Ship stability for masters and mates by D. R. Derrett M.I.N.. Extra Master LONDON: THE MARITIME PRESS LIMITED
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