Index Abbreviations and symbols 378±9 After draft, maintaining 149±51 Angle of heel 43, 48 Angle of list 231 Angle of loll 46, 48±9, 227±32 correcting 51±4 formulae 385 Angle of vanishing stability 168 Appendages 79±82 Archimedes Principle 22 Area calculations 68±77, 84±5 Attwood's formula 131 Beam, effect of increase on stability 225±6 Beam theory 325 bending moments 330, 331±3 bending stresses 356±61 freely supported 333±9 shear forces 331±3 shearing stresses 361±4 stresses 325±30 Bending see beam theory Bending moments: in beams 330, 331±3 in ships 347±8 Bending stresses, in hull girder 368±70 Bilging 204±207 effect of permeability 201±10 effect on stability 214±15 in end compartments 210±14 in side compartments 296±300 Block coef®cient 62, 280 Blockage factor 280, 306 BM: determination of transverse 102±105 formulae 105, 135, 382 Bonjean Curves 345 Boot-topping area 57, 66 Box-shaped vessel: BM calculation 105, 135 KB calculation 99 Broken stowage 207 Buoyancy 22±3 reserve 27 Buoyancy curves 346±7 Capsizing moment 46, 48, 49 Centre of buoyancy 22, 34, 43, 88 Centre of ¯otation 85±6, 134 determination using trim 148±9 Centre of gravity 9, 43, 114 effect of adding mass 12±13 effect of removing mass 10±12 effect of shifting weights 13±14 effect of suspended weights 14 Centre of pressure 267±70 by Simpson's Rules 270±76 Centrifugal force 287 Centripetal force 287 Centroid of area 9, 85 Change of draft, due to change of trim 138±9 Coef®cient of ®neness 61 Complementary stress 328±30 Compressive stress 326 Conversion tables (metric/imperial) 387 Deadweight (Dwt) Scale 302±304 Density 19 effect of change 33 effect of change on draft and trim 315±18 effect on displacement for constant draft 38±9 Displacement curves 57±8 Dock water allowance 37 Draft: change due to change of trim 138±9 effect of density change 315±18 effect of hog and sag 236±7 formulae 380 increase due to list in box-shaped vessels 179±81 increase due to list in vessels having rise of ¯oor 181±3 loading to requirement 151±3 maintaining 149±51 see also true mean draft correction Draft Surveys 434±6 Drydocking process 246±55 formulae 383±4 Dynamical stability 218±23 Effect of free surface, formulae 383 Equilibrium 44±7 correcting 47 Equivalent girder calculation 369, 370 Examination papers 401±428 Examination tips 432±3 Five/eight rule 72, 76-7 Force of buoyancy 22 Forces 1±4 Form coef®cients formulae 380 Free surface effect (FSE) 192±203 on stability 50±54 Freeboard, effect of increase on stability 225±6 Freely supported beams 333±9 Fresh Water Allowance (FWA) 35±6 Fully loaded drafts 65±6 GM (initial transverse metacentric height) from inclining experiment 239±40 working values 49 Grounding 246, 278 GZ (righting lever) 43, 45 stability cross curves 162±6 Heel 43 due to turning 287±9 formulae 385 Hog, effect on draft amidships 236±7 Hogging stress 342 Homogeneous logs, rectangular section 29±30 Hydrometer, variable immersion 24±5 Hydrostatic curves 172±6 Inclining experiment 238±41 Initial metacentre 125 444 Index Centre of gravity (cont.) Initial metacentric height 125, 169 Interaction effects 305±306 reducing 311 ship to ground 306±308 ship to ship 308±311 ship to shore 311±13 squat 306±308 KB: for box-shapes 99±102 curve 109 determination by Morrish's for- mula 99±102 determination by Simpson's Rules 88±91 formulae 382 for triangular prisms 99±102 KG: determination for light condition 238±40 ®nal determination 94±6 KM curve (locus of metacentres) 109 KN cross curves of stability 167±8 Lifeboat capacities 63 List: de®nition 43 determination 114±16 due to bilging side compart- ments 296±300 formulae 383 with zero metacentric height 319±21 List and trim, combined 188±91 Load curves 347 Load line marks 36 Locus of metacentres (KM curve) 109 Longitudinal metacentric height 134 determination using change of trim 153±6 Longitudinal stability see trim Mass, de®nition 6 Maximum Permissible Deadweight Moment Diagram 373±4 Merchant Shipping (Safety Convention) Act 1949 393±4 Metacentre 43±4 Metacentric diagrams 107±12 Metacentric height 44 longitudinal 134, 153±6 Midships coef®cient 64, 65±6 Moment of forces 5±6 Moment of statical stability 45, 124 at large angle of heel 126±30 at small angle of heel 125±6 Moment to Change Trim one centimetre (MCT1cm or MCTC) 136±8 Moments about the centre line 117±19 Moments about the keel 116 Moments of mass 6±7 Morrish's formula 100, 102 Moseley's formula 219±20 M.S. (Load Lines) Rules 1968, extracts 388±94 Murray's Method 350±52 Neutral equilibrium 46±7, 231 correcting 47 Normand's formula see Morrish's formula Parallel axis theorem 258±60, 385 Permeability: compartment 207±10 formulae 384 Point of suspension 14 Pressure: at any depth 184±6 in liquids 266, 384 Prismatic coef®cient 64, 65±6 Range of stability 168 Relative density see speci®c gravity Index 445 Reserve buoyancy 27 Resolution of the component moments 5 Resolution of forces 1±4 Resolution of moments 5 Resultant force 1 Resultant moment 5 Resultant thrust 266±7 Revision questions 429±31 Righting couple 43 Righting lever see GZ (righting lever) Rolling, in still water 290±95 Rolling period, formulae 385 Sag, effect on draft amidships 236±7 Sagging stress 342 Second moment of area 256±7 Section modulus 360, 361 Shallow water indications 279±80 Shear forces, in ships 347±8 Shearing stresses 326 beam theory 361±4 with ¯anges 364±6 without ¯anges 366±7 Ship squat: de®nition 278±9 formulae 385 governing factors 280±84 interaction 306±308 supertanker 284±5 Ships: construction rules 390 shape volumes 77±9 stability rules 391±3 strength formulae 384±5 types and characteristics table xi Simple harmonic motion 290±91 Simpli®ed stability information (Merchant Shipping Notice 1122) 372±7 Simpson's Rules: for determining centre of pressure 270±76 Simpson's Rules (cont.) for determining waterplane area 260 First 68±9, 72±4, 381 Second 70±71, 75±6, 381 Third 71±2, 76±7, 381 use of radian intervals 220 Speci®c gravity 19 Squat see ship squat Stability: effect of bilging 214±15 effect of increasing beam 224±5 effect of increasing freeboard 225±6 formulae summary 380±86 Stability cross curves: GZ set 162±6 KN set 167±8 Stable equilibrium 44±5, 231 Statical stability curves 168±71 Statutory freeboard 36 Stiff (ship condition) 47 Still Water Bending Moment (SWBM) 350±52, 354 Stowage factor 207 Strength curves 346 Stresses: de®nitions 325±30 longitudinal in still water 340±41 longitudinal in waves 341±2 Syllabuses, Department of Transport 395±400 Tank soundings, effect of trim 243±5 Tender (ship condition) 47 Tensile stress 326 Thrust 184±7 resultant 266±7 total 266 Time period 47 Tipping centre see centre of ¯otation 446 Index Tonnes Per Centimetre immersion (TPC) 26, 55 curves 55±7 in dock water 26 Total Bending Moment (TBM) 355 Total pressure see thrust Total thrust 266 Transverse stability formulae 382 Transverse statical stability formulae 382±3 Triangular-shaped prism BM calculation 105, 136 KB calculation 99 Trim 133 effect of density change 315±18 effect on tank soundings 243±5 effects of loading/discharging weights 141±8 effects of shifting weights 139±41 formulae 381, 382 use of change to ®nd longi- tudinal metacentric height 153±6 use to determine centre of ¯otation 148±9 Trim and list, combined 188±91 Trim and Stability book 322±4 True mean draft correction 233±7 Turning, effect on heel 287±9 Unstable equilibrium 46 correcting 47 Volume calculations 77±9, 84±5 Wall-sided formula 127±30, 320 Water pressure 184±7 Water-plane area 72±7 Wave Bending Moment (WBM) 352±3 Wedge of buoyancy 43 Weight, de®nition 6 Weight diagram 344 Weights: effect on trim of loading/ discharging 141±8 effect on trim of shifting on board 139±41 loading to keep after draft constant 149±51 loading to produce required draft 151±3 Index 447 . immersion (TPC) 26, 55 curves 55 ±7 in dock water 26 Total Bending Moment (TBM) 355 Total pressure see thrust Total thrust 266 Transverse stability formulae 382 Transverse statical stability formulae 382±3 Triangular-shaped. 432±3 Five/eight rule 72, 76-7 Force of buoyancy 22 Forces 1±4 Form coef®cients formulae 380 Free surface effect (FSE) 192±203 on stability 50 54 Freeboard, effect of increase on stability 2 25 6 Freely supported. bilging 214 15 effect of increasing beam 224 5 effect of increasing freeboard 2 25 6 formulae summary 380±86 Stability cross curves: GZ set 162±6 KN set 167±8 Stable equilibrium 44 5, 231 Statical stability