MERCHANT SHIP STABILITY

(METRIC EDITION)

A Companion to "Merchant Ship Construction"

B Y

H. J. PURSEY E X T R A M A S T h R

Lecturer to thc School of Navigation University qi Southan&ptulr

GLASGOW BROWN, SON R: FERGUSON, LTD., NAUTICAL PUBLISHERS

CONTENTS CHAPTER 1 . S O M E GENERAL INFORMATION

The Metric System . . . . . . . . . . . . Increase of pressure with depth . . . . . . . . The Law of Archimedes . . . . . . . . . . Application to Ships . . . . . . . . . . . . Floating bodies and the density of water . . . . . . Ship dimensions . . . . . . . . . . . . Decks . . . . . . . . . . . . . . Ship tonnages . . . . . . . . . . . . Grain and bale measurement . . . . . . . . . . Displacement and deadweight . . . . . . . . . . Draft . . . . . . . . . . . . . . Freeboard . . . . . . . . . . . . . . The effect of density on the draft of ships . . . . . . Loadlines . . . . . . . . . . , . . .

CHAPTER 2.-AREAS AND VOLUMES Areas of common plane figures . . . . . . . . . . Surface areas and volumes . . . . . . . . . . Areas of waterplanes and other ship-sections . . . . . . The Trapezoidal Rule . . . . . . . . . . . . Simpson's Rules . . . . . . . . . . . . The "Five-Eight Rule" . . . . . . . . . . Sharp ended waterplanes . . . . . . . . . . Volumes of ship shapes . . . . . . . . . . Half-intervals . . . . . . . . . . . . Caefficients of fineness . . . . . . . . . . Wetted surface . . . . . . . . . . . .

CHAPTER 3.-FORCES AND MOMENTS Force . . . . . . . . . . . . . . Resultant forces . . . . . . . . . . . . Moments . . . . . . . . . . . . . . Properties of a moment . . . . . . . . Combinations of moments . . . . . . . . . . Centre of gravity . . . . ... . . . . . . Effect on centre of gravity of added weights . . . . . . Effect on centre of gravity of removing weights . . . . . . Effect on centre of gravity of shifting weights . . . . . . Use of moments to find centre of gravity . . . . . . To find the centre of gravity of a waterplane . . . . . . To find the centre of gravity of a homogeneous ship shape . . . . The use of intermediate ordinates . . . . . . . . Appendages . . . . . . . . . . . . Inertia . . . . . . . . . . . . . .

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Moment of inertia and radius of gyration . . . . . . Moment of inertia of a body about its centre-line . . . . . . . . Moment of inertia of a waterplane about its centre-line . . . . . . Equilibrium . . . . . . . . . . . . . . . .

CHAPTER 4 . A E N T R E OF GRAVITY

Centre of gravity of a ship-& . . . . . . . , KG . . . . . . . . . . . . Light IfG . . . . . . . . . . . . Shift of G . . . . . . . . . . . . KG for any condition of loading . . . . . . Real and virtual centres of gravity . . . . . . Effect of tanks on G . . . . . . . . . .

OF SHIPS

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Centre of Buoyancy-B . . . . . . . . . . . . KB .. . . . . . . . . . . . . . . . . Centre of Flotation-F . . . . . . . . , . . . Shift of B . . . . . . . . . . . . . . . . Horizontal and vertical components of the shift of B . . . . . .

CHAPTER 6.-THE RIGHTING LEVER AND METACENTRE

Equilibrium of ships . . . . . . . . . . . . . . The righting lever.. 4 Z . . . . . . . . . . . . The metacentra-M . . . . . . . . . . . . . . Metacentric height.. G M . . . . . . . . . . . . Stablo . unstable and neutral equilibrium . . . . . . . . Longitudinal metacentric height-GMh . . . . . . . . . .

CHAPTER 7.-TRANSVERSE STATICAL STABILITY

Moment of statical stability . . . . . . . . . . . . Relation between G'll and G Z . . . , . . . . . . . . Initial stability and range of stability . . . . . . . . Calculation of a ship's stability . . . . . . . . . . . . Calcul~~tion of EM for ship shapes . . . . . . . . . . Calculation of EM for box shapes . . . . . . . . . . Approximate formula for BM . . . . . . . . . . . . The Inclining Experiment . . . . . . . . . . . . Statical stability a t small angles of heel . . . . . . . . . . Statical stability a t 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 . . . . . . . . . . . .

CHAPTER 8.-FREE SURFACE EFFECT

The effect of free surface of liquids . . . . . . . . . . The effect of rectangular free surfaces . . . . . . . . . . Free surface effect when tanks are filled . . . . . . . . . . Free surface effect when tanks are emptied . . . . . . . . The effect of density on free surface effect . . . . . . . . Free surface in divided tanks . . . . . . . . . . . .

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CHAPTER B.-TRANSVERSE STATICAL STABILITY IN PRACTICE

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 . . . . . . . . . .

CHAPTER 10.-DYNAMICAL STABILITY

Dynsmical stability . . . . . . . . . . . . . . Dynamical stability from a curve of statical stability . . . . . . . . Calculation of dynamical stability . . . . . . . . . . . . Moseley's formula . . . . . . . . . . . . . . . .

CHAPTER 11.-LONGITUDINAL STABILITY

Longitudinal metacentric height-GML . . . . . . . . . . . . Calculation of BML for all shapes . . . . . . . . . . . . Calculation of BML far box shapes . . . . . . . . . . . . Tons pcr centimetre immersion . . . . . . . . . . . . . . Trim . . . . . . . . . . . , . . . . . . Momcnt to change trim by 1 ccntimetre . . . . . . . . . . . . Change of draft due to change of trim . . . . . . . . . . . . The effect of shifting a weight . . . . . . . . . . . . . . Change of mean draft due to change of trim . . . . . . . . . . Displacement out of designed trim . . . . . . . . . . . . Effect of adding weight at the centre of flotation . . . . . . . . . . Moderate weights loaded off the centre of flotation . . . . . . . . Large weights added off the centre of flotation . . . . . . . . Loading weights to obtain a desired trim . . . . . . . . Position to load we i~h t not to change draft aft . . . . . . . . . . Loading a weight to produce a desired draft aft . . . . . . . . . .

CHAPTER 12.-STABILITY CURVES AND SCALES

Information supplied to ships . . . . . . . . . . . . . . Curves of displacement, etc . . . . . . . . . . . . . . . Use of the curves . . . . . . . . . . . . . . . . The deadweight scale . . . . . . . . . . . . . . . . Use of the deadweight scale . . . . . . . . . . . . . . Curves of statical stability . . . . . . . . . . . . . . Cross cuwes . . . . . . . . . . . . . . Effetfect of height of G . . . . . . . . . . . . The metacentric diagram . . . . . . . . . . . .

CHAPTER 13.-BILGING

The effect of bilging a compartment . . . . . . . . . . . . Permeability . . . . . . . . . . . . . . . . Bilging an empty compartment amidships . . . . . . . . . . Bilging an amidships compartment. with cargo . . . . . . . . . . Rilging an empty compartment, not amidships . . . . . . . . . . Effect of a watertight flat . . . . . . . . . . . . . . Compartments with cargo. not amidships . . . . . . . . . .

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CHAPTER 14.-MISCELLANEOUS MATTERS

Drydocking . . . . . . . . . . . . . . Grounding . . . . . . . . . . . . . . The effect of density on stability . . . . . . . . The effect of density on the draft of ships . . . . . . Derivation of the fresh water allowance . . . . . . . . Reserve buoyancy . . . . . . . . . . . . Continuous watertight longitudinal bulkheads . . . . . . Non-continuous longitudinal bulkheads . . . . . . . . Bulkhead subdivision and shocr . . . . . . . . Pressure on bulkheads . . . . . . . . . . The effect of water in sounding pipes. etc . . . . . . . Stability requirements under Loadline Rules . . . . . .

The formation of waves The Trochoidal Tlleory The true period of waves The apparent period of waves Tho period of a ship . . Synchronism . . Unresisted rolling . . Resistances to rolling . . The effects of bilge keels Cures for heavy rolling

CHAPTER 15.-ROLLING

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CIIAPTER 16.-SIJAIMARY

Abbreviations . . . . . . . . . . Formulae . . . . . . . . . . . . Definitions . . . . . . . . . . . .

PROBLEMS . . . . . . . . . . DISI'LACEMENT CURVES AND DEADWEIGHT SCALE . . Insert in back of book

I N D E X

A Abbreviations . . . . Added weights. effect on G Added weights. effect on

draft. etc . . . . . Angle of loll. or list . . Angle of vanishing stability Appendages . . . . Archimedes' Law . . Areas. general . . . . Areas of waterplanes . . Athvood's Formula . .

. . . . Block coefficient . . . . Bodies. moment of inertia Box shapes. B. BM and G Box shapes. area and velum,

Calculation of stability . . o 1 y . . Cvt81re uf i?ut.tliun . . Ccnrre cf cra\.lrv of area Centre of Zravitb of body

Change oidraftwith trim Change of mean draft . . Circle . . . . . . CoeTficients of fineness . . Common interval . . "Conditions" . . . . Critical period . . . . Cross curves . . . . Cube . . . . . . Cures for instability . . Curve of floodable iengths Curves of displacement . . Curves of statical stability Cylinder . . . . . .

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Deadweight . . 26.38 94 D eadwei~bt scale

PACE

5. 138 106 .

Decks . . . . . . . . . . 4 94, 1.36 Deck line . . . . . . . . .. 7 61. 134 Deck cargoes . . . . . . 76

l07. 138 Deep tanks . . . . . . 42.75.77 . . 33 . Definitions . . . . . . . . 133 Density . .

133 Density. effe'cts of" . . 135 Dcpth of ships . . . . 135 . Dcpth. effect on pressure

Urn\-nrion of fresh \rarer allo Urrrirks and weights lifted

I? 3 l . ~ c ~ i ~ n ~ . l 134 . ~esiFed trim. to produce 134 Dimensions . .

5 Displacement . . . . 74 . Displaccmcnt. coefficient of

133 ! Disolacomcnt curves . . 130 1 ~isblaccmcnt out of trim 106 1 DiGded tanks . . . . .. 36 Double bottom tanks . . 134 Draft . . . . . . 136 Draft. effect of trim . .

4 Draft . effect of density . . . . 5.6. 122 124 Draft. effect of weights . . 94 .. . . . .

. . 121 Draft. increase with bilging . . . . 112

. . 125 Draft . constant or desired . . 102 . 134 123. 139 I nryd&king . . . . . . 119; 134

1 D?-namical stability . . 79.135. 138

.. 5 3 . 44.'48. 53. 83. 138 E

41. 83. 138 Emerged wedge . . . . . . . . 44 . . 21.28 . Emptying tanks . . . . . . 66 . . 25. 28. 31 I Equilibrium . . . . 37..48. 133

31. 38 . 83. 133 . . 26.38 1 F . . 41. 63 F . . . . 44.83. 138 . . 88. 92 . Factors nffkEting stabiliti . . . . . 69

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. . . . 17. I06 . . . . . . . . 14 . . . . 11 Floating bodies . . . . . . . . 3 . . . . 104 Floodable lengths . . . . . . 124 . . . . 119 1 ~ o r c e . . . . . . . . 20. l:i8 . . 108 ! Formation of waves . . . . . . 127 . . 9. 136 Formulae: summary . . . . . . 133 . . 73 Framing depth . . . . . . 4 . . . . 124 ' Freeboard . . . . . . 5. 7.'69. 138 . . . . 105 Freeboard dcck . . . . 4

69 . 79. 107 Free suriace . . . . 63.'72.77.'i24 . 135 . . 10. 136 Fresh water allowance . . . . 6.8. 123

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G . . . . . . GM . . . . G Z . . Grain measurement Gross tonnage . . Grounding . .

Height of G . . Height of M . . Hollow round sections ~ ~

Hollow sphere . . Hydrostatic curves

I Inclining experiment . . Increase of draft with bilging Immersed wedge . . Inertia . . . . . . Inertia, moment of . . Information supplied to ships Initial stability . . . . Intermediate ordinates . . Isochronous rolling . . Interval, common . .

1 Jettisoning cargo

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. . "' I Oil tankers . . . . , , 44 Ordinates . . . . 34. 138 D

Parallelogram of forces . . Pcriod of ships . . . . Period of waves . . . . Permeability . . . . Plimsoll mark . . . . Practice of stability . . Pressine uo tanks . . pressure, &crease with depth . . 74 Pressure on bulkheads . . Pressure on tank tops . . Prisms . . . . . .

44. 53 Prislnatic coefficient . . 38, 110, 138 Pr~smatic wedges . .

50.53 Pro-metacentre . . . . 1 Problems . . . . I

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INDEX

Sounding pipes . . . . Sinkage through bilging . .

. . . . Specific gravity Snhere . . . . . .

stiff ships . . . . Subdivision . . . . Summary . . . . Surfam areas . . . . Synchronism . . . .

T Tanks . . . . Tender ships . . . . Timber deck cargoes . . Timber loadlines . . Tipping centre . . . . Tonnage deck . . . . Tonnages . . . . . . Tons per inch immerswn Trapezium or trapezoid . . . . . . Trapezoidal rule Triangle . . . . . . Trim . . . . . . Trochoidal theory . .

U Under deck tonnage . . . . <Inresisted rolling . . . . Unstable equilibrium . . . . Unstable ships . . . . . . Unsuitable numbers of ordinates

Virtual centre of gravity Volumes . . . . . . Vanishing stability . .

W Wall-sided formula . . . . Water . . . . . . water bana;t . . . . . . Wator ia pipes . . . . . .

. . . . Watcmlane coefficient Waterplanes . . . . . .

. . . . Watertight flats . . Wave formation . . . . . . Wedges. common . . . . Wedges. immersed and emerged Wetted surface . . . . . . Winging-out weights . . . . tV.N.A. line . . . . . . Work . . . . . .

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