Ship Stability for Masters and Mates

Hydrostatics and Stability of ships are important subjects that are studied not only by naval architects but also by deck and engineering officers who are working aboard ships. The topics in this book are similar to the volume 1 of Basic Ship Theory and another ship theory book written by Russian naval scientists entitled Statics and Dynamics of the Ships.

I like this book very much because it provides a lot of worked examples ranging from simple up to complicated ones. The concept of mathematical integration using Simpsons' rules is introduced in page 68. These rules are used in most of the hydrostatics and volume calculations of ship forms.

Hydrostatic components such as form coefficients, ship displacement, center of buoyancy, center of gravity, metacenter height are discussed in the first few chapters of the book while more complicated subjects related to transverse stability, and effect of free surface of liquids on stability of ships are presented in later chapters of the book.

Although most of the ship form calculations are now executed using naval architecture and ship design software such as Maxsurf, Delftship and Fasthip, the author of the book deliberately provides samples of manual calculations to help students and practicing naval architects understand the philosophy and the theoretical foundation involved in ship theory and design.

The followings are the table of contents of the book

Preface vii

Introduction ix

Ship types and general characteristics xi

1 Forces and moments 1

2 Centroids and the centre of gravity 9

3 Density and speci®c gravity 19

4 Laws of ¯otation 22

5 Effect of density on draft and displacement 33

6 Transverse statical stability 43

7 Effect of free surface of liquids on stability 50

8 TPC and displacement curves 55

9 Form coef®cients 61

10 Simpson's Rules for areas and centroids 68

11 Final KG 94

12 Calculating KB, BM and metacentric diagrams 99

13 List 114

14 Moments of statical stability 124

15 Trim 133

16 Stability and hydrostatic curves 162

17 Increase in draft due to list 179

18 Water pressure 184

19 Combined list and trim 188

20 Calculating the effect of free surface of liquids (FSE) 192

21 Bilging and permeability 204

22 Dynamical stability 218

23 Effect of beam and freeboard on stability 224

24 Angle of loll 227

25 True mean draft 233

26 The inclining experiment 238

27 Effect of trim on tank soundings 243

28 Drydocking and grounding 246

29 Second moments of areas 256

30 Liquid pressure and thrust. Centres of pressure 266

31 Ship squat 278

32 Heel due to turning 287

33 Unresisted rolling in still water 290

34 List due to bilging side compartments 296

35 The Deadweight Scale 302

36 Interaction 305

37 Effect of change of density on draft and trim 315

38 List with zero metacentric height 319

39 The Trim and Stability book 322

40 Bending of beams 325

41 Bending of ships 340

42 Strength curves for ships 346

43 Bending and shear stresses 356

44 Simpli®ed stability information 372

Appendix I Standard abbreviations and symbols 378

Appendix II Summary of stability formulae 380

Appendix III Conversion tables 387

Appendix IV Extracts from the M.S. (Load Lines) Rules, 1968 388

Appendix V Department of Transport Syllabuses (Revised April 1995) 395

Appendix VI Specimen examination papers 401

Appendix VII Revision one-liners 429

Appendix VIII How to pass exams in Maritime Studies 432

Appendix IX Draft Surveys 434

Answers to exercises 437

Index 443

Hydrostatics and Stability

Ship’s hydrostatics and stability are the first subjects which students in naval architecture study before they deal with other subjects such as resistance and propulsion, ship’s strength and ship design.
Naval architecture is art and science of ship design and construction. In dealing with hydrostatic properties of ships, naval architects have to use mathematical approaches that are not exact calculations especially in determining the area of waterplane, the displacement of the ship and the position of the center of buoyancy and center-gravity of the ship.
Although naval architecture is not an exact science, it is a science. It is one of the most complicated yet fascinating engineering fields that demand every person involved in these subjects to have high proficiency in mathematics. The number of articles related to hydrostatics and stability on this blog, if you want to read, check them at  label Ship Stability of this blog. posts are still growing. So, if you find that the topics that you are looking for are not available, please come back again next time.

Simpson’s Second and first Rules for ship’s waterplane area calculation

Naval architects mostly use Simpson's first rule when calculating the waterplane area, the displacement of ship from curves of sectional areas which had been obtained from bonjean curves plotted against ship's draught and many other curves in ship design. In fact there are two other Simpson's rules which can be used for calculating areas of curve forms. They are Simpson's second and third rule. The latter is also called Simpson's 5, 8 minus 1 Rule. In today's post, I am going to explain how to calculate the area under a curve using Simpson's second rule and then compare the result with the calculation based Simpson's first rule.

The half breadth ordinates of a ship which are 20 meters equidistantly spaced are tabulated as follows:

Simpson's second rule calculation for waterplane area of a ship

We should remember that the sum of the area function calculated above is for half breadth only. To obtain the area of the waterplane for both sides of the ship, we have to multiply it with 2. Obviously the waterplane area of the ship will be:

Area WP = 3/8 x CI x Total of Area Function x 2 (for both sides of the ship)

= 3/8 x 20 x 81.9 x 2 = 1228.5 square meters

If the half breadth same ordinates is calculated using Simpson's first rule, then the tabulation will be as follows:

Simpson's second rule calculation for waterplane area of a ship

Area = 1/3 x CI x Total Area Function x 2 (for both sides of the ship)

= 1/3 x 20 x 92.3 x 2 = 1230.666 square meters

The small difference in the two calculations shows that the area obtained from both of the Simpson's rules are only close approximation to the correct area. We should remember that naval architecture is art and science of designing a ship. It is not an exact science but it is a science. As we dive deeper into the science of ship stability, we will use Simpson's rules more often for determining the area, the displacement and other hydrostatic properties of the ship. by Charles Roring