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Merchant Ships WAKEOF MERCHANT SHIPS B Y SVEND AAGE HARVALD THE DANISH TECHNICALPRESS COPENHAGEN 1950 ..'M . I / ;4 i) .; ,# 3.. - ' f- f .- t ':. -- . , f ç.. - t : . '.- ,.. Denne afhand].ing er s.f Daninarks tekniske Hjsko1e antaget tu Í'orsvar for den tekniske doktorgrad. Danmarks tekniske Højs1o1e,.23. juni1950. Anker Engelund. Rektor. PREFACE. It is the hope.of the author that this treatise will be a help and guidance to the designer in the shipyard as well as. tothe scientist working in the laboratory. The dissertation princlpally.dea].s with.the problems connected with wake, seen partly from a practical, partly from a theoretical point Of view; but further It, considers questions closely connected tò wake. Thus amongst others the problem of thrust deduction has been taken.up fora. brief discussion, The principal part of the, work connected with this treatise has been carried out at the shipbuilding depart- ment at the DANMARXSTEKNIS HØJSKOLE, Køberthavn.The. leader of this department ProfessorC.. PROHASKA, D.Sc., has during the progress-of the work given the author a great deal ol' sùpport and assistance. Some of the work had.to be done abroad, partly in Sweden and partly in Holland. In Sweden the author hada whole series of experiments performed and in Holland stati- stical material was collected. For five nontha the author was temporarily employed as half-day assistant at the STATENS SKEPPSP,ROVNI.NGSANSTALT, Gtoborg, under Professor. H.F.NORDSTROM, D.So,superinten- dent. During this same period the HUGOHAMMRS FOND FR IN- TERNATIONELL FORSKNING INOM SJFARTENsupplied the funds enabling the carrying out, of model experiments. Thus the autboi'ha4 good opportunity to study wake. As these experi- monts are described in detail in "Meddelanden frân Statena Skeppsprovningsanstalt' nr 13", only the results are given in this dissertation. For three month the author was the guest of the 1EDER- LANDSCEE SCHEEPSOTJYJKUNDIG PROEFSTATION, Wageningen, and worked at the scientific department of the tank; work sole- ly connected with investigations of wake. The staff of the tank was of great help and support to the author, especial- ly Mr. J.D. VAN MMEN, M.Sc., with whom many probleme were 2. ficaSed,.and the. superintendent, Professor L. TROOST, who wasoxceedingly hospitable and most helpful. The results of one part. of the work in Holland has been published earlier iñ the Dutch magazine "Schip en Werftt. Soñe shipyards and. institutIons have put at the authors disposal model experiment data. ProfessorE. Petersen, Ph.D., Darmmrks tekniske Højsko- lé, has checked the mathematical expressions in sections D-c and D-cl. Mr. J, SVÈNSEN and Mr. H.E.GULDHAMMER, M.Se., hâve assisted in preparing the many diagrams, and Mr. GULDÄU1ER has given much good advice The translation f ro Danish has been .perforned by'lMr. T.E.BLUI, B.Sc., and Mr. G. BUCHANAN, B.Sc., hâsveriied the transiátion. ±ather of' the author Mr. AA. HARVALD has assisted byreadingthe proofs and hs. been of great encouragement to the authói' In accomplishing his work. The expenses of the work in Denmark were met through grant s from AKADEMIET FOR DE TEKNISKE VIDENSKABER, København and. THOMAS B. THRIGES FOND, Odense. The author tanks most cordially all the above Lnentioned persons and. institutions for their great and valuable 1elp.. Kgs. Lyngby, Deceñiber 1949. Sver4 Aage Harvald. CONTENTS. page Introduction 5 CHAPTER_I DEFINITIONS Definition, measurement and determination of the wake nd the wake coefficient 7 CHAPTER I : C0MPOENTS OF WA C. Frictional wake 12 D. Potent1a1 wake 23 a. Potèntial wake of cylindrically 3liaped bodies. with similár fore and after ends (tvro-dimension]. flow) ' 24 ai . The potential wake coefficient 's dependence on the angle of tnc1ination of the waterline to the cönre :.. line aft . 39 The variation of the potential wake coeff.iciet with the propeller diameter 44 The longitudiral variation of the potential.*ake coeffiòient - - b. Potential wake of cylindrically shaped bodies with different fore and after ends (two-dimensional flow) 48 -e. Potential wake of ellipsoids (three-dimensional flow). .. ..... .......oo..-. .-..o là .-. 54 ci.-Comparisonof two- arid three-dirnensiönalflovs(el-- liptical cylinders -and eliipsoid-s 64 d, Potentiji wake of' solids of revoluticn (three dimensional flow) - 69 --e....Potential wake of' ships (three-di nional- f-low)-.-. 76 Wave wake - .77 CHAPTER III :P?EDETERMINATION- OF iA -Construction of a new diagram for determining the wáké coefficient of' single screw ships ......................,. 85 a. Parameters on which the wake coefuic.eñt dends. 85 b.- Analysis of model experirents --- bi. Variation of wake coefficient with speed 103 b2. Relation between nominal and effective wake Construction of a new diagram for determIning the wake coefficient of twin screw ships - 105 4. H. The wake coefficient of special types of ships 112 Fishing vessels 112 . .. Tug 'coats . 115 ships inhioh the propellers are fitted in nozzles or tunnels 116 Ferries with forward and after propellers 118 Patrol and pilot boats 119 Ocean yachts 120 CHAPTER IV: FORMrJIAE OF VJA1OE AND THRUST DEDUCTION I. Earlier formulae and diagrams for- determining the coef- ficients of wake and thrust deduction of single and twin, screw ships 121 J. Testing of the wake-formulae and diagrams for. single screw ships 147 K. Comments on the wake-formulae and dia'ams for twin screw ships and for special types of ships 157 CHAPTER V DEPENDENCE OF WA' ON VARIOUS' FACTORS L. Influence of rudder on wake 159 M. Dependence of wake coefficIent on condition of ship 166 N. Dependence of wake coefficient on depth of water 167 O. The influence of the degree of turbulence on the wake measured by experiments 169 CHAPTER VI¡ WA DISTRIBUTION P. Distribution of wake of single and twin screw ships 171 Q. The optimum coefficient and distribution of wake 178 CHAPTER VII: DEPENDENCE 0F VARIOUS FACTORS ON V/A R. The Influence of the wake on the nwnber of revolutions of the propeller 182 S. The influence of the wake on the steering of the ship 185 T. The influence of wake on propeller cavitation and vibration . -. 189 CHAPTER VIII: THRUST DEDUCTION U. The relation of the wake coefficient to the coefficient of thrust deduction in single and twin screw ships 191 V. Summary - 204 Summary in Danish 207 210 Synthols and units - . .. Bibliography . .' 213 5. A. INTRODUCTIbN, It is always the hope of the pÌ'oje].ïe±designerto design a propeller such that: Fir'stly it'ill wörk as he wants lt to, i.e. th.t the prd1lor & êrtairi ed and a certain number of revolutioÍis wi1I absóxb a cèrtaln amount of power. Secondly that the ptirnwn intration between ship and propeller is attained, Still further nowadays there Is a third requirorent, èspecially in the case of fast ships:that the propeller must be free from cavitation. In order to get these wishes fulfilled he must know the velocity or rather the velocities with which the water flows to the propeller disc. What happens outside this region does not concern him. But in the study of the velocities of the flow of water, it is necessary, to examine what takes place outside the pro- peller disc, in order more easy to ascertain the actual con- ditions at the propeller. In this monograph the conditions of wake from forward to aft, even up to about one ships length abaft the propel- 1er, have been examined. The base flow, i.e. the flow present without propeller, as well as the flow present when the pro- peller is working have been studied. The examinations have first of all covered the ordinary types of merchant ships, but in addition many special types of ships have been inclu- ded, An analysis of the three components of wake: frictional wake, potential wake, arid wave wake has been made. The ana- lysis has principally been theoretical, and only as regards wave wake have experiments been performed. Further a statistical examination of the measurement of' wake,. of the effective as well as of the nominal wake coefficients, has been Carried out, and the results have been compared in a diagram to be used for quick predeteruii- nation of the wake coefficient. A comparison of the different approximate fornmlae and diagrams for predetermination of the wake coefficient bas also been made. At the end of' this treatise are given curves of wake distribution, obtained from numerous model experiments, to 6. be used by the designer. who, for his designe, employs the theory of circulation. Finally the relation of the wake coefficient to the coefficient of thrust deduction, and the influence of the wake on steering and on the number of revolutions of the propeller have been dealt with. 70 CHAPTER I: DEFINITIONS. B. DEFINITION., ASUREIVNT AND DETERMINATION OF T WAKE AND THE WAKE COEFFICIENT. By te wake is understood the difference between the velocity of the ship and the velocity with which the water flows to the propeller. By dividing this difference either by the velocity, of' the ship or by the velocity of flow òf water, two wake coefficIents are obtained. The first coéffiient w V -Ve V is ternied TAYLOR's wake fraction. This is employed in Ame- rica and in the continental part of Eürope, aìid will sole- ly be used in the following. The other coefficient w VV0 F y e is termed FRQUDEs wake percentage and is much used in Great Britain. For the sake of completeness the formulae for transforming or.e coefficient to the other are given: 'F. w = and w = By potential wake is understood. the wake obtained 1f the ship movedn an.ideal'fluid.without friction, and wave making. In other words the potential wake.. is that wake which mathematically can.
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