Ship Stability for Masters and Mates Ship Stability for Masters and Mates Fifth edition Captain D. R. Derrett Revised by Dr C. B. Barrass OXFORD AUCKLAND BOSTON JOHANNESBURG MELBOURNE NEW DELHI Butterworth-Heinemann Linacre House, Jordan Hill, Oxford OX2 8DP 225 Wildwood Avenue, Woburn, MA 01801-2041 A division of Reed Educational and Professional Publishing Ltd First published by Stanford Maritime Ltd 1964 Third edition (metric) 1972 Reprinted 1973, 1975, 1977, 1979, 1982 Fourth edition 1984 Reprinted 1985 First published by Reed Educational and Professional Publishing Ltd 1990 Reprinted 1990 (twice), 1991, 1993, 1997, 1998, 1999 Fifth edition 1999 Reprinted 2000 (twice), 2001 # D. R. Derrett 1984, 1990, 1999 and Reed Educational and Professional Publishing Ltd 1999 All rights reserved. No part of this publication may be reproduced in any material form (including photocopying or storing in any medium by electronic means and whether or not transiently or incidentally to some other use of this publication) without the written permission of the copyright holder except in accordance with the provisions of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London, England W1P 0LP. Applications for the copyright holder's written permission to reproduce any part of this publication should be addressed to the publishers British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloguing in Publicaion Data A catalogue record for this book is available from the Library of Congress ISBN 0 7506 4101 0 Typesetting and artwork creation by David Gregson Associates, Beccles, Suffolk Printed and bound in Great Britain by Biddles, Guildford, Surrey A member of the Reed Elsevier plc group Contents Preface vii Introduction ix Ship types and general characteristics xi 1 Forces and moments 1 2 Centroids and the centre of gravity 9 3 Density and speci®c gravity 19 4 Laws of ¯otation 22 5 Effect of density on draft and displacement 33 6 Transverse statical stability 43 7 Effect of free surface of liquids on stability 50 8 TPC and displacement curves 55 9 Form coef®cients 61 10 Simpson's Rules for areas and centroids 68 11 Final KG 94 12 Calculating KB, BM and metacentric diagrams 99 13 List 114 14 Moments of statical stability 124 15 Trim 133 16 Stability and hydrostatic curves 162 17 Increase in draft due to list 179 18 Water pressure 184 19 Combined list and trim 188 20 Calculating the effect of free surface of liquids (FSE) 192 21 Bilging and permeability 204 22 Dynamical stability 218 23 Effect of beam and freeboard on stability 224 24 Angle of loll 227 25 True mean draft 233 26 The inclining experiment 238 27 Effect of trim on tank soundings 243 28 Drydocking and grounding 246 29 Second moments of areas 256 30 Liquid pressure and thrust. Centres of pressure 266 31 Ship squat 278 32 Heel due to turning 287 33 Unresisted rolling in still water 290 34 List due to bilging side compartments 296 35 The Deadweight Scale 302 36 Interaction 305 37 Effect of change of density on draft and trim 315 38 List with zero metacentric height 319 39 The Trim and Stability book 322 40 Bending of beams 325 41 Bending of ships 340 42 Strength curves for ships 346 43 Bending and shear stresses 356 44 Simpli®ed stability information 372 Appendix I Standard abbreviations and symbols 378 Appendix II Summary of stability formulae 380 Appendix III Conversion tables 387 Appendix IV Extracts from the M.S. (Load Lines) Rules, 1968 388 Appendix V Department of Transport Syllabuses (Revised April 1995) 395 Appendix VI Specimen examination papers 401 Appendix VII Revision one-liners 429 Appendix VIII How to pass exams in Maritime Studies 432 Appendix IX Draft Surveys 434 Answers to exercises 437 Index 443 vi Contents Example 1 Whilst moving an object one man pulls on it with a force of 200 Newtons, and another pushes in the same direction with a force of 300 Newtons. Find the resultant force propelling the object. Component forces 300 N A 200 N The resultant force is obviously 500 Newtons, the sum of the two forces, and acts in the direction of each of the component forces. Resultant force 500 N A or A 500 N Example 2 A force of 5 Newtons is applied towards a point whilst a force of 2 Newtons is applied at the same point but in the opposite direction. Find the resultant force. Component forces 5 N A 2 N Since the forces are applied in opposite directions, the magnitude of the resultant is the difference of the two forces and acts in the direction of the 5 N force. Resultant force 3 N A or A3N (b) Resolving two forces which do not act in the same straight line When the two forces do not act in the same straight line, their resultant can be found by completing a parallelogram of forces. Example 1 A force of 3 Newtons and a force of 5 N act towards a point at an angle of 120 degrees to each other. Find the direction and magnitude of the resultant. Ans. Resultant 4.36 N at 36  34 1 2 H to the 5 N force. Note. Notice that each of the component forces and the resultant all act towards the point A. 2 Ship Stability for Masters and Mates Fig. 1.1 <> >> EE E E E E )) ) ) [...]... the point for the force of 3 N towards the point as shown in Figure 1. 4, or a force of 5 N towards the point for the Fig 1. 4 3 4 Ship Stability for Masters and Mates Fig 1 .5 force of 5 N away from the point as shown in Figure 1 .5 In this way both of the forces act either towards or away from the point The magnitude and direction of the resultant is the same whichever substitution is made; i.e 5. 83 N at... heel when measured veri®es that this assumption is indeed correct 18 Ship Stability for Masters and Mates Exercise 2 1 2 3 4 5 A ship has displacement of 2400 tonnes and KG ˆ 10 .8 metres Find the new KG if a weight of 50 tonnes mass already on board is raised 12 metres vertically A ship has displacement of 2000 tonnes and KG ˆ 10 .5 metres FInd the new KG if a weight of 40 tonnes mass already on board... gravity Example 5 A tank will hold 15 3 tonnes when full of fresh water Find how many tonnes of oil of relative density 0.8 it will hold allowing 2% of the oil loaded for expansion Mass of freshwater ˆ 15 3 tonnes ; Volume of the tank ˆ 15 3 m 3 Volume of oil ‡ 2% of volume of oil ˆ Volume of the tank or 10 2% of volume of the oil ˆ 15 3 m 3 10 0 3 m ; volume of the oil ˆ 15 3  10 2 3 ˆ 15 0 m Mass of the... this weight is raised through 1 .5 metres vertically and is suspended by a derrick whose head is 17 metres above the keel Find the shift in the centre of gravity of a ship of 15 0 0 tonnes displacement when a weight of 25 tonnes mass is shifted from the starboard side of the lower hold to the port side on deck through a distance of 15 metres 20 Ship Stability for Masters and Mates Example 2 Find the density... distance of 0 .5 Forces and moments metres from one end and a second load of mass 30 kilograms is placed at a distance of one metre from the other end Find the resultant moment about the middle of the plank Fig 1. 8(b) Moments are taken about O, the middle of the plank Clockwise moment ˆ 30  0X5 ˆ 15 kg m Anti-clockwise moment ˆ 10  1 ˆ 10 kg m Resultant moment ˆ 15 À 10 Ans Resultant moment ˆ 5 kg m clockwise...Forces and moments Fig 1. 2 Example 2 A ship steams due east for an hour at 9 knots through a current which sets 12 0 degrees (T) at 3 knots Find the course and distance made good The ship' s force would propel her from A to B in one hour and the current would propel her from A to C in one hour The resultant is AD, 0X97 1  11 X6 2 miles and this will represent the course and distance made... clockwise 7 8 Ship Stability for Masters and Mates Exercise 1 1 2 3 4 5 A capstan bar is 3 metres long Two men are pushing on the bar, each with a force of 400 Newtons If one man is placed half-way along the bar and the other at the extreme end of the bar, ®nd the resultant moment about the centre of the capstan A uniform plank is 6 metres long and is supported at a point under its midlength A 10 kg mass... the ship with a mass of w tonnes on board at a distance of d metres from G G to G1 represents the shift of the ship' s centre of gravity due to discharging the mass In Figure 2.4(a), it will be noticed that the mass is vertically below G, and that when discharged G will move vertically upwards to G1 12 Ship Stability for Masters and Mates In Figure 2.4(b), the mass is vertically above G and the ship' s... gravity of a ship with a weight of `w' tonnes in the starboard side of the lower hold having its centre of gravity in position g1 If this weight is now discharged the ship' s centre of gravity will move from G to G1 directly away from g1 When the same weight is reloaded on deck with its centre of gravity at g2 the ship' s centre of gravity will move from G1 to G2 14 Ship Stability for Masters and Mates Fig... the ship takes a list and a quantity of grain shifts so that the surface of the grain remains parallel to the waterline Show the effect of this on the ship' s centre of gravity 16 Ship Stability for Masters and Mates f Fig 2.9 In Figure 2.9, G represents the original position of the ship' s centre of gravity when upright AB represents the level of the surface of the grain when the ship was upright and . BM and metacentric diagrams 99 13 List 11 4 14 Moments of statical stability 12 4 15 Trim 13 3 16 Stability and hydrostatic curves 16 2 17 Increase in draft due to list 17 9 18 Water pressure 18 4 19 . 0X5  15 kg m Anti-clockwise moment  10  1  10 kg m Resultant moment  15 À 10 Ans. Resultant moment  5 kg m clockwise Forces and moments 7 Fig. 1. 8(b) 8 Ship Stability for Masters and Mates Exercise. 19 72 Reprinted 19 73, 19 75, 19 77, 19 79, 19 82 Fourth edition 19 84 Reprinted 19 85 First published by Reed Educational and Professional Publishing Ltd 19 90 Reprinted 19 90 (twice), 19 91, 19 93, 19 97, 19 98, 19 99 Fifth