MERCHANT SHIP STABILITY (METRIC EDITION) A Companion to "Merchant Ship Construction" BY H J PURSEY EXTRA MASTER Formerly Lectllrer to the School of Navigation University of Southampton GLASGOW BROWN, SON & FERGUSON, LTD., NAUTICAL PUBLISHERS 4-10 DARNLEY STREET Copyright in all countries signatory to the Berne Convention All rights reserved First Edition Sixth Edition Revised Reprinted Reprinted 1945 - 1977 1983 - 1992 1996 ISBN 085174 442 (Revised Sixth Edition) ISBN 085174 274 (Sixth Edition) ©1996-BROWN, SON & FERGUSON, LTD., GLASGOW, G41 2SD Printed and Made in Great Britain INTRODUCTION D URING the past few years there have been considerable changes in the approach to ship stability, so far as it affects the merchant seaman The most obvious of these is the introduction of metric units In addition, the Department of Trade have already increased their examination requirements: they have also produced recommendations for a standard method of presenting and using stability information, which will undoubtedly be reflected in the various examinations This revised edition has been designed to meet the above-mentioned requirements The basic information contained in the early chapters has been retained for the benefit of those who are not familiar with such matters The remainder of the text has been re-arranged and expanded, as desirable, to lead into the new material which has been introduced; whilst a new chapter on stability information has been added to illustrate the Department of Trade recommendations The theory of stability has been covered up to the standard required for a Master's Certificate and includes all that is needed by students for Ordinary National Diplomas and similar courses This has been carefully linked-up with practice, since the connection between the two is a common stumbling block Particular attention has been paid to matters which are commonly misunderstood, or not fully appreciated by seamen H SOUTHAMPTON, 1982 v J P CONTENTS CHAPTER I-SOME GENERAL INFORMATION PAGE The Metric System Increase of pressure with depth · Effect of water in sounding pipes The Law of Archimedes · Floating bodies and the density of water Ship dimensions Decks Ship tonnages Grain and bale measurement Displacement and deadweight Draft Freeboard Loadlines · · · · · · CHAPTER 2-AREAS Areas of plane figures Surface areas and volumes Areas of waterplanes and other ship sections Simpson's First Rule · Simpson's Second Rule The 'Five-Eight Rule' Sharp-ended waterplanes Unsuitable numbers of ordinates Volumes of ship shapes Half-intervals Coefficients of fineness Wetted surface AND VOLUMES CHAPTER 3-FORCES Forces Moments Centre of gravity Effect of weights on centre of gravity Use of moments to find centre of gravity To find the centre of gravity of a waterplane To find the centre of buoyancy of a ship shape The use of intermediate ordinates Appendages Inertia and moment of inertia Equilibrium AND MOMENTS CHAPTER 4-DENSITY, Effect of density on draft Tonnes per centimetre immersion Loading to a given loadline · · · 2 4 4 5 6 8 10 12 12 13 13 15 16 17 18 · DEADWEIGHT AND DRAFT · Vll 19 20 23 25 27 28 30 31 32 33 36 · 37 39 40 CONTENTS VIl1 CHAPTER 5-CENTRE Centre of Gravity of a ship-G · KG · · · · · Shift of G · · · KG for any condition of loading · Deadweight moment · Real and virtual centres of gravity Effect of tanks on G · OF GRAVITY · · · · CHAPTER Centre of buoyancy-B Centre of flotation-F Shift of B · · 6-CENTRES · · OF SHIPS · · · · · · OF BUOYANCY · · · · · · · CHAPTER 9-FREE The effect of free surface of liquids · Free surface effect when tanks are filled or emptied Free surface in divided tanks · Free surface moments · · · CHAPTER 10-TRANSVERSE Factors affecting statical stability Placing of weights · Stiff and tender ships Unstable ships · Ships in ballast The effect of winging out weights Deck cargoes Free liquid in tanks · Free surface effect in oil tankers 49 49 50 · AND FLOTATION · · · · · 42 42 42 43 45 46 47 · CHAPTER 7-THE RIGHTING LEVER AND METACENTRE Equilibrium of ships · · · · · The righting lever-GZ · · · The metacentre-M · · · · · · · Metacentric height-GM · · · · · · Stable, unstable and neutral equilibrium Longitudinal metacentric height-GML · CHAPTER 8-TRANSVERSE Moment of statical stability · Relation between GM and GZ · Initial stability and range of stability Calculation of a ship's stability · Calculation of BM The Inclining Experiment · · Statical stability at small angles of heel Statical stability at any angle of heel GZ by the Wall-Sided Formula · Loll, or list · · Heel due to G being out of the centre-line Loll due to a negative GM · · · PAGE STATICAL STABILITY · · · · · · SURFACE STATICAL 57 57 57 58 58 60 62 62 64 64 65 68 EFFECT · 53 55 55 55 55 56 70 72 73 75 · STABILITY · IN PRACTICE 76 78 78 80 81 82 83 84 85 CONTENTS CHAPTER 11-DYNAMICAL IX STABILITY PAGE Dynamical stability Dynamical stability from a curve of statical stability Calculation of dynamical stability CHAPTER 86 86 88 12-LONGITUDINAL STABILITY Longitudinal metacentric height-GML · Calculation of EM L Trim Change of mean draft due to change of trim Displacement out of designed trim · Moment to change trim by one centimetre The effect of shifting a weight Effect of adding weight at the centre of flotation Moderate weights loaded off the centre of flotation Large weights loaded off the centre of flotation To obtain special trim or draft Use of moments about the after perpendicular CHAPTER Hydrostatic curves The deadweight scale Hydrostatic particulars Curves of statical stability Cross curves Effect of height of G KN curves The Metacentric Diagram 13-ST ABILITY CURVES AND SCALES 117 118 118 119 120 122 123 123 CHAPTER 14-BILGING The effect of bilging a compartment Permeability · Bilging an empty compartment amidships Bilging an amidships compartment, with cargo Bilging an empty compartment, not amidships Effect of a watertight flat CHAPTER IS-STABILITY Stability requirements · Information to be supplied to ships · The Stability Information Booklet The use of maximum deadweight moments Simplified stability information 90 91 92 9496 98 99 101 103 106 108 113 OF COMPARTMENTS 126 126 127 128 129 131 AND THE LOAD LINE RULES 133 134134 139 140 CHAPTER 16-MISCELLANEOUS Drydocking and grounding The effect of density on stability · The effect of density on draft of ships Derivation of the fresh-water allowance Reserve buoyancy Longitudinal bulkheads Bulkhead subdivision and sheer Pressure on bulkheads MATTERS 143 145 146 147 147 147 148 149 CONTENTS x CHAPTER 17-ROLLING CHAPTER Abbreviations Formulae Definitions Problems DEADWEIGHT CURVES PAG£ 150 150 150 151 151 152 152 153 153 The formation of waves The Trochoidal Theory The period of waves The period of a ship Synchronism Unresisted rolling Resistances to rolling The effects of bilge keels Cures for heavy rolling 18-SUMMARY 154 156 161 164 SCALE, HYDROSTATIC PARTICULARS AND HYDROSTATIC Insert at end of book MERCHANT SHIP STABILITY CHAPTER THE METRIC SYSTEM Length.-The basic unit of length is the Metre metre (m) = 10 decimetres (dm) = 100 centimetres (cm) = 1000 millimetres (mm) Weight.-The metric ton, or tonne, is the weight of cubic metre of fresh water tonne = 1000 kilogrammes (kg) = 1,000,000 grammes (gr) The gramme is the weight of cubic centimetre of fresh water Volume.-Is cm -3) Area.-Is measured in cubic metres (m-3), or cubic centimetres measured in square metres (m-2), or square centimetres (cc, or (cm-2) Force.-When a force is exerted, it is usually measured, in stability, in tonnes or kilogrammes To indicate that it is a force or weight, as distinct from mass, an 'f' is often added; e.g "tonnes f", or "kilogrammes f." Moment.-For (tonne f-m) our purpose, this is usually expressed as tonne-metres Pressure.-May be given as tonnes per square metre (tonnes fjm2), kilogrammes per square centimetre (kg fjcm2) or as Density.- This is usually defined as mass per unit volume For our purpose it can be regarded as the weight of one cubic metre or of one cubic centimetre of a substance We may express it as either: Grammes per cubic centimetre (grsjcm3) Kilogrammes per cubic metre (kgjm3) Tonnes per cubic metre (tonnesjm3) Relative Density.-Was formerly called "specific gravity" It is the ratio between the density of a substance and the density of fresh water MERCHANT SHIP STABILITY Water.- The following values are usually taken for purposes of stability ;Fresh Density (grs/cm30rtonnes/m3) Density (kg/m3) Relative density Weightpercubicmetre Weight per cubic metre Volumepertonne (cubic metres) water 1·000 1000 1·000 1·000 1000 1·000 Salt water 1·025 1025 1·025 1'025tonnes 1025 kilogrammes 1'~25 Increase of Pressure with Depth.-The pressure on an object which is placed under water is equal to the column of water above it Consider Fig 1, which represents a column of water having an area of one square metre Let A, B, C, D, E and F be points one metre apart vertically The volume of water above B is one cubic metre; above C, two cubic metres; above D, three cubic metres; and so on If b is the density of the water in tonnes per cubic metre, the weight above B will be tonnes; above C will be 2b tonnes; above D will be 3b tonnes; and so on We can see from this that if point A is at the sea surface, then the pressure per square metre at a depth of, say, AF metres, will be AF x b tonnes From the above, it is obvious that the pressure at any depth, in tonnes per square metre, is equal to b times the depth in metres Since water exerts pressure equally in all directions, this pressure will be the same horizontally, vertically, or obliquely We can say, then, that if a horizontal surface of area A square metres is placed at a depth of D metres below the surface, then:Pressure per square metre = x D tonnes Total pressure on the area = b x AD tonnes The Effect of Water in Sounding Pipes, etc.-When water rises in sounding pipes or air pipes to above the top of a tank, pressure is set up on the tank-top The actual weight of water in the pipe may be comparatively small, but its effect may be considerable Water exerts pressure equally in all directions and so the pressure per square centimetre at the bottom of the pipe is transmitted over the whole of the tank-top This pressure will not depend on the actual weight of water in the pipe, but on the head of water and will be approximately the same whatever the diameter of the pipe For this reason, tanks should not be left "pressed up" for long periods, because this can exert considerable stress on the tank-top SOME GENERAL INFORMATION ExampZe.-A rectangular double bottom tank is being filled with sea water If the water is allowed to rise in the sounding pipe to a height of metres above the tank top, find the pressure per square metre on the tank top Pressure = ~D = 1·025 x = 7·175 tJm2 The Law of Archimedes.-A body immersed in a liquid appears to suffer a loss in weight equal to the weight of liquid which it displaces From this, we conclude that a floating body displaces its own weight of water This can be shewn as follows:A block of iron, one cubic metre in size and of density 8,000 tonnesfm3 would weigh tonnes in air If placed in fresh water it would displace one cubic metre of water, which would weigh one tonne; so the weight of the block would thus appear to be tonnes when it was under water If we now take the block and make it into a hollow, sealed box, its weight in air will remain the same but its volume will increase If placed in water, it would displace more of the water and its apparent weight will decrease accordingly For instance, if the box were cubic metres in volume it would displace cubic metres of water (or tonnes), so that its apparent weight in fresh water would now be tonnes If we increase the volume of the box still further, it will displace still more water and its apparent weight under water will decrease still more Eventually, when the volume of the box became greater than cubic metres, an equivalent volume of water would weigh more than the box So if the box were now placed under water, it would be forced upwards, until the upward force exactly equalled the weight of the box In other words, the box would rise until it floated at such a draft that it would displace its own weight of water Application to Ships.-A ship may be regarded as a closed iron box, so that two conclusions can be drawn from a study of the last section:(a) So long as the weight of the ship does not exceed'the weight of its own volume of water, it will float (b) The draft at which it floats will be such that the weight of water displaced will be equal to the weight of the ship PROBLEMS 189 262 In a Tropical Zone, a ship which has a summer draft of ·94 metres, arrives in port with salt water drafts of ·98 metres forward and 8·16 metres aft Her T.P.C is 23,2, M.C.T.IC is 208, F is 3·0 metres abaft amidships and her Fresh Water Allowance is 164 mm She then has to cross a dock sill, where the relative density of the water is 1·010 and where her mean draft must not exceed 8·00 metres How much cargo must she discharge, before entering the dock, from each of two holds, one of which is 18 metres forward of amidships, and the other 36 metres abaft amidships? A nswers258 Forward, 74 t; Aft, 146 t 259 Forward, 25 t; Aft, 170 t 260 Forward, 175 t; Aft, 167 t 261 No I, 165 t; No.4, 218 t 262 Forward, 171 t; Aft, 223 t The Use of Moments About the After Perpendicular 263 A ship displaces 9870 t and B is 58·25 metres from the after perpendicular She loads 750 t at 22·0 metres from the after perpendicular If B is then 58,37 metres from the after perpendicular, what is the moment changing trim? 264 A vessel displaces 5260 t and her B is 59·72 metres from the A/P She then loads 250 t at 94 metres from the A/P and 320 t at 35 metres from the A/P: she also discharges 180 t from 16 metres from the A/P If B is then 59,74 metres from the A/P, find the moment changing trim 265 The following is an extract from the ship's hydrostatic information:- Her present drafts are 6·08 metres forward and 6·04 metres aft She then loads 260 t at 84 metres from the A/P, 430 t at 37 metres from the A/P, and discharges 180 t from 54 metres from the A/P What is the moment changing trim? 266 A vessel is 120 metres long and floats at drafts of 5·28 metres forward and 6·14 metres aft At this draft she displaces 7620 t, her T.P.C is 15'94, B is 58,76 metres from the A/P, whilst F is 58·02 metres from the A/P She then loads 920 t of cargo at 67 ·80 metres from the A/P The T.P.C is then 16,18, M.C.T.IC is 114'0, B is 58·67 metres from the A/P and F is 57·90 metres from the A/P Find the new drafts 267 A ship is 164 metres long and has drafts of 8·02 metres forward and 8·10 metres aft At this draft her displacement is 18050 t, T.P.C is 27,80, B is 82·14 metres from the A/P, whilst F is 78,94 metres from the A/P She then:Loads Discharges Discharges Discharges 810 650 430 720 tat 69 metres from the t from U8 metres from t from 64 metres from t from 56 metres from A/P the A/P the A PROBLEMS 193 287 From the cross curves in Fig 77, find the righting levers for a KG of 7·00 metres and displacement of 5000 t Use these to draw a curve of statical stability and from this find the range of stability, amount and angle of maximum stability and the approximate GM 288 Use the cross curves (Fig 77) to find the Gzs for a displacement of 8500 t and KG of 6,50 metres Draw a curve of statical stability and find the angle of vanishing stability and the approximate GM 289 Use the KN curves given in Fig 78 to find the righting levers for:(a) Heel 30°, Displacement (b) Heel 45°, Displacement (c) Heel 15°, Displacement (d) Heel 75°, Displacement 6000 7900 9800 8500 t, t, t, t, KG 6·00 metres KG 7·25 metres KG 6·43 metres KG 6·92 metres 290 Use the KN curves given in Fig 78 to find the righting levers for s displacement of 7600 t and a KG of 6,78 metres From these, draw a curve of statical stability and find the range of stability and the amount and angle of maximum stability 291 A ship has a KG of 6·56 metres and a KM of 6·45 metres as follows:Heel KN (m) 5° 0,56 10° 1·13 15° 1·72 30° 3·43 45° 4,80 Her KNs are 60° 5,63 Find the righting levers, draw a curve of statical stability and find the range of stability, the approximate angle of loll and the amount and angle of maximum stability A nswers286 (a) 0,37 m; 287 85°; 288 85°; (b) 0·18 m; (e) 0·79 m; 1·02 m at 44°; 1·02 m 0·77 m 289 (a) 1·17 m; (b) 0·41 m; 290 85°; 0,79 m at 45° 291 57°; 12; 0·19 m at 38° (d) 0·26 m (e) 0·28 m; (d) 0·05 m The Metacentric Diagram 292 Construct a metacentric diagram for drafts of between 3·00 and 8·00 metres for the ship for which the hydrostatic information is given in the back of this book From this, find KE, KM and EM for drafts of (a).4·50 metres and (b) 6·25 metres 293 Calculate the KM and EM of a box-shaped lighter, 30 metres long and metres beam, for every half-metre of draft from 1·00 to 4,00 metres Construct a metacentric diagram and from this find the KE, KM and EM for drafts of (a) 2.60 metres and (b) 3,40 metres Answers292 293 (a) KB 2·44 m (b) KB 3,40 m (a) KB 1·30 m (b) KB 1·70 m IUd 8,50 m KM 8·04 m KM 2·46 m KM 2·59 m BM 6,06 8111 4·64 BM 1·16 BM 0·89 m m m m 194 MERCHANT SHIP STABILITY Bilging 294 Find the permeability of the following cargoes:(a) Stowage factor 2·60; Relative density 1·12 (b) Stowage factor 0·40; Relative density 8·00 (c) Stowage factor 1·50; Relative density 1·75 295 A box-shaped lighter, 30 metres long and metres wide, floats at drafts of 1·00 metres fore and aft It is divided into three equal compartments by two transverse bulkheads Find the new drafts if the centre compartment, which is empty, is holed below the waterline 296 What would have been the draft, in the last question, if the compartment had been filled with cargo of permeability 40%? 297 A box-shaped vessel is 75 metres long, 12 metres beam and floats at a draft of 6,20 metres fore and aft A compartment amidships is 15 metres long and has a permeability of 60% Find the new drafts if this compartment is bilged 298 A box-shaped vessel is 60 metres long, 12 metres beam and 5·75 metres deep She floats on an even keel at a draft of 4,80 metres What will happen if an empty compartment amidships, 12 metres long, is bilged? 299 A ship is 120 metres long, 18 metres beam and floats at a mean draft of 6·00 metres The coefficient of fineness of the waterplane is 0·750 A rectangular compartment amidships is 15 metres long, extends for the full width and depth of the ship, and has a permeability of 60% Find the sinkage if this compartment is bilged 300 A box-shaped lighter, 30 metres long and metres beam, floats at drafts of 1·20 metres fore and aft Find the sinkage and the new drafts if an empty compartment, right forward and 3,0 metres long, is bilged 301 A box-shaped vessel is 80 metres long, 15 metres beam and floats at drafts of 3,00 metres fore and aft Find the sinkage and new drafts if an empty compartment, right forward and 12 metres long, is bilged 302 A ship, 120 metres long, floats at drafts of 4·50 metres fore and aft The waterplane area is 1400 square metres, the displacement is 5800 tonnes, M.C.T.IC is 96, whilst B is 1·50 metres abaft amidships At this draft, the forepeak, which is empty, has a volume of 50 cubic metres below water, a waterplane area of 25 square metres, whilst its centre of gravity is 3·5 metres abaft the stem Find the sinkage and change of trim if the forepeak is bilged 303 A box shape, lIO metres long and 12 metres beam, floats on an even keel at a draft of 5,00 metres An empty compartment, 10 metres long, has its centre of gravity 30 metres forward of amidships Find the new drafts if this compartment is bilged M.C.T.IC is 102·4 tonne-metres 304 A box-shaped vessel, 72 metre$ long and metres beam, floats at drafts of 4,00 metres fore and aft An empty compartment, right forward, is metres long and has a watertight flat 3·0 metres above the keel Find the new drafts if this compartment is bilged below the flat 305 A box-shaped lighter is 30 metres long and metres beam She floats at a draft of 1·50 metres fore and aft An end compartment, metres long, has a watertight flat 1·50 metres above the keel and has a permeability of 45% Find the new drafts if this compartment is bilged PROBLEMS 195 306 A ship is 120 metres long and floats on an even keel at a draft of 6·00 metres Her displacement is 8000 tonnes; M.C.T.IC is 110; the waterplane area is 1680 square metres; B and F are both 2·0 metres abaft amidships The after peak has a capacity of 240 tonnes of salt water and its centre of gravity is 53 metres abaft F Find the new drafts if the after peak is bilged A nswers294 295 296 297 298 299 300 (a) 66%; (b) 68%; 1·50 m 1·15 m 6·74 m Vessel sinks 0,67 m 0·13 m; F 1-117m; (e) 62% A.0·88 301 302 303 304 305 306 0·53 m; 3,6 em; F 6·45 F 4·93 F 1·89 F 5·54 F 6,06 m; 31 em m; A 4,65 m; A 3,57 m; A 1·33 m; A 6·70 A 1·66 m m m m m m Drydocking 307 A ship enters a drydock with drafts of 3,00 metres forward and 3·50 metres aft Her displacement is 3000 tonnes KG, 7·30; GM, 2'00; M.C.T.1C., 88 The centre of flotation is 55 metres from aft What will be the ship's GM at the instant of settling on the blocks, fore and aft? 308 In the case of the ship in the last question, what would be her GM when she was flat on the blocks and the water-level had fallen to 2·80 metres, her displacement then being 2500 tonnes? 309 The ship is trimmed 60 centimetres by the stem when she enters a dock Her displacement is 4300 tonnes; KG, 6,90 m; KM, 8·40 m; M.C.T.IC., 100: whilst the centre of flotation is 70 metres from aft Find the GM at the instant before the ship comes flat on the blocks fore and aft 310 A box-shaped vessel is 100 metres long, 12 metres beam and floats at drafts of 2·40 metres fore and aft Her KG is 4·90 metres Find her new GM when she is flat on the blocks in a drydock and the water-level has fallen so that the draft is 2·00 metres fore and aft Answers307 1·75 m 308 0·45 m 309 1·33 m 310 0·27 m INDEX A PAGE Abbreviations 154 · Added weights, effect on G 25,99 Added weights, effects on 39, 101, 159 draft, etc Adjustment of TPC 40 After perpendicular, moments about 113 Alternative tonnage Angle of heel 64, 65, 68, 156 Angle of101I 68, 77, 156 Angle of vanishing stability 57,77,134,161,163 Appendages 32 Archimedes' Law 3,162 Areas, general 8,156 Areas of waterplanes 9, 156 62, 158, 159 Atwood's Formula 00 • • B 0 • 0 00 B Bale measurement Ballast, ships in Base line Beam, effect on stability Bilge keels Bilging o Block coefficient BM " BML Box shapes Breadth moulded Bulkhead subdivision Bulkheads, longitudinal Bulkheads, pressure on Buoyancy Buoyancy, reserve PAGE Coefficients of fineness 17 Common interval 10 'Conditions' 135 Condition sheet 138 Couples 23 Critical period 143 Cross curves 120, 122 Cures for instability 80 Curve of f100dable lengths 148 Curves, hydrostatic 117, 118, end of book Curves of statical stability 76,86, 119, 122, 123 30, 49, 90, 156, 161 o 81 44 77 o 153 126, 156 17 58, 60, 157 90, 91, 92, 157 o 9, 24, 49, 59, 92 · o 148 85, 147, 148 149 49 147, 163 0 C Calculation of stability 58 30,49,90,156,161 Centre of buoyancy 50, 51, 156 Centre of buoyancy, shift of 49,90,161 Centre of flotation " o 23,27, 161 Centre of gravity 23,27 Centre of gravity of areas 24,27 Centre of gravity of bodies 25, 42, 47, 158 Centre of gravity, shift of Centre of gravity of ships 42 46 70, 90 46, 60 Centre of gravity, virtual 28,49 Centre of gravity, waterplanes 93 Change of draft with trim 6,90,94, 157, 161 Change of mean draft 93, 99, 103, 106 Change of trim • D Deadweight 5, 161 Deadweight moments 45, 139, 161 Deadweight scale 118, end of book Decks o Deck line Deck cargoes 7,83 Deep tanks 47,81 Definitions 161 Density Density, effects of 4,37,40, 145,157 Depth, effect on pressure 2, 158 · Depth, framing Depth, moulded Depth of hold Depth of ships Derricks lifting weights 46 Designed trim 95 Desired trim, to produce 109, 159 Dimensions Displacement 5, 161 Displacement, coefficient of 17 Displacement out of designed trim 96 Divided tanks, for free surface · 73 Dock water allowance 38 Double bottom tanks 2, 46, 47, 81 Draft Draft at F o 95, 114, 157, 161 Draft by moments about AlP 113 Draft, constant or desired 110,111,112,157 Draft, effect of density 37, 146, 157 Draft, effect of trim 93 " Draft, effect of weights 39, 101, 103, 106, 159 Draft, effect of bilging 126 Draft, loading for desired 112 Draft, mean " 6, 90, 94, 157, 161 Draft, mean to F o 95, 157 Drydocking 143, 157 Dyna1Dical stability 86, 88, 158, 161 • 0 O' • 199 MERCHANT 200 E SHIP 49 36,53 F F 49, 90, 161 Factors affecting stability 76 Fineness, coefficients of 17 Five-eight Rule 9,12 Floating bodies · 3,4 Floodable lengths 148 Fluid GM · 70, 72, 161 Force 1, 19, 161 Formation of waves 150, 152 Formulae, summary of 156 Framing depth Freeboard 6,77, 161 Freeboard deck · Free liquid in tanks 70, 84 Free surface effect 46,70, 84, 158 Free surface moment 75 Fresh water allowance 7, 37, 147, 157, 161 G G 42, 46, 70, 90 · GM 55,60,77,81, 133, 157, 158, 162 GM, negative 56, 68, 77, 80 GM, solid and fluid 70, 72, 161, 163 GML 56,90, 162 Grain measurement Gross tonnage Grounding 145 GZ 55, 57, 62, 64, 76, 122, 133, 158, 163 16 10 · 151, 153 · 64, 65, 68, 156 30,49 42, 43, 47, 122, 162 55, 81, 161 · · 117, end of book 118, end of book I Immersed wedge · Inclining experiment · Increase of draft through bilging Inertia · Inertia, moment of Information booklet · Information, simplified Information supplied to ships Initial stability · · Intermediate ordinates Interval, common · Interval, half Isochronous rolling J KB KG Klvl KN curves PAGE 30,49 42, 43, 47, 122, 162 55,81, 161 123, 162 L Large weights loaded 106 " Law of Archimedes 3,162 Layer correction 97, 158 Length Light displacement 5,162 Light KG 42 Liquids, free surface of 46, 70, 84, 158 Liquids, pressure in 2, 149, 158 List · 64, 65, 68, 156 Loaded displacement 5,162 · Loading for constant draft, aft · 110 Loading for desired draft 111,112 Loading to load lines 40 Loading for desired trim 109 Loadlines · Loadline disc Loadline Rules, requirements 133, 134 Loll 64, 68, 156 Longitudinal BML 90,91,92, 157 Longitudinal GML 56, 90, 162 · Longitudinal bulkheads 85, 147, 148 Longitudinal metacentre 56,91 Longitudinal position of B 30,90 Longitudinal position of G 90 Longitudinal stability 90 M H Jettisoning cargo K PAGE Emerged wedge Equilibrium Half intervals Half ordinates Head of water Heavy rolling Heel · Height of B Height of G Height of M Hydrostatic curves Hydrostatic particulars STABILITY 49 60, 158 126, 156 33, 162 33,35 133 139, 140 134 57, 162 16,31 · 10 16 151, 162 81 M 55, 162 ML 56,91 Margin line 148 Maximum deadweight moments 139 M.C.T.IC 98,158,162 · Mean draft 6,90,94, 157, 161 · Metacentre, longitudinal 56,91 Metacentre, transverse 55, 162 Metacentric diagram 123 · Metacentric height, drydocking 143 Metacentric height, longitudinal 90 Metacentric height, negative 56, 68, 77, 80 Metacentric height, transverse 55, 60, 77, 81, 133, 157, 158, 162 Metric system Midship section coefficient 17 Moderate weights loaded 103 Modified tonnage · Moment 1, 20, 27, 162 " Moment changing trim 98, 100 Moment of inertia 33, 35, 82, 158 Moment of statical stability 57, 62, 159, 162 Moments about the AlP 113 Moseley's Formula 88, 158 Moulded breadth Moulded depth Multipliers " 11 · · INDEX Negative GM Nett tonnage Neutral equilibrium Oil tanke~s Ordinates N P Parallelogram of forces Period of ships Period of waves Permeability Plimsoll mark Practical stability Pressing-up tanks Pressure, increase with depth , Pressure on bulkheads Pressure on tank tops Prismatic bodies Prismatic coefficient Problems " Pro-metacentre PAGE 56, 68, 77, 80 35, 54, 56 85 10, 13, 16, 31 " 20 151, 162 150, 162 126, 158 76 2, 158 149 9,163 18 164 55 R Radius of gyration Range of stability 57, 77, 134, Relative density Reserve buoyancy Resistances to rolling Resultant force · Requirements of Loadline Rules 55, 57, 62, 64, 76, Righting lever Righting moment Rolling , S · 161, 147, · 122, 158, 57, 62, 159, · 33 163 163 152 19 133 133 163 162 150 Second moment 33,35 Sharp-ended waterplanes 13 Sheer 148 · Shift of B 50, 51, 156 · Shift of G 25,42,47, 158 Ship dimensions " Ship sections, areas · · Ship shapes, volumes · 15 Ships in ballast · 81 Simplified stability information 139, 140 Simpson's Rules Sinkage through bilging 126, 156, 159 Sinkage through weights " 101, 103, 106, 159 Slack tanks · 46 Small ships, information for 139 Solid GM · · 70, 72, 163 Sounding pipes · · Special draft and trim 108 Specific gravity · · Stability, calculation of · 58 Stability curves and scales 117, 118, 119, back of book Stability information booklet 134 201 Stability requirements Stable equilibrium Statical stability Statical stability curves Statutory freeboard Stiff ships Subdivision Surface areas Synchronism PAGE · 133 36,54 57, 62, 76, 159 76, 86, 119, 122, 123 78,79, 163 148 8, 18, 159 151, 163 T Tabulation of Information 135 Tanks 2, 46, 47, 70, 84 Tender ships 78, 79, 163 " Timber deck cargoes 83 Timber loadlines Tipping centre 49, 90, 161 Tonnage 4, 5, 163 Tonnage deck Tonnage mark Tonnes per centimetre immersion 39, 159, 163 Transverse stability 57 Trim 92,103,106,108,159,163 Trim, by moments about the AlP 113 Trim, change of 93, 99, 103, 106 Trim due to bilging 129 · Trochoidal Theory 150 U Under deck tonnage Unresisted rolling Unstable equilibrium Unstable ships Unsuitable ordinates V Virtual centre of gravity Volumes of ship shapes Volumes, general 152 35, 54, 56 68, 77, 78, 80 13 " 46,70 15 1,4,8, 159 W Wall-Sided Formula 64, 158 Water · · Water ballast 47,81 · Water in pipes · · · 2l) Waterplane areas · Waterplane coefficient 17 · Waterplanes, centre of gravity · 28 Waterplanes, sharp-ended 13 Water pressure · · · 2, 149, 158 Watertight flats 131 · Wave formation 150, 152 · · 49 Wedges Weights to load, for trim or draft 109, 110, 112, 157, 159 , Weights to load, to loadline 40 Weights added at F · · 101 Weights, effect on G 25,99 · 18, 160 Wetted surface · Winging out weights 82 86 Work · · HYDROSTATIC CURVES & SCALES ... will be equal to the weight of the ship Ship Dimensions.-The following are the principal dimensions used in measuring ships LIoyds' Length is the length of the ship, measured from the fore side... many tonnes {) MERCHANT SHIP STABILITY Draft.-This is the depth of the bottom of the ship' s keel below the surface of the water It is measured forward and aft at the ends of the ship When the... 18 MERCHANT SHIP STABILITY Prismatic Coefficient of Fineness of Displacement.This is the ratio between the underwater volume of the ship and that of a prism having the same length as the ship