Pianc - Harbour Approach Channels

PIANC Report 120

Report n° 121 - 2014

Harbour approacH cHannels

Design guiDelines

PIANC‘Setting the Course’

The World association for Waterborne Transport infrastructure

in co-operation with

A

B

PIANC Report 120

Harbour approacH cHannels

Design guiDelines

pianc reporT n° 121MariTiMe naVigaTion coMMission

pianc ‘setting the course’

2014

PIANC Report 120

PIANC has Technical Commissions concerned with inland waterways and ports (InCom),

coastal and ocean waterways (including ports and harbours) (MarCom), environmental

aspects (EnviCom) and sport and pleasure navigation (RecCom).

This report has been produced by an international Working Group convened by the

Maritime Navigation Commission (MarCom). Members of the Working Group represent

several countries and are acknowledged experts in their profession.

The objective of this report is to provide information and recommendations on good

practice. Conformity is not obligatory and engineering judgement should be used in its

application, especially in special circumstances. This report should be seen as an expert

guidance and state of the art on this particular subject. PIANC disclaims all responsibility

in case this report should be presented as an official standard.

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isbn 978-2-87223-210-9

© all rights reserved

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Table of Contents 1 General Aspects ................................................................................................................ 1

1.1 Scope................................................................................................................... 1

1.2 Introduction ......................................................................................................... 1

1.2.1 Terms of Reference ...................................................................................... 1

1.2.1.1 Objective ......................................................................................... 1

1.2.1.2 Matters Investigated ......................................................................... 1

1.2.2 Structure of Report ....................................................................................... 2

1.2.3 Related PIANC Reports ............................................................................... 2

1.2.4 Members of the Working Group .................................................................... 2

1.2.5 Meetings ...................................................................................................... 3

1.2.6 Acknowledgements ...................................................................................... 3

1.3 General Aspects of Channel Design .................................................................. 4

1.3.1 Maritime Configuration of Ports ..................................................................... 4

1.3.2 Approach Channel Design Considerations .................................................... 4

1.3.3 Basic Definitions ........................................................................................... 5

1.3.4 General Project Criteria ................................................................................ 6

1.3.4.1 Basic Criteria ................................................................................... 6

1.3.4.2 Elements Defining a Channel ........................................................... 6

1.3.4.3 Types of Ships and Characteristics .................................................. 6

1.3.4.4 Limiting Operational Conditions ........................................................ 9

1.3.4.5 Human Error and Project Uncertainties .......................................... 10

1.3.5 Physical Environment Data ......................................................................... 10

1.3.5.1 Data Requirements ........................................................................ 10

1.3.5.2 Physical Environment Issues.......................................................... 11

1.3.5.3 Data Analysis and Modelling .......................................................... 12

1.3.6 Elements of Channel Dimensions ............................................................... 12

1.3.6.1 Channel Depth .......................................................................................... 12

1.3.6.2 Channel Width ........................................................................................... 13

1.3.6.3 Links between Vertical and Horizontal Dimensioning ................................. 13

1.3.7 Design Verification Procedures ........................................................................... 14

1.3.7.1 Deterministic Verification ........................................................................... 14

1.3.7.2 Probabilistic Verification ............................................................................. 14

1.3.8 Safety Factors..................................................................................................... 14

1.4 Processes in Channel Design and Design Philosophy ................................... 15

1.4.1 Design Process ................................................................................................... 15

1.4.1.1 Concept Design ......................................................................................... 15

1.4.1.2 Detailed Design ......................................................................................... 17

1.4.2 Design Methodology ........................................................................................... 18

1.4.2.1 The ‘Design Ship’ Concept ........................................................................ 18

1.4.2.2 Channel Depth, Width and Alignment ........................................................ 19

1.4.2.3 Aids to Navigation...................................................................................... 19

1.4.3 Probability Aspects in the Design Process ........................................................... 19

1.4.3.1 Marine Traffic and Risk Analysis ................................................................ 19

1.4.3.2 Vertical Channel Dimensions ..................................................................... 20

1.4.3.3 Horizontal Channel Dimensions ................................................................. 20

1.4.4 Risk Assessment ................................................................................................ 21

1.4.5 Upgrading Existing Channels .............................................................................. 21

2 Design of Vertical Channel Dimensions ......................................................................... 22

2.1 Channel Depth Factors ..................................................................................... 23

2.1.1 Water Level Factors ............................................................................................ 23

2.1.1.1 Reference Level (Datum) ........................................................................... 23

2.1.1.2 Design Water Level ................................................................................... 24

2.1.1.3 Tidal and Meteorological Effects ................................................................ 24

2.1.2 Ship-Related Factors .......................................................................................... 25

2.1.2.1 Static Draught............................................................................................ 26

2.1.2.2 Allowance for Static Draught Uncertainties................................................. 26

2.1.2.3 Change in Water Density ........................................................................... 26

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2.1.2.4 Ship Squat................................................................................................. 26

2.1.2.5 Dynamic Heel ............................................................................................ 30

2.1.2.6 Wave Response Allowance ....................................................................... 30

2.1.2.7 Net UKC (UKCNet) ...................................................................................... 33

2.1.2.8 Manoeuvrability Margin (MM) ..................................................................... 33

2.1.3 Bottom-Related Factors ...................................................................................... 34

2.1.3.1 Allowance for Bed Level Uncertainties ....................................................... 34

2.1.3.2 Allowance for Bottom Changes between Dredging ..................................... 34

2.1.3.3 Dredging Execution Tolerance ................................................................... 34

2.1.3.4 Muddy Channel Beds ................................................................................ 34

2.2 Air Draught Clearance (ADC)............................................................................ 36

2.3 Concept Design – Vertical Dimensions ........................................................... 37

2.3.1 Design Water Level ............................................................................................. 37

2.3.2 Ship-Related Factors (Fs) .................................................................................... 37

2.3.3 Air Draught Clearance (ADC) .............................................................................. 38

2.3.4 Concept Design Example Problems .................................................................... 39

2.3.4.1 Example 1: Finland, General Cargo Ship ................................................... 39

2.3.4.2 Example 2: Richards Bay, South Africa, Coal Bunker ................................. 40

2.3.4.3 Example 3: Zeebrugge, Belgium, Container Ship ....................................... 40

2.3.4.4 Example 4: Panama Canal, Tanker............................................................ 41

2.4 Detailed Design – Vertical Dimensions ............................................................ 42

2.4.1 Water Level Factors ............................................................................................ 42

2.4.2 Ship Factors ....................................................................................................... 42

2.4.2.1 Squat (SMax) ............................................................................................... 42

2.4.2.2 Dynamic Heel (ZWR) ................................................................................... 42

2.4.2.3 Wave Response Allowance (ZMax) .............................................................. 49

2.4.3 Bottom Factors ................................................................................................... 61

2.4.3.1 Allowance for Bed Level Uncertainties ....................................................... 61

2.4.3.2 Allowance for Bottom Changes between Dredging ..................................... 61

2.4.3.3 Dredging Execution Tolerance ................................................................... 61

2.4.3.4 Muddy Channel Beds ................................................................................ 61

2.4.4 Air Draught and ADC .......................................................................................... 61

2.5 Probabilistic Design Considerations ............................................................... 61

2.5.1 Criteria for Probability of Exceedance .................................................................. 62

2.5.2 Risk 63

2.5.3 Long-Term Probability Criterion ........................................................................... 64

2.5.4 Probabilistic Design ............................................................................................ 65

2.5.4.1 Monte Carlo Simulation Technique ............................................................ 66

2.5.4.2 Probabilistic Design Tools .......................................................................... 66

2.5.5 Operational Channel Allowance .......................................................................... 71

2.5.6 Tidal Window Design .......................................................................................... 72

3 CHANNEL WIDTH, HARBOUR ENTRANCES, MANOEUVRING AND ANCHORAGE AREAS.............................................................................................................................. 73

3.1 Concept Design - Horizontal Dimensions ........................................................ 74

3.1.1 Channel Width .................................................................................................... 74

3.1.1.1 Introduction to the Concept Design Method................................................ 75

3.1.2 Channel Alignment and Width Consideration ....................................................... 76

3.1.2.1 General ..................................................................................................... 76

3.1.2.2 Bend Configuration .................................................................................... 77

3.1.2.3 Basic Manoeuvrability ................................................................................ 77

3.1.2.4 Environmental Forces ................................................................................ 79

3.1.2.5 Visibility ..................................................................................................... 81

3.1.2.6 Bank Clearance and Ship-Ship Interactions ............................................... 81

3.1.2.7 Fairway Marking and Positioning Systems ................................................. 82

3.1.3 Outer Exposed Channel and Inner Protected Channel......................................... 82

3.1.4 One- or Two-way Channels ................................................................................. 82

3.1.4.1 Example 1 ................................................................................................. 85

3.1.4.2 Example 2 ................................................................................................. 85

3.1.5 Concept Design Methods for Straight Channels .................................................. 86

3.1.5.1 Basic Manoeuvring Lane WBM .................................................................... 86

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3.1.5.2 Environmental and Other Factors Wi .......................................................... 86

3.1.5.3 Additional Width for Bank Clearance .......................................................... 89

3.1.5.4 Additional Width for Passing Distance in Two-Way Traffic .......................... 90

3.1.5.5 Additional Width for Large Tidal Range ...................................................... 90

3.1.6 Concept Design Methods for Curved Channels and Bends .................................. 90

3.1.6.1 Turning Radius and Swept Path................................................................. 90

3.1.6.2 Additional Widths in Bends ........................................................................ 92

3.1.7 Introduction to Spanish and Japanese Concept Design Standards for Channel Width .......................................................................................................... 92

3.1.7.1 Spanish Recommendation for Maritime Works ........................................... 92

3.1.7.2 Japanese Design Method .......................................................................... 94

3.1.8 Harbour Entrances and Manoeuvring Areas ........................................................ 95

3.1.8.1 Introduction ............................................................................................... 95

3.1.8.2 Stopping Procedure and estimation of stopping distance ........................... 96

3.1.8.3 Harbour Entrance ...................................................................................... 97

3.1.8.4 Turning Basin ............................................................................................ 97

3.1.8.5 Clearance for Moored Ships ...................................................................... 98

3.1.9 Anchorage Areas .............................................................................................. 100

3.1.9.1 Introduction ............................................................................................. 100

3.1.9.2 Design Factors ........................................................................................ 100

3.1.9.3 Anchorage Design for a Vessel with One Anchor Ahead .......................... 101

3.1.10 Pilot Boarding and Landing Areas ..................................................................... 103

3.2 Detailed Design – Horizontal Dimensions ..................................................... 105

3.2.1 Motivation ......................................................................................................... 105

3.2.2 Tools and Methods ........................................................................................... 105

3.2.2.1 Detailed Parametric Design and Special Formulae................................... 105

3.2.2.2 Simulation Models ................................................................................... 106

3.2.3 Ship Manoeuvring Simulation Models ................................................................ 106

3.2.3.1 Introduction ............................................................................................. 106

3.2.3.2 Fast-Time Simulation ............................................................................... 107

3.2.3.3 Real-Time Simulation .............................................................................. 108

3.2.4 Traffic Flow Simulation Models .......................................................................... 109

3.2.4.1 System Boundaries ................................................................................. 110

3.2.4.2 Model Description .................................................................................... 110

3.2.4.3 Simulation Language ............................................................................... 111

3.2.4.4 Verification and Validation ....................................................................... 111

3.2.4.5 Capacity Estimation ................................................................................. 111

3.2.5 Traffic Flow Simulation Model to Determine Capacity ........................................ 112

3.2.5.1 Generator Component Process ............................................................... 113

3.2.5.2 Ship Class ............................................................................................... 113

3.2.5.3 Ship Length ............................................................................................. 113

3.2.5.4 Draught and Tidal Window ....................................................................... 113

3.2.5.5 Destination in the Port and Incoming and Outgoing Routes ...................... 113

3.2.5.6 Separation Times .................................................................................... 114

3.2.5.7 Inter-Arrival Time and Service Time Distribution ....................................... 115

3.2.5.8 Ship Component Process ........................................................................ 116

3.2.5.9 VTS Components Process ....................................................................... 117

3.2.6 Traffic Flow Model to Determine Safety Levels .................................................. 118

3.2.6.1 Introduction ............................................................................................. 118

3.2.6.2 Safety Domain ......................................................................................... 119

3.2.6.3 Vessel Paths ........................................................................................... 120

3.2.6.4 Evaluation of Simulation Results .............................................................. 121

4 OTHER ASPECTS .......................................................................................................... 123

4.1 Risk Management and Analysis ..................................................................... 123

4.1.1 General ............................................................................................................. 123

4.1.2 Maritime Incidents ............................................................................................. 125

4.1.3 Types of Incidents ............................................................................................. 125

4.1.4 Risk Analysis Methodologies ............................................................................. 126

4.1.5 Simplified Qualitative Matrix Method.................................................................. 126

4.2 Training ........................................................................................................... 128

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4.3 Operational Rules and Environmental Limits ................................................ 129

4.3.1 General ............................................................................................................. 129

4.3.2 Channels .......................................................................................................... 129

4.3.3 Harbour Entrances ............................................................................................ 130

4.3.4 Stopping Areas ................................................................................................. 131

4.3.5 Turning Areas ................................................................................................... 132

4.3.6 Anchorage Areas .............................................................................................. 132

4.3.7 Moorings Areas and Buoy Systems ................................................................... 132

4.3.8 Basins and Quays ............................................................................................. 133

4.4 Winter Navigation and Channel Design ......................................................... 135

4.4.1 General ............................................................................................................. 135

4.4.2 Factors Affecting the Design of a Channel for Winter Navigation ....................... 135

4.4.2.1 General Conditions .................................................................................. 135

4.4.2.2 Alignment and Geometry ......................................................................... 135

4.4.2.3 Channel Width ......................................................................................... 136

4.4.2.4 Channel Depth, Gross Underkeel Clearance ............................................ 136

4.4.2.5 Channel Markings/Aaids to Navigation ..................................................... 137

4.4.2.6 Harbour Basin ......................................................................................... 137

4.4.2.7 Pilotage ................................................................................................... 137

4.5 Environmental Issues ..................................................................................... 137

4.5.1 Regulations and Sustainability .......................................................................... 138

4.5.2 Work on Channels and Dredged Materials Management ................................... 139

4.5.2.1 Dredge Planning Activities ....................................................................... 139

4.5.2.2 Dredging ................................................................................................. 139

4.5.2.3 Disposal of Dredged Material ............................................................................ 139

4.5.3 Biodiversity ....................................................................................................... 140

4.6 Aids to Navigation (AtoN) ............................................................................... 140

4.6.1 Channel Markings ............................................................................................. 141

4.6.2 On-Board Navigation Systems .......................................................................... 142

4.6.2.1 Visual Navigation ..................................................................................... 142

4.6.2.2 Electronic Aids......................................................................................... 142

4.6.3 VTS/VTMS Systems and Impact ....................................................................... 143

4.6.4 Future Development of AtoN ............................................................................. 144

5 REFERENCES ................................................................................................................ 145

List of Appendices APPENDIX A: TERMS OF REFERENCE .................................................................................. 156

APPENDIX B: GLOSSARY, ABBREVIATIONS AND SYMBOLS ............................................. 159

B.1 GLOSSARY .............................................................................................................. 159

B.2 ABBREVIATIONS ..................................................................................................... 161

B.3 SYMBOLS ................................................................................................................ 162

APPENDIX C: TYPICAL SHIP DIMENSIONS ........................................................................... 169

C.1 Typical Ship Dimensions from ROM 3.1 ................................................................. 171

C.2 Japanese Statistical Analysis of Ship Dimensions................................................ 177

C.3 Relationship Between DWT and Hkt ........................................................................ 179

C.4 Relationship Between CB, Δ, Δm and ................................................................... 180

C.5 Relationship Between Ship’s Draught and Water Density .................................... 180

C.6 Japanese Metacentric Height Estimates ................................................................ 181

C.7 References ............................................................................................................... 181

APPENDIX D: PREDICTION OF SHIP SQUAT ......................................................................... 182

D.1 Ship Characteristics ................................................................................................ 182

D.1.1 Dimensionless Parameters .................................................................................. 182

D.1.2 Block Coefficient .................................................................................................. 183

D.1.3 Water Plane Cross-Sectional Area ....................................................................... 183

D.1.4 Ship Speed .......................................................................................................... 183

D.1.5 Calculated Ship Parameters................................................................................. 183

D.2 Channel Characteristics .......................................................................................... 184

D.2.1 Channel Types .................................................................................................... 184

D.2.2 Channel Parameters ............................................................................................ 185

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D.3 Combined Ship and Channel Parameters .............................................................. 186

D.3.1 Relative Depth Ratio h/T ...................................................................................... 186

D.3.2 Blockage Factor S ............................................................................................... 186

D.3.3 Velocity Return Factor S2 ..................................................................................... 187

D.3.4 Depth Froude Number Fnh .................................................................................... 187

D.3.5. Critical Speed in Canals VCr ................................................................................ 187

D.4 Empirical Squat Formulas....................................................................................... 188

D.4.1 Tuck (T) ............................................................................................................... 190

D.4.2 Huuska/Guliev (H) ............................................................................................... 191

D.4.3 ICORELS (I) ........................................................................................................ 194

D.4.4 Barrass3 (B3) ...................................................................................................... 195

D.4.5 Eryuzlu2 (E2) ....................................................................................................... 196

D.4.6 Römisch (R) ........................................................................................................ 197

D.4.7 Yoshimura (Y) ...................................................................................................... 200

D.5 Example Problems .................................................................................................. 200

D.5.1 BAW Model Container Ship in Unrestricted Channel ............................................ 200

D.5.2 SR108 Container Ship in Unrestricted Channel .................................................... 202

D.5.3 FHR Model Container Ship in Restricted Channel ................................................ 203

D.5.4 BAW Model Container Ship in Restricted Channel ............................................... 205

D.5.5 Esso France Model Tanker in Suez Canal............................................................ 206

D.5.6 Global Challenger Bulk Carrier in Panama Canal ................................................. 208

D.6. Special Effects on Squat ........................................................................................ 209

D.6.1 Passing and Overtaking Ships ............................................................................. 209

D.6.1.1 Head-On Passing Encounters ..................................................................... 209

D.6.1.2 Overtaking Manoeuvres .............................................................................. 210

D.6.2 Proximity of Channel Banks ................................................................................. 210

D.6.3 Channel Bottom Configurations............................................................................ 211

D.6.4 Muddy Bottoms .................................................................................................... 211

D.6.5 Ship Stern Transoms ........................................................................................... 215

D.7 Numerical Modelling of Squat................................................................................. 216

D.7.1 Numerical Methods .............................................................................................. 216

D.7.1.1 Slender-Body Models ................................................................................. 216

D.7.1.2 Boundary Element Models .......................................................................... 216

D.7.1.3 Computational Fluid Dynamic (CFD) Models ............................................... 217

D.7.2 Modelling System to Predict Ship Squat ............................................................... 218

D.7.3 Numerical Modelling Examples ............................................................................ 218

D.7.3.1 BAW Model Container Ship in Unrestricted Channel ................................... 218

D.7.3.2 SR108 Container Ship in Unrestricted Channel ........................................... 219

D.7.3.3 FHR Container Ship in Restricted Channel ................................................. 219

D.7.3.4 Esso France Tanker in Suez Canal ............................................................. 219

D.7.3.5 Global Challenger Bulk Carrier in Canal ...................................................... 219

D.8 Future of Squat Research ....................................................................................... 219

APPENDIX E: WATER DEPTHS IN MUDDY AREAS-THE NAUTICAL BOTTOM APPROACH 221

E.1 Introduction ............................................................................................................. 221

E.2 Mud Characteristics ................................................................................................ 221

E.2.1 Rheology ............................................................................................................. 221

E.2.2 Density ................................................................................................................ 223

E.2.3 Density-Rheology Relationship ............................................................................ 223

E.3 Criteria for Determining the Nautical Bottom ......................................................... 226

E.3.1 Echo-Sounding Criteria ........................................................................................ 226

E.3.2 Rheology-Related Criteria .................................................................................... 228

E.3.3 Ship Behaviour Criteria ........................................................................................ 229

E.3.4 Mud Density Level Criteria ................................................................................... 229

E.3.5 Actual Practice ..................................................................................................... 230

E.3.5.1 Belgium ...................................................................................................... 230

E.3.5.2 France ........................................................................................................ 231

E.3.5.3 Germany..................................................................................................... 231

E.3.5.4 The Netherlands ......................................................................................... 231

E.3.5.5 United States .............................................................................................. 232

E.4 Behaviour of Ships in Muddy Areas ....................................................................... 232

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E.4.1 Causes of Changed Behaviour ............................................................................. 232

E.4.2 Internal Undulations at the Interface (Internal Waves)........................................... 232

E.4.3 Resistance and Propulsion ................................................................................... 233

E.4.4 Manoeuvrability .................................................................................................... 234

APPENDIX F: AIR DRAUGHT .................................................................................................. 236

F.1 Introduction ............................................................................................................. 236

F.2 Air Draught Clearance (ADC) .................................................................................. 237

F.3 Concept Design ....................................................................................................... 238

F.4 Detailed Design ........................................................................................................ 238

F.4.1 Japanese Statistical Analysis of Air Draught Hst ................................................. 238

F.4.2 Detailed Design of ADC ........................................................................................ 239

F.4.3 Comparison Ballast Draught with Appendix C .................................................... 239

F.4.3.1 Oil Tanker, 300,000 DWT .................................................................................. 239

F.4.3.2 Container Ship, 100,000 DWT ........................................................................... 239

APPENDIX G: SPANISH AND JAPANESE METHODS FOR DESIGN OF CHANNEL WIDTH . 243

G1: SPANISH RECOMMENDATIONS FOR CONCEPT DESIGN WIDTH ................................. 244

G1.1 General Design Criteria ......................................................................................... 244

G1.1.1 Design Lifetime .................................................................................................. 244

G1.1.2 Elements Defining a Navigation Channel and Harbour Basin ............................. 245

G1.1.3 Design Criteria ................................................................................................... 245

G1.2 Horizontal Dimensioning of Channels and Harbour Basins................................ 248

G1.2.1 Introduction........................................................................................................ 248

G1.2.2 General Criteria ................................................................................................. 248

G1.2.3 General Layout Recommendations .................................................................... 249

G1.2.4 Fairway Width .................................................................................................... 250

G1.2.4.1 General Criteria ........................................................................................ 250

G1.2.4.2 Determining Nominal Width Bn by the Deterministic Method ...................... 251

G1.2.4.3 Determining Nominal Width Bn by the Semi-Probabilistic Method .............. 272

G1.2.5 Point of No Return ............................................................................................. 276

G2: JAPANESE NEW DESIGN METHOD OF FAIRWAY WIDTH DETERMINATION AT CONCEPT DESIGN ........................................................................................................ 277

G2.1 Basic Formulae of Fairway Width Determination ................................................ 277

G2.2 Ship Types ............................................................................................................. 278

G2.3 Estimation of Fundamental Manoeuvring Lane ................................................... 278

G2.3.1 Width Requisite against Wind and Current Forces ............................................. 278

G2.3.1.1 Drift Angle due to Wind Forces ................................................................. 279

G2.3.1.2 Drift Angle due to Current Forces.............................................................. 280

G2.3.2 Width Requisite against Yawing Motion ............................................................. 280

G2.3.3 Width Requisite for Drift Detection ..................................................................... 282

G2.3.3.1 Drift Detection by Observing Light Buoys with Naked Eye ......................... 283

G2.3.1.2 Drift Detection by Observing Light Buoys with RADAR .............................. 284

G2.3.1.3 Drift Detection by GPS .............................................................................. 284

G2.4 Estimation of Additional Width for Interaction Forces ........................................ 285

G2.4.1 Width Requisite against Bank Effect Forces ....................................................... 285

G2.4.2 Width Requisite against Two-Ship Interaction in Passing ................................... 287

G2.4.3 Width Requisite against Two-Ship Interaction in Overtaking ............................... 288

G2.5 Safety Factor Based on Risk Level ...................................................................... 290

G2.6 Fairway Width Determination ............................................................................... 290

G2.6.1 Determination Procedures ................................................................................. 290

G2.6.2 Design Examples ............................................................................................... 291

G2.7 Bend Curvature Determination ............................................................................. 295

G2.8 Calculation of Drift Angle due to Wind Forces (Addendum) ............................... 296

G2.8.1 Drift Angle and Check Helm ............................................................................... 296

G2.8.2 Linear Derivatives of Hull Forces and Rudder Forces ......................................... 296

G2.8.3 Wind Force Coefficients ..................................................................................... 297

G2.9 Calculation of Check Helm against Interaction Forces (Addendum) .................. 299

G2.9.1 Check Helm against Bank Effect Forces ............................................................ 299

G2.9.2 Check Helm against Two-Ship Interaction .......................................................... 300

G3: DETAILED JAPANESE FORMULAE ON WIND-WAVE-CURRENT EFFECTS VERSUS SHIP TYPE-SIZES ................................................................................................................... 303

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G3.1 Equations of Ship Manoeuvring Motion ............................................................... 303

G3.2 Wind Forces .......................................................................................................... 304

G3.2.1 Representations of Wind Forces ........................................................................ 304

G3.2.2 Estimations of Wind Force Coefficients .............................................................. 305

G3.3 Wave Forces .......................................................................................................... 306

G3.3.1 Lateral Deviation due to Yawing Motion ............................................................. 306

G3.3.2 Representations of Wave Drifting Forces ........................................................... 307

G3.4 Current Forces ...................................................................................................... 307

G3.5 Hull Forces and Rudder Forces ............................................................................ 308

G3.5.1 Hull Forces ........................................................................................................ 308

G3.5.2 Rudder Forces ................................................................................................... 308

G3.6 Linearised Motion Equations ................................................................................ 309

G3.6.1 Linearisation of Hydrodynamic Forces ............................................................... 309

G3.6.2 Linearised Sway and Yaw Equations ................................................................. 310

G3.6.3 Estimation of Linear Hull Force Derivatives ........................................................ 310

G3.7 Drift Angle and Check Helm in Course Keeping Motion under Wind Forces ..... 311

G3.7.1 Equilibrium Equations ........................................................................................ 311

G3.7.2 Drift Angle and Check Helm ............................................................................... 311