Table of Contents
Acknowledgements xiv
Nomenclature xv
Introduction 1
1 Flotation and Buoyancy 2
Aims and Objectives 2
Archimedes'Principle (OOW, MCM, ENG) 3
Displacement or Tonnage? (OOW, MCM, ENG) 6
Form Coefficients (OOW, MCM, ENG) 7
Block coefficient 7
Waterplane area coefficient 8
Amidships area coefficient 9
Hydrostatics (OOW, MCM, ENG) 10
Hydrostatics and Linear Interpolation (OOW, MCM, ENG) 11
Displacement and Deadweight Scales (OOW, MCM, ENG) 14
Hydrostatic Curves (ENG) 15
Load Line (OOW, MCM, ENG) 18
The TPC (OOW, MCM, ENG) 22
Fresh Water Allowance (OOW, MCM, ENG) 25
Dock Water Allowance (OOW, MCM, ENG) 26
Accuracy of the TPC (OOW, MCM, ENG) 28
Lumber or Timber Load Lines (OOW, MCM, ENG) 29
Assigning a Load Line (MCM, ENG) 30
Tabular freeboard 31
Block coefficient correction 33
Length and depth correction 33
Deck line correction 34
Superstructure correction 34
Sheer and bow height correction 34
Flotation and Buoyancy - Learning Checklist 35
2 Small Angle or Initial Metacentric Stability - Will My Ship Float Upright? 37
Aims and Objectives 37
The Centre of Buoyancy (OOW, MCM, ENG) 39
The Centre of Gravity (OOW, MCM, ENG) 40
Adding loads 40
Removing loads 43
Moving loads 43
Suspended loads 44
The Transverse Metacentre (OOW, MCM, ENG) 46
Minimum Initial Metacentric Heights (OOW, MCM, ENG) 53
Vessels carrying grain cargoes 53
Vessels carrying timber deck cargoes 53
Other vessels 54
Large Metacentric Heights (OOW, MCM, ENG) 54
Calculating KB, BM and GM for a Box Shaped Vessel (MCM, ENG) 55
Metacentric Diagrams (ENG) 58
Angles of List (OOW, MCM, ENG) 59
Angles of List for Vessels with Zero GM (MCM, ENG) 64
Fluids and Free Surface Effects (OOW, MCM, ENG) 65
Free Surface Effects in Rectangular Tanks (OOW, MCM, ENG) 75
A Summary of Formulae for Real Ships and Box Shaped Vessels (MCM, ENG) 76
Instability and Angles of Loll (OOW, MCM, ENG) 77
Heel Angle in a Turn (MCM, ENG) 80
Increase in Draught due to Inclining (MCM, ENG) 81
Small Changes in GM due to Small Changes in Loading (ENG) 83
Small Angle or Initial Metacentric Stability - Learning Checklist 85
3 Large Angle Stability - Just How Far Can She Roll? 89
Aims and Objectives 89
Calculating GZ and Drawing GZ Curves (OOW, MCM, ENG) 95
Calculating GZ at Small Angles (OOW, MCM, ENG) 97
Finding GM from the GZ Curve (OOW, MCM, ENG) 98
Cargo Shifts and Down-flooding (OOW, MCM, ENG) 101
Corrections to GZ due to Changes in the Vertical Centre of Gravity (Assuming Displacement Remains Fixed) (OOW, MCM, ENG) 101
Corrections to GZ due to a Transverse Centre of Gravity (OOW, MCM, ENG) 104
Changes in GZ due to Vertical and Transverse Changes in the Centre of Gravity (OOW, MCM, ENG) 111
GZ Curves and Unstable Vessels (OOW, MCM, ENG) 112
GZ Curves and Neutrally Stable Vessels (OOW, MCM, ENG) 115
GZ Curves and Combined Angles of List and Loll (OOW) 117
Instability and Recovering Loll Using GZ Curves (MCM, ENG) 117
Deck Edge Immersion Angles (OOW, MCM, ENG) 119
Moment of Statical Stability (MSS) or Righting Moments (OOW, MCM, ENG) 120
Using Righting Moment Curves to Find Angles of List (MCM, ENG) 121
Dynamic Stability (OOW, MCM, ENG) 126
How Accurate is Simpson's Rule in Determining the Area under a GZ Curve? (MCM, ENG) 131
Approximating GZ at Larger Angles (MCM, ENG) 137
Finding the angle of loll using the wall-sided formula (MCM, ENG) 140
Effective GM at the Angle of Loll (MCM, ENG) 141
Variations in GZ with Changes in Freeboard (Including Timber Deck Cargo) (MCM, ENG) 143
Changes in GZ with Variations In Beam (MCM, ENG) 146
Changes in GZ with Symmetrical Ice Accretion (MCM, ENG) 147
Changes in GZ with Asymmetric Ice Accretion (MCM, ENG) 148
Changes in GZ with Changes in Trim (MCM, ENG) 149
Changes in GZ with FSE (MCM, ENG) 151
Fixed and Free to Trim Curves (MCM, ENG) 152
GZ Curves for Vessels with Large Freeboards and Small Draughts (MCM, ENG) 155
GZ Curves for Vessels Showing Port and Starboard Angles (OOW, MCM, ENG) 156
Overview (OOW, MCM, ENG) 156
Effects on GZ approximation and dynamic stability (MCM, ENG) 159
Heeling Under the Effect of Wind (MCM, ENG) 161
Grain Regulations (MCM) 164
Large Angle Stability - Learning Checklist 170
4 Longitudinal Stability-Fore and Aft Balance 174
Aims and Objectives 174
Calculating GML for a Box Shaped Vessel (MCM, ENG) 177
MCTC - The Moment to Change Trim by 1 cm (OOW, MCM, ENG) 178
Calculating the Trim (OOW, MCM, ENG) 179
Changes in Trim (OOW, MCM, ENG) 180
Aft, Forward, Mean and True Mean Draughts (OOW, MCM, ENG) 182
Longitudinal Stability - Learning Checklist 184
5 Additional Calculations and Processes 185
Aims and Objectives 185
'Real Ship' Hydrostatic Data and Loading in Different Densities (MCM, ENG) 186
Layer Correction (MCM, ENG) 189
The Effect of Hogging and Sagging on Layer Correction (MCM, ENG) 194
Inclining Tests (OOW, MCM, ENG) 197
Changes in Hydrostatics with Trim and Heel (MCM, ENG) 204
Dry-docking and Grounding (MCM, ENG) 206
Draught Surveys (MCM) 213
Additional Calculations and Processes - Learning Checklist 220
6 Bilging and Damaged Stability 222
Aims and Objectives 222
Parallel Sinkage (MCM, ENG) 223
The Centre of Buoyancy after Bilging (MCM, ENG) 239
BM after Bilging a Full Beam Compartment (MCM, ENG) 243
BM after Bilging a Side Compartment (MCM, ENG) 244
The parallel axis theorem 245
Calculating the transverse inertia of the waterplane after bilging aside compartment (MCM, ENG) 248
BML after Bilging a Full Beam End Compartment (MCM, ENG) 250
BML after Bilging a Full Beam Compartment (ENG) 251
KG after Bilging (MCM, ENG) 253
GM and GML after Bilging (MCM, ENG) 253
Trim after Bilging (MCM, ENG) 254
List after Bilging (MCM, ENG) 256
GZ Curves for Vessels after Bilging a Side Compartment (MCM, ENG) 260
Damaged Stability Requirements 261
Passenger vessels pre-2009 (MCM, ENG) 261
The Stockholm Agreement (MCM) 264
Safe return to port regulations (MCM, ENG) 265
Damaged stability requirements - 'Type A' and 'Type B' vessels (pre-2009) (MCM) 265
SOLAS damaged stability rules post-2009 266
Bilging and Damaged Stability - Learning Checklist 268
7 Calculating Hull Shear Force and Bending Moment 270
Aims and Objectives 270
Basic Load, Sheer Force and Bending Moment Calculations 270
Calculating Hull Shear Force and Bending Moment - Learning Checklist 283
8 Calculating Hydrostatics Using Simpson's Rule 284
Aims and Objectives 284
Finding the Moment of Area about the X Axis, and the Centre of Area from the X Axis (ENG) 285
Finding the Moment of Area about the Y axis, and the Centre of Area from the Y Axis (ENG) 288
Finding the Second Moment of Area, or Inertia, Relative to the X Axis (ENG) 290
Finding the Second Moment of Area, or Inertia, Relative to the Y Axis (ENG) 291
Graphs and Parallel Axis Theorem (ENG) 292
Half Stations (ENG) 294
The Lines Plan (ENG) 297
Calculating the Underwater Volume and Displacement from the Lines Plan (ENG) 299
Finding KB (ENG) 301
Estimating KB Using Morrish's Method (ENG) 303
Transverse Inertia of the Waterplane and BM (ENG) 303
Calculating GM Using the Lines Plan Data 305
Finding the Tonne per Centimetre Immersion Value (ENG) 309
Calculating the Free Surface Moment in a Non-Rectangular Tank (ENG) 311
Multihulls (ENG) 313
Sponsons (ENG) 315
The Longitudinal Centre of Buoyancy (ENG) 318
The Longitudinal Centre of Flotation (ENG) 319
Longitudinal Inertia of the Waterplane and BML (ENG) 321
Moon Pools and Removed Areas of the Waterplane 323
Calculating Hydrostatics Using Simpson's Rule - Learning Checklist 324
9 Ship Resistance 326
Aims and Objectives 326
Components of Ship Resistance (ENG) 327
Frictional resistance (ENG) 328
Residuary resistance (ENG) 329
Form drag or viscous pressure resistance (ENG) 329
Wave making resistance (ENG) 329
Bulbous bows reduce wave making resistance (ENG) 330
Eddy drag (ENG) 332
Air drag (ENG) 332
Calculating Frictional Resistance Using Froude's Method (ENG) 332
The Froude Number (ENG) 335
Corresponding Speed (ENG) 337
Model Testing Using Towing Tanks (ENG) 338
Calculating the Resistance of a Ship from a Model Test Using Froude's Method (ENG) 340
Scaling of Geometrically Similar Vessels (ENG) 341
Laminar and Turbulent Boundary Layers 343
The Reynolds Number 345
Calculating Frictional Resistance Using the 1957 ITTC Friction Line 346
Form Factors and Viscous Resistance 347
Wave Interference Effects on Ship Resistance 350
Modern Methods for Calculating the Resistance of a Ship from a Model Test 355
Ship Resistance - Learning Checklist 359
10 Ship Propulsion 360
Aims and Objectives 360
Converting Resistance to Effective Power (ENG) 360
Powering a Vessel (ENG) 361
Losses in a Ship Propulsion System (ENG) 362
Mechanical efficiency (ENG) 362
Transmission efficiency (ENG) 363
Propeller efficiency (ENG) 364
Hull efficiency (ENG) 364
Propulsive coefficients (ENG) 365
Estimating Ship Power Requirements (ENG) 365
Admiralty coefficient (ENG) 366
Estimating Ship Fuel Requirements (ENG) 367
Fuel coefficient (ENG) 367
Estimating voyage fuel requirements (ENG) 368
Ship Propulsion - Learning Checklist 368
11 Screw Propellers 369
Aims and Objectives 369
Screw Propeller Terminology (ENG) 370
Blade back and face 371
Propeller rotation or walk 371
Propeller Performance (ENG) 372
Theoretical speed (ENG) 372
Apparent slip (ENG) 373
Advance speed and the Taylor wake fraction (ENG) 373
Real slip (ENG) 375
Speed relationships 375
Propeller thrust and torque (ENG) 376
Hull efficiency (ENG) 377
Propeller Design 378
Propeller design principles 378
Propeller efficiency 379
BP-δ propeller design charts 379
KT-KQ-J diagrams 380
Cavitation 382
Screw Propellers - Learning Checklist 383
12 Propeller Alternatives for High-Speed Craft 384
Aims and Objectives 384
Surface Piercing Propellers 384
Propeller efficiency 385
Cavitation 386
Appendage drag 387
Variable geometry 387
Shallow draught 387
System selection 388
Surface piercing propeller types 388
Vibration 390
Backing performance 390
Transitional speeds 391
Waterjet Propulsion 391
Waterjet Operating Principles 392
Main features of a waterjet system 392
Advantages of waterjet propulsion 392
Disadvantages of waterjet propulsion 393
Waterjet System Components 393
Jet system 393
Duct system 395
Pump system 395
Interaction between the waterjet system and hull 396
Overall efficiency of the waterjet system 396
Propeller Alternatives for High-speed Craft - Learning Checklist 397
13 Rudders 398
Aims and Objectives 398
Rudder Forces 398
Rudder Torque and Bending Moment 400
Equivalent Torque 401
Rudder Stock Stress 402
Rudders - Learning Checklist 402
14 Hydrostatic Force, Pressure and Centre of Pressure 403
Aims and Objectives 403
Hydrostatic Pressure (ENG) 403
Hydrostatic Centre of Pressure (ENG) 406
Hydrostatic Force, Pressure and Centre Of Pressure - Learning Checklist 408
15 Wind Propulsion for Ships 409
Aims and Objectives 409
Apparent Wind 410
Aerodynamic Forces 415
Kite Systems 417
Flettner rotors 417
Wind Propulsion for Ships - Learning Checklist 423
16 Solutions to Questions 424
Appendix 1 MV Reed - Sample Stability Data Booklet 683
Appendix 2 Derivation of Archimedes' Principle for Box Shaped Vessels 720
Appendix 3 Derivation of Archimedes' Principle for Semi-Circular Section Vessels 723
Appendix 4 Linear Interpolation Using the Equation of a Straight Line 726
Appendix 5 The Derivation of the TPC Formula 729
Appendix 6 The Derivation of the Fresh Water Allowance Formula 732
Appendix 7 The Derivation of the Change in KG Formula 735
Appendix 8 The Derivation of the Formulae Giving the Transverse Inertia of a Rectangular Waterplane and a Ship Shape Waterplane Measured through the Centreline 737
Appendix 9 The Derivation of the Relationship between Transverse Inertia, BM and Underwater Volume for a Box Shaped Vessel 740
Appendix 10 The Derivation of the Relationship between Transverse Inertia, BM and Underwater Volume for a Ship 745
Appendix 11 Maximum Angles of List on Passenger Vessels Due to Passenger Crowding 748
Appendix 12 The Derivation of the Formula Giving the Angle of List for a Neutrally Stable Vessel 749
Appendix 13 The Derivation of the Formulae Describing the Effect of Free Surfaces on Metacentric Height 753
Appendix 14 Passenger Vessel Heel in a Turn 757
Appendix 15 Derivation of the Increase in Draught When Heeling Formula 758
Appendix 16 The Mathematical Proof of the Determination of GM from the GZ Curve 760
Appendix 17 The Derivation of the Angle of Heel in a Turn Formula 761
Appendix 18 The Mathematical Proof of Simpson's Rule 763
Appendix 19 Alternative Criteria for Large Angle Stability (Timber Deck Cargo) 768
Appendix 20 The Direct Calculation of the Area Under a Generic GZ Curve 769
Appendix 21 The Derivation of the Wall-Sided Formula for Approximating the Righting Lever 770
Appendix 22 The Derivation of the Formula Giving the Effective Metacentric Height at an Angle of Loll 775
Appendix 23 The Derivation of the Formula Giving the Longitudinal Inertia of a Rectangle 778
Appendix 24 The Derivation of the Formula Giving the Longitudinal BM for a Box Shaped Vessel 780
Appendix 25 The Derivation of the Moment to Change Trim By 1 CM Formula 784
Appendix 26 The Derivation of the Trim Equation 787
Appendix 27 The Derivation of the Formula Linking Cargo Density, Stowage Factor and Compartment Permeability 788
Appendix 28 Derivation of the Formula Giving the Transverse Inertia of a Rectangular Waterplane Measured from the Long Edge 790
Appendix 29 Derivation of the Parallel Axis Theorem (Huygens-Steiner Theorem) 792
Appendix 30 Direct Calculation of Shear Force and Bending Moment 795
Appendix 31 Properties of Water 797
Appendix 32 Hydrostatic Force, Pressure and Centre of Pressure for Various Shapes 799
Appendix 33 The Derivation of the Formulae for Apparent Wind Speed and Angle 812
Works Cited 818
Index 819
