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In this paper an attempt is made to study the relative economics of a group of similar merchant ships while in their embryonic stage of preliminary design in order to determine the optimum ship, Linear progr mming is proposed as a method of analysis, and a digital computer is suggested and-expected to be used for the solution of the fital equations of the problem at hand, eThe equations developed herein' are general, in order to cover as many phases and variations of a ship's design and operation as possible'~ Thus, for each particular design problem, these expressions should be modified to correspond to the requirementts and specifications set forth by the shipowner requesting that design. No attempt is made here to translate the problem into a computer lauguage for the final computations,

TABLE O$ CONTENTS Introduction Outline A. PART I. 1. Linear programming. 2, Definitions 3* Design Considerations 4, The Model 5. Inputs 6. Input Constraints 74 Disposal Process 8. Input Output iiquations and Relations 9. Calculations of Unit Productivity 9.1 For the first input 9.,2 For the second input 9*3 For the third input 9,4 For the fourth input 10. A comment on unit productivity 11. Final form of the equations 12. Basic and feasible solutions B. PAR1T II. DE;IGN 13. Introduction-statement of the problem 14. Explanation of controlling statements 15. Computer storage capacity 16. Output constraints 17. Stowage factor 18. Capacity coefficient 19. Output constraint # 1 20. Output constraint # 2 C. PART III,* EGONOIOI ASPEiCTS 21. Introduction 22, Criterion of profitability 23*. laximization of the criterion 24. Calculation of the investment 25. Present worth of annual income 26. Present worth of annual costs 26.1 Crow wages 26.2 Fuel cost

26.3 Maainten ance and repairs cost 26.4 Stores and supplies cost 26.5 Subsistance cost 26.6 Insurance cost 26.7 Capital cost 26*8 Miscellaneous cost 26.9 Cargo handling expenses 26.10 Pilotage cost 26.11 Custom, Immigration, and miscellaneous costs 26.12 Tonnage tax 27. Profitability equation 28. Obtaining the optimum ship 29*. Evaluation of the method 30. Summary of the application steps

The worl is presented in a sequence which Is dictated by the logical execution of the steps necessary to fulfill the pose Of this paper. bhe main objective of this analysis 8s to determine one ahip A which will meet two major requirements. The ship should have oharacteristios that: 1. will meet the owner's specifications ooncerming deadweight 2. will render itself the most profitable ship possible. Actually, the second requirement is implied in the first. evelrtheless, we can Olarify matters considerably if we disting iish between them and label the first one the Design part.and the seod the Boonomics part of our analysis. Moreover, it is obvious that both parts are inter.-related Since the7 have the ship characteristics as a common variable. But for a specified deadweight, the Design part govears, because the economically optimal characteristics might not satisfy the demands for the storage of the deadweight. Therefore, the Design part should be treated first9 However since some theory and explanations will be necessary, the subject matter is presented in the following order. In the first section, linear programming is explained and the necessary general equations are derived. In the second section, the Design part and the use of the computer are introduced, anA the accumulation of data is descrilbed.

In the last section, the eonomios parb is used to determine the optisun ship according to equations derived in the first part 'ad to results obtained in the seoona. General remars are oceasionally made.

INTRO-DUCTION A naval architect who is confronted with the design of a new ship can use a few basic equations and arrive at a set of characteristics for a ship which will meet the owner's specified requirements, However., by varying (within limits) one or more of these characteristics, and there is no reason as to why he could not or should not, he can obtain a new set of dimensions defining another ship which will again meet the initial ownsr's requirements, Obviously then, he can propose many designs, a whole group of ships that can do the same Job. Assuming now that all th.ese ships are feasible as far as their construction and pera.tions are concerneda which ship should he propose to D7e lbuilt as the best one? Analyzing the group of all the Lifferent feasible ships, he should be able to choose one as the optimum9 judged by certain criterion either of economics or performance, or bothe oupposi-cng that he is to design a merchant ship whos' economics is more important than performance., stability characteristics, for example, the optimum vessel from his group of ships wvill be that wrhich will meet the architect s economic cri'ierion to the highest degree.-f Nowv, what technique can he employ, and what economic criterion can he use to arrive at his choice of the optimIum shiTp? Of course, a long-ahand detailed economic analysis based on some criterion, the capit-al Recovery factor. for

ns.:e;iouc.' ac bee ci otkiQ o~l.' '-z.' 1.. a"t- the encd prboduc ti3tei.mT<n4tixmw; 5hip,;j o?3::~G:-i- >e' consiAdeoing the3 n umber of feasible ships t>fi (ahe propotsed gr'-oup 'this ro@es ted-i-ous anct. LflvOes a z ---eat atrount of paper workP, ~Thcstrfce. ib.s d.esirable that; another method be employed for carry tng ouAb this detailed analysis. Thze new method shoul'd RL'mI dc-.l..i; J. r e> ^; ^esults IW'ith. a minimum amount of wo r~-k a:.t cosst (,.o o:, the technMiques that might answue th:ese demands > line1.er rrogr.amming, This nethod, as app,ted to t-.he dcR,:es~., e t..oIIruction and operati; ons of the ship s, is not i-n,it;self simp.le Ne vertl.he'less it can be use,, to ana.yze the shippiung bs.ts.uess a ccurately an-d e'ti.cintly, because iit can. be progrear'.mi.zed and put thr'ouh. a digital compulter w3hich twil3fl [giv.e:ht e, proper answier afi ter a reasonable amount of tire OanL, I as w.111l Se shown later, witb. a reasonable cost, oornsi.der.ig tthese ad.vanta.s. of cA.T.sr porioiga.ing, that is, - its accuracy an ide rawe Vf &XjoS - tMe amt of time, and. the co mparaPtl.iv'ely small amc.o ut of manual. wor. and cost requi,:ref, xs.:el, shall develop linear programming in s.ch Ua " ay that:, can be used in tle field of Naval Architecture.

PART I tIear pr8o;plum'ug, in general, as h name iMplies treats only 4ea funotions, andt i a mahematical ethod which can be used to maximise or amnimise a given function whose variablese re subJect to a set of conntraints in the form of inequalitie. A typical mathematical problem solved by linear progLauuing ocan be stated as foll.lovs: MA, iizie or minims the uhe ction ftolX11 + o2I2 + *X3 +.. c ' (1) subjeot to -_~ Xi + a.ak + aX3 +. +. a3: 4, a211 + aa2ka + a23.t3 +,<,.***......*....... **.**......... ****** *** (2) amlXl + am2X2 +' alm3X3 +* + tmnX~ & n vhere all c's, a's and e's are " k~ m and X's are the variables. Vleak inequalities are acceptable. The mathematioal solution and proof of linear proamuzing will not be given here as being outside the soope of this paper. HoVIever, it should be noted at this point, that one condition for this problem to have a solution is bhat all Variables included in equation (1) and the set of inegqalities (2) shoula be non-negative, that is, they can assume any positive value or else be zero. * Nuimbext parentiheses refer to bibliog~rapy at the end of this paper.

In economics, linear programm-ing is used to determine the optimum production aonditioas and output levels pertinent to free enterprise systems and purely competitive firms. Whenever, there is a variety of prooesses that. a fim oan use to produce a oertain good, linear programming analysis is the best adaptable one for determin~i the most economical prooees and the most profitable, the optimum, level of output of that good. The method is primarily based on the neoclassical theory of the fim, that is, the mrginal analysis of the firm, and in most cases ignores the quality of the product, assuming it to be the same for the outputs of all the available processes. More about this analysis will be said later, when some ot the conoepts invsolved will be defined and explained. At this point, we ma add that for an economics problem equatioya(l) is usually the criterion of profitability of a process and the system of inequalities (2) expresses the input constraints as is explained later. Ie shall prooeed with the introduction of the method in Naval Architeeure by defining some related concepts of linear progamming. A "proces&" is defined as a part;iular method for manufaoturing a certain product by using definite quantities of a number of inputs. The distinction between processes of a production program is based on the fact that both the

quantities of each input used in the produotion of one unit of output, and the number of inputs utilized in each process are characteristic of that process. This leads to the definition of the "unit productivity" of each input desisnated by ai3, as the quantity of the i input absorbed in the production of one unit o output of the J process. Thus, knowig the process jw ae know a, an vie versa. In Naval Architecture, however, ad in this paper, the above defintion of a process should and will be modified. We define as a process, any ship 3 whih -will have definlte characteristios for a certain displacement Ae. Here the total displacement of a ship has been ohosen as the output, each long ton being the unit of that output. Hence, the unit productivities will be expressed as the amount of the inputs absorbed in the production of one long ton of total displaoement. Since linear programming determines not only the optimoum poceas iv4. CIso W~ op+i4Yn kv le o%' io s A ApA, & shall manipulate the total dlaulaoemeat of a jCouj, of ships and determine the optimum one to satisfy the owner's requirements. Later in the paper, we shall elaborate further on our choice of the displacement as an output... DESIGN TO0_ID_ OHSA_ IO ~ Any production program implies that there is substitution of inputs between processes, but there is nb such substitution between the inputs of the same process. This implication has a number of consequences in our analysis, the most

itportant of them being the tact that we cannot compare two iential ships, one having a geared turbiAe ntallation and the other a diesel, in order to determine the merits and profitability of each istallation. This is so because the two identical ships with different maohinery units are two different products, two different outputs. The fact, however, that these two ships are considered as two different produots, suggests the following method of comparison, if at all desired, between the diesel and the stoea turbine. le can set up two linear programs, one for each ship, having among their inputs, the first a steam turbine unit productivity and the second a diesel. Then following the steps outlined +n this paper, we can determine the optimum ship with the diesel installation and the optimum one with the steam turbine. These two ships will probably be of different characteristics. Next, we can compare these two ships by using an economic criterion, like the capital recovery factor, and determine which of the two is the most profitable. This same method can be followed when other minor features are to be investlgated and compared. With the same token, we cannot compare a steel ship with an identical alumim.n one. Hoowever, we will always arrive at the optimal ship, in cases like the ones mentioned above, ~by using two or more linear prograus, since we are really talktng about two different products or outputs, as far as linear programming is concerned.

With this backpound, we can now list some of the variables and the paramete of lineai progmmiiz_, as defined a-d related in a Naval Arohitectre economics problem of aeaisiin and operating a merchant ship. Assume that the problem involves the analysis of combIning i different inuts and produoing 3 different ships. VARIAN: I C the nuaber of dollars invested by the owner in his 3 ship. c = the urmber of dollar' worbh of cost incurred annally by the owner in hts J ship. p3i the number of dollars' wvoth of net profit earned a,3nually by the owner in his 3 ship. 0C. the nunber of phI ioal units of pay-load capaoity rented annual by She owner in his J ship. xji* the number of pbysical units of the i input used by a shi!yard for oonasttdting the owner's 3 ship. ai - tihe unit roductivity of the i nput defined as thS nuaber of pbhsical units of the i iprNt absorbed per physical unit of total displaoement of the J ship, a parameter noot to be anipulated. nL the price of a unit of the i inpu, not to be mantpulated. no " the price of a unit of the pay-load oapacity, cargo rate, not to be manipulated. Aj - the number of phsical units of total displacemeat of the J ship, a parameter to be the of o tip of thte e the nube ofr ouwA tripe of the 3 ship per yere

TPhez for each ship we oa write the folloaiJg egquations. 1, *u.tment. equabion) (Cons=truotion or Mnufactuwirn costs) Later this equatio is8 somewhat modified ~ order to correspond to the shipyazd bill for the ~onetmuction of the tesselS Th sVpyal4 bill is a part of the cost breakdoov which in wvel*y used today. 2. Oost e uatio_: (Averase ag nual operatin costs). 4 ' ~.4{sHi')1 4 ((h c) (4) where 0 covers misell aneou expnseso. 3J tzome eua io (Atvrage aanua). inoe), Tfcomn& zVI. rs (5) wheoe aO is the capacity coefficient. 4, P. oit$ eMuatioa: (7) 5. i~u1~-Moutrst 9mati~zL!Jrhies -b acsij e is i Sfo i r l(t),e hese baequatio eQties will laten enable nW to rhazlate the equations necessay tor our analysis. e shall- start; ~ith our input ielsatior b ~s

As inpts we shall consider the stiiture al material of the ship, all measue in lon ton, a8s shown in TABLE 1, below,.TA XI EPuts. Inpb item abe'bscrip; Desigatiom OonstRcution Steel I Ws Hull Outf~ittig 2 Materials o ihll gineezr:n 3 materials Ma4h*ery laterial; 4 |VI It is imprtant to eaphasize that the nma-hours an the aobn-houra which will be required for the construmOtiO of the 3 ship Ahould be included here as inputs. Howsver, in order to reduce the number of our equatios and therefore the number of solutions for a given number of displacements to be analyzed, we otit these two items fro= the group of inputs, and we include their costs itead in the cost of the four inputs above as $ per ton of each material.

AeordAi to equation (4) the optimum ship 3 will absorb a quantity aijSA of each inpst i. The utilized amount of any inpaut, however, is limited for at least two reasons. Pirst, there ndIht be preatioal limitations, for instance, the amount of steel required to construct a ship a mile long might be psrhased, b;twe just cannot build a ship a mile lonSg Herce, we have to' limit the amount of steel to be used to some reasonable quantity, dbtermined, with a good margin, from similar exisng ships. Seoad, there might be "fixed plant" limitations. If, for ecample, there is only one welding machine in a:hipyard, we cannot count but to use only one aohin-hour per hour. Or if the size of a dry dock limits the size of a ship that can be built in it, it limits the amount of the inpats, If, further, the steel mills are on strike, the available quantity of steel that a shipyard can purchase is perhaps only 5,000 long ton, iL spite of the fact hat the shipyard might ha" a pending construction oontraot callin for 10000 tons of steel., In our study, although we can assume that a shlyard can employ at an time all the needed man-power, supply the machinery, and purchase the neceesesary gquantties of each input, we are still foroed to plae an upper limit on all our inputs,. Of course, a naval architect does not carry out a Cost study for a shipyard, when designing a ship, in order

to worry about the yard's practices. Nevertheless, in this type of study, we should oonceren ourselves with shipyard teo ques and capacities so that we may take full advantage of thla when we limit the inputs. Cinoe these limits should not necessarily be exact, expeiileaO is a good piide to the naval archlteot. *hat is, if ke has a "hunohu that the optiaum ship will require, say abtut 5,,00 tons of steel he can safely assign 7,000 tons eat an upper limit for the steel input. Actually, he may, in t;is ease, assiEn with his pleasurethe amount of 200,000 tna of steel. this will not affect his analysis, as will le explained in the discussion of the disposal process,.ecause he may very wll assume that the shipyard can sell;:he extra steel with no loss at all on its part in the iransactions. Actually, the shipyard never bought the steel!;haa the architect worries about. huns, lwe may say that for the optimum ship, the weight ~f steel, hull outfitting, hull engineering, and aohinery 3hould be less or at most equal to the available or specified uantities of WV, Wo, We *n', respectively. Equation (8) laen becomes: a 1 + alA2 2 + j.. + a W a21 1 + a22 2.;O a531A + a32 2 *1 +aaMAj e a14 1 + aa2a + ' '. + aj,;l < he inequalities of system (9) are the input constraints to w.;ich the oriterion of profitability is sub ect.

. DI8ISAL PR aCiS8 Por a geometrie solution of linear progamming, the inequalities expressing the input eonstraints are very easy to handle, However, for an algebraic solution these inequalities complicate matters considerably, andit would be desirable to have them transformed into equalities. The introduction of the disposal processes will make such a tranformation possible. The disposal process can be definad as a process whieh has one input and no output at all. Let this process be designated by S (delta). Then, delta represents the quantity of the i input disposed of as waste or idling material not utilized for the production of the optimum quantity of the output. It is equal to the difference of the initiallT specified quantity of the i input and the amount absorbed by the output of the optimim process. Generally, it is assumed that the disposal process has only a certain cost attached to it, and no profit.. The cost is taken to be equal to the value of the input to be disposed of, and is given by the expression: c =,i -i i^i (10) If linear programming is applied to a firm with a fixed plant, the disposal process might include idling man-power or machinery, and in this case the cost of this plrocess should be carefully considered, In our problem, however, we can assume that a shipyard can empaloy only the Ieeded manpower and purchase exactly the necessary anount (with an

allowance for crap and 10osses) of the input materials to be utidise for the oanstruotion of the optimn ship. 8heretfore, we can igor. the coeb of this isposal Pooss entirely and we only use the ooncept for the sake of the equaities. I&troduciag the disposal prooess into aystem (9) we obtain the following equations a11 1 + a122 2 + * + al ZJ + S 1 we a21 1 + a2 2 + "' j + t- 2 wo a31 41 + a2 A2 +... + a4j j + 3 - 1) where aij unit produotivity of the i inpt, Si * disposeld quantity of the I inpt in long tons, Aj a outat, the total displacement, to be maipulated. i - 1. 2, 39 49 3 - 1, 2,... 3?. Fro mathematic, in addition to the condtions stated previously, the system (11), in order to have a solution, should be a nondegenerate one, When linear prograng is applied in Baal Architecture it has a peculiarrd imBportant carateristic which should be brout out at this point. bi8 ohacteristio is the relation between the output and the unit produtivity of each input. Usually, when the level of outlet for eaoh

prooess is speoified, the quantities of each input absorbed by that output are also specified, Nor e aomple, it a television set requires only one amplifier, the unit produotvitLr of a -plifiers is one (1) and a simple statement that a firm produoe e thousand television sts per month autoaatically neans that a fim uea s one tond p3lifers per month. In Naval Arohitectaue, heowver a similar statement is almost menaniglest, because by nowing the displacement, that is the output, we do not Ikow the quantity of the in at absorbed by that displacmaent unle1sse9 know the oharaoteristio of the ship, For instance, the ateel and the =a hinery weights of a ship depend on the cubio number ad the shaft horsepower of that ship. By knowing only the total displaoement of that ship, we have no idea what these two items will be at all. At this point, we cam draw an important oonlusion, that is, when we calculate the unit paoductirity aui in the nest seotion, we ust e apress then in terus of ship chaEracteistios rather than total displacemente. A coneuaene. of the relationhips between the total displacement and the ship construotioI materials will be taken up in section to his consquenoe affects the method of solution of equation (11) and will be better uterstood if the a ssits for the individual utni produtivitiee are= derived first;

UCALCOULATION OF - UJIT PRODU0tIVITX 'I. o.e:r. to solve system (11), we must compute the ';;:,i: p.o-:;l..ctivity aijfor each of the four inputs. 9.,1 or the Pirst Input, a1 Considerinm the first input, the construction steel, ai is the number of tons of steel per ton of total displacement. ~F definition then, Weight of steel - W8 (12) Displacement A ~The steel weight of a ship is conveniently calculated for our purposes by the cubic number method, A similar ship is selected an the steel weight coelfficient is calculated. Thern the hull steel wetgt of the proposed ship is computed a.d corrected for azy differences in aimensions and constzruction betveen the proposed ship and the ezistin simSlar one. For the calculations we can use either an everall weight coefficient or one for the main hull and one for the supsr. struoture, depending on the degree of similarity between the two ships, and also on the accuracy desired. PFo our comparative purposes of the similar ships, however, an overall steel weight coefficient will give satisfactor7 results. It should be emphasized that Telfer's or any other method of steel weight calculations could be used equally well. sence, the steel weight of the hull is: A. JE~ t _ _ _ 1 Dn

where OG = steel weiet coeffioient dete emed froeom a silar ship oalled basis ship C o coorreotiou faobor for block coerficient Ob differen es. OL/D = o'eotion faoetbr for L/D ratio di~~ferenoes. The last two corr etion factors aret + 0.5 C) b and - CV;2 (Y/)X ihere subscripts p and b refer to proposed design and basis ship respectively. The displacement A is given b;y: _ __LEtd Cb 3s Substituting L& we obtain: tLeiJ CI P 3 5 C,, Cs, c. CYp C~/ ~ too L McA CIO o' the 3 ship: a 36$ c (i* 0.6Cb)p 1?'(L -g~ (14) 56,* _.%3)i*- C O~q A Ioo LjB d 0

Nov if we use the following designations8 or the a ship of a familr.: L PL djj equation (14) becomes: '5J 5 C's +oC1scb%)6:/ V., ( 3oo,... -?'-: Cb:o (-* 0,5 C I Equation (15), hence, is the expression of the unit productivity of the first input for any ship J. Equation (15) will be applicable when the structure of the ship is to be built only out of steel. In eases -where it is desirable to use alumn~1um for the superstructure, we should include aluminum as a fifth input, with a unit produtiity of a5j. The weight of alumim3m to be absorbed by any ship j will be a function of the cubio number of the superstructure of that ship. Assuming similar superstriuctures for all ships, we can calculate a coefficient for the altumtinum weight from a basis ship, and express the quantity of~ alurminum to be absorbed by a ship s as a fTuction of that coeoffiietnt and the cubic number of superstructure of the 3 ship. In fact, this breakdown could be used for steel ships also, where more accuracy is desired.

Considering next the second input, the hull out ~i.t-ting mat-erials, by definition we have: Vleight of hull outfit*t materials U, a2j ' ' 'trcj Total displacement The vwesieht of hull outfitting is assumned to be a functi on of the cubic number and the total number of persons aboard the ship, or: V40 C4 CBD. CIot Cl7) where a outfitting waight coefficient, determined from a basis ship. Cio= an estimated coefficient giving the outfittin weight per person, and P = total number of persons aboard the ship. Mhe total number of persons aboard the ship incJudes both passengers amn crew, The number of passengers!% Cof a particular family of ships, can be expressed in,:.,..-., oW f their displacement.(10) By assigning a certain nu:,I' -". passengers to a prototype ship, we can assume that NEp f ow1 any other ship of the same family will vary in some fashion with L, like 3, for instance, Bor a passenger-soargo ship, the variation of the anmber of passengere with the total displacement-l-c. A -will be sim lar to the one shown in Fig. 1. (10) 8iAnce 'lhe relation will be linear, we can irite: -, k.) -

Pig. 1 Number of passengers for passenger and passenger-cargo vessels Soo t4i 400 4d 0 S 00 Xot6L Dt~t;ACt~iAW MOO Fig. 1, shows the variation of the number of paseenge;s with the total displeceraent for a particular family of p seenver-.cerro ships. (lo)

By substitution, the previous equation becomes: where C2 should be computed from the curve of Np versus A. The number of crew 'No, on the other hand, depends on the S H P of the ship, the deck area, and the number of pasCssngers aboard. Nm then includes, (a) engine hands N, (b) deck hands Nd, (c) staff No, and (d) stewards Ns or J = 'e; + NdJ + No3 + JTj (18) The number of hands of each department, in the form of an equation, can be obtained ae follows: For the engine room, iwe = t (8 P), For the deck, Nd f2 (L r B), Por the staff, N0 w3 (N), ana.For the stewards, wf4 (N) Appropriate functione f1 f2 f, and f4 are found:o d.ata on. exiting siamiar ships,. nd for passenger and paouenrzef cargo vessels the oorresponding gaphs ae shorin in euiog es 2, 9, 4, and 5. Por illustratisve purpose6s, these graphs were pro "ammized and fed into the IBI 704 computer of the Universit of Miohigan, with the instructions that the computer uill derive equations to fit each curve. She results are ehorIxk next.

-24 -Fig. 2 Engine room hands for passenger and passenger-cargo vessels 3 o 280 0 24 411 tO 4 o80o 804 L.t 2.aq ooiAmP

-25 -FIG. 53. DEv cl Tr PSEng Cr $ eAiWr COC4L O,e~seA$ o) Its lap j5o *o 0 0 Q3 So / 170 so?.o \45F ~ a~et /v~qt uBlrl'~o

IF% c 4t. W u e. ov SvIF e A" s v Ir- -- 4iU$?iso C G -cttoo,'GSELS II s( ISO" 1600 1450 X so 9'500 It I.......... -.. -... L. -.. o t o oo 4.0 Ft G. 4.

cps09- w,.w I co r'ai OL3;~a~l~as-si sf p~dn~~ b ~9W"CV'Ij'B~~!rt

The equations which the computer produoed are the following: )e —23.48 s 58.3CsP)z. ~ (2.Ss,U) (~',i: - -.~23, 3(.-B)~'s- 3.8S, YToC(L,,B)-4 (20) 22.73 + 1 Z70O7S(Np- 4G&Q+ - - 4bpLS (20l) )- 5I 3451. 2.6 ) (22) Retumrnin to equation (17), we can write: *0 - Co L,- ). C,oC,,,+ c,) or o_ co J C ~tit 4 toe k &*BO*U) MlJ, = Co too, V. Upon substitution, and for the ship, t;his becomes: c CV5 L~C%"No Express4, JL ) 4Cj S FiaZly acoording to equation (16) a2 bA._ i t;e of "l nn.oal chaacteristics and divlvind e atch tera separately, we obtain: 09..3SCO t3 3V.-Si2 _ __ _ C, L3, C cf i e46 + lo A,; oi V.-Si Cb! $~.C,,ltr ~L~s~Y C itL3~CbJA.s

Cancellation of equal characteristics in some of the above terms, has been purposely omitted in order to save the generality of the equation, for C0o might not always be a constant coefficient. Note also, that in some cases,of ahip design, some or all of the categories of crew hands might be kept constant without serious error. The terms, then, of the final equation are somewhat simplified. Equation (23), thus, is the nit productivity a2j of the second input, that of the hull outfitting mateiIalIs. 9,3 'Por the Third Input, a~ For the tuni productivity of the third input, the hull engiLeerinD materials, by definition we have: Hull engineering materials a- M.. ~. - (24) T otal displacement A The we~ht of hull engineering materials is assumed to be a function of the cubic number of the ship, or \IN e Ce aftwheOrXe e hull aineering weight coeffioent, determined from a basis ship. Substituting the epreessions for the zgineerig weight and the displacement ~i equalioa (24), we obtain: t.; z, d~ C.,' ~Cs - L S Cs,j Cj

-30-. which becomes -. 0.35 CQ 13 (25) Equation (25) gives the unit productivity of t-he thirc't input7 the hull engineering weight. 94 For the Fourtb Input, a4 For the machinery materials we define a4j as the total maohinery weight per ton of total displacement. This machinery weight could include not only the main propulsion units, but also all auxilliaries such as equipment for hotel services, refrigeration, heating and ventilation, etc. The latter group depends, of course, on the number of persons aboard the ship and may be accounted for by the use of a coefficient. Hence, Weight of machinery T otal displacement 4 2i5) where OC4 a coefficient, is to be empirically determined, see TAdLE 2. Pt ti $he number of persons served. The weight of machinery is a tunction of the shaft horsepower required for the propulsion of the ship. As such, it is quite accurately given by: WN - 24Z y co (27) Wu,, \ 6S+ ~\~,>GS (28)

-31 -'Ai'ItE 2. Avernage:?ue'I Co.nsr-mption Rat-esi 1, Passenger ships:-.For propulsion puposs 0 A8 1b/3./S L o,_ For hotel services 1.29 -Ts'/' H 2.ur 2 2t 'igu:, -e:.r r-~Paergo vessels: 2/: propulsion purposes V.. ' _ _'~:~ hotel services i,.:::.."l:::::,::.:..2or refrigeration '-'?:,'or cargo handling in ports 1l:..;:.enneral cargo shipsFor propulsion purposes 0,52 1bs/S H P hibot:-. For others Satiie az pas enro)gn"r a:-:e For propulsion- puerposes 0 52!bs/S { P? -::ko::,? 5s. Ore carriers: Ti'o propulsion po2 es C052.bs./ P.i Uhxs fPI\G %X 0i9 M A,%c sAd3y va ZX04-: -C S E q r. C e. S. C4 =D.\85 tb DIS S I/.so vA4;ur CKA1 %Z. LS o' 4\a.

depending on the type of machinery to be installed. Equation (27) gives the weight of a steam turbine installation, whereas equation (28) gives that of a diesel. For the moment, let us say that W= a CI f s(S H P) where C' could be a coeffioient for equation (27) or (28). The 8 H P, next, is a function of the effective horsepoletr, E H P, and will vry for each hull. Vith an appropriate propulsive coefficient, (P.C.) we can write: s H P P (PC.)E H P where (P.CO.) will depoend on the tpe and hull of the manalyzed ship. The $ H P should now be cons dered. The experimental results of model tests are the only sources from wfihih data for th E H P calculations can be obtained. The two main test data generally used are those of Taylor for twin screw vessels and those of Series-60 for single screw hulls. TFor each design problem the resistance data pertinent to the design hull should be used. FBo either twin or s-rinle screw vessels the E H P is given by: E H P = aO x S x T3 x t (29) where 05 = a onstant a 0.0048 x S = the vetted surface of the vessel, and Ct = the to.t1 resistance coefficient as determined t fromn the model test data. The wetted su'feae, using Teaylors expression is:

Cs = the ivetted surface coefficient, and l' a (C.i L- L), assumed constant for all ships, C0e veies rith the mid-ship section coefficient Om and the beam-draft ratio. For our analysis, haowever, without serious error we can assume a value of Cm = 0.951, YblCh is an average for the hulls used for merchant ships, and express a as a function of the beam-draft ratio. Again for illustrative purposes, the values for. wetted surface coefficients at Cm - 095 and different beam to draft ratios, were read of() and plotted a shown in Fig 6. h faired points were then progremaized accordin-1 to th'.3 stepwise regression method, and equation (31) v;as obQ)iiu~ed. C s 2.4S + 0o.004 4.48j (1) T2he calculation of Ct, on the other hand, is one of the moot tedious steps of this analyis. Since eve hing has to be programmized for the computer in the form of equations, t; must be expressed as a fuwction of some variables for each family of ships, so that the computer can calculate the appropriate value of Otifor each ship of that family. The total resistaues coefficient 0, followXn fbOUdB e' method, is the sum of the frio$ion resistance coefficient Of, the residual resistance coeffiocent. C,, and a flat roughness allowante, or ot a oC+t Fa + a. (32) Ca is a s tna 4 x l0' in acoordance ~iih the ArL'P V 1.47 recowmmendatio o

IS al) \ 3;'P L3 Se Vt, 40 i0 % ZL z

-55 -of in the form of an equation can be obtained by awr formulation, and for this work that of Prandtl and Von Kerman has been chosen because of its simplicity. Hence, - 0.O7 ' S or C4= o0o7Z \/V,.,; (L +(5f,) v a the speed of the $iip in feet per second, Vkr = the speed of the ship in knots, t the length of the load waterline in feet, W' = an estimated difference between andc L, constant for all ships of a flaly, and 7/~ = the kinematio viscosity of either salt or fresh water. Now for the determination of C., in order to be more specific in our disussion, let us dietinguish two cases, Oht t efa s %ng-t aind *e.g,,tthat of a twin screw hull. VWe shall carry our the analysis for only twin screw vessels using Taylor's datt-, with the underst niia g that thbe general statemrents 5-vZ.dA3 noboutt twin screw ships hold true for single screw -also, O course, Series - 60 resistance data have been -plotted diffeaently than waylor s. However, both systems are equivalent, and therefore the difference in plottitn does not prevent us from deriving similar equations for both cases, Hence, let us attempt to calculate CO for twin screw vessels. Obviously, C, depends on many variables, namely,

the beam to draft ratio B/d, the block or te.o loit-diia. coefficient C1, the speed to length ratio, ad- the volumetric coeffieient C * Our answer must be in the fox. of an equation such as: Unfortunately, up to the present time, no single equation has been brived to give values of Or for all possible values of all the variables, even within the ranges covefri by tests. Nevertheless, this is s not an impossibility. 1' fact, concurrently with this paper, this author has und. staken the task of deriving such an equation. It is hoped t-h; the result will be shortly available for use. Although, ~.. problem is outside the scope of this work, it is ~e?; 4:t a brief description of the method used for the de-:a.:.~ t-o of the said desired equation might be. of som.e be;.c.'. to this analysis, and so a short outline is in. order, The equation is derived by a digital compute: with the data wrogammized acoording to the steps of eitiV:s the imulation" method or the "stepwise regressio-r with simple learnSng" method, as outlined in reference 4, The data are first grouped as shogwn in TABIL 3. Then they are transferred to computer cards andaa ed into the computer vrith the proper controlling statements. The solution will be an equation of the foum of a polynomial involving a eirtain small percentage of error, whieh for our purposes will be entirely inignifica$. It should be stated tha. simulation and Btepwifse regression progras fcor problems involvtri up to

TABLE 3 Data for Oomputer Card.s it... I I. I -. ' *.. O n 3. __ | _ _._|_ - -- -- |__._.. - -i 60 va=aiab3es have already been set up. (4) I BShoud be further emphasized that tLthe equation so Cb.J:'L< 3 b valid for any value of any of the variables tith 2 -the limits used as data for tABL1 3* If for ay reason the method proposed above is not acceptbd or desiable, a different method1 the folloinrt

-38 -is suggested. For reasons to be explained in the next section, a number of displacements will be known from the computing work of the Design paa t before t.he actua. calculations of the residual resistance will be necessary, Knowing these displacements which will cor oespond to definite sets of characteristics. we can follow the steps outlined below. It is recommended that the variation of r, writh the beam-draft ratio be neglected and all, resistance coefficients be calculated at a chosen B/d ratio which will be an average for the type and size of ships considered, This proced.re will, of course, add to the uncertainties of the bil:c C. D but it is not easy to calculate Cc for each.;i/d w 'inu::: bT;'. the beam and the draft are variables. Taki 'gne tDo Pd. varlation into consideration would result in a considerable a.iount of manual work which might not justify the accuraey obtained by including this variation. The steps then involved might be: 1t. lake a table showing the feasible displaceaents selected by the computer. 2. Assuming a constant mid-ship section coefficient, list the longitudinal coefficients correspondinag to each displacement. 3, For each displacement calculate the volumetric coefficient,, Ov 4'. From the tables of Taylor's data(6)read off the residual resistance coefficient for each Cv and longitudinal coefficient Ci at different speed-length ratios. 5, Plot these C versus speed-length z<t:-Lo a'o constant 1i and C1 as.io.)v........ >

The maximum number of graphs neceasary will be equal to the number of feasible displacements multiplied by the number of the assigned longitudinal coefficients 01. 6. Use a digital computer to derive the eiuLations of all these curves and properly id.nt.ify each equation in order to be used ag'ain as a computer's input, As an ex.s4ple of this step,........;. computer found that the equation of the curve of Fig. 7 is C, = o. z 64 * o.,V 4(-~) Elther of these two steps can be used. However, it is felt 'that the general equation derived or to be derived, accordimg to the first procedure, possesses definite advantages, for instance, requires less work once dertved, and as suoh will be the one used in tthis paper. Assuming that we have completed the derivation of the equation for C0, we can proceed with the derivation of the expression for a4j* Thus C 5(s i )i or _ 3S C ckL CkC 35 C Pg " C1 S~i c) G.; b

Cr 0 0 "- I V P f<- o. \ 0a s o \ 4 t~~~~~~~~~~~~

Further substitution of the functions of the wetted surface S, the total resistance coefficient Ct, and the total number of persons served Pt, yields: L~j C~=, C [C. C. CSP); i B LC is $L ) (34) Equation (34) gi'ves the unit productivity of the mahineryg material and applies to both steim turbines as well as diesels, provided the proper value of ~O4 nd form of the function f will be used for each case. Also, equation (34) has been derived for twin screw ships, but as \ias stated earlier, a similar equation can be easily derived for single screw hulls, from data based on Serie - 60.

N oth that ue a ca:2.culateo. the eF-o-orr-,.. unit; o-Z' all inputs, vie can bettet7 Uniemstan.3 the _eLation of each ip vznt i thb the o]ut*,. U th'at Ls tbhs total displaceoent~.Jeo hBave preAviousl y sta-ted th.a f-i.know only the displaoeenLet Wito&ou&; knowin, it$s sb.ip" c.L...acteristios %e do not n1mor the unuIt productivi+tds iun o4ho,~ o;ords, do not mow t1he) process fox each ship, huit by t-ot - ing t;he characteristio, we automatically know tihe d.i':s. ^.emiert,:; a. the unit productivities, This "t AY t P!.]lr't.Vx:7..~ - us to tbDei derivationL of theo t i;Q-t.. -r>; u.nlt a func tiKo of the dimensio.. of each ship ca.-,'o-s be calculated indspendoently of thoe e.'D.:.':",..... (yi:, deezids on the volet ric- coeffXticient 07 of each s. 1i HEnoe", t Ais reverses t;he oIder of owa tnhiDlfnd irtn thii caso we bhave to calculat;e t-he displaceaent fist atnd then ccr:apuwte the smc, i ernii - h9mC!5cG-tivt@y cm proceSs iPra;oe ObIA..,....h c..... e of this is 'that i~in elolv.ineg -t:,-, e.quatiozos; (1i) o ttea-/ "e,wnnn dof.i;3 d'tiPm -,h, opt- ismm levrel of the output but xatther the opbiM-am prrcc.:ess Ac ozd!ing then to out definition ot gprocess a, bsn..n a-i rshi-o j o: def-Initer chaxator-isti ces. ou0, _iiea, Pr2 rona. w will L-ea!Qly produto the opt'imum dimensions of the sh~. d2& eons;t,:~ti~ y1 the optisum displacemeon Th sat C:: solve t.c, ai instead of unioS xrtc..ov:i,::....sc3lvigr' $inea prograrming equatiom is i$wBm.r~r-,;& - axoble"l' becaus. of the rela'2io.a bztw.aen,,.;L -... -:,;..-....:_:,:o.b..;,

T2-~~-...:..-:f.3,..~ttI.::- C0 0'4. 'JO:,..V.,t.: O 't>-i-'+t~r Ciui i-;' 0;'- i ' C.,.,-..? t., S T3 ti T.c;xt ~;Xi;,*.~, r- " ~ [-1d,- i: C':O - T.'::: T:'r-"i... o ST r- o.. rio f* I — - r '"t~..is IQ dorU.. T~'(? "~' C,!~t' (:): C'~CL: CI,.,~~~; ':~ ---'.f57)" f't": - -'-.I:.,.. Tr, % 3I '-..., T_:, T'-.:J T ',: 2. i t -. ' i-:::..? '~w:1'i.'-, —tn -'-a' i'3^Vt''OXt.j'4('f:.-' [,tr~, -'.,:-'tf1 Fi.;-,''. - - sq=@-r l s#l. lr5E+T i ~ ~e - 'r'R, 'SQ ', '., Y?CSE Sn.;.: 'i s '< i., ~e':.t-~-;i u xw-) -Rt gi~ f;.................................... '$ i.r Fof - t:1".O.t'C. t '''i3 o::-X6 ii; '' 't'n -l"-{ t'~~jf l, areAiTM1 ~*x Y -;- P j*T- t- i,~>~ R JK'-;*' r,,7? & C iA- - f - -

44W11o F INAL FORM OF TfHE, INPUT-OUTPUJT E UATIONS Having, thus, derived the expressions for the unxiit productivitles, we substitute them in system (ll) and obtain: OIO.S CO pi \I4C (cp 0.03S Coss l, S C,0,) 0, \S /_ CbS, %; ebi I;~ Ce; CS cV. I L.c / V.o,...33- 1 C4tt t(L; C Go;, rfft

$_4 '5L; Coig ~4~ s, +13 C J \4 tl' L;C: CIb 3S C ki * jt! = W 't 3![ System (35) is the final form of the equations of our, iput-output relations to be programmimed for the computer,

12. BBASIC AND FE iASIBLE SOLUTPIONS Our syatsm (35) of the input constraint equations obviously has no unique solution, since the number of the proposed ships is much greater than the number of our equations. Nevertheless, from mathematics we know that a system of (m) equations in (n + m) unknowns will normally have a number of unique solutions given by: n + m (a t m)l 11 nl ml This nmmber rresents the possible combinations of (m) unknowns left after we set arbitrarily any (n) number of uknowns equal to zero. The solutions so obtained are called "basic".solutions ~ Some of the basic solutions might involve negative values for the output/ ~ and/or the disposal proocess Not accepting these solutions leaves us with the so-called "basic feasible" solutions, defined as solutions involving no more than (a) unknowns and giving non-negative tvalues for the output and the disposal process, Te thus have one constraint to be placed upon our solution, Two more constraints follow.

PAR T it DES VozG'H. Up t;o this po.ilt-, we have considered the theozwy of liioar programming and havew der-ived all the equations which:.:Ill enable us to design any ship j. The meaning.of the woxrd "'design"t as used in this paper, should be clarified, to avoid any misunderstandinjg By "design" we mean the pt-.;.diction of the optimum ship having a definite set of ohr.acteristics, The arrangements, accommodations and c;:. —:.:' m:iaor details and items are not considered here, but,u:- i::i1 -* entirely to the initiative of the archit;c.;z.th; hovwever. follow as closely as he can the b'a.:.;:biM.;:;L N4h.ich he will pick all his di fferent officiets a..t C;'.3e:,3 data.. In this part, we shall describe the procedure fo',m tht: development of a number of ships by assignngin to each oie. of them a different set of dimensions, T ie e ssence of tAi;i.-.s step will be better vxnderstood if we assumo that we are actually car.ryinyg ot a zeal si a.: problem. Thus, suppose that a shipowner has sypeciied.,,.`.s a usual, the amount and kind of deadvweight to be i;rasport-ed4 and the trade route - Eence we knowi only the total dteadwesight and the maxisum allowable operating draft, and ',;u now ventt'. to design the most profitable ship to mee t; ' b:, requiremonts. Furthermore, we assume thiat:a;t37~-~:'i&.:." —' have been allotted for the projec, tho be K::'.::-:b.:-::!;.:::: i:'.i::. c n mpu seri

In oder to car:.ry out t':is- dev,.nJ we de<cie to ~..!c only the specified dead.wei-:;ht consta:zat and vary all the other dimensions. Then, we break the solution d~ow.n to-i logical seeps to Ib prograimized and ied into the compic-ac, One of the possible arrangements of -these stsps foTho??:: in TAABDE 3. * $ * *4*4' zd a

| 4 tx va /s atO, ',, Li L l., ob cn 4 _f..t A',~t! 3 3-. -_CccA \c:: -* 3 s c cd L_ \4~ ~ II t I. 5. I-\$|i| i (.-*_ ~. 0=u! A Iv *. ~c~I*- L ~J1 -,. I. 4; 1.~ A ( CL-JI )2 ' - 2 xlv% CZ A C |. sS:5;53vi: |,- 4. or k f ~ ~ ~ S~~t~~L r c~~~~j~~i El `6~~~~~~~~t383 C~~~~3le~~~ ~~ ("i ~~ i C-"' ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~, i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~S 4ssigr\: Id 'r c~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

f I,-:r i I rI As> ' -A.,~ -t- IL _,.C.. 3 ' Z: '-:E II I I c r~~~~~~~~~~~~~~~~~~~~~~o

1 —.PL.,,PJ;NAT~OI OP TE.,2 CONTlOLF 0IN'" ~ S.i';:.:''':'' Tht deovelo-e-n-' of the siAps oi e2ah '-?2.i.? -..'a:-;,.. ' cvt. acco3rding to the steps of' TABLE TA, B._sf wle o........:. - the deadvweight specified by the owne:r, It's amirout a. nd nature will give us a good idea what th>, lengtth o0f the shi' will about be, plus o- n.tinus, say 50 fLee.t" If Pe cannot guess, tw; can tan:aly: e a ro:up Co sirmJ.l'i-r ships aud see ewh.' the variation of ler <;',_ with deadweilght is for that t.ype f I shipo(3) '"ith this ttsntative leng;th as a basis, swe de i.e to vary the length btew.ween p-rpendicular~s of tbe ship every! feet in tho inteirmal ', (a ppha) hfeet to (- c.j The draft is then varied as desi:?ed.:ud the ID/d ratic i.; calo.cu.> eca To this;?atio -wT iraos. thZ constrant..-Ut L/d should be neither! hss than ( nor -o.c:,t,.X;:..:: where t'l ].imits 3 and will depend on - '";..:;-f This tro. of owontroi.ing - statements si I.z.!er. t:?,-.:-,::i,:;.: 1Th, Fs (euhps:ioan) a:ef -]z rthi- zcreamens b yPi iA.-i xxx.;L a-xy eac% dxmenasiLon, The svibscripp jcto ea ch vn r i abl e characteristic are iiusei for?ialn 'lL;1..foati.on rj. pcus0;s and. thn highent value at, eat h. ~o orki'g stbsc?.iopt% sz,'t;~tte thbe =m bite)zt of ~h's t'f-;z*.abe, ';; I::-:-iGv_.: S':t-1in a s)cifiecd in te'.:-'i., 'fhe i:a:;t'ervaLs:_:.: dict ite.i by3- the amotimt and hi.d do:' deadvJeighbt and thi:l.eectin i' n ea ch d.esign case is a 6 A oy experience and ana8lysis o. similis ships hwiteneer necessaryv 1jhJe cofs(ntaint finally. thilicLh arye ':;','.Szj X each rza;i~t o;lsi,: h{.:, are~ dis:.rab... -b,;le 'h f'o ') ot i}.

lassu~e - 1ad w. quate c4:K;t;r;':.,;t-r and se. a?;i.i-;!2:hJs a.E thie 3hirAps Second' They;r"e,.e th,-s ' a'sibc:t: oc: ih hei to be Turther analyzed, by 'id..scatdig 'he orns s whicih will be unsatisfactory, itshex tioo b&E or too;ca3..l to carry the desired deadweight: o- vunstabl9 e or too osta&ble, The reduction in the nurrbsr of shiLps will resu>;t:, saving- of oomputt er time d wJ13 uil re a''aU-.Lable nz.o:c,:M.O'.;e-:.i:, storage cells, whose nutmber 1Eilght be ci8.::.: the compubations involved in oul probIe- i sorageo problen is taken up *in the nex- C.:ct'cioijr 0COMO- 0 E A Ptt C The ITP31R 7041 compt.er has a iotre " capa:ty o 8192 wto-ersh hic, c ' r~. e te coclu3d:in.etz>i;cmr.s; for each 8stte of the zsoltion, c-c,4. i.rs1; d1a &ac- =d. aa2 diti:n three magnetic tEaps co ul..d p.~sib2y b- u st P- oroge o with a capacity of 25Ci.,000 woids each9 a.Ci. four ma:neaiic drsums, oah witih a cap.ci.ty ca a liZtle. over- 29,000 vrords Sinoe. most- of o.? pov a:.ye.iua coml tatio:i~ of the eaxci-J..r j'a:"~ must' be stored irn oc t-o bt a'iv- a1it.e b; nbe ".: tiio;@} a*{usa lzt. c: ss*te3p^s ~wo ma. CSi-Ly rvn. ouAo c, -t- r age ^ Ho0eve?' i:.o cases whea it i is dei.zi:,able i. ~:,:: a:.-:.,; number o' -variables 'b;.oe 2ts i.....-r - i'; '":3o:?,Y3.- in ';he h compute:-., ve ca a'2/7~s ot'.: -c..;-.5: f:: '::~ tlWi..2y by b-es~aklir -Giasl 'r~oblemI dLown ixitc? s-ar'-atX s28.1ns..: pa:ta as t >......C.,jA,,

acll tL h; - o ' he S &Ge3 4 r bO, 1ft ox, a 0f cour.se, e c 1 aly:.3 use 2 y..', cha,30ct-er is-tbics, i the deman d fo arcourc;. c/ 7.e:;: d.!i: m a I df T-he toll whIi.ch vwe -wJi3l i:y for g0I::yu;,:t ais.,;,s accuracy by usiung a larger n.u':rer c' -:aza'.tbles t-h..a i ib4 necessitate the enploywnn-t of m-ogtnt;ic -L? d......X,cums3,, oi be inoreas ed cost due i;o the iacese incP reasea o-he 30, —......: - for the s-ol 'Ubionl: t a: t. i-. * -. nct:.~e.~s- thi h n-bo, O1' compute-bx.ow:l-s o23?(2C:.-r,::~':1e-i., o?, <o Zr ui-rh po'b x.em thC. desired accuracyby s;hkou.dL be ba: — ac-a"c. ~ '.m- a' al; lo.-lIe ost, and the nuraber ofs v.i - -'. ouI be., e13'D. -t.a., or,. to that coT.Ipromic e _,~s 5.,;~pla~.ement'.,..,. L;: fn 0 uz............ - which '4h}e c ozmpuPrm;e has lefine... acsord.'g -,.-: - -....... * —b,.- 1 I;o 17. bear::o dIrxeoi?e'5. u- e t'.I;",-",:'44;' '-.fi4-zrd d SadW",sh.... * —u '"' -... Withirnwh. i we dc:. '......... t'..... and tl~'-"," _':''bis,,. ':';:.1i. " s,':,o?:S.... - Gjea 1. --.... should r ia-et he 1;.?:'_ -.i; X;,s _ as:thie;c.:,/:igh'b s!.-,.t:~i;i ox-9o Thkbe Zdart u is a rf: ~d..i;iy Irzc; J &~j~ gcst; U Ci 3c o:'ap 2 'T- i,ove, hence. all o..u'a sh' ps aasve ai'r:-.dry ic om!i'.i.'6. i-ih -its re_,t::L. i,,. uent redhe +. —, a c o..:"relat-tio:.i o,... /\x. w.;hV th B~a~-a '~p:' I: o -

Thc~~~~~ "eite~t::u~ 1,=;a-; ~i,... ~~, m;:ose~s 'b~v~o oo:~s';a~i~n'{~ The dadwpe-26-~e~ht rt,. u z t,o:....La t& on each A PLCta e a n ip uLcC xe muh,,:~:~nqusOPeteo~ hpsiu i.hv nuh buoyancy to caryr the exact weight o f —the c:rgo, but 1:.:.t:!ith: more rnor 3.;, sso S3econa each ship should Law, ve i,'-.:::i;. volu i'2 1:o Ctore 'he exact ~..-.oo cubage,::g':.:::::.~~~~~~~~~~~~~ nor Iess, If a shIp of of the constaintsi, houd 'bit; oue rz.e-ai:-c: a::t::.:; 'rom the economicBs point of viW 2. ip e on, one oxr none, of these constra&inus it; n ' s be ',c.ed &he:est oI the,,,Udy. ]e' s co' aiCdo:"c the -o C,-,. cons;L3'b.%'.ir~:I more 'i,..01'yt la... ".. ': obmd.:iouE' V:aC.oV,. 0 0~~~~~~~~~a~,...MO.~~S-t. -,o.ua 8.7.1. U MOrfP of r;.16J -'173; be ~d 'he to-lei;:ri '2 ille loaded. ar;-o we sha:!I si'ta, wiirh a U:xc o:? f t:; 'h:-: related t.yi.s op stcag e f~act, ad ai:. acity -.:oeffic e:"::.!7,. o' o,:.GE FA0T(-;-PA'"-:'"s f 'i:.oa fs~a~;jcv is tE he spec 2i:i. 1:.i:...: to b:,":port'ed. and:s eessed:.in t:.e ~!c:.of a ne'; ship shounld. Lbe., i-~::~'a.('i,] g'eat4- inSuences -ae eio: -..:......"; ' ':, ~ ' " ~ '~. i:a -1 d d o v -u n " uodpt o s u g? e; o.. o i i: h -: '".......': ~ ~ ~ ~ y 1iC (... 0 b,.:..-1 -,... one to sail a sh1ip 8xr~~ i.t~, ix'boi:.i 'C.he &i.:. ~oodl'tioI~:.'.b ou.e be considered herexe Fozs a r,.~duested i-..-gn~, it.Is not oon'~%:,the ca:*rf.o io b:~ tra':.~:yc:,'?:cz'e. '":1f, s.~Lo. ic~di c. te.ri~:,.ine -;-c~... BS~@ai:.? ~, j.~:i:~ 7".!! ~ir~c~ireJ~x

;:3hj~ ~~ilS~:....uL,.L... ~ i?~!' ~::.2 2C' "o:'e s O ~ f - ' P in s"~ trce ~ vJ i 1 3. ~:a h..; s i 2 S t xf t., tcr 'b1ils o sc '.2. - i! t e i.spce or t urse in J. oVta. c,,sto.::Z &'t suf.-0,2-CMt tzold v olut~:.e) in Et ship ar —e io:h u.J;: be as oW) OI o ", T Ota;:~. v'I.C'liS il,:;a?'aC in t f.., i'L' o~~~~~~b-fe jiio i, ia —r~ a i2ycn to nluCT.e 'acd. u:tse i. our,:,~. t St Ns -g C hv a a stlit,, _ txb i it3 in Ul 2 e~c On ou I ~~~Ti_ I L~.. ~V ~ ~ ( K v~~ ~ or ~. ~c~ic~z'~~fI (~~7~7'7.7 ~ *. * oI a2z*)7)

tQ~~~~t:~~~~:~~~ 5>~ ~ 11 Wi: ~th1 JZ )1t0 124 W) e()23 ~ ~ ~ ~ ); t._ Uft>4 '1 Gt;t G irK Jo lint; cc:; r 0!-t,'' " (4s~''- ~" Al-"7C) ''I-stT \E rIC qvt, },$O t, O <K) UU,/,.;Ct t O $s4!1. t4XUA tIt; "0~~~~~ (4. 4a.. i Rvcc~~n v74 4rm 202 e&TQ ~ta9- tUtr 1t tjt~~~~~~~~~~~> cm. ~ fz4 *. A- t'ci.y:rx 9X5:.SkS20;1Sii:-:-W-i ~~~~~~~~~~~~~ Z t!<, 's tt tt 'c., 'd.; uI L)k~ + '%A tcx.;1:cbo; r *V073. t10W1 tE~a *; JTIz' ~~~~~~Wr O t.a> w;. *~.rJI.s rQ aiTlo 'I '-_.- 3&*, 1 Fjr. )-2 -.n - r.. * 3 t-.-5 T: T1jt tni i.,~~~~~. L( O~~t tj~~~tJ~~t~t' rirrnf~~~~~it?~~ '" "' C tC)rvr~Jo ~ ~1~OLC C)' &o~~~~~~~sTP 7 ' VC4 SUP~~~~~~~~~~~~~~~~~~~~~~~I D11G C 0 II: 0:~ ~~~~V *"* ';C' 'A<r[ wr * c t., fw~~~~~~~~~~~~ ad,~~~~'

-57 -Thu, or this constraint, we can write: Bc~vc z C ubqd b nce the unit productivities in equation uted by their expressions in terms of st ia..rcow-~~L~ - B ov3; + ffit (s*fa t b t*;3 5s "O 4 CL (CX, (36 1~tics, as we have eaplained, equation (36) becomes: 0. Bs Cs,"~ ' _ (c e: A. Cj V%!.1iCIO{t Cu 16 COMA towf% O~

-58 -O~5Ce \&3 4 C e V. z:,4s1@ ws \i30007 Z' 9k L 5S CTS P.C*V LC S p. Cc n 36i the fir (L t% a aJ Ct feil shi3uld c

CO oat, w s >s ~~~"';,.-. e:~ L t ]'a! i'>.:::'.'- f: {f.e'. " * Pcl4;; 'i1e +$ jj>4z~wwv TIr i:b;....;, i.. be.: i( i'- - ' ot,';'t a'a;.i; q.& '-1:.. I, 'The~~~~~~~~< |Jx %~e CO g 3 (1 Ofl W _v;. j };). L <i t;},2*, ra -!ts0,-' N.. i Iatiotx m 4 'S ot thmr-Nip Us' 'a_ 'l''m.' Xis 5h~~~~vc ~ ~ ~ "t i -i ~~?c4.r~~ CL CS - 6 S

versus the cubic nudber let us say, of each ship, into diita l computer which will give us the equation desired Itshould be pointed out that we mast find the hold volume as a function of the ship characteristics, and not the total displacement. Assuming that a satisfactory expression has been fod the second output constraint will be of the form '('-.~ c.) _... (3?)~ Eqjuation (37) is-the secon6 constraint that o~ur inj., Sfips Whould comply with, This step ends our Design part, sinc'e by now w'e. have selected and stored the characteristics of all the feasible ships and discarded the, unsatisfactory ones. Anyone of these shrips could be built to satisfy the specificatioxns of the owner, but the prof~it~ability of each ship has yet to be tested. The comparison of the profitability of' all the ships is described in'the third part of this paper,, the EeonomieB, which follows.

P A R T III ECONOMIC ASPeCTS 21~2 -I 2UOT After the completion of step 19, to be sure, e ve retained only the ships of displacement jthat will meet satisfactorily both of the owiner's requirements Tow t rema to see which one of these ships will be the most profitable In order to do that, we select an appropriate criterion of profitability, and acoordinly, we copare all ships so that we can choose the one shich ill ee our criterion to the highest degree. The ecm criteriono follows next* The criterion of profitabiility which is most suitable to a linear proar~am~nn analysis, since it can be exrpressed in linear form,, is the present worth criter-'ion., In thae form of an equation, this criterion can be stated as follows:, Present worthb of awnrza3.a income Intial investment + Present~ worth of innlalse operating ezp-pnses.v or P.W *Present worth of annualI income -(ntial. investment + Present worth of a Iua operating eipoense.) (8 rin't ohw aanalysis.hi In~vb oilNAnw

As can be seen, this method judges profitability by comparing the investment and the present worth of the average future annual costs.with the (as of now) value of all the future income of the ship. It should be emphasied here that the average annlal income and operating epeses of the ship are assumed to be constant for thehole life expectancy of the ship. The difference between the present worth of the anal ino a total investment and expenss becomes a dollar measure of profitability. Thus a positive differne mea sure3 the ship's income potential over and above the cost of aital a ship's operating expenses. e disadvantage of this criterion, though, is the fact that the dollar value of the difference between present worth of earnings and investment bears no direct relationship to the magn~itude of the original investmenxt, *Therefore,) it should not be used for a comparison of-two entirely different investments,, that of a ship,, for example,, and anailne In our analyrsin't hoeve 1, where only shPs are e oinpared and. the differvene in alternative investments is' not pronounced, it is felt that the present worth cmiterion will produce satisfaotory resUlS. M j~AIX TION_ 0?F THtE CRT O FPRFA'usin the present worth mbthod, thxe naval architeet

consists in maximizing the expression for our criterion of pfitability, subject to the constraints of our for inputs The calculations of the terms involved and ther coefficients are shown neext. 24. (GAIULkTION OP THB XV~i~8TMUfNT~ The term Investment as used here refers to he ocalled shipyard bill, and is the sum of money which the oner i pay a spyard for the construction of a ship nvestment is synomous with the initial cost of the spir As such it ludes the cost of the materials, the cests of diect labor and overhead, miscellaneous expenses, as well as the shipyard's nominal profits and charges for insurance and drydocking. All these cost items can be grouped differ-i a nt waysa *However., in order to simplify our equations, the *followin forPm of the shipyard bill will be used as shown *in TA34. TABL 4, The Shipyard Bill Item squation Units Steel cos't nja A S$/Iong ton.3j Hull outfitting cost r a ~ A3I~/ons ton Pbill enguering cost tla /ontn Liachinery cos8t A as/long ton I=isellueos 0osts n 3hipyar profit A 0 ofsub-t otal A

-64.. Trefore, the total shipyard bill is: It should be pointed out that rn,.D n the cost per long ton of input material includes the cost of the respective material plus the appropriate ch S for the assoiated direct and overhead labor. The miscellaneous osts, which include launching, trwols and dlare expressed as where n6 is a suitable charge per ton of toal displacement for each type of ship to be designed The shipyard profits and lnearance are accounted for as a flat.. percentage of tbje sub~-total. Dryswdocldng is given by fl1vwhere n7 is an estimated cba' per ton of total dis. plaoemen Lastly,, the owner's extra costs, for ohampeagne, are included as a percentage for the sub-mtotal'. -I0 to be analytically dtrmined In ummryaocoriding to equation (3) Xa& our shipyard bill broakdowins the investment is: n X+.' * Ms

-65 -TABLE 5. Unit Costs (10) Unit ostso in o/ton of m teriLaI It em Pssenger ssen-m Item | kers | i PgoTnkes 8hips C&~' r'O Shi~ps Hull steel 608,*00 70000 O25, 00 Hull outfittin & engineer in 057.80 3tO06000 3,060.00 Machiney 3,856.50 3,5865.50 3,806.00 * Unit costs for general cargo ships and ore caxriers are the same as those for tankers. T!his figure applies to S H P up to 30,000 and increases to *6,48000 per ton at 400 000 8 H P. Also see reference 3, Fig 0, 30pp. 80 The unit costs of the items above, include both the cost of each material and the associated labor costs for fabrication and erectiona All costs are based on the 1957 value of the dollar.;ee Pig. 8.

Fi. 8 below shows the relative U. S. shipbuilding Costs since 1946, drawn fron data supplied by the ritie Ado 1,0 210 it'o 4 ' 40.3~/ 11*6 '4 O 1 $64 66 'G 6 'F~iG. 8. Al1J poin~ts are plotted as of January lot of each year..

25. CAIOULATION OP OF TH BU WORTH OF THE AV ABE AMIE1JAL 1N00M3 If R be the average annual inome and P its present North, then P= z Li v. r-l ~ the annual rate of interest, an = the life expectancy of the ship in year The interest rate and the litfe expectancy of the ship are easily establish for each design problem. The average annual income R is given by: where, 2,,ce "~c! na + ~7" DP,] " the nnmber of round trips of the ship per year 0- the cargo coefficient to be determined, from the type of ship and the owner' s e"perience # ri the average cargo rate b.-sed only on the oarlo 0 ~weight. In case a light cargo, may 40 ftV-/ton or more is to be transported its chaarge, usaly based on its volumes, should be converted on the base~8 of Its weight, -the cargo deadwet kit in long tons, the taydmload,, n 7 the average price of. all passenger tiockets, and N -the average nubrof passen~ers carried on each p trip, The nubrof round tripB per yar of each ship will not be the same for all ships, sine their speed will. vary, N evertheless', we ca~n apswaeM thab all, ships of the grotup wgill be out of service for an equal rnbrof days, let us sa

-68 -where the average distance in nautical ies of th trade route, and an estimated average number of hous ent in each port of call. F rmore, the cargo deadweight is equal to the total displacement minus the light ship, fuel otil- luding h resereuel-and also the weight of all persons aboard, their effects, subsistence, sbtoes, fresh water swimming pol others, In our problem, however, the total deadweight is assumed ov, and therefore, the pay-load o 'will be equal to that deadweight inus the items named above included i n the deadweight. Hence: where = the weight of the fuiel, incliadja the reserve (Items) u refer to the weights of all. persons aboard, their effects, subsitence, fresh water, swimmin pool water and others., It is~ seen th~ata fze igkkt of all the Items its a func — tion of the number of persons aboard,, and as..such, we may expes it as a constant O, inluin al nt weights —n *** T&A 6we-, times the function which gives the total numez'of persons, that is, equation of page 38. The w6igtit of total fuel-Wro in turn,- is: 115z (c~y atSooewya vr - k U- o#Ooltm 4 ~~ '~k reSr fue. actor

IW69 -For the ship, substitution of equations (41), (42), (43) and into (40) yields: )4 WSW C (T + for ot Z 4 -Q01 7 c Of t *4 Z "Dart 1+ sit Sri CIAM" " + O 1) c IDS CL 7 Ss tA '4A %Alp

TAL 6. Average DeadweSigkbs Item ~~~~Dead-weight Passengerse an ffeobs 2,50 pounds/person Ornand ef~fects 32.5 pounds/person Daggage 200 pounds/passenger Stores 10 Pounads/person day Fresh water 4 gallons/person day

26. CALCULATION OF THE RSSE1N WORTH - It is customary, in ship cost studies, to onsidr the folowing groups of operating expenses;. Vessel expensese. II Cargo. handling expenses. III Port charges. Iv Miscellaneous expenses. In more detail, each of these groups iacludes I Vessel expensea: l. Crew wages, 2. Fuel cost. 3.& Maintenance and repai-rs., 4. Stores and su~pplies. 56 Subsistence. 6.a Insu - rance 7.Oapital costs. 8. M~iscell.aneous costs. II. Cargo -hand ling expenses: 9.. Vltiarfage coat. 10. Receiving clerks and checkers. Il. 8te~beorla4. 12.v Watohuien 13. Dwinage. 1-4. Insuranoe..

III Port charges: 16. Pilotage. 17. Customs. 18. Immigration fees. 19. Tonnage tax. 20. Miscellaneous expenses. IV Miscellaneous costs8: All these expenses depend, of ourse, on many factors, Lbut all an be expressed in terms of the nuer Of roud trips O Lf te ship per yes, and the sis f the hipof tLet us consider ahitem separately and derive te equations whose sum Will give the average annual expenses of the ship ******* * ** * 26j1 tem1-.Orww~aies This cost item includes the amiUal wages paid to all the crew) uenbez*8, that is,, to the staff, en in$ hanuds, deck hands and. stewards. Heonce,, 12a.~ - aMe tn.04 r it J (45) where n,1 ris %'1 T1w are average annUal salaries of the officers,, erkgine n deck hads and stewards, respectively. T1he&V avrage MOnthl sa:lary of each category w~ill depend, of' couXse, on the type and size of the vessel adthe contracts of eaoh shi.powneor with the labor unions, and also his obli-~ gation~s to the country Of i'efistry of the veagel. Uowever, af surveyWj. A o40uren prctce AwM'oAi ll — a otAI3d. yield theA-L average ---

-73 -the matter in the literature. F'or instance, reference 10, given the followin data: verage monthly base wage for: 1 Deck enine hands m:$353.00 2. taff and stewards = ~280.00 Thse wages are based on the 1957 value of the dollar or the J ship, by substitution equation (45) becmes J4 t' I. * n,(s4jP) * (L ) ~~~I M COPt aL~62~ 0. 04'r ZtataxCt, ~~4\~~~ o*~~~vIv~oc oO to J~iL.CU.OALSc W& rsA4

_'/4 -26.2 Item 2 —fel Cost The fuel cost per year is a function of the round trips T. ana the S H P of the ship, and for the J ship, it is obtained from the relation: ' o0. zt T.- -P n (f,. F ) where n12 = cost of fuel expressed in dollars per long ton. t number of round trips of the sthip per year. V.T. voyage time (one way) n hours. P*R. = Fuel rate for both the main propulsion plant and the auxilliaries, in long tons per S H P per hour, In all cases where the speed of the vessel is not held constant, the voyage time will be a variable of the problem in the form S/Vk where s, given in nautical miles, should be the average one way distance of the trade route, and V the speed of the vessel in knots. Henoe: -a.,(3 C S- 4 ) 74.n(w,Q*.2 t47 *2 V.P. v (47) rote that the reserve fuel is not included in the above equation, altIough if desirable, we could add the reserve fuel factor as given in equation (44) ********* 260.~ Ite.m 1 3.-.Al teAnoe anLieair costs The total cost of this item can be broken down to that of the mohbiner and that of the main hull. The cost of maintenance and repairs of the uahixnec will be a function

-75 -o the S H P, and that of the main hull, a function of the total displacement. Appropriate functions can be derived from data on similar ships as furnished by ship operaing c)panies Hence, for the j ship, the am average mainte and repair cost over the whole life of the ship will be# SAP * 48) where the functions f7 and f8 must be derived On the other hand, this cost item can be computed as a percentage ot the total investment TA 7 gives te cost for mainbenance and repairs for the whole lifetime of the shin for different types of ships, as a percentage of the initial investmet.For our analysis. either formulation can be used. TABL 7 Maintenance and Repair Oosts (10) Type Of Shrip Percent of Intial Investment Geea c-argo23 Passenger-cai'go 24' Pageenger 2? Tanr2.5 Ore coarier 22

-76 -26.4 Item 4-.Stores and. 8u.plies The cost of stores And supplies is usually c uated as a ntion of the number of crew. Fig. 9the varia tion of this cost item with the total number o crw, for passenger and passenger-cawgo combination vessels Thus, we can write:;e: 04J A ~~~~~~~~~(49) The function f9 must be derived. For the rve of ig for only the cost per day, the computer gave the following equation: s c -3 1 4- v otz, In the last equation, % must be substituted by the functions giving the number of crew of each crew oatbegory in berms of ship characteristics., These functions for paissenger. and passenger car~go vessels have been Given on page 28 and will not be repeated here. ~ -Iem, ~ubwSuistenec.Co t T~he subsistence costs depend entirely on the number of P exuaozw -Pt aboard the ship., For each type of ship, 4TABLE8 gives the aver'age cost per zeal*-day poer person. Hence,, we Gan write:. 06"P

C0b-t5 or 5"UPj fuP V 1t00 iooo 1Q00 Igo Soo 0) 1500 Otm~e. lq~V or Va5? 100 ~ ~ ~ 0100 Z6

-78 -Assuming that the ship will be operating d1 days each year, we obtain: c5j dl x C06 (NP + No ) (50) In the last equation, the appropriate functions of N p and N 0 in termas of the characteristics of the ships should be used. It should be stated that the subsistence costs vary for different ship operators and types of vessels TABI 8 Subsistence Cooets*!l ~ ~ ~......................11 ~ _..! 1 Tye of ship | $/meal-nda;y person Passeer 3.50 Passenger-cargo 3.00 General 'cargo 2.00 anker 2.00 Ore carrier 2.00 * Figures are based on the 1957 value of the dollar.( 25w~~ S. 26.6 Item 6-.I-Suranc e The average annual insurace for each ship, wh ther Ameria Or foreit built, can be expressed in ters of the mi ia Izivestwint, or: o6 10 (51) where r0should be empirically detervmined for cur-rent iastancerates for simlar shp.The e Mcresion for 1,9

-79 -Professor Benford in reference 3, suggests the olloing equations for tankers: a. For American built vessels: = 5,0o0 + 0.012 (I) b For foreign built vessels: a 4,000 + 0.015 (I) Ay formlation can be used. Item ct1 osts This cost item includes depreciation (based on no )20 year lie taken as 5%l of the initial investment interest taken as about 3% of the in.estment, or 071i 0.08 (Ij(2 where Ij should be substituted by its value as given by equ~ation (39). TIs tem might include medical examination, excpense accou~nts,, transportation., postage adother incidentals. For our purwpose, we can assume that this cost will be the same fo.r all ships bein analysedt and assign an appropwit" ate constant value to it. ience, as 07 (.53) where 07 L to be emiically determ!ineda

-80 -2 GrOUp II. _Ca~io Handlian _Renses Allost items of this group, item 9 to 15 inclusive, are fctions of the deadweight to be carried Since e assume tt the deadveight is the same for all ships include all hese cost items as a luUp sum.Hence C~_5) IS -a-t nib CG % Dwor(4 vheze is to be appropriate for the kind of caro nd c is the capacity coeffioient. or - equation (42) should be substituted into (A) 26.10 GrouD III. Cost Item 16: Pilotage Sino the pilotare charge depends on the draft of the ship, asswuing tihat the ~J ship sails always "full anld drown", we can write: C. IsI dw ~~~~(55) where tyA. Lo t1o be assigned for each type of ship,, Again equation (4~2) should be used for ' Thkese costs are fucions of either the deadw~ei~Lht or' the number of passengers or both,, dependin on the type of ship. Por a cargo ship ~ cc).) i Za;3 ts c C4. DWI (56) Pora asseigr hi L

w1~ere and ri6 are appropriate charges, and.6~~~~~~~~~~~~~~~~~~~~~. a P in both equations should be substituted by their:respective expressions. * **t* * ** * * * 26.1 Iter9 T e Tax. IBtem is based on the tonnage of each ship and will va both with the sine of the ship and the anals of the trade route. This cost migt be expressed in tems of the total displacement of each ship,or M3 (58) where %A isL to be determndMed. For example, port charges for tankers and ore carriers can be given in tenms of port.-days per year. For a tanker this VAriation is given in Big. o(1 ) For this curve the computer gave the foll~owing equation: where 4, is the nber of porb-days.&

FIG, 10. Port -harges for Tankersles d Z400 Aloo 2400 2 oc0o s 0 0

Having, thus, computed the average operating costs c: their present worth PAWo will be: ______ t(**^*ltA cx(59) Equation (59) then should be substituted in the expression of our economic criterion, equation (38). *i*** *' $ ****

92? THEi MOFIT ABII EYQ~UATION* Subtitutixg equations (39), (44a), and (59) int equatio (38) we obtain: W* ztih+- {ZccntWgi + rn C2 A I _ All the tezus of this equ~ation are either coeffticients determndempirically or variables to be assigned and handled b~y the digital computer, as instructed. TIherefore, care mwst be taken to express all terms of equation. (60) only as funotions of thie ship characteristics uised in the Design part as shown in TU-ABLB 3.,

28. ODAINING THE OPTINAUL SHIP, The optum ship is determined as follows The system of equations (35) will have for equations with a mber of terms which will be equal to the dis placements all of definte ekharacteristics, 2each shrip will be identifiable byr a workin subscript J6 Application o-f the criterion of profitability, equation (60), will single out the term J which will be the optimum ship having characteristics designated by the subscripts ft~~uz

29. EVALUATION OFTHE MEJTHOD. If this method is to have any value and be of any practical usefulness, it must have at least the following dit izctBons: It must be satisfactorily accurate, 2 It must be easy to apply, and It must be comparatively inexpensive In order to evaluate the method with respect to the firt requirement, we consider the two possible sources of errors, the computer, and the naval architect, The digital computer, as far as the solution of the equations is concerned, is exact to more deci points that we can use In contrast, when the computer is sed to derive equations, as suggested, from either "raw" or is erratic. The percentage of error introduced by ti~-.o computer will depend on the amount of data supplied for each curve and also the nature of each curve, its continuity, sharp chanes of slope etc, However, since all our curves are continous, the very small percentage of error that can be introduced at this point is negligible and the results quite satisfactory. Besides, the amount of this error can be controlled adkept to a minimum by the naval architect, if he supplies sufficient amount of data.,.Aotually, it is the naval architect who controls the accuracy not only of the computer but of the whol~e method. In particular, it is not the amount of data that will iutro...

-87 -yards, the acouracy and the handlin of ths inomtion. by the naval architect will be the main source of the ero Obviouy, thea, care and persistance will imr:ove the Suts n Drodblce dependable answers. Therefoe method is as accurate as the aata supplied and, U is as or more accurate than any otaer reLati'ver jjII ongand calculations since the computer elimiat L babilty and possibility of human errors involved the other methods, With respect to the second requirements, that o the ease to apply the method, some comforting remarks can and should ade. becaur.e the method is not really as compi ated as it may appearo True,, there are many steps and long equations involved, but the use of the computer can mak~e th]is;) method the easiest one to apply for the desigrn of a nei ships, even easier than the artistic one of pointing the thumb,, Most of the work is handled by the computer and all of JU.P can be programmized step by- step, once and. for alii, IINQyI,_~IV the resistance calculationis can be prograrnise~-,d. lcl-a~], 4i. h tion of the residual resistance coeffieieiT~ der4vd~ld~trd for Thaturxe use., Then the controlling statements — or a ver-y SC..neral problem inclu~ding any design, can again be -.-ro,,,ramzi.:1ie both for the design and the economics parts, so that this program can be permanently ready to use for any particular problem. Moreover, no cu~rves -'have to be drawn for the derivation

.!_n', b A i.:o '. of* the Points so obt'a.ned - veil ixh T (i'" '* maka vhy not use tj,'O or more poin"is of lesso one place instead of i-..eN ploint carryig.x the to;al waii Use judant to decid& on thie imnportance of iof represented by each pJoint and the numtber of e that can be used instead of that si.nge point idle computer plot the curve, if desired: and derive its simultaneously, Therefore, the onLy oork requi. o naval rchitect's part will be tihe careful collctI. anal of a group of similar ships suppiyinr; information, and the decision which he ha.s. to values and limits involved 'in the CnOLA thie, Design Part. Lastly, the cost f or carrying out a cdesion conIc this_.r method car.. favorably be compared with that of caniy L.& method of. car'rying~ out an economic snalysis of The i e d staryting- from secrato'llz. In tbe f~itrst place,7 the uzae- of o. digital computer ~r~''o hsmethod with the bi~ S ss&e thiat all possible com~binations of the vari3able Ship car istios can be considered, and that for the optimttm Sh I"T ai&' one of these characteristics will1 be tule optimumi one., ou-i'x-I wise the stdiip would not- be called optimum. Furt~lermore11- i~.1c optimumn ship as dete13rmined by this Methaod is not 'ba c.!cK. proftability or perf orman-ce of any other sh'ip '.K.~~ which shp tel igt ey el otb P 2>:mvn

thif.u WYi p -':wi e T-m lid I f2) CfJhe type, and -,Lefiec~j Dvso, e J.:-x tN p >eGriot: o f t h r z ts rx,- building and. naaiAnir- th.{.se,ips and n L d ind vcat r ct current trends and Laws common to all t1Iese s operation. It is believed that the-e advantages cc Wc~h sfoul not be overlooked in the design of a shoul e Aken into consideration when a oo0~ c made b een The result and the cost of ae' ll, the cost of a design ccarrti, pr ID ni s not that hi-,h- It' includes te. tarchitect -or select dinr tlhe iput -3 zLxi the steps., and 'he cinior of' the oo e-Q, far as the archiltIect's work 'is concerned. once a greneral -Prograim i's set LIT tile u~nof anyq s~pCz&?a be Jc-rried ot-A" v~ithJin on Montkb., program ~snt already ava ilible~, ocx man's hours of aacrt Cc:Ai ay fo-r? twio x-morths ilbio than sufficient to deomxethe or~timJ h~ O ~eoi hand,, an IBAM 704 computer." vhose costU is e`505,-20 ani hot~rcx handle all thie work off a usual,. design -roblem 0within three hou~rk-1C Of eourSe, as stated previously there w ill a lvvay.s be ~a irni3eto be madeo between 'the deired. dopeD..i d.:. of lihe uisand the, costs required, bat Jo iio'; -re u.t U hs etod is farl less exr-ensivs re, ~i> me, bhod~

Alt i h Mthi 1 s me bcpicd &Dis ac uJaie?:- e s3 n f psive, it does hkave sois limib-aia o a irs Place., Ic, itJ.o it ecs i<. it rened ally reclaLre.5 a. no~' bot.val -'cL:lii~tw.tu.I:ae and coap-tzer tbee the opti snip i}s de;ernmined to the as-of-n one the money vlues Or could it be oth-i.r""? C? of th money value constitute a g.eat advantlwe' o a rai zed d~esign while being a lin2iGation al the ot design a -eti~ods? Could a compuiter sto2? ptast and cui --- bou SiJ. E"'S) Lx.z-,nds and,, after Projecti-'nrrb te m I t t b any cc date, incoxoporAAta thered.;i in the Juisxdiction of tlile optimum, ship P T.Il~~ bl3.e acrL could eLasily be donee. As a st4-ep.. "a i~' k5~L —,i )aip or since 't Is a z:g&t~. cf~f tie sCOI)o of this viorks6 "Howeve:0. it ~shou-lid not b ~ of as an inv,-ossibility baeawZe it really i-S au-~a~a the use of4. the opul;c- insip dtesirgx'4

30. t$SUlARY OF THE APPLICATION ST-WES. u summary, for carrying out a design request, ener ally the followig procedure may be used. Consider the specifications thoroughly. carefully a number of ships to which the ves to be designed will be similar. Analyze thee ships and along with other relative information tabulate the data neesr 3y for the compubation of the various coefficients and functions of the operations of the ships, 3elect one ship, the basis ship, out of this group, and determine the struxctural ooefficients. According to the demanded accuiracy of the result and the information gathered thus far, decide on the nurbe-r and ran~'e of the variable dimensions to be used in Wihe Design Programmize: 1. Data on coefficients and functions., 2.0 Unit produc tivity. 3.a The Desi~gn steps. 4. -nu~out eqaationsan 50Criterionx of profitability.

Geraly, for a paper of this nature, it is mpotant that an example be included as worked out acodig to the method proposed in the work. Due to school work, ovievr, and oth ime limitations this has not been possible for thiB paper, but it is planned that such an example be in*eluded in another complementary paper which is to Zollow

ACKNOWLED. _ o many people who assisted me in the course of viritg tis paper either by encouraging me or by offering valuablesuggestions, I would like to expressmysine ebtees and thanks I vwould,) in particular, like to msention Prof, E4. Br-erns, of the University of Illinois,, who gave me the inspir:0.tion for the theme of this paper, and rofessors R. B~. Couch and HU. Be, Benford, for their gatidanoe in treating the material. My thanks are also extended to iUr,, J. Squire, of the Computin Center of the University of Nichigan,, viio pro~jxammized my problems for the oOMPUter.

BIBLIOGRA 3 Brems, H. Output, employmont capital and. rowth. New York: Harper & Brothers, 1958., Dorfman, R. A pliation of linea rormmn to ~he_ h. eo.oj uthe frm. Berkley and Los Angeles: The University of California Press, 1951.. Bnfotrd, H. Reerina econom in tanker desin: Transactions, The Society of Naval Architects and Marine.ngineers, Vol. 65, 1957. 4 Vestervelt, F. H. A ic stems ation Egorammin-. Ph.D Dissertation, University of ichigan, Ann Arbor, 1960. 5b Dr. Todd, F. H. Btuntz, G.R., and Dro Pien, P. C0. e.riee 60..the effect upon resistance and poer er of v_.ami1ons in shZin::ortions: Transactions, The 8ooiety of Naval Architects and Marine Engineers, Vol. 65, 1957. 6. Gertler,!L A aalysiso the oRiSIMl -test -data _yxthe Ta.Sor Sanda Series. David Taylor Model of ing are andShipbuild, Vol.l* 72,, 1955,-56.

-95 -8., froad,, Re Outfit estimatin coefficients for si hesis University of Michigan, Ann Arbor, 1956. 91, Kari, A, ~Desit and cost etimat Tecnical Press 1948. 10. onkin, D. i and others,.0onomics ofnuear yventional shis. United States Atoi ergy ommision, Washington, D. O., 1958. 11. Arnott, D. D~a~ and onstructioa of steel merchant D. M._ — -WIMM ships New York; Society of Naval Architects and marine w~~nere, 9155.* 12 Saunders, H in desn Vol 5 NewYrk: Society of Naval Arohitects and e iee, 1957.