THE DESIGN PRESENTATION OF SHIP MODEL RESISTANCE DATA

¡ C HARGING TWO-STROKE DIESEL ENGINES THE DESIGN PRESENTATION OF SHIP MODEL RESISTANCE DATA By Prof. E. V. TELFER, Ph.D., D.Sc., Fe/low 26th April, ...
Author: Meredith Holmes
54 downloads 1 Views 3MB Size
¡

C HARGING TWO-STROKE DIESEL ENGINES

THE DESIGN PRESENTATION OF SHIP MODEL RESISTANCE DATA By Prof. E. V. TELFER, Ph.D., D.Sc., Fe/low 26th April, 1963 SYNoPsrs.- The paper starts by commenting on the early use of ship model experiments and the general development of methods of storing the informa/ion derived from such experiments. B. J. Tideman is acknowledged as being in 1878 the He was pioneer in the non-dimensional presentation of model resistance data. fol/owed by R. E. Froude in 1888 whose work has long and rightly dominated tlze subject. Departures from the classic work of Froude due to D. W. Taylor and others have probably greatly disturbed the steady assimilation of the practica! design /essons of the model experiment. Other hybrid presentations have received official backing and ha ve been the vehicles of much valuable experiment work. Modern developments in presentation endeavour to abstrae! the maximum amount of design information from available data. Examples are given which show the defects of earlier presentations in portraying the true lessons of experiments. A presentation suggested by the author many years ago and now again offered, is contrasted with the Froude and B.S.R.A. presentations. Its convenience is illustrated by application to the B.S.R.A. and Moor's data. Sorne consideratioJi is given to Moor's treatment of the Mumford index idea. The Washington Tank series 60 data are converted to the presenta/ion; and convenient design tabulations are prepared which can be applied to the powering of most ordinary merchant forms. The presentation is suggested as the best for the statistical treatment of model data now made possible by the electronic computer. Such work as that rece11!ly published by Doust before this Institution is already in terms ofthe systemproposed and it is suggested tlzat any such analysis would be impossible using the Froude or B.S.R.A. presentations. This possibility of rapid development by computer analysis should pro ve the necessary impetus-hitherto lacking- in the selection of one single and satisfactory system of ship resistance data presentation for design purposes. Introduction

T is always a source of personal satisfaction to be able to retum either to a place orto a subject which one has known many years earlier. It is now forty years since I gave my first paper before this Institution and it dealt very largely with the same subject as does tbe present. I remember the paper1 chiefl.y by the wonderful discussion it provoked. There are very few members of this or any other shipbuilding institution who can claim to have had their first paper simultaneously discussed by such pioneers of tbe subject as R. E. Froude, D. W. Taylor, Rota, Kempf, Baker, Gebers, Schaffran, Sadler, Hok, Mumford and others, in all by sorne twenty-five contributors! In tbe present paper I return cheerfully to the subject, looking nostalgically at sorne of its earlier and intervening history. If the su bject of tbe non-dimensional presentation of ship resistance data can be real! y said to ha ve hada single creator the credit, I feel, must go to B. J. Tideman who in 1878 2 clearly anticipated

I

as Fia 30 aJ,er .r.1 ru . o · washmg

1

Numerals refer to list of References at tbe end of the paper.

QQ

1!

358

i 1

TELFER: TIIE DES!GN PRESENTATJON OF SHIP MODEL R ESl STANCE DATA

R. E. Froude's classical work of 1888. 3 Very little, if any, work since Froude's time has added strikiogly to the facility with which a desigoer can imbibe the lessons of model experiment work. Our British Admiralty would categorically deny in fact that any progress had been made at all. This indeed is almost sufficiently true, for the majority of the departures from Froude either have offered nothing better or were at best merely spurious " simplifications " of his work. Whilst thus unashamedly a Froudephil I now feel that Froude was probably too influenced by the Admiralty coostant and Tideman's earlier suggestioo of a non-dimensional speed of V/t:.!. Had he not been, his own unique knowledge as an experimenter must have led him automatically to prefer a V/VI non-dimensional speed. He could then, through R /1':., have proceeded to RL/!:J. V 2 and certainly saved everybody an awfullot of trouble! I advanced this alternative sorne thirty years ago• and still now submit itas the only possible improvement over Froude. Put another way, had R. E. Froude originally recommended the use of the e . M * product to a base of L, the present paper would have been quite superfluous ! As has been recently shown before this Institution by Mr. D. J. Doust the statistical analysis of model experiment data can be immensely facilitated by electronic computer use. 5 For this Mr. Doust used my Re Ve presentation. The computer work would have been impossible using the Froude e - K presentation, since in no sense of the word can e physically and generally be a function of K. Undoubtedly computer work in the subject is just beginning. It is suggested therefore that designers should now rapidly accustom themselves to the Re Ve language and be prepared to forego presentations which, however useful they may have been in the past, must necessarily have now to be jettisoned on the long and difficult voyage of shipbuildiog progress which líes ahead. U ltimately the computer must dictate the final form taken by the design presentation of ship resistance data. Before this rnillenium arrives, however, there are many useful stopping points along the way. Sorne of these are discussed in the present paper. If this discussion can influence the outlook of the many young designers now findiog their way in an industry whose future is still worth fighting for, it is probably not so important what it does to the tolerant outlook of m y good frieods, the others.

§l. The subject of ship model resistance data presentation has long engaged the attention of this Institution. The first paper and one much too rarely referred to is that ofHok published in our 1893/4 Transactions. 6 The paper is noteworthy from many points of view. Essentially it referred to ship tria! data rather than to model data. Hok adopted the 100ft. ship as a standard and referred displacement, speed and indicated horsepower, all to this basis. (The 100ft. length was a suggestion made in 1880 by F. P. Purvis, later Prof. Purvis, then in charge of Messrs. Denny's tank). The value of Hok's paper was greatly enhanced by a contribution from R . E. Froude whose earlier work had just introduced the now classic "Constant System of Notation ". Froude's criticism of Hok's work was, as usual, courteous and constructive; and whilst the criticism helped Hok to simplify his method it was not sufficient to persuade him to forsake his 100ft. ship-speed basis for the Froude K, orto change from his t:.f(L/100)3 displacement-length factor to the Froude M = L/vt; or finally to depart from his power factor of IOPf(t:.yL) in favour ofFroude's proposal of p ¡t:.t V3 • Hok in fact felt it entirely wrong to distort the actual power-speed relation by dividing by speed cubed or by logarithrnic presentation or in any other way. He insisted that a designer should have the cost of speed always brought vivid! y and pictorially to his notice. This, in his opinion, was a vital requirement of any practica! • In all references to the Fraude symbols preserved in teavy type.

ce

circular" notation tbe circumscribing circles are dropped and tbe

TELFER: THE DESJGN PR~

system of power data presentati his attit ude; and it would appe< Taylor's early outlook on the st: length, the factor 1':. /(L / 100)3 ar ton displacement factor. What ratio. Taylor in effect adopted the speed-length ratio being mos with the Hok 100ft. standard le numerically lead to confusion "" the Hok method. Saunders has certainly did not introduce the acceptable terminology. Taylo formula S = const. y!':. .L. F. far as I am aware, for the firs operating the Froude frictional superior to that of Froude. Looking back on Hok's woü widespread adoption. It certain College lectores on the subject standabfy given a very full tre; subject- probably the next pap include Hok's paper in my listo I was entirely unaware of it. ' and made his presence felt by a also similarly honoured by a cor both on the power and speed pr and firmly held opinions. In t dictated by maximum internatio; power, displacement in tons an national units, a system of pre1 only. The system proposed, P following HolSe who may shelter behind official

played by our own Institution in the m more general historicallines. It is •ays be presented to a base of speed. 1 comparison of their own resistance n the pre-Reechian and pre-Froudian mation which could be legitimately deis had the same length and/or the :ls was always better than the other, aminar fiow and parasitic resistances :atively be expected also to apply to 1f Reech it was impossible to use the respective ships. What was missing tis Reech produced in 1832. From model tests to predict ship resistance; est naval tank to analyse the corresal vessel whose tria! data were availin the form that the resistances were Ltio. Reech was fully aware that the notion in a gravity field. I am not he too k the next (to us) now obvious ~nsional form, i.e. showing that the lotted to a base of speed-length ratio be independent of the absolute size tve done so, but under the restriction ;istance. iect sorne thirty years later he had at tan the Reech law. It is unthinkable ;ase his contemporaries undoubtedly ·er, I have not been able to trace any eh law in the writings of either ofthe J ~xplore this issue further (although lltam Froude undoubtedly is entitled >t al! of the resistance followed the quired quite separate cónsideration. William Froude magnificently establaw. However, justas Reech never r, s'? far as I can trace, did William ~ d1splacement to a base of speedlshed works. Where this fact not !Xtraordinary to find that the first s~p resistance data is clearly due f h1s own tests on wax-models carried Amsterdam, in the form of residuary nt to a base of speed in metres per tsplacement. Tideman's work2 was ~~- ~s he refers to the Greyhound JlicatiOn date is probably nearer to s quite different from Froude's· and ~ took place in 1879 the publi~tion IS known that William Froude and oral problems of ship model work. ModelBasinin 1951 oneofFroude's

TELFER: THE DESIGN PRESENTATION OF SHrP MODEL RESJSTANCE DATA

361

letters to Tideman. The letter we could now describe as dealing with a hovercraft problem !) The question of extreme historical interest is thus whether W. Froude told Tideman how to present model data non-dimensionally or did Tideman tell R. E. Froude? Ten years later when R. E. Froude published the "Constant System", which had obviously already been then in use for sorne years, i.e. both in Torquay and Haslar, was he building on his father's unpublished work or the published work of Tideman? I would here like to ínterpose that Mr. A. J. Vosper, R.C.N.C., the present Superintendent of the Admiralty Experimental Works has been good enough to research this point for me in the Haslar records. His findings are extremely interesting. There is no obvious record of William Froude thinking non-dimensionally in the modern sense of the word; and R. E. Froude's first non-dimensional work appears to date from 18th July 1881 when he states in the Torquay progress book that he had decided to use the Admiralty constant ~i V3 fe.h.p. for resistance presentation and the expression v¡~i for relative speed. In the progress book under the date, 29th Sept. 1881 the Admiralty constant was inverted to obtain the "new constant " e.h.p. 1~~ V3 and this, as C, has persisted ever since. It would appear probable from this that the Froudes never actually thought in terms of resistance per ton; and the C was not originally produced by dividing R/~ by K 2 but by simple inversion of the Admiralty constant and most probably then to operate the skin friction correction. If R. E. Froude had originally used R / ~ and had been really dissatisfied with it then his subsequent use of the Admiralty constant would have produced a much steadier coefficient than C. This follows from the fact that the lirniting value of the former is zero whilst that of the latter is infinity. The Admiralty constant convenience was made full use of by Schaffran and the presentation is still standard Swedish practice. Thus we see that whilst C is not such a good " steadier " as is the Admiralty constant it is certainly much more convenient to present in diagram form than is R/~. It is thus clear that faced with this choice R. E. Froude in Hok's discussion did not hesitate to defend his "distortion" of an R/ ~ curve. When it is recalled, however, that William Froude and Tideman (and of course later D. W. Taylor) al! made the frictional correction as separate calculations for model and ship, the advance represented by R. E. Froude's length correction will be appreciated. He obviously introduced the "modern" idea of scale-effect when he standardized a total C value for a length of 300ft. and gave simple corrections for other ship lengths. Froude shared with Tideman the use of L/~t as a means of defining the lengti1 of a model of unit displacement. It is curious that he also shared a speeddisplacement constant and would have nothing to do with the intrusion of length into bis resistance-displacement constant. However, whether Froude was infiuenced by Tideman in his choice of a displacement basis without evidently seriously considering the choice of a length basis is no longer important. The fact is that his " Constant " system has been in constant use by the British Admiralty for sorne eighty years, which either proves the perfection of the system or sirnply that one can eventually get used to anything! Certainly Admira! Taylor in discussing my 1922 paper had no hesitation in stating that something much simpler than the Froude system was required for practitioners' use; and as the 1896 U.S. Act authorizing the construction of the Washington tank was iotended to encourage the use of the tank by American shipbuilders sorne simpler system had to be devised. The result was the pounds per ton, speed length ratio presentation; but later in the same discussion Taylor confessed that division of a power constant by speed cubed was "almost necessary" particular! y for high-speed vessels since otherwise the rapidly varying resistance curves would not be then "comfortable to handle ". Taylor, however, had nothing to say in favour of v¡~t and everything in favour of V/vi. In fairness to R. E. Froude it should be stated that he did not exclude V/VL (in the form of L) when he exercized his major choice of v¡~t. An auxiliary curve ofL was always plotted to the M base of each iso-K diagram, but the issues here will become clearer when we narrow attention to the main thesis of the present paper, the design

362

TELFER: THE DESIGN PRESENTATION OF SHIP MOD EL RESISTANCE DATA

presentation of resistance data. We propose to confine attention to nondimensional or ratber to pseudo non-dimensional presentations. The absolute expansions of a given form over a range of displacement and ship speeds as developed by Inglis, Biles, Doyére, Bragg, Baier and others are extremely useful presentations. Inglis first introduced the idea in William Froude's time and Froude developed its theory. As its chief function is to generalize one form rather than to compare a generality of forms, it is merely mentioned here and need not be further discussed.

§3. Let us now consider the resistance data non-dimensional presentation problem itself. Starting from a plot of resistance against speed we can nondimensionally present the data two ways. Both involve accepting resistance per ton as tbe dependent variable but the speed can be divided either by the square-root of the length or by the sixth root of the displacement. Now if it is desired, for reasons already sufficiently discussed, to include in the resistance per ton sorne function of the speed, it must be sorne function of the non-dimensional speed used as the abscissa since then all resistance curves plotted to the first presentation will preserve exactly the same order of merit in the second. For example, if we wish to change from a resistance to a power presentation we must use (as the simplest change) (R/tl)V/ó.t, i.e. P fó.¡, when plotted toa base of Vft!.i,or(R f t:.)VfyL,i.e.Pft>..yl when plotted toa V/vl,or as I will now call it a v. base. The point here is that we cannot plot P f D.; to a Ve base or P / t:.yL to a K base without destroying the merit order of the original curves except when these curves all refer to the same M, or as I prefer to call it Le = L fv !i value. This exception, of course then follows from the simplefact that V/D.t = (V/vi)/ VLó.l = Ve X Const. It should be noted, however, tbat it is possible to ha ve a simple power constant which is not subject to this restriction. Thus, since R / t1 = RV/ ó. V = P /D. V, this latter, as it is still a resistance per ton, can be used with either a K or Ve speed base. Generally the purpose of modifying the simple resistance or power .constant by a speed modification is to steady the value of the constant. If, for example, we suspect that the resistance varíes as the nth power of the speed and we then divide the resistance per ton by K" or Ve" we obtain a resistance factor which then will indeed be constant. Thus when we accept n = 2 we obtain e = (R/ó.) (Vft>.i/ = P ft>.1V 3 ; and alternatively, Re = (R /ó.)f(VfyL) 2 = RL /ó.V 2 • The original choice of n = 2 dates back to the introduction of the Admiralty constant or even earlier to the recognition of Newton's work on viscous resistance. The choice is an extremely fortunate one in the production of a resistance constant intended to express both frictional resistance and residuary resistance non-dirnensionally, the 2 index very nearly (and when the surface is rough, exactly) expresses the frictional resistance per unit area variation; and it also exactly satisfies the law of corresponding speeds for the residuary resistance per ton. From the designer's standpoint the 2 index presentation also, of course, quite wonderfully reveals the changing wave interference effects on the resistance as speed is changed. This ability is peculiarly a property of the 2 index and is not influenced by the choice of the speed function. As interference effects, however, do align themse!ves in terms of a length-speed function, and not at al! in terms of a displacement-speed function, the advantages of the former to the discerning designer and experimenter need little emphasis. Whilst the use of the 2 index is complete! y valid presentationa!ly, it can safely be said that no merchant ship is ever designed to operate on a resistance varying as the square of the speed or on a power varying as the cube. It would appear that for merchant ships n can be taken as 3 for optimum design. It is difficult to give a rigorous proof of this fact, although if a model series of fixed linear dimensions be tested with only the block coefficient (and hence also the displacement) variable, it is usually found that the optirnum block at the desired Ve

TELFER: THE DESlGN PRESENT

corresponds to that of the model wh whose. res!stance p~r ton is varyi conditwn mvolved IS evidently tha1 due to block increase should, at th' ponding reduction in frictional 1 optimum Ve if too small a block c1 too much frictional resistance per t( have too high a residuary resistat optimum block for the series abov the necessary envelope and within Re varíes as Ve, i.e. when R varíes a as so defined is given by drawing a tange the curve. The Ve value of since the tange-poi~t is indeed pro favourable wave interference the me If we accept this design criterion e constants embodying the criterion therefore need (R /ó.)f(Vft:.1í) 3 = P , Again to a base of Ve we would m the resistance function. These a: results in the same way as do the generally produce a distinct minim mínimum is not sharp presumably range of speeds, but this conclu a!ternatives. There is a lot to be said for usir criteria. We merely note the mini relative speed at which it occurs an really requires from a particular me coefficient suitable for the desired s can be quickly determined. Not o varying as V 4 the power at say ± 1 culable. It is not proposed in the ¡: particular design presentation. V emphasise that its lessons are of presentation; and could well have 1 presentation.

§4. Coming now to the pure desi¡ can be no doubt that the R. E. Frot led and still holds the field. A de iso-K sheet which contains all resis· ment of his design which previous rr The resistance data in e form are J of L is constructed to the same ba~ its M value known, its speed-lengtt If L is likely to correspond to a b< the advantages of safer M valu~ does not use the iso-K sheet te must as a capable designer, alr He then selects the best e at therefore he is also selecting a fe the e merit order at M constant The vital factor in the C K system bered that the M value of a design the designer's fancy but is prse to confine attention to nonanal presentations. The absolute displacement and ship speeds as ier and others are extremely useful ea in William Froude's time and unction is to generalize one form ., it is merely mentioned here and

tta non-dimensional presentation stance against speed we can nonBoth involve accepting resistance >eed can be divided either by the t of the displacement. Now if it :ussed, to include in the resistance : sorne function of the non-dimentl! resistance curves plotted to the me order of merit in the second. stance to a power presentation we i.e. P / t:/ when plotted to a base of d to a V/ yL, or as I will now call : plotP/C>.; toa Ve base or PjC>.yL of the original curves except when prefer to cal! it Le = L /v t value. simple fact that VjC>.t = (VJvL)J 10wever, that it is possible to have :t to this restriction. Thus, since ll a resistance per ton, can be used Je purpose of modifying the simple ification is to steady the value of tt the resistance varíes as the nth >istance per ton by Kn or Ven we eed be constant. Thus when we = PjC>.ifV3 ; and alternatively, Re choice of n = 2 dates back to the ven 'earlier to the recognition of oice is an extremely fortunate one tended to express both frictional .sionally, the 2 index very nearly es the frictional resistance per unit ·"'! of corresponding speeds for the stgner's standpoint the 2 index · reveals the changing wave inter_anged. This ability is peculiarly Y the choice of the speed function. LSelves in terms of a length-speed :nt~speed function, the advantages Jenmenter need little emphasis. alid presentationally, it can safely :o operate on a resistance varying ng as_the cube. It would appear r_opttmum design. It is difficult . If a model series of fixed linear :iel!t (and hence also the displaceptunum block at the desired Ve

TELFER: THE DESIGN PRESENTATION OF SHIP MODEL RESISTANCE DATA

363

corresponds to that of the model whose Re is then varying directly as Ve and hence whose resistance per ton is varying as the speed cubed. The fundamental condition involved is evidently that the increase in residuary resistance per ton due to block increase should, at the optimum block, be balanced by the corresponding reduction in frictional resistance per ton. At the corresponding optimum Ve if too small a block coefficient were adopted the form would ha ve too much frictional resistance per ton. If too large a block is used the form will have too high a residuary resistance per ton. The Ve corresponding to the optimum block for the series above described is easily derived by constructing the necessary envelope and within the limits of experin1ental error occurs when Re varíes as Ve, i.e. when R varíes as Ve 3 • A simple construction for optimum Ve as so defined is given by drawing a ray from the origin of an Re, Ve diagram to tange the curve. The Ve value of the tange-point gives the economic Ve; and since the tange-point is indeed probably the point of first detectable maxirnum favourable wave interference the method evidently has sorne scientific justification. If we accept this design criterion of n = 3 we can usefully devise other resistance constants embodying the criterion. Thus using K as speed function we would therefore need (R /C>.) /(VjMr) 3 = P fyt;.. V 4 or C /K, as the resistance function. Again toa base of Ve we would need (R /.ó.)/(V/yL) 3 = PVt /C>.V 4 or Re /Ve as the resistance function. These alteroatives do not " steady " the resistance results in the same way as do the alternatives based on n = 2. Instead, they generally produce a distinct mínimum value at the economic speed. When the mínimum is not sharp presumably the form can be regarded as economic for a range of speeds, but this conclusion should be checked by testing further alternatives. There is a lot to be said for using either of these latter alternatives as design criteria. We merely note the mínimum value of the resistance constant and the relative speed at which it occurs and this is all the information which a designer really requires from a particular model. Having selected a model having a block coefficient suitable for the desired speed-length ratio (or K value) the best model can be quickly determined. Not only is this the case but since the power is then varying as V 4 the power at say ± 1 koot about the desigoed speed is at once calculable. It is not proposed in the present paper to develop the advantages of this particular design presentation. We may leave it for future work except to emphasise that its Jessons are of use in the routine evaluation of any design presentation; and could well ha ve been adopted as the basis of the Ayre type of presentation.

§4. Coming now to the pure design presentation of model resistance data there can be no doubt that the R. E. Fronde " Constant System of Notation " has long Jed and still holds the field. A designer merely has to consult the appropriate iso-K sheet which contains al! resistance data for the desired speed and displacement of his design which previous model tests ha ve shown are likely to be relevan t. The resistance data in e form are plotted to a base of M. Additionally a curve of L is constructed to the same base so that once a model is selected and hence its M value known, its speed-length ratio L is also known for the given K value. If L is likely to correspond to a bad interference zone the designer can explore the advantages of safer M values. In actual practice, however, a designer does not use the iso-K sheet to determine an appropriate M value. He must as a capable designer, already know the M value of his design. He then selects the best C at this M for fue basic K value. In effect therefore he is also selecting a form having a constaot Ve or L value and the e merit order at M constant would be exactly the same as the Re merit. The vital factor in the e K system is thus the M value; and it should be remembered that the M value of a design is not a piece of elastic to be pulled about at the designer's fancy but is probably the most constant factor characterising a particular type of vessel. It is therefore completely vital that any system of

'

·~

11

364

TELFER: THE DESIGN PRESENTATION OF SHlP MODEL RESISTANCE DATA

resistancc data presentation should visually emphasise just what M does to the resistance properties of a particular form. Inspection of any iso-K sheet will invariably show that reduction of e requires an iocrease ofM to produce it. This is certaioly so over the normal merchant M range. A designer is thus led to believe that he must adopt high M val ues to get efficient forms. For example, Ayre actually talked about the penalty for "stumpiness ", i.e. low M value; aod he would be fully entitled to have drawo this conclusion from a Froude iso-K sheet! Once however a designer appreciates that high M value forms are always wasteful in wetted surface per ton he begins to doubt the visual validity of the Froude presentation. He then realizes that an iso-K con tour which shows e reducing with M increase is giving him a false lesson. Such a behaviour is merely the result of a model of constant length having a smaller and smaller displacernent being run at a lower aod lower speed in relation to its /ength. The behaviour is therefore no indication of form excelleoce-as it should be if the presentation is to assist design-but merely shows very ambiguously that if speed is reduced in relation to length, lower e values can be obtained. It was surely never Froude's intention to produce a design presentation which would hide so simple a truth so effectively and give so wrong a picturization of the influence of a true design parameter. In this basic defect it is not unfair to say that the Froude presentation is schizophrenic, it shows one thing and generally means exactly the opposite. In this criticism of the Froude system I wish it to be clearly understood that the numerical accuracy and compatibility of the system are not being questioned. The criticism is entirely confined to the pictorial distortion of the M influence which the graphical presentation of the system inevitably suggests. To illustrate this point more forcibly reference can be made to G. S. Baker's analysis of R. E. Froude's 1904 experiments. The diagram shown here as Fig. 1 gives Baker's Fig. 42 taken from the 1933 edition of his " Ship Design " (vol. 1). This presentation is a condensation in the classic Froude manner and gives K contours of e to a base of M. Exactly the same information was subsequently used by Lindblad and is given in Fig. 71 of his "Design of Lines for Merchant Ships" 1961 edition. This diagram is redrawn in our Fig. 2. Lindblad's base of 6./(L/100) 3 has been converted to give M, the ordinales are still e values, but the contours drawn by Lindblad are Ve and not the K contours used by Baker. Finally these diagrams have been converted in our Fig. 3 to read Ve contours of Re = RL /6. V 2 to a base of M. Attention is invited to the visual1essons to be drawn from these three diagrams, particularly so far as M influence is concerned. Fig. 1 clearly recommends high M values. Fig. 2 still recommends high M va1ues. Fig. 3, however, completely changes the picture. We see that there is a distioct virtue in low M values even at the relatively high Ve values in question. In other words there is always virtue in forms which hove the lowest wetted surface per ton displacement. A probably unexpected corollary of this dictum líes in the further fact that as such forros get rougher in service their resistance will increase less for the same roughness than will that of forms having greater wetted surface per too. Since moreover low M value forros mean lower bending moment on given displacement, such forrns naturally also have minimum steel weight. It is clear frorn a study of Figs. 1, 2 and 3, that only the Re Ve presentation is giving a true design picture of the basic data, since only this preseotation brings out the effect of the high wetted surface per ton of the higher M value models. Fig. 2 showing the B.S.R.A. presentation gives the same erroneous impression of M infiuence as does Fig. 1 the original Froude presentation. Actually in this particular case the B.S.R.A. presentation appears somewhat to moderate the M effect inversion. This again is a distortion and arises from e Ve incompatibilíty. As it is practically impossible to infer from the e Ve presentation the true advantages of low M values it would be of interest to learn why this particular system is officially encouraged to persist. It is, for examp1e, discouraging to find that Japanese shipbuilders are now extolling the advantages of low M value tankers, almost as a new and revolutionary invention, when we are apparently doing our best to hide the advantages from the profession by our reluctance to

TELFER: THE DESIGN PR ESE!'.

change from defective data prese who defend or have defended th justify the retention of t.; in e as hence of frictional resistance.' A resistance per ton displacement a also does not measure wetted surf; wetted surface varíes as ti~ and constant of the form R /( , / -:;:L) restricted application and of lit criticism of the B.S.R.A. system m be defective. The most telling cri son of Figs. 2 and 3. Admittedly deliberately taken from our earli however, how long such defects in of course, still persist. Finally, in concluding this secti R.I.N.A. paper on resistance pres native presentations of Todd's excellently, develops the discussior study- especially by the B.S.R.A.

§5. To bring the data presentatic now usefully be made to the R.I. I Harper and Moor, dealing with ¡; results of sorne evidently very ex These were summarized in diagra It will be seen that the diagram g1 with contours of speed-length ra facilitate the designer's choice of dimensions of the ship. In discus exactly the same data in Re form again in the form of Ve contours. Fig. 4 favours the lower block c• since tbey correspond to lower 1 resistance per ton displacement. here again we see that faulty data J away from the most economical S< In the manipulation of these pan has very usefully drawn professi Mumford índices and particular)) model resistance data. It is of int of Moor's work to examine wh< concept and particularly from th Mumford started from the assumJ a model or ship of standard length be expressed by R =k Ex dY He then referred to model data co Moor has shown that this expressi form e may be written, e = k Bx-2 !3 . d y-2/3 By means of a variant of (2) ~oo form all referring for convemence x and y were known, easily be 1

:HJP MODEL RESISTA.."'CE DATA

:mphasise just what M does to the Inspection of any iso-K sheet will n increase ofM to produce it. This M range. A desígner is thus led For example, , get efficient forms. ;tumpiness ", i.e. low M value; and is conclusíon from a Froude iso-K tes that high M value forms are begins to doubt the visual validity that an iso-K contour which shows false lesson. Such a behaviour is Jgth having a smaller and smaller speed in relation to its length. The t excellence-as it should be if the tows very ambiguously that if speed es can be obtained. It was surely presentation which would hide so a picturization of the influence of a is not unfair to say that the Fraude thing and generally means exactly ;ystem I wish it to be clearly undertibility of the system are not being d to the pictorial distortion of the of the system inevitably suggests. :nce can be made to G. S. Baker's ts. The diagram shown here as 933 edition of his " Ship Design " in the classic Fraude manner and xactly the same information was in Fig. 71 of his "Design of Lines iagram is redrawn in our Fig. 2. erted to give M, the ordinates are blad are Ve and not the K contours ! been converted in our Fig. 3 to of M. Attention is invited to the iiagrams, particularly so far as M mmends high M values. Fig. 2 however, completely changes the tue in low M values even at the er words there is always virtue in er ton displacement. A probably further fact that as sucli forms get ! less for the same roughness than e per ton. Since moreover Iow M 1 given displacement, such forms t~at only the Re Ve presentation is smce only this presentation brings on of the higher M value models. ~s the same erroneous impression ·roude presentation. Actually in tppears somewhat to modera te the d arises from e Ve incompatibility. t the e Ve presentation the true t~rest to learn why this particular 1s, for example, discouraging to ng the advantages of low M val ue 1vention, when we are apparently te prafession by our reluctance to

365

TELFER: THE DESIGN PRESENTATION OF SHIP MODEL RESISTANCE DATA

change fram defective data presentation systems. Admittedly there are those who defeod or have defended the B.S.R.A. presentation. For example, they justify the retention of ó.~ in e, as it is (they say) a measure ofwetted surface and hence of frictional resistance. Apart fram the fact that it does not measure resistance per ton displacement at given Ve (as it does when used with K), it also does not measure wetted surface per se. For given or standard ship length, wetted surface varíes as ó.t and not as ó.!. This would require a resistance constant of the forro R/( y ' D-.L) V 2 , which would appear to be of somewhat restricted application and of little use for design purposes. This detailed criticism of the B.S.R.A. system mere! y serves to emphasise why the system must be defective. The most telling criticism in any case is provided by the comparison of Figs. 2 and 3. Admittedly the data on which these figures are based were deliberately taken from our earliest systematic experiments, merely to show, however, how long such defects in presentation have been with us. The defects, of course, still persist. Finally, in concluding this section the reader is referred to Lackenby's 1954 R .I.N .A. paper on resistance presentation which deals in particular with alternative presentations of Todd's 1931 R .I.N.A. coaster series. This paper excellently develops the discussion of Todd's paper and is worthy of the closest study-especially by the B.S.R.A.

§5. To bring the data presentation controversy right up to date, refereoce can now usefully be made to the R.I.N.A. paper read last year by Messrs. Turner, Harper and Moor, dealing with passenger-ship design. The paper repórts the results of sorne evidently very extensive tests on high-speed passenger forms. These were summarized in diagram form and Fig. 4 is taken from their paper. It will be seen that the diagram gives values of e to a base of block coefficient with contours of speed-length ratio Ve. The purpose of the diagram is to facilitate the designer's choice of the optimum block coefficient on the fixed dimensions of the ship. In discussing the paper I offered Fig. 5 which presents exactly the same data in R e form to a base of block coefficient (and hence Le) again in the form of Ve contours. A comparison of the two figures shows that Fig. 4 favours the lower block coefficients whereas Fig. 5 favours the higher since they correspond to lower Le or M values and have therefore a lower resistance per ton displacement. The difference is not shattering of course but here again we see that faulty data presentation can divert the designer's attention away from the most economical solution of his problem. In the manipulation of these particular data and of much other data Mr. Moor has very usefully drawn professional attention 8 to what are known as the Mumford índices and particnlarly to their application to the condensation of model resistance data. It is of interest, however, in view of the above criticism of Moor's work to examine what is really involved in the Mumford index concept and particularly from the standpoint of the compatibility principie. Mumford started fram the assumption that the e.h.p. or the total resistance of a model or ship of standard length and given speed, i.e. at given Ve value could be expressed by R = k Bx dY .......................................... · .. ( 1) He then referred to model data covering B and d changes to determine x and y. Moor has shown that this expression can also be put into e form. In one such form e may be written, e = k Bx-2J3 . d y-2/3 (2) •••





o

•••

o

•••

o

•••

o

•••••••••••••

o.

o

•••

o

By means of a variant of (2) Moor showed that model data expressed in e Ve form all referring for convenience to a standard length of 400ft., could, when x and y were known, easily be brought also to refer to standard transverse

, ' l¡

!:

366

TELFER : THE DESIGN PRESENTATION OF SHIP MODEL RES!STANCE DATA

dimensions, i.e. to standard beam and draught. The so corrected e value would still refer. toa model of the same block, basic lines and centre of buoyancy position. The validity of this step, however, must be controlled against the compatibility principie since a comparison is then being made of e values at constant Ve through a variable M value. It is clear, however, that as the comparison is made with block coefficient identity, the standard dimensions also involve M identity, the compatibility principie is satisfied. Moor's condensation process as such would thus appear to be perfectly valid, at least in principie. A body of statistical data can thus be assembled which can be extremely useful for design purposes. It is at this point, the reversa! of the condensation process, that the neglect of the compatibility principie can arise and lead to the erroneous interpretation of the basic data expansion. In this case it must be appreciated that we are then no Jonger dealing with a constant M value; and the change in e value between the standard and non-standard cases is no Jonger a prediction of the resulting resistance per ton change as it would have been had the comparison been on a K basis. To get the true pounds per ton comparison in such a case the C ratio must be multiplied by the M ratio to the standard. This does not mean of course that had the derived e itself been used to determine the resistance or e.h.p. the result would not have been correct. It would, but the use of e as a merit coefficient in itself would be invalidated; and it becomes impossible to recognize good or bad forms merely from their e value alone. To be of any use toa designer a resistance coefficient has to be a merit coefficient; and hence to make the Moor adaptation of the Mumford index idea complete!y free from ambiguity it should be transformed to operate using Re on Ve. Various developments suggest themselves. For example Jet us divide total resistance into wave-making and non-wavemaking components, the former being a fraction p of the total and the latter (1 - p ). Wave resistan ce theory suggests that resistance varíes as B 2 , whereas since wetted surface varíes as M, frictional and eddying resistance can be taken as varying as Bt. From these relations we can deduce an expression for the percentage change in resistance due to percentage change in beam and draught. Thus for beam change we have, aR

R

as

1-p

+

2p.

7i

~:

cp: 1)

- 2-

aB B ... . ................ .. ............. ... (3)

When p = O, 0·10, 0·20, 0·30, 0·40 the values of

CP:

1 ) are 0·50, 0·65,

O· 80, O· 95, 1 · 10 and these latter are the Mumford x índices. Sirnilarly when we consider the influence of draught it is evidently necessary to assume that the wave-making fraction varíes directly as draught whereas the frictional resistance will vary as dJ¡. Therefore proceeding as before we can write: aR

R

p . ad

d

+

1- p

ad

2

d

a: c-~p)

·

....................................... (4)

and thus when p =O, 0·10, 0·20, O· 30, 0·40 the values of

e P) ~

are 0·50,

O· 55, O· 60, O· 65, O· 70 and these Iatter are the Mumford y índices. The value of p is obviously a function of Ve and inspection of Moor's work shows that x, y and p are plausibly related.

TELFER: TH E DESIG N PR ESEN"

If we use the índices for echa n ae

aR

2

2

as

e

R ·- 3 · F - 3

~

(

~~B +

y .

0.:)

which finally reduces to,

~

=

a:(x - D+

If instead of using e we use Re t oRe

R"

aR

as

. ad

R - 73 --



as

+ ([

B (x - 1)

ad

It is to be expected that p, the relat and the block coefficient. An ex; expression

p =

(~ + ~~ - {)

quantifies the respective influence deduced chiefly from the Mumfon than that derived from subtracting total since the eddy resistance, wl probably behave as the frictional r as beam and draught changes are should be quite closely assessablefi course be greater. It is evident ti values offers considerable scope fo It is obvious, for example, that standard beam of 55ft., will certai beam differentials of wave-making former increasing with beam and H Re value at some beam to pass thro1 x will be unity. For narrow< for wider beams greater than uni1 the greater the speed-Iength rat block coefficient. This same influc effect and one would expect that th smaller must become the unity ind this optimum beam should be regar• form of ship should be extended. block coefficient vessels of the Gre; vessels are being designed with optir to be fantastic to the designer o probably brought out by Todd's !S Re Ve representation of the data. existing coaster proportions and r systematic series. It is probable t beam series as above defined. R< valuable and could have useful re¡ In passing it is intriguing to use t form in Figs. 1 to 3 with the Moor f are 400 x 65 x 25 with a block din1ensions are 400 x 55 X 18. I

TELFER: THE DES!GN PRESENTATION OF SH!P MODEL RESISTANCE DATA

• MODEL RES!STANCE DATA

The so corrected e value 1sic Jines and centre of buoyancy must be controlled against the .hen being made of e values at is clear, however, that as the .ty, the standard d imensions a_Jso satisfied. Moor's condensaban ly valid, at least in principie. A ·hich can be extremely useful for ;al of the condensation process, n arise and Jead to the erroneous is case it must be appreciated that value; and the change in e value is no longer a prediction of the have been had the comparison r ton comparison in such a case to the standard. This does not 1 used to determine the resistance . It would, but the use of e as d; and it becomes impossible to ::: value alone. To be of any use 1 merit coefficient; and hence to ndex idea completely free from using Re on Ve.

;ht.

For example Jet us divide total 1g components, the former being Wave resistance theory suggests d surface varíes as M, frictional iS Bt. From these relations we hange in resistance due to perbeam change we ha ve,

..... . .. .. ........ . . . ..... (3)

·.s of (3p 2+ 1) are O· 50, O· 65, ·ard x índices. draught it is evidently necessary directly as draught whereas the re proceeding as befare we can

............ . ...... . ...... (4)

le values of

e p) ~

are

o. 50,

Mumford y índices. The value on of Moor's work shows that

If we use the índices for

ae

e

aR

2

367

e change we ha ve, since, 2

aB

ad

lf ·- 3·s - 3·(1

ae

2 aB

e

2 ad

- 37i- 3([

which finally reduces to,

aee __ a B 8

(x _ 32)

+ ad d

(

y-

2)

3

............ ... ....... (5)

If iostead of using e we use Re then it is easily seen that oRe aR aB . ad Re R-B d aB ad ]j (x -

1)

+ d

(y -

1)

.................... ...... (6)

It is to be expected that p, the relative wave-making, must iocrease both with Ve and the block coefficient. An examination of Moor's work suggests that the expression

p =

(~ + ~~-

i)

.................................. (7)

quantifies the respective influences reasonably well. This relation has been deduced chiefty from the Mumford x index. It is likely to be distinctly Jower than that derived from subtracting only the Fraude frictional resistance from the total sioce the eddy resistance, whether it has a scale-effect or not, will most probably behave as the frictional resistance and not as the wave-making so far as beam and draught changes are concerned. Given complete model data p should be quite closely assessablefor the model. For the smooth ship p must of course be greater. It is evident that the determination of reliable x, y and p values offers considerable scope for future research. It is obvious, for example, that relation (7), reasonable as it may be for the standard beam of 55ft., will certainly not apply to all beams. The opposing beam differentials of wave-making per ton and frictional resistance per ton, the former increasing with beam and the latter decreasing, must inevitably cause the Re value at sorne beam to pass through a mínimum. At this point the Mumford x will be unity. For narrower beams x will be less than unity and for wider beams greater than unity. The unity index beam will be smaller the greater the speed-Jength ratio and also presumably the greater the block coefficient. This same influence must also be felt in centre of buoyancy effect and one would expect that the further forward the centre of buoyancy the smaller must become the unity index beam. One is tempted to conclude that tlus optimum beam should be regarded as the limiting beam to which a particular form of ship should be extended. For example in the narrow-beam, very fullblock coefficient vessels of the Great Lakes it may probably be found that such vessels are being designed with optimum beam, although their proportions appear to be fantastic to the designer of ocean-going vessels. The same point is probably brought out by Todd's 1931 coaster series as seen by Lackenby's 1954 Re Ve representation of the data. The series were a cross plot of the then existing coaster proportions and related fullnesses. They were not the usual systematic series. It is probable however that they do represent an optimum bean1 series as above defined. Research on this point would be particularly valuable and could have useful repercussions in super-tanker design. In passing it is intriguing to use the Mumford índices to compare the Fraude forro in Figs. 1 to 3 with the Moor forro in Figs. 4 to 5. The Froude dimensions are 400 x 65 x 25 with a block varying between O· 49 to O· 54. The Moor dimensions are 400 x 55 x 18. If no allowance were made for the difference

368

TELHR: TIIE DESIGN PRESENTATION OF SHIP MODEL RESISTANCE DATA

in dimensions one would be somewhat astonished by the relative excellence of the Fraude form. However, reducing the Fraude dimensions to the Moor standard would explain by the Mumford índices alone a 15 per cent reduction in Re value in favour of the Froude dimensions. When this correction is made the Froude form still appears to be sufficiently good to cause one to wonder what the intervening sixty years of technical progress have really achieved. A re-test of some of these old Froude models might be quite rewarding, since prevalent as laminar flow has undoubtedly been in the past one hesita tes to impute its invalidating influence also to higher speed-Jength ratios. In concluding this section it is interesting to note that Mumford in the discussion of my 1922 paper gives what is probably his first hint of the index idea. In this contribution he clearly suggests that the índices will depend on the inter-relation of the vessels proportions.

§6. Having available a mass of experiment data, how best can a designer harness it for his everyday use and with the maximum perpective? This is the major problem. Having tried out many alterna ti ves over a long period of years - and incidentally been disgusted by the frequency with which one's work has been completely wasted by the prevalence of laminar flow models- I haye been gradually led to prefer a tabular presentation of the resistance data instead of a graphical presentation. One such tabular presentation is of Moor's data.8 An example is shown in Table l. This gives, for a speed-Jength ratio of O· 65, the variation of R e over a range of centre of buoyancy position and block coefficient. The table refers to the standard B.S.R.A. dimensions of 400ft. x 55ft. x 26ft. draught; and to obtain the Re value for any other draught and beam, the differentials given derived from expn. (6) must be applied. The table also gives for each block coefficient the 400ft. Froude frictional Re symbolized by Rcr. Por any other ship length this Jatter value should be multiplied by the ratío of the corresponding Fraude f values. A study of this table and others similar to it shows the curious influence of block coefficient. From o = · 62 to o = O· 73 the Re value decreases with increase in block coefficient. This is seen to be entirely due to the reducing frictional resistance per ton, itself a consequence of the corresponding reducing M orLe value. These, of course. and the Re¡ values continue to decrease up to the fu llest block coefficients but the total Re increases above o = O· 73 due to increased wave-making. This tabulation duly corrected for eddying enables the p value of expressions 2 and 3 to be calculated and hence also the corresponding Mumford índices, thus facilitating the extension of the tabulated results to other transverse dimensions. Broadly speaking it will be seen that a 10 per cent beam increase, for a O· 70 block will only reduce the Re by about 1t per cent but a 10 per cent increase in draught can be expected to produce about 6 per cent further decrease in Re value. Whilst this particular tabulation is attractive it is felt that it may depend too greatly on the Murnford index accuracy. There is indeed a lot to be said in favour of the index method; but at the moment the author inclines to the use of the most systematic model data available especially those covering a wide range of beam and draught. He prefers, although the task is not too easy, to attempt to interpolate these, making as few assumptions as possible in the process.

§7. In principie, the most modern, comprehensive and systematic model experiment data available today for merchant-ship forms are undoubtedly the Washington Series 60.9 Their standard 20ft size, their generally successful turbulence stimulation and their probable freedom from wall-effect encourages one to undertake their simpler re-presentation. One difficulty was soon found. The whole of the data, despite a clear statement to the contrary, are all expressed in

TELFER: THE DESIGN PRESENV

terms of a speed-length ratio based , forms, on the more usual b.p. Jeng to. c~:>nvert t~e data to a 400ft. b. f~Ict1~mal res1stance basis. Any re twn 1s finally adopted in the future, was further decided onJy to use the d position. The block coefficient vah.: included; and for each of these ti draughts were available. All tl;e presentation. Todd in his own treatment of the pseudo iso-K form. He also follo1 pounds per ton contouring in a serie corresponding to constant Ve and opinion at Ieast from a design prese distinguish between residuary resista of proportions on the latter are prot To get a clear picture of the problen· of what is involved in wetted surfac I gave the following formula for w< S = Ld (28 /x

+

B8)

As this can be written, S = LBd

o

(¡a

+ ~)

we can deduce from this the non-dÍJ

SL

=

[!:. f:-B

+ ~]

d If SL /v be multiplied by C1 = R /p: V

a

.

SL V

and hence,

x

R

p.sv•

.

In this expression C 1 can either refer only. In the latter case where C¡ i could express the R cr frictional varü base of 1 /d. To thÍs base the varia and for a range of beams the result the greater the beam, the lower woul greater the draught the lower would the greater the waterplane a the I0\1 that increased fullness reduces the ~ more subtle. It is the load waterp· Increase of a on given 8 will generall hence reduce the R e¡ value. When 1 block and Ve are plotted to the dra case only being defined by three s Sometimes the line is straight, som convex. Obviously three basic drat mínimum of four is really required. data the mean for the three draught drawn through this and the two e

p MODEL RES!STANCE DATA

TELFER: THE DES!GN PRESENTATION OF SHIP MODEL RES!STANCE DATA

;hed by the relative excellence of ~roude dimensions to the Moor :es alone a 15 per cent reduction ;. When this correction is made •ood to cause one to wonder what ; have really achieved. A re-test quite rewarding, since prevalent past one hesita tes to impute its gth ratios. .te that Mumford in the discussion st hint of the index idea. In this . will depend on the inter-relation

terms of a speed-length ratio based on waterline length and not, for single-screw forros, on the more usual b.p. length. It was decided after due consideration to convert the data to a 400ft. b.p. Jength and also to correct to a Froude frictional resistance basis. Any re-conversion to whatever frictional formulation is finally adopted in the future will be quite a simple matter in any case. It was further decided only to use the data referring to optimum centre of buoyancy position. The block coefficient values of O· 60, O· 65, O· 70, O· 75 and O· 80 were included; and for each of these, the data for three beams each having three draughts were available. All the resistance data were con verted to an Re Ve presentation . Todd in his own treatment of the data gave a total C and K presentation in a pseudo iso-K forro. He also followed Taylor and gave a residuary resistance pounds per ton contouring in a series of L 18 on block coefficient diagrams, each corresponding to constant Ve and beam draught ratio. I am now of the opinion at Jeast from a design presentation standpoint, that it is unnecessary to d.istinguish between residuary resistance and fractional resistance, since the effect of proportions on the Jatter are probably even more marked than on the former. To get a clear picture of the problem at issue it is useful to examine the structure of what is in volved in wetted surface per ton d.isplacement. Many years ago 10 I gave the following formula for wetted surface:

data, how best can a designer aximurn perpective? This is the 1tives o ver a long period of years ency with which one's work has minar fiow models-I have been .f the resistance data instead of a entation is of Moor's data. 8 An a speed-length ratio of O· 65, the tCY position and block coefficient. ensions of 400ft. x 55ft. x 26ft. ter draught and beam, the differJpEed. The table also gives for 1al Re symbolized by Rcr. For Je multiplied by the ratío of the

S

Ld (2ofx

=

+

Bo)

...................................... (8)

As this can be written, S

LBd

=

o (}CY. +

ti)

we can deduce from this the non-dimensional relation, V

[3. [:B

SL

R

SL

=

+ ~]

.................................... (9) d If SL/v be multiplied by C1 = Rfp SV 2 we obtain, after sorne reduction,

t shows the curious influence of 73 the Re value decreases with be entirely due to the reducing :e of the corresponding reducing r values continue to decrease up increases above o = O· 73 due to · corrected for eddying enables d and hence al so the correspondnsion of the tabulated results to : it will be seen that a 1(), per cent : the Re by about 1t per cent but ted to produce about 6 per cent

IX

2

V

and hence, Re

it is felt that it may depend too re is indeed a lot to be said in the author inclines to the use of ally those covering a wide range : task is not too easy, to attempt ; as possible in the process.

ive and systematic model experilS are undoubtedly the Washinggenerally successful turbulence wall-effect encourages one to lifficulty was soon found. The he contrary, are all expressed in

369

1

X

R.L. 100 1:1 v•k

p.sv•

Re 100

2

100C1

[3

~ +

IX.B

~]

............................ (lO)

In this expression C1 can either refer to total resistance or to frictional resistance only. In the Jatter case where C¡ is a constant at Ve (for the 400ft. ship) we could express the Rcf frictional variation in a diagram having, from expn. 8, a base of 1 /d. To this base the variation R e¡ would be linear at constant beam; and for a range of beams the resulting straight lines would all be parallel, but the greater the beam, the lower would be the Rifvalue. Similarly of course, the greater the draught the Jower would be the Re¡ value; and it is further seen that the greater the waterplane IX the lower is the Re¡ value. This generally means that increased fullness reduces the wetted surface per ton but the implication is more subtle. It is the load waterplane fullness which is the operative factor. Increase of IX on given o will generally improve the wetted surface efficiency and hence reduce the Re¡ val u e. When the series 60 total Re values for given beam, block and Ve are plotted to the draught reciproca! base, the variation in each case only being defined by three spots, the behaviour is far from uniform. Sometimes the line is straight, sometimes concave to the base and sometimes convex. Obviously three basic draughts are insufficient for this purpose and a mínimum of four is really required. However, to make the safest use of the data the mean for the three draughts was determined and the best straight line drawn through this and the two extreme spots. Sorne divergence from the

370

TELFER: THE DES!GN PRESENTATlON OF Sl-IIP MODEL RESJSTANCE DATA

individual basic data has therefore to be tolerated and particularly when the mean line has to be extrapolated to derive Re values at draughts of 16ft., 21ft. and 26ft., the standard draughts of the B.S.R.A. series. The information so obtained for each block tested was then cross-plotted to a base of beam and extended where necessary to embrace a beam range of 45 to 65ft. In making this beam crossplot it was again occasionally found that a Ve contour was concave to the base line. This would appear to be extremely improbable if not impossible, since with wave resistance varying theoretically as s~, the wave resistance per ton displacement should vary directly as beam. Admittedly the actual variation may oscillate round the linear relation, suggesting the possibility of good and bad beam interference; but few researches ha ve been sufficiently extensive to establish this as yet. If it were the case one would expect to trace the intensification of the effect as Ve is increased but series 60 gives no certain evidence of this. It would appear to be more likely that the narrowest beam series 60 models show a tendency to laminar flow at the lower speeds. To control these possibilities it was felt useful to determine the residuary Re values at each speed and plot these to a base of beam. One would expect these results to lie on a series of straight lines radiating, with block coefficient constant, from a common initial positive value representing the eddying Ree value. One might further expect that this same value could be deduced from the tests at all draughts since the block coefficient is still constant. The results of such an analysis show, however, that the data are very jumpy and that the method proposed would appear to be essential for the valid fairing of the data. Al! the test data ha ve been so scrutinized and a plausible assessment made of the approxirnate eddying Ree at each block coefficient. These values are tabulated for the 26ft. draught and are assumed to be constant for all draughts and Ve values. They enable p, the wave-making fraction, to be more closely approximated and hence also the Mumford x and y índices to be more easily assessed. All the Re data so obtained were next plotted for constant Ve value in the forro of beam contours to a base of block coefficient. The results found were found to be quite unexpected and appear to be somewhat unique. Normally one would have expected such contours at low Ve values to have high Re values at low block coefficients, then to reduce as block is increased owing to the reduced frictional resistance per ton and finally to increase again towards the highest blocks owing to increased wave-making. This is certainly the case with the Moor and B.S.R.A. data but is not the case with series 60. For sorne not very evident reason the bearn contours after falling frorn O· 60 block to O· 65 thereafter rise quite sharply through O· 70 block and fall back to O· 75 finally rising again to O· 80. As it is obviously ridiculous to argue that all the rnany model tests at O· 70 block must be erroneous we are led to the single unpleasant conclusion that the O· 70 block coefficient lines may be the " odd rnan out " and possibly have retained sorne of the bad series 57 defects. Dr. Todd in Ref. 9 does not cornment on this possibility, but as is evidentfrom Fig. 15 of his paper he must have been, if not consciously, then at least subconsciously aware of its existence. The O· 70 block model of the 57 series was particularly bad and was actually irnproved the rnost in series 60. I now feel, however, that the material improvement obtained deterred Dr. Todd seeking still further irnprovernent and this definitely lirnits the real design value of series 60. It is clear that the design gap between O· 65 and O· 75 block is much too great to be interpolated by only one model at O· 70 block. Interrnediate models of O· 675 and O· 725 over this very irnportant range are vitally necessary. * To illustrate this particular feature, Fig. 6 gives the Ve = · 65 beam contours to a block coefficient base for a draught of 26ft. This figure can be conveniently cornpared with Table I based on Moor's data and the 55ft. beam contour from these data is also drawn in. Obviously the Moor trends conflict with series 60. Since the paper was written a study has been made of Ref. 12 in which further tests on the ·70 block form are descr:ibed. These show that the basic afterbody lines can be improved and bring about a 3~ per cent improvement in resistance. U this improvement is maintained for all proportions-as is not unlikely- the hump at the ·70 block can be eliminated, the resulting contours being more of the nature to be ex~ected from Moor's anct B.S.R.A. work.

TELFER: TIIE DESIGN PR ESE N"

Despite this the mean difference b It was fe!t therefore justifiable te Three such tabulations were therel draught, 21ft. and 16ft. Each tal and 65ft. bearn and rows of block , from O· 50 to O· 85 at O· 05 interval~ It is suggested that despite or ev; has emphasized sorne of its defe, appeal to the ship designer since it the vast majority of merchant shij and even block coefficient is kep sufficiently flexible to allow the da· which the performance of any new such work the possibility of wall-ef well in mind and due correction n after such correction could well b• beams and draughts. lt is proba would prefer tabulations entirelv 200ft. standard adopted by Da\~se The most attractive systematic universal acceptance if presented ¡ Taylor standard series. This serie: standard with which to measure th is used by the American Bureau e part of the American Society of Na data sheets. We have recen ti y rete over a range of block-coefficient coefficient values. When the lessc proposed to undertake the necessar that the discussion of the present p the value of this conversion. In all this cornparison work the At the moment, convention corn resistance values. These for mod require complete revision. So fru simple method of making the nece this paper. It is probable that 1 corrections once sorne rneasure of 1 value.

§8. In this concluding section o probable future development of ti Whilst there is little doubt that 1 in the problem of the optirnum dirr clearly there will be no necessity t· occasion. The lessons of the con easy access and reference, particu suggested that the presentation nc convenient for the storage of design to the effects of dirnensions chang• covere'd either to be interpolated e the presentation could give fully features of these are knoWll a de: dirnensioning and fullness. In Me of generalising and refining the M1 to convert to one standard set o

MODEL RESISTANCE DATA

·ated and particularly when the 1alues at draughts of 16ft., 21ft. .A. series. The information so -plotted to a base of beam and ange of 45 to 65ft. n occasiona!ly found that a Ve would appear to be extremely resistance varying theoretically t should vary directly as beam. mnd the linear relation, suggest'erence; but few researches have ~- If it were the case one would as Ve is increased but series 60 •pear to be more likely that the 1cy to laminar fl.ow at the lower useful to determine the residuary se of beam. One would expect radiating, with block coefficient •e representing the eddying Ree value could be deduced from the is still constant. The results of a are very jumpy and that the for the valid fairing of the data. Jlausible assessment made of the nt. These values are tabulated onstant for all draughts and Ve on, to be more closely approxiiices to be more easily assessed. Jr constant Ve value in the form The results found were found newhat unique. Normally one ·alues to have high Re values at ; increased owing to the reduced ·ease again towards the highest s is certainly the case with the h series 60. For sorne not very Jm O· 60 block to O· 65 thereafter .ck to O· 75 finally rising again to all the many model tests atO· 70 ~ unpleasant conclusion that the man out " and possibly have L'odd in Ref. 9 does not éomment of his paper he must have been, 1ware of its existence. The O· 70 i and was actually improved the material improvement obtained 1ent and this definitely Jirnits the 1e design gap between 0·65 and >Y only one model at O· 70 block. this very important range are ·es the Ve = · 65 beam contours This figure can be conveniently nd the 55ft. beam contour from or trends conflict with series 60. 12 in which further tests on the · 70 block ~an t;>e improved and bring about a 3 t per lmta.med for all proportions-as is oot !S.ultmg contours being more of the nature

TELFER: 1HE DESIGN PRESENTATION OF SIDP MODEL RESISTANCE DATA

371

Despite this the mean difference between the two series is less than 2 per cent. It was felt therefore justifiable to prepare tabulations of the series 60 data. Three such tabulations were therefore made for each Ve value namely for 26ft .

draught, 21ft. and 16ft. Each tabulation has beam columns of 45, 50, 55, 60, and 65ft. beam and rows of block coefficient at O· 02 intervals. The Ve range is from O· 50 to O· 85 at O· 05 intervals thus providing tables 2 to 9. It is suggested that despite or even because fue method of presenting the series has emphasized sorne of its defects, the presentation should have a natural appeal to the ship designer since it gives at a glance the true relative power for tbe vast majority of merchant sbips. The general economy of beam, draught and even block coefficient is kept constantly before him and the scheme is sufficiently flexible to a!low the data to serve as a standard of comparison from which the performance of any new model can be easily and safely reviewed. In such work the possibility of wall-effect distorting the comparison should be kept well in mind and due correction made. For example, Dawson's coaster work after such correction could well be used to extend the series 60 data to greater beams and draughts. It is probable, however, that a British coaster designer would prefer tabulations entirely based on the Dawson data alone, using the 200ft. standard adopted by Dawson . The most attractive systematic data which I am sure would find almost universal acceptance if presented in the form now recommended is the classic Taylor standard series. This series is still used by many designers as a reference standard with which to measure the relative exce!lence of tbeir own designs. It is used by the American Bureau of Ships and also forms one extremely useful part of the American Society of Naval Architects' valuable Project H-2 resistance data sheets. We bave recently retested in Trondheirn a number ofTaylor models over a range of block-coefficient, centre of buoyancy and rnidship section coefficient values. Wben the lessons of these new tests ha ve been digested it is proposed to undertake the necessary conversion of the Taylor data. It is hoped that the discussion of the present paper may invoke useful suggestions to add to the value of this conversion. In all this comparison work the question of Re correction for length arises. At the moment, convention compels us to adhere to the Fraude frictional resistance values. These for modern welded ships are hopelessly archaic and require complete revision. So far as the Fraude coefficients are concerned a simple method of making the necessary corrections is given in the appendix to this paper. It is probable that the same method can be used for modero corrections once sorne measure of professional agreement is obtained as to their val u e.

§8. In this concluding section of the paper it is useful to contemplate the probable future development of the subject. Whilst there is little doubt that the computer will play a dominant part both in the problem of the optirnum dirnensioning as well as in the powering of ships, clearly there will be no necessity to appeal to the computer on each and every occasion. The lessons of the computer will have to be placed on record for easy access and reference, particularly for provisional design purposes. It is suggested that the presentation now adopted for series 60 is in principie very convenient for the storage of design information. It directs inm1ediate attention to the effects of dimensions change and allows any data within the dirnensions covere'd either to be interpolated or fairly safely extrapolated. In Doust's case the presentation could give fully optimized forms since once the geometric features of these are known a designer is only interested in their subsequent dimensioning and fullness. In Moor's case, the presentation serves as a means of generalising and refining the Mumford index idea. Thus, instead of having to convert to one standard set of dimensions, any particular model can be



111

TELFER : T H E D ES!G N P RESENT t

372

TELFER: THE DES!GN PRESENTAT!ON OF SHIP MODEL RES!STANCE DATA

referred back to the neGI'est dimensions in (or outside) the series 60 range. In this way any effect which may be peculiar to dimensions is better preserved and not wrongly ascribed to form as it may easily be when the dimension change is too great. The possibility of this happening is suggested by Doyere's and Baier's work on the expansion of a given model through a displacement range; and whilst strictly speaking this type of expansion only requires the usual single resistance curve for its construction, the sustaining of a bad interference zone, or vice versa, over a range of size expansion can obscure the intrinsic purity of the basic data. The series 60 presentation is of necessity restricted to the use of only th.ree parameters to ch.aracterize the required ship, i.e. the beam, draugh.t and block coefficient. Al! other parameters are presumably optimized. For example this is deliberately (but not entirely) so in the case of the centre of buoyancy position. lt is generally found however that if the centre of buoyancy is within ± t per cent of its optimum position for a particular fullness it is difficult to be sure of any resistance difference over this range. For design purposes therefore the ornission of centre of buoyancy as a form variable would appear to be reasonably justified. For forro diagnosis, say of an existing ship, the possibility of bad centre of buoyancy position must however be investigated. Th.e influence must also be really investigated to make propulsive cornparisons possible which duly allow for wake ch.ange caused by centre of buoyancy change. In Moor's presentation, of which table 1 is an example, this can be very simply done. One has, of course, h.ere to assume that centre of buoyancy influence is independent of a vessel's transverse dirnensions; and the assumption undoubtedly requires more extensive investigation than has yet been given to it. There is probably sufficient information in the series 60 data to determine this issue, * but again such an investigation is best left to the computer. lt could be got from Moor's analysis, but for fuller forros and well-forward positions of the centre of buoyancy Moor's data appear to suggest a strongly increasing wall-effect compared with the series 60 data. For other and particularly aft positions of the centre of buoyancy there does not appear to be much conflict and Moor's work can evidently be safely used, always presurning, of course, constancy of the Murnford index over the dimension change. There is one clear advantage of the Moor presentation which should be appreciated. In our series 60 presentation we have to accept the optimurn centre of buoyancy position for a given block coefficient, but we know that this position for a given fullness must also change with the speed-length ratio. Thus where it becornes essential to specify an optimurn position for a given fullness this specification has to be con.fi.ned to the Ve value at which the particular rnodel would normally be designed to run. lf, however, for example, a very full form has to be overdriven then it can only be run relatively econornica!Iy provided the centre of buoyancy is moved distinctly aft of what would be regarded as its normal position for the fullness in question. This fact is autornatically incorporated in the Moor and B.S.R.A. presentations. As a directional guide to the optirnum position, the relation 0 = 10 (8- Ve) ........................................ (11) is sufficiently accurate. Here the symbol 0 means the centre of buoyancy position expressed as a percentage of the length and when positive is forward of arnidships. This expression shows whether the series 60 data of our tabulations can be further irnproved by centre of buoyancy adjustrnent from the value given in the table. When the tabular value gives a position further forward than does the formula there is a case for a somewhat lower Re value being realizable than is irnplied by the tabulations. It is of interest to note that the standard centre of buoyancy position adopted for series 60 (except for 8 = O· 65) is also that adopted for the B.S.R.A. series. Corrections for departures from this standard can be got from Refs. 8 and 10. The standard is expressed by the following simple relation: 0 = 20 (8- 0·675) ......... . ........ . ......... .......... (12)

Expression 11 should gene¡aJiy be u is being overdriven. In the opposit< suggests the advisability of forward the standard value. This, however higher block coefficient should pn with a more normal centre of buoy The tabulations of series 60 now ! information possible at the momen future the B.S.R.A. were to repeat ti would be a good case for reverti1 influence giving in effect three pr influence then remains to be asses additional beams and at O· 60, O· 7( 31ft. draught and the other at 161 corresponding Murnford índices, th to be made. If we have the four d 12 tabulations for each speed-lengtl This may appear rather formidabl< usefulness of such tabulations to extension to the two additional bea knowledge of beam effect ; and eit draught differentials or the lVIun necessary. In any such work the whole of tt Iight of intervening ship-model corr to the time when this can be carri Personally I feel that if we can det ship resistance we should subtract f1 írom the model and thus obtain · should be studied on its own merits line. We could thus derive a ship hull without any direct reference to of so much controversy. Such a~ of Reynold's number but rather relation is eventually agreed the n difficult. In conclusion one should empha: series 60 resistance tabulations to Ji for the particular block coefficiení given lavish information on series therefore in repeating this inforr information can however be very but a consideration of the methods future occasion, when one may he progressed much beyond its presen

• As was actually shown by Mr. D. P. Roseman in the discussion of Ref. 9.

PR

TELFER: THE DESIGN PRESENTATION OF SlliP MODEL RESISTANCE DATA !P MODEL RESISTANCE DATA

Expression 11 should generally be used to indicate that the basic optimum form is being overdriven. In the opposite case of a vessel being underdriven expn. 11 suggests the advisability of forward movement of the centre of buoyancy beyond the standard value. This, however, is hardly a design problem. If it were, a higher block coefficient should presumably have been selected in association with a more normal centre of buoyancy position. The tabulations of series 60 now given are subnútted as yielding the maximum information possible at the moment to the ship designer. If, however, in the future the B.S.R.A. were to repeat their series, say for 45ft. and 65ft. beams, there would be a good case for reverting to the inclusion of centre of buoyancy infiuence giving in effect three presentations of table I. Only the draught infiuence then remains to be assessed. Possibly two models for each of the additional beams and at O· 60, O· 70 and O· 80 block could be tested one at say 31ft. draught and the other at 16ft. to control the draught changes and the corresponding Mumford índices, thus eventually enabling complete tabulations to be made. If we have the four draughts 31, 26, 21 and 16ft., there would be 12 tabulations for each speed-length ratio, say possibly 150 tabulations all told. This may appear rather formidable but there can be no doubt of the extreme usefulness of such tabulations to the ship designer. In the meantime the extension to the two additional beams would add greatly to the certainty of our knowledge of beam effect; and either the computer called in to produce the draught differentials or the Mumford index method further developed as necessary. In any such work the whole of the data will eventually require revision in the light of intervening ship-model correlation. We are undoubtedly getting nearer to the time wben this can be carried out, but much still remains to be done. Personally I feel that if we can deternúne from our trials just what is the final ship resistance we should subtract from this the residuary resistance as calculated from the model and thus obtain the ship specific frictional resistance. This should be studied on its own merits rather than as an extrapolation of any model line. We could thus derive a ship frictional resistance line for the clean welded hull without any direct reference to the " roughness " allowance still the subject of so much controversy. Such a ship "line" will probably not be a function of Reynold's number but rather one of relative roughness. When such a relation is eventually agreed the revision of our powering data should not be difficult. In conclusion one should emphasise that it is obviously necessary in using the series 60 resistance tabulations to link these up with the corresponding lines plan for the particular block coefficient under consideration. Todd in Ref. 9 has given lavish information on series 60 lines reproduction. There is no purpose therefore in repeating this information here. The Todd and similar lines information can however be very greatly condensed from a design standpoint but a consideration of the methods involved are probably best deferred to sorne future occasion, when one may hope that the subject of lines optimisation has progressed much beyond its present somewhat elementary state .

· outside) the series 60 range. In limensions is better preserved and be when the dimension change is g is suggested by Doyere's and .el through a displacement range; ;ion only requires the usual single úng of a bad interference zone, or obscure the intrinsic purity of the ~stricted

to the use of only three i.e. the beam, draught and block mably optim.ized. For example e case of the centre of buoyancy f the centre of buoyancy is within ticular fullness it is difficult to be ~- For design purposes therefore rm variable would appear to be of an existing ship, the possibility ·er be investigated. The infiuence 1lsive comparisons possible which of buoyancy change. In Moor's tis can be very simply done. One •uoyancy infiuence is independent ~ssumption undoubtedly requires n given to it. There is probably determine this issue, * but again :er. It could be got from Moor's •ositions of the centre of buoyancy :easing wall-effect compared with :!y aft positions of the centre of 1 conflict and Moor's work can :ourse, constancy ofthe Mumford me clear advantage of the Moor [o our series 60 presentation we ancy position for a given block a given fullness must also change becomes essential to specify an ification has to be confined to the normally be designed to run. If, be overdriven then it can only be ~ of buoyancy is moved distinctly •sition for the fullness in' question. v1oor and B.S.R.A. presentations. on, the relation . . . . . . . . . . . . . . . . . . . . . . . . . . (11) means the centre of buoyancy h and when positive is forward of ~series 60 data of our tabulations ' adjustment from the value given osition further forward than does ver Re value being realizable than . to note that the standard centre :xcept for o = O· 65) is also that for departures from this standard trd is expressed by the following

373

1_

. ......................... (12) 1ssion of Ref. 9.

PR

1'

/!

¡; 11

1.'11.

374

TELFER: THE DESIGN PRESENTATION OF SHIP MODEL RESISTANCE DATA

T ELFER: TH E DESIG N PRES ENTA

APPENDIX I.- Th REFERENCES l.

2.

3.

4.

5.

TELFER, E. V., " Note on the Presentation of Ship Model Experiment Data," N.E.C. lnst., 1922/23, 39, p. 221. TIDEMAN, B. J.," Uitkomsten van Proeven op den Wederstand van Scheepsmodellen," Memoriaal van der Marine, II Afdeeling, 9e Aflevering; 1876-1880. FROUDE, R. E., "The 'Constant' System of Notation of Results of Experiments on Models used at the Admiralty Experiment Works," R.l.N.A., 1888, 29. TELFER, E. V.," Miscellaneous Notes "In ter. Con. ofTank Superintendents. The Hague 1933, p. 133.

In making the Froude length con the resistance R in lb. for a 400ft. shi in knots. This is given by

R

7.

AYRE, A. L., "Essential Aspects of Form and Proportions as affecting Merchant Ship Resistance and a new Method of estimating EHP," N.E.C. Inst., 1927/28, 44, p. 47.

8.

MooR, D. I. and SMALL, V. F., "The Effective-Horsepower of SingleScrew Ships," R.l.N.A., 1960, 102, p. 269.

9.

Tonn, F. H., STUTZ, G. R. and PIEN, P. G., "Series 60-The Effect upon Resistance and Power of Variation in Ship Proportions," S .N.A.M.E., 1957, 65, p. 445.

10. TELFER, E . V., "The Wetted Surface of Ships," Mar.Eng. and Naval Architect 1922, p. 355. 11.

MooR, D. I., PARKER, M. N. and PATULLO, R. N. M.," The BSRA SeriesAn Overall Presentation," R.I.N.A., 103, 1961, p. 329.

12.

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," S.N.A.M.E., 68, p. 291, 1960.

O· 00883 S Vk1. s25

This can be shown to reduce to R /SV 2k = 0·005234 / V/· 175 It can easily be demonstrated for anl

SL /v

y2rr =

-'7

. L/t

and SL /

In these expressions '7 is the wetted s the wetted surface of a cylinder of : length and displacement as a ship, tl Combining (2) and (3) we get,

DousT, D. J. and O'BRIEN, T. P., " Resistance and Propulsion of Trawlers," N.E.C. lnst., 1958/59, 75, p. 355.

6. HoK, W., "A Method of Comparing Steamship Performances and of Estimating Powers and Speeds of Ships," N. E. C. Jnst., 1893/94, 10, p. 21.

=

Re¡ =

R SV2k

O

SL

=-

X11

which reduces, with 7J taken as 0·48 1 Re¡ =

V

e

o.115



0·95~

Lc l

This can be written more generally a and in (6), .L/B

~~~

................................... . (7)

If the rJ> values in the table above are multiplied by O· 972 f'r¡ they will then accurately refer to the Doust 200ft. standard. In these expressions (J is the midship section coefficient and 'P the prismatic coefficient. These two parameters together with the ,other two, L/B and B fd, also u sed in (7) constitute four of the six chosen by Doust for his statistical analysis. It is felt that if Doust had used such a function as L/B

/ B/d, his statistical work would

'V fl 'P

have been greatly simplified and made more physically purposeful. Pursuing this point, however, we see that this friction parameter can be still further simplified since it obviously reduces to L/ Bd(J