Reseaveln L Devel yp ; sor (a eee age oe HYDROMECHANICS =: SERIES 60 = METHODICAL EXPERIMENTS WITH MODELS OF SINGLE-SCREW MERCHANT SHIPS by AERODYNAMICS F. H. Todd, Ph.D oTRUCTURAL MECHANICS RESEARCH AND DEVELOPMENT REPORT APPLIED MATHEMATICS July 1963 Report 1712 ede IMMUN iii (WN 0 0301 O08b? July 1963 Ve Ne 4 SERIES 60 METHODICAL EXPERIMENTS WITH MODELS OF SINGLE-SCREW MERCHANT SHIPS by F. H. Todd, Ph.D Report 1712 For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C., 20402 — Price $2 (Paper Cover) TABLE OF CONTENTS Page CHAP ALESR,] Sl IN DRO DU CiLION iirscsesscecceasocesenecorsscceere eesscosrstuseatscsectctectsicsscasteeseesaserace I-1 CHAPTER II — SELECTION OF THE RANGE OF PROPORTIONS HOR SRHIEGSERIE Sees rrtte cers seseritet ee toes teeccem settee es any ese cciesonsseetentteee Il-1 CHAPTER Il —- CHOICE OF HULL FORM FOR THE PARENT MODELS ................. I-1 CHAPTER IV — CHARACTERISTICS OF SERIES 60 LINES ........ cece cee eeseeseeeeeeee Iv-1 CHAPTER’ V — RESISTANCE TESTS ON SERIES 60 PARENT MODELS ................. V-1 CHAPTER VI — EFFECT ON RESISTANCE OF VARIATION IN E@B- POSITION | <2::-2: seeceevuscccecs vavescsdesuotognsdtenetucevestecesscenesosescaetametereseaeees VI-1 CHAPTER VII — EFFECT ON DELIVERED HORSEPOWER (DHP) OF VARIATION IN LCB POSITION ..........ccccccceceeesessesseeceseeecereeeaeenes Vi-1 CHAPTER VIII —- EFFECT ON RESISTANCE AND DHP OF VARIATION IN SHIP PROPORTIONS. ..........ccccscccsseesseseecsseesseeeeeeneeees VIl-1 CHAPTER: IX — DESIGN (CHARTS ....:.c-ccuscsscccccssecessesnsuctsocroretsenssnssovcasssovoroesisseiscasteerenes IX-1 CHAPTER X — EFFECT OF VARIATIONS IN PROPELLER DIAMETER AND SHIP “DRAFT AND: TRIM) 330-:0s-ss0s0--sccecsssctesesess.cesese-sotsseesetaeeeeene X-1 CHAPTER XI — EFFECT OF VARIATION IN AFTERBODY SHAPE UPON WAKE DISTRIBUTION AND POWER. 0.00... ceceeccecccceseceeseseeensseeeeneees XI-1 CHAPTER XII — REVIEW OF SERIES 60 PROJECT ..0.0....... cc ccccecssscseesceeeseeeseeceseeeeseees XIl-1 CHAPTER XIII — POSSIBLE EXTENSION OF SERIES 60 AND PUDURE RESEARCH site ctsccs cv ccuctscccestccsces suotedesuteceesscostvesteree ree XIII-1 APPENDIX A — EFFECTS OF TURBULENCE STIMULATORS ....0.0. cee ecseee cere A-1 APPENDIX B — USE OF CONTOURS AND CHARTS ....0..... cee cesesesesessessceceseeeesseaeseee ee B-1 APPENDIX C — METHODS OF ANALYSIS AND FAIRING QEORESULDS ve tecicc ccs fevregadteacectestesbacgece sctetetscdsareceguneteueesareacte ss eee C-1 APPENDIX D — NUMERICAL EXAMPLE OF USE OF SERIES 60 CEA Ce sresscrsee suas autce oss Wisi stcbescnsatusetasvincecce sensi peuleisease eee D-1 APPENDIX E — INTERNATIONAL TOWING TANK CONVERENCE 1957 MODEL-SHIP CORRELATION LINE. ..............cecssssceseccescereeeeeeeseneeeseees E-1 IVERENCES ree ccesssscrsecerssssenn-nsesdeahdentachaess-tssasistidinnlen tase ee ee Rel li FOREWORD The research on Series 60 was carried out at the David Taylor Model Basin of the United States Navy. The results were published in the first instance in a number of papers before the Society of Naval Architects and Marine Engineers. From time to time the wish has been expressed that the results of this research should be assembled in a single volume for easy reference and use. The original papers described a great deal of preliminary work carried out before the final Series 60 was adopted, and because they were read at inter- vals over a period of nearly 10 years, they also contained a certain amount of duplication and connective matter. The opportunity has therefore been taken to completely rewrite the text, which is new, eliminating the preliminary work and much of the history, and also, it is hoped, most of the errors which are seemingly inevitable in a research of this magnitude. In presenting the collected results in this new version, the author wishes to express his indebtedness to all the Staff of the Model Basin who have worked on the project since its inception in 1948, particularly those who have been co- authors in the original papers—Capt. F.X. Forest, U.S.N., Mr. J.B. Hadler, Mr. G.R. Stuntz, Dr. P.C. Pien, W.B. Hinterthan, and N.L. Ficken. Mr. Hadler and Mr. Stuntz have been most helpful in reviewing the present text, although any opinions expressed are those of the author. The whole project was carried through under the general guidance of a Panel of the Society of Naval Architects and Marine Engineers, the mémbers of which devoted much time and thought to the choice of parameters and the detail design of the Series. The following people served on this Panel from time to time—Professor L.A. Baier, Mr. J.P. Comstock, Mr. H. de Luce, Capt. F.X. Forest, U.S.N., Mr. J.B. Hadler, Admiral C.O. Kell, U.S.N., Professor G.C. Manning, Mr. V.L. Russo and Dr. F.H. Todd—the successive Chairmen being Admiral Kell, Dr. Todd, and Mr. Hadler. Thanks are especially due to successive Directors of the Model Basin who have throughout supported the research—Admirals C.O. Kell, G.H. Holder- ness, A.G. Mumma, W.H. Leahy, E.A. Wright, and Captain J.A. Obermeyer— and to the Bureau of Ships which supplied the finance for most of the work under the Fundamental Hydromechanics Research Program, assisted towards the end by the Maritime Administration and the Society of Naval Architects and Marine Engineers. iii SYMBOLS Dimensions L Length in general Leap Length between perpendiculars (LBP) Lot Length on designed waterline Ly Length of ship Ly Length of model Le Length of entrance Ly Length of parallel Lp Length of run B Beam H Draft A Displacement in tons V Displacement in cubic feet ny Wetted surface LCB Longitudinal centre of buoyancy A Op Half-angle of entrance on load waterline Form Coefficients Cp Block coefficient Cy Midship area coefficient Cp Prismatic coefficient Cpr Prismatic coefficient of entrance Cpy Prismatic coefficient of parallel body Cpr Prismatic coefficient of run Mid-point of LBP Position of LCB as function of length from forward perpendicular Bilge radius Coefficient of bilge radius =-——————=—_ 2 ; VBxH Scale of model to ship Resistance Coefficients R Rr FR General symbol for resistance Frictional resistance Residuary resistance Total resistance Speed in general Speed of ship Speed of model Mass density of water Acceleration due to gravity Wave length Speed-length ratio R Resistance coefficient in general = ———— Yep SV? Frictional resistance coefficient (ATTC) Frictional resistance coefficient (ITTC) Residuary resistance coefficient Total resistance coefficient Ship correlation allowance coefficient Froude resistance coefficient for model Froude resistance coefficient for ship RV : : ; Effective or tow rope horsepower = maa with F in pounds and V in knots V 5 : : Froude speed coefficient = 0.5834 Al/6 with V in knots and A in tons Froude resistance coefficient = ————— x 427.1 with V in knots and A in tons. A2/3y3 Propulsion Symbols Diameter of propeller Pitch of propeller Pitch ratio Revolutions per minute Blade area ratio Blade thickness fraction Wake fraction (Taylor) Thrust deduction fraction Hull efficiency Propeller efficiency (open) Relative rotative efficiency Delivered horsepower absorbed by propeller Shaft horsepower measured in shafting Longitudinal velocity of water in wake Vertical velocity of water in wake Horizontal velocity of water in wake vi Longitudinal wake fraction Vertical wake fraction Horizontal wake fraction Transverse wake fraction compounded of w,, and w, vii CHAPTER | INTRODUCTION One of the problems which faces the naval architect at an early stage in the design of any new ship is the determination of the necessary horsepower to fulfill the speed require- ments and to assess the effect on this power of making different choices for the size, propor- tions, and fullness of the ship. To assist him in this problem, he will have recourse to a number of'different sources of data. He will have his own experience to draw upon, covering previous designs and ships built to them, and, possibly, results of model tests carried out in this connection. Then there are available many results of specific model tests published in various technical papers and, in particular, the design data sheets published by the Society of Naval Architects and Marine Engineers (SNAMBE).! Such data, although extremely useful, suffer from the fact that they refer to a large number of models which are unrelated one to the other and in which the variations in design parameters are quite random. Much more valuable are the results of experiments on families of models in which the different design parameters are varied systematically and, so far as is possible in ship design, one at a time. Many such methodical series of model tests have been carried out in the past, perhaps the best known being that due to Admiral D.W. Taylor.” Other such series covering different types of ships have been run by many people 3-43 including one by the British Ship Research Association more or less concurrently with the present Series 60 at the David Taylor Model Basin.*% The results of such tests can be expressed in design charts from which the naval architect, by interpolation where necessary, can select a number of forms suitable to a partic- ular problem, determine their relative resistance and propulsive qualities, and so make an informed choice of the best combination of parameters to give minimum power within the other limitations of the design conditions. Many methodical series of the past are not suitable for modern single-screw merchant ship design for a variety of reasons, and although taken together they cover a large range of values of the usual design parameters, they lack any overall coordinating factor. Also, some doubt exists about the results in a number of the older series because of the absence of any turbulence stimulation on the models. The need for more systematic information on the design of lines for modern, single- screw ships has been recognized at the Taylor Model Basin for many years. The subject was revived after the war at the meetings of the American Towing Tank Conference (ATTC) and the Hydromechanics Subcommittee of SNAME held in Ann Arbor in 1948. The Society agreed to sponsor the preparation of parent lines suitable-for a series of single-screw AP eferences are listed on page Rel. merchant. ship forms, and appointed a Panel to select the pattern and range of parameters to be used in the work.* The methods of deriving the parent lines and presenting the data were developed at the Model Basin, and the experiments were carried out there as part of the Bureau of Ships Fundamental Hydromechanics Research Program during the years 1948-1960. At the time of the inception of this project, there was beginning a great upsurge in the provision of hydromechanic research facilities all over the world, with the certainty that in consequence many programs of research into hull form, in smooth water and in waves, would be initiated. One of the objects of Series 60 was to provide a parent family which, within the type of ship covered, could serve as a starting point for any such work, so that new series might be related one to the other by having a common datum line. Considerable success has been achieved in this way, and parents of the series are being used for research into sea- going qualities of ships, both under ATTC and International Towing ‘Tank Conference (ITTC) sponsorship. Other examples include methodical launching calculations, the effect of bulbous bows on power, the estimation of propeller forces acting on a ship’s hull and shafting, and the representation of ships’ lines by mathematical methods. The results of the model experiments have been published before the SNAME from time to time to make them available to the profession as soon as possible; this led inevitably to some duplication and the occurrence of a number of minor errors. In the discussions on these papers, a number of requests have been made that the results be brought together in a single publication. In carrying out this suggestion, much of the preliminary work has been omitted since it did not have any bearing on the ultimate results. Readers who are interested in these historical and development phases of the Series can find a full account in the individ- ual papers. For convenience, these are listed separately on page R-5 immediately following the list of specific references. * The membership of the Panel is given in the Foreword. I-2 CHAPTER II SELECTION OF THE RANGE OF PROPORTIONS FOR THE SERIES At the time of the inception of the program, a survey was made of the current practice in shipbuilding to ensure, as far as possible, that the series would cover the normal range of proportions of modern ships. In the course of this, some 40 individuals and organi- zations were consulted, and after analyzing these comments, the SNAME Panel agreed upon a series of parent forms and variations which would cover the general field of design for single- screw merchant ships. This was in 1949, and already it is obvious that the Series is no longer adequate for modern single-screw ships, which, on the one hand are being made finer and driven to higher and higher speeds in order to obtain the increased efficiency possible with single-screw as compared with twin-screw propulsion, and on the other hand are being made larger and fuller to achieve the resultant economy in bulk carriers of ore, oil and similar cargoes. At the time of the inception of the program, it appeared that lower and upper limits in block coefficient of 0.60 and 0.80 would be satisfactory, but) the intervening years have shown that 0.55 and 0.85 would have been better forecasts. The future extension of the series to such forms would be a very worthwhile project. The basic parameter chosen for defining the series was block coefficient (Cp). This was used in preference to the prismatic coefficient (Cp) because in the preliminary design stages for merchant ships it is a direct measure of the displacement carried on given dimensions, usually a basic consideration. This approach in no way prevents the use of prismatic coefficient in the subsequent presentation of the results if so desired. The decision to use Cp in preference to Cp has been a point of comment by numer- ous contributors to the discussions on the Series 60 papers. In general, the ship designer and operator seem to favor block coefficient. Sir Amos Ayre said that ‘‘for the type of ship dealt with, I am pleased to observe that the block coefficient has been chosen as the basic parameter in preference to the prismatic coefficient” (discussion on Reference 44). Mr. Ericson, commenting on the same paper, stated that he ‘‘should like . - . to put in a few words which will present the viewpoint of the ship operator himself. First, I should like to endorse the use of the block coefficient as a basic parameter. It is fairly useful in making a study, particularly an economic study, where displacement is considered, which is reflected immediately in the carrying capacity of the vessel.” On the other hand, naval architects and hydrodynamicists have emphasized the merits of the prismatic coefficient as being a more meaningful parameter for interpreting resistance results, although even here some doubts have been expressed by Dr. Weinblum: ‘‘Other calculations show the now well-known extreme sensibility of the wave resistance to varia- tions of pure form for a given prismatic coefficient. The wave-resistance values corres pond- ing to two such forms can easily reach a ratio of 3:1, so that sometimes one even is inclined II-1 TABLE 1 ; B A Variation of —= ,.— 5 B br) H al 3 y 1/3 100 CR for the Parent Models , and LCB Position with LCB as oe of Lpp from X) BP to doubt the value of the prismatic coefficient as a standard form parameter’? (discussion on Reference 45). In the present series, the midship area eoctficient does not vary very much, and so the resistance qualities can be related either to Cp or Cp without introducing any conflicting Situations. Since the results of such a methodical series will essentially be used by the designer, Cp is probably the better choice for presentation of the various curves and contours. Five block coefficients were chosen, each associated in the first instance with given longitudinal center of buoyancy (LCB) positions, midship area coefficients, length-beam | — and beam-draft a ratios (Table 1 and Figure 1).’ B and H are the moulded beam and draft in feet, res asbuvely. and L is the length between perpendiculars (LBP) measured from the centerline of the rudder stock to the forward side of stem at the designed load waterline, as adopted by the SNAME in its Model Resistance Data sheets. It corresponds with that used by the classification societies such as the American Bureau of Shipping. L : The variation in 5 with Cp, was chosen by the panel to take into account the fact that the finer ships were, in general, relatively longer and narrower than the fuller ones. LE OB ae To cover the general spread of Be a » and for existing designs, and the 3.5 28 2) © 7.5 — 8 : : ane L B Figure 2 — Typical Variation of a ands ioe STO-PARENT Moves A Ratios for a Given Value of Cp apeee Me 0.60 0.65 0.70 0.75 0.80 0.85 BLOCK COEFFICIENT Cg Figure 1 — Variation of Proportions etc., possible variation in LCB position, a grid was adopted as shown by the dotted lines in Figure 1.* For any one block coefficient and LCB position, a total of nine models was run in ; B ; : 5 : which es and 7 ratios were varied. The pattern for a typical case (Cp = 0.60) 1s shown in Figure 2. eB A *The values of —, —, and ———— are not independent but are related by the expression = ———— x 28570 with dimensions in feet and displacement ENG ( L } B in tons, salt water. ea) B ( H ) Il-3 CHAPTER III CHOICE OF HULL FORM FOR THE PARENT MODELS In the past, the models of most methodical series have been derived from a single parent form Ly proportioned geometrical changes. When carried to very different proportions and to fullness coefficients suitable to very different values of speed-length ratio Wie ' such changes must inevitably lead to unrealistic forms regardless of how good the parent lines might be for the original design conditions. In planning Series 60, therefore, another approach was tried. A review was made of the resistance results of the single-screw merchant ship models available at the Model Basin, and some 20 were selected which appeared to give good performance as judged by a comparison with Taylor’s Standard Series. These models covered a range of fullness, and plots were made of sectional area coefficients and waterline half-breadth coefficients to a base of fore- and aft-body prismatic coefficients. Cross curves were then drawn which, while being fair lines, followed the actual points as closely as possible. In this way it was hoped to obtain, by interpolation at the correct values for the parent forms, a series of models which would retain most of the good resistance qualities of the models on which the coefficient curves were based, while also incorporating the changing characteristics necessary to ensure good performance of each model at its appropriate speed- length ratio. At the same time, these parent forms would be related to one another in accord- ance with a definite graphical pattern. Once the series was complete and the resultant resistance curves available, a form could be quickly obtained by interpolation of the cross curves to fulfill any desired combination of Cp, L, B, H, A, and LCB position. Moreover, this design could be immediately associated with a corresponding resistance and effective horsepower. From these contours, five parent forms were drawn having block coefficients of 0.60, L B 0.65, 0.70, 0.75 and 0.80, with B ratios, mi ratios, and LCB positions as shown for the parent models in Figure 1. This group of models was designated Series 57 in succession to earlier TMB Series, and the details of their derivation and the results of the model resistance tests were given in a paper before the SNAME in 195i The resistance results of Series 57 were compared with those for a number of recent successful modern designs of single-screw ships and found to be disappointing. In view of the apparently good qualities of the models on which the contours were based, this was at first sight surprising. Further investigation suggested that although the departures from the actual design lines made when fairing the contours were small, they may have been critical in certain cases, and also that possibly some of the results of the resistance tests on the chosen models were suffering from the effects of laminar flow. Apparently in ship IlI-1 models, as in human beings, the selection of good parents does not necessarily lead to better — or even as good — offspring! Although the original conception of the project was to derive a series of related parent forms which would serve as a point of departure for future model programs, and which there- fore should have reasonably good but not necessarily optimum resistance qualities (the quest for which might indeed last forever), it was evident from the very lengthy and valuable dis- cussion on the paper that the members of the profession desired something better in quality than Series 57 as a basis for any such systematic program. The panel thereupon reviewed the. original series and agreed that the real merits of the Series 57 models could best be established by comparison with the performance of actual successful ship designs. In this way, differences in proportions and in LCB position could be eliminated and the effects of differences in shape of area curves, waterlines and section shapes evaluated. Five designs were chosen as being typical of good, modern, single-screw ships, which, of necessity, had to meet many requirements in addition to those of good resistance qualities, Three of these were Maritime Administration vessels of the MARINER, SCHUYLER OTIS BLAND, and C.2 classes. The other two were Bethlehem Steel Company designs. One was the tanker PENNSYLVANIA. The other did not represent any built ship but was a design for a 0.70 block coefficient ship given by Mr. H. de Luce in his contribution to the discussion on the Series 57 paper. Models of the first four were available at the Model Basin, and a model of the fifth design was made and tested. For comparison with each of these, an equivalent Series 57 model was made to lines drawn out from the contours. Each pair of models represented a ship of given length, beam, ‘draft, displacement, and position of LCB so that the differences in each case were restricted to the shapes of area, waterline, and section curves. The results of these model tests are given in full in Reference 45. Briefly, at speeds appropriate to the different fullness coefficients, the Series 57 models were in general some- what worse than those of the actual ships by amounts up to a maximum of 6 percent. . The area and load waterline (LWL) curves of any pair of these models were not very different in shape or character, and the chief differences lay in the shape of the cross sections. An analysis of the bow and stern lines indicated that the actual ships had, in every case, more U-shaped sections than the Series 57 models, and the Panel decided that sil contours should be drawn using the sectional area and waterline curves for these actual designs as guides, thus giving a more U-shaped character to the transverse sections while paying due attention to stability considerations. This change was also expected to lead to improved propulsive efficiencies. These new contours formed the basis for Series 60. IIl]-2 CHAPTER IV : CHARACTERISTICS OF SERIES 60 LINES The principal! particulars of the Series 60 parent models are set out in Table 2. Attention must be drawn to a number of details which are important in using the contour charts and resistance results. a. Midship section area coefficient (C y) The midship section has no deadrise, in accordance with current practice, and a linear relation between block coefficient and midship area coefficient was adopted. This relation and the corresponding values of the bilge radius are shown in Figure 3. b. Position of LCB Reference to the published data on the selection of a suitable position of the LCB for different fineness coefficients failed to show any unanimity as to the most desirable location, TABLE 2 Particulars of Parent Forms, Series 60 nor did the information for the selected basis models give any clear guidance. All the data showed a progressive movement aft with reducing block or prismatic coefficient, resulting in finer entrances for the models running at the higher speed-length ratios, as one would expect. A linear variation of position of LCB with fullness was therefore adopted, as shown in Figure 1. Although arbitrary, this line was in general a mean of the available data. Since the effect of LCB position was the next point to be investigated in the program, this line was considered to be an acceptable point of departure. c. Load waterline half-angle of entrance (% ap) This angle varies from 7.0 to 43 deg, as shown in Table 2 and Figure 4. d. Sectional area and waterline coefficient contours The length of parallel body and its fore and aft position for the parent models with the selected position of LCB are shown in Figure 4. The corresponding lengths of entrance and run (Ly; and Lp) were determined, each divided into 10 equal intervals, and contours of cross-sectional area coefficients were plotted to a base of prismatic coefficients of entrance and run respectively (Cpr and Cpr). These contours are shown in Figures 5a and 5b. The body plans were treated in the same way; contours of waterline half-breadth coefficients to a base of prismatic coefficients of entrance and run are given in Figures 6a to 6p. The positions of the centroid of volume of the entrance and run are shown in Figures 7 and 8 for different values of the respective prismatic coefficients. (Text continued on page IV—23) 0.60 0.65 70 075 0.80 Ca Figure 3 — Variation of Cy, Cp and Bilge Radius with Cp IV-2 ] > Of , DEGREES Figure 4 — Variation of Angle of Entrance, Position, and Amount of Parallel Body for Series 60 Parents IV-3 Vadav WAWIXVW AO NOILLOVAA SV VAAV NOILOAS ss°0 co) 0) 0c°0 oe°o Ov'o os‘0 09°0 0L°0 08°0 06°0 aouenuq ‘Sino}UuOD Bely [BeuOT{IaSg — Bg oINnBTYy OILVWSIAd AONVALNA 09°0 s9°0 0L°0 SZ°0 09 Selleg ‘SqUSTOTJJOOD volY [BVUOI}DEG-SSOID JO SanojuO,) — G oINSI 08°0 | IV-4 Vaav WOWIXVW JO NOILOVAA SV VAAV NOILOAS 06°0 ung ‘Sino}u0D early [euoT}IaSg — qg ein3Ty OILLVWSIad NN& IV-5 LNAONVL JV WVdd WOWIXVWN AO NOILOVAA SV NV 020 00 0v'0 0s*0 09°0 04°0 08°0 00°T aoueijuq ‘SeAIND SSOID yuesueyl — eg ainstiy OILVWSIYd AONVALNGA 09 Selleg ‘SUSTOTJJOON YIPVoIg-J[VH OUT[I97v A JO SanoqUoYy — g amnst IV-6 LINAONVL LV NVad WOWIXVYW AO NOILLOVaAA SV NVA IV-7 0.70 0.65 RUN PRISMATIC Figure 6b — Tangent Cross Curves Run IM SLO°O LV WVAd WAWIXVW JO NOILOVAA SV NVag or’o 02°0 oc*0 or'o 0s‘0 09°0 04°0 06°0 oo*t? s 0 0 9 0 aoueijuq ‘SeAMD SSOID “TM SLO'0 — 29 ans OILVWNSIAd AONVALNGA $9°0 0L°0 Ss L ‘0 08°0 IV-8 IM SL0°0 LY NVA WOWIXVW AO NOILOVAA SV NVad 06°0 00°T ‘ ung ‘SeAmMD SSOID “J'M SZ0'0 — Pg ainsTy OL OILVWSIdd NN S' 9 0 IV-9 TM S70 LV NVAd WOWIXVW JO NOILOVad Sv Nvad fo} SX) 020 o0e°0 te) aa0) os*0 09°0 0L°0 08°0 aouedjuy ‘S8AIND SSOID “I'M SZ'O — 29 BNBTYy OILVWNSIad AONVALNA s9°0 0L°0 IV-10 0.80 TM S70 LV WV4d WAWIXVW AO NOILOVad SV NVad ° ° ° ° S w = ise) N Lol So ro) co S fo) fo) 0.70 0.65 IV-11 RUN PRISMATIC Figure 6f — 0.25 W.L. Cross Curves, Run WVdd WOWIXVW JO NOILOVAA SV NVae ss°0 (o) Sie) 02°0 ° of S oe) os*0 09°0 0L°0 08°O 00°T 10) 9 0 aoueijuq ‘S8PAMD SsSOID “7M 0S'0 — 39 emMBIY OILVWSIAd HAONVALNA s9°0 0L°0 Ss L 0 08°0 IV-12 WVdd WAWIXVW 4O NOILOVAA SV NVaa 00°T uny ‘ S@AIND SSOID "T'M OS" OILVWSIdd NN 0 — 49 aInsTYy IV-13 WVad WAWIXVW JO NOILOVad SV Wvaa 02°0 oe"0 ov'0 0s ‘0 09°0 0L°0 08°0 06°0 aouenug ‘SeAMD SSOID “T'M SL‘O — 19 eMBIY OILVWSIAd AONVALNY s9°0 0L°0 08°0 IV-14 WVdd WOAWIXVW AO NOILOVAA SV NVaAd ung “S9AMD SSOID “"JT'M SZ'9 — fg amMBIY (o) x) Or'o 0s‘0 09°0 08°0 06°0 ‘ L OILVWSINd NN IV-15 Wvad WOAWIXVW AO NOILOVA4 Sv Wvad ss°0 fo) xe) 02°0 oe'o (oh aie) os*O 09°0 0L°0 06°O 00 OAT SGGee—5. — 0 9 0 aoueduq ‘SeaAinDd SSolD “7'M 00'T — A9 eMaTY OILVWSIdd AONVALNA s9°0 0L°0 Ss L (e) 08°0 IV-16 WVadd WOWIXVYW JO NOILOVaAA SV WV ad fo) 0) 0z'0 oe°0 Oro 0s*0 09°0 0L°0 08°0 06°0 00°T ung ‘ S@®AIND SSOID “JT'M OO'I — 19 eMstIy OILVWSIad NONA IV-17 WVdd WOWIXVW AO NOILOVAd SV NVad 02°0 o€*O 0r'0 0s*O 09°0 08°0 06°0 00°T souejuY ‘SaAND SSOJD “T'M SZ — wo ematy OILVWSIAd AONVALNG s9°0 0L°O L 0 IV-18 Wvad WOWIXVW AO NOILOVas SV NvVaa 08°0 06°0 ‘ ung ‘saAinD SSOID “J'M SZ TI — Ug amary OILVWSIad Nona 0L°0 $9°0 IV-19 WVad WOWIXVW AO NOILLOVAd SV NVAd ss*°0 OT‘o 072°0 0e°O oro 0s*o 09°0 0L°0 08°0 06°0 09" 0 S9AIND SSOID “T'M OST — 09 ound OILVWSIdd AONVALNGA s9°0 020 Z ° 0 8 0 IV-20 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.60 0.65 0.70 RUN PRISMATIC Figure 6p — 1.50 W.L. Cross Curves IV-21 BEAM AS FRACTION OF MAXIMUM BEAM 0.39 NOTE: xX, MEASURED FROM E—10 0.38 0.37 0.34 0.33 ENTRANCE PRISMATIC Figure 7 — Position of Centroid of Volume of Entrance PECEEEEEEEEEEEE EC EEEEEEEEEEEEEEEEEEELEEREELE 0 . 4 0 NOTE: X, MEASURED FROM R-10 0.39 0.38 0.37 Xp/LR 0.36 0.35 0.60 0.65 0.70 0.75 RUN PRISMATIC Figure 8 — Position of Centroid of Volume of Run IV-22 —— AFT FORWARD——= 0.80 1 [ieee POSITION OF LCB ib 25 20 15 10 05 @ os 10 5)o 20st? See SOs s5 . ° 9 POSITION OF LCB Figure 9 — Ratio of for Different BP Figure 10 — Ratio of for Different Values of Cp and Positions of LCB Cpr Values of Cp and Positions of LCB , In order to use the contours to obtain a model having any desired fullness and location of LCB, certain auxiliary curves are necessary. These show: L E 1. the ratio of length of entrance to total length otal (Figure 9) and BrP . . . . . Cp E 2. the ratio of entrance and run prismatic coefficients —— for different block PR coefficients and positions of LCB (Figure 10). In a particular case, the dimensions and displacement of the ship and the desired loca- tion of the LCP will be determined first from the general design conditions. A number of different solutions may be tried to explore the effects on horsepower, weights, costs, and so on. In any one case, the block, midship area, and prismatic coefficients can be calculated and the length of parallel body (Ly) can be found from Figure 3. Figures 9 and 10 will then give the length of entrance (L,,) and the ratio of prismatic coefficients of entrance and run Cpr C . We can then write PR from which Cp, and Cpr can be determined. IV-23 These values can be used to enter the area and waterline coefficient contours, and the area curve and lines plan can then be drawn. The stations to which the ordinates refer must be spaced equally along the lengths of entrance and run. e. Bow and stern contours These are shown in Figure 11. The stern has an aperture suitable for a single screw with cruiser stern. The bow profile is almost vertical below water, the waterline endings being drawn with a radius. The radius corresponds to 2 in. at 1.1 WL and 24 in. at 1.95 WL for a ship having an LBP of 400 ft. (1.00 WL is the designed load waterline.) f. Although it was realized that the incorporation of a bulb in the bow lines would be of benefit in the finer models of the series, this would have introduced a discontinuity in the graphical representation of the forms. The Panel decided that this was not desirable in a methodical series of this type, and that the effect of bulbs of different shapes and sizes could well be the subject of a future research project of the kind for which Series 60 was designed to be a starting point. g- Another future research project which might stem from the Series would be concerned with the behavior of such models in waves, and the effect of changes in fullness and propor- tions upon their motions and speed loss. It was therefore important that the above-water forms should be realistic in terms of sheer and flare, and after consultation with the Maritime Administration, they were drawn out to represent modern average practice. IV-24 sinoquoD ulo}S puv MOG — TT eINDTYY wel aM Ol OL dn Sniave MOG ,,0'2 Sniavy Mos, Z'¢ moe d@7 dIHS ,00b YO4 aN SNOISNSWIC i ,0-,0l = | ONIOVdS NOILVLS ,O2 S31140ud 09 SAlNaS a 6| £61 02 202 : ae 2 1M S20 1M 0¢'0 —— as O09 S3IY3aS 40 S13S0OW 11V OL NOWWOD SYNOLNOD NY3LS GNV MOS 4O4S 3YV SNOISNAWIG SSSHL i ; "0-01 TM OS’ sniGvY MOg,,9'2 1M S6°1 LV SNIOVYE MOE HONI v2 TM S2‘| LV SNIOVY MOS HON! SI : FL0NV IV-25 oe ahs IpGitisse CHAPTER V RESISTANCE TESTS ON SERIES 60 PARENT MODELS The five parent models were made to lines drawn out from the new contours and had the numbers and particulars given in Table 2. The lines are shown in Figures 12 through 16; the area curves are given in Figure 17 and the offsets in Tables 3 through 7.* The models were made of wax, 20 ft LBP, and towed in the deep-water basin at the Taylor Model Basin, which has a cross section 51 ft wide and 22 ft deep. Experiments were made with and without turbulence stimulation. The latter was provided by studs, 1/8 in. in diameter, 1/10 in. high, spaced 1 in. apart along a line parallel to the bow contour, the fore and aft position being controlled by the angle of entrance on the LWL as described by Hughes and Allan. 4° When these series experiments were begun in 1949, the question of turbulence stimu- lation was under intensive study, and its importance, especially in full models, had only recently been widely appreciated. At that time, there was no agreement as to the best method of stimulating turbulent flow, and indeed the subject is not satisfactorily resolved even today. Several methods were being advocated, the principal ones being sand strips, struts, trip wires and studs. The Series 57 models were run with sand strips, but these were abandoned in favour of studs for the Series 60 parents mu LCB series. The studs were replaced by trip wires for the final series of variations in — and — ratios because experience had shown that trip wires gave slightly higher resistances than studs for the full models. Moreover, it was hoped that other experiment tanks would in the future use Series 60 as a point of depar- ture for series work, and most of them used trip wires. In the final presentation based on the L B 3 . BM a ; 5 Me Series, the contours all apply to tests made with trip wires. An account of the experi- ments carried out to evaluate the different types of stimulation is given in Appendix A. The resistance results from the models have been converted to apply to ships of 400 ft LBP and with other dimensions as listed in Table 2. In making this conversion, the ATTC 1947 friction formulation was used together with an addition of + 0.0004 for model-ship correla- tion allowance C,. The ship values haye been expressed as values of Cp and are plotted to V a base of —— in Figure 18. VeyL *The sections shown in all body plans are equally spaced along the length between perpendiculars, Lpp (Text continued on page V-10) (MOTSF [2 POW) i) 09°90 ‘sjueIVg Q9 Selieg Jo Soury — ZT ond yf Apog — 97] esnaty 1ings2e0 ¢20°0 Ysz0'0 g2°0 11N8 V-2 Sueen FE, = BLT LAIN NN NY ie TN 198 TMS 20 1M0S"0 1MSZ0 1MO0'! 1MG2"1 (ASIL3F TEPOWN) "9 02°0 “S}UeIeg 09 Selleg Jo SouIT — FT ool y Apog — op] asnary 1MO00'! TMS2"! 1MOS"1 MOU — QbT asn3ty x ula}S — Bpt ainaty x81 61 x6! | 02 18 1MS2'0 1M0S'°0 1MS2Z0 1M00'! IMG2'1 TMOG"! V-4 (F-AMFTZF 19POW) 79 08°90 “squcIeg C9 Sordos Jo SouI] — 9] ounsTy Apog — 99] einsty MOE — GOT ainsi wa}g — BOT ainsty dj % ! ‘Al 8! “81 4 *“6l dv V-6 V3ayV WNWIXVW JO NOILIVYS SV VI" ° ° ° ° ° ° ° ° Ss n oO ty o o Mm nw ° 2s ° ° ° ° ° ° fo) fo) ° V-7 STATIONS Figure 17 — Area Curves, Series 60 Parents Table 3 — Table of Offsets—Parent Forms—0.60 Block Coefficient (Half-breadths of waterline given as fraction of maximum beam on each waterline) Model = 4210W Forebody prismatic coefficient = 0.581 W.L. 1.00 is the designed load waterline Afterbody prismatic coefficient = 0.646 Total prismatic coefficient = 0.614 Area as fraction of ‘Waterlines max. area Sta. Tan. 0.075 0.25 0.50 0.75 1.00 1.25 1.50 to 1.00 W.L. FP 0.000 0.000 0.000 0.000 0.000 0.000 0.020 0.042 0.000 4% 0.009 0.032 0.042 0.041 0.043 0.051 0.076 0.120 0.042 1 0.013 0.064 0.082 0.087 0.090 0.102 0.133 0.198 0.085 1% 0.019 0.095 0.126 0.141 0.148 0.160 0.195 0.278 0.135 2 0.024 0.127 0.178 0.204 0.213 0.228 0.270 0.360 0.192 3 0.055 0.196 0.294 0.346 0.368 0.391 0.440 0.531 0.323 4 0.134 0.314 0.436 0.502 0.535 0.562 0.607 0.683 0.475 5 0.275 0.466 0.589 0.660 0.691 0.718 0.754 0.804 0.630 6 0.469 0.630 0.733 0.802 0.824 0.841 0.862 0.889 0.771 7 0.666 0.779 0.854 0.906 0.917 0.926 0.936 0.946 0.880 8 0.831 0.898 0.935 0.971 0.977 0.979 0.981 0.982 0.955 9 0.945 0.964 0.979 0.996 1.000 1.000 1.000 1.000 0.990 10 1.000 1/000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 11 0.965 0.982 0.990 1.000 1.000 1.000 1.000 1.000 0.996 12 0.882 0.922 0.958 0.994 1.000 1.000 1.000 1.000 0.977 13 0.767 0.826 0.892 0.962 0.987 0.994 0.997 1.000 0.938 14 0.622 0.701 0.781 0.884 0.943 0.975 0.990 0.999 0.863 15 0.463 0.560 0.639 0.754 0.857 0.937 0.977 0.994 0.750 16 0.309 0.413 0.483 6.592 0.728 0.857 0.933 0.975 0.609 17 0.168 0.267 0.330 0.413 0.541 0.725 0.844 0.924 0.445 18 0.065 0.152 0.193 0.236 0.321 0.536 0.709 0.834 0.268 18% 0.032 0.102 0.130 0.156 0.216 0.425 0.626 0.769 0.187 19 0.014 0.058 0.076 0.085 0.116 0.308 0.530 0.686 0.109 19% 0.010 0.020 0.020 0.022 0.033 0.193 0.418 0.579 0.040 AP 0.000 0.000 0.000 0.000 0.000 0.082 0.270 0.420 0.004 Max. half beam 0.710 0.866 0.985 1.000 1.000 1.000 1.000 1.000 Table 4 — Table of Offsets—Parent Forms—0.65 Block Coefficient (Half-breadths of waterlines given as fraction of maximum beam on each waterline) Forebody prismatic coefficient = 0.651 Model = 4211W Afterbody prismatic coefficient = 0.672 W.L. 1.00 is the designed load waterline Total prismatic coefficient = 0.661 Area as fraction of as SSS Waterlines. max. area Sta. Tan. 0.075 0.25 0.50 0.75 1.00 1.25 1.50 to 1.00 W.L. FP 0.000 0.000 0.000 0.000 9.000 0.000 0.019 0.045 0.000 “4 0.008 0.037 0.056 0.058 0.060 0.066 0.090 0.138 0.055 0.016 0.081 0.110 0.122 0.126 0.135 0.166 0.236 0.115 1% 0.024 0.125 0.174 0.194 0.204 0.216 0.251 0.336 0.184 2 0.041 0.177 0.244 0.277 0.291 0.308 0.350 0.434 0.261 3 0.109 0.298 0.401 0.455 0.480 0.508 0.552 0.625 0.432 4 0.239 0.452 0.570 0.636 0.667 0.694 0.734 0.788 0.609 5 9.408 0.619 0.729 0.794 0.821 0.842 0.867 0.903 0.765 6 0.604 0.767 0.853 0.905 0.920 0.930 0.946 0.964 0.879 Ub 0.788 0.886 0.939 0.966 0.972 0.978 0.984 0.991 0.951 8 0.928 0.962 0.982 0.996 0.995 0.997 0.998 1.000 0.987 9 0.999 0.996 0.999 1.000 1.000 1.000 1.000 1.000 0.999 10 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 11 0.980 0.993 0.996 1.000 1.000 1.000 1.000 1.000 0.998 12 0.922 0.954 0.976 0.997 1.000 1.000 1.000 1.000 0.987 13 0.808 0.873 0.928 0.976 0.992 0.998 1.000 1.000 0.958 14 0.659 0.760 0.837 0.920 0.963 0.984 0.994 1.000 0.898 15 0.492 0.620 0.705 0.813 0.894 0.949 0.980 0.995 0.797 16 0.322 0.460 0.544 0.658 0.778 0.875 0.941 0.976 0.662 ily 0.170 0.304 0.377 0.472 0.601 0.755 0.864 0.930 0.492 18 0.066 0.170 0.217 0.270 0.370 0.572 0.736 0.845 0.303 1814 0.034 0.113 0.145 0.178 0.250 0.458 0.651 0.779 0.209 19 0.016 0.063 0.080 0.094 0.135 0.331 0.547 0.693 0.121 1914 0.011 0.020 0.020 0.022 0.037 0.205 0.427 0.584 0.042 AP 0.000 0.000 0.000 0.000 0.000 0.084 0.272 0.426 0.005 Max. half beam? 0.739 0.904 0.992 1.000 1.000 1.000 1.000 1.000 Table 5 — Table of Offsets—Parent Forms—0.70 Block Coefficient (Haif-breadths of waterlines given as fraction of maximum beam on each waterline) Forebody prismatic coefficient = 0.721 Model = 4212W Afterbody prismatic coefficient = 0.698 W.L. 1.00 is the designed load waterline Total prismatic coefficient = 0.710 Area as fraction of ‘Waterlines max. area Sta. Tan. 0.075 0.25 0.50 0.75 1.00 1.25 1.50 to1.00 W.L. FP 0.000 0.000 0.000 0.000 0.000 0.000 0.020 0.051 0.000 % 0.009 0.049 0.072 0.081 0.086 0.094 0.119 0.176 0.076 1 0.026 0.110 0.158 0.177 0.184 0.194 0.229 0.299 0.165 1% 0.054 0.183 0.252 0.281 0.294 0.310 0.350 0.421 0.266 2 0.100 0.266 0.350 0.389 0.407 0.430 0.472 0.536 0.370 3 0.239 0.450 0.550 0.599 0.627 0.655 0.689 0.734 0.579 4 0.437 0.625 0.724 0.778 0.802 0.827 0.851 0.877 0.755 5 0.646 0.783 0.856 0.904 0.920 0.935 0.948 0.961 0.882 6 0.830 0.896 0.942 0.971 0.980 0.985 0.990 0.992 0.958 7 0.939 0.970 0.984 0.994 0.998 1.000 1.000 1.000 0.990 8 0.998 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 9 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 10 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 11 1.000 0.997 0.999 1.000 1.000 1.000 1.000 1.000 0.999 12 0.961 0.978 0.989 1.000 1.000 1.000 1.000 1.000 0.994 13 0.855 0.917 0.958 0.993 1.000 1.000 1.000 1.000 0.977 14 0.705 0.815 0.887 0.957 0.980 0.991 0.998 1.000 0.930 15 0.532 0.675 0.768 0.868 0.927 0.961 0.985 0.998 0.844 16 0.344 0.510 0.605 0.726 0.825 0.897 0.950 0.982 0.713 17 0.186 0.338 0.427 0.533 0.658 0.788 0.881 0.939 0.543 18 0.077 0.192 0.245 0.314 0.425 0.614 0.765 0.854 0.343 18% 0.042 0.126 0.165 0.207 0.292 0.499 0.680 0.789 0.239 19 0.023 0.070 0.089 0.107 0.164 0.368 0.572 0.704 0.140 194 0.014 0.022 0.022 0.024 0.043 0.228 0.444 0.589 0.047 AP 0.000 0.000 0.000 0.000 0.000 0.089 0.286 0.438 0.005 Max. half beam? 0.771 0.926 0.998 1.000 1.000 1.000 1.000 1.000 Table 6 — Table of Offsets—Parent Forms—0.75 Block Coefficient (Half-breadths of waterlines given as fraction of maximum beam on each waterline) ’ Forebody prismatic coefficient = 0.792 Model = 4213W Afterbody prismatic coefficient = 0.724 W.L. 1.00 is the designed load waterline Total prismatic coefficient = 0.758 Area as fraction of Waterlines max. area Sta. Tan. 0.075 0.25 0.50 0.75 1% 1.25 1.50 to1.00 W.L. FP 0.000 0.000 0.000 0.000 0.000 0.000 0.025 0.062 0.000 % 0.021 0.075 0.113 0.128 0.138 0.149 0.176 0.235 0.120 1 0.067 0.180 0.251 0.276 0.290 0.304 0.338 0.403 0.261 1% 0.138 0.290 0.380 0.423 0.441 0.460 0.495 0.557 0.401 2 0.235 0.406 0.504 0.560 0.585 0.608 0.639 0.690 0.535 3 0.466 0.625 0.718 0.777 0.806 0.824 0.845 0.867 0.754 4 0.700 0.800 0.870 0.911 0.930 0.943 0.954, 0.962 0.845 5 0.883 0.920 0.959 0.978 0.985 0.990 0.994 0.998 0.969 6 0.979 0.983 0.994 0.999 0.999 1.000 1.000 1.000 0.995 ia 1.000 1:000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 8 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 9 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 10 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 12 0.985 0.992 0.999 1.000 1.000 1.000 1.000 1.000 0.998 13 0.914 0.953 0.979 0.997 1.000 1.000 1.000 1.000 0.987 14 0.784 0.860 0.925 0.976 0.990 0.996 1.000 1.000 0.953 15 0.612 0.728 9.820 0.908 0.953 0.975 0.990 1.000 0.880 16 0.420 0.565 0.667 0.781 0.863 0.921 0.958 0.987 0.760 17 0.242 0.388 0.483 0.592 0.712 0.817 0.899 0.951 0.594 18 0.105 0.225 0.288 0.365 0.488 0.660 0.794 0.875 0.391 184% 0.058 0.151 0.197 0.249 0.354 0.554 0.715 0.812 0.282 19 0.0238 0.084 0.109 0.135 0.211 0.427 0.614 0.726 0.172 19% 0.012 0.021 0.025 0.028 0.061 0.278 0.486 0.610 0.060 iP 0.000 0.000 0.000 0.000 0.000 0.115 0.320 0.451 0.006 Max. half beam? 0.807 0.947 1.000 1.000 1.000 ¥.000 1.000 1.000 Table 7 — Table of Offsets—Parent Forms—0.80 Block Coefficient (Half-breadths of waterlines given as fraction of maximum beam on each waterline) Forebody prismatic coefficient = 0.861 Model = 4214W-B4 Afterbody prismatic coefficient = 0.750 W.L. 1.00 is the designed load waterline Total prismatic coefficient = 0.805 Area as fraction of Waterlines max. area Sta. Tan. 0.075 0.25 0.50 0.75 1.00 1.25 1.50 to1.00 W.L. FP 0.000 0.000 0.000 0.000 0.000 0.000 0.044 0.098 0.000 % 0.053 0.162 0.235 0.258 0.267 0.286 0.318 0.378 0.243 0.160 0.324 0.435 0.486 0.505 0.522 0.554 0.613 0.458 1% 0.286 0.467 0.581 0.650 0.681 0.700 0.728 0.779 0.620 2 0.423 0.591 0.702 0.774 0.808 0.830 0.852 0.890 0.746 3 0.696 0.793 0.867 0.921 0.948 0.964 0.975 0.984 0.901 4 0.903 0.929 0.962 0.983 0.994 0.999 1.000 1.000 0.975 5 0.990 0.991 0.995 0.998 1.000 1.000 1.000 1.000 0.997 6 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 7 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 8 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 9 1.009 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 10 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 ll 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 12 0.996 0.997 1.000 1.000 1.000 1.000 1.000 1.000 0.999 13 0.958 0.976 0.996 1.000 1.000 1.000 1.000 1.000 0.995 14 0.858 0.906 0.958 0.991 1.000 1.000 1.000 1.000 0.974 15 0.686 0.780 0.872 0.941 0.97: 0.988 0.996 1.000 0.915 16 0.486 0.625 0.726 0.831 0.900 0.941 0.969 0.991 0.806 17 0.302 0.442 0.542 0.656 0.765 0.851 0.915 0.964 0.649 18 0.146 0.266 0.337 0.427 0.560 0.712 0.832 0.896 0.449 18% 0.092 0.185 0.232 0.298 0.425 0.617 0.764 0.840 0.336 19 0.045 0.105 0.130 0.166 0.263 0.503 0.670 0.760 0.212 194 0.013 0.026 0.032 0.035 0.071 0.353 0.546 0.644 0.079 AP 0.000 0.000 0.000 0.000 0.000 0.160 0.370 0.476 0.100 Max. half beam 0.850 0.970 1.000 1.000 1.000 1.000 1.000 1.000 “R The symbols are defined as follows: Cr= where Ff is the ship resistance in pounds, ? 5; lb ft is the mass density of water in end ; S is the wetted surface in square feet, v is the speed of ship in feet per second, V is the speed of ship in knots, and Ly, is the length of ship on designed load waterline in feet. The results are also shown in Figure 19 as curves of ©) to a base of (k) . These two “‘constants,’’ introduced by Froude, are nondimensional, involve only speed and displace- ment (the two factors which usually control the preliminary design of a merchant ship), and are very useful in comparing forms at this stage. They have been used also in the SNAME Model Resistance Data sheets. In English units they are defined as (&) = 0.5834 - A1/6 V-10 TAA A o 49 Jo soning — BT omnsty 0O'l S6°O 06'0 s8:0 O80 SZ‘o os'0 = Sb'0 Si DSonE cna Bae A | b t tH ogz sane === = . oe 2 Hee ; : = heme aa t + art E F BRE oo'e 5 : oe HEHE & 19°O = F9 or E| 009'0 =99 : : oz" erbacee 199"0=49 Eat eeaee ebsersezsess os9'0=99 errors oe peace Ove janeuen eens : -| ATSAILI3dS3Y SG33dS IWIdt Joo ; GNv 3QIAN3S 3LONSG SMOUYY t= t o nl [-T.. T r TT oo : - Se : olz0=%9 ars BE PEP : 0020-994 4 ae if mA ‘ os ee) a E 8sz'0=%9 oH -osz'02%9 HE 00'r + oa 908'0=99 apaesaany | Pt 008'0 =89 satees eseal Oz'b - ah : Hf n —] Y } Ov'o 4 ; ; t f pesca e aan: 5 a ot HE a cH Beeceee 09" ot ; ee I cei +H : Seane PLETE EY 4 EER | E Eeeaan ett +H \ 4 r ii 5 o ne V-11 pe) 8°0 6°0 s'l g°2 S}UeI8 J (9 SOLIES 10] @) 07 (2) JO SeAIND — 6T candy o°2 19°90 2995 009'0=99 199°0=99 0s9'0 29 012°0299 00L'0:%5 ) iz 0'2 6'I 8"! a 911 "| o Culaenec | ia 0" ma we borere ae t | AV3A1L93dS3Y $033dS IWieL ONY 39IAW3S 3L0N30 SMOMUY T it ! esz'0 = 99 : osz'0:% 908045 H F 008'0 =9 cs | | V-12 and © ehp x 427.1 eye rvs where V is the speed of ship in knots A is the displacement of ship in tons salt water, (2240 lb), and ehp is the towrope horsepower for the ship. The values of ehp used in calculating © have been deduced from the model experi- ments by the use of the ATTC 1947 friction formulation and include the ship correlation allowance of +0.0004. Therefore both the Cr and ©) values are based on the same data and are directly comparable in this respect. 5 , and are related linearly for any one model. A corresponding Veg, VEgp © set of values is given below, from which any other conversion can be made: TABLE 8 : V Relation between C,, ——, and «) VL Model Number 4210W 4211W 4212W 4213W 4214WB-4 A vast accumulation of model resistance data based on the Froude skin-friction coefficients is available in the transactions of societies and reports of model basins. Since 1948 this method of extrapolation from model to ship and that based on the ATTC 1947 (Schoenherr) line have both been recognized by the ITTC as acceptable for use in all pub- lished data. A quick graphical method of mutually converting the © values based on these two formulations was published by Gertler in 1948.47" The ATTC values used therein include the allowance of +0.0004 for ship correlation allowance, so that the application of this chart to the ATTC ©) values given in this present report will yield directly the equivalent C) values based on the Froude coefficients. *The chart in this report is reproduced as Figure D4 in Appendix D. V-13 In 1957 at the Madrid Conference, the ITTC agreed upon a new ‘‘model-ship correlation line”? for use in all published work, which would give ship results differing somewhat from those based either on Froude or the ATTC line. However, pending agreement on the appropri- ate correlation allowances to use with the new line, it has not come into common usage as yet. When such agreement is reached, a chart similar to that in Reference 47 can easily be constructed. In comparing a number of closely allied forms, all suitable to fulfill certain design conditions, this ©) - () presentation has the advantage that for a given displacement and speed, @) is the same for all models. An ordinate erected at this value of ) will indicate the relative merits of the forms since © also involves only the speed and displacement. The other differences in the various hulls can then be considered to determine which features are responsible for the differences in resistance and power. Before proceeding with the methodical variations in LCB position and hull proportions, the results of the actual ship models and the Series 60 equivalents were compared. For this purpose, the same five designs as before were used as the control models, and equivalent Series 60 models having the same dimensions, displacement, and LCB position were made and tested. The exception was for the MARINER design where the Series 60, 0.60 Cp parent was used in the comparison. Such comparisons must be made at speeds appropriate to the individual designs, and for this purpose, service and trial speeds have been chosen based on two suggested relations between fullness and speed-length ratio. The first of these is an old formula first given by F.H. Alexander, but using coeffi- cients suggested by Sir Amos Ayre as being more appropriate to modern ships: 4 =—— =2(1.08 - C,) for trial speed VL ep (1) V —— = 2(1.05 - Cp) for service speed VL gp These formulae give reasonable speeds for the fuller ships, but for the fine ships, such as that of 0.60 Cp, they give speeds which are too high from the standpoint of economic performance. In 1955, Troost proposed a new formula to define the ‘‘sustained sea speed.’’*® Based on a survey of many single-screw models run in the Netherlands Ship Model Basin (NSMB) over some 20 years, the formula generally gives speeds higher than the Alexander service speed for full ships and lower for fine ships, a result in conformity with modern practice. For all forms, the Troost sea speed lies at that point where the ©) curve first begins rising steeply, and for some range above it the resistance is varying approximately as the cube of the speed, or the power is varying as V*. Troost therefore assumed a trial speed V7 some 6 percent above the sea speed V,, so that the power on trial at speed V ; is approximately V-14 25 percent greater than the power on trial at speed V;. This is in keeping with the general design practice that the service speed should be attained under ¢rial conditions at 80 percent of the maximum continuous power. Troost defined the speeds as follows: Vs ——— = 1.85 -1.6 Cp for sustained sea speed JT : [2] and V7 = 1.06 V, for trial speed. For the Series 60 models, these two formulae lead to the following speeds for ships 400 ft in length. TABLE 9 List of Alexander and Troost Speeds ALEXANDER SPEEDS TROOST SPEEDS (Equation (1)) (Equation (2)) T SERVICE RIAL SEA TRIAL V V Ve v A comparison of these speeds with modern American practice was made by Mr. H. de Luce in his discussion on the first series paper.** He examined the @) curves for a * 4 number of ships and plotted the value of the speed-length ratio JL against prismatic coefficient for the point on the © curve where there was a sharp ‘‘upturn’’ (Figure 20). He drew a mean curve through these points, designated as the mean ‘‘upturn’’ on Figure 20. This figure also shows the Alexander and Troost lines, and it is clear that the latter conform much more with the general trend of the points and the de Luce line. An examination of the Cy curves for the Series 60 parent models, as given in Figure 18, shows V that the values of Wha for the ‘‘upturn’’ points for these designs also lie very nearly on the Troost ‘‘sustained sea speed’’ line, and the latter would therefore seem to be a close guide to modern design trends (Figure 20). *Mr. de Luce used Lpp for single-screw ships and Lyy for twin-screw ships. V-15 Vv @ SINGLE SCREW DESIGNS Te (7 Lop, o TWIN SCREW DESIGNS (ze) ow : fy MEAN “UPTURN fr de LUCE ALEXANDER, EQUATION '@° TRIAL SPEED m4 SERVICE SPEED. TRIAL SPEED } TROOST SUSTAINED SEA SPEEDS EQUATION @) O “UPTURN” IN © CURVE FOR SERIES 60 PARENTS FIG. 18 Figure 20 — Comparison of Alexander and Troost Speeds with Modern American Data Mr. de Luce emphasised the need to relate the ‘‘upturn’’ speed to the speed considered in preparing an actual design. In Figure 21, prismatic coefficients are plotted against the speed-length ratio VE corresponding to the speed on trial at designed draft with the machin- ery developing maximum rated continuous shaft horsepower, mostly taken from actual ship data. The ‘‘upturn’’ curve reproduced from Figure 20 is again a reasonable mean through the trial points, indicating that ‘‘many designers over the years have believed it desirable to select dimensions and proportions leading to a flat ©) curve up to the point corresponding to trial speed’’ (de Luce, discussion on Reference 44). Designs I, II, and III in Figure 21 represented three modern (1951) designs of good performance. The ‘‘upturn’’ speeds for these three ships are close to the mean line in Figure 20, but the design speeds are higher than the average line in Figure 21 by about 0.05 : V in terms of JL - Mr. de Luce stated that all three designs were being ‘‘pushed,”’ I because of the economics of transporting petroleum, and II and III for military considerations; he concluded that for the purpose of evaluating hull form parameters and performance, the “‘upturn’’ speed was satisfactory and independent of economic and other considerations. Since 1951, when these comparisons were made, high speed has become more and more a V-16 0.82 +— a lead 078 0.76 | J 0.74 + 0.72 +— eee 2 070 (= Saal é | @ SINGLE SCREW DESIGNS ar iia = ose | © TWIN SCREW vESIGNS(7~ ) — MEAN"UPTURN' CURVE FROMFIG 20 \@ o---- DESIGN SPEED AT MAXIMUM NG eee || hee POWER ' Paealrural ----— TRIAL SPEED TROOST, 064 |—-— SUSTAINED SEA SPEED J EQUATION O "UPTURN"IN© CURVE FOR SERIES 60 PARENTS FIGI8 0.62 | j= 0.60 + | | =I 0.58 | | al — SS 056 bs ee) 04 05 06 0.7 08 09 1.0 i v= Yo Figure 21 — Relation between Design Speed and Upturn Speed characteristic of the modern dry-cargo ship, and this has led to the use of block coefficients lower than the range covered by Series 60. Before leaving the discussion of these data for modern American ships, as given by Mr. de Luce, it is interesting to compare the coverage of Series 60 with actual ship proportions. This has been done in Figures 22, 23, and 24 which show the same points as given by de Luce with the addition of the corresponding ones for the Series 60 parents and the limits covered by the whole series. In general, the coverage for single-screw ships appears to be adequate, with the exception that some models having a — value of 2.0 would have been a valuable addition to the program. In regard to the LCB variation, the ‘‘upturn’’ speeds for Series 60 occur in general with the LCB somewhat further aft than in the case of the actual designs, but the latter are covered by the limiting models. Comparisons between the (C) values for the actual ship models and Series 60 equiva- lents are shown in Figures 25a through 25e. The MARINER-Class ships (Figure 25a) differed somewhat in coefficients and propor- tions from the Series 60 parent of 0.60 block coefficient; also, the latter had no bulb at the forefoot. However, the differences were not considered sufficient to justify making an entirely new Series 60 equivalent model. @ SINGLE SCREW DESIGN| de LUCE, DISCUSSION O TWIN SCREW DESIGN ON REFERENCE 44 ° SERIES 60 PARENTS UO LIMITS OF SERIES 60 VARIATIONS Figure 22 — Comparison of Series 60 with L B Wits DEVE = Anite = B H 350 @ SINGLE- SCREW EBC de Luce, © TWIN SCREW DESIGN J DISCUSSION sf ON REFERENCE 44 JE FOR MEAN “UPTURN” SPEED sicy L=Lgp FOR SINGLE SCREW SHIPS L=L,, FOR TWIN SCREW SHIPS © SERIES 60. PARENTS Cl LIMITS OF SERIES 60 VARIATIONS 250 [ee ° ayo 5 200 150 100 50 OAT “UPTURN” SPEED Figure 23 — eee) of Series 60 with U. S. Data, aa VL” (L100) V-18 de Luce, @ SINGLE SCREW DESIGN Discussion ° TWIN SCREW DESIGN OW REFERENCE 44 xr FOR MEAN "UPTURN" SPEED L=Lgp FOR SINGLE SCREW SHIPS Le Ly FOR TWIN SCREW SHIPS O SERIES 60 PARENTS 4 LIMITS OF SERIES 60 VARIATIONS © SERIES 6O MODELS FOR OPTIMUM LCB POSITIONS 4.0 AFT Lee. ‘pear Re es Lap aoe De FWD Figure 24 — Comparison of Series 60 with U. S. Data, cm and LCB Figure 25 — Comparison between the © Values for Models of Actual Ships , and Series 60 Equivalents toa | ones | come Le | ox | oe a =a le eee ]44i4 | MARINER as built | 0,610 | 0.981 | 0.622 | 0.515 | 0.50 ait |e | ) 4440W | MARINER without bulb | 0.611 | 0.982 | 0.622 [0.516 | 0.50 e7528 Series 60 equivalent (Series 60 parent cor- tected to MARINER dimensions) SERIES 60 EQUIVALENT TO MARINER (ESTIMATED) S60 PA TROOST 2 SERVICE SPEED TRIAL SPEED ALEXANDER | | Figure 25a — Comparison, Series 60 and MARINER Class V-19 SCHUYLER OTIS BLAND 0.651 | 0.980 Dates 0.510 | 0.503 0.497 | 9.5° Series 60 equivalent 0.651 | 0. 982 | 0.663 | | 0.663 | 0. 510 | 0.472 ce 498 | 9.7° ScHuvuer OTIS BLAND SERVICE SPEED TRIAL SPEED } TROOST SERVICE SPEED TRIAL seco } ALEXANDER Figure 25b — Comparison, Series 60 and SCHUYLER OTIS BLAND ae = 3 Description Curve ea ed lca SGaaes C.2. Ships Sa a a Series 60 equivalent i fe au fo} SROs 3 eee ea | 4 ; ce eee 0.7 —— a mace \ ——— a P| SERVICE SPEED TRIAL SPEED } TROOST 0.6 }— Sle 4 4 SERVICE SPEED TRIAL sreeo} ALEXANDER ane es eee [eesaecfe L | | oceans 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 i) Figure 25c — Comparison, Series 60 and C.2 V-20 400 FT 0. TROOST TRIAL SPEED f ALEXANDER ee pee ea pennsvuvamia | ~--~~ |o.765 | 0.994 | 0.770 ivalent_| ———|0.764 [0.991 | Series 60/equivalent 0.764 New casting of 4435W | O---—-o SERIES 60 EQUIVALENT ° wo PENNSYLVANIA MODEL 4435 WA 08 o7 o6 ° a ‘ice es ee Seeretenne ° PENNSYLVANIA— MODEL 4435W |__| TROOST TRIAL SPEED ALEXANDER Figure 25e — Comparison, Series 60 and PENNSYLVANIA V-21 The Series 60 parent gave a lower resistance than the MARINER model over the useful speed range, but above this the ©) curve turned up more rapidly, at least partly because of the absence of the bulb. However, the Series 60 model was finer than the MARINER (Cp being 0.60 instead of 0.61), and to obtain a better comparison the MARINER model was changed by removing the bulb, and the Series 60 parent resistance was corrected for the difference in fullness and proportions by using Taylor Standard Series data. There was then no appreciable difference in performance over the service and designed speed range. There was no essential difference in results in the case of SCHUYLER OTIS BLAND, (Figure 25b), the slightly better ©) value of the SCHUYLER OTIS BLAND at the trial speeds probably being due to the 2 percent bulb. The C.2 ship model (Figure 25c) was somewhat better than the equivalent Series 60 model by some 1 percent and 4.5 percent at the service and trial speeds respectively, prob- ably again partly due to a small bulb on the C.2. The Series 60 equivalent was some 1 to 2 percent better than the 0.70 Cp design, (Figure 25d) in the neighborhood of the service and trial speeds. Several models of the PENNSYLVANIA (Figure 25e) were made at different times, some in wax and some in wood. There was a certain amount of scatter in the results, influenced to some extent by questions of turbulence stimulation. Over the useful speed range, this difference amounted to some 2 to 4 percent, and the highest results for the PENNSYLVANIA model were the same as those for the equivalent Series 60 model. No modern cargo vessel design of about 0.80 block coefficient and of approved merit was available for comparison with Series 60. A number of models with a variety of bow and stern shapes were therefore made and run. The sterns were usually U-type, similar to those of Series 60, and the bows ranged from U- to V-forms. In general, the models with the V-shaped bows showed to some advantage, but they did not fit well into the cross-sectional area and | waterline contours since the other. model lines were predominantly of U-type. The Panel was of the opinion that seagoing merchant ships were unlikely to be built with such fullness coeffi- cients. -The somewhat fuller lake steamers would have much greater — ratios than those covered by the present series, and in fact were considered to be: another problem. The 0.80 Cz model of the series could therefore be considered as really only an end point to which the contours could be anchored. Rowever, subsequent evidence suggests that the form as finally adopted had some intrinsic merits of its own as well as being an ‘‘end point’? to the series. In the discussion on one Series 60 paper (Reference 45), Professor Baier said that since block coefficients of 0.80 to 0.87 were of particular interest to the Great Lakes region, he had carried out a series of tests with models in this range in the tank at the University of Michigan. He reported that ‘‘seven models were designed with rather extreme variations in sections at blocks of 0.857 and 0.872. At each of these block coefficients one form was derived from the contours of Series 60, with some adjustments in the forebody for lake-traffic requirements. It is gratifying to report thst these two models were definitely superior to the V-22 other five designs, both in t.r.h.p.* and propulsive coefficients when self-propelled.”’ In Professor Baier’s opinion, ‘‘the parent form finally adopted by the panel for the 0.80 block was @ suitable and wise decision.”’ As in the case of the lower limit of the series being taken as 0.60 block coefficient, this idea that the 0.80 block model could be treated as an end point seemed a good one at the time, but events have already overtaken the program in this respect also. Just as single- screw ships are now being built with block coefficients well below 0.60, so in the range of supertankers and bulk carriers, designs in the neighborhood of 0.80 to 0.85 block coefficient have become of great importance. There is therefore a good practical case for extending the series at both ends. In the light of the above survey, the members of the Panel came to the conclusion that the new contours of Series 60 formed a suitable basis for use in defining parent models for a systematic investigation of resistance and propulsive qualities, and it was then possible to proceed to the next phases. *tr.h.p = towrope horsepower or ehp CHAPTER VI EFFECT ON RESISTANCE OF VARIATION IN LCB POSITION In planning the Series 60 parents, a decision had to be made as to the longitudinal distribution of displacement for each model. This distribution is conveniently described, other things being equal, by the position of the LCB. This is an important parameter in ship design for more than one reason. So far as resistance is concerned, the optimum position of the LCB depends very much on the speed- length ratio at which the ship is torun. At high values of JL , it is essential to keep the bow fine to delay the onset of wavemaking resistance; at the same time, the stern cannot be made too full or eddymaking resistance will increase. The result is a ship of overall low block coefficient with the LCB aft of midships. For low Tig values, the stern must still be kept reasonably fine to avoid excessive resistance, but the bow can be made much fuller, since at such speed-length ratios the wavemaking resistance is only a small percentage of the total. The result is a ship with a fine run and full entrance, with the LCB forward of amidships. This trend is well illustrated in the Series 60 parents. The prismatic coeffi- cients of the afterbody range only from 0.646 to 0.750 in going from the 0.60 to the 0.80 block coefficient designs, whereas the forebody prismatics go from 0.581 to 0.861. If the efficiency is measured by the resistance per ton of displacement, the fuller ship is the more efficient at low spéed-length ratios, and the advantage passes to finer and finer ships as V Tih is increased. The position of the LCB also affects propulsive efficiency for, in general, as it moves forward for a given overall coefficient, wake and thrust deduction both decrease, but the effect of the former usually predominates. Thus it is not unknown for a forward shift of LCB to reduce both resistance and propulsive efficiency in such a way that the final shaft horse- power* is increased. Insofar as hydrodynamic efficiency is concerned, the location of LCB therefore rests finally on the delivered horsepower* required and not on the resistance, although the latter is an important component of the former. There is also another feature in ship performance which depends on the LCE position, and that is the behaviour in waves, both as regards ship motions and loss of speed. There is little doubt that in the past ships have been built with too full bows, which may have given excellent smooth-water results but have militated greatly against good seagoing qualities. This question is one which should have an early priority in future methodical series testing. ’ *Shaft horsepower is the power measured in the shafting, for example by torsionmeter. Delivered horsepower is the power absorbed by the propeller. VI-1 In. the design of a ship, the LCB position is also dependent to some extent on consid- erations other than low power and good sea behavior. Chief of these is the problem of achieving correct trim under a variety of loading conditions, particularly in tankers and other bulk carriers. The tendency to place machinery aft in dry-cargo ships and passenger ships also gives rise to trim problems and in such cases the size of machinery may restrict the hull shape aft and, by requiring additional volume there, also influence the LCB position. In the discussion on one of the Series 60 papers (Reference 63), Professor Manning set out very clearly the importance of LCB position in designing the single-screw merchant ship, and one cannot do better than quote his remarks. ‘‘Taylor states very clearly that his use of tha prismatic coefficient as a major parameter was based on the fact that it is an excellent measure of the longitudinal distribution of the volume of displacement... In the case of the Taylor Standard Series, the prismatic coefficient was sufficient in itself as a measure of the longitudinal distribution of displacement by reason of the process used in determining the offsets of all the models of this family and the fact that none of the models had parallel middle body. Whenever a ship has parallel middle body, a substantial change in the longitudinal distribution of the displacement may be made without any change in the prismatic coefficient. For example, if the lengths of entrance, parallel middle body and run are held constant, and the prismatic coefficient of entrance is given to the run, and that for the run to the entrance, the prismatic coefficient of the entire hull has not been altered, but the longitudinal distribution of the displacement certainly has. The wave-making resistance and viscous form-drag have therefore also been changed in substantial magnitude. The difference between the longitudinal distribution of the displacement of vessels which have the same value of prismatic coefficient may be related to differences in the longitudinal position of the centre of buoyancy. This paper (Reference 63) is essentially a study of the effect of changes in the longitudinal position of the centre of buoyancy on the resistance and power required for parallel middle body ships at speeds which reflect current practice. . . From this paper, the ship designer can not only estimate with good precision the position of the centre of buoyancy which gives the least resistance or shaft horsepower, but how much he must pay in terms of these if other conditions favor a different location for this point. The latter is just as important as the former.’ For all the above reasons, it was agreed by the Panel that before proceeding to ve last phase of this project—the effect upon resistance and propulsion of variations in = and W ratios—the effect of change in LCB position should be investigated for each of the Series 60 parents in order, if possible, to determine the optimum location. The positions of the LCB chosen for the five parent 2.odels are shown in Figure 1, together with the variation in these positions for the other 17 models making up the complete set. The positions of LCB are shown in Table 10, and the principal particulars of the models are given in Tables 11 through 15. VI-2 Table 11 — Principal Particulars of 0.60 Block Table 10 — Pattern of LCBSeries Models Coefficient Forms Model numbers Model No........... 4215 4210 4216 4217 Cz —Position of LCB as % Lp from ()pp-—— ae fnsseeyns crac 400.0 rae nae 400.0 oan 4 42 4217 fh 9 Serer Pa ee 53.33 .33 4 53.33 oe Bo CLL We Ores ee 21.33 21.33 21.33 21.33 0.65.... 4231 4218 4211 4219 4220 DEtonshinsc eect 7807 7807 7807 7807 246A 1.544 0.50A 0.38F 1.37F. Le/Lop............- 0.5 0.5 0.5 0.5 O870).-.. 4230). 4221 A210) 4202) 4223 Lx/Lpp......-.----- 0 0 0 0 205A 0.554 0.50F 1.54F 2.55F Lr/Lep.......-..... 0.5 0.5 0.5 0.5 ON75 eee 4224 4213 4225 4226 (CASS Sree eens ee 0.60 0.60 0.60 0.60 0.48F 1.50F 2.57F 3.46F (SF doers aC OnE 0.977 0.977 0.977 0.977 0.80.... 4227 4228 4214 4229 CEA ys ereaeier 0.614 0.614 0.614 0.614 076F 1.45F 2.50F 3.51F CH Sen ee 0.558 0.581 0.603 0.626 aie (CE ae fo nae pe Bae pena ree 0.671 0.646 0.624 0.602 Note: Column3 of model numbers applies to Series 60 Parents. CER eee Poi Aen Roe 0.558 0.581 0.603 0.626 PRs ccaiee seers 0.671 0.646 0.624 0.602 PY. SOP aet on eosin 0.857 0.850 0.843 0.839 Gpyatehice cies 0.910 0.910 0.912 0.919 CPVvaassi cme Pes 0.818 0.802 0.785 0.770 Woe actrees ea 0.700 0.706 0.712 0.715 Ow tic oe beer eee 0.598 0.624 0.646 0.666 WA oaierensten ene 0.802 0.788 0.777 0.765 ; Tr st aes ayedond wasn 0.5383 0.543 0.549 0.553 The lines for each model were drawn Wir Glyen oe Guerre 6.2 7.0 7.6 8.3 E f Dewi titecorc- mics nes 406.7 406.7 406.7 406.7 out by using the contours of sectional area LCB % Lapfrom@®.. 2.484 1.54 0.514 0.52F . Ree : TE) Bree Rae gucwetivnere 7.50 7.50 7.50 7.50 and waterline coefficients already described. BY Hive ae eee 2.50 2.50 2.50 2.50 Ub uBio A ERIC ee 6.165 6.165 6.165 6.165 The models are therefore related to one A/G 100) 2st ee 122.0 12250 122.0 122%0 % S/N Fee eee Cietoeiats 6.478 6.481 6.504 6.527 another by the graphical charts, and for a WS) sates wesc: 27270 27280 27380 27470 : : ae : Kr = R/V BH...... 0.229 0.229 0.229 0.229 given set of design conditions a unique hull eG ss 0.831 0.899 0.966 1.040 form is determined. The models were made and the tests carried out in exactly the same manner as described for the parent models. The model results have been converted to apply to ships with 400-ft LBP by using the ATTC line for the friction extrapolation with an addition of +0.0004 for ship correlation allowance, as before. The ship figures are given in Tables 16 through 20 as values of C, to a base of V and in Tables 21 through 25 as values of © to a base of {) , all for a standard V Ly, temperature of 59°F (15°C). To obtain a visual picture of the resistance results, the ©) values can be plotted as cross curves to a base of LCB location, using (kK) as a parameter. When this is done, it is found that for the speeds within the range of economic performance for these models a locus of LCB position to give minimum resistance is usually well defined. At high speeds, beyond the useful range, the minimum lies in general in a region where the LCB is much further aft than was used in any of these experiments. As might be expected, there is in general no unique relation between block coefficient and optimum LCB location—it depends on what speed is chosen as the criterion for comparison. Figures 26 through 30 show cross-curves of ©) to a base of LCB position for (Text continued on page VI-13) VI-3 Table 12 — Principal Particulars of 0.65 Block Coefficient Forms adel NOvisrs eens 4231 4218 4211 4219 4220 nae Ft ee aye ne 400.0 400.0 400.0 400.0 400.0 BMitentaes ous eeyccnen 55.17 55.17 55.17 55.17 55.17 AC See een 22.09 22.09 22.09 22.09 22.09 De AON. seis nce tecl ee 9092 9051 9051 9051 9065 Lee / Eppes eee ere 0.477 0..475 0.472 0.470 0.469 Dx Epp 0.035 0.035 0.035 0.035 0.035 Tep/ Lape os ans css jatar 0.488 0.490 0.493 0.495 0.496 BEM cry rentracidsesimcee ee 0.652 0.650 0.650 0.650 0.650 (OF cin ouoda cme cand oealaaay 0. 982 0.982 0.982 0.982 0. CBee a oe sey S82 eons 0.664 0.661 0.661 0.661 0. Cope tee ma tone neenens 0.612 0.628 0.651 0.670 0. ey ecmere tr mote nee eey 0.715 0.694 0.672 0.652 0. Cen es Scr se ltsenniats G 0.594 0.609 0.630 0.649 0. Cong amen case 0.709 0.688 0.667 0.648 0. Fearn RENO pratt 0.871 0.874 0.871 0.865 0. (of ihe cunvotiens cau aie Hist cee 0.920 0.924 0.927 0.929 0. PY Ahgs Recuserieetslayone 0.833 0.832 0.823 0.808 0. Wane e aioe Maehyeop hones 0.749 0.744 1.746 0.750 0. Corp esciicite dstigee Wine cele 0.654 0.668 1.690 0.708 0. 728- Cw isin se. jsune nt ae 0.843 0.819 0.802 0.792 0.781 Cire Gatien nsage tants 0.594 0.593 0.597 0.601 0.619 Wag) deg... 2. cesiaisccye Ts? 8.3 9.1 11.2 13.8 Lewis ft pews sn. es o 406.7 406.7 406.7 406.7 406.7 LCB % Loe from {%)...... 2.464 1.54A 0.54 0.38F 1.37F L/ Bee hose on ete 7.25 7.25 7.25 7.25 7.25 B/H oii c.cionsiece sce te 2.50 2.50 2.50 2.50 2.50 L/W Wisctate asters losin: ees 5.860 5.869 5.869 5.869 5.866 (A/ CEJ 100) Pee see ee eee 142.0 141.4 141.4 141.4 141.5 S038 septic serge ness 6.320 6.326 6.328 6.328 6.347 WS, saftic. 2 ucts. ct 29380 29380 29390 29390 29480 Rig = UR/ NB Heese ase: 0.205 0.205 0.205 0.205 0.205 PE/Cpp ccc cr te 0.838 0.885 0.945 1.001 1.067 ModeluNomsess see tee 4230 4221 4212 4222 4223 apiitiee th ck emit , 400.0 400.0 400.0 400.0 400.0 BEEN Ser ed Pe 57.14 57.14 57.14 57.14 57.14 AEs ee Betas: 22.86 22.86 22.86 22.86 22.86 Dstonsc sles. 10441 10456 10456 10456 10456 Pe Dep Ancteyocee ch cee 0.434 0.420 0.410 0.400 0.390 ES / Depp hac ae ee 0.119 0.119 0.119 0.119 0.119 ER Bpi ot coe eee eee 0.447 0.461 0.471 0.481 0.491 Boke ire WA co erg meee 0.699 0.700 0.700 0.700 0.700 A, Sep Seater ae 0.986 0.986 0.986 0.986 0.986 CEM Pls eae 0.709 0.710 0.710 0.710 0.710 CER Roe tree eee 0.667. 0.700 0.721 0.744 0.766 Chi ee ee ee 0.752 0.721 0.698 0.675 0.654 Crp eh eee eae 0.616 0.642 0.660 0.680 0.700 Grp seeeg eee 0.722 0.698 0.680 0.662 0.647 Cpyi does eae eines 0.887 0.890 0.891 0.886 0.880 VR Pen ee 0.932 0.940 0.944 0.948 0.950 PUAN creer 0.852 0.846 0.842 0.827 0.811 Tie, BE eee aN centrale Od tee 0.788 0.787 0.785 0.790 0.795 CWE Greene 0.706 0.734 0.753 0.774 0.795 (Oe nel Part ads Aer 0.871 0.841 0.818 0.805 0.795 Cre ee oe 0.650 0.651 0.653 0.658 0.663 Vite i ae ees 9.3 11.6 14.5 17.1 20 Lee rare ete 406.7 406.7 406.7 406.7 406 LCB % Lup from @...... 2.05A 0.55A 0.5F 1.54F ty Dearie deel ieee aa gaat 7.00 7.00 7.00 Bye Se eh eee oie 2.50 2.50 2.50 2.50 E/T ee ee 5.593 5.593 5.593 5.593 5.5! A/(E/100)3.... 0. nk. on 5 163.4 163.4 163.4 163.4 163.4 S/VSGue aes, ae eee 6.220 6.230 6.200 6.224 6.224 WS) sal fttc.te. cerca ake 31777 31859 31705 31830 31828 Kr = R/VBH.......... 0.181 0.181 0.181 0.181 0.181 Cor/Cpp- cote cee 0.853 0.920 0.971 1.027 1.082 Table 14 — Principal Particulars of 0.75 Block Coefficient Forms IModelliNoie sos nc. eecth cues ie seuehe 4224 ERP ALG a ysirae iss Acvcretocst eens Grane 400.0 BOR teagecshesezessien Meine Acres crareheveaht 59.26 J 5) nhs coe eo ea ee 23.70 ID EtOnS 273s CER ciara 12048 IGFET ree Sane Moe ee 0.360 ex PRPs oe ar per ene e 0.210 DEF FN sor Per R PS aioe eee ean le 0.430 Bey ea rover aie af Rear 0.750 (OF Coes ORE SC ORE 0.990 (CF eka ath Gene Or iO CR ent re 0.758 (Gees batten o EoD OnE 0.770 (Goa tultre 3 Se cee Be Oe 0.745 ( Ors Ory mae enn ee 0.680 BR rece percee Co enut ereces 0.704 Opyipcinfreisin cca repstr sacri ais 0.905 Cpyp scene it perire cca rene 0.956 GRY KR CRiae orice: Bas nani carn 0.858 [A ES Caceres ere RES ee 0.828 GWE eee oniiae cies Gees 0.797 (Oa tr atone tae Een 0.860 (Qotsdd abso Aen Oo DRS eEOe 0.708 WSF ie ol BG Gee an CORR De 18.9°- PEW torn hins by aa on tere 406.7 LCB % Lee from (60) PSO 0.48F Whe} cals Peet Calais cea Ne ete eer 6.75 1 BSB 8 (ee acs tes Psy ERE eNO aH 2.50 TS 7 aetna Nein ssltee Raho 5.335 A/C /IOO) 22 eher: eyogerin creve chee 188.2 MS /U2S Re oteerstrcistet sano eicnonnee 6.104 IWSHisqift:< aacuceeieecuae as 34308 KR RNIB ee se 0.153 Cor/Cpr Siete a period sila «s+e* 0,966 Model® Node: tii: ote ca accts 4227 Sprit oe aelacnie iettieteiniers peta 400.0 WR Ete eas em cuansisicas Ais egorataga costs 61.54 7g BGs § creeds hoa a IER 24.59 DStOnsitian cies xecuie Sarees 13859 Sp) pos anne ainsi eke teres 0.307 x Epp ovcters ota = eyeaue ered 0.300 Te pomp iets cet cesolere eects Teeake 0.393 POE Re eer oe eee Re oan 0.800 CR ees lates fas 0.994 (Fy AOS CHEE Oa OCR RCE 0.805 Cpr a eee enon womcanrenelenee 0.822 Capen eee roped parses Sepesee 0.787 Geri ee eee cents 0.710 PR ere Satine eo HDs Guelers 0.730 PV ei Meteistepe alone sents ear stets roparotsie 0.921 (a) Bois So ous Beene 0.966 Gpvaion er eee nat ae OA pinion’ 0.878 Wim cke stot stale tate erustonscs 0.869 Gye ee ars eh ee ovepeneh 6 0.845 Cw Rl tors eine eon 0.892 Gree antec toPas te keys asters 0.769 AS pero on AOE BE Canoe 26.6° J OF ont Oe ARH AEE BRT RCS Oe 406.7 LCB % Loup from (%)......... 0.76F J bf ES OORT HOG Dee Oe aoe 6.50 Bigs Sok seascral eee nacoen Ge heke fol 2.50 JN PLIES RA PRO eo Ge 5.092 IN{UGAUY Lege asetinoonacccr 216.5 ISI SSI Aw oeie) aval Sr oucus ce are roverets eet ie 6.011 WISMSQIUaein nisi aston 37098 RY A/SB ci eee 0.118 Cor COR Sip eisa chanemen eich ets 0.973 VI-5 0.907 0.800 4214 400.0 61.54 24.59 13859 0.290 0.300 0.410 0.800 0.994 0.805 0.861 0.750 0.761 0.695 0.920 0.971 0.867 0.871 0.881 0.860 0.776 43.0° 406.7 2.5F 6.50 2.50 5.092 216.5 6.028 37200 0.118 1.095 V Table 16 — Resistance Data as Values of C, to a Base of , ViyL LCB Series 0.60 Block Coefficient Models (Ship dimensions—400.0 ft x 53.33 ft x 21.33 ft x 7807 tons. Turbulence stimulated by studs) Model No. 4215 4210 4216 4217 LCB as % Lap from %) 2.48A 1.50A 0.514 0.52F Vv Viwr C: X 10? for 400-ft L3»>———————— 0.35 0.925 2.641 2.654 2.620 2.599 0.40 1.057 2.611 2.624 2.604 2.577 0.45 1.189 2.596 2.618 2.597 2.564 0.50 1.321 2.618 2.618 2.602 2.563 0.55 1.453 2.629 2.628 2.613 2.573 0.60 1.585 2.641 2.639 2.627 2.589 0.625 1.651 2.650 2.640 2.632 2.612 0.65 1.717 2.666 2.648 2.653 2.647 0.675 1.783 2.685 2.671 2.681 2.676 0.70 1.849 2.697 2.689 2.706 2.694 0.725 1.915 2:715 2.701 2.712 2.705 0.75 1.981 2.736 2.699 2.718 2.713 0.775 2.047 2.765 2.713 2.711 2.729 0.80 2.113 2.783 2.727 2.727 2.755 0.825 2.179 2.814 2.744 2.794 2.814 0.85 2.245 2.861 2.792 2.873 2.953 0.875 2.312 3.008 2.933 3.003 3.120 0.90 2.378 3.236 3.197 3.252 3.392 0.925 2.444 3.511 3.497 3.627 3.677 0.95 2.510 3.811 3.787 3.952 3.967 0.975 2.576 4.046 4.037 4.157 4.217 1.00 2.642 4.173 4.197 4.292 4.407 1.025 2.708 4/225 4.268 4.382 4.508 1.05 2.774 4.236 4.272 4.412 4.497 1.075 2.840 4.226 4.258 4.408 4.459 1.10 2.906 4,223 4.273 4.413 4.484 1.15 3.038 4.471 4.534 4.656 4.776 1.20 3.170 5.196 5.223 5.188 5.373 V Table 17 — Resistance Data as Values of Cy to a Base of ~7~— Lyt LCB Series 0.65 Block Coefficient Models (Ship dimensions—400.0 ft x 55.17 ft x 22.09 ft x 9051 tons. Turbulence stimulated by studs) Model No. 4231 4218 4211 4219 4220 LCB as % Lp from % 2.46A 1.544 0.50A 0.38F 1.37F ViLars ® Go 10! for 400-ft. £3. 0.25 0.644 2.883 2.745 2.795 2.680 2.675 0.30 0.773 2,840 2.707 2.752 2.652 2.632 0.35 0.902 2° 805 2.677 2.717 2.622 2.602 0.40 1.031 2.777 2.649 2. 687 2.607 2.597 0.45 1.160 2.760 2.649 2.661 2.601 2.609 0.50 1.289 2.749 2.661 2.650 2.631 2.639 0.55 1.418 2.746 2.676 2.653 2.668 2.673 0.60 1.546 2.746 2.686 2.689 2.696 2.706 0.65 1.675 2.785 2.743 2.727 2.745 2.767 0.675 1.740 2. 837 2.777 2.750 2.787 2.807 0.70 1.804 2.888 2.810 2.770 2.830 2. 863 0.725 1.869 2.903 2. 825 2.800 2.861 2.923 0.75 1.933 2.906 2.841 2.826 2.886 2.986 0.775 1.997 2.899 2.864 2.855 2.919 3.070 0.80 2.062 2.902 2. 883 2.886 2.978 3.173 0.825 2.126 2.928 2.913 2.948 3.063 3.298 0.85 2.191 3.012 3.027 3.060 3.242 3.507 0.875 2. 255 3.210 3.287 3.340 3.557 3.797 0.90 2.320 3.596 3.799 3.811 4.000 4.176 0.95 2.448 4.721 4.971 5.066 5.246 5.476 1.00 2.577 5.771 5.941 6.201 6.296 6.501 1.05 2.706 6. 163 8.313 6.532 6.573 6. 832 1.10 2.835 6.104 3.224 6.443 6.542 6.793 1.15 2.964 6.055 3.161 6.316 6.438 6.696 1.20 3.093 6.628 6.918 VI-6 V Table 18 — Resistance Data as Values of Cy toa Base of =— Model No. Vey, LCB Series 0.70 Block Coefficient Models (Ship dimensions—400.0 ft x 57.14 ft x 22.86 ft x 10456 tons. Turbulence stimulated by studs) LCB as % Loup from % VAS. 0.25 0.30 2 ey on Morr ooooooooSooSocS SRSRSSSRSATNIIRSASHS Table 19 — Resistance Data as Values of Cr toa Base of Model No. 4230 4221 4212 4222 4223 2.05A 0.55A 0.50F 1.54F 2.55F C: X 108 for 400-ft Lap————_. 2.960 2.829 2.894 2.824 2.752 2.932 2.786 2.851 2.776 2.713 2.915 2.750 2.815 2.738 2.688 2.903 2.729 2.794 2.716 2.681 2.900 2.738 2.793 2.742 2.695 2.904 2.762 2.796 2.754 2.719 2.937 2.793 2.803 2.758 2.760 2.971 2.811 2.866 2.836 2.826 3.001 2.867 2.915 2.908 2.945 3.033 2.896 2.923 2.943 3.041 3.054 2.931 2.956 3.003 3.151 3.083 2.976 3.039 3.092 3.274 3.117 3.050 3.155 3.238 3.448 3.171 3.148 3.311 3.451 3.706 3.235 3.255 3.445 3.650 4.005 3.436 3.495 3.711 4.023 4.675 4.220 4.457 4.652 5.152 5.650 5.882 6.172 6.602 6.965 7.502 7.647 8.002 8.662 8.887 9.627 8.693 9.180 9.918 10.330 11.143 8.884 9.312 10.049 10.554 11.409 8.516 9.126 9.596 10.151 11.006 Q 292 V V Lyr LCB Series 0.75 Block Coefficient Models (Ship di mensions—400.0 ft x 59.26 ft x 23.70 ft x 12048 tons. Turbulence stimulated !by studs) LCB as % Lpp from VALyy 0.35 o cs a on on RE SSITIIARSAS a & ® oo a8 NNR RRR ee Ree Ree ie,e) i) 4224 4213 4225 4226 0.48F 1.50F 2.57F 3.46F C: X 10% for 400-ft L3ae—— ——.. 2.947 2.917 2.892 2.897 2.947 2.887 2.875 2.867 2.943 2.882 2.877 2.841 2.971 2.907 2.887 2.824 3.014 2.939 2.878 2.877 3.101 2.982 2.899 2.981 3.185 3.140 3.151 3.210 3.237 3.227 3.314 3.452 3.320 3.362 3.525 3.748 3.463 3.568 3.803 4.053 3.711 3.876 4.156 4.423 4.110 4.235 4.630 4.830 4.473 4.628 5.093 5.253 4.758 4.988 5.403 5.693 4.942 5.277 5.662 6.142 5.217 5.567 5.977 6.529 5.746 6.026 6.481 6.986 VI-7 V Table 20 — Resistance Data as Values of Cy to a Base of Jism WL LCB Series 0.80 Block Coefficient Models (Ship dimensions—400.0 ft x 61.54 ft x 24.59 ft x 13859 tons. Turbulence stimulated by studs) Model No. 4227 4228 4214 4229 LCB as % Lup from & 0.76F 1.45F 2.50F 3.51F v VL ® G,!<103! for’ 400.ft, Epp 0.25 "h 0.600 3.472 3.194 3.075 3.090 0.30 0.720 3.452 3.172 3.040 3.055 0.35 0.840 3.434 3.147 3.012 3.017 0.40 0.960 3.432 3.134 2.997 2.992 0.45 1.080 3.444 3.128 2.998 3.016 0.50 1.200 3.476 3.144 3.014 3.059 0.55 1.320 3.528 3.196 3.061 3.146 0.575 1.380 3.564 3.238 3.121 3.256 0.60 1.440 3.616 3.306 3.241 3.441 0.625 1.500 3.682 3.407 3.392 3.690 0.65 1.561 3.785 3.565 3.590 3.987 0.675 1.621 3.945 3.772 3.862 4.297 0.70 1.681 4.175 4.015 4.215 4.622 0.725 1.741 4.463 4.323 4.583 5.038 0.75 1.801 4.843 4.778 5.008 5.718 0.775 1.861 5.475 5.390 5.660 6.580 0.80 1.921 6.393 6.088 6.543 7.378 0.85 2.041 Vole 7.487 7.732 8.737 Table 21 — Resistance Data as Values of © to a Base of &) LCB Series, 0.60 Block Coefficient Models (Ship dimensions—400.0 ft x 53.33 ft x 21.33 ft x 7807 tons. Turbulence stimulated by studs) Model No. 4215 4210 4216 4217 LCB as % Lup from (% 2.48A 1.504 0.51A 0.52F VAL yy ® © for 400-ft Lap 0.35 0.925 0.681 0.685 0.679 0.676 0.40 1.057 0.674 0.677 0.675 0.670 0.45 1.189 0.670 0.676 0.673 0.666 0.50 1.321 0.675 0.676 0.674 0.661 0.55 1.453 0.678 0.678 0.677 0.669 0.60 1.585 0.681 0.681 0.680 0.673 0.625 1.651 0.684 0.681 0.682 0.679 0.65 Tews 0.688 0.684 0.687 0.689 0.675 1.783 0.693 0.689 0.694 0.696 0.70 1.849 0.696 0.694 0.701 0.700 0.725 1.915 0.700 0.697 0.702 0.703 0.75 1.981 0.706 0.697 0.704 0.705 0.775 2.047 0.713 0.700 0.702 0.709 0.80 25113 0.718 0.704 0.706 0.716 0.825 2.179 0.726 0.708 0.724 0.731 0.85 2.245 0.738 0.721 0.744 0.768 0.875 2.312 0.776 0.757 0.778 0.811 0.90 2.378 0.835 0.825 0.842 0.882 0.925 2.444 0.906 0.904 0.940 0.956 0.95 2.510 0.983 0.978 1.024 1.031 0.975 2.576 1.044 1.042 1.077 1.096 1.00 2.642 1.077 1.083 1.118 1.145 1.025 2.708 1.090 1.102 1.135 1.172 1.05 2.774 1.093 1.103 1.143 1.169 1.075 2.840 1.090 1.099 1.142 1.159 1.10 2.906 1.089 1.108 1.143 1.165 1.15 3.038 1.153 1.170 1.206 1.241 1.20 3.170 1.341 1.348 1.344 1.397 Table 22 — Resistance Data as Values of ©) to a Base of «&) LCB Series, 0.65 Block Coefficient Models (Ship dimensions—400.0 ft x 55.17 ft x 22.09 ft x 9051 tons. ‘turbulence stimulated by studs) Model No. 4231 4218 4211 4219 4220 LCB as % Lup from @%) 2.46A 1.54A 0.504 0.38F 1.37F VAL ay ® © for 400:§t £a3p—£_ oo —_ 0.25 0.644 0.726 0.691 0.705 0.675 0.676 0.30 0.773 0.715 0.682 0.694 0.668 0.665 0.35 0.902 0.706 0.674 0.685 0.660 0.658 0.40 1.031 0.699 0.667 0.678 0.657 0.656 0.45 1.160 0.695 0.667 0.671 0.655 0.659 0.50 1.289 0.692 0.670 0.668 0.663 0.667 0.55 1.418 0.692 0.674 0.669 0.672 0.676 0.60 1.546 0.692 0.676 0.678 0.679 0.684 0.65 1.675 0.701 0.691 0.688 0.691 0.699 0.675 1.740 0.714 0.699 0.693 0.702 0.709 0.70 1.804 0.727 0.708 0.698 0.713 0.724 0.725 1.869 0.731 0.711 0.706 0.721 0.739 0.75 1.933 0.732 0.715 0.712 0.727 0.755 0.775 1.997 0.730 0.721 0.720 0.735 0.776 0.80 2.062 0.731 0.726 0.728 0.750 0.802 0.825 2.126 0.737 0.734 0.743 ORCA 0.834 0.85 2.191 0.759 0.762 0.772 0.817 0.886 0.875 22255 0.808 0.828 0.842 0.896 0.960 0.90 2.320 0.906 0.957 0.961 1.007 1.055 0.95 2.448 1.189 e252 W277 L321 1.384 1.00 PVH 1.453 1.496 1.563 1.585 1.643 1.05 2.706 1.552 1.590 1.647 1.656 tPA, 110. 2.835 1.537 1.567 1.624 1.648 ilerAly/ 1.15 2.964 1525 1.551 1.592 13622 1.692 1.20 3.093 1.671 1.748 ? Table 23 — Resistance Data as Values of ©) to a Base of ®) LCB Series, 0.70 Block Coefficient Models (Ship dimensions—400.0 ft x 57 14 ft x 22 86 ft x 10456 tons. Turbulence stimulated by studs) Model No. 4230 4221 4212 4222 4223 LCB as % Lop from 2.05A 0.55A 0.50F 1.54F 2°55F VAL yy ® Qilor 400 2. ————— 0.25 0.629 0.732 0.702 0.715 0.700 0.682 0.30 0.755 0.726 0.691 0.704 0.688 0.672 0.35 0.881 0.721 0.682 0.695 0.678 0.666 0.40 1.006 0.718 0.677 0.690 0.673 0.664 0.45 1.132 0.718 0.679 0.690 0.680 0.668 0.50 1.258 0.7185 0.685 0.690 0.682 0.674 0.55 1.384 0.727 0.693 0.690 0.683 0.684 0.60 1.510 0.735 0.697 0.708 0.703 0.700 0.65 1.636 0.742 0.711 0.718 0.721 0.730 0.675 1.698 0.750 0.718 0.722 0.729 0.754 0.70 1.761 0.756 0.727 0.730 0.744 0.781 0.725 1.824 0.763 0.738 0.750 0.766 0.811 0.75 1.887 0.771 0.756 0.779 0.802 0.854 0.775 1.950 0.785 0.781 0.818 0.855 0.918 0.80 2.013 0.800 0.807 0.851 0.904 0.993 0.85 2.139 0.850 0.867 0.916 0.997 1.159 0.90 2.264 1.044 1.106 1.149 1.277 1.400 0.95 2.390 1.455 1.531 1.630 1.726 1.859 1.00 2.516 1.892 1.985 2.139 2.202 2.386 1.05 2.642 2.151 2.277 2.449 2.533 2.762 1.10 2.768 2.198 2.310 2.481 2.616 2.828 1.15 2.894 2.107 2.264 2.369 2.516 2.728 1.20 3.019 2.302 VI-9 Table 24 — Resistance Data as Values of ©) to a Base of @) LCB Series, 0.75 Block Coefficient Models (Ship dimensions—400.0 ft x 59.26 ft x 23.70 ft x 12048 tons. Turbulence stimulated by studs) Model No. LCB as % Lup from (%) VAC yy ® 0.35 0.860 0.40 0.983 0.45 1.106 0.50 1.229 0.55 1352 0.60 1.474 0.65 1.597 0.675 1.659 0.70 1.720 0.725 1.782 0.75 1.843 0.775 1.904 0.80 1.966 0.825 2.027 0.85 2.089 0.875 2.150 0.90 2.212 Mmm SSSSSSSOSSS9 4213 4225 4226 1.50F 2.57F 3.46F © for 400-ft Lp»p— ——_. 0.707 0.702 0.704 0.700 0.698 0.696 0.699 0.698 0.690 0.705 0.701 0.686 0.713 0.698 0.699 0.723 0.704 0.724 0.761 0.765 0.780 0.782 0.804 0.838 0.815 0.855 0.910 0.865 0.923 0.984 0.940 1.008 1.074 1.027 1.124 1.173 1.122 1.236 1.276 1.210 1.311 1.383 1.279 1.374 1.492 1.350 1.450 1.586 1.461 1.573 1.697 Table 25 — Resistance Data as Values of ©) to a Base of ® LCB Series, 0.80 Block Coefficient Models (Ship dimensions—400.0 ft x 61.54 ft x 24.59 ft x 13859 tons. Turbulence stimulated by studs) ® Model No. LCB as % Lp from (%) VIN Er 0.25 0. 0.30 0. 0.35 0. 0.40 OF 0.45 0.50 0.55 0.575 0.60 0.625 0.65 0.675 0.70 0.725 0.75 0.775 0.80 0.85 | El ll oe ee Poti > eel OS VI-10 4228 4214 4229 1.45F 2.50F 3.51F Ofer 400-10... 0.766 0.739 0.743 0.760 0.730 0.734 0.754 0.724 0.725 0.751 0.720 0.719 0.750 0.720 0.725 0.754 0.724 0.735 0.766 0.736 0.756 0.776 0.750 0.783 0.792 0.779 0.827 0.817 0.815 0.887 0.855 0.863 0.958 0.904 0.928 1.033 0.962 1.013 1.111 1.036 1.101 1.211 1.145 1.203 1.374 1.292 1.360 1.582 1.459 1.572 1.774 1.795 1.858 2.100 1.10 T Lean T Service Speed ® = 2.358 (Alexander) Trial Speed (K) = 2.515 (Alexander) Sustained Speed (K) = 2.275( Troost) Trial Speed (K) = 2.411 (Troost) ©2585, 20.96 1.00 Locus of LCB Location for Minimum Resistance 0.90 0.80 0.70 A LCB From (X) as % LBP F Figure 26 — Cross Curves of © on LCB. Cp = 0.60 Service Speed ®) = 2.046 (Alexander) Trial Speed (K) = 2.198 (Alexander) Sustained Speed «® = 2.025 (Troost) Trial Speed (K) = 2.146 (Troost) a Locus of LCB Location Minimum Resistance A LCB From @ as % LBP FF Figure 27 — Cross Curves of ©) on LCB. Cp = 0.65 VI-11 Service Speed ® = 1.745 (Alexander) Trial Speed (K) = 1.896 (Alexander) 0.9 Sustained Speed ® = 1.777 (Troost) Trial Speed (K) = 1.884 (Troost) Vee ®:1.896 gp =0.76 Vv 4 ——= O27. 54 Wi ®=1.88, cer 7075 Locus of LCB Location for Minimum Resistance 0.8 ? sl. VR = = 1.745, —=0.70 \LBP OFT, 4.0 3.0 2.0 1.0 (00) 1.0 2.0 3.0 4.0 A LCB From @&% as % LBP F Figure 28 — Cross Curves of © on LCB. Cp = 0.70 ak |b al Service Speed (K) = 1463 (Alexander) Trial Speed (K) =1.610 (Alexander) | Sustained Speed (K) =1.552 (Troost) Trial Speed (K) = 1.645( Troost) 0.9 OPES, Ste Aah T sil Locus of LCB Location for Minimum Resistance Vv 21645,—— = 0.675 © VLBP ®=1610, nae 0.66 Vv =1.552, —— = 0.637 ® * JcBP Vv ® 1463,—— = 0.60 ; VLBP 0.8 0.7 40 3.0 20 1.0 Ww 1.0 2.0 3.0 4.0 A LCB From % as % LBP F Figure 29 — Cross Curves of © on LCB. Cp = 0.75 VI-12 r une Service Speed (K) «1.190 (Alexander) 1.0 j ule Trial Speed (K) = 1.332 (Alexander) { Sustained Speed (K) =1.335 (Troost) Trial Speed (K) =1.415 (Troost) 0.9} = Locus of LCB.Location for Minimum Resistance © | ® =1.415, Tear" 0-596 Sele ® 08 ® 1.332 & 1.335, v s Tear 70-56 8 ES Vv ® = 1190, Fame e0.50 0.7 | 4.0 3.0 2.0 1.0 100) 1.0 2.0 3.0 4.0 A LCB From (X) as % LBP F Figure 30 — Cross Curves of @ on LCB. Cp = 0.80 values of «) corresponding to the Alexander and Troost speeds set out in Table 9. The locus of the LCB position for minimum resistance is indicated on each figure. Table 26 summarizes the data from all five figures. The optimum LCB locations and the corresponding minimum ©) values are given in Figure 31. This shows how, for a given block coefficient, the optimum LCB location moves aft as the desired speed is increased. When the block coefficient and speed are known, this figure will give the optimum LCB position and the corresponding minimum ©) value which will result if the lines of the ship conform with those of the Series 60 contours. Thus for a block coefficient of 0.65 and a speed corresponding to ® = 2.1, entering Figure 31 on the ®) scale, we find the best position of LCB is 1.45 percent LBP aft of ), the correspond- ing minimum © 400-ft value being 0.73 and Via = 0.82. This chart, in fact, summarizes BP the conclusions to be drawn from the resistance data and should be of considerable use to designers in all cases where the lines and proportions are not too different from those of the series. One point of considerable interest which arises from these data is the remarkable constancy of the minimum @) value at the sustained sea speed as defined by Troost. These speeds are shown in Figure 31; for block coefficients varying from 0.60 to 0.80, the minimum ©) 400-ft values at 0.05 intervals in coefficient are respectively, 0.735, 0.720, 0.730, 0.740, and 0.740. VI-13 Table 26 — Comparison of Resistance Results for LCB Series Position of © Values for 400+t Ship Cp LCB as % —Service speed?— —Trial speed*@—. —Sustained speed’. —Trial speed’—~ (Cp) Lp from (X) ® © ® © 0.60 2.48A 2.358 0.815 2.515 0.990 2.275 0.750 2.411 0.872 1.50A 0.803 0.983 0.736 0.866 (0.614) 0.51A 0.822 1.027 0.754 0.890 0.52F 0.858 1.038 0.785 0.922 Optimum LCB & © 1.69A 0.802 1.80A 0.980 1.65A 0.735 1.73A 0.865 0.65 2.46A 2.046 0.731 2.198 0.763 2.025 0.731 2.146 0.741 1.544 0.723 0.766 0.722 0.739 (0.661) 0.50A 0.725 0.778 0.722 0.750 0.38F 0.745 0.822 0.740 0.781 1.37F 0.797 0.890 0.788 0.849 Optimum LCB & © 1.014 0.722 2.50A 0.763 0.90A 0.720 1.85A 0.740 0.70 2.05A 1.745 0.754 1.896 0.773 ak 0.759 1.884 0.772 0.55A 0.726 0.760 0.731 0.757 (0.710) 0.50F 0.728 0.783 0.735 0.778 1.54F 0.743 0.811 0.752 0.803 2.55F 0.776 0.866 0.790 0.856 Optimum LCB & © 0.25A 0.725 0.954 0.757 0.25A 0.730 0.90A 0.754 0.75 0.48F 1.463 0.751 1.610 0.777 1.552 0.768 1.645 0.783 1.50F 0.722 0.765 0.747 0.777 (0.758) 2.57F 0.702 0.773 0.741 0.795 3.46F 0.720 0.791 0.752 0.823 Optimum LCB& © 2.60F 0.702 1.70F 0.764 2.30F 0.741 1.20F 0.776 0.80 O.76F 1.190 0.792 1.332 0.806 1.335 0.807 1.415 0.819 1.45F 0.752 ‘0.768 0.769 0.786 (0.805) 2.50F 0.731 0.739 0.740 0.771 3.51F 0.736 0.760 0.761 0 807 Optimum LCB & © 2.70F 0.730 2.56F 0.739 2.56F 0.740 2.23F 0.770 @ From Alexander Formula [1] in text. +b From Troost Formula [2] in text. i The optimum locations of LCB for Series 60 at the sustained sea speed and trial speed, as defined by Troost, are plotted in Figure 32. If desired, the effect of speed can be brought | out by treating it as a parameter for a series of curves such as the two shown. From the cross| curves of Figures 26—30, the permissible movement of the LCB forward or aft of the optimum position has been determined in order that the minimum © value shall not be exceeded by more than 1 percent. The resultant limits are shown as dotted curves in Figure 32 for both sea and trial speeds. | It should be noted that all the Series 60 forms have a vertical stem line but no bulb at the forefoot, and that the recommended LCB locations refer to such designs. In the finer forms, it is probable that in many cases a bulb would be fitted which would result in some variation in LCB position, depending upon how much the bulb was treated as an addition or how far the extra displacement was used to fine down the load waterline and forebody generally. VI-14 } 1.30 1.20 ce] 3 1.10 ra g LW } o ad} ‘= 3 1.00 Fe 2 0 & = } a a 0.90 is g 0.80 SUSTAINED SEA SPEED s LINE (TROOST) = 0.70 oe 2.2 2.4 0.65 Cg (K): 2.10 Figure 31 — Minimum © Values and Optimum LCB Position A ereat deal has been written in the past upon the best location for LCB, but there has been no unanimity among the recommendations in the literature. It is therefore of interest to look at the results for Series 60 against this wider background. Comparisons are shown in Figures 33 and 34. Dr. van Lammeren has given three curves based upon Netherland Ship Model Basin (NSMB) experience showing the recommended mean position for the LCB and the limits which should not be exceeded.*9 These curves are shown as A, B, and C in Figure 33. Professor Volker has summarized many of the results of previous tests,°° and Bocler gave a collection of data from very widespread sources in 1953.°! Much of the information shown in Figures 33 and 34 has been taken from these two papers. Hecksher’s curve is based upon extensive data compiled at the Hamburg Tank,°? Ayre’s from an exhaustive analysis of published data,°* and Todd’s from experience at the National Physical Labora- tory (NPL) tanks at Teddington. °* The positions and shapes of the recommended optimum lines vary considerably. This no doubt reflects the differences in the sources from which the data were drawn, the presence or absence of turbulence stimulation in some of the model tests, the choice of the relation- ship between fullness and speed and, to some extent, the personal interpretation of the data. It must also be remembered that these suggested curves represent an average for a large VI-15 V. === SUSTAINED SEA SPEED JERE = 1.85-1.6 Cp. TRIAL SPEED V,=1.06 V, PARENTS FOR GEOMETRICAL VARIATIONS FULL CURVES SHOW OPTIMUM LOCATION OF LCB FOR SERIES 60 DOTTED CURVES SHOW LIMITS OF 0.55 MOVEMENT FOR LCB WITHIN WHICH DOES NOT INCREASE MORE THAN | FROM MINIMUM VALUE. Co 0.65 0.65 Cp oto SUSTAINED SEA SPEED RAN 0.70 4 I SCSEN NY “TCC PN “tas 0.80 TO 0.80 MH -——— | avme - rer. (1) SCHIFFBOU KALEMDAR, 1935 - REF. (9) TODD — REF. (12) TROOST — REF. (6) 0.85) 3.0 2.0 1.0 jo] 1.0 2.0 3.0 : UCB FROM AS % LOP si See 4.0 oe m® 10 20 30 40 Figure 32 — Permissible Variation in LCB ‘ Lcp From Bas %LePe © Location for 1 Percent Variation in Resistance Figure 33 — Recommended Locations of LCB | number of unrelated models in which many factors are varying in addition to LCB position. In contrast, the results from Series 60 have the merits that the models are all related one to the other in an orderly and quite definite way, the forms represent good, modern, single-screw designs, and all the results were obtained in the same basin, employing the same instruments and techniques and method of turbulence stimtlation, and thus form a homogeneous set of data. In general, comparison between the optimum LCB locations derived from Series 60 experiments and those suggested by other sources shows that although conforming in general shape to the older lines, the Series 60 results indicate an optimum location somewhat further | aft. The comparisons given here have been made at certain speeds chosen to give economic | performance of the different forms. The criterion has been that the sustained sea speed | VI-16 should be that at which the ©) value begins to rise steeply, i.e., where the resistance is beginning to increase at a rate higher than VAN LAMMEREN-AG|JUSTED — POR \Lpp BY BOCLER-REF.(9) ‘the square of the speed. It is realized that ! ie [o © o |GEMMELL~REF.(9) [% 3% a] DAWSON —REF. (13) today many considerations other than economic performance, so defined, come into the choice of ship speed, either for defense reasons or because of a demand for high speed for certain ‘specialized cargoes. However, all the models | were run to considerably higher speeds in the course of the tests and these results are given here in the form of tables and charts, so that Ce similar comparisons can be made at higher speeds if desired. The minimum resistance values for ‘ships with the lines and proportions of the Series 60 parents are shown in Figure 31. An ‘analysis of the resistance of single-screw ships has been published by Lap of the NSMB, Holland,°® and it is of some interest to compare these two sets of data. He carried out a survey of the results obtained from single-screw ship ° . ~~ 4.0 3.0 2.0 1.0 1.0 2.0 3.0 4.0 models run in that establishment over the last A LCB FROM Bas Wige . IF gD years, determined the most important Figure 34 — Recommended Locations of LCB parameters, and produced curves of optimum Cp values. He found these parameters to be i B ie? WH’ Cp, LCB location, % @ g, and Cy , the same, incidentally, as those chosen as the basis of the Series 60 variations. He gave diagrams of sectional area curve ordinates for different values of the prismatic coefficients of fore and aft bodies which agree very closely with those for Series 60. Professor Troost has compared the NSMB results with those of the Series 60 parents. 78 For the Dutch results, he found that the optimum LCB position could be approximated by the | equation @= 17.5 Cp -12.5 [3] where a equals the distance of LCB from & as a percentage of Lp p»* and is positive if -LCB is forward of Gand negative if aft. For Series 60, the optimum positions from this | *For Series 60 parents, as originally tested, the LCB positions correspond to the equation a = 20 Cp -— 13.5. | VI-17 formula and as found from the actual modei tests for the sustained sea speed defined in Equation [2] compare as follows: OPTIMUM LCB POSITION From Equation 3 From Series 60 Tests 0.60 1.65A 0.65 0.90A 0.70 0.25A 0.75 2.30F 0.80 2.50F In comparing Lap’s results with Series 60, Troost designed a parent model family of five ships: Series 60 400 ft 6.5—7.5 2.5 0.977—0.994 0.805 0.758 0.710 0.661 0.614 In making the resistance comparison, Troost assumed that the finest models of 0.60 Cp would have a bulbous bow, and he reduced Lap’s estimates for a conventional bow by 1 percent for sea speed and 6 percent for trial speed. In order to compare the estimates made from the NSMB family with the results of Series 60, which has no bulb, these allow- ances have been restored. The comparison with Series 60 is now as set out on the follow- ing page and shown in Figure 35. VI-18 NSMB Models Series 60 Models NSMB MODELS SERIES 60 MODELS. TRIAL SPEED Vy 21.06 Vg 0.9 a & ip) ie Rane

” The rake was reduced from 15 to 6 degrees to suit the Series 60 aperture. The principal particulars of the propellers are given below for a ship with LBP of 600 ft, and a typical drawing is shown in Figure 37. PROPELLER PARTICULARS Model block coefficient 0.75 0.80 Propeller Number 3378 3379 3377 Diameter D, ft 22.40 24.89 | 25.82 Pitch P, ft over outer disk | 24.08 26.40 | 25.51 | 23.75 P/D 1.075 1.025 | 0.920 Blade Area Ratio 0.550 0.475 | 0.450 Blade Thickness Fraction 0.045 0.045 0.045 0.045 0.045 Rake, deg [Se 4 4 Number of blades 4 4 The pitch ratios were chosen to give maximum efficiency for the given diameter and power absorption on the parent models, and the revolutions per minute (rpm) were derived from the experiment results. No bilge keels were fitted, and studs were used for turbulence stimulation. The tests were run in the Continental method at a loading corresponding to the ship self-propulsion point with a ship correlation allowance of +0.0004. The models were fitted with standard TMB pendulum dynamometers, and measurements were made of speed, thrust, torque, and revolutions per minute (rpm). The data were extrapolated to apply to a ship with LBP of 600 ft by the method outlined in Reference 58. The propulsive efficiencies VII-1 FIGURES ABOVE THE LINE GIVE VALUES OF THICKNESS ORDINATES IN TERMS OF THE CHORD A FIGURES BELOW THE LINE GIVE RATIO OF EACH THICKNESS P ORDINATE TO MAXIMUM THICKNESS ORDINATE es ’ tia RU ee ele et Tegan Rc in role OS tN ao am Io 0 9, ®o wm Mw wow moO S- tn t+ HOO I QO Amo $2 GS GH we CO NM MONNOH OR BGZOOR off mo FO st Cen) = o > at < Og OF ao O= OM ROKRM OF OF @O HG 20 KR OM ON Bo Ce) 9, Om FHra Oo OO 5B OD OW O8 06 OP20H 6H SHOR oe Dn om =) tH Ooo On O® » de SB ere Sed ESE Vv CS MONT MDB og OW LN jroo = tm oo” 0? " =m no om =. ow oS pe IR O=ZO Olas STANDARD STRUT SECTION 1.50 WL 1.125 WL 0.875 WL “~~ wy, == peaey, (Ease eal 0.75 WL aime FROM THIS TANGENT POINT UP 0042LBP eo ORIGINAL PROFILE CURVE : eal 0.625 WL laa ee 0.50 WL RUDDER AREA ] = 1.5 % LBPxH a r) 0.25 WL ro} + 2 o t+ 5 ame BASELINE -0343H }-—.0226LBP 19 Figure 36 — Details of Stern Arrangement VII-2 Jo|[edoig Jopoyw [voIdAy, jo sutmeig — yg eins y fo) a @ o 0960 — oz nT oKe) Ovb'l — of 122'°0 N 026’1 — Ov = as | ine . ce mae. 6t1'0 ie og¢e'e — oz THi9) N Sag 08's — 08 (eo) To) fe} ro) Se To) oO ) ° / Ca eee ee 4800°' ay NN ie O2ze"b — 06 SSN : =i 4b 00" SS Sor ~4800" US eT ye 39v4 OL TVWYON = eels = SEL ERM SS3NWOIHL WAWIXWW vos S3HONI GNV NOISNWdx3 NoILOarOud FAYND HOLId : — VII-3 were calculated using the resistance of the model as measured during the self-propulsion tests, in association with the corresponding values of torque and rpm. This is a correct measure of propulsive efficiency since all the quantities apply to the model in the actual condition of test. However, for a variety of reasons, the actual resistance of the model at that time may not agree exactly with that measured during the original resistance tests, and on which the ehp values are based. The model has a keel piece, rudder, and propeller hub installed, and the surface and shape of the wax model may have changed slightly. The dhp values deduced straight from the torque and rpm will therefore correspond to a different resistance from that used to calculate the ehp values. For this reason, the dhp values have been calculated from. the ehp values, using the propulsive efficiencies measured during the propulsion experiments but ignoring the actual torque and rpm values, i.e., ehp dhp = ————_____ Propulsive efficiency In this way there is no inconsistency between the dhp values and the ehp values previously given from the resistance experiments and made when the models were new and in the bare- hull condition with no appendages and a new, clean surface. The choice of a 600-ft ship to illustrate the propulsion tests was made principally because it was considered more representative of modern ships than the 400 ft chosen for the resistance presentation. This latter is made in coefficient form and may be corrected quite easily to any other desired ship length; most of the resistance data published else- where are on the 400-ft basis. The propulsion data, on the other hand, cannot be so corrected, | and must be completely recalculated for any other length. Moreover, unless the model has been run at a number of loadings, it is possible to make such correction only for a small change in length. The results are presented in detail in Tables 27 through 31. The change in wake fraction with movement in LCB affects the optimum pitch ratio for the highest propulsive efficiency, but series chart calculations show that this effect does not amount to more than 1 or 2 percent. Cross curves of dhp similar to those of (@)have been drawn for the same four chosen speeds. The data are tabulated in Table 32 and the cross curves are shown in Figure 38. On these have been drawn the loci of optimum LCB location to give minimum dhp. Those already derived from the resistance data to give minimum ehp are also shown for purposes of comparison. In general, the minimum dhp is not so well defined as the minimum ehp, but, within practical limits, the dhp and ehp results agree in defining the same optimum LCB loci for each set of models except the fullest — that with Cp = 0.80. For this set, the dhp results indicate reducing power the further forward the LCB , even beyond the extreme position of 3.51 percent used in the experiments. The ehp results indicate an optimum location at about 2.50 percent of the length forward of midships, and this is a more practical answer — any VIl-4 Table 27 — Results of Self-Propulsion Experiments, 0.60 Block Coefficient (All figures are for ship of 600-ft LBP) Model No. 4210 4215 4216 4217 LCB ——1.50 per cent A 2.48 percent A ——0.51 percent A ——0.52 per cent F 74 EHP N SHP EHP N SHP EHP N SHP EHP N SHP 12 2304 52.4 2931 2296 51.2 2789 2299 52.0 2796 2273 52.8 2884 13 2940 56.9 3712 2943 55.6 3585 2933 56.7 3608 2896 57.1 3665 14 3685 9 4607 3687 60.0 4501 3675 61.3 4560 3631 61.8 4597 15 4549 65.7 5693 4549 64.7 5644 4540 65.9 5689 4499 66.3 5695 16 5545 70.4 7091 5577 69.6 6998 5565 70.7 7053 5575 71.2 7057 17 6730 75.6 8740 6764 74.7 8561 6796 76.1 8713 6796 76.2 8624 18 8063 6 10445 8113 79.2 10231 8162 80.9 10518 8145 81.2 10551 19 9531 85.1 12203 96 83.6 11977 9555 85.9 12360 9635 86.8 12728 11219 90.4 143 11484 88.5 14355 11316 91.1 14696 11445 92.6 15119 20.5 12142 93.0 15667 12454 91.1 15886 12422 93.9 16132 12571 94.6 16606 1 13280 95.5 17292 13631 94.5 17725 13726 96.9 17990 13973 97.7 18458 21.5 14778 8.8 19470 15202 98.1 19976 15253 99.8 20044 15873 101.0 21051 22 16961 102.9 22615 17273 101.6 22727 17297 103.1 22971 18217 104.9 24551 22.5 19533 107.3 26468 19726 105.9 26093 20247 108.3 27324 20887 109.8 28730 23 22466 112.2 30903 22587 110.1 30399 23541 113.6 32248 23818 114.8 33219 23.5 25894 117.4 36165 25772 115.6 35794 26860 119.0 37566 27084 119.7 38146 24 28773 121.9 40755 28864 120.7 41059 29850 123.2 42281 30392 124.6 43170 25 34202 129.8 49354 34363 128.1 49301 35157 130.6 50011 36288 131.9 51839 26 39112 135.5 56196 38795 133.2 55739 40595 137.0 57663 4149 137.6 59443 Table 28 — Results of Self-Propulsion Experiments, 0.65 Block Coefficient (All figures are for ship of 600-ft LBP) Model No. 4211 4218 4219 4220 4231 LCB 40.50 percent A—~. ——1.54 percent A—— .38 per cent F—. ——1.37 percent F——. ——2.46 per cent A—~ Vv EHP N SHP EHP N SHP EHP N SHP EHP N SHP EHP N SHP 10 1475 41.4 1993 1453 41.0 1856 1428 41.8 1833 1427) 41.0 1695 1526 441.8 2221 11 1949 45.4 2547 1933 45.3 2453 1898 46. 2446 1908 45.3 2288 2022 45. 2905 12 2516 49.6 3238 2526 49.4 3169 2485 50.5 3203 2505 50.0 3051 2613 49.8 3706 13 3 54.1 3225 63.6 4017 3204 54.9 4134 3226 «54.6 3997 3322 53.8 4652 14 4011 58.7 5243 4040 57.9 5031 4046 59.3 5214 4067 59.4 5122 4147 57.9 5728 15 5010 68.1 6472 4992 62.3 6311 5018 63.6 6458 5064 64.4 6501 5116 62.1 6989 16 6172 67.7 7985 6172 67.4 7963 6197 68.3 7965 6267 69.3 8128 6214 66.4 8466 17 7505 72.4 9536 7581 72.5 9858 7627) 9073.1 9753 7724 74.2 10045 7782 72.3 10763 18 9044 77.0 11504 9113) «77.3 11835 9235 78.0 11750 9500 79.2 12337 9369 77.3 12976 19 10818 81.8 13941 10852 -1 14094 11051 3 14371 11641 84.8 15118 11010 81.6 15208 19.5 11789 §=684.2 15291 11779 =©82.5 15317 12118 86.1 15903 12910 87.6 16788 11903 83.7 16417 12881 87.0 16882 12777 -8 16681 13319 88.7 17501 14322 90.6 18673 12879 86.0 17788 20.5 14145 1 18834 13944 89.2 18347 14800 91.9 19473 16026 94.1 21031 14013 88.5 19436 1 15771 93.8 21458 15565 92.8 20809 16753 95.5 22043 18191 98.0 24062 15469 91.6 21605 21.5 18129 99.0 25534 17803 7.0 24288 19353 99.7 25565 20815 102.4 27865 17477 95.5 24860 21555 104.4 31014 21338 102.6 29719 22705 104.4 30559 24031 107.5 32830 20326 100.5 29935 22.5 864 109.2 37539 25648 108.5 36484 27138- 111.0 37797 28204 113.0 39612 24428 106.5 36459 31221 115.7 45913 30621 115.0 44703 32 118.1 46974 33510 119.4 48848 29254 112.4 43991 23.5 7337 121.7 36588 121.9 54527 38626 125.2 57308 40546 127.0 61063 34704 118.9 53064 24 43782 128.8 67048 42542 128.6 65248 44889 132.1 68638 47386 133.7 73353 40734 125.6 64047 Table 29 — Results of Self-Propulsion Experiments, 0.70 Block Coefficient (All figures are for ship of 600-ft LBP) Model No. 4212 4221 4222 4223 4230 LCB 40.50 percent F—~ -——0.55 pereent A——. ~—1.54 percent F——. ——2.55 percent F——. ——2.05 percent A—— V "EHP N SHP EHP N SHP EHP N SHP EHP N SHP EHP N SHP 10 1660 41.1 2065 1625 40.0 1972 1618 40.2 1951 1596 §40.3 1977 1729 40.2 2145 11 2207 45.3 2762 2172 44.0 2627 2173 44.5 2609 2131 44.2 2635 2305, 44.4 2859 12 2867 49.6 3643 2842 48.5 3474 2835 48.9 3375 2790 48.9 3419 2995 48.6 3725 13 3652 54.0 4700 3652 52.8 4536 3607 53.1 4336 3593 53.1 4393 3821 52.7 4746 14 4597 58.4 65970 4594 57.0 5742 4542 57.5 5566 4553 57.5 5573 4814 57.1 6018 15 5788 63.2 7517 5690 61.5 7139 5754 62.4 7257 5729 62.2 7073 6010 61.7 7607 15.5 6454 65.4 8393 6322 63.5 7943 6428 64.8 8137 6419 64.7 8033 6673 64.1 8501 16 7117 67.5 9267 7026 «66.1 8860 7127~—s67.1 9033 7208 67.4 9136 7378 66.5 9471 16.5 7827 69.7 10205 7770 = 68.5 9835 7895 69.5 10019 8113 70.3 10428 8145 69.0 10564 17 8603 71.8 11246 8581 70.8 10903 8754 72.0 11109 9137 72.9 11882 8954 71.3 11735 17.5 9545 74.4 12510 9468 73.4 12122 9733 74.7 12352 10275 76.1 13555 9831 73.7 12987 18 10634 77.2 13991 10452. 76.1 13469 10894 77.2 13860 11567 79.1 15443 10781 76.3 14436 15.5 11934 .O 15724 11597 78.9 15060 12306 80.3 15919 13127 82.4 17763 11827 79.0 15897 19 13470 el 17770 12892 81.5 16809 14067 83.7 18412 15038 86.3 20488 12983 81.6 17545 19.5 15097 86.4 20048 14317 84.5 18838 15980 87.2 21222 17400 §=90.5 23803 14285 84.5 19515 16775 89.3 22367 15912. 87.3 21047 17985 90.8 24206 20027 94.9 27738 15697 87.2 21621 21 20756 95.3 28086 19583 93.1 26216 22619 98.3 31328 26381 103.9 37741 19187 93.3 26986 22 29724 107.5 41631 26948 102.7 37016 31477 109.9 45685 35065 114.2 52180 25803 103.8 37780 VII-5 Table 30 — Results of Self-Propulsion Experiments, 0.75 Block Coefficient (All figures are for ship of 600-ft LBP) Model No. 4213 4224 4225 4226 LCB ——— 1.50 per cent F —0. 48 per cent F- ——2. 57 per cent F ——3 . 46 per eent F. EHP N SHP EHP N SHP SHP N SHP EHP N SHP 10 1851 40.0 2193 1912 40.3 2192 1846 40.6 2222 1837 40.7 2159 11 2465 44.6 3002 2554 44.4 2902 2459 45.0 2991 2427 44.9 2939 12 3216 48.9 3961 3332 48.8 3875 3203 49.1 3864 3135 49.0 13 4142 53.3 5126 4276 53.1 2 4102 53.3 4930 4020 -6 4944 14 5210 57.7 6489 5435 57.6 6548 5184 57.5 6238 5126 58.3 6399 14.5 5824 59.9 7279 6111 59.9 7425 5831 60.0 7051 5777 .8 7248 15 6526 62.1 8178 6850 62.5 8374 65 62.7 8015 6529 63.3 15.5 7348 64.8 9278 7649 64.9 9431 7368 65.3 7404 65.9 9360 16 8278 67.3 10505 67.1 10542 8313 68.1 10430 8446 6 10691 16.5 9311 70.2 11937 9465 69.6 11757 9491 71.4 12215 9821 72.1 12479 17 10483 73.0 13527 10535 72.1 13136 1 74.9 14330 11526 75.8 14834 17.5 11871 76.4 15538 11805 74.9 14793 12577 78.3 16680 13412 79.7 17601 18 13654 | 1 13341 78.0 6887 14630 82.0 19455 15593 atl 20791 19 18592 89.0 25858 18125 5 23880 20275 90.8 27399 21254 92.3 29235 20 25004 97.8 35669 24328 96.0 34120 27518 101.2 39367 28474 102.1 40620 21 32135 107.5 47749 30356 103.5 804 33361 108.8 50318 37471 113.2 55595 22 40815 116.3 62504 39029 112.3 57396 42478 118.1 65250 47694 123.2 72705 Table 31 — Results of Self-Propulsion Experiments, 0.80 Block Coefficient (All figures are for ship of 600-ft LBP) Model No. 4214 4227 4228 4229 LCB ——2.50 per cent F ——.76 per cent F —— 1.45 per eent F ——3 .51 per cent F- Vv EHP N SHP EHP HP EHP N SHP EHP N SHP 9 1531 37.8 1858 1751 2 2678 1599 38.9 1955 1530 37.5 1620 10 2096 42.2 2552 2 47.0 3696 2187 43.2 2697 2089 42.1 2336 11 2791 46.6 3433 3212 51.8 4964 2914 47.7 3620 2800 46.5 3203 12 3639 51.2 4531 4197 56.6 3786 52.0 4744 3680 51.1 4230 12 4127 53.3 5172 4772 59.0 7399 4305 54.3 5422 4187 54.2 4812 13 4666 55.6 5892 5405 61.7 8367 4878 56.9 6182 4756 55.7 5473 13.5 5274 58.2 6693 6096 64.1 9 5 59.5 7031 5405 58.0 6263 14 5970 60.6 7625 66.7 10594 6208 62.1 7990 6190 60.7 7248 14 6796 63.3 8713 7693 69.3 11927 6993 9 909: 7162 63.7 84: 15 7792 66.2 10028 8635 72.1 13470 7896 67.7 10363 27 67.5 9997 16 10315 72.9 13519 10876 78.2 17345 10222 9 13684 11456 74.4 14231 17 14009 81.0 18975 14117 85.5 22955 13546 81.3 18658 15580 82.4 20286 18 19249 90.5 27381 18642 93.4 30763 1810 -0 26273 21280 92.0 29271 19 26847 101.3 40432 25823 103.1 42542 25703 101.2 38826 31410 104.0 45522 VII-6 Table 32 — Comparison of DHP Results for LCB Series (Speed and dhp are given for ship 600 ft long, between perpendiculars) ee — (a) ut = (a) SEA — (b) TRIAL SPEED | TRIAL SPEED (b) V 4 2 = knots a= knots vL knots jj ki Position of LCB as Percent (a) From Equation 1 (b) From Equation 2 Figure 38 — Cross-Curves of DHP for LCB Series (Speeds and dhp given for ship 600 ft long, between perpendiculars) 40,000 + +—+ 4 VALUES OF | SPEED V IN KNOTS [ | Vv ' 25,000 ier 23.52 + ame ees a 5,00 2\.06 SPEED V nea 4 ak MINIMUM RESISTANCE IN-KNOTS [eal — LOCUS OF LCB FOR 2056 + | | 4 | MINIMUM dhp r —-— LOCUS CHOSEN FOR 20,000 + a a5 PARENTS OF 5 | | | SERIES aa 30,000 |— at ‘Penal a er ara 19.407 | = 7 - 22:54 ——}—+—| & 15,000 a I 0.921 + ficmal aas = 22.04 oe a i be hens : | | 10,000 + | | 20,000 n ps] cae 2126 18,000 4 — 5000 L A 3.0 20 10 ° 1.0 2.0 3.0 4.0 3.0 2.0 10 a 10 2.0 3.0 4.0 ART. LCB FROM m& AS PERCENT Lee FORWARD —> -— AFT LCB AS PERCENT LgpFROM & FORWARD —* Figure 38a — C,, = 0.60. Figure 38b — Cp = 0.65 VIl-7 20,000 v | H | V IN KNOTS ig.62 Yep 18.54 0.760 u 0.757 Jt 15,000 | 0.714 | 17.49 | : 17.15 | 0700 | | 10,000 3.0 2.0 10 0 Lo 2.0 30 40 LCB FROM & AS PERCENT Lop Figure 38c — Cp = 0.70 15,000 Fae | ; = i} VIN KNOTS = 2” = | Vogp mI SHIP LENGTH 600 FT BP! D & == zl = 10,000 lea 2 t i lee 5,000 | 3.0 20 1.0 a 10 20 3.0 40 —+— AFT LCB FROM@AS PERCENT Lep FORWARD —> Figure 38d — Cp = 0.75 20,000 = ; iho oe 15,000 + Vv l=an|imnailaemmernlec ait a Lene ' + 0.596 H 210,000 |} —++ ——] 0.560 | V IN a i‘ HE KNOTS 14, T 0.500 eo t 13.72 5,000 + =] t 12.25) 1°) L | 3.0 2.0 1.0 a 10 20 30 40 AFT LCB FROM & AS PERCENT Lap FORWARD —> Figure 38e — Cp = 0.80 VII-8 further movement forward would result in excessively full entrance waterlines and probably poor behavior and heavy speed loss in a seaway. It can be concluded that if the LCB location is chosen to give minimum ©) values and so minimum ehp, the dhp also will be practically a minimum except for the very fullest models of the series. The charts given in Figures 31 and 32 can thus be used by the designer with the knowledge that, within practical limits, they will-lead to ship forms having both minimum ehp and dhp in smooth water. The detailed results of the self-propelled experiments are given in Tables 27 to 31. Cross plots of these data show a general waviness of character, associated with changes in wake fraction w consequent upon changes in wave formation with speed, but for a given full- ness, both wake fraction and thrust deduction fraction tend to decrease as the LCB moves forward, due to the progressive fining of the afterbody. As a result, the hull efficiency remains fairly constant, although showing considerable variation due to the interplay of the changes in u and ¢. The one exception to this pattern is the set of models of 0.80 Cp, where the value of w remains fairly constant with LCB movement, but ¢ decreases rapidly as the LCB moves forward. As a result, the hull efficiency increases continually, and the resultant increase in propulsive efficiency and decrease in dhp is the reason why this set shows no optimum LCB location for minimum dhp within the range tested. VII-9 CHAPTER VIII EFFECT ON RESISTANCE AND DHP OF VARIATION IN SHIP PROPORTIONS The experiments described in the last section showed that the original choice of LCB positions had not been too far from the optimum, although improvement could be obtained in certain areas. For the final series of experiments, in which the effect of variation in Cp, ome and ( =) upon resistance and propulsive efficiency were determined, the five 100 models chosen as parents were those of the LCB series having the LCB in the position nearest to the optimum. 0.60 0.65 0.70 0.75 4210 4218 4221 4213 1.54 aft | 0.55 aft | 1.5 fwd 1.5 aft 0.5 aft 0.5 fwd 1.5 fwd Model Number LCB as Percent Leap from Dp p LCB in Original Series 60 Parents It will be seen that the change involves a movement of the LCB aft in the 0.65 and 0.70 Cp models. The models chosen for the final phase are also indicated in Figure 1. In developing this geometrical series, the assumption has been made that the optimum location of LCB for L B the model having the — and — ratios of any one parent will remain near-optimum with changes of =e and W for the same block coefficient. This assumption has not been tested in the present research, but any other would have led to a great extension of the test program. Faving chosen the new parents, eight additional models were made for each block coefficient, making a total of 45 models in all, including the original parents. L B VARIATION OF es AND a RATIOS Range of Variation in A (L/100)3 6.5—8.5 67.8—162.4 0.65 6.25-8.25 78 .0—190.3 0.70 6.0—8.0 89 .3-222.4 0.75 5.75—7.75 102.0—259.3 0.80 5.5-7.5 116 .2—302.4 A typical pattern of the variation (for Cp = 0.60) is shown in Figure 2. VIll-1 The eight new models of any one set were derived from the parents by a straightfor- H values. The lines of the parents for Cp values of 0.60, 0.75, and 0.80 are shown in Figures ward geometrical variation of beam and draft to give the required combinations C= and — 12, 15, and 16 and those for the new parents of 0.65 and 0.70 Cp, are shown in Figures 39 and 40. Particulars of all 45 models are given in Tables 33 through 37. The models were made in wax, 20 ft LBP, as before, but the turbulence stimulation was provided by a trip wire instead of studs; the 0.036-in. diameter wire was placed around a station 5 percent of the length from the forward perpendicular. This change was made for — the reasons set out in Appendix A. The model results have been converted to apply to a ship 400 ft LBP, using the ATTC 1947 model-ship correlation line with an addition of + 0.0004 for ship correlation allowance. The ship figures are given in Appendix B as values of Cy and ©) for a standard temperature of 59°F (15°C). For the propulsion experiments, the models were fitted with a rudder and keelpiece and the experiments carried out as described in Chapter VII. The propeller diameter was in every case 0.7 of the draft. The propellers for the parent models were specially made for the Series 60 tests, and, as already described, were of the Troost B-type with four blades. As the draft was varied in this geometrical series, so also the propeller diameter had to be changed. To avoid making large numbers of new propellers, and since the principal objective of the propulsion tests was to obtain systematic data on the components of propulsive efficiency, such as wake and thrust-deduction fractions, stock model propellers were used whenever possible. These were chosen to have rake, blade-area ratio, sections, and other features as near to the Troost standard design as possible. Table 38 shows the propeller particulars. The propulsion tests were run without bilge keels, and trip wires were used for turbulence stimulation. They were carried out at a propeller loading corresponding to the 600-ft ship self-propulsion point with a ship correlation allowance of +0.0004. The data extrapolated toapply to a ship 600 ft LBP are presented in detail in Appendix B. VIII-2 (1 3F Jepoyw) Sella A a JOJ JUOIB J a4 G9°Q jo seuly — 6€ ast ad aN 38v8-7— — =a SI MigISLOl wae Apcer comers amma comnton@ ami |P7 Tm 6 < S 1M =a v TM srr € Tm O01 areal 7 / / 1 Toh 7 NY3LS MOS ‘ 8 Kel 61 __ 6! dv Sia Ba ge al ee <= ' =| — SS — = oe ; \ | | { | 2S) - | —. 2 Hi \ a ||| eee - nese ae —— —t ATT| — za WS, sq ft S/y 2/3 Ly tt Lap, ft Lp/Lpgp L y/Lgp Ly pp Cir LCB, % LBP from & VIII-8 Table 37 — Principal Particulars of 0.80 Block Coefficient Models [ Model Number | azia | 263 | vei | azes | azo | za | zs | zee | a0 | 62 L/B 7.5 B/H 3.0 B, ft 53.33 H, ft 47.78 A, tons 8675 1/2q@,, deg 38.9 L/y 3 5.9542 A/(L/100)° 135.5 WS, sq ft 29617 Vy 2% 6.559 Eg ft En pant Lp/Lpp L/Lpp L ppp Cir LCB, % LBP from (& _ VIU-9 Table 38 — Propellers Used on Series 60 Models Propeller D P P/D EA/DA | BTF | Rake | Number of Number (ft) (ft) (deg) Blades VIII-10 CHAPTER IX DESIGN CHARTS The resistance and propulsion results for ships exactly similar to each of the 45 models of the geometrical series have been given in Chapter VIII. This form of presentation is not very useful to the designer, however, since he will almost always have to do some interpolation to fit his particular problem of the moment. A great deal of thought was given to the most desirable method of plotting these data so as to make them of the greatest value and yet simple to use. It was finally decided to present the resistance information in the form of contour charts similar to those made so familiar by Taylor. To reduce the data to this form presented a formidable proposition in fairing since there were 45 models in all and contours had to be drawn for a number of values of Vay WL and ®) . To expedite this phase of the work, the fairing was done on the UNIVAC computer in the Applied Mathematics Laboratory at Taylor Model Basin. The process is described in detail in Appendix C. The contours are given in Appendix B. The first set shows contours of residuary resistance in pounds per ton of displacement RR oath B V -—— }, each individual chart showing, for given values of — and 7 — , the variation of A H Vly, Reha 3 L. ra with block coefficient and B ratio. The second set is of the same kind but shows pout of © for a ship with LBP of 400 ft against Cp and for chosen values of ®) and a The third set gives contours of wake and thrust deduction fractions plotted against L 4 B C, and — for chosen values of andes 4 B Be Vey, H Both the x and the © values have been derived on the basis of the Froude assump- 6 tion that the total resistance can be divided into two parts, the skin friction of an ‘‘equivalent plank’’ and the residuary resistance, the latter obeying Froude’s Law of Comparison. In the present work, the skin friction resistance for both model and ship has been calculated in accordance with the ATTC 1947 line, the appropriate values of C,, and Reynolds number being taken from previous Model Basin reports. °9’°° R R ‘ In using the first set of contours, the value of re is first determined for the desired speed-length ratio. To it must be added the frictional resistance, which can be RF expressed in the form wa , where S is the wetted surface. The total resistance is. then To simplify the use of the contours, a nomograph is given in Appendix B from which the frictional resistance per square foot of wetted surface — can be determined. Contours S are also given for estimating the wetted surface for any combination of design parameters. The ©) - ®) contours are for the total resistance, residuary plus frictional, and the © values are those appropriate to a ship of 400 ft LBP. For any other length, a correction must be made which depends upon the actual length and the wetted surface coefficient. spe Vv! For those who wish to compare the Series 60 ©) values with those of other models in which the Froude values of 0, and O, have been used in the analysis, a rapid method of making the conversion has been given by Gertler.*” See aioe Appendix D. In the@) charts and the nomograph for determining orale? an allowance for ship correla- | tion amounting to + 0.0004 has been made in accordance with the ATTC 1947 recommendation. Calculation forms for finding the © 400 ft and ehp values for any single-screw merchant ship having lines derived from the Series 60 contours and proportions within the range covered by the Series are also given in Appendix B. Methods are also described there for calculating © for a ship of other than 400-ft length and for including a ship correlation allowance C, having some value different from +0.0004. Although the calculation forms are largely self-explanatory, a numerical example is worked out in Appendix D to clear up any difficulties still remaining after reading the text. As stated on page V-14 the ITTC agreed in 1957 to the use of a new ‘*model-ship correlation line’’ in future published work. However, pending some agreement on a standard ship correlation allowance to be associated with the new line, it has not yet come into general use. The ITTC and ATTC lines differ both over the model and ship ranges of Reynolds number, and so affect the division of the model resistance into its ‘‘frictional’’ and “‘residuary’’ components, as weil as the values of the corresponding ones for the ship. It is thus not merely a question of using different values of fe ;; all the values of residuary | R resistance ae will be different also. Some riotes and an additional nomograph are given in Appendices D and E for readers who may wish to make estimates using the ITTC line. IX-2 CHAPTER X EFFECT OF VARIATIONS IN PROPELLER DIAMETER AND SHIP DRAFT AND TRIM A propeller diameter equal to 0.70 of the designed load draft was adopted as a standard in the LCB and geometrical variation series. Although this is fairly representative of average practice, there will be many occasions on which a different diameter will be necessary because of the design of machinery used or for other reasons. In order to give some guidance on this matter, each of the five parent models of Series 60 was run with additional propellers having diameters smaller and larger than the standard. Also, the main test program covered the models only at the full load draft and level trim. To get some information on the performance at other displacements and trims, additional experiments were made on three of the parent models, those with Cp of 0.60, 0.70, and 0.80. The stern arrangement was identical with that already described in Chapter VII and shown in Figure 36. The vertical dimensions are given there as functions of the designed draft or propeller diameter, and all longitudinal dimensions are given as functions of LBP. The propeller position is so defined that the generating line at 0.70 radius is 0.94 percent of the LBP forward of the after perpendicular. The stern details are therefore defined completely regardless of the selection of design draft or propeller diameter, so that Figure 36 defines the arrangement for all the models. The clearances were rather larger than normal practice at the time, but this was considered desirable in view of the ever-increasing horsepower of single- screw ships, and théir use has been justified by later developments. One method of achieving larger clearances or, alternatively, of using a larger diameter propeller without sacrificing clearance is to fit a semi-balanced rudder and no rudder shoe. This arrangement was fitted to the MARINER ships, and has become known as a ‘‘clearwater stern,”’ which is now used on many seagoing ships. In the course of the propulsion tests, the opportunity was taken to run the 0.60 Cp model with such a stern arrangement for com- parison with the normal streamlined rudder results. The standard propellers for the parent models had a diameter equal to 0.7 of the draft and have already been described in Chapter VII. For the experiments with larger and smaller diameters, propellers as similar as possible to the Troost type were selected from stock. The selection was made on a basis of general similarity, and the actual diameters of the propellers departed somewhat from the desired values. The selection of propeller characteristics was based on the assumption that diameter was fixed and revolutions could be chosen to obtain maximum efficiency. The values of expanded-area ratio were selected on the basis of current design practice and checked for suitability as to cavitation by Lerb’s data.4? Table 39 — Particulars of 600-Ft Ships Corresponding to Series 60 Models 0.60 0.70 0.80 600.0 600.0 600,0 600.0 600.0 80.0 82.76 85.71 88.89 92231 32.0 26.5%* | 20.6 33.14 34.29 28.0°° | 21.6t 35.55 36.93 30.0°° a2et 26349 | 21080 15810 | 30547 35289 | 28230 21170 | 40662 46774 | 37420 28060 a a a as 75) 2,50 3.02 6.75 2.50 2.50 Number of Blades Note: *LCB Measured from forward perpendicular + Previously used on Model 4278 ** Trim by stern = 1 percent LBP A Previously used on Models 4265, 4275 tTrim by stern= 2.5 percent LEP The details of the propellers and hulls referred to a ship length of 600 ft LBP are shown in Table 39. In fitting the different diameter propellers, the shaft cenierline was altered vertically to maintain the same vertical position of the blade tips at their lowest point in the disk, and so also the same minimum clearance between blade tips and the rudder shoe. This was considered to be the more practical approach rather than fitting all propellers to the same shaft elevation. In the latter case, the hull lines would have to be adapted to the largest propeller, with excessive clearances for the smaller ones, and with these any advantage inresistance which might result from a lower and longer cruiser stern would be lost. The end lines from Station 18 aft were modified to suit the different apertures, and the rudder area was kept constant by narrowing the rudders associated with the larger diameter propellers. The stern lines and aperture arrangements are shown in Figures 41 through 45, and the curves of power, wake, thrust deduction and other data in Figures 46 through 50. These figures all apply to ships of 600 ft LBP, as in the case of Chapters VII and VIII. The extrapolation used was the ATTC 1947 line, with a ship correlation allowance of +0.0004 During these tests, which chronologically were run before the LCB and geometrical variation series, turbulence was stimulated by studs and no bilge keels were fitted. The propulsion (Text continued on page X-il1.) X-2 BASELINE ees 25 ee | 195 198 194 19g 19 Figure 41 — Stern Lines for Propeller Diameter.Variations, 0.60 Block Parent (Model 4210) 1.50 WL 1.50 WL i enees \ Ee WaN\ \aaRN BASELINE a 4 cz BASELINE | 3 i | i AP 195 19g 19g 19g !9 185 Figure 42 — Stern Lines for Propeller Diameter Variations, 0.65 Block Parent (Model 4211) Figure 43 — Stern Lines for Propeller Diameter Variations, 0.70 Block Parent (Model 4212) 1,50 WL , (SOWL \ " L25 WL ‘\ oe 2B WL. ¢ SHAFT WL \ \ TANGENT— \ \ 1.00 WL Ss \ SEES O.75WL | ; Seer 0,50 WL a ce Biz | Be ai oa am hi aise 0.25WL Ps s2s flea HP BL | JS oT | 1.50 WL ALP | 3 95 IS9gl9y | i959 ist Figure 44 — Stern Lines for Propeller Diameter Variations, 0.75 Block Parent (Model 4213) X-4 1.50 WL oe 2 0.50 WL tle coal VN laste! | AP. I95 195 195195 19 Figure 45 — Stern Lines for Propeller Diameter Variations, 0.80 Block Parent (Model 4214) X-5 See He OF 502) 00 sO RPM & PROPULSION EFFICIENCY 8 N fe) (>) (e) 0.60 BLOCK PARENT (MODEL 4210) PROPELLER NO. 3375 ——--——-- PROPELLER NO. 2422 —-———— PROPELLER NO. 3378 RPM EHP SHP SHP Jy Ja Wr Wo EHP tH abd dpeedehsouGGngenceee pean 14 15 16 \7 18 19° 20° -2l 2 SPEED IN KNOTS 50,000 45,000 40,000 3,000 30,000 25,000 20,000 15,000 10,000 5,000 24 «25 Figure 46 — Power, RPM, and Coefficient Curves for 0.60 Block Parent, at Even Keel and Designed Displacement—Model 4210 X-6 HORSEPOWER 150 S$ = ® o OG °9O RPM & PROPULSION EFFICIENCY wo fo) 0.65 BLOCK PARENT (MODEL 42!1) PROPELLER NO. 3380 12 3 14 50,000 PROPELLER NO. 3375 ——--——-- PROPELLER NO. 2852 —-———— 45,000 40,009 RPM at 35,000 SHP 30,000 25,000 de 20,000 Ja 15,000 Wr Wo 10,000 EHP t 5,000 5 6 7 8 © [20 2 22 2 SPEED IN KNOTS | Figure 47 — Power, RPM, and Coefficient Curves for 0.65 Block Parent, at Even Keel and Designed Displacement—Model 4211 X-7 HORSEPOWER 12 0.70 BLOCK PARENT (MODEL 4212 40,000 PROPELLER NO: 2966 = o> es ee PROPELLER NO. 2852 ——— —— His aeeoo lO | PRPRORELEERGNOS SG Sansome ape o z Get ra ESI AaGeEEE Gay ig RPE PEE fate fea vend ese fede vas tests (dead eta ref 36,000 TOO 1 TU ST Hy Tage Ti TST EET TE ive B HEAT + 7 Wy a0 fox HT 1 a 90 ti WT H aicticll | He itt ty! ii i | i lita BET 34,000 Zz Beaiiedanian } HHRPM Z B BO fete Ste EE ate RE eae ee 132,000 — rat EF cad bs 3 i & ff , d0 © 70 #450,0 is : = 60 28,000 a. ttt 50 sua iniiia 26.000 40 : SHP 24,000 70 ie : 22,000 Jy 60 20,000 70 Ts 18 ,0OO Jo 60 16 000 30 al 414,000 W, 20 Hf | 12,000 W, cer FEE EEEEEEEE EE 30 : saiitians 10,000 Wo Ani a ed : 8,000 on Hb ee HH EHP : 5 seer eat honey an t}t35 fi Et me atu eect atte te het se tate HEHEHE] 6,000 10 ie atte a mth EB eee te 4 4,000 i ry fea ee i HEE it t Ltt i i rt it HHT ee : i AOR Tas SHeE OEE ed 2,000 : Fs HAH Hd : ae | File TH + att SPEED IN KNOTS Figure 48 — Power, RPM, and Coefficient Curves for 0.70 Block Parent, at Even Keel and Designed Displacement—Model 4212 X-8 HORSEPOWER 0.75 BLOCK PARENT (MODEL 4213) PROPELLER NUMBERS 140 3648 - 3066 —— --——_ i] Bee 30S 50,000 2828. ——-—_ —— = 120 0 110 45,000 100 RPM > [e) 2 w 90 40,000 ° Ww i 80 5 EHP oH 70 SHP 35,000 =I) =) S 60 ing a 6 50 30,000 = a a 40.70 ie TS * TEGO 25,000 © o a 70 S Ja ar.) 20,000 40 Wr wt .30 15,000 SHP 40 w Q 30 10,000 Wa .20 EHP 20 5,000 t 10 t e) ) (Ome diveniaarets 14, |S. Ligh: 47> IS" vI9)) eOnesor ico SPEED IN KNOTS Figure 49 — Power, RPM, and Coefficient Curves for 0.75 Block Parent, at Even Keel and Designed Displacement—Model 4213 X-9 0.80 BLOCK PARENT (MODEL 4214) i 40,000 PROPELLER NO. 2944 ———--——-- 100 PROPELEER NO: 1356) — =e Se sane PROPELLER NO. 3377 > ss ce EHE 36,000 = H SHP fs) moe 34,000 WwW 2 OQ 70 on shee % =) orn 30,000 oc a os 50 oe fe a ae 26,000 =e 24,000 60 se Ja Ja : 50 : ; W (2) 3 & 40 acon a i 16,000 uP ie 14,000 SHP a 12,000 We ann 10.000 - # 8,000 Wo EE OE 6,000 i t EHP es 4,000 t - ny a He 0 ieee Eaeetaa : 2,000 SE H EES ere F : f hee 9 0 WW if iB fa 6 6 7 8 19 SPEED IN KNOTS Figure 50 — Power, RPM, and Coefficient Curves for 0.80 Block Parent, at Even Keel and Designed Displacement—Model 4214 X-10 tests on the parent models with the propellers of standard diameter (= 0.7H) were run over a complete speed range, and those with the larger and smaller diameters were made only from speeds 10 percent below the service speed to 10 percent above the trial speed. The three parent models of 0.60, 0.70, and 0.80 Cp were run at two lighter conditions, with the standard propellers of diameter equal to 0.7H only. The conditions chosen were 60 and 80 percent of the load displacement. With the models in the lighter of these conditions, the propellers were just submerged at a speed about 10 percent below the service speed; this was considered essential if reliable wake data were to be obtained. In addition to tests on even keel, the models were also run at 80 percent of load displacement with a trim of 1 per- cent of the LBP by the stern and at 60 percent of load displacement with a trim of 2.5 percent by the stern. These were chosen after reference to much data in the records of the Maritime Administration. The results of the propulsion tests in these conditions are shown in Figures 51 through 53. Figure 54 shows the variation with diameter in the values of the propulsive coefficient and its various components for the five parent models. The trial and service speeds used throughout the presentation of these propulsion experiments are those derived on the Alexander basis given in Equation (1), page V-14. The wake fraction shown is the Taylor wake fraction calculated on the basis of thrust identity in open and behind the model. Having obtained actual wake fractions from these model experiments, estimates were made from the Troost design charts for Troost-type propellers for all the different conditions in which stock pro- pellers had been used. These showed that any increase in propeller efficiency which would result from such a change was quite small—on the average less that 0.5 percent, the maximum being 1.1 percent. | Figure 55 shows the propulsive efficiency factors plotted against block coefficient. Figure 55b for the standard propellers represents actual test data. The results given in Figures 55a and 55c are for the smaller and larger diameter propellers, respectively, modified to suit the variation of diameter with block coefficient shown in Figure 56. Similar curves for the 80- and 60-percent displacement conditions are shown in Fig- ure 57. In the 60-percent condition for the 0.60 Cp model, even keel, there was some indi- cation that air was being drawn into the propeller, and it is significant that the wake curve for this model appears to be inconsistent with the other data. The principal reasons for running the experiments described in this section were to compare the propulsive performance of the parents with existing modern designs of ships and to give the practicing naval architect guidance on the general effects on propulsive efficiency of changes in propeller diameter, in ship displacement, and in trim. As to the first of these, comparisons were made between models of the SCHUYLER OTIS BLAND and PENNSYLVANIA and their Series 60 counterparts. The corresponding pairs of models were run under as nearly similar conditions as possible. Thus the Series 60 sterns were modified to give the same aperture and rudder arrangements as in the actual (Text continued on page X-18.) X-11 Ja Wr gle Xx vlo o (©) 120 110 100 RPM 90 80 0.60 BLOCK PARENT (MODEL 4210) (iL PROPELLER NO. 3378) Soh PE EBUBE ROE iceecdRaHEa eee PRUHAEEAEEEaEE (yi |: a ee TARE aay a ted LH EA UE LETTE aE A fpr 4b 7 : HRAREE ESSN qd F THe if ASUREeeOER eee HH EH tye {| a Hat 4 i cept a F iy q E Hy FB rt : i Y ht Wel al E a t 4+SHP EHP ISHP EHP. RPM 80% DISPLACEMENT TRIM |! % OF LBP BY STERN EVEN KEEL 2l 22 23 24 25 SPEED IN KNOTS EHP DISPLACEMENT TRIM 22% LBP BY STERN| 2,000 EVEN KEEL. 24 Hit 30,000 1 28,000 26,000 24,000 22,000 20,000 18,000 16,000 14,000 12,000 10,000 8,000 6 000 4,000 25 Figure 51 — Power, RPM, and Coefficient Curves for 0.60 Block Parent at Light Displacement Conditions X-12 HORSEPOWER _| 0. 70 BLOCK PARENT (MODEL 4212) 2 PROPELLER NO ae ‘tte + Ge Jo sR SE et Wy Wo .20 st : t af ll ; 10 foals Fades sazestasei tees t ps Seas beeaseece se bessegueks pessgeeeeeae at pos ageeanl f hit eo He eH EHP aso SERGE ir iat ag Har ee SHP i : 4 EHP sever sees easstin new fe a : SHP 70 faaEaaee seaed Sesasece ana : = t+ crt Sao = See ee tera ae pee HE HP wtp = be pe ete seeeeeeee 90 fa areitreiar et age gebasecay tore? soap raz caer abou? cape tee 80 ie ee ais uote! = a6 ass 6 Geese breeecia Q epee t an cr 170 : : Heeb alte eats pails Pails aee ae Sead pede eos foto agase Page otzoa dag aore stint sees est ateemtatecs 80% DISPLACEMENT [2j2)f454) oS 160% DISPLACEMENT [i= 60 TRIM | % OF LBP BY STERN att ae TRIM 22% LBP BY STERN EVEN KEEL Hy iru EVEN KEEL IG) ir "18? B19" 20" “I 6 7 8 9 2 2 SPEED IN KNOTS 22,000 20,000 | 8,000 16,000 14,000 12,000 10,000 8,000 Figure 52 — Power, RPM, and Coefficient Curves for 0.70 Block Parent at X-13 Light Displacement Conditions HORSEPOWER qo ee BLOCK PARENT (MODEL 4214) oe NO. 3377 vee feed teat = a ona stele at} ; mars aes Saga awe a ba UA a n i ‘eggs 29 Ra Shaye Bie tein —- fakes a sal man sgt edges eal eet eee eet pte et Fee ee pote a ere te eee fe] | deel heed SREP Sea ate sci ieee iene ES H H ai ETE ais 3 pefel tt aioe 2 Oeees oe fie : 6,000 fi os HH = ee 2,000 iH 12 3 14 15 16 i 12 13 “14 15 16 Figure 53 — Power, RPM, and Coefficient Curves for 0.80 Block Parent at Light Displacement Conditions X-14 HORSEPOWER 1N39I34309 49018 020 ‘ S}USTOTJJEOD YAIOT OL'O PUS S9°0 41N39153309 49018 S90 ‘ 09'0 — BPs emary LN39144509 H9071E 09'0 1334 NI ¥aL3SWVIG ¥3a714ad0ud Q33dS 39IAY3S — Q33dS 1VI¥L JOJOW VIG SNSIOA ssojoB’y AousIoIJjy OATS[ndoig — Fg oinsdIy S3S9VLN3S9U3d X-15 WatI1JJ20D AT O8'O Pue SZ‘0 — APS emt 1333 NI Y3L3NVIO ¥3113d0¥d 82 92 1333 Ni Y3L3WVIG ¥37173d0ud 92 be 22 02 — 033dS$ 33IAY3S G33dS WIML ae 02 : O ae ies eo. —— 033dS 39IAYN3S ee EEE TAARE BE S39VLN3IIN3d X-16 JUSLOIJJOOD YOo[Y snsioa siojyoeq Aousoijjy eatstndoig — Gg ond y Ja}awerq ediey oy — IG¢g aindtTy Jajawmerqd JeUIO, JO — qgg aindtTy Jajawerg [Jews Joy — Bog amary 1N391343309 99018 41N39133300 9018 4N39143309 49018 1N391345309 49018 080 sZo 020 s90 090080 iV fe) 020 S90 09008°0 sZo 020 s90 o9':0080 S20 0O ‘ os | oe | 0Oo| | Ot ae a) os co oe O2l —— 033dS 39!IAN3S — — 033dS 1VIdL Ovi x 2 . Es 2 a - ogl X-17 S39VLN390U3d TABLE 40 Comparison of Series 60 Propulsion Results with Actual Ships Series 60 SCHUYLER Equivalent of OTIS BLAND SCHUYLER OTIS BLAND as Built Series 60 Equivalent of PENNSYLVANIA PENNSYLVANIA Represeating SSeBuilt shp ehp/shp ships, and the model propellers used were made to the designs fitted to the ships. The results given in Table 40 show that the performance of the Series 60 designs was very comparable with that of the two ships. The designer can find the wake and thrust deduction fractions for any ship within the limits of the series and fitted with the standard diameter of propeller from the contours) in Appendix B. The results given in this | PROPELLER DIAMETER IN FEET chapter will enable him to make estimates of the probable change in these and other factors when it is necessary or desirable to use larger or smaller propellers, and also for conditions of tighter displacement with or without trim. Figure 56 — Variation of Diameter with Cp It is not intended here to attempt to draw any overall conclusions regarding the variation of the propulsive factors. The data given can be applied to individual designs or used by the naval architect for his own research purposes to set up his own methods of estimating such coefficients for future use. Much addi- tional information is included in Reference 61 for those. who wish to study this part of the work in more detail. X-18 PERCENTAGES 5000 690770. «79.7; "80 160), .:65) 9:70" 75) 80 BLOCK COEFFICIENT BLOCK COEFFICIENT 80 % DISPLACEMENT 60% DISPLACEMENT Figure 57 — Propulsive Efficiency Factors at Light Displacements PERCENTAGES One other comparison made in the course of these tests is of general interest. A number of modern single-screw ships, including the MARINER class, have been fitted with | propeller to be fitted without sacrifice of clearances or, conversely, larger clearances on | a semi-balanced rudder and norudder shoe. This arrangement enables a larger diameter the same diameter, both very desirable features in view of the large powers now being trans- _ mitted through a single shaft and the accompanying risk of propeller-excited vibration. In the endeavor to obtain such clearances with the normal single-screw aperture and rudder, the rudder shoe has become longer and more vulnerable, and a number of fractures have occurred, so that on this score also the new arrangement, generally known as a ‘‘clearwater stern,”’ has something to offer. The stern arrangements of the Series 60 parent of 0.60 Cp with the normal and clear- water sterns are shown in Figure 58, and the results of the model propulsion tests in Figure | 59 and Table 41. At a service speed of 22 knots, there is no noticeable difference in propeller performa) The shp is higher for the conventional stern only because of its higher ehp, and this | persists throughout the speed range. TABLE 41 Comparison of Clearwater and Conventional Sterns on 0.60 Cp Model 4210 of Series 60 (Principal dimensions: 600 ft x 80 ft x 32 ft x 26,349 tons) Stern Arrangement | Normal | Clearwater Propeller Number 2422 1967 Deeatt 25.62 25.33 eat 25.62 26.67 BAR 0.456 0.464 Rake, deg 6.9 6.0 Number of blades V, knots shp ehp/shp (OLSF [OPOW) JUeI’g YOO[ 090 JO} sjuowesueIIy uloIS — gE ond gy v | 3NI13SVa JNiIn3SvVa SSS 7] Ova N IMOO'! . 1M G2'1 s 1M S2'l TVNOILNSANOD —— — Y3LVMYV3I19 1M OG’! 1M OS‘! RPM & PROPUSION EFFICIENCY 0.60 BLOCK PARENT (MODEL 4210) 150 PROPELLER NO. 2422 (CONVENTIONAL STERN) PROPELLER NO. 1967 (CLEARWATER STERN) amc 1ZOr L. / Oo) ————— 100 |——_—_______—__ om Pains 0/0 N N PA ee \J N sa Pas (ies : f 3) Cy SEY ESSE) il HAE 5 eet VE Vy Se .30 4 pa eee es 20 PD - #4 30+ T | Wo 20: —S J pedkeot 10 | Mica 202i 22 es ete 2 wi SPEED IN KNOTS Bis : 50,000 45,000 40,000 35,000 8 g 25,000 8 8 15,000 10,000 5,000 HORSE POWER Figure 59 — Power, RPM, and Coefficient Curves of Clearwater and Conventional Sterns for 0.60 Block Parent—Model 4210 CHAPTER XI EFFECT OF VARIATION IN AFTERBODY SHAPE UPON WAKE DISTRIBUTION AND POWER The original conception of Series 60 was a‘set of related basic hull forms which, in terms of fullness and proportions, would cover the general field of single-screw merchant ships. The principal purpose was to indicate the trends which might be expected in resistance and power by changes in these basic parameters, but it was also realized that the results were likely to be used for making power estimates for new designs. It was therefore necessary that the resistance and power characteristics of the series models should be of reasonably good standard, and an effort was made to ensure this by the preliminary work with Series 57 and the later comparisons with models of existing ships of accepted good performance.®?+63 On the other hand, any effort to explore all the possible changes of shape in waterlines and sections before embarking on the series proper would have been prohibitive both in time and money. One of the objectives in setting up the Series 60 design contours has always been the hope that they would be used as a point of departure in future research so that there would always be a link with new work, and this hope has been in a large measure fulfilled. The variation of hull shape as exemplified by changes in waterline and section shape is one such research which could well begin from Series 60 as a basis, and a start on this phase has been made at Taylor Model Basin. Since a great deal of interest has been gener- ated in recent years’in the effects of afterbody shape upon the wake distribution, propeller- excited forces on the hull, and horsepower, the first experiments covered the measurement of wake pattern behind the five parent models, together with the effect upon wake pattern and power of two additional models of 0.70 block coefficient having, respectively, more U- and more V-shaped afterbody sections than the parent. This work was sponsored by the Bureau of Ships, the Maritime Administration and SNAME, and carried out at the Taylor Model Basin. The results have been given in detail in Reference 64. The parent 0.70 block coefficient model was No. 4280, made in wood, and identical as regards lines with the parent wax model No. 4221. Two additional wooden models, No. 4281 and No. 4282, were made with the same forebody, identical with that of No. 4280, but with more U- and more V-Type stern sections, respectively. The section area curve, load water- line (WL No. 1.00), deck waterline (WL No. 1.50), and stern profile remained unchanged. As a result, all coefficients of form and dimensions except those related to wetted surface and section shape are the same for all three models (Table 42). A comparison between the after end sections is shown in Figure 60. Table 42 also includes values of a coefficient 7 to describe the slope of Station 18 at the level of the propeller shaft. This coefficient was 3 65 : : first proposed by Harvald "and is measured as shown in Figure 61. Average values of T XI-1 Table 42 — Principal Particulars of Models 400-ft ship 600-ft ship Tew reek te ie euansll ncuneer rete) cota tenn ieee Compa nameless 406.7 610.0 Y BG paves § Sal ae reteset REE Ural pd 400.0 600.0 BCR Hs Memcscpeen Oh cy cheat Sud ates dere ae Te oe ens 57.14 85.71 ET EG aah oe es tn, cha eetun eealeyene on eckee ats eer aremeiiene vs 22.86 34.29 PANGS Co) vos ores Oo Lonel Py shane eter rane Way tea 10456 35289 Dp CBg LEB orale yor 8 oete fen as Seser ae ee eae ieee RRS 11.6 11.6 *WS, sq ft, (Model 4280).................. 31859 71683 *WS: sqft? (Model’4281). 20. ae. 32008 72018 *WiS, sqft; CModel!4282))) 22 228). sue ss 31759 71458 Hull Coefficients WEY Baise secrete tate ss 7.00 ABB PET en See Reve age cde 2.50 By BIO eRe ie sratteters 5.593 Catasee 0.700 Opry naverteeies 0.890 AY GE / M00) Boece: 163.4 Cx ENS een 0.986 Cpvr......... 0.950 S/V213 (4280) ae see cis 6.230 Cras ee 0.710 Cpva......... 0.846 S/N 28 (4281) eat 6.260 Cpr. cc: 5 «) 04760 Gwe ee 0.787 SAV 21804282) neem a 6.210 ( OF Natrona 0.721 OCW. oso sch 0.734 EE/E gp cn ae cca. (O420 Crr.... ... 0.642 (OW) Caren is Be 0.841 EExd Lp penctessia © eran: 0.119 CPR aqsneteneses 0.698 Cities ree 0.651 ER PE RP Ace rie el see ee 0.461 LCB, per cent LBP from ( 0.55A * Does not include rudder. Section Coefficient + Series 60—Forms Parentiformy, «cece Model 4280: 7 = 0.359 U-shaped form...... Model 4281: r = 0.179 V-shaped form...... Model 4282: rt = 0.543 Average Values Moderate/stern)sections: ...... suacdcs seme elon tote zr = 0.500 Extreme U-shaped stern sections.................... 7 = 0.20 Extreme V-shaped’ stern sections:)./.....).....3..0. rt = 0.75 1.50 WL 1.00 WL PROPELLER SHAFT | | } BASELINE ) \\ T q V\\ \ LY | ~ \ \ ea C7 Si WIE io'g PEN NN NEN NSS KAY al 8 — SS SOS panent roma MODEL 422° (1957 WAX) _ — t U - FORM MODEL 4281 —— — = = Vv - FORM MODEL 4282 Figure 61 — Definition of Section Shape 1 i . Coefficient Figure 60 — Comparison of Afterbody Lines Cored of 0.70 Block Parent Stern Variations XI-2 | | from a number of existing designs are also given in Table 42, and these show that the Series | 60 parent of 0.70 Cg is somewhat U in character to start with, and the V-shaped variation is rather moderate in this respect. The models were fitted with rudder and propeller as previ- | ously described, the propeller used being TMB 3376 which was that fitted to the original 0.70 Cp parent, Model 4221. It represented a 24-ft diameter propeller on a 600-ft ship (or (16 ft on a 400-ft ship). | Models 4280, 4281, and 4282 were all made in wood, had an LBP of 20 ft, and a smooth enamel finish. They were fitted with a trip wire and run in the deep-water basin which is 51 ft wide and 22 ft deep. Experiments were made at the designed displacement, level trim, and at 60 percent of this displacement and a trim of 2.5 percent of LBP by the stern. The results of the resistance and propulsion tests are given in Tables 48 through 48 and in Figures 62 through 70. The change in resistance, as shown in Figures 62 to 65, is relatively small, the U- form being about 2 percent worse and the V-form 3 percent better than the parent at the Troost service speed. On the other hand, the U-form favors the propulsive efficiency, but this ‘is insufficient to offset the superior resistance qualities of the V-stern, with the result that the latter has the lower dhp at all speeds in the full-load condition and over most of the speed range at 60-percent displacement. These changes in resistance and propulsive efficiency are of the kind to be expected as a result of such stern changes. In general, the increase in propulsive efficiency with the U-stern is usually sufficient to more than offset the increase in resistance, although not in this particular case. Velocity surveys were also made in the plane of the propeller for all five of the Series 60 parents and for the two stern variations of the 0.70 Cp model. This plane was normal to the propeller shaft (and to the baseline) and 0.94 percent of the LBP forward of the after perpendicular. In accordance with the stern arrangement shown in Figure 36, it passed through the 0.7 radius point on the propeller generating line. The velocities were measured at 59 points over a rectangular grid extending from the baseline to a waterline at 0.85 of the load draft and on the port side from the centerline out to a vertical line distant 0.425 of the load draft. They were all made at the full-load displacement and at the Troost,service speed, using a 5-hole spherical pitot tube, which determines the velocity vector at each point (for details, see Reference 64). Tiiese velocities have been analysed into longitudinal (fore and aft), vertical and horizontal components V_, V,,, and V,, defined as shown in Figure 71. These can be con- verted to Taylor wake fractions Vy Doe — eee 1100) a V Vs w, = 1- y 100 Vi and w, = 1- —y1 h V 00 Table 43 — Results of Resistance and Self-Propulsion Experiments for Parent Form— Model 4280, 100-Percent Displacement v/vig, &x10° ®©) © vvt,, VN SBP W, t oo © ©, EHP/SHP 0.80 9.825 0.755 0.708 0.824 6.0 89.7 1917 0.898 0.907 1.180 0.618 0.971 0.702 0.85 8.701 0.881 0.698 0.364 9.0 28.5 1698 0.8830 0.204 1.188 0.651 0.972 0.752 0.40 8.762 1.008 0.690 O405 10.0 40.8 158 0.898 0.199 1.192 0.652 0.995 0.773 0.45 2.728 1.188 0.680 0.445 11.0 44.6 9788 0.880 0.197 1.181 0.657 1.004 0.779 0.50 8.719 1.258 0.678 0.488 19.0 48.6 8606 0.815 0.194 1.177 0.660 1.004 0.780 0.55 2.724 1.884 0.681 0.528 18.0 652.7 4645 0.818 0.192 1.176 0.662 0.998 0.777 0.60 2.787 1.510 0.697 0.568 14.0 87.8 6908 0.810 0.190 1.174 0.668 0.998 0.773 0.65 2.840 1.686 0.710 0.607 15.0 61.5 7886 0.807 0.192 1.165 0.668 0.998 0.767 0.70 2.890 1.761 0.722 0.628 15.5 68.7 8212 0.806 0.195 1.160 0.661 0.998 0.765 0.75 9.900 1.887 0.747 0.648 16.0 66.1 9093 0.805 0.198 1.154 0.659 1.008 0.768 0.800 8.216 2.018 0.804 0.668 16.5 68.5 10100 0.805 0.199 1.151 0.658 1.004 0.761 0.825 8.308 2.076 0.838 0.688 17.9 70.7 11180 0.808 0.200 1.148 0.657 1.006 0.759 0.85 8.412 2.189 0.858 0.708 17.5 78.2 12390 0.808 0.200 1.146 0.655 1.009 0.758 0.875 3.682 2.202 0.920 0.729 18.0 75.8 13740 0.801 0.200 1.144 0.658 1.010 0.756 9.90 4.367 2.265 1.086 0.749 18.5 78.8 15350 0.800 9.200 1.148 0.6528 1.011 0.758 0.925 GALL. 428271), 1.277 0.769 19.0 81.2 17150 0.800 0.201 1.141 0.649 1.018 0.750 0.950 6.028 2.890 1.506 0.790 19.5 84.0 19200 0.299 0.202 1.188 0.645 1.016 0.748 0.975 6.997 2.458 1.749 0.810 20.0 87.1 21380 0.298 0.208 1.185 0.642 1.016 0.740 1.000 7.857 2.616 1.964 0.880 20.5 90.4 28840 0.297 0.205 1.181 0.685 1.019 0.738 1.025 8.592 2.579 2.147 0.851 21.0 93.8 26890 0.296 0.207 1.126 0.628 1.018 0.720 1.050 9.088 2.642 2.271 0.871 21.5 98.0 31160 0.204 0.208 1.122 0.618 1.018 0.708 1.075 9.28! 2.705 2.820 0.891 22.0 108.1 37580 0.298 0.208 1.120 0.602 1.024 0.691 1.10 9.311 2.768 2.829 1.195 9.200 2.881 2.299 (All numbers are for ship of 600-ft LBP) 1.180 8.901 2.894 2.247 1.175 8.792 2.957 3.197 1.20 8.724 3.019 3.180 1.295 8.789 3.082 2.197 (All numbers are for ship of 400-ft LBP) Table 44 — Results of Resistance and Self-Propulsion Experiments for U-Shaped Form— Model 4281, 100-Percent Displacement Wyly, C,x10° (Kk) © VW/VUg, V NSHP W, t e, e, ¢, EHP/SHP 0.30 2.868 0.755 0.720 0.324 8.0 821 1178 0.858 0.198 1.257 0.885 0.982 0.744 0.35 2.821 0.881 0.708 0.364 9.0 86.0 1575 0.367 0.190 1.260 0.681 0.987 0.797 0.40 2.788 1.006 0.699 0.405 10.0 39.8 2078 0.366 0.188 1.281 0.688 1.009 0.818 0.45 2.757 1.182 0.692 0.445 11.0 48.8 2692 0.851 0.185 1.956 0.645 1.015 0.822 0.50 2.784 1.958 0.686 0.486 12.0 47.8 8467 0.843 0.181 1.247 0.650 1.014 0.822 0.55 2.754 1.884 0.692 0.526 «13.0 51.8 © 4428-«-0.848 «—«0.178-1.251 0.649 1.011 _—0.821 0.60 2.885 1.510 0.712 0.566 14.0 58.0 5611 0.848 0.179 1.250 0.648 1.012 0.820 0.65 2.890 1.686 0.726 0.607 15.0 60.4 7072 0.848 0.181 1.247 0.644 1.019 0.819 0.70 2.955 1.761 0.742 0.628 15.5 62.8 7918 0.843 0.184 1.242 0.643 1.028 0.817 0.75 8.082 1.887 0.774 0.648 16.0 65.0 8809 0.848 0.187 1.287 0.642 1.026 0.815 0.80 8.281 2.018 0.824 0.668 16.5 67.4 9744 0.841 0.188 1.232 0.641 1.029 0.818 0.825 8.371 2.076 0.846 0.688 17.0 69.7 10790 0.841 0.188 1.280 0.640 1.080 0.811 0.850 8.472 2.189 0.872 0.708 «17.5 += 72.1 «11880 0.889 ©««0.188-«:1.228 (0.636 «1.037 ~—-0.810 0.875 3.780 2.202 0.949 0.729 «18.0» 74.5 18220 0.888 + 0.188 1.227 0.685 1.086 0.807 0.900 4.367 2.965 1.097 0.749 «18.5 += 77.1.«:14810 (0.887 ~=—«0.189 1.228 0.688 «1.038 ~=—«0.804 0.925 5.261 2897 1.321 0.769 19.0 79.8 16540 0.336 0.189 1.221 0.628 1.043 0.800 0.950 6.156 2.390 1.546 0.790 19.5 82.5 18430 0.885 0.190 1.218 0.625 1.044 0.795 0.975 7.191 2.458 1.806 0.810 20.0 85.6 20880 0.884 0.191 1.215 0.620 1.046 0.788 1.000 8.017 2.516 2.018 0.830 20.5 88.7 229740 0.882 0.198 1.208 0.618 1.041 0.777 1.025 8.762 2.579 2.200 0.851 21.0 92.4 25910 0.380 0.195 1.201 0.609 1.046 0.765 1.050 9.168 2.642 2.801 0.871 21.5 96.8 30450 0.898 0.195 1.189 0.600 1.051 ~ 0.750 1,075 9.893 2.705 2,841 0.891 22.0 102.1 36700 0.826 0.195 1.194 0.588 1.045 0.734 1.100 9.8387 2.768 2.844 z 1225 9.200 2.881 2.810 (All numbers are for ship of 600-ft LBP) 1,150 8.991 2.894 2.258 1.175 8.792 2.957 2.208 1.200 8.724 3.019 2.190 1.225 8.789 8.082 2.207 (All numbers are for ship of 400-ft LBP) XI-4 Table 45 — Results of Resistance and Self-Propulsion Experiments for V-Shaped Form— Model 4282, 100-Percent Displacement Ve, C,x1° ®© © Vlg, V ooN SHP We t 0 © , EHP/SHP 0.80 2.746 0.755 0.684 0.824 8.0 82.7 1184 0.323 0.229 1.189 0.652 0.945 0.702 0.85 2.736 0.881 0.679 0.864 9.0 86.7 1590 0.384 0.228 1.159 0.648 1.001 0.752 0.40 2.697 1.008 0.673 0.405 10.0 40.5 2098 0.384 0.226 1.162 0.649 1.025 0.773 0.45 2.657 1.182 0.662 0.445 11.0 44.6 2691 0.820 0.222 1.144 0.660 1.032 0.779 0.50 2.614 1.258 0.651 0.486 12.0 48.6 3480 0.814 0.220 1.187 0.663 1.035 0.780 0.55 2.635 1.884 0.657 0.526 18.0 52.8 4475 0.815 0.219 1.140 0.662 1.029 0.777 0.60 3.703 1.510 0.678 0.566 14.0 57.1 5717 0.814 (0.219 »=«-1.188 §=0.660 ~=—-11.029 0.773 0.65 2.758 1.6386 0.687 0.607 15.0 61.5 7175 0.811 0.220 1.182 0.660 1.025 0.766 0.70 3.788 1.761 0.695 0.628 15.5 63.7 7976 «0.308 0.220 1.127 0.660 1.027 0.764 0.75 2.874 1.887 0.716 0.648 16.0 66.1 8871 0.306 0.221 1.122 0.660 1.026 0.760 0.80 8.119 2.018 0.777 0.668 16.5 68.5 9797 0.804 0.224 1.114 0.659 1.031 0.757 0.825 8.203 3.076 0.798 0.688 17.0 70.6 10800 0.804 0.227 1.111 0.658 1.033 0.755 0.850 8.312 2.189 6.825 0.708 17.5 78.2 12000 0.803 0.229 1.108 0.657 1.033 0.751 0.875 8.592 2.202 0.895 0.729 18.0 75.8 18300 0.801 0.282 1.099 0.653 1.040 0.747 0.900 4.127 2.265 1.028 0.749 18.5 78.8 14800 0.801 0.234 1.0968 0.651 1.043 0.744 0.925 4.969 2.827 1.238 0.769 19.0 81.2 16620 0.802 0.237 1.093 0.648 1.044 0.739 0.950 5.876 2.390 1.464 0.790 19.5 84.0 18600 0.8308 0.238 1.093 0.642 1.047 ).735 0.975 6.851 2.458 1.707 0.810 20.0 87.1 20900 0.804 0.289 1.098 0.635 1.050 0.729 1.000 7.697 2.516 1.918 0.880 20.5 90.4 23450 0.804 0.240 1.092 0.628 1.051 0.721 1.035 8.472 2.579 2.111 0.851 21.0 93.8 26530 0.804 0.240 1.092 0.620 1.050 0.711 1.080 9.008 2.642 2.244 0.871 21.5 98.0 80820 0.805 0.241 1.092 0.610 1.046 0.697 1.075 9.203 2.705 2.298 0.891 22.0 103.0 87040 0.805 0.241 1.092 0.597 1.048 0.680 EeLOO) 9-181 512-768" (2.268 (All numbers are for ship of 600-ft LBP) 1.125 9.040 2.881 2.252 1.150 8.831 2.894 2.200 1.175 8.647 2.957 2.154 1.200 8.558 8.019 2.181 1.225 8.579 3.082 2.188 (All numbers are for ship of 400-ft LBP) Table 46 — Results of Resistance and Self-Propulsion Experiments for Parent Form— Model 4280, 60-Percent Displacement, Trim 2% Percent Lp p by Stern VAN, CC, x 103 ) © V/ty, OC N SHP WL t ey e, ®,, | EHP/SHP 9.30 2.886 0.822 0.794 0.324 8.0 29.2 851 0.393 0.210 1.302 0.654 0.975 0.830 0.35 2.837 0.959 0.781 0.364 9.0 32.9 1201 0.393 0.207 1.306 0.653 0.979 0.835 0.40 2.810 1.096 0.774 0.405 10.0 36.6 1605 0.390 0.205 1.303 0.654 0.984 0.839 0.45 2.795 1.233 0.769 0.445 11.0 40.2 2061 0.384 0.204 1.292 0.661 0.984 0.840 0.50 2.774 1.370 0.764 0.486 12.0 44.2 2703 0.376 0.202 1.278 0.663 0.995 0.843 0.55 2.809 1.507 0.773 0.526 13.0 48.0 3438 0.366 0.200 1.262 0.669 0.998 0.843 0.60 2.857 1.644 0.786 0.566 14.0 52.2 4338 0.356 0.200 1.242 0.671 1.008 0.840 0.65 2.902 1.781 0.799 0.607 15.0 56.6 5462 0.347 0.201 1.224 0.672 1.011 0.832 0.70 2.967 118 0.817 0.628 15.5 58.8 6121 0.343 «40.203 «1.213 0.672 1.014 0.827 0.75 3.029 2.055 0.834 0.648 16.0 61.0 6839 0.339 0.204 1.204 0.672 1.914 0.821 0.80 3.089 2.192 0.850 0.668 16.5 63.2 7645 0.337 0.207 1.196 0.672 1.016 0817 0.825 3.153 2.260 0.868 0.688 17.0 65.4 8473 0.334 0.210 1.186 0.672 1.017 0.811 0.850 8.272 2.829 0.901 0.708 17.5 67.6 9338 0.831 0.212 1.178 0.672 1.019 0.807 0.875 3.492 2.397 0.961 0.729 18.0 69.8 10250 0.3828 0.218 1.171 0.672 1.023 0.805 0.900 3.847 2.466 1.059 0.749 18.5 72.1 118380 0.326 0.215 1.165 0.672 1.022 0.800 0.925 4.261 2.584 1.178 0.769 19.0 74.5 12470 0.323 0.217 1.156 0.671 1.026 0.796 €.950 4.681 2.608 1.289 0.790 19.5 76.9 13680 0.321 0.220 1.149 0.669 1.029 0.791 0.975 5.121 2.672 1.410 0.810 20.0 79.2 15060 0.321 0.222 1.146 0.668 1.028 0.787 1.000 5.539 2.740 1.525 0.830 20.5 81.8 16650 0.320 0.228 1.148 0.667 1.027 0.782 1.025 5.852 2.808 1.611 0.851 21.0 84.7 18660 0.319 0.223 1.141 0.662 1.028 0.776 1.050 5.966 2.877 1.642 0.871 21.5 88.0 21390 0.318 0.222 1.141 0.654 1.029 0.768 1.075 6.038 2.945 1.662 0.891 22.0 92.2 24960 0.817 0.220 1.148 0.643 1.026 0.A 1.100 6.100 3.014 1.679 0.911 92.5 97.0 29740 0.314 0.216 1.143 0.632 1.020 0.737 1.125 6.157 3.082 1.695 0.932 23.0 102.4 55360 0.310 0.212 1.142 0.619 1.017 0.719 1.150 6.210 8.151 1.710 1.175 6.300 3.219 1.784 1.200 6.450 3.288 «1.776 1.225 6.669 3.356 = 1.836 (All numbers are for ship of 600-ft LBP) (All numbers are for ship of 400-ft LBP) XI-5 Table 47 — Results of Resistance and Self-Propulsion Experiments for U-Shaped Form— Model 4281, 60-Percent Displacement, Trim 2 % Percent Lp p by Stern vivo, C, x10? ({«) © vvi,, VY oN SHIP WwW, t oo 0 «@, ENP/EP 0.30 2.986 0.822 0,822 0.324 6.0 8620.1 682 0.396 0.150 1.407 0.658 0.958 0.680 0.85 2.933 0.959 0.807 0.364 9.0 82.7 1185 0.809 0.165 1.408 0.652 0.9638 0.883 0.40 2,928 1.096 0.805 0.405 10.0 86.3 594 0.398 0.159 1.897 0.6538 0.970 0.885 0.45 2.917 1.283 0.803 0.445 11.0 40.0 2046 «(0.894 0.164 1.878 0.655 0.988 0.688 0.50 2.894 1.370 0.797 0.486 12.0 48.6 2678 0.890 0.168 1.864 0.688 0.992 0.691 0.55 2.913 1.507 0.802 0.526 18.0 47.6 8484 0.886 0.173 1.847 0.657 1.006 0.680 0.60 2.962 1.644 0.815 0.566 14.0 51.7 4820 0.888 0.177 1.882 0.656 1.017 0.869 0.65 3.002 1.781 0.826 0.607 15.0 55.9 5480 0.877 0.181 1.815 0.657 1.021 0.882 | 0.70 38.070 1.918 0.845 0.628 15.5 58.1 6088 0.874 0.184 1.804 0.687 1.028 0.878 ) 0.75 3.142 2.055 0.865 0.648 16.0 60.2 6736 0.870 0.187 1.290 0.656 1.080 0.872 | 0.80 38.218 2.192 0.884 0.668 16.5 62.4 7495 0.867 0.189 1.281 0.656 1.082 0.867 | 0.825 8.258 2.260 0.897 0.688 17.0 64.6 8273 40.864 0.102 1.270 0.656 1.085 0.862 } 0.850 3.965 2.329 0.926 0.708 17.5 66.6 9122 0.360 0.105 1.288 0.657 1.039 0.650 : 0.875 3.632 2.397 1.000 0.729 18.0 69.0 10060 0.857. 0.197 1.249 0.658 1.040 0.885 0.900 4.017 2.466 = 1.106 0.749 18.5 71.2 11040 0.354 0.199 1.240 0.658 1.044 0.868 0.925 4.451 2.584 1.225 0.769 19.0 73.6 12110 0.351 0.208 1.230 0.657 1.052 0.060 0.950 4.904 2.603 1.350 0.790 19.5 76.0 18820 0.849 0.205 1.221 0.657 1.084 0.846 0.975 5.356 2.672 1.474 0.810 20.0 78.5 14630 0.847 0.208 1.218 0.653 1.0860 0.640 1.000 5.759 2.740 1.585 0.830 90.5 81.0 16300 0.3846 0.210 1.208 0.652 1.056 0.838 1.025 6.025 2.808 1.658 0.851 21.0 64.0 18210 0.846 0.210 1.208 0.64% 1.052 0.888 1.050 6.158 2.877 1.695 0.871 21.5 87.4 20870 0.347 0.311 1.208 0.638 1.058 0.618 1.075 6.242 2.945 1.718 0.891 23.0 91.5 24510 0.347 0.210 1.210 0.627 1.064 0.800 1.100 6.287 3.014 1.730 0.911 $3.6 926.2 29210 0.346 0.207 1.212 0.610 1.058 0.768 1.125 6.317 8.088 1.789 0.932 28.0 101.8 85050 0.343 0.208 1.218 0.599 1.044 0.759 1.150 6.371 3.151 1.754 1.175 6.477 $.219 1.788 (All numbers are for ship of 600-ft LBP) 1,200 6.648 3.288 1.830 1.225 6.892 3.358 LAagz (All numbers are for ship of 400-ft LBP) Table 48 — Results of Resistance and Self-Propulsion Experiments for V-Shaped Form— Model 4282, 60-Percent Displacement, Trim 2’, Percent Lp p by Stern W/Viy, C,x 10? (®) © 0.80 2.754 0.622 0.759 0.35 2.711 0.959 0.747 Wig, V NSHP Wy t ©, = y= EI P/BP 0.40 2.668 1.096 0.7835 0.324 8.0 29.9 818 0.847 0.246 1.155 0.678 1.018 0.798 0.45 2.643 1.288 0.728 0.364 9.0 34.0 1168 0.846 0.246 1.158 0.672 1.088 0.800 0.50 2.651 1.870 0.780 0.405 10.0 37.6 1560 0.843 0.946 1.158 0.672 1.088 0.804 0.55 2.675 1.507 0.787 0.445 11.0 41.6 2080 0.888 0.246 1.189 0.678 1.044 0.808 0.60 2.717 = 1.644 0.748 0.486 12.0 45.8 2678 0.384 0.246 1.182 0.681 1.047 0.807 0.65 2.763 1.781 0.761 0.526 18.0 49.2 8424 0.829 0.946 1.114 0.682 1.062 0.807 0.70 2.827 1.918 0.779 0.566 14.0 58.8 4805 0.825 0.946 1.117 0.682 1.055 0.804 0.75 2.896 2.055 0.798 0.607 15.0 57.8 5458 0.820 0.945 1.110 0.685 1.044 0.794 0.80 2.966 2:192 0.817 0.628 «615.5 59.5 6119 0.817 0.944 1.107 0.685 1.085 0.785 0.825 3.089 2.280 0.837 0.648 16.0 61.7 6851 0.815 0.248 1.105 0.683 1.081 0.778 0.850 3.187 2.829 0.864 0.668 16.5 63.9 7630 0.812 0.248 1.100 0.684 1.027 0.778 0.875 3.320 2.397 0.915 0.688 17.0 66.3 8506 0.808 0.248 1.094 0.688 1.029 0.769 0.900 3.632 2.466 1.000 0.708 17.5 68.5 9410 0.802 0.244 1.091 0.681 1.081 0.766 0.925 4.041 2.584 1.113 0.729 «=©18.0 70.7 10870 0.806 0.945 1.088 0.680 1.081 0.768 0.950 4.444 2.603 1.294 0.749 18.5 73.0 11460 0.805 0.246 1.085 0.679 1.082 0.760 0.975 4.851 2.672 1.336 0.769 19.0 75.8 12590 0.804 0.248 1.080 0.678 1.032 0.756 1.000 5.227 2.740 1.440 0.790 19.5 77.6 13880 0.805 0.250 1.079 0.678 1.027 0.751 1.025 5.532 2.808 1.524 0.810 20.0 80.0 15280 0.806 0.258 1.076 0.675 1.027 0.746 1.050 5.718 = 2.877 1.575 0.8830 20.5 82.5 16810 0.806 0.254 1.075 0.671 1.081 0.744 1.075 5.801 2.945 1.598 0.851 21.0 85.3 18720 0.807 0.254 1.076 0.668 1.028 0.739 1.100 5.834 3.014 1.607 0.871 21.5 88.6 21260 0.807 0.254 1.076 0.658 1.035 0.788 1.125 5.873 3.082 1.618 0.891 22.0 92.4 24690 0.806 0.258 1.076 0.650 1.037 0.735 1.150 5.921 3.151 1.681 0.911 22.5 97.0 28980 0.805 0.250 1.079 0.640 1.041 0.719 1.175 5.999 3.219 1.652 0.932 23.0 102.0 34410 0.302 0.245 1.082 0.625 1.044 0.706 1.200 6.188 3.288 1.691 1.995 6.339 3.856 1.746 (All numbers are for ship of 600-ft LBP) (All numbers are for ship of 400-ft LBP) XI-6 0.70 Block Coefficient and 100-Percent 10.0 V - SHAPED FORM Displacement MODEL 4280 MODEL 4281 MODEL 4282 — ————— 9.0 8.0 7.0 6.0 5.0 aes 7 Bec) mp bee py i mee PEPE EE eee eer r 0.3 0.5 0.7 VA, Figure 62 — Curves of Resistance Coefficient C 7 to a Base of for Series 60, 0.70 Cp Models V VL y, XI-7 Ce X 103 sjepow 79 02°0 ‘09 setseg Joy ——_ jo osvg 8 0) / 9 quatoljoog oourysisoy Jo Soaing — gg ainsi Mas e*t bab ort 6°0 8°O L°0 9°0 S°0 v°O £°0 Pee iets Beeman ies) Pe ei WuOd dad VHS - A ————_ a oy cgcy ‘TH0ON WHO Wen CO Gd VA Sp 0 | tec .1a00n O8cy TadOn XI-8 U = SHAPED FORM Vv = SHAPED FORM MODEL 4280 MODEL 4281 MODEL 4282 XI-9 1.0 1.2 1.4 1.6 1.8 2.0 202 2.4 2.6 2.8 3.0 (©)to a Base of s 0.8 Figure 64 — Curves of Resistance Coefficient (Kk) for Series 60, 0.70 C p Model dIHs °Lai 0ov (©) 8°0 ort at ian § 9°T ert o°e STOPOW 7 9 02°0 ‘09 Setseg 10] JO aseg B OY (0) JUSIDIJJOOD soUBISISAY JO SeAINT) — Gg ondIy ae SCT a ae = WuOd CG VHS - O —______———= -ogev. Lan Oger Ta00n quoweoridsiq UGdI9g-09 PUB JUSIOIJJOOD YOOTT 0L"0 XI-10 PROPULSION EFFICIENCY 8 ‘xo °o @ fe} 70 60 SERIES 60 Cg = 0.70 100 $ DISPLACEMENT LJ MODEL 4280 ————————_—_—_———— PARENT. FORM [J MODEL 4281 MODEL 4282 [a ec a ies ino ee ee eee ie it cee ov eee yy SPEED IN KNOTS Figure 66 — Comparison of Power, RPM, and Efficiency Curves XI-11 HORSE POWER U = SHAPED V = SHAPED COEFFICIENT CURVES rg 100 2 DISPLACEMENT MODEL 4280 MODEL 4281 MODEL 4282 = e350: = Se SY eS SS =—="_= en 1.20 }———_+—_+ cosa eg ae eee Pel — FS i Secos 1.10 ex eat err 1.00 ala = se He a ae Ea eeiaay fee es! - z te OG esis ae a ei sel ee ae Jp 0.70 —— ee Se ee 0.60 | er 0.40 4 Wr aa Eo + + |Et We 0.30 C= SR me ee Se Bi 0.20 E+ ee Se Fae - i ee 10 12 oO 14 SPEED IN KNOTS w @ pe) fo) | Peas =) Ei eles be ec gill eee Figure 67 — Comparison of Coefficient Curves XI-12 ee ee a SERIES 60 Cp s 0.70 60 £ DISPLACEMENT MODEL 4280 MODEL 4281 MODEL 4282 mies 7 hi cSess: eee POPE ar a a ic ae cea PROPULSION EFFICIENCY SPEED IN KNOTS Figure 68 — Comparison of Power, RPM, and Efficiency Curves XI-13 HORSE POWER eh rr ®p Jt Wr MODEL 4280 MODEL 4281 MODEL 4282 SERIES 60 CR ze 0.70 60 $ DISPLACEMENT BS eee on ee fae ee ae ay) Seeealeefeeeo +-— - ae [aeaai ae eed 12 14 16 SPEED IN KNOTS ce See ee mz PARENT FORM U - SHAPED FORM V - SHAPED FORM Get Reee Renee ees Coo ie i SER aia 18 - 20 Figure 69 — Comparison of Coefficient Curves XI-14 Ir] SERIES 60 Cp zs 0.70 COMPARISON OF COEFFICIENT CURVES 60 % DISPLACEMENT — — — — — — — — — — — — ( TRIM: 2+% LBP BY STERN ) 100 @ DISPLACEMENT ( TRIM: EVEN KEEL CONDITION ) SHIP SPEED es 17.5 KNOTS ae L | is ia 0.85 0.80 EH P S H P 0.75 ea a 1.25 en 1.20 fe ert al AVA fo) cere ee ol rs (ie ale ole 1.05 A ee ee | ee ee ap | aes SS a ie ae SSS Ey [ele eae soc i eee] eS 2=pesee uae ee ee Sea lashed La a Seve Se a me) Eel ae | | | ae ae Hite U - SHAPED FORM PARENT FORM Vv - SHAPED FORM MODEL 4281 MODEL 4280 MODEL 4282 Figure 70 — Comparison of Coefficient Curves XI-15 STARBOARD DIRECTION OF ROTATION VELOCITY COMPONENTS IN THE PROPELLER PLANE RELATIVE TO THE MODEL THE SHIP SPEED IN KNOTS (17.5) THE HORIZONTAL COMPONENT. THE SIGN IS POSITIVE IF FLOW IS DIRECTED TOWARD THE CENTERLINE OF THE SHIP. THE VERTICAL COMPONENT. THE SIGN IS POSITIVE IF FLOW IS DIRECTED UPWARDS. THE TRANSVERSE COMPONENT. THE TANGENTIAL COMPONENT. THE SIGN IS MINUS IF THE COMPONENT IS IN THE DIRECTION OF THE ROTATION (RIGHT-HANDED PROPELLER). THE RADIAL COMPONENT. THE SIGN IS POSITIVE IF THE COMPONENT IS TO- WARDS THE CENTERLINE OF THE SHAFT. ANGLE OF BLADE POSITION. Figure 71 — Velocity-Component Vectors in Propeller Plane XI-16 Contours of constant values of w,, w,, and w, are shown in Figures 72 through 77 for the five parent models and the two stern variations of the 0.70 Cp design. In designing a propeller for a ship, we are interested in the fore and aft and transverse components of the wake. The total transverse wake w,,, compounded of the values of w,, and w,,, 1s shown for the seven models in Figures 78 through 84. Figure 75 shows that the wake in the fore and aft direction has the same general pat- tern for all block coefficients; there is a steady increase in the wake values with increase in block coefficient, and the same is generally true for the transverse wakes in Figures 81 through 84. One rather important feature of the transverse wake pattern for the three different stern designs for the 0.70 Cp model should be noted in Figures 78, 79, and 80. In the V-stern model, there is a strong upward component over most of the disk except for an inward and downward component near the centerline immediately above the propeller. For the parent form, intermediate between V and U, there is an indication of a definite rotation in the wake below the propeller centerline (Figure 78) and with the more pronounced U-stern, this rotation seems to be definitely established (Figure 79). Flow tests carried out in the circulating water channel at the Taylor Model Basin have shown that when a model has excessively U stern sections, a definite vortex may leave the bilge line some distance ahead of the propeller and extend aft right through the disk. In such cases, this downward flow ahead of and into the propeller may cause cavitation with consequent noise and vibration. It is therefore wise to avoid a very hard bilge radius aft when using U sections, and it would be good practice to carry out flow tests before deciding on the final shape of the aft end sections of fuller ships. The principal,uses of the wake data are in the design of the propeller and the calcu- lation of the variation in thrust and torque on the blades. The average circumferential wake around a circle of any particular radius within the propeller disk can be found from such diagrams, and from this the appropriate pitch and blade section can be determined. Wowever, in actual operation, the propeller section at that radius will meet constantly changing velocity conditions in the course of a revolution and so experi- ence constantly changing thrust and torque forces. Integrating such forces over the blade will give the variation of thrust and torque on that blade during a complete revolution, and summing these forces for all blades will give the variation in total thrust and torque on the whole propeller. While the forces on a single blade will vary over 360 deg, the pattern for the whole propeller will repeat itself as the blades successively reach the same position. Thus for a 4-bladed propeller, the pattern of thrust and torque variation will repeat every 90 deg; in other words, at blade frequency. The importance of these variations in thrust and torque is that they are one of the causes of hull and machinery vibration; the varying pressures around the blades cause varying pressures on the neighboring hull structure, and the varying force and torque are also transmitted through the shaft and stern bearings to the hull and XI-17 O0T(A/*A — I) = *% syueuodwog oye, [eurpnytsuo7T [enby jo soury — zy ond1y Z8Zb I9POW ‘WsaIS Ppadeys-A — OZL amnBrA I8Zb 19PoW ‘UsaIg pedeys-q — qzz em3ry O8Zp TePoW ‘Wioy yueeg — eZ, em3ry 5 Gi > ol Ge ol Se 1 eT ENG 3 oz : ' : ge Of H WAN 1 SN | oe 06 Eel x MEE BN (cK NT ANS XI-18 00T'(A/* A) 3 Th T2ePpo 9 ol " 8 8 vl Wes i \ m% nx aes \ BY : HN “i =) Se —_ = f = a —= ss Za zs (( \ Bs ROW : SS ——— mS: REN =n syuauodwo) oye [POTMeA | enby jo se uly — gL oInst gy 6 of tl 2 2 i ol XI-19 ) ha ee ° ° ° wo Tm N N \)\ XI-20 We ° ro) a + _ pats: ' 7 = ntal Wake Components w, = (V;/V).100 1 Horizo of Equa Figure 74 — Lines OOT[(A/*A) - T] = *% syuouoduog oye [eutpnytsuoy jenbg jo soury — Gg) candy oso = 45 vITp 12POW — PSZ ana y sz0= 45 s9'0 = 45 090 =49 €LZbh T9POW — OSL ain3ty 8IZp T8POW — 4SZ eMart y OLZp T9PoW — esy amBry aia 2 7 —— Ze 7 : Ni woo [—} nee \, fe = RRS NNSS XI-21 00T((A/*A)] = ° syusuodwoy oyeM [eONNIEA [enbyY JO sour] — g) oindry aru eoete| oso = 25 : sto = 45 bp T2POW — POL eMsty €LTb IPPON — COL esn3Ty 29 a soo = 95 09'0 = 45 8IZb TPPOW — FOZ emsty OIZp T9POW — POL eINSTYy 9 S S a s- > Le Wa —F i) ANN WS). ie VOWS. nih — == —__ — A WW / AA } aS eet 9c 8:0) =2 (un) Ee SpBeE XI-22 OOT[(A/A)] = 4 sjueuoduog oyeM [eIUOZIIOH [enby Jo soury — )) eindty os'0 = 45 bITb T9POW — PLL einsIy -2- e-i=r.0ual rs sz0= 49 €1p TAPOW — ILL 9MBIYy s90=45 8IZb 1@POW — 4Zz ematy i} rt 090 = 45 OIZp T9POW — BLL am3ty ' £ ( SENS Sy) Wy (re is yy ZH | ll ==s=N Ss SSS Gi \| | | = SSS nee oc XI-23 DISPLACEMENT- 100% SHIP SPEED-17.5 KTS. -O.SOWL THE WAKE SURVEY WAS MADE IN A PLANE PERPENDICULAR TO THE LONGITUDINAL AXIS AT A DISTANCE 0.94% LBP FORWARD OF THE A.P. O25We = THE ARROW INDICATES THE DIRECTION AND MAGNITUDE OF THE TRANSVERSE WAKE COMPONENT. —Q.O7SWL = = = DISPLACEMENT- 1007, SHIP SPEED-17.5 KTS. O50 WL THE WAKE SURVEY WAS MADE IN A PLANE PERPENDICULAR TO THE LONGITUDINAL AXIS AT A DISTANCE 0.94% LBP FORWARD OF THE A.P. OQ25Wi THE ARROW INDICATES THE DIRECTION AND MAGNITUDE OF THE TRANSVERSE ' WAKE COMPONENT. 0.075 TRANSVERSE SECTION LOOKING FORWARD. TRANSVERSE SECTION LOOKING FORWARD. > a Figure 78 — Wake Diagram for Parent Form, Model 4280, Cp = 0.70 ss Figure 79 — Wake Diagram for U-Shaped Form, Model 4281, Cp = 0.70 DISPLACEMENT- 100% SHIP SPEED-17.5 KTS. OSOWL THE WAKE SURVEY WAS MADE IN A PLANE PERPENDICULAR TO THE LONGITUDINAL AXIS AT A DISTANCE 0.94% LBP FORWARD OF THE’A.P. O25WE _ THE ARROW INDICATES THE DIRECTION AND MAGNITUDE OF THE TRANSVERSE WAKE COMPONENT. Q.O7TSWL ‘cic TRANSVERSE SECTION LOOKING FORWARD. ——— Figure 80 — Wake Diagram for V-Shaped Form, Model 4282, Cp = 0.70 XI-24 } ‘ X : | 18 DL _ 18-1/2 19 OWA ve N 360° 0.75 wL .95R 17 A Lo DISPLACEMENT — 100% SHIP SPEED — 22.0 KNOTS Re ce LOR 0.50 wL 285 HUB DIA. al CENTERLINE THE W, SURVEY WAS MADE IN A PLANE RPENDICULAR TO THE LONGITUDINAL AXIS AT A DISTANCE 0.94% LBP FORWARD OF THE A.P. 0.25 WL THE ARROW INDICATES THE DIRECTION AND MAGNITUDE OF THE TRANSVERSE WAKE COMPONENT. TRANSVERSE SECTION LOOKING FORWARD. 180° _| BASELINE Figure 81 — Wake Diagram for Model 4210-Cp = 0.60 XI-25 DYL 19 19-1/2 20 BTA, 18 ' 360° 0.75 WL -95B .7R DISPLACEMENT — 100% SHIP SPEED — 19.4 KNOTS .4R 0.50 WL HUB DIA 270 CENTERLINE THE WAKE SURVEY WAS MADE IN A PLANE PERPENDICULAR TO THE LONGITUDINAL AXIS AT A DISTANCE 0.94% LBP FORWARD OF THE A.P. 0.25 WL THE ARROW INDICATES THE DIRECTIG: AND MAGNITUDE OF THE TRANSVERSE WAKE COMPONENT. TRANSVERSE SECTION LOOKING FORWARD. - 0.075 WL 80° BASELINE XI-26 18-1/2 19 STA. 19-1/2 20 0.75 WL DISPLACEMENT — 100% SHIP SPEED — 15.6 KNOTS 0.50 WL rad , a 270 e CENTERLINE THE WAKE SURVEY WAS MADE IN A PLANE PERPENDICULAR TO THE LONGITUDINAL AXIS AT A DISTANCE 0.94% LBP FORWARD OF THE A.P. 255 ay 0.25 WL waa ZT i 240 [At THE ARROW INDICATES THE DIRECTION / | AND MAGNITUDE OF THE TRANSVERSE WAKE COMPONENT. 0.075 WL -+ BASELINE Figure 83 — Wake Diagram for Model 4213—Cp = 0.75 XI-27 ' STA, 18-1/2 19 0.75 WL 19-1/2 20 us ‘ = FF DISPLACEMENT — 100% SHIP SPEED — 13.7 KNOTS &f | oR 0.50 WL Pak Pal 0.25 WL 0.075 WL ee CENTERLINE THE WAKE SURVEY WAS MADE IN A eye Co ~° PLANE PERPENDICULAR TO THE \ LONGITUDINAL AXIS AT A DISTANCE 0.94% LBP FORWARD OF THE A.P. A 255 \ \ g is, es THE ARROW INDICATES THE DIRECTION Y | AND MAGNITUDE OF THE TRANSVERSE ar WAKE COMPONENT. l | [ \ 225 0 el «2 ———_L SCALE 210 eal) BASELINE TRANSVERSE SECTION LOOKING FORWARD, Figure 84 — Wake Diagram for Model 4214—Cp, = 0.80 XI-28 thrust block. Any smoothing of the wake will therefore not only improve the hydrodynamic performance of the propeller but also reduce one of the causes of hull vibration. Knowing the wake components at any point, it is possible to calculate the forces on the section of the propeller blade at that point on the assumption that they will be the same as those it would encounter in a steady flow of the same pattern and, by summation, the total force and moment on the whole propeller. This method of analysis is called the ‘‘quasi- steady’? method, and Figure 85 shows the variation in total thrust for a 4-bladed propeller behind the three 0.70 Cp models calculated in this way. Much theoretical work is in pro- gress directed towards taking into account the dynamic effects of variations in wake velocity— the so-called ‘‘unsteady’’ method—but in the meantime the ‘‘quasi-steady’’ method is com- monly used for comparative qualitative calculations when considering the effects of possible changes in propeller design. Wake diagrams of the type given will be useful in this respect. The longitudinal and tangential velocity components around any circumferential line in the propeller disk can be analysed into harmonic components, and the relative magnitudes of these will have an important influence on the vibratory thrust and torque forces. The wake pattern should therefore be considered as one factor whenever any decision is to be made in the choice of number of propeller blades. MODEL 4280, PARENT FORM ——-— MODEL 4281, U-SHAPED FORM — MODEL 4282, V-SHAFED FORM ANGLE MEASURED FROM UPWARD VERTICAL IN CLOCKWISE DIRECTION BLADE ANGLE IN DEGREES (6) Figure 85 — Thrust Fluctuation XI-29 240 230 220 210 200 THRUSZ x 1073 (1bs) CHAPTER XII REVIEW OF SERIES 60 PROJECT In the design of any given ship the naval architect has always to meet a number of conflicting demands which, to a greater or lesser extent, limit his choice of dimensions, proportions, fullness, and other features. An increase in length is generally favorable from the points of view of low resistance in smooth water and maintenance of speed in rough weather, but it is expensive structurally, carries penalties in crew numbers, and, in specific cases, may be limited by dimensions of locks, piers, drydocks, etc, which may also restrict beam and draft. The depth of water in the world’s harbors today is also a definite limitation on draft, particularly for large tankers and other bulk carriers. On the other hand, beam is limited on the minimum side by the need for adequate stability, and questions of trim and weight distribution, especially in bulk carriers, may exercise some control over the necessary longitudinal distribution of displacement and so on the LCB position. In practice, therefore, the naval architect has usually to design a ship within dimen- sions already defined to a large extent by such considerations, but there is generally some latitude available for adjustment to suit the demands of good resistance and propulsion qualities. The results of the Series 60 experiments can be of material help to the designer in any single-screw ship design which in its proportions and other features falls within the area of variables coyered. If the designer adopts the lines of Series 60, the position of LCB as used in the parent forms, and a propeller having the standard ratio of diameter to draft of 0.7, he can make a very accurate estimate of both the ehp and shp of a ship for any particu- lar selection of length, beam, draft, and displacement. If for trim or other reasons, the LCB has to be placed in some other position, allow- ance for this can be made using the data given in Chapter VII or in Tables 49 through 53, and for departures from the standard propeller diameter the values of w, ¢, and relative rotative efficiency (e,,) from the contours can be corrected by using the results of the experiments with different diameter propellers detailed in Chapter X. The w and ¢ data can also be used for assessing the propulsive efficiency to be expected for power plant condi-- tions different from those assumed in the propeller designs used with the series models. In addition to estimating the required power for a particular ship design having agreed characteristics, the data are also useful in assessing the penalties which must be paid or the advantages to be gained by changing such characteristics. This is a problem which occurs at some time or other in almost every design study, and this use of the data may well be as important as estimates of actual power. XI-1 7123-988 O - 64 - 11 Table 49 — Effect of Change in LCB Position — 0.60 Cp Figures show increase or decrease in resistance for movement of LCB from position in parent model, in percentage of © LCB Position 2.48A 1.50A 0.51A | 0.52F Parent XII-2 Table 50 — Effect of Change in LCB Position — 0.65 Cp Figures show increase or decrease in resistance for movement of LCB from position in parent model, in percentage of © LCB Position Mi ® V_ [246A] 1.54A | 0.50A | 0.38F | 1.37F Voy, VL pp Parent Ney) Table 51 — Effect of Change in LCB Position — 0.70 Cp ¢ = . . . Figures show increase or decrease in resistance for movement of LCB from position in parent model, in percentage of enon re LCB fame eee CB Position =» = 3. | 2.05A | 0.55A O50 aE 255F Parent XII-3 Table 52 — Effect of Change in LCB Position — 0.75 Cp Figures show increase or decrease in resistance for movement of LCB from position in parent model, in percentage of LCB Position 0.48F 1. OF 257 Fe 346k Parent Table 53 — Effect of Change in LCB Position — 0.80 Cp Figures show increase or decrease in resistance for movement of LCB from position in parent model, in percentage of a LCB Se AECEPesitcns eee 0.76F | 1.45F 2.90F | 3.51F Parent XIJ-4 The number of models run had to be limited both on the score of time and expense. In view of the wide field covered, the question may be asked as to how well the contours of residuary resistance, ©, wake fraction, thrust deduction fraction, and relative rotative effi- ciency represent the probable values of these quantities at points not directly supported by test results—in other words, how reliable would be estimates made of these quantities from the interpolated contours? One such comparison is giyen in Appendix C (see Figure C-3) where it is shown that the particular set of contours chosen represents extremely well the results of the nine models on which they were based. A more general method of answering this question is available, however. In the pro- cess of assessing the merits of the Series 60 parents, actual models of Series 60 equivalents of the SCHUYLER OTIS BLAND, C.2., and PENNSYLVANIA were made and tested. These models had the corresponding dimensions, displacement, and LCB position of the actual ship but Series 60 lines. It is now possible to estimate the ehp for these three forms from the contours and to compare the results with the ehp actually measured on the models. Such comparisons are shown in Figures 86, 87, and 88. Two estimated curves are shown in each LCB CORRECTION WITH LCB CORRECTION HORSE POWER Fi Pa IZ "ey (al 144 #15 #16 17 «#218 «+419 —= «20 fae eI ela lg pale ne Sy eae ale aS Ae a a Ae Bas feaaineale Hall lal ae ae a | Zola esi ae ia 12 SPEED IN KNOTS Figure 86 — Comparison of EHP obtained by testing a Model having Series 60 Lines and Proportions of SCHUYLER OTIS BLAND with Corresponding Estimate from Series 60 Contours 1000 XII-5 SERIES 60 C2 (MODEL 4490) ————_—_ ESTIMATE COMPUTED FROM B./A CONTOURS WITHOUT LCB CORRECTION WITH LCB CORRECTION HORSEPOWER SPEED IN KNOTS. Figure 87 — Comparison of EHP obtained by testing a Model having Series 60 Lines and Proportions of C.2. Class with Corresponding Estimate from Series 60 Contours case, one for a ship having the LCB in the position used in the Series 60 models on which the contours are based, the other for a ship having the LCB in the same position as the actual ship in question. The change in ehp for the shift in LCB was estimated from the data in Chapter VII and Tables 49 to 53. . For the SCHUYLER OTIS BLAND and PENNSYLVANIA, the actual LCB positions were within 0.5 percent LBP of those used in the Series 60 models from which the contours were developed, and the effects on ehp were extremely small (Figures 86 and 88). In the case of the C.2. design, the actual ship had the LCB 1.4 percent forward of midships, and the position corresponding to the Series 60 contours was 1 percent aft. The actual and estimated ehp did not differ materially below 15 knots, but above this speed, the estimated ehp from the Series 60 contours was lower than that of the C.2. Series 60 equivalent, the reduction at 18 knots being some 12 percent (Figure 87). This illustrates the advantage of the finer entrance at these higher speeds. The estimated curve for the Series 60 equivalent with the LCB in the actual ship position (1.4 percent forward), corrected by the data in XII-6 SERIES 60 PENNSYLVANIA SPEED IN KNOTS Figure 88 — Comparison of EHP obtained by testing a Model having Series 60 Lines and Proportions of Ss PENNSYLVANIA with Corresponding Estimate from Series 60 Contours Chapter VII, shows excellent agreement with the ehp measured on the model. Thus when allowance is made for differences in LCB position, the ehp estimated from the contours is in very good agreement with that measured on these three models. This fact should give confidence in the use of the contours throughout the range, for of course the results of the tests on these three Series 60 equivalent models were not used in any way in the process of deriving contours. Self-propulsion tests were also carried out on the Series 60 equivalents of the SCHUYLER OTIS BLAND and the PENNSYLVANIA. The values of w, ¢, and e,, measured in the tests are compared in Figures 89 and 90 with the corresponding values estimated from the appropriate contours, and the agreement is again very satisfactory. Although estimates of power made from the contours apply strictly only to ships having lines derived from the Series 60 charts, they can, with proper exercise of caution, be used as guides over a somewhat wider field. For example, in developing the original Series 60 lines, Bethlehem Steel Company provided a set of lines equivalent to the MARINER class of fast XI-7 TEST RESULTS FROM CONTOURS Figure 89 — Comparison of w, ¢, and e,, for Series 60 SCHUYLER OTIS BLAND from Contours and Test Results t&w 33) Baeae TEST RESULTS FROM CONTOURS 13 16 Figure 90 — Comparison of w, ¢, and e,, for Series 60 PENNSYLVANIA from Contours and Test Results cargo ships but without a bulbous bow (Model 4440). A comparison of this model with the Series 60, 0.60 Cp, parent (Model 4210) showed the latter to have appreciably lower © values at the service and trial speeds (Figure 6 of Reference 45). Although the lines were rather similar, the hull form coefficients were different—for example, the block coefficient of Model 4440 was 0.611—and a comparison of the ehp for Model 4440 with that derived from the contours for a Series 60 equivalent form of Cp, 0.611 (Figure 91) indicates that again the agreement is good. The contours can also be used for comparative purposes in much the same way as is done with the Taylor Standard Series. If a new design has secondary characteristics which differ from those of its Series 60 equivalent but model results are available for some other snip which more closely resembles it in these respects, the latter may be used as a ‘‘basic”’ ship. Calculations of ehp can be made from the contours for the ‘‘Series 60 equivalents’”’ of both the new design and the basic ship. Then the approximate ehp for the new ship will be ehp of Series 60 equivalent x Sues been Shy ehp of Series 60 equivalent of basic ship XII-8 ee Jae Se ee RR Bey 8PEED IN KNOTS Figure 91 — Comparison of EHP obtained by testing a Model having Proportions of MARINER Class, but without Bulbous Bow, with Corresponding Estimate from Series 60 Contours 8 * Figure 92 shows the predicted ehp for an ocean-going ore carrier of 0.78 Cp compared with actual model test results; the estimate was made as outlined above, using the PENNSYL- VANIA as the ‘‘basic”’ ship. Even more extreme uses can be made of the Series with some success, as shown by Professor Baier’s adoption of the series bow and stern lines with parallel body in the design of lake ships (page V-22). The demonstration of the qualitative uses of Series 60 is easy, but the establishment of their absolute quantitative value is more difficult. In discussing the very first paper in the series (Reference 44), Mr. V. L. Russo made the following obser- vations: ‘‘The real value of the contours proposed in the paper could be established best by determining what results these contours would give by comparison with acceptable results exemplified not by the standard of a phantom form but by actual successful ship designs ... This way of comparison... would have the advantage of being conclusive as it would furnish a true comparison under practical conditions and be devoid of imponderable XII-9 B CARRIER ( OCEAN-GOING) © FROM SERIES 60 (USING PENNA. AS BASIC SHIP) & FROM TEST Figure 92 — Comparison of EHP obtained by testing a Model of an Ocean-going Ore Carrier with Corresponding Estimate from Series 60 Contours using SS PENNSYLVANIA as Basic Ship discrepancies.’’ This suggestion was taken up by the SNAME Panel (of which Mr. Russo was a member), and the subsequent Series 60 parents were developed using just this method, as described earlier in this report. It is believed that these parents now compare very well in performance with the successful ship designs on which they were based. Comparisons with results of similar work at the Netherlands tank have already been mentioned in Chapter VI, and in this connection, it is of interest to quote the remarks of Professor L. Troost, one-time Director of that establishment, with a vast experience in the model testing field: ‘‘The writer has applied the computations as presented in the paper to the results of some high-quality hulls and propellers of foreign (European) design. He is satisfied that the optimum Series 60 data are indicative of very high performance and that it will require great skill and experience to improve on them for an amount of 2 percent in total ehp and shp in regular designs. He also found that an extrapolation to 0.82 block, which will often be necessary in the field of super-tankers and comparable ships, not too hazardous.’’ (Discussion on Reference 64). XII-10 | | | Although no claim can possibly be made that Series 60—or indeed any other Series— represents optimum resistance qualities, the above remarks and other evidence do suggest that the contours will be of help in preliminary design work and can be used with some confi- | | | 1 | | | | dence in the estimation of ship performance, both in the absolute sense and also in the investigation of various alternative choices which may face the naval architect. In using the Series 60 results, it is worth recalling that the hull forms are all related to one another in a clear and unambiguous way by means of graphical methods. As has been pointed out before, this has the advantage over geometrical variation of one parent form in that the characteristics can be varied with fullness to suit the corresponding changes in speed-length ratio. The alternative use of a single parent form to cover such a wide range of variables as used in Series 60 would have led inevitably to unrealistic designs towards the limits of the area covered. Another point to remember is that all models were of the “same length and run in the same tank with the same instrumentation, thus eliminating other possible sources of difference. In the course of the discussions on the many Series 60 papers, much has been said about various methods of presenting the data. The two most commonly used are to give FR values of residuary resistance per ton of displacement oe . in terms of speed-length ratio V fw , almost universally used in the United States, or values of Oxo ft In terms of (©) 5 as used in Great Britain. Both systems have merits and demerits, as one might expect, but they are well-entrenehed in their respective homes. The Series 60 results have therefore R R been given in both ways as contours of 70 and of (€) to their respective bases. There is a vast amount of model data expressed in one or other of these forms, with which the Series 60 results can be compared directly. The SNAME Model Resistance Data sheets also give the information in both these forms. aes V nee The presentation of —— in terms of has the advantage of simplicity but suffers A Vey, from two drawbacks. In the first place, a true merit comparison has to be made on the basis FR of total resistance per ton of displacement, and comparisons on the basis of can be quite misleading. Skin friction resistance is the major component of total resistance in most if not all single-screw merchant ships, and this depends on wetted surface, not directly on displacement. To make a merit comparison from data presented in this way, it is therefore necessary to estimate the frictional resistance in each case and so obtain total resistance or ehp. The true merit comparison of interest to the naval architect and ship owner is the a ae total resistance per ton of displacement oe To present this properly in curve form it is X-11 necessary to have the abscissa and ordinate values compatible. For abscissa, the speed- V length ratio Wes is preferred by many naval architects for its simplicity. In order to keep the values of within a reasonable numerical range, it is usual to divide them by some function of (speed)? since this makes the ordinates almost constant over the lower speed ; W. range. If it is desired to use i as the speed parameter, then the ordinates should be Rr A Rr +L aoe Rr-L-V If the comparison is to be made on a power basis, then the ordinate becomes A.¥V3 EHP - L SHP - L or ———— Co Age V3 A.¥3 Dr. Telfer has made this point very clearly in discussing the Series 60 papers. ‘¢. . . the designer’s problem is usually to find the model having the lowest resistance per ton displacement on a given length, length being usually approximately fixed by conditions other than resistance’’ (discussion on Reference 44). And again, ‘‘Figure 16 gives us an : : SHP incompatible presentation of a power-displacement function ———— presented in terms of A2/3y3 V : 5 ; 4 a speed-length function JL . From this diagram a designer is led to infer that the finest ships are always the most economical. Such a conclusion from the basic data would be completely erroneous. To review the data correctly they must be presented in a compatible Wax: : : : : form. As the speed-length ratio JE is preferred by most practical ship designers it must by retained and the requisite change for compatibility made in the power-displacement function. This must be converted to a power-length basis, still using, however, power per ton P-L : ‘ . SH displacement. The conversion produces the function ————— which correctly grades the A. V3 power per ton of all vessels having the same length and speed’’ (discussion of Reference 61). The basic resistance and dhp data for the Series 60 parents are presented in this form in Figures 93 and 94. To again quote Dr. Telfer: ‘‘A designer now sees that if his speed is low the most economical ships have the fuller and not the finer forms. Certainly as the speed is increased the finer form becomes the more economical, and by drawing a tentative envelope to the individual curves a mean scale of optimum block coefficient and optimum power constant for given speed-length ratio is at once available.’’®! Dr. Telfer has recently converted the results of the resistance experiments on the Series 60 models to this method of presentation, and compared them with other available data. (‘‘The Design Presentation of Ship Model Resistance Data.’’ E.V. Telfer, Trans NECI, Vol. 79 (1962-63).) XII-12 O©TROOST SERVICE SPEEDS 0.40 050 060 O70 080 090 1.00 aVe ‘lee : Vi Figure 93 — on ~—— for Series 60 Parents ay2 VE The ©) and (k) constants were introduced by R.E. Froude. At corresponding speeds : ae . : for model and ship, UB is the same, Y (volume of displacement) is proportional to Land sO WE is the same. This ratio has different values in different systems of units, and : 1/3 Froude therefore related the ship speed to the speed of a wave having a length equal to 5 1/3 [ga lg Vi 1/6/[ 9 Wave speed = /— = /—- = a GS Qq7 Qn 2 v 4n ship speed V [4 Hence 8) ee a , which is nondimensional., The resistance wave Speed yi/e g is expressed in terms of a which is also nondimensional in a consistent system of units. If this is to be presented to a base of (k) , we must divide by (kK) 2, and Froude added 1000 XII-13 SHP XL y 92 avs 10 © TROOST SERVICE SPEEDS | (0.03) 0.40 0.50 0.60 0.70 0.80 0.90 1.00 ‘to the numerator to avoid unnecessarily small numerical quantities. Thus he defined his resistance constant © as Rr Ge © ‘x 1000 and speed constant ® V | Ae Vise Vg both being nondimensional. For use in usual ship units of V in knots and displacement A in tons, these assume the well-known forms &®) = 0.5834 - A1/6 XII-14 Rr Al/3 Rr and © - + —— ~ 1000 = ——— « 2938 (0.5834-V)2 A2/3. y2 where Ff and A are both in tons or, in terms of horsepower, ©-= ERE TA A2/3y3 A presentation of resistance data in the ©-® system is therefore compatible and places models or ships in a correct merit order. In the design of a merchant ship, the two principal basic design factors are the speed and displacement—how much displacement (and therefore deadweight) has the ship to carry at a given speed? The ©-® system involves only V and A and leaves length along with other dimensions and coefficients among the variables which are at the designer’s disposal in attempting to find that combination which will result in the most economical overall design. From the various charts and tables presented in this report, the designer can extract the data he desires in either form, according to his needs and in keeping with the method with which he is most familiar or in which his own data are recorded. The conversion of the © data using the ATTC line, as given in this paper, to the equivalent © data using Froude, or vice versa, can also be quickly made by the use of the chart given in Appendix D (Figure D-4), thus giving a connecting link with the large quantity of © data in existence in this form. , XII-15 i i Ve CHAPTER XIII POSSIBLE EXTENSION OF SERIES 60 AND FUTURE RESEARCH Although at the time the original series was planned, the numerical ranges adopted for the variables seemed adequate for future designs of single-screw ships, developments over the last 15 years have already overtaken the choice made in 1948. The single-screw arrangement is preferred by most ship owners because it results in higher propulsive coefficients, cheaper machinery installations and lower running costs than equivalent twin-screw machinery, and in recent years single-screw ships have been built of greater and greater size, with more and more power, higher speeds, and larger propellers. For the dry-cargo or refrigerated ship there has been a demand for increasing speed which, with these other factors, has resulted in many single-screw ships having block coefficients less than the smallest one of 0.60 used in Series 60. Coefficients of 0.55 have been used, and to take care of the future and have adequate design information, it would be useful to extend the series down to a block coefficient of at least 0.55 and perhaps 0.50. At the other end of the scale, the economics of carrying bulk cargoes, whether oil, ore or grain, have resulted in the mammoth supertankers of today with block coefficients in the neighborhood of 0.825 to 0.85. An extension of Series 60 to 0.85 block coefficient would therefore be of great,interest to designers in this field. B : : The range Ob the Series is from 2.5 to 3.5. The former figure is rather too high : B (many cargo ships have ratios around 2.25), and an extension to a value of — equal to 2.0 would be of interest. The upper limit of 3.5 is probably adequate for most ships in fully loaded condition, but with draft restrictions in many ports and canals, it is reasonable to suppose that supertankers and similar ships may well spend appreciable time in a : ope B ; partially loaded condition when Fi may quite likely exceed 3.5. Asa first step, a few B : . models having m7 values of 2.0 and 4.0 could be run to see howreliable an'extrapolation outside the present limits might prove to be before embarking on an extensive program. - Studies of seakeeping characteristics have shown the advantages of longer ships in maintaining sea speed, and an extension of the series at the finer block coefficients to ' L Sere A higher values of RB would be of interest in this respect; at the full end, a similar increase _ ae In a would cover ships designed for the Great Lakes trade. The extension of Series 60 to cover any or all of these areas would be a worthwhile research project. In addition, there remain the planning and running of additional series to cover twin-screw ships, trawlers, tugs, and high displacement-length craft of all kinds. In XIHI-1 { the latter types, the effect of shallow water on performance would also be a matter of special interest. The availability of such systematic information would provide the naval architect with much basic and background information and greatly reduce the need for routine model testing. The results presented in this report are for models tested for resistance and propul- sion in smooth water only. They cover the major features of single-screw merchant ships such as proportions, fullness, LCB position, and variation in propeller diameter. They enable a designer to obtain very quickly from contours a lines plan having the correct dimeng! Sions, displacement and LCB. Moreover, because of the graphical relationship between the models, he can also associate with these lines a close estimate of resistance and shaft horsepower. As pointed out earlier, although no claim can be made that such a design is an optimum one, the comparisons made between Series 60 and new successful ships indicates that it will be of a reasonably high standard. When the series was begun, the hope was expressed that it would provide an accept- able starting point for additional series planned to investigate many other facets of the hull design problem. This hope has been realized to a very considerable extent—models of Series 60 have been used for a number of comparisons of models in waves, sponsored by the ATTC and the ITTC, for a methodical investigation into launching, and forcalculations of the forces, on ships in a seaway and their responses to such forces. They have also been used in studies of wavemaking resistance and of the effects of adding different sizes of bulb at the bow upon resistance and ship motions. As described in this report, the Series 60 parent { models have also been used for the measurement of wake patterns and the resultant propeller } forces, and for the median model of 0.70 Cp, the effects on these and upon resistance and | propulsion of changes in shape of stern sections from U to V have also been evaluated. r Probably the most urgent need for extension of this methodical series work lies in the realm of seagoing qualities. It by no means follows that the hull form chosen for good performance in smooth water will be equally successful in waves, either as regards mainten- | ance of speed or minimum ship motions. This applies particularly to the fuller, slower ships, | where the absence of any significant wavemaking calls forfull bows and slender sterns to achieve good smooth-water performance. A methodical program should be carried out first, to test key models of the series in waves, and this should include experiments to find the effect of LCB position upon maintenance of sea speed. The next step would be to evaluate the effects of changes in section and waterline shapes, both below and above water. These would include, for example, an examination of the relative merits of U- and V-sections, and the best type of above-water form at the bow to ensure a Clean, dry ship by the provision of adequate freeboard and flare. An extensive program of experiments of this kind, based on Series 60 models as parents, has been designed at the NSMB. The results of some tests have already been published, but much yet remains to be done. XIII-2 In order to keep the original program at the Taylor Model Basin within reasonable bounds, a graphical method of delineating the models was adopted, and except for the fact ‘that comparisons were made with existing “‘good’’ ships, no attempt was made at that time to explore the vast field of possible changes in the shapes of area curves, sections or ‘waterlines. At the time of publication of the earlier papers, this adoption of certain area curve and section shapes was subject to some criticism as having been done too arbitrarily /and accepted too easily. But the fact that it has taken 15 years to reach the present position is sufficient indication of how long it might have taken had we been led astray in the early days by the temptation to explore all the delectable byways, opening up vistas of attractive | changes in area curves, waterline and section shapes. Now that the main framework has ‘been finished, such exploration is undoubtedly necessary; it could well form the subject of ‘a number of research projects in different tanks. There are a number of possible approaches to this type of research. One would be the trial and error method of trying different shapes of area curves, waterlines and sections, be- ing guided in successive choices by the results of each step in turn. A second would be to apply statistical methods to the results of previous model tests—both Series 60 and others— to determine the influence of the different design parameters, and so approach closer to an optimum combination to suit any given design conditions. Considerable success has been achieved in this way in the particular field of trawler design.°® Thirdly, one may seek guidance from the mathematical work being carried out in the field of wavemaking resistance. As a matter of history, it is perhaps worth recording that “much thought was given to this aspect of ship resistance research when the original series was being planned. At that time, Dr. Weinblum was a consultant at the Taylor Model Basin, and he took an active part in the planning and in the early phases of the project. The ques- tion of using mathematically defined lines was seriously considered, and it is perhaps of interest to record some of Dr. Weinblum’s views as set out in his discussion on the first series paper (discussion on Reference 44, pp 722-4). ‘‘For a considerable time attempts have been made to establish a rational theory of ship resistance as the function of its form by using analytical methods and pertinent basic experiments. Although this approach is developing successfully, if slowly, the choice of proper ship forms for practice has still to rely widely upon experimental data, obtained by testing methodical series or single models. Clearly, the latter procedure is the most waste- ful way of getting results which are capable of appropriate generalization. Therefore, from a practical point of view, the need for Series work cannot be denied at present. On the contrary, the substitution of methodical experimenting for single testing promises within plausible limits decisive advantages in various respects ... when the present series was being planned the authors received proposals to base the work on algebraically defined lines . .. There is no magic in mathematical lines. Their use in research work is desirable essentially XIII-3 1. to obtain well-defined expressions for the ship forms, which admit especially of clearly defined variations in these forms... 2. to enable us to perform resistance, seaworthiness and similar calculations ina simple and systematical manner. . .. in the writer’s opinion a reasonable evaluation of the existing theories (of wave resist- ance and sea-going qualities) could be reached by using graphically-defined parent hulls, by approximating these forms mathematically and using the latter for the calculations involved.. . .- This reasoning together with some difficulties ... in representing full sections justifies | the use of empirical lines at present... The idea of the proposed wave resistance calcu- lations is essentially two-fold: we intend to make a contribution to the analysis of the experi- mentally-obtained resistance curves and to indicate what improvements in the parent forms are suggested by theory. Especially the latter purpose can become rather interesting. On | the other hand, since we are dealing with a first order theory, valuable checks of its validity may be obtained from systematic experiments. ... Finally, the series work may make use of other procedures applied in hydrodynam- | ics and thus stimulate the whole field of model research. It dces not give credit to theoretical naval architecture and to general hydrodynamics that in text books on the latter subject the | ship has nearly disappeared.”’ : In view of such opinions, the basic lines of Series 60 were developed empirically and defined graphically, and Dr. Weinblum showed in his discussion how the waterlines and | sections could be closely represented by polynomial expressions. Today much effort is being applied to the problem of representing a ship form mathe- matically, either by means of sections and waterlines or as a three-dimensional surface, for use on a digital computer.©7»©8»®9 Such an approach would enable calculations of wave- making resistance, velocity distribution, and motions in waves to be made very quickly and permit examination of many alternative ideas. In the particular case of calculations of wave- © making resistance, these will still suffer in the absolute sense from limitations in the theory, particularly as regards the inclusion of viscosity effects, but they should furnish a guide to the experimenter in the choice of hull changes likely to reduce wavemaking resistance. It must be remembered, however, that in the type of ship with which this research is concerned, the wavemaking resistance is, in general, only a small part of the total. By fining the entrance for example, it may well be that the reduction in wavemaking resistance will be equalled or even exceeded by an increase in viscous form drag.and eddymaking occasioned by the corres- | pondingly fuller stern. On the other hand, the wavemaking resistance is the part over which we have most control since it depends essentially on the hull shape, and every use should be | made of any guidance that mathematical work can provide as to the type and character of changes likely to reduce it. This approach will be most fruitful in high-speed ships, but at | present it seems that for low-speed cargo ships we must in the final analysis still have | resort to experiments. XIII-4 Finally, it is believed that much of the value of ship model research in the past has not been realized because of the lack of a common point of departure. Indeed, as a result of this lack, there has been much duplication of effort. It is suggested that Series 60 provides such a common Starting point. Used in this way, it would have the effect, in its own limited field, of unifying research everywhere. Much more research, both fundamental and applied, remains to be done; there are staff shortages in most places, but with such a link these problems could be shared among towing tanks everywhere and the rate of progress much enhanced. XIII-5 APPENDIX A EFFECTS OF TURBULENCE STIMULATORS The need for artificial stimulation of turbulence on ship models in order to avoid the Spurious results obtained in ship predictions based upon model experiments in which some laminar flow persisted was recognised in some tanks, including Hamburg and Wageningen, before 1930. Its importance was not generally appreciated, however, until around 1948 when it was realised that on some hull forms, notably those with a full forebody and raked stem, laminar flow could persist to an alarming extent. Thus experiments with LIBERTY ship models showed that the effect of stimulation over the lower speed range could amount to 15 or even 20 percent. A number of methods of stimulating turbulence have been devised from time to time. Kempf early proposed a ‘‘comb’’ which made a pattern of grooves in the wax hull around a station about 5 percent of the length aft of the stem, while a ‘‘trip-wire’’ placed around the hull at the same place was adopted very early in the work and has maintained its place as one accepted method to the present time. Sand strips down the stem and along the LWL for -a short distance from the fore end are also used. All these devices add some parasitic drag to the hull, and to avoid this use has been made of struts ahead of the model attached to the towing carriage. Some experiments of this kind made with fine models in which no lami- nar flow effects could be detected suggested that the wake from the strut could actually reduce the measured resistance of the hull. In order to avoid some of these effects, studs similar to those developed on aircraft models were tried; they have the stimulating effect of trip wires or sand strips but a very low parasitic drag. These were described by Hughes and Allan in 1951.4° The original Series 57 models were run with and without turbulence stimulation. The standard method used on all models was a sand strip 4in. wide down each side of stem and along the LWL for a distance of 4 ft or one-fifth of the length of the model. In eddineny some models were run with a trip wire, 0.04 in. in diameter placed around a station at a0 ‘from the stem. Others were fitted with studs, as described in Reference 46; these have a diameter of 1/8 in., were 1/10 in. high and spaced 1 in. apart along a line parallel to the stem profile. The distance of the line from the stem depends on the half angle of entrance on the LWL (1/2 a). For the three Series 57 models of 0.70, 0.75, and 0.80 Cp, the 1/2 &p values were 13.3, 27.1, and 44.0 deg, the distance of the studs from the stem being, respec- tively, 2.13, 2.70, and 3.25 in. The effects upon resistance were somewhat erratic but never very serious. Model 4200 (0.60 Cp) Slight increase over lower | No change speeds No change except at very lowest speed, C ; rising 4201 (0.65 Cp) me (70) 4203 (0.75 Cp) 4204 (0.80 Cp) slightly with decreasing speed Be low_ = Ora VL large increase in resis- tance—some 60 percent on Cp. At service speed, increase in Cp was 4 per- cent and in Cy about 1% percent Slight increase at all speeds—Cy up 1 per- cent, at service speed No change except at very lowest speed, Cy level with de- creasing speed (The percentage increases are for a 400-ft ship) In view of the small effects of stimulation, it was decided to use results with sand strips without deduction for any parasitic drag. The first step in developing the new Series 60 was a comparison between the results Studs No change Same as sand strips Somewhat larger in- crease—C up 3 per- cent at service speed of certain good ships and the Series 57 equivalents. Studs were used for these tests because ~ they were easy to fit, were positive in location, had some theoretical backing as a means of stimulation, and had very small parasitic drag. The only peculiar results found were with the _ models of the PENNSYLVANIA series. The- PENNSYLVANIA was a tanker of 0.76 Cp and a number of variations were tested. The models are listed in the order in which the tests were carried out. For the first five, the increases in resistance were quite substantial, averaging 10 and 7.5 percent at the service and trial speedsrespectively. For the last four, the cor- responding figures were 0.8 and 1.2 percent. It should be noted that Models 4435W and 4435W.A are built to identical lines, both of wax, and yet they fall into the two groups as regards stimulation effects. The @re. f_ Values listed are those derived from the model results with stimulation; they show no serious change in the resistance picture, indicating that the differences occurred in the tests in the unstimulated conditions. The only division one can make is a chronological one, and no explanation has been found for this peculiar behaviour. A-2 © 400 ft with Percentage Increase Details in €) with Studs Stimulation Service Trial Service Speed Speed PENNSYLVANIA (as built) 4420 4420W-1 PENNSYLVANIA fore body—Series 57 aft body 44685" 4468WA-1 PENNSYLVANIA forebody with Series 60 stem profile—Series 60 stern aft body 4435WA-1 PENNSYLVANIA with Series 60 stem and stern contours 4435WA-2 PENNSYLVANIA with Series 60 stern and PENNSYLVANIA bow contours 4435W.A. PENNSYLVANIA (new casting of 4435\) Series 60 equivalent with PENNSYL- VANIA stem contour For the actual Series 60 parent models, studs were used throughout and the following effects were measured: Cp = 0.60 and 0.65 Resistance unaffected Cp = 0.70 ©) 400 ¢¢ Values increased 0 to 3 percent Cp = 0.75 and 0.80 ©) 400 gt Values increased 0 to 12 percent | The propulsion tests on the Series 60 parents were all carried out with models fitted , with studs. The LCB series were all run in the first place with studs. For comparison, 14 of the 22 models were also run with trip wires. The results for the models without stimulation and with studs were as follows: Cy Studs LCB from® Effect of Studs = Cy Bare All Models No measurable effect Sea Speed Trial Speed ONG 1.037 1.022 1.030 Mean 1.028 Mean 1.090 1.050 1.098 1.050 1.068 1.075 The average increase with the two fuller block coefficients is 5 to 6 percent. For the 0.75 Cp, there appears to be some tendency for the increase in resistance with stimulation to be higher the further forward the LCB, and therefore the fuller the forebody and entrance. The 0.80 Cp does not show such a definite trend, however, and no generalization can be made on this point. When trip wires were used in place of studs, there was no difference in the results except for two of the 0.80 Cp models, when the service and trial speed © values were about 2 percent higher with wires than with studs. — For the models used in the main series to explore the effects of changes in— and W ratios, turbulence was stimulated by trip wires, 0.036 in. in diameter, placed around a section of the model 5 percent of the length from the stem. This choice was made basically on two grounds. Although in general there was no difference in the results using studs or trip wires, the latter did give the higher results on some fuller models, as described above, and, secondly, a review of practices in other model basins indicated a more general accept- ance of the trip-wire technique rather than studs. The results of the main series of models, from which all the contours of Cp and © have been derived, were therefore consistent in that they were all measured on models fitted with trip wires. APPENDIX B USE OF CONTOURS AND CHARTS In order to make the data derived from the very extensive Series 60 research project readily available and useful to naval architects, they have been presented wherever possible as design charts and contours. From these the designer can very quickly make an estimate of performance for any normal single-screw merchant ship whose proportions fall within the area covered by the series. The essential! data are shown in the following figures and tables: Figure 3 Figure + Figure 5 Figure 6 Figure 9 Figure 10 Figure 11 Figures 26-30 ’ Figure 31 Figure 38 | Figures 54-57 Figures B1—B39 Figures B40—B78 Figures B79—B120 Figures B121—B123 Figures B124—B126 Figure B127 Figure D4 Tables 16—26 Tables 27-32 Tables 49-53 Tables B1—B45 Variation of Cy, Cp, and Bilge Radius with CR Variation of Angle of Entrance, Position, and Amount of Parallel Body for Series 60 Parents Contours of Cross-Sectional Area Coefficients Contours of Waterline Half-Breadth Coefficients Le Ratio of for Different Values of Cp and Positions of LCB BP CPE Ratio of for Different Values of Cp and Positions of LCB Bow and Stern Contours Cross Curves of @) to Base of LCB Position Minimum Values of ©) and Corresponding Optimum LCB Locations Cross Curves of DHP on LCB Position Variation of Propulsive Factors with Propeller Diameter and Draft Contours of Residuary Resistance in Pounds per Ton of Displacement Contours of ©) for Ship with 400-Ft LBP Contours of Wake Fraction and Thrust Deduction Contours of Relative Rotative Efficiency e,, Contours of Wetted Surface Coefficient Nomograph for Calculating Frictional Component of Resistance Rk, on Basis of ATTC Line Chart for Conversion of © Values from Froude to ATTC Basis Resistance Data for LCB Series Propulsion Data for LCB Series Corrections to (GON r, for Change in LCB Position L Results of Resistance and Self-Propulsion Experiments on = ; Series Bel To assist in the use of the data, calculation forms for the prediction of ehp and Gy. e | are given in Tables B46 and B47. The tables are largely self-explanatory, but a few points . call for a little comment. ep ; B The contours give and ©) for three values of Th — 2.5, 3.0, and 3.5. For any particular ship, therefore, it is necessary to interpolate between these to obtain the correct B value for the actual a of the ship in question. This could be done by plotting the three B values and lifting off the ordinate at the correct W value. In Table B46, it is suggested that this interpolation be done by assuming a parabola to pass through the three points. This, | RR Be in effect, means that all users will obtain the same value of neg or ©) for the desired jy i.e., it removes personal interpretation of the data; moreover, experience has shown that the B data can thereby be extended to Fi values of 2.0 and 4.0. For comparison purposes, it is sometimes desirable to compute © and (k) for the actual ship under consideration, and this can be done by completing columns O, P, and Q in Table B46. This value of ©) will be different from that for the equivalent 400-ft ship, of course, since frictional resistance is a function of length. The value of ©) for lengths other than 400 ft can be estimated approximately from the differences shown in Table B48, due to Professor L.A. Baier (discussion on Reference 63, page 571). Much of the resistance data published elsewhere refer to a standard ship length of 400 ft and the ©) contours given in this report are for such a standard length, and for Fh. values of 2.5, 3.0, and 3.5. Table B47 © B will enable the value of Ove f, to be interpolated for any other desired value of ae R F The ies nomograph in Figure B127 gives a rapid graphical method of finding the D frictional resistance per square foot of wetted surface for ships of different lengths operating — at various speeds. The results apply to a ship in sea water at a temperature of 59°F (15°C), ! which has been adopted as a standard figure by the ITTC. A standard ship correlation allow- | Rr ance of + 0.0004 has been included. 5 is obtained by passing a straight line through appropriate values of VL and V and reading the answer at the intersection of this line with Rp . . iy MS i the aa scale which is connected to the V-scale used. Estimates for other than standard D R correlation allowance of +0.0004 can be made by taking the above a values and increasing them in the ratio of the total C,, values for the desired allowance and +0.0004, respectively. Incomputing the frictional resistance for estimating power for a proposed vessel, it | is recommended that the wetted surface for the proposed vessel be used. If this figure is not known, the wetted surface for the equivalent Series 60 hull can be obtained from the contours in Figures B124 to B126. B The models used in the E ar series had, for any given block coefficient, a fixed position of LCB, determined from the earlier series of models in whichthe LCB position was varied. In making an estimate of power for a new ship using the Series 60 resistance con- tours, the result will apply to a ship having the LCB in the position chosen for the parent series. If for one reason or another, the new design must have the LCB in some other fore and aft position, then a correction must be made for this difference. If it is assumed that the effect of movement of LCB on the parent model of given Cp and values of a and 2: H L applies also to a model of the same Cp but different values of B and HW? appropriate to the design in question, then the correction can be made from the data given in Chapter VI of this report; see Tables 49-53. In applying results of the kind given in this report, there are often a number of points which at first are somewhat obscure tothe new user and may create difficulties or even errors in making estimates. For this reason, a numerical example has been worked in some _ detail in Appendix D in the hope that it will obviate any such problems arising in the present _ work. Figures B1 through B39 Contours of Residuary Resistance in Pounds per Ton of Displacement ‘ 6.0 ~ | KGS Rae | CNP ECEECE ee PSCeEr PTET 9 SECT A SCEERCT CCIE eo SECC CEB err ress] | rT et a rt Jia Cec eee ie Se eee CEC eerie : Zao Eves een SS oe 55 0.60 062 0.64 0.66 068 0.70 072 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B1 oa ese CCC 0.60 0.62 0.64 0.66 0.68 070 072 0.74 0.76 0.78 0.80 } BLOCK COEFFICIENT Figure B2 B-4 he) 0.60 0.62 064 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B3 INS SREB S eee eA GCe NE RG RRR Se ee eee See J SAE a ee eee aes ieageeceocatecaeeeen 5 0:60 0.62 0.64 0.66 0.68 0.70 072 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B4 B-5 NERA ee ee RANE PRR BRE ie | ACS RDS Sarai Eee eeea | Neel Ae iA TT Hee Bee pet ft tA 80 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B5 9 a Bey TAME Pea (4a Zeer Rae eeteees | | A pes ea Pet ey eee Ta4RSReASE Rew Heb bt Et RARER eae ae. SiPasee caer PELE ao. ee a eee Oe en Se JOO eee Ae Se | 0.60 0.62 0.64 0.66 0.68 0.70 072 0.74 0.76 0.78 0.8¢ BLOCK COEFFICIENT 65 6.0 Figure B6 B-6 NJ Hee com mee ee ze Waite) eae ee ae ee HA HH} a i) 5.5 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B7 ee eae ae Sept dh esas aa eases A pe Ra sa oes TL (CS ee Mee et PERCEPT ba PRR a aes sie eaig 2 Ae eee eee SLE eG! 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B8 B-7 85 B/H=2.5 ETE mie AP Gm Wae |, SRE Bear ARIeeeNe S| | PE AA ee SRS eee eee Pa eee ee ee ea PE Ee ea 5:5 | 0.60 0.62 064 0.66 0.68 0.70 072 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT 65 6.0 Figure B9 ried) At | LU sal Tn ee CMT at | | CEHREEE 0.60 0.66 0.68 0.70 = 8=6—0.60 0.62 0.64 0.66 a7o | BLOCK COEFFICIENT Figure B10 Figure B11 B-8 TH] emas Lae eal Hip aS oH el UT | A (Es a al of Teel | eT eo (EINES) en aa) Vow 055} | |_| 0.60 0.62 064 0.66 0.60 062 064 0.66 BLOCK COEFFICIENT Figure B12 ioc i eRe Rea ss FS a TT ee | ENGI th) Te A a 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B14 BREA tt Ie ES Ani e NECA AIL A SEY E EAA BRR See BERBERS eeeee ee Pres ae Pa EE ee ae az Beas fs Bi 6.5 L}ie) | 0.60 0.62 064 0.66 0.68 0.70 072 0.74 0.76 0.78 0.80 i BLOCK COEFFICIENT Figure B15 SEV II Saves s) : ae |e SR A eee ei Ee Sale So pelt Ett Tri LE aaa 5 0.60 0.62 0.64 0.66 0.68 0.70 072 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B16 B-10 =A Cee oer te SEES ial | deearentiaer? | aes, ey SEERA adm er eee si ea NEVER Sa GSS Rees 2 JE Vere Ss Sap eta he ERR Se aes ess ae ea ee Je eee eRe kaa 5.5 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B17 RHA coy Sch Revie Wid or ei Pe vr i PEELE SELES EPP EERRSUale Leb nea 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B18 B-11 5 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 — BLOCK COEFFICIENT Figure B19 Reese eee Phe | Ee aa NG Ae eer) ee PT AE LY) ve Se Ht AL iy eT eee Ear | | ReRae =| Per WT ae RRR NESENe jeer eee pLdeh | SS eae 5 0.60 0.62 0.64 0.66 0.68 0.70 072 0.74 0.76 0.78 0.80 | BLOCK COEFFICIENT Figure B20 B-12 064 0.66 068 0.70 BLOCK COEFFICIENT Figure B21 060 + 062 064 0.66 0.68 0.70 072 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B22 B-13 65 8.0. hel || AV 7 pe A AA SGaaay | | ail T VJ owe 0.85 0.60 0.62 0.66 0.68 0.70 Figure B24 85 8.0 a HC A/a ewan Toca nett ae FS ee ele || 0.60 0.62 0.64 BLOCK COEFFICIENT 1p) L/B 7.0 65 0.66 Figure B25 Figure B26 : PN rea Bie : a = ie gale + ele ae oS a : Bawa KHER 6.0 aS aeeee ies Cues Beet ere 0.60 0.62 0.64 0.66 0.68 0.70 072 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT CHIL re : Figure B27 = . 0.60 0.62 0.64 0.66 0.68 0.70 072 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B28 B-15 ttt tf Oe ee i 7.5 L/B 7.0 65 . Si Bie Gimbie e Rn eing: | LEE EE Ee eee 0.60 0.6? 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 » BLOCK COEFFICIENT Figure B29 “NORE CLE oe PNUNUET RS EE ee 8.0fP P XQ Y ed See Rae: | 7.5 L/B 7.0 6.5 6.0 5.5 0.60 0.62 0.64 0.66 0.68 0.70 072 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B30 IBSNEREC EEE <4 SAS a Se CANES | Maw arina CARS | EAE sa N en a an P= ne COE CEP I Oe VA Fh mn a 2 "0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B31 5.5 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B32 0.60 0.62 0.64 0.66 0.68 0.70 072 0.74 0.76 0.78 0.80 | BLOCK COEFFICIENT ; Figure B33 0.60 062 064 0.66 068 0.70 072 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B34 0.60 0.62 064 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B35 Ea ae ae aol mele aeee SR eae ewe i eS eae ess BUPA 2 eee ee a TTT et VT HT Ae ! (OE re ee ee eee ante as ee ba i a SE lee, a BRE Sey ERE ee [Pale Ce ae 0.60 0.64 0.66 0.68 070 060 0.62 0.64 0.66 0.68 0.70 BLOCK COEFFICIENT 65 Figure B36 Figure B37 a5 B/H = 3.5 i = ee eee Pa VAS mettle tele f— arivaaem eae aT TE A ee eer an IE 0.60 0.62 0.64 0.66 BLOCK COEFFICIENT Figure B38 85 PEIN] Nees A Saw: ieee a [Teel tt Faace ie Sia AVAVATAE eae WSO." 1.00 P| 0.60 0.62 0.64 0.66 BLOCK COEFFICIENT 80 7.5 L/B 7.0 6.5 Figure B39 Figures B40 through B78 Contours of ©; 400 Ft Ship LBP B-21 76 Le + \ BER LJ \ 1 \ 1 : -| : . ° aaa fo) t ares 0.70 0.68 BLOCK COEFFICIENT Figure B40 B-22 BLOCK COEFFICIENT Figure B41 0.76 BLOCK COEFFICIENT Figure B42 | Fai ae ena | et PSS ae 9° o fo) 4 : o KR a 0.70 BLOCK COEFFICIENT 0.68 Figure B68 B-34 0.60 0.62 064 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B69 0.60 062 0.64 0.66 0.68 0.70 072 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B70 . 0.60 062 0.64 0.66 0.68 0.70 072 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B71 0.60 0.62 0.64 0.66 0.68 0.70 .74 BLOCK COEFFICIENT Figure B72 76 .78 0.80 BLOCK COEFFICIENT Figure B73 L/B a Pee nee viviN Bard We [A VIAA Va VA ZA ape PT: ae Ae ar, if Cleat 0.60 0.62 0.64 0.66 0.68 070 0.60 0.62 0.64 0.66 0.70 BLOCK COEFFICIENT CONTOURS OF ©, 400 FT. SHIP LBP Figure B74 Figure B75 pessoa I Varwe(AY e V H A aA AA AY PEAR GVA AE! [| LLEVA AV Reiciel ae Ae 2 eA Sr eal al SANZ ia Figure B77 Figure B78 Figures B79 through B120 Contours of Wake Fraction and Thrust Deduction B-39 BJ Tanne anna fiamesaceneerar ait JE ea eee ‘—eaniia Preece OCTET RENT Ale 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B79 0.60 0.62 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B80 B-40 pee be Pete =e Nel EOS Sees poe NARUS Te 0.60 t 064 0.66 068 0.70 0.72 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B81 WAKE THRUST V= 15.0 =r V//LwL 2 0.607 0.60 0.62 0.64 0.66 0.68 0.70 072 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B82 B-41 | 0.60 062 0.64 0.66 0.68 0.70 072 0.74 0.76 0.78 0.80 | BLOCK COEFFICIENT Figure B83 0.60 0.62 0.64 0.66 068 0.70 0.72 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B84 B-42 BLOCK COEFFICIENT Figure B85 WAKE Uns = <= = ei HAVIN, Pe EIN USS ZaieS 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B86 B-43 eee ine ee LA IN SC poate j eel sell 0.60 0.62 0.64 0.66 0.68 0.70 072 74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B87 0.60 0.62 0.64 0.66 068 0.70 0.60 0.62 0.64 0.66 0.68 0.70 BLOCK COEFFICIENT Figure B88 Figure B89 B-44 WAKE TERARUST == — — NIA a Ap \ 85 8.0 235W THRUST —- — — Ve aan | B/H=2.5 ital NURI AA 24w Ke 223W APS [\s\| MI | ty V=25.0 V/ofLwi = 0.972 0.60 0.62 0.64 0.66 0.60 0.62 0.64 0.66 0.60 0.62 BLOCK COEFFICIENT Figure B90 Figure B91 SEES RE | ZZ Vi/Ewr 21.013 0.64 0.66 Figure B92 0.74 0.76 0.60 0.62 0.64 0.66 0.68 0.70 072 BLOCK COEFFICIENT Figure B93 B-45 0.60 0.62 064 0.66 068 0.70 BLOCK COEFFICIENT Figure B94 0.72 0.74 WAKE THRUST pe 0.76 6.0 }—+—__+—_+—__+—_++ VA/CwL = 0.566 — 0.62 0.64 0.66 0.68 0.70 BLOCK COEFFICIENT Figure B95 B-46 0.80 0.60 0.62 0.64 0.66 068 0.70 0.72 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B96 v/J/CwL 7 0.648 0.60 0.62 064 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B97 0.60 0.62 064 0.66 068 0.70 BLOCK COEFFICIENT Figure B98 WAKE THRUST 0.60 0.62 064 0.66 068 0.70 BLOCK COEFFICIENT Figure B99 B-48 0.76 Ie WAKE THRUST L/B 65 60 | VA/Cw. = 0.769 | 060 062 064 0.66 068 0.70 072 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B100 0.60 0.62 0.64 0.66 0.68 0.70 072 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B101 B-49 Ti T =n T WAKE —————— WAKE as — THRUSTS THRUST == ee B/H = 30 21.0! wa, :0.85! V/-/ow. 70.891 eae eae oes ele 0.60 0.62 0.64 0.66 0.68 070 0.60 _ 062 0.64 0.66 0.68 0.70 BLOCK COEFFICIENT Figure B102 Figure B103 WAKE ————____; Crcaanas Teer aa WAKE THRUST ===> '== ee ane THRUST — — — B/H=3.0 B/H= 3.0 85 iNere cs 80 7.5 L/B 7.0 65 0.60 0.62 0.64 066 0.60 0.62 0.64 0.66 0.60 0.62: 0.64 0.66 BLOCK COEFFICIENT Figure B104 Figure B105 Figure B106 B-50 a ete ——— a ea 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B107 8.5 Cfebe Ware .64 60 3:5 0.60 0.62 0 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B108 Py Ma ics ieeaeeeceaes 0.80 0.78 0.70 0.72 0.74 0.76 BLOCK COEFFICIENT 0.68 0.66 0.62 0.64 0.60 Figure B109 TARUS Te : = = 0.607 V/o/ Le al 0.62 0.64 0.60 BLOCK COEFFICIENT Figure B110 0.60 062 0.64 0.66 068 0.70 072 0.74 0.76 0.78 BLOCK COEFFICIENT Figure B111 WAKE 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 BLOCK COEFFICIENT Figure B112 B-53 THRUST BLOCK COEFFICIENT Figure B113 8.5 SSE ts NCS eh AS a are OKCCE ak LL [a VEED@nani” EAREMNEARS |. PARE tea eReeee i. ACL A eel TT | ee 8.0 L/B (so 2eeecrkwe a A} 65 & - : ==—=— cae | [wore | | | || Sgaaacer shoe ” PEE 0.60 0.78 0.80 oe perente ENT Figure B114 85 Pty Tt | | | | yy tf wee —— NESS a ge Ul See ZW eases nee Ge AE NCR an aan a 80 i Fle ie one Oe 4 4 aes 70 J 6.5 60 wees} T1111 TT We a ee 0.60 0.62 0.74 0.76 0.78 0.80 ius eee Figure B115 8s THRUST — — — | | | ee ! 7 vege [wit roes: [| )2e4 2. J 0.60 0.62 0.64 0.66 0.68 0.70 BLOCK COEFFICIENT Figure B116 Figure B117 0.60 0.62 0.64 0.66 BLOCK COEFFICIENT BLOCK COEFFICIENT Figure B118 Figure B119 WAKE 0.60 0.62 0.64 0.66 BLOCK COEFFICIENT Figure B120 "St Figures B121 through B123 Contours of Relative Rotative Efficiency, e,, B-57 ise a aA a Bea Fie NI NI SNe) SRS 0.60 0.62 0.64 0.66 0.68 0.70 072 0.74 BLOCK COEFFICIENT Figure B121 ne oi ea CPSC aC “dae eee as Sey, WA ae He NA one vai a= ie ea ae V// Lap = 1o6[185- 1.6 Gp aaa Es ARR Se Seheees 0.60 0.62 0.64 0.66 068 0.70 072 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT Figure B122 0.60 0.62 0.64 0.66 0.68 0.70 BLOCK COEFFICIENT Figure 123 Figures B124 through B126 | Contours of Wetted Surface Coefficient ; 0.70 0.72 0.74 0.76 0.78 0.80 BLOCK COEFFICIENT 0.68 0.66 Figure B124 Shee | le SRVieivite " ° x \ 50 | ey o 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 BLOCK COEFFICIENT 0.62 Figure B125 B-61 Booeac ll ee eS || ase al i 1.8(K ee Ena Same > ee aoa Pep Pe oe ee EERE ee 0. 60 0.62 06 0.68 07 0.76 0.78 0.80 ee fa ed Figure B126 - 13.5 ° a e - 12.5 ae 12 ° 11.5 on = fe) ll 4 < 10.5 + 005 5 : 9.5 1.20 9 8.5 8 1.30— 7.5 U 1.40: 6.5 1.90 aes 1.60 60,000 5.5 59,C0O 40,000 1.70 30,0C0 5.0 20,000 A 1.80 4.5 10,000 Came a ’ 4.0 7,000 aS 6,000 3.8 2.00 5,000 a5 4,000 ae 2.10 3,000 ae 263 o2 2.20 2,000 : : 2.30 ae 2. 1,000 2 2.50: 700 2.6 2.5 204 203 2.2 2.1 2.0 Figure B127 — Nomograph for Calculating Frictional Component of Resistance Fr, on Basis of ATTC Line B-63 TABLES B-1 through B-45 Results of Resistance and Self-Propulsion Experiment for 45 Models of Series 60 €€2°0 220°T 619°0 = SOT°T g60°0 = HOT'O.-COzhdd TIT «682 GOT S22°0 690°T €19°0 90T*T TIT‘O 96T'0 «=: ozEL—s«—“«iaT'GOT «= S92 ~—S HLO'T ST2°0 T90°T 909°0 CUbst 42T°0 ATA) ozZod Z2°90T 0°92 €S0°T +02°0 640°T T09°0 ZIT'T TET*O zz2°0 09449 «4HOT) «6S *S2 €€o°T g69°0 6£0°T 009°0 O2T*T €€T‘o 922°0 ooTH9 TT°2OT 0°S2 €TO°T £02 "0 €fo°T €09°0 get°t TET*O of2"0 ot98S 0°66 S*ne 266°0 ozZ°0 6£0°T +09°0 SHT'T 62T°O = OH". 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Loz2 znt°z 240°2 zto°2 Lr6°T ege°T gTe°T €62°T 889°T €29°T QSS°T genrT g62°T B9T°T 6£0°T @ SP9E J9qQuMN ZaTJado1qg ‘S*¢ = H/g ‘Sz°9 = g/7 ‘S90 = {5 ‘cozy s9qunN Jopow sjueutsedxy uols[ndoig-jjeg pue eouvjsisey jo sj[nsoy ve-d ATaVe 492°9 946°S T69°S 9G62°S 9EL°h wer geL°€ ISE°E zeT°€ gso°t 2z0°€ £zo°€ 200°€ €26°2 of6°2 6gg°% 848° e ozg°2 Tog*z €62°2 29Z°2 9ed°2 992°2 got x 49 dd U33ue7 34 CO JO dyys Jos e1v sein3ty TIV So°t S20°T 00°T $26°0 $6°0 S26°0 06°0 S28°0 Sg°o Szg°0 08°0 $22°0 $2°0 S2L°0 02°0 $49°0 $9°0 S29°0 09°0 SS°0 0S°0 SH°0 04°0 MYA B-98 g2S°0 €go°t S2S°0 zot’t 9€S°0 CITT 9€S°0 O2T°T zHS°0 zeT°t b4S°O TST°T gSS°0 9ST°T +445°0 6ST°T €gS°0 = Z9T° TT 98S°0 ecT°T €9S°0 goe°T £9S°0 gT2°Tt 28S°0 6z2°T T9S°0 one°T TeS°0 gne*T TeS°O 64e°T 29S°0 gne°T zeS°0 = gS2°T 08S°0 g9e"T TeS°0 642°T z9S°0 zge°T 485 °0 462°T 485°0 Coe°t TeS°0 TZE°T 29S°0 Leet 0gS°O = SEPT dg Ye SET°O OnT*O ZT" 94T°O gnT°O 6nT°0 oST°o oST°o oST°o oSt°o g4T°O L4T°O 9nT°0 gnT°O SaT°O SrT“O LnT°0 LaT°O LaT°0 THT'O OhT“O z€T°0 ofT°O gzT°O S2T°o ZTT°0 2 Toz°0 0zz°0 gzz°o gtz°o gnz°0 192°0 S92°0 99z°0 142°0 gde°o €62°0 g62°0 Sot°O TIE°o HTE°0 STE°O ZTE°0 zze°0 L2t°0 6zt°0 62f°0 oft°0 C4 ide) One oO Ont°O fnl°o Ty omnsd S°Ste S°S2 09499 0°d22 = 0°S2 odzgS S°dT2 Ss S* 42 0690S 4°4oz o°re OnS€h 2°g6T Ste osn9t = T°SBT =o" £% of00€ 4°dd2T 8 S°e% o062he 2°89T 0°22 0960¢ 0°09T «=S°T2 odngt 6°fST o°T2 OSS9T T’SHT S°0z Of0ST H°ERT 0°02 oddetT O°6€T S°6T O6hZT S°HET 0°6T OgeTT HOLT SET o9tot S°92T O°8gT 06€6 Scaamee Seot 8Sh8 €°gIt o°dt L092 €°HTT S°9l S989 €°oTtT o°9t 9619 S*90T S°ST SSSS L°zot 30° ST 8964 6°86 S*at QT +h 0°S6 O° AT S6nE 0°88 o°et tLe o°Tg 0°2eT dus N A da 433ueT 44 009 JO dus Joy exe somNn3ty TIV €£o°T £To°T 266°0 246°0 256°0 2£6°0 T16°0 T6g°0 128°0 TSg°0 ofe°o oTg°0 062°0 692°0 6nL°0 622°0 904-0 889°0 99°0 849° 0 g29°0 409°0 28S°0 99S°0 92S°0 98h°0 T/A SET ete’ TET CCT°T 9z0°T 226°0 L4g°0 062°0 4dL°0 192°0 2S2°0 gnL°0 THZ°0 9€2°0 otZ"0 h2L°0 612°0 412°0 602°0 2TZ°0 9T2°0 22"0 © aa ug3uey aq OO JO dtus Joy eB seIn3Ty ITTV 96L°% ged°e 099°% 265°% €25°% SSH°e Letrz2 6TE°S TS2°2 zet*2 HIT? a gd6°T OT6*T Tag*T €22°T S0d°T LE9°T 00S°T HOE°T gze°T T60°T ® S9LZ 19quINN saTTedosq ‘S*€ = H/g ‘StL = g/7T ‘S90 = a5 ‘ELTp JequUNN [apoW gc-d ATAVL syueutiedxy uors[ndoig-j[9g pus oouBysIsoy jo s}[nsoey 9S0°S Té6g°* T6S°h gee°n gee°t gene 6ST°E 626°2 gee" dter2 Sog°2 Ted*2 z9L°2 SrLrz €el°z2 z0L*2 Tg9°2 €99°2 £49°% 4S9°% 229°2 T69°2 got x 40 $2o°T 00°T $26°0 S6°0 S26°0 06°0 S28°0 S8°0 Szg"0 0g°0 $22°0 $2°0 S22°0 04°0 S49°0 S9°0 S2z9°0 09°0 SS"0 oe) SHO 0h°0 T/A B-99 695°0 025°0 025°0 945°0 485°0 26S °O 209°0 2T9°0 gt9°0 TS9°0 29°0 6S9°0 49°0 SS9°0 259°0 259°0 €59°0 459°0 199°0 699°0 Te9°0 269°O 2020 S02°0 422°0 +h 4GL°0 dHS/dHa 2TS°0 = S90°T eTS°0 $2o°T 91S°0 €2o°T TeS*o = 0°T 925°0 zg0°T z€S°0 T60°T THS°O = TOT’T 2nS°O = QTT’T 0SS°0 = HAT’T 4S5°0 = LST°T 2SS°0 SST°T 855°0 9ST°T 6S5°0 T9T'T 655°0 B9T°T 655°0 = TLT’T 655°0 6ZT°T 6SS°0 9gt*t 2S5°0 €6T°T 465°O 4T2°T €5S°0 = gzz"T TSS°0 = dae"T BHS*O HOUT SHS*O Tee'T gS °0 9Z2°T OnS°O = TET HES*O SEET €€S°0 Geert a, Ya 022-0 gz2°0 9€2°0 rare) 0S2°0 9S2°0 492°0 022°0 Tg2°0 292°0 Sy2°0 982°0 062°0 €62°0 S62°0 662°0 €o€"o 40c°0 STE*O zze°o 62£°0 gtt’o ge "O SHEO 6S£°0 69£°0 S9t°O Tp 06ShS S°Tde 0S°S2 onz0S S*t92 00°S2 OLESH O°HSZ OS*HE OSTOR O°+he 00°HZ ozos€. g°f€z os°tz Ogtoe S°tzz o0°t2 02652 o°tte 0°22 ooTz2 S*°20e@ 00°22 O606T S*€6T O0S*T2 ofg9t T'98T O0'TZ OneST L°OgT 0S°02 Of6ET S°SLT 00°02 OTg2zt 2°OdT OS*6T oLdTT 0°S9T 00°6T QZgOT O°09T OS*gT €066 T'SST OO0°QT +H06-—Z°0ST «0S°LT Seg ASHE «00°2T gThL = TORT «0S 9T 0599 SET O0°9T 2265 T°OLT 0S°ST GheS 0°SZT ~00°ST OS9h = @0ZT_—OS*HT ZETH = 6° STL. 00° HT gtze L4°9OT O0°ET 96nz = 2°86 = 00° 2T 9€6T 20°6 OO°TT dus N A d@ uz3ueT 44 009 10 drug soj ore somata ITY €to°T €To'T 266°0 246°0 256°0 z€6°0 TI6°0 T68°0 TZ8°0 TS8°0 ofg'o oTg‘0 062°0 694°0 642°0 622°0 goZ"o 889°0 899°0 8h9°O g29°0 209°0 29S°0 99S°0 925°0 984° 0 S+rh"0 Wy//s ATE°T Lye T6T°T 62T°T 9S0°T 146°0 T68°0 628°0 T6Z°0 42°O 494°0 092°0 $S2°0 0S2°0 +h" gt2°o 2€2°0 424°0 G22°0 gzZ°0 g22°0 €€2°0 onZ°o L4Z°0 ©) d@ W33ueT 44 OOH JO dtUs Joy ore sematad ITV T66°2 6T6°2 84e°? LLL°2 904°2 4E9°% €9S°2 2642 Ten°z ost*2 glz°2 Loe°2 9€T°z S90°2 h66°T ze6°T TSe°T ogZ*T 602°T gto°T 99S°T Hea zge°T 6ET°T @ OP9E JoquinNn soT[edoig ‘s*e = H/g ‘St°8 = g/T ‘S90 = G5 ‘oot soquinN Tepow syuewtiodxq uors[ndoig-jjeS pus oouvysisay JO si[Nsoy 9s-d A TaVL 469°* 9Sh°H 952° 9f0°4 9t2°€ TLh°€ 9eT°€ 496°2 429°2 99L°2 z€L°2 StL*2 004°2 0g9°2 659° £t9°2 gt9°e 009° €6S°2 465°C T09°z zz9°% +9" 699°% got x #0 0S0°T S20°T 000°T $26°0 0S6°0 S26°0 006° $28°0 0S8°0 Sz9'O 009°0 SZL°0 0S2°0 $24°0 002°0 S29°0 0S9°0 S29°0 009°0 S2S°0 0SS°0 00S °0 0Sh°0 00*"0 TAY// A B-100 26S°0 éT0°T TLh°O Leer € “o1zp s2qUNN [2poW sjuewtiedxgy uors[ndolg-j[eg pue souB}sIsoy JO si[nsey ob-d ATAVL 1Z0°% 208° 909°F 6Se"F sl0°% Z0L'E OL¥'s 068°¢ yale 090°¢ 8968'S 828°% 9189'S OLL'S T¥L'6 FILS 89'S 669°3 6613 got x*9 918°0 98°0 928°0 08°0 GLL°0 $20 S2L'0 020 919°0 s9°0 $29°0 09°0 915°0 $9°0 S29"0 0$°0 s¥°0 0r0 s¢°0 TATA/A | B-106 S19°0 €£9°0 499°0 202°0 gzd"0 gtd°0 €52°0 992°0 124°0 £92°0 S92°0 £92°0 2220 4g°O g62°0 428°0 428°0 dHS/ dua 4Z0°T ofo°T stort FHO*T 2S0°T 4S0°T 9S0°T SSO°T 2S0°T gS0°T z90°T T90°T S2o°Tt Sgo°T 2£60°T 62T°T Z9oT°T ile LSh°0 Zeno 00S°0 TIS"0 22S°0 S2S°0 925°0 425°0 425°0 4zS°0 225°0 €26°0 €25°0 TzS°0 61S°0 OTS*°O 964°0 de HIET 922°T Sgz°T HTE'T Geert HEE'T SSE°T 9gt°T T6E°T €ge°t Tgl°T zget zde°T See°T €on°T Oth’ T Ten Ye +hT°O 2dt*0 gcT°o 48T°O 68T°0 S6T°0 46T°O z6T°O L6T°O S0z°0 €T2°0 TIz°0 S12°0 4TZ°0 oTz"0 T12°0 4€2°0 3 009"9 §=«—2°SST 90°02 og6th 4°SfT O°6T O9TOE S°E2T O°gT 024602 = h°0TT = O° LT OzOoSt 6°66 0°9T ofget 2°46 S°ST Og60T 0°06 O°ST L646 9°SB GAT 98¢8 6°Ts O° HT ened 2°ea Ss G* ET £649 S°S2 o° et otds S°2d S°eT 220 9°69 oreT 9SEh 9599 S°TT g9dt — S* £9 O°Tt 9222 2° 2 o°oT L102 6°TS 0°6 dHS N A dd u32uey 34 Q09 JO dtys s0s ere sein3ty TIV oTg°0 692°0 624°0 889°0 849°0 g¢9°0 409°0 2gS°0 998°0 9vS°0 92S°0 90S°0 984° 0 99h°0 Sth°O SOh"O 49£°0 JIMT// 1 dd uy2uey 4 prot Joqunn sajedord “S*€ = H/g *S*S = G/T *08°0= fe) “orZp JOqUNN TePoW sjuewuiedxy uots;ndoig-j[og pus souBysIsoy JO sj[Nsey er-d ATAVL - €26°T 602°9 08°0 208°T 2£0°S SL°0 239°T SLT°* 02°0 229°T S9g°e S29°0 29S°T on9°e S9°0 20S °T Tene $29°0 eth? T GHEE 09°0 eget ene°e S2S°0 AAT e gST°E $S°O 292° STT°E S2S°0 zoe*Tt TOT'E 0S°0 Tg0°T 6IT°E Sh°O T96°0 EnT*E on°0 THE*O TAT°€ SE°O @ got.x 39 T/A OOh JO dtys Jos ee seinsty TIV B-107 Sth°O SS°0 BI°0 = 2.444 vo 648.35 vic = 80.52 Ss 39994 = = 6.168 p23 648.35 For the interpolation process, we need the values of X and X?, where : B X= {2 - 3.0) = 2 (2.444 - 3.0) =-1.112 and X? = + 1.2365 The value of the wetted surface S used above was calculated from the lines drawing. An approximate value can be obtained from the contours shown in Figures B124 to B126 for use in the first ehp estimates, which will probably be made for a number of forms before any lines are drawn. D-5 COLUMN B 7 from contours See we for TS 2.444 pe a =C+E-X+F. X2 H = 6.38-0.228+ 0.031 3.0 3.5 +0.205 | +0.025 This compares with a value of Vv’ /3 of only 0.24 percent. Fr Table D3 shows the calculation of ehp and ship © values from the ie contours given in Figures B1 to B39. The table is largely self-explanatory. Columns B, C, and D RR V B give the values of oe, lifted from os contours for different values of ps and ap é These are corrected to the desired oe for the ship in columns E, F, and G by the interpola- tion process described in the text and illustrated above in its application to the 2/3 contours. R Vv F Column J shows the values of obtained from the nomograph in Figure B127. The final ehp in column M is for the bare hull, without bilge keels, rudder, or other appendages. For comparison with other models, the values of © and ® for the actual ship are given in columns P and Q. Estimates of the © value for a 400-ft standard ship ( (Oyen ft) can be made directly from © ft Contours given in Figures B40 through B78. These are useful for estimates and comparisons with other data when considering various alternative choices of length, beam, draft, fullness, etc., before the design is finalized and an actual ehp for the ship is required. The calculation is shown in Table D4; it follows the same method of interpolation as used in Table D3 but is much shorter for the purpose in view. The ©) and ehp estimates made up to this point are for a ship having the LCB in the LB : ; position chosen for the parents of the B : a series. For a block coefficient of 0.65, this position was 1.54 percent Lp p aft of midships, whereas for this particular ship SCHUYLER D-6 of 6.168 from the calculated wetted surface, a difference eaz'z | 92670 | velL zer'zat| age'sc | seer | 6oea | sec‘ze oog'o+ | ozt"0- ger'z | e9zo | 0109 eSS'9t1| O6I'TZ e98'Sb ozt'o+ | o9t°0+ ZIVLI 66646 | 066'69 60v'EE arora | zar’o+ | ozg'z | 08° | 2p0°9T stz‘se | 2u2'9S ep6'82 | — 66E6I oso'o+ | ogo | —o60°z 0f6'T } so | £L6°bI ely'ze | e6e'6b ozo'ez | 6zps"t too | ezo'o+ | 00z"1 £06°EI 918'09 | 96/'2b zzo'ar | 6L02"1 Lo0°0+ OLzT voc'os | pze'9e ose'er | 01e6"0 o10°0- O10"! | eay'ze | str'te 6LSL°0 to0°0* | 06€0°0+ Tos've | 920°92 9885°0 soo'o- | sovoo+ | 929° ize | e962 | cse'tz{ vesto | sory | 1199 | evo | stoto- | seroro+ | —aesto eso'zz | ctret | = azv'o | Stee | over | THEE‘ 7 3 ° + . ydesBowon | T47°N | Ved TEIN. 9seeol! Ath |. Ser is Ra A GEN a dy 5 1A dy Vv dH] = dy sinojuod woly avs eR et De Se Sie eS ae ee ee ee a/v isetro= eae (suo) *yaw) ——— =, . mo 4 cA oseso Laer EO) = ez ggez't+ x eel 7. e/eV Spolt0= ——-= 4 5 Ay (suo) *jaw) =f A = 49 —— LS2b (OD. GDy (Sy Zit X; 966'6£ s 1 ee T+ 4 = TA t-te (w) 787° A+ 192° = TA 7 Fj ; d 4 a 296"p g/t 026'NT \ SHI 9°Sze 2 = Day Ul — -dH] = 0D . 7 ° H Gigene on Nid yA co, SO, 61°909 ay orLz 4) a pale H — 1 7 z=ih\e u u ver'z = rc (w) TAA ell Tet= — sjouyur A LoS ) SO a u qd A 5 (adAjojoid JON q Ss es d ene = . ee i pon a é (Sais es ove =| 28°9 == 5 d@ (urbs) sy, ) 88" By UW dy 7 q dq 0°0Sb 1 (suoy iu) y(S\ponro= “84 ur Yy Vv al qu ur Yay axg+xo+ (ore =“ 1) ¥ = Y_ i990 (287) 8 gusy 744 dy Uy q Yy Uy swun a1iayy syup ysi8uq . siun 21}@W 40 ys!|8u3 Syue}Suod pue aejnwioy suoisuawig diys ONV18 SILO YITANHOS JO uajeaind 3 Mb8pp “ON 1300W 09 Saluas dius Vv vy SINOJUOD 09 Seles WO eyBUITISY Jomodosioy 8AI}NEIJY — Ed 91qBL V 8/J2/3 Table D4 — © Estimate from Series 60 ©) Contours SERIES 60 MODEL NO. 4484W Shi pala P Equivalent of SCHUYLER OTIS BLAND Ship Dimensions Formulae 497.6 Cy(Lgp) __0.651 yoo =Oaoo ctor B/H = 3.0) + 2X + 6X 450.0 Lap/B 6.82 X = 2[B/H (of prototype) — 3.0] 66.0 B/H 2.444 a -Oroo 3.5) -©y00 0.5) =e 2 ZO x ~1.112 ©),00 (3.5) +©yoo (2.5) —~ 2©voo (3.0) 522,200 x2 + 1.2365 i 2 ae ee ee eae | Polanski ® DB \(D+B=26. B/H=25 B/H=3.5 C+EX+FX? B/H = 3.0 12 | oss | ose | o.ma_| +0022 | oo | 0.667 _| p14 | 0677 | 0689 | 0.708 | +o.015 | +0.003 | 0.676 (15 {| 0.60 | oss | 0.709 | 0.015 | +0.0083 | 0.678 ies | Ova 0713 | +0014 | +0002 | 0.683 | j17 | 0695 [0.706 | 0.722 pom | ons | os | +001 | +0006 | om | Fes [ica [ors | oes | one | 0.052 | 1.052 _| pea [et [ee [os [26 [00s [a0 OTIS BLAND, the required position is 1.00 percent L pp aft. The correction can be made from the data given in Tables 49—53, and the resultant ehp and © values are shown in Table D5. The parent model of 0.65 Cp had the LCB 1.54 percent L pp aft of midships, whereas the position required in the Series 60 equivalent of SCHUYLER OTIS BLAND is 1.00 percent L pp aft. The corrections given in Tables 49—53 were cross plotted to a base of LCB position and the values lifted off at the desired point are shown in Table D5. Because of the erratic variation of@) with LCB position, linear interpolation is not possible. These values are plotted in Figures D2 and D3. The two © curves in Figure D2 are in very good agreement, remembering that the one for the 450-ft ship should be lower than that for the 400-ft ship because of the difference in skin friction coefficient. This agreement is R of considerable interest because one © curve is derived from the “Ae contours, the other from the Oro s_ Contours, and although both sets of contours are based ultimately on the same model experiment results, the subsequent fairing to obtain the contours was done quite independently. The agreement indicates that both sets represent the results very closely. In the course of the analysis of the Series 60 original parents, a comparison was made between the model of the actual SCHUYLER OTIS BLAND and a model of the Series 60 equi- valent. It is thus possible to make a direct comparison between these model results and the estimates made from the Series 60 contours. The actual model results are shown in Table D6 and plotted in Figures D2 and D3. They give considerable confidence in estimates made from the Series 60 contours. For propulsion data, the wake and thrust deduction fractions and the relative rotative ’ efficiencies can be obtained from the respective contours in Figures B79 through B123, using the same method of interpolation as with the t and © contours. With this information and suitable propeller design charts, estimates can easily be made of propulsive efficiencies for different engine conditions, provided the propeller diameter is about 0.7 of the draft. For any other diameter/draft ratio, corrections can be made from the data given in Chapter X of this report. Much of the model data in the world is published in the form of Gy fe USIng the Froude Oy and 0. frictional coefficients in the extrapolation from model to ship. As stated in the text, Gertler has given a quick method of converting Oss s, from the Froude values 47 to the ATTC values, or vice versa,’’ and his chart is reproduced in Figure D4. As an example, take the case of the Series 60 equivalent of SCHUYLER OTIS BLAND ata ® value of 2.0. 1, = 20.338 ft 400 \* : A = 14,920 tons for 450-ft ship and A = 14,920 ‘() for 400-ft ship (S) = 6.168 = 10,473 tons. D-9 Table D5a — Correction to Actual Ship@) and EHP for Shift in LCB Position Percent Correction | Uncorrected | © Ship Uncorrected EHP from Series 60 Ship from | Corrected EHP from Corrected LCB Position Table D3 Table D3 Table D5b — Correction to C) 99 -, Ship and EHP for Shift in LCB Position Percent Correction ©; ft Orxoo ft from Series 60 Uncorrected | Corrected LCB Position from Table D4 D-10 dius (0) S{seJ, [opoW Woy ssoyy 4M peyuUnsy se QNV'Td SILO YATANHOS 10} dHa pus ©) diyg jo uostuedwog — eq oindig dIHS YO4 SLONM NI A oz eI 91 ol ZI ol 8 $1S31 1300W WONS O 4dIHS 897 YO 03193409 SBNOLNOD O9 S3IN3S WON A3AIN30 O SEES See ee ae eee ooo! ooo¢g 000% 000s 0009 000d 0006 GNV'Td SILO Yd'TANHOS 403 sinojyu0D aS YU Yd pus (0) wojj SeAIND (0) jo uostaeduog — gq eind1y SL1NS3Y 1300W NOS O--O v dIHS 143 0G YOd SYNOLNOD iy Wous G3AIN30 O--O D-11 Table D6 — Model Results for Series 60 Equivalent of SCHUYLER OTIS BLAND EHP for Ship Osco ee Shiv 8 514 1.058 725 De12 | 6.0 2.0 1.0 0.0 -H30-Foot Model t 25-Foot Model 20-Foot Modal IS-Foot Model 10-Foot Model 8-Foot Model 2,000 Tons 8,000 Ton 10,000 Tors tot Ssaansa) sang oqadey Genesequssessrnan ace suche OS PL AAE Temperature Correction jf 7 ee ones So 5 | 10] 18 | 20] 25] 30] 35 trot Gane ore I t ~~80 __|a003] a000}-a002}-a003 |-.qo0s }ap04}.a004 ea ap 43 Ar 75 04] a001| ao0o 1 }a003 opo2}-a002 = THT vi rabawasal 70 |a005] aooe| ap01 | a00}-a001 \[-op01 = - sasasssddessaessee 65 |.a004] ao01| ao] aooo] ap00} apo0} ap00 + ; + + 59 {a000| aD00} ad0c] a000] A000] an00} a000 35 03]-a00 1|-a001 |-a001 | 900] ao00] a000 ft 50 0. 08|-0904]-a002 |-ao02|-a002|-a001|-2901 Where: §R is the difference between the totol resistance calculated using Schoenherr-Schoenherr and thot using Froude - Froude. is the displacement. is the speed, is the volume of displacement. is the oreo of wetted surface. is the acceleration due to gravity. eund

Gh models Conia oael (ITTC) (ATTC) (ITTC) or 0.001950 + 0.003415 - 0.003490 or 0.001950 -— 0.000075 or 0.001875 Entering Figure E1 with this value for (C’;, + 0.0004) and a speed of 14.973 knots, the R value of —* is 1.197, whence A , = 1.197 x 39994 = 47873 lb. Hence Rp =Rp+Fhp S = 23020 + 47873 = 70893 lb 70893 x 14.973 325.6 = 3260 Then ehp = The corresponding ehp using the ATTC line is 3330 (Table D3), so that using the ITTC line gives about 2 percent less ehp in this particular case. D-15 APPENDIX E INTERNATIONAL TOWING TANK CONFERENCE 1957 MODEL SHIP CORRELATION LINE Meeting in London in 1948, the ITTC* agreed that in future published work the extrapo- lation of model resistance results to estimate resistance and power for the ship would be carried out by using either the Froude coefficients or the ATTC 1947 line, the latter being based upon the work of Schoenherr. In using this latter line, a ship correlation allowance is usually made of +0.0004 on Cp. The 1948 Conference also set up a Skin Friction Committee which was instructed, inter alia, ‘‘to survey the problem of skin friction in general, and in particular to recommend what further research should be carried out to establish the minimum turbulent friction line for both model and ship use.’?”° This committee finally reported to the 8th ITTC in Madrid in 1957, making two alter- native proposals, Both were designed to increase the slope of the ATTC line at the low values of Reynolds number associated with the use of small ship models while giving values close to the ATTC line at high Reynolds numbers. One of these proposals was, in effect, adopted by the Conference, which decided that ‘‘the line given by the formula 0.075 ( ; (logo Bn - 2) is adopted as the ITTC 1957 model-ship correlation line, it being clearly understood that this is to be regarded only as an interim solution to this problem for practical engineering purposes.”?” 4 Tables of values of C, derived from this formula have been given at various times (see for example Reference 72), and the differences between them and those represented by the ATTC 1947 line can be illustrated by the following figures: Values of Cp x 10° ATTC 1947 | ITTC 1957 | Difference log, F,, Line Line 6.0 4.410 4.688 +0.278 7.0 2.934 3.000 +0.066 8.0 2.072 2.083 +0.011 9.0 1.531 1.531 “- 10.0 1.1738 1,172 —0.001 af — *Then called the ‘International Conference of Ship Tank Superintendents. ”’ E-1 7123-988 O - 64 - 21 One or two points are worth mentioning in connection with this new formulation. 66 In the first place, the Conference was careful to label the line a ‘‘model-ship correla- tion line,’’ thereby emphasising that the members did not consider it to be a line representing the skin friction of the hull nor of an equivalent plank. It is, as the resolution states, ‘‘for ’ and may be taken as including some allowance for form practical engineering purposes,’ effect. At the time of the 1957 Conference, a great deal of research was in progress on the problem of extrapolation from model to ship, and it was generally felt that great developments ‘interim solution.’’ were likely in the not too distant future—hence the emphasis on an These will probably take the shape of a three-dimensional system of extrapolation, allowing for the effects of hull form and proportions upon the viscous resistance. Such methods have been proposed, but the profession will no doubt wish to gain experience in their use before making what will be, after all, a radical departure from the practice of nearly a hundred years. Secondly, the values of C; quoted above show that the 1957 ITTC line is everywhere steeper than the 1947 ATTC line, and it is this slope which is important in the extrapolation problem. Since the ITTC line is higher over the model range, the C p values derived from the model results will be smaller. When added to the ITTC C, values over the ship range, which are nearly equal to or less than the ATTC values, those Cp values will result in a lower prediction of the total ‘‘ smooth’’ ship resistance and corresponding ehp. This will apply whatever the model scale, but the effect will be larger with small models run at low Reynolds numbers. In the third place, in adopting the new correlation line, the ITTC made no recommenda- tion regarding the ship correlation allowance to be used in predicting ehp for the actual ship, contenting itself merely with a general recommendation to continue work ‘‘to improve model and ship correlation’’ and ‘‘to determine roughness allowances.’’ In adopting its line in 1947, the ATTC considered a number of model-ship correlations available at that time and while recognizing the sparseness of the data and the possible dependence of the allowance on a number of factors other than roughness, did finally recommend a ‘ ‘roughness”’ allowance of +0.0004 for all ships; this allowance has been used since in all published work based on the ATTC 1947 line. For most merchant ships of the seagoing types, the resultant ship ehp did not differ much from that obtained using the same model results and the Froude coefficients. For the same model results and the same full-scale ship trial results, the use of the ITTC line will call for a somewhat greater correlation allowance than would the use of the ATTC line in order to obtain the same agreement. If a new three-dimensional method of extrapola- tion is devised in the future, the value of the correlation allowance necessary to reconcile the same model and ship results will have a still different value. It is very obvious, as pointed | out by the present author in 1957, that this factor is not just an allowance for the relative roughnesses of model and ship but involves such things as the method of extrapolation used, the relative sizes of model and ship, scale effect on wake, thrust deduction, and propeller E-2 efficiency, factors which are involved in the comparison of the resistance of the model with that of the ship as deduced from shaft horsepower measurements made on trial—and other quantities besides hull surface finish.’ The term ‘‘roughness”’ allowance is therefore very misleading, and for this reason has not been used in the present text. The more rational name ‘‘ship correlation allowance”’ or ‘‘factor’’ has been suggested and the ITTC Presentation Committee has proposed the symbol C ,, where the suffix stands for ‘‘additional.’’ In Great Britain, where the Froude coefficients are still in general use, the NPL tanks have for some years used a “‘ship correlation factor’’ which has different values for different types of shell construction, these values being derived from comparisons of actual ship trial results with corresponding predictions from model tests. The British Admiralty tanks use a similar method of correlation in the form of a quasi-propulsive coefficient factor. The weight of evidence today is that the allowance of +0.0004 above the ATTC line is somewhat too high for modern merchant ships of good welded construction, with a clean, newly painted hull surface, using a standard commercial paint. Hadler et al have recently given correlation allowances for 13 merchant ships for which good full-scale and model data were available.’* They found that the correlation allowances decreased in magnitude both with increase of length of ship and with the date of construction, but were unable to disentangle the relative importance of these two effects because of the small number of ships available. The newer the ship, the better the probable finish of hull surface, but also the newer ships in general are longer. When they considered only seven ships built since World War II, they found the average values of C , were +0.00015 for the ATTC line correlation and +0.00020 for the ITTC. This difference is small, and will be so for correlations carried out from experiments with large models of the order of 20 ft in length. Because of the divergence of the ATTC and ITTC lines at low Reynolds numbers, the differences in correlation allowances for the two methods will increase with the use of smaller models. A large number of ship trials have been correlated with model experiments in Great Britain.’> The trials were carried out on some 69 single-screw and 21 twin-screw ships by the British Ship Research Association and the models were run in the NPL tanks. There was some variation in C , with speed, but no length effect was obvious. For all-welded hulls, the average value of C , using the ITTC line was +0.00015 (with a total scatter of 0.0004) and for half-welded hulls (generally welded butts and riveted seams) +0.0004 (with a total scatter of 0.0007). Using the ATTC line, the corresponding C , values were +0.00005 and +0.0003. Clements pointed out in this paper that the best results achieved to date corre- spond to a correlation allowance C , of zero. More recently, results of British ship trials embracing modern large tankers have suggested a definite trend towards lower correlation allowances with increasing length, and a proposal to represent this by the straight line C 4 = 0.00160 - 0.0000023 + L pp E-3 has been made by Moor (discussion on Reference 74). This equation leads to a value of +0.00045 for a ship with an LBP of 500 ft, zero for 700 ft, and negative values for longer lengths, all based on the ITTC line. In order that the Series 60 results based upon the ATTC line can be compared with others derived from model tests by the use of the ITTC line, it is desirable to provide a rapid method of conversion from one method to the other. This involves the choice of a correlation allowance C ,. In view of the above discussion, the ATTC allowance of +0.0004 would appear too high for modern ships, and moreover it should quite possibly be varied with length of ship, but there is no finality in these matters at present. Since there is little difference in the ship prediction from the Series 60 models whichever line is used for extrapo- lation, the only logical choice would seem to be to use the same allowance of +0.0004 with the ITTC line until such time as a more definite value is recommended by the ITTC. A second nomograph has therefore been prepared on the basis of the ITTC line using a correlation allowance of +0.0004; see Figure E1. In any individual case, if some other value of C , is preferred, an appropriate allowance can be made. The relative values of the frictional and residuary resistances for a given model total resistance will be different when using the ATTC and ITTC lines, so that it is not sufficient merely to correct the frictional part of the total. Using the suffixes ¢, 7, and f for total, residuary and frictional, m and s for model and ship and C and C’ for resistance coefficients using ATTC and ITTC lines, respectively, we can write Crm = Crm + © fn =O rm OF and CeCe. Cy -C%,, also Cg = Cet Ce. C,, is the residuary resistance coefficient as obtained using the ATTC line, and so the R values of —* can be lifted from the contours and inserted in Column G of Table D3 as A : before. The frictional resistance coefficient to use with the nomograph for the ITTC line will now be OF + (Gr = C im) i.e, ITTC ship coefficient + (ATTC model coefficient-ITTC model coefficient). E-4 * (Cy + 0.0004) x 10° 1. (Cy + 0.0004) x 10° VL ra o 60,000 $0,000 40,000 1.7 30,000 20,000 1.8 10,000 1.9 2-0 5,000 4,000 2.1 3,000 2.2 2,000 2.3 2.4 1,000 4.0 2.5 a 3.€ eae xe 2 3.9 2e7 2s 3. 2.8 Lent 3 2.9 200 3.0 3.1 3.2 100 363 80 3.4 ce) 365 366 « 3.7 3.8 AdleanG: 1947 LINE ae LINE R . . e Figure E1 — Nomograph for md Computation based on ITTC 1957 Model-Ship Correlation Line 8 - E-5 In Figure El the V- L and Cs scales have been extended to cover model values, so that Cin can be found. For convenience, extended scales of VL and Cy for the ATTC line are also given at the left-hand side, but these form no part of the nomograph itself. As an example, consider a ship 500 ft in waterline length with a speed of 20 knots. V = 20 knots Vie Ei = 10,000 The Series 60 models have a WL length of 20.388 ft, so that the scale will be 500 Se Tae. = 20 20 20 For the model, Vila = —— = 4,039 knots Va V 24.52 4.952 and L = 20.388, whence VL = 4.089 x 20.388 = 82.34. For VL = 82.34, from Figure E1 ae + 0.0004 = 0.00830 for ATTC line fe + 0.0004 = 0.00337 for ITTC line and for VL = 10,000 oun + 0.0004 = 0.001879 for the ITTC Hence the final value of the resistance coefficient to be used is C’, +(C, -—C%, ) = 0.001879 + (0.00330 — 0.00337) f. Vn ue ’ = 0.001879 — 0.00007 = 0.001809 On Figure E1, starting with this value of Cis for the ITTC line, a straight line F through a speed of 20 knots on the V scale will give a value of ms of 2.069, which will be inserted in Column J of Table D3 and the calculation completed in the usual way. REFERENCES The following standard abbreviations are used in these references: Trans. INA — Transactions, Institution of Naval Architects, London SSPA - Statens Skeppsprovnings Anstalt (Swedish State Ship- building Experimental Tank), Goteborg Trans, NECI — Transactions, North East Coast Institution of Engineers and Shipbuilders, Newcastle, England Trans. IME — Transactions, Institute of Marine Engineers, London Trans. IESS — Transactions, Institution of Engineers and Shipbuilders in Scotland, Glasgow NSMB -— Netherlands Ship Model Basin, Wageningen SNAME -— Society of Naval Architects and Marine Engineers, New York TMB -— David Taylor Model Basin 1. Project 2 of the Hydromechanics Subcommittee of the Society of Naval Architects and Marine Engineers, ‘‘Model and Expanded Resistance Data Sheets.”’ —€2,) Taylor, D.W., ‘‘Speed and Power of Ships,’’ published by the Department of Commerce, Washington, D.C. (1933). 3. Kent, J.L., ‘‘Model Experiments on the Effect of Beam on the Resistance of Mercantile Ship Forms,’’ Trans. INA (1919). 4, Lindblad, A., ‘‘Experiments with Bulbous Bows,”’ Pub. 3, SSPA (1944). 5. Lindblad, A., ‘‘Further Experiments with Bulbous Bows,”’ Pub. 8, SSPA (1948). 6. Nordstrom,’H.F., ‘‘Some Systematic Tests with Models of Fast Cargo Vessels,’’ Pub. 10, SSPA (1948). 7. Nordstrom, H.F., ‘‘Further Tests with Models of Fast Cargo Vessels,’’ Pub. 14, SSPA (1949). 8. Nordstrom, H.F., ‘‘Systematic Tests with Models of Cargo Vessels with Block Coeffi- cient =0.575,” Pub. No. 16, SSPA (1950). 9. Edstrand, H., et al., ‘‘Experiments with Tanker Models I,’’ Pub. 23, SSPA (1953). 10. Edstrand, H., et al., ‘‘Experiments with Tanker Models II,’’ Pub. 26, SSPA (1953). 11. Edstrand, H., et al., ‘Experiments with Tanker Models III,’’ Pub. 29, SSPA (1954). 12. Lindgren, H., ‘‘Experiments with Tanker Models IV,’’ Pub. 36, SSPA (1956). 13. Edstrand, H., et al., ‘‘Experiments with Tanker Models V,’’ Pub. 37, SSPA (1956). 14. Warholm, A.O., ‘‘Tests with Models of Coasters,’’ Pub. 24, SSPA (1953). 15. Lindgren, H. and Warholm, A.O., ‘‘Further Tests with Models of Coasters,” Pub, 35, SSPA (1955). 16. Edstrand, H. and Lindgren, H., “‘Systematic Tests with Models of Ships with orn = 0.525,’’ Pub. 38, SSPA (1956). 17. Freimanis, E. and Lindgren, H., ‘‘Systematic Tests with Ship Models with 5,p = 0.675 — Part I,’ Pub. 39, SSPA (1957). 18. Freimanis, E. and Lindgren, H., ‘Systematic Tests with Models of Ships with bop = 0.675 — Part II,’’ Pub. 41, SSPA (1957). 19. Freimanis, E. and Lindgren, H., ‘‘Systematic Tests with Models of Ships with Sop = 0.675 — Part III,’? Pub. 42, SSPA (1958). 20. Freimanis, E. and Lindgren, H., ‘‘Systematic Tests with Ship Models with Bors = 0.600 to 0.750,’’ Pub. 44, SSPA (1959). 21. Lindblad, A., ‘‘Some Experiments with Models of High-Speed Cargo Liners,”’ Pub. 25, Trans. of Chalmers University Goteborg (1943). 22. Lindblad, A., ‘‘Experiments with Models of Cargo Liners,’’ Trans. INA (1945). 23. Lindblad, A., ‘‘Some Experiments with Models of High-Speed Ships,’’ Trans. INA (1948). 24. Lindblad, A., ‘‘Further Experiments with Models of High-Speed Ships,’’ Trans. INA (1950). 25. Todd, F.H., ‘‘Further Model Experiments on the Resistance of Mercantile Ship Forms — Coaster Vessels,’’ Trans. INA (1981). 26. Todd, F.H., ‘‘Screw Propeller Experiments with Models of Coasters — the Effect of a Cruiser Stern,’’ Trans. NECI (1934). 27. Todd, F.H. and Weedon, J., ‘‘Further Resistance and Propeller Experiments with Models of Coasters,’’ Trans. INA (1938). 28. Todd, F.H. and Weedon J., ‘‘Experiments with Models of Cargo-Carrying Type Coasters,’’ Trans. IME (1940). 29. Todd, F.H. and Weedon, J., ‘‘Further Experiments with Models of Cargo-Carrying Coasters,’’ Trans. NECI (1942). 30. Dawson, J., ‘‘Resistance of Single-Screw Coasters, Part I,’’ Trans. IESS (1952-1953). 31. Dawson, J., ‘‘Resistance of Single-Screw Coasters, Part II,’’ Trans. IESS (1954-1955). 32. Dawson, J., ‘‘Resistance of Single-Screw Coasters, Part III,’’ Trans. IESS (1955-1956). ; 33. Dawson, J., ‘‘Resistance of Single-Screw Coasters, Part IV,’’ Trans. IESS (1959-1960). 34, Haaland, A., ‘‘Some Systematic Variations in the Shape of Coasting Vessels, Etc.,” Report 4, Norwegian Tank, Trondheim (1951). R-2 35. Koning, J.G., ‘‘E.H.P. of Small Seagoing Cargo Ships,’® Pub. 37, NSMB. 36. Ackerson, J.L., ‘‘Test Results of a Series of 15 Models,’’ Trans. SNAME (1930). 37. Davidson, K.S.M. and Suarez, A., ‘‘Tests of Twenty Models of V-Bottom Motor Boats, EMB Series 50,’? TMB Report R-47 (Mar 1949). 38. Almy, N.V. and Hughes, G., ‘‘Model Experiments on a Series of 0.65 Block Coeffi- cient Forms, Part I,’’ Trans. INA (1954). 39. Ferguson, J.M. and Meek, M., ‘‘Mcdel Experiments on a Series of 0.65 Block Coeffi- cient Forms, Part II,’’ Trans. INA (1954). 40. Ferguson, J.M. and Parker, M.N., ‘‘Model Resistance Tests on a Methodical Series of Forms C p = 0.65 to 0.75,” Trans. INA (1956). 41. Balckwell, R.E. and Goodrich, G.J., ‘‘Model Experiments on a Series of 0.70 Block Coefficient Forms, Part I,’’ Trans. INA (1957). 42, Blackwell, R.E. and Doust, D.J., ‘‘Model Experiments on a Series of 0.70 Block Coefficient Forms, Part II,’? Trans. INA (1957). 43. Moor, D.I., Parker, M.N., and Pattullo, R.N.M., ‘‘The B.S.R.A. Methodical Series — An Overall] Presentation,’’ Trans. INA (1961). 44, Todd, F.H. and Forest, F.X., ‘‘A Proposed New Basis for the Design of Single-Screw Merchant Ship Forms and Standard Series Lines,’’ Trans. SNAME (1951). 45. Todd, F.H., ‘‘Some Further Experiments on Single-Screw Merchant Ship Forms — Series 60,’’ Trans; SNAME (1953). 46, Hughes, G. and Allan, J.F., ‘‘Turbulence Stimulation on Ship Models,’’ Trans. SNAME (1951). 47. Gertler, M., ‘‘A Method for Converting the British ©) Coefficient Based on the Froude ‘0’ Values to an Equivalent © Coefficient Based on the Schoenherr Frictional Formula,”’ TMB Report 657, Rev. Ed. (Jun 1949). 48. Troost, L., ‘‘A Simplified Method for Preliminary Powering of Single-Screw Merchant Ships,’’ SNAME, New England Section (Oct. 1955). 49, van Lammeren, W.P.A., Troost, L., and Koning, J.G., ‘‘Resistance, Propulsion and Steering of Ships,’? H. Stam, Haarlem, Holland (1948). 50. Volker, H., ‘Optimum Location of L.C.B. of Merchant Ships,’’ Schiff und Hafen, Jahrgang 5, Heft 3 (Mar 1953). 51. Bocler, H., ‘‘The Position of LCB for Minimum Resistance,” Trans. IESS (1953). 52. Heckscher, E., ‘‘Erfahrungen uber Formegebung von Seeschiffen,’’ Hydromechanische Problem des Schiffsantriebs, Hamburg, Germany (1940). 58. Ayre, Sir Amos, ‘‘Approximating EHP,’’ Trans. NECI (1947-48). 54. Todd, F.H., ‘‘Fundamentals of Ship Form,’’ Trans. IME (1940). 55. Dawson, J., ‘‘Resistance of S. S. Coasters,’ Trans. IESS (1952—53). 56. Lap, A.J.W., ‘‘Diagrams for Determining the Resistance of Single-Screw Ships,”’ Pub. 118, NSMB (1954). 57. Troost, L., ‘SOpen Water Test Series with Marine Propeller Forms,’’ Trans. NECI (1951). = 8) Saunders, H.E. ‘‘The Prediction of Speed and Power of Ships by Methods in Use at the U.S. Experimental Model Basin, Washington,’’ C & R Bulletin No. 7, U.S. Government Printing Office, Washington, D.C. (1933). 59. Gertler, M., ‘‘The Prediction of the Effective Horsepower of Ships by Methods in Use at the David Taylor Model Basin,’? TMB Report 576, Second Edition, (Dec 1947). 60. Gertler, M., ‘‘A Reanalysis of the Original Test Data for the Taylor Standard Series,”’ TMB Report 806 (Mar 1954). 61. Hadler, J.B., Stuntz, G.R., and Pien, P.C., ‘‘Propulsion Experiments on Single- Screw Merchant Ship Forms—Series 60,’’ SNAME (1954). 62. Todd, F.H. and Pien, P.C., ‘‘Series 60 — The Effect upon Resistance and Power of Variation in LCB Position,’? SNAME (1956). 63. Todd, F.H., Stuntz, G.R., and Pien, P.C., “Series 60 — The Effect upon Resistance and Power of Variation in Ship Proportions,’? SNAME (1957). 64. Stuntz, G.R., Pien, P.C., Hinterthan, W.B., and Ficken, N.L., ‘‘Series 60 — The Effect of Variations in Afterbody Shape upon Resistance, Power, Wake Distribution, and Propeller-Excited Vibratory Forces,’? SNAME (1960). 65. Harvald, S.A., ‘‘Wake of Merchant Ships,’? The Danish Technical Press, Copenhagen (1950). 66, Doust, D.J. and O’Brien, T.P., ‘‘Resistance and Propulsion of Trawlers,’’ NECI, Vol. 75, (1958-59). 67. Kerwin, J.E., ‘‘Polynomial Surface Representation of Arbitrary Ship Forms,’’ Journal of Ship Research, Vol. 4, No. 1 (1960). 68. Gerritsma, J., Kerwin, J.E., and Newman, J.N., ‘‘Polynomial Representation and Damping of Series 60 Hull Forms,”’ International Shipbuilding Progress, Vol. 9, No. 95 (Jul 1962). 69. Hess, J.L. and Smith, A.M.O., ‘Calculation of Non-Lifting Potential Flow about Arbitrary Three-Dimensional Bodies,’’ Douglas Aircraft Division Report E.S. 40622 (Mar 1962). R-4 70. Fifth International Conference of Ship Tank Superintendents, London, 1948, p. 114, H.M. Stationery Office, London (1948). 71. Eighth International Towing Tank Conference Proceedings, Madrid, 1957, p. 324, Canal de Experiencias Hidrodinamicas, El] Pardo, Madrid (1959). 72. Hadler, J.B., ‘‘Coefficients for International Towing Tank Conference 1957 Model- Ship Correlation Line,’? TMB Report 1185 (Apr 1958). 73. Todd, F.H., ‘‘Skin Friction and Turbulence Stimulation,’’ Eighth International Towing Tank Conference Proceedings, Madrid 1957, p. 88—89, Canal de Experiencias Hidrodinamicas, El Pardo, Madrid (1959). 74. Hadler, J.B., Wilson, C.J., and Beal, A.L., ‘‘Ship Standardization Trial Performance and Correlation with Model Predictions,’’ SNAME, Chesapeake Section (Dec 1961). 75. Clements, R.E., ‘‘An Analysis of Ship-Model Correlation Data Using the 1957 I.T.T.C. Line,’’ Trans. INA (1959). SERIES 60 PAPERS I. ‘‘A Proposed New Basis for the Design of Single-Screw Merchant Ship Forms and Standard Series Lines,’’ Todd, F.H. and Forest, F.X., SNAME (1951). II, ‘‘Some Further Experiments on Single-Screw Merchant Ship Forms—Series 60,’’ Todd, F.H., SNAME (1953). II. ‘‘Propulsion Experiments on Single-Screw Merchant Ship Forms—Series 60,”’ Hadler, J.B., Stuntz, G.R., and Pien, P.C., SNAME (1954). IV. ‘‘Series 60—The Effect upon Resistance and Power of Variation in LCB Position,”’ Todd, F.H. and Pien, P.C., SNAME (1956). V. ‘Series 60—The Effect upon Resistance and Power of Variation in Ship Proportions,”’ Todd, F.H., Stuntz, G.R., and Pien, P.C., SNAME (1957). VI. ‘‘Series 60—The Effect of Variations in Afterbody Shape upon Resistance, Power, Wake Distribution and Propeller-Excited Vibratory Forces,’’ Stuntz, G.R., Pien, P.C., Hinterthan, W.B., and Ficken, N.L., SNAME (1960). 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Wehausen Dr. E.H. Kennard, LaVerne, Calif Dr. H.H. Jasper, US Navy Mine Def Lab Panama City |), Dr. Willard J. Pierson, Jr., Col of Engin, NYU, New York Dr. Finn Michelsen, Dept of Nav Arch, Univ of Mich, Ann Arbor Prof. Richard MacCamy, Carnegie Tech, Pittsburgh 13 Dr. T.Y. Wu, Hydro Lab, CIT, Pasadena Dr. Hartley Pond, 4 Constitution Rd, Lexington 73, Mass Dr. J. Kotik, TRG, 2 Aerial Way, Syosset, N.Y. Prof. Byrne Perry, Dept of Civil Eng, Stanford Univ, Palo Alto, Calif Prof. B.V. Korvin-Kroukovsky, East Randolph, Vt Prof. L.N. Howard, Dept of Math, MIT, Cambridge 39, Mass Prof. M. Landahl, Dept of Aero & Astro, MIT, Cambridge 39, Mass Pres, Oceanics, Inc, 114 E 40 St, N.Y. 16 U. S. 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