G. J., Bleick, W. E., and Faulkner, F. D. (1968). A Proposed Method for

Ship Routing Using Long Range Weather Forecasts. Monthly Weather

Review, 96(5), pp. 319-322.

Harries, S., Heimann, J., and Hinnenthal, J. (2003). Pareto Optimal Routing of Ships.

transformation, 772, pp. 1.

Havelock, T.H. (1942). Drifting Force on a Ship among Waves, Philosophical

Magazine. Volume 33.

Hermans, A. J. (2005). Added Resistance by Means of Time-Domain Models in

Seakeeping. Journal of ship research, 49 (4), pp. 252-262.

Hinnenthal, J., and Clauss, G. (2010). Robust Pareto-Optimum Routing of Ships

Utilising Deterministic and Ensemble Weather Forecasts. Ships and Offshore

Structures, 5(2), 105-114.

Hoffman, D. (1976). The Impact of Seakeeping on Ship Operations. SNAME Paper.

New York Metropolitan Section.

Hogben, N, Da Cunha, N.M.C. and Oliver, G.F. (1986). Global Wave Statistics,

Unwin Brothers, London.

Hogben, N. and Lumb, F.E. (1967). Ocean Wave Statistics, HMSO

178

Holtrop, J. and Mennen, G.G.J (1982). An Approximate Power Prediction Method.

International Shipbuilding Proqress, Vol 29, No. 335, pp l66-170.

Holtrop, J. (1984). A Statistical Reanalysis of Resistance and Propulsion Data.

International Shipbuilding Progress, Vol. 31, 1984.

Hong Kam, L. O., and McCORD, M. R. (1990). Value of Ocean Current Information

for Strategic Routing.

IMO (1983). Recommendation on Weather Routeing. Resolution A.528 (13). London.

IMO Publications.

IMO (1999). Guidelines for Voyage Planning. Resolution A.893 (21). London. IMO

Publications.

IMO (2002). Participation of Ships in Weather Routeing Services. MSC/Circular

1063. London. IMO Publications.

IMO (2007). Revised Guidance to the Master for Avoiding Dangerous Situations in

Adverse Weather and Sea Conditions. MSC/Circular 1228. London. IMO

Publications.

IMO (2009). Second IMO GHG Study 2009. International Maritime Organization

(IMO). London, UK.

Insel, M. (2008). Uncertainty in the Analysis of Speed and Powering Trials. Ocean

Engineering, 35(11), pp. 1183-1193.

Isherwood, R. M. (1973). Wind Resistance of Merchant Ships. RINA Supplementary

Papers, pp. 115.

ISO. (1985). Evaluation of Human Exposure to Whole-body Vibration, Part 3:

Evaluation of Whole-body z-axis Vertical Vibration in the Frequency Range

0.1 to 0.63 Hz. International Organization for Standardization.

ITTC (2008). Testing and Extrapolation Methods, Propulsion, Performance,

Predicting Powering Margins. ITTC Recommended Procedures and

Guidelines.

James, R.W. (1957). Application of Wave Forecasts to Marine Navigation, U.S

Oceanographic Office.

Journée, J. M. J. (1976). Prediction of Speed and Behaviour of a Ship in a Seaway,

ISP, Vol. 23, No. 265.

Journée, J. M. J., and J. H. C. Meijers (1980) Ship Routeing for Optimum

Performance. IME Transactions Vol. 92: pp. 1-17.

179

Journée, J. M. J., Rijke, R.J. and Verleg, G.J.H. (1987). Marine Performance

Surveillance with a Personal Computer. Finish Society of Automatic Control,

12-14 May 1987. Helsinki.

Joanna, S. and Roman, S. (2008). Adopted Isochrones Method Improving Ship

Safety in Weather Routing with Evolutionary Approach. R&RATA #2 (Vol.

1). pp. 139-147

Jurdziński, M., and Guze, S. (2010) An Approach to Modelling the Ship

Performance in Application to Ferry ‘Stena Baltica’. Annual of Navigation.

Klompstra, M. B., Olsder, G. J., and Brunschot, P. K. (1992). The Isopone Method in

Optimal Control. Dynamics and Control, 2(3), pp. 281-301.

Kwon, Y.J. (1982). The Effect of Weather, Particularly Short Sea Waves, on Ship

Speed Performance. Ph.D Thesis. University of Newcastle-Upon-Tyne.

Kwon, Y.J. (2008). Speed Loss due to Added Resistance in Wind and Waves. The

Naval Architect, 3: pp. 14–16.

Lee, H., Kong, G., Kim, S., Kim, C., and Lee, J. (2002). Optimum Ship Routing and

It’s Implementation on the Web. Advanced Internet Services and

Applications, pp. 11-34.

Lewis, E. V. (1967). Principles of Naval Architecture. The Motion of Ships in Waves.

Society of Naval Architects and Marine Engineers.

Li, C.H. (2006). Case Study Performance Evaluation Ship's Weather Routing Service,

National Cheng Kung University.

Lo, H. K., and McCord, M. R. (1998). Adaptive Ship Routing Through Stochastic

Ocean Currents: General Formulations and Empirical Results. Transportation

Research Part A: Policy and Practice, 32(7), pp. 547-561.

Lundblad, P., Eurenius, O., and Heldring, T. (2009, July). Interactive Visualization

of Weather and Ship Data. Information Visualisation, 2009 13th International

Conference. pp. 379-386.

Lloyd, A. R. J. M., and Andrew, R. N. (1977). "Criteria for ship speed in rough

weather." In Proceedings of the Eighteenth General Meeting of the American

Towing Tank Conference, Annapolis, 23-25 August 1977, Volume 2.

Llyod, A. R. J. M (1998). Seakeeping: Ship Behaviour in Rough Weather. United

Kingdom. A.R.J.M Llyod.

180

Maki, A., Akimoto, Y., Nagata, Y., Kobayashi, S., Kobayashi, E., Shiotani, S.,

Ohsawa, T. and Umeda, N. (2011). A New Weather-Routing System That

Accounts for Ship Stability Based on a Real-Coded Genetic Algorithm.

Journal of marine science and technology, 16(3), pp. 311-322.

MAN B&W (2001). Basic Principles of Ship Propulsion. MAN B&W Diesel A/S.

Maruo, H., (1957). The excess resistance of a ship in rough seas. International

Shipbuilding Progress 4 (35).

McKenzie, J. S. (1971). The Routeing of Ships. Journal of Transport Economics and

Policy, pp. 201-215.

Molland, A. F. (2008). The Maritime Engineering Reference Book: A Guide to Ship

Design, Construction and Operation. Butterworth-Heinemann.

Molland, A. F., Turnock, S. R., and Hudson, D. A. (2009). Design metrics for

evaluating the propulsive efficiency of future ships.

Moody, R. D. (1996). Preliminary Power Prediction during Early Design Stages of a

Ship. Cape Technikon Theses and Dissertations. Cape Peninsula University of

Technology.

Motte, R. (1981). Ship Based Weather Routieing (Using Dynamical Meteorogy).

Doctoral dissertation, Institute of Marine Studies, Polytechnic South West,

UK.

Motte, R., and Calvert, S. (1988). Operational considerations and constraints in ship-

based weather routeing procedures. Journal of Navigation, 41(03), pp. 417-

433.

Nabergoj, R., and Prpić-Oršić, J. (2007, April). A Comparison of Different Methods

for Added Resistance Prediction. 22nd International Workshop on Water

Waves and Floating Bodies, Plitvice/Croatia (Vol. 18).

NMRI (2006). Database of Winds and Waves - Internet Version, National Maritime

Research Institute.

OCIMF (1994). Prediction of Wind and Current Loads on VLCC's – 2nd Edition, Oil

Companies International Marine Forum , Witherby and Co. Ltd.

Oosterveld, M.W.C. and Oossanen, P. van (1975). Further Computer-Analyzed Data

of Wageningen B-Screw Series. NMSB Report No. 479.

Padhy, C. P., Sen, D., and Bhaskaran, P. K. (2008). Application of Wave Model For

Weather Routing of Ships in The North Indian Ocean. Natural Hazards,

44(3), pp. 373-385.

181

Panigrahi, J. K., and Umesh, P. A. (2008). Minimal Time Ship Routing Using IRS-

P4 (MSMR) Analyzed Wind Fields. Marine Geodesy, 31(1), pp. 39-48.

Panigrahi, J. K., Padhy, C. P., Sen, D., Swain, J., and Larsen, O. (2012). Optimal

Ship Tracking on Navigation Route between Two Ports: A Hydrodynamics

Approach. Journal of marine science and technology, pp. 1-9.

Pedersen, B. P., and Larsen, J. (2008). Modeling of ship propulsion performance. In

World Maritime Technology Conference WMTC2009, Jan. 21 (Vol. 24).

Prpić-Oršić, J., Nabergoj, R., and Trincas, G. (2008). The Methods of Added

Resistance Estimation for Ships in a Seaway. Symposium Sorta.

Prpić-Oršić, J., and Faltinsen, O. M. (2012). Estimation of Ship Speed Loss and

Associated CO2 Emissions in a Seaway. Ocean Engineering, 44, pp. 1-10.

Salvesen, N., Tuck, E. O., and Faltinsen, O. (1970). Ship Motions and Sea Loads.

Trans. SNAME, 78, pp. 250-287.

Sariöz, K., and Narli, E. (2005). Effect of criteria on seakeeping performance

assessment. Ocean engineering, 32(10), pp. 1161-1173.

Satchwell, C. J. (1984). The Evaluation of Wind Power for Commercial Vessels.

Ship Science Report No. 16, University of Southampton, Southampton.

Schrady, D. A., Smyth, G. K., and Vassian, R. B. (1996). Predicting Ship Fuel

Consumption: Update (No. NPS-OR-96-007). Naval Postgraduate School

Monterey Ca Dept of Operations Research.

Schultz, M. P. (2007). Effects of Coating Roughness and Biofouling on Ship

Resistance and Powering. Biofouling, 23(5), pp. 331-341.

Schultz, M. P., Bendick, J. A., Holm, E. R., and Hertel, W. M. (2011). Economic

Impact of Biofouling on a Naval Surface Ship. Biofouling, 27(1), pp. 87-98.

Sen, D., and Padhy, C. P. (2010). Development of a Ship Weather-Routing

Algorithm for Specific Application in North Indian Ocean Region. MARTEC

2010. pp. 21-27.

Shi, W., Grimmelius, H. T., and Stapersma, D. (2010). Analysis of ship propulsion

system behaviour and the impact on fuel consumption. International

Shipbuilding Progress, 57(1), pp. 35-64.

Sierevogel, L. M., Hermans, A. J., and Huijsmans, R. (1996). Time-Domain

Calculations of First and Second-Order Forces on a Vessel Sailing in Waves.

Proc. 21st Symp. Naval Hydrodynamic. pp.177-188.

182

Slavin, M. W. (1996). Weather Routeing using On-Board Guidance. British

Maritime Technology

Stoter, P. H. (1992). Ship Weather Routeing, the Meteorologists' Job? Meteo

Consultant B.V. Wageningen.

STX (2008). Analysis of Speed Test Results (Yard Standard Method). STX Corp.

Changwon.

Townsin, R.L. and Kwon, Y.J. (1982), Approximate Formulae for the Speed Loss

Due to Added Resistance in Wind and Waves, Royal Institution of Naval

Architect, Vol. 125, pp. 199-207.

Townsin, R.L., Kwon, Y.J., Baree, M.S. and Kim, D.Y. (1993). Estimating the

Influence of Weather on Ship Performance, Royal Institution of Naval

Architect, Vol. 135.

Townsin, R. L. (2003). The Ship Hull Fouling Penalty. Biofouling, 19(S1), p.p 9-15.

Tsujimoto, M., Kuroda, M., Shibata, N., Sogihara, N. and Takagi, K. (2009). On a

Calculation of Decrease of Ship Speed in Actual Seas. Conference

Proceedings, JASNAOE, Vol. 7E, pp. 77-80.

Tsutsumi, N., Takahashi, K., Igarashi, T., Ohyama, M., Saitoh, Y., Kaku, I., and

Nakamura (1998), M. Assessment of the 15-Year Service of the LNG Carrier

Bishu Maru, Kawasaki Heavy Industries Ltd. Japan. 12th International

Conference and Exhibition on Liquefied Natural Gas, Perth, Australia.

Uriarte Aretxabala, J. I., Iglesias Baniela, S., and Melón Rodríguez, E. (2007). The

Optimum Track Using the Classic Method Width the Help of a Personal

Computer. Journal of maritime research: JMR, 4(1), pp. 63-76.

WMO (1998). Guide to Wave Analysis and Forecasting. WMO-No. 702, World

Meteorological Organization, Second Edition.

WMO (2011). Manual on Codes - Part A, WMO-No. 306, World Meteorological

Organization, Section E, Vol. I.1.

Zhang, J., and Huang, L. (2007). Optimal Ship Weather Routing Using Isochrone

Method on the Basis of Weather Changes. International Conference on

Transportation Engineering: pp. 2650-2655.

Zoppoli, R. (1972). Minimum-Time Routing as an N-Stage Decision Process.

Journal of applied Meteorology, 11, pp. 429-435.