Ship stability

for masters and mates

by D. R. Derrett

M.I.N.. Extra Master

LONDON: THE MARITIME PRESS LIMITED

Contents

Part One

1 Forces and moments

2 Centroids and the centre of gravity

3 Density and specific gravity

4 Laws of flotation

5 Effect of density on draft and displacement

6 Transverse statical stability

7 Effect of free surface of liquids on stability

8 TPC and displacement curves

9 Form coefficients

Part ?'WO

10 Simpson's rules for areas and centroids

11 Fmal KG

12 Calculating KB, BM, and metacentric diagrams

13 List

14 Mom nts ~f statical stability <.&..; . , . 171,

15 Trim

16 Stability and hydrostatic curves

17 Increase in draft due to list

18 Water pressure

19 Combined list and trim

20 Calculating the effect of free surface of liquids

21 Bilging and permeability

Part Three

22 Dynamical stability

23 Effect of beam and freeboard on stability

24 Angle of loll

25 True mean draft

vii

Page

nii

26 The inclining experiment

27 Effect of trim on tank soundings

28 Drydocking and grounding

Part Four

29 Second moments of areas

30 Pressure and thmst. Centres of pressure

31 Metacentric height at the angle of loll

32 Heel due to turning

33 Unresisted rolling in still water

34 List due to bilging

35 Radial integration by Simpson's rules

36 Launching

37 Effect of density on trim

38 List with zero metacentric height

39 Tchebycheffs rules

Part Five

40 Shear force and bending moments

41 Aids to stability and seaworthiness

Appendices

I Extracts from the M.S. (Load Line) Rules, 1968

11 Summary of stability formulae

111 Standard abbreviations and symbols

IV Examinations syllabuses

V Conversion tables

V1 Specimen papers

Answers to exercises

Index

Page

220

224

227

INDEX

. . . . . . ALLOWANCE. Dock water 36 Prcsh watcr . . . . . . 34

. . . . . . . . . . . . . Angle a€ Loll .45. 2 L2 correction of . . . . . . 49 metacentric height at 256

. . . . . Angle of vanishing stability 163 . . . . . . . . . . . . . . . . Appendages 73

. . . . . . . . . . Archimedes' Principle 22 Areas. by Polar co-ordinates . . . . . 276

. . . . . . by Simpson's Rules 63 . . . by l'chebycheff's Rules 296

. . . . . . . . . . of warerplanes 67 . . . . . second moments of 236

. . . . . . . . . . . Attwond's Formula 125

. . . . . BF.AM. effect on stability 210 Beams. bending moments in . . . 308

. . . . . . . freely supported 313 . . . . . . . . . . . . . Bcnding moment 303

. . . . . in beams 308

. . . . . diagrams 309 . . . . . . . curves 326

. . . . . . . . . . . . . Bending stresses 329 . . . . . . . . . . . . . . . . . . . Bilging 190

. . . compartments amidships 190 . . . . . . . effect on stability 200 . . . . . . . end compartments 195 . . . . . . . side comparrments 270

. . . . . . . . . . . . . . Block coefficienr 59 . . . . . . . . . . . BM. longitudinal 129

transverse . . . . . . . . . . . . . . 97 . . . . . box-shapes 100

triangular prism . . 100 . . . . . . . . . . . Box.rhapcr. BM 100 . . . . . . . . . . . BML 130

KB . . . . . . . . . . . . 94 . . . . . . . . . . . . . nonjean curves 324

. . . . . . . . . . Buoyancy. centre of 22 by Simpson's Rules . 83

. . . . . . . . . . . . forcc of 22

. . . . . . . . . . . curves 325 . . . . . . . . . diagrams 322

. . . . . . . . . . . . reserve 26

CALIBRATING HYDROMETERS . . 24 . . . . . . . . . . . . . . . . . Cantilevers 309

. . . . . . . . . . . . Capsiring moment 44

Centre of buoyancy . . . . . . . . . 22. 41 . . . . . . . . . . . . Centre of flotation. 129

Sihpsan's Rules . . 79 Centre of gravity . . . . . . . . . . . . . 9. 41

by Simpson's Rules . . 79 effect of adding wcighr 12 .. "removing .. 10 .. s3shifting .. 13 .. ,.suspended .. 14

. . . . . . . . . . . . Cenrrc of pressure 245 by Simpson'sRuler . 248

Ccntroids . . . . . . . . . . . . . . . . . . . . 9 & centre of gravity . . . . . . . 9 by radial inregrarion . . . 278

. . . . . . by Simpson's Rules 79 Change of. draft due to Trim . . . . . . 133

. . . . . . . . . . . Coefficients Block 59 Form . . . . . . . . . . . . 58

. . . . . . . . Midships 61 Prismatic . . . . . . . . 61

. . . . . . . . Warerplane 58

. . . . . . . Combined list and trim 178

. . . . . . . Complementary rtresscs 306 . . . . . . . . . . . Compressive stresses 303

. . . . . . . . Correcting. angle of loll 49 . . . . Neutral equilibrium 44

Unstable equilibrium . . 44 . . . . . . . Curves. Bending mamenr 326

. . . . . . . . . . . . . Bonjean 324 . . . . . . . . . . . Buoyancy 325

. . . . . . . . . . Displacement 54 . . . . . . . . . . . . . . . GZ 156

. . . . . . . . . I%ydrostatic 166 . . . . . . . . . . . . . . . KN 160

. . . . . . . . . . . Launching 284 . . . . . . . . . . . . . . . Load 325

. . . . . . . . . M.V. Tankcr 167 . . . . . . . . . . . Shear force 326

. . . . . . . Sraticai stability 162 . . . . . . . . . . . . . . T.P.C. 52

. . . . . . . . . . . . . . . Cross curves. 156 . . . . . . . M.V. Tanker 157

. . . M.V. Cargo-carrier 161

DENSITY . . . . . . . . . . . . . . . . . . . 3 effect on draft & dlrplacemcnt 32 relative . . . . . . . . . . . . . . . 3

1b

Density of fresh water . . . . . . . . . . . 3 of salt water . . . . . . . . . . . 3

. . . Diagrams. bending moments 309 . . . . . weight and load 322

. . . . . . . . . shear force 309 . . . . . . . . . . . . Displacement curves 54

. . . . . . . . . . Dock water allowance 36 Draft. change due to trim . . . . . 133

effect of change of density . 289 . . . . . increase due t o list 170 ~~~. ~

. . . . . . . when launching 286 Drydocking . . . . . . . . . . . . . . . 227 Dynamical Stability . Definitions . . 204

evrecl' OF . . . beam & freeboard an stability 210

bilging on stability . . . . . . . . . 200 . . . . . . . . . change o f density 289

. . . . . drvdockine on stabilitv 227 0

free surface . . . . . . . . . . . . . 182 . . . . . trim on tank soundings 224

Equilibrium. Neutral . . . . . . . . . . 44 Stable . . . . . . . . . . 43

. . . . . . . . Unstable 44 Exercises:

1 . Forces and moments . . . . . . . . . . 8 2 . Centroidr and the ccntrc of gavity . 18

. . . . 3 . Density and Specific Gravity -21 . 4 L ~ W S O ~ flotation . . . . . . . . . . . . 31

5 . Ltfect ofdensity ondraft&di~plaoemnt 39 Trrnsvcrse statical stability . . . . . . 46

. . . . . . . . . . 7 Free surfdce effect 5 1 6 . . . . 8 . TPC and displacctncnt curves 56 9 . Form coefficients . . . . . . . . . . . . 62 0 . Simpson's Kuler . . . . . . . . . . . . 87

1 . Final K C. . . . . . . . . . . . . . . . . 92 . KB, BM, and mctacentricdiagrams . 108 8 1 3 . List . . . . . . . . . . . . . . . . . 116

14 . Mornentsof statical stabilitv . . . . . 126 15 . Trim . . . . . . . . . . . . . . . . . 15 1 16 .Stability and Hydrostatic curves . . 169

. . . . . 17.. lnc~ease in draft duc t o list 173 l 8 . U'atcr pressure . . . . . . . . . . . 177 1 . Combincd list and trim . . . . . . . 181

Frce surface effect of liquids . . . 189 l . Bilging . . . . . . . . . . . . . . . . . 203 @

22 . Dynamical stability . . . . . . . . . 209 24 . Annlc of loll . . . . . . . . . . . . . 215 25 .True mean draft . . . . . . . . . . . 219 26 .The inclining experiment . . . . . . 223 2 .Effect of trim on tank soundings . . 226

. . . . . . . . . . . . . d Drydocking 235 29 . Sccand mnoments of areas . . . . 213 ~ ~

i d Pre,.drc ~ n . 4 ihru.1 .. colrr 'c .S I I r rxm 2 5 5 j l \letd%.. 1tmlm3l>t a! d!:an$c at $011 2 0 0 I ? . Hrcldur 1.1 lurnlnf . . . 2 0 1

JDEX 393 33 . llnrciiitcd rollinpinstill walcr . . . 269 34 . List due $0 bilging . . . . . . . . . . . 275 35 .Radial Integration by Sin~pson'sRules 282 36 .Launching . . . . . . . . . . . . . . . 288 37 . Effecl of density on trlrn . . . . . . . 292 38 . List wlth rrro metilcrntris heighl . . 295 39 . Td~cbychc f f s Rules . . . . . . . . . 302 40 .Shear force and bending moments . . 341

FINAL KG . . . . . . . . . . . . . . . . . . 89 l'irsr Rule. Simpson's . . . . . . . . . . 63 Flotation. centre of . . . . . . . . . . 129

by Simpson's Rules . 79 Force. of buoyancy . . . . . . . . . . 22

resultant . . . . . . . . . . . . . 1 Forces. and moments . . . . . . . . . . . l

resolution of . . . . . . . . . . . 1 t'orm coefficients . . . . . . . . . . . . 58 Free surface effect . . . . . . . . . . . . 47 1:reeboard. effect on stability . . . 210 Freely rupporred beams . . . . . . . 313 Fresh warer allowance . . . . . . . . . . 34

GM . . . . . . . . . . . . . . . . . . .43 . 119 a t the angle of loll . . . . . . . . . 256 by inclining test . . . . . . . . . . . 220 effect of drydocking . . . . . 227 from stability curves . . . . . . . 163 list with zero GM . . . . . . . . . 293 virtual ioss duc to free surfacc . 182

Gotaverken's 1.odicaror . . . . . . . 350 Gravity. specific . . . . . . . . . . . . . . 19 Grounding . . . . . . . . . . . . . . . . . 227 G Z cur5.e~ . . . . . . . . . . . . . . . . . 156

effect of bilging . . . . . 201 for M.V. Tanker . . . . . 157

HARMONIC MOTION . . . . . . . . . 264 Heel. definition of . . . . . . . . . . . . 41

due to turning . . . . . . . . . 261 Height of the Metacentre . . . . . . . . 43 Hogging . . . . . . . . . . . . . . . . . . . 321 Homogeneous logs . . . . . . . . . . . . 29 Hydrometer . . . . . . . . . . . . . . . . 23 Hydn~static curves. . . . . . . . . . . . 166

for M.V. Tanker . . . 167

INCLINING 1~;XI'EKIMkNT . . . . . 220 Increase in draft due to list . . . . . 170 Inertia. mass moment of . . . . . . . 265 Initial metacentric height . . . . 119 . 163 Initial rnctacentre . . . . . . . . . . . 119 lntcrmediatc ordinates . . . . . . . . . . i 5

KB . B Y rMOKKISH'S FORMULA . . 95 hy Slmpson's R u l e s . . . . . . . . 83 for box-shapes . . . . . . . . . . . . 9 4

394 IE KB. for triangular prisms . . . . . . . . 94 Kelvin Hughes Stress Finder . . . . . 342 KG. by inclining test . . . . . . . . . 220

final . . . . . . . . . . . . . . . . . . 89 KM minimum . . . . . . . . . . . . . 105 KN curves . . . . . . . . . . . . . . . 160

for M.V. Cargo-Carrier . 161

LAUNCHING . . . . . . . . . . . . . . . 283 curves . . . . . . . . . 284 drafts . . . . . . . . . 286 Etern lifting . . . . 285

. . . . . . . . . tipping 283 1.aver. neutral . . . . . . . . . . . . . 330 . . Lever . r~ehrinv . . . . . . . . . . . . . . 43 . -~~~ L i f ~ b o a t s . . . . . . . . . . . . . . . . . . 59 Liquid pressure and thrust . . . . 244 List. and trim . . . . . . . . . . . . . 178

definitions . . . . . . . . . . . . . . 41 due to bilgirg sde comp~~tmcnts . 270 increasc in draft . . . . . . . . . 170 problems . . . . . . . . . . . . . 109 wlth zero GM . . . . . . . . . . . 29 3

Load. curves . . . . . . . . . . . . . 325 diagrams . . . . . . . . . . . 322 Lines . . . . . . . . . . . . . . . . 35

Loading Calculators. Kelvin Hughes . 342 SpcrryISintef . 347 Gotaverken's . 350

Logs. homogeneous . . . . . . . . . . . . 29 Loll. Angle o f . . . . . . . . . . 45 . 212 1.ongitudinal. BM . . . . . . . . . . . 129

Mcracentre . . . . . . . 131 stresses in still water. 318 stresses in waves . . . 320

MASS. AND WPICHT . . . . . . . . . 6 first moments of . . . . . . . . . 7 moment of inertia of . . . 265

Mean draft. true . . . . . . . . . . . . . 216 Metacentrc . . . . . . . . . . . . . . 41 . 119

hcighr of . . . . . . . . . . 43 longitudinal . . . . . . . 13 1

Mctacentric. diagrams . . . . . . . 102 height . . . . . . . 4 3. 119

at the qlcleof loll . 256 homstabiiliry m m . 163

Midships coefficient . . . . . . . . . . . . 61 Minimum KM . . . . . . . . . . . . . . . 105 Modulus of section . . . . . . . . . . . 333 Moment. of a force . . . . . . . . . . . 5

of sratical stability . 43. 118 resultant . . . . . . . . . . . 5 righting . . . . . . . . . . . . 43 to chanye nimonecentimerre 130 trimming . . . . . . . . . 128

Moments. and forces . . . . . . . . . . . 1

4DEX Moments. bending . . . . . . . . . . . 303

of inertia . . . . . . . . . 265 . . . . . . . . . . . . . of mass 7

Morrish's formula . . . . . . . . . . . . 95 Moreley's formula . . . . . . . . . . . 204 Motion. simple harmonic . . . . . . . 264

NEU1'KAL.EQUILIBRIUM . . . . . . 44 layer . . . . . . . . . . . . . 330

PARALLEL AXES 'I'HEORUM . . 238 Period of roll . . . . . . . . . . . . . . . 266 Permeability . . . . . . . . . . . . . . . 192 Pressure . . . . . . . . . . . . . . . . . . . 174

and thrust in liquids . . . 244 at any depth . . . . . . . . . 174 centre of . . . . . . . . . . . 245

by Simpson's Kules 248 Principle of Archime<!es . . . . . . . 22 Prismatic coefficient . . . . . . . . . . 61

RADIAL INIK~;RATION . AREAS 276 Centroids 278

Ralston Srability & Trim Indicator . 355 Rangc of stability . . . . . . . . . . . 163 Relative density . . . . . . . . . . . . . . l Y Reserve buoyancy . . . . . . . . . . . . 26 Rerolurion of. forces . . . . . . . . . . . l

mnments . . . . . . . . . 5 Resultant. forcc . . . . . . . . . . . . . . . 1

moment . . . . . . . . . . . . . 5 Righting. lever . . . . . . . . . . 43. 118

moment . . . . . . . . . . . . 43 Rolling . . . . . . . . . . . . . . . . . . . 264

pcriod . . . . . . . . . . . . . . . 266 Rules. Simpson's five-eight minusone . 66

first . . . . . . . . . . 63 second . . . . . . . . 64

SAGGING . . . . . . . . . . . . . . . . . 322 Sccond moments. of areas . . . . . 236

of warerplancs . 239 Sccond rule . Simpson's . . . . . . . . . . 64 Section modulus . . . . . . . . . . . . . 333 Shcar forccs. and bending moments 303

cuwcs . . . . . . 329. 335 diagrams . . . . . . . 326

Shearing stresses . . . . . . . . . . . . . 304 Simple harmonic motion . . . . . . . 264 Simpson's Rules . . . . . . . . . . . . . . 63

First rule . . . . . . 63 Second rule . . . . 64 Third rule . . . . . . 66 Appendages . . . . 72 Centreof buoyancy . 83 Centreof flotation . 79 Centre of gravity . . 79

INDEX 395

Simpson's Rules. centroids . . . . . . 79 Tonnes per centimetre immcrsk. n . . 25 radial integration . 276 curves 52 volumes . . . . . . . . 72 Transverse . BM . . . . . . . . . . . . . . 97

Specific gravity . . . . . . . . . . . . . . . 3 statical stability . . . . . . 41 SperryISintef . . . . . . . . . . . . . . . 347 Triangular prisms . BM . . . . . . . 100 Stable equilibrium . . . . . . . . . . . . 43 KB . . . . . . . . 94 Stability. and trim indicator . . . . . 355 Trim . . . . . . . . . . . . . . . . . . . . . . 15

cross curves . . . . . . . . . 156 and list . . . . . . . . . . . . . . . 178 for M.V. 'Tanker 157 change o f drafr due t o . . . . . 133

dynamical . . . . . . . . . . . 204 due to bilging . . . . . . . . . . 195 effect of beam . . . . . . . 210 effect <, f discharging weights . 136 effect of bilging . . . . . . . 200 effect of loading weights . . . 136

Stability. effect of freeboard . . . 210 effect uf shifting weights . . . 134 range of . . . . . . . . . . . 163 effect o n tank soundings . . . 224

Statical stability. curves . . . . . . . 162 moment . . . . . . . . . . . . . . . 128 moment of . . . 43 . 118 to find the centre of flotation 143 transverse . . . . . . 41 to find the longirudinai GM . . 148

Stern lifting . . . . . . . . . . . . . . . 285 to keep a constant draft aft . . 144 Strength of ship . . . . . . . . . . . . . 303 to produce a requcred draft aft . 146 Stress finders . . . . . . . . . . . . . . . 342 True mean draft . . . . . . . . . . . . . 216 Strerres . . . . . . . . . . . . . . . . . . . 303 'Turning. heel due ro . . . . . . . . . . . 261

bending . . . . . . . . . . . . . 329 co:nplcmrntnry . . . . . . . 306 hogging . . . . . . . . . . . . . 321 UNRESISTED rolling in still water 264 longitudinal. in still water 318 Unstable equilibrium . . . . . . . . . . 44

in waves . . . 320 correction of . . 44 sagging . . . . . . . . . . . . . 322 shearing . . . . 304. 329. 335 tensile and cornpressive 303

TANK SOUN1)INC.S. effect of rrim 224 Tchebycheff's Ruler . . . . . . . . . . . 296 Tender and sriff ships . . . . 4 5 . 119 l'rnsile and compressive stresses . . . 303 Theorem of parallel axes . . . 238 Third rulc. Simpsun's . . . . . . . . . . 6 6 Thrust. and pressure . . . . . . . . . 244

total . . . . . . . . . . . . . . . 244 . . . . . . . . . . . resultant 244

Tipping centre . . . . . . . . . . . . . 129 Tipping . . . . . . . . . . . . . . . . . . . 283

VANISHING STALIII.ITY, angle of 163 . . . . Variable immersion hydrometer 23

Virtual loss of GM. duerofrcesurfacel82 due to drydocking227

Volumes. of ship shapes . . . . . . . . 72

WALL-SIDED FOKMIJ1.A . . . . 120 Waterplane . Areas and second rrumena239

coefficient . . . 58 Water pressure . . . . . . . . . . . . . 174 Weight. and mass . . . . . . . . . . . . . 6

diagrams . . . . . . . . . . . 322

ZERO GM. list due t o . . . . 293