On the Great Trimaran-Catamaran Debate

Lawrence J. Doctors, Member, School of MechanicnJ and Manufacturing Engineering, The University of New South Wales, Sydney, NSW 2052, Australia

Abdmct

In the cumwtt work, a aydewaatic investigation into a variety of monohulls and multihulls is carried out with an emphasis on finding optimal forms. Vessels with up to six identical subhulls are taken into consideration and a large range of lengths is studied. hT- thermore, sidehuli trimaran configurations are included in the investigation. There are two main purposes to this investigation. Firstly, one is interested in mini- mizing the wave resistance, becawe this is closely related to the wave generation and is of critical importance to the operation of river ferries. Secondly, it is also important to minimize the total resistance, in order to reduce fuei costs and to permit long-range trips for ocean-going vessels. The theoretical predictions show that increasing the length beyond that normally accepted is beneficial in reducing both the wave Resistance and often the total resistance. I. the goal is to minimize wave resistance and if the length is constrained, the calculations also demonstrate that trimarans are superior to catamarans, which are in turn superior to monohulls. On the other hand, if the goal is to minimize the total resistance, then all the muh!ihulis (~m catamarans to hezamarans) are inferior to monohulls, except possibly at low speeds which are not of interest in thw study. Similarly, sidehull trimarans are shown to be inferior to catamarans except perhaps if rather great lengths are permitted.

Nomenclature r = Longitudinal stagger of sidehulls x = Longitudinal coordinate B= Waterline beam Transverse coordinate CA = Correlation allowance Y= z = Vertical coordinate cB = Block coefficient Cp = Prismatic coefficient A= Displacement mass F = Froude number v= Displacement volume Fv = Volumetric Froude number L– Waterline length = Trim j5/@/3 : Slenderness coefficient P 6 = Stern wedge angle Nhull = Number of subhulls R= Resistance Dedication RA = Correlation resistance RF = liMctional resistance The author would like to dedicate this paper to the RH = Hydrostatic resistance late Sir Christopher Sydney Cockerell (1910 to 1999), RT z Total resistance the inventor of that remarkable form of high-speed RW = Wave resistance marine transportation, the hovercraft, or air-cushion T= Draft vehicle. The first large person-carrying machine, the u = Speed SRN1, was launched forty years ago in May 1959. Be- u= Mean speed cause the hovercraft possesses virtually no frictional w= Weight resistance and low wave resistance, it is still the marine vehicle which can claim the highest transport factor or 9= Acceleration due to gravity efficiency for calm-water operation. 283 1 Introduction ran as well as its response in head seas. Following that effort, Doctors, Renilson, Parker, and Hornsby (1991) 1.1 Background presented the results of an investigation into a modern ferry catamaran, the RiverCat, which is characterized In recent years, considerable interest has been as having very slender hulls. They demonstrated that shown in reviving the trimaran concept. The justifica- the traditional thin-ship theory could be used to good tion for the expenditure of research and development effect to predict the resistance behavior of this full-size effort on this type of vessel is as follows: the essential vessel. claim is that a very slender monohull would exhibit the The monohull has not escaped the attention of lowest overall resistance, particularly at high speeds, latter-day researchers in the quest to discover im- when compared with either the traditional monohull proved forms, but now in much slenderer forms in or- or the catamaran, However, the optimal monohull is der to minimize its resistance. It has been been gener- so slender that it would be laterally unstable. Hence, ally shown that as the length of the vessel is increased the design must be slightly compromised by adding beyond that traditionally considered acceptable, so the sidehulls with a displacement which is relatively small wave resistance is reduced and the frictional increased compared with the displacement of the main hull. is increased, as would be anticipated if the displace- To better understand the philosophy of the development of vessels with more than one hull or sub- ment is to be maintained constant during this stretching process. The optimal length for the minimal total hull, it is worthwhile to consider some of the literature drag is much greater than that normally chosen. Un- on the most ‘traditional” of modern multihull vessels, fortunately, such optimal lengths lead to vessels which the catamaran. An example of research in this area are laterally unstable, It has been suggested that this is the work of Everest (1968), who reported results of problem can be solved by using small outriggers; a cu- both towing-tank resistance experiments and computations. He expounded on the matter of interactions rious example is the Super Outrigger vessel proposed by Daniel and Daniel (1990). This vessel would employ a between the wave systems generated by the two demi- single outrigger on one side, which has the advantage hulls, as well as viscous interactions between them. Good agreement was achieved between the predictions of possessing less resistance than the more obvious lat- and the measurements. erally symmetric layout requiring two such outriggers. Turner and Taplin (1968) did their experiments on Slender monohnlls were also the subject of research a catamaran whose demihulls were laterally asymmet- by Jullumstr@, Leppanen, and Sirvi6 (1993), who con- ric. It is thought that this feature was selected in order firmed the necessity for large values of the slenderness to minimize vortex shedding at the demibows due to coefficient in order to reduce the resist ante. cross-flow effects. Laterally symmetric demihulls were In recent years, considerable interest has been dis- also tested and these were found to be better in terms played in trimaran designs. The general philosophy of resistance at lower speeds only, supporting this investment of research effort, as noted The importance or otherwise of demihull asymme- above, is that from a purely hydrodynamic-resistance try was also the subject of work by Yokoo and Tasaki point of view, the slender monohull appears to be (1969a and 1969b). Their conclusions appear to be the best choice. The outriggers are added only to somewhat different in that asymmetric hulls were sig- provide lateral static stability. Therefore, the ques- nificantly bet ter over the entire speed range, with re- tion is how one can minimize the severe drag imposed spect to the total resistance. Pien (1976) studied both by the sidehulls, which is caused by their large wet- catamarans and smrdl-waterplane twin-hull (SWATH) ted surface in relation to the gained buoyancy. An ships in his work. Unozawa and Shimizu (1977) con- early paper following this path was written by Wil- centrated their efforts on other design aspects, such as son and Hsu (1992). Different longitudinal positions seakeeping and structural loads — rather than on the of the sidehulls were considered, as well as different resistance alone. Kusaka, Nakamura, and Kunitake hull forms. These concepts were analyzed within the (1980) analyzed a SWATH, with a view to minimiz- framework of linearized ship-resistance theory, with ing the wave resistance. They developed optimal hull the aim of gaining favorable wave interferences be- forms, based on the wave-resistance theory of Michell tween the hulls. Towing-tank experiments were also (1898). conducted and these verified their theoretical predic- More recently, Doctors (1991) did a series of calcu- tions. Similar work was done by Suzuki and Ikehata lations for both resistance and motions of catamarans. (1993), in which five different positions for the two In that work, he showed that by increasing within rea- sidehulls were examined. son the slenderness of the demihulls, one could gener- Summers and Eddison (1995) carried out a care- ally reduce both the overall resistance of the catama- ful investigation on a trimaran frigate which not only 284 z z z Pointed–stern parent hull A

Z-kA’-I I

Figure 1: Definition of the Problem Figure 1: Definition of the Problem (a) Principal Dimensions (b) Pointed-Stern Parent Hull

z Blended-stern parent hull % Transom-stern parent hull & A

Figure 1: Definition of the Problem Figure 1: Definition of the Problem (c) Blended-Stern Parent Hull (d) Transom-Stern Parent Hull

included the matter of resistance, They were also Sirvio, and Yli-Rantala (1995). concerned about motions and safety after a specified A very extensive experimental study was reported amount of damage, They demonstrated distinct re- by Ackers, Michael, Tredennick, Landen, Miller III, sistance advantages in comparison with conventional Sodowsky, and Hadler (1997). In this study, a sys- monohulls as well as reduced pitching in head waves. tematic set of towing-tank tests was conducted, in Work on the same project was reported by Pattison which the sidehulls were positioned in several locations and Zhang (1995) and Andrews and Zhang (1995). both longitudinally and laterally at different Froude The last two papers included a brief history behind numbers. They supplied a number of contour plots the trimaran concept and mention was made of one of providing data on the interference effects on the re- the early examples in recent times, the Ihm Voyager. sist ante. For one particular configuration, they too Trimarans with slender main hulls were also studied by demonstrated the superiority of this trimaran in com- Li, Tieli, and Huang (1993). Not unexpectedly, their parison to the equivalent frigate, at the higher speeds theoretical predictions also indicated a lower resistance being contemplated. for the trimaran compared with that of a standard One of the most mathematical optimization stud- monohull. Furthermore, they showed that the relative ies was that of Lazauskas and Tuck (1998). They con- position of the sidehulls was not a major factor in the sidered a number of layouts of the subhulls. These lay- design. A similar investigation was done by Lindstri5m, outs included laterally symmetric catamarans, Wein- 285 Item Symbol Units Values Condition 3 6 9 Trim P degrees 0.0 0.0 0.0 Stern wedge angle 6 degrees 6 6 6 Waterline length L 1.771 1,754 1.731 Displacement mass A ; 10.84 7.949 5.059 Block coefficient cB 0.5696 0.5238 0.4485 Prismatic coefficient Cp 0.7483 0.7230 0.6758 Slenderness coefficient L/V~/3 8.000 8.784 10.08 Length-to-beam ratio L/B 12,94 13.05 13.18

Table 1: Geometry of the Test Demihull in Three Conditions

Item Symbol units Values Parent 1 2 3 Type of stern Pointed Blended Transom Waterline length L m 30.0 30.0 30.0 Waterline beam B m 2.000 2.000 2.000 Draft T m 1.631 1.527 1.353 Displacement mass A t 50.0 50.0 50.0 Block coefficient cB 0.4984 0.5325 0.6011 Prismatic coefficient Cp 0.6174 0.6671 0.7630 Slenderness coefficient L/@/~ 8.210 8.210 8.210 Length-to-beam ratio \ LIB 15.0 15.0 15.0

Table 2: Geometry of the Three Parent Monohulls

bium catamarans (in which the two demihulls are stag- hulls, catamarans, and trimarans. They were able to gered longitudinally), and tetramarans (where the sub- demonstrate advantages of the trimaran with respect hulls were positioned in a diamond pattern). Some to resistance, at Froude numbers of around 0.4. Nu- very impressive reductions in wave resistance at quite merical optimization of the hull forms has been done specific speeds of operation were demonstrated; these by a number of researchers. Recent examples include hulls would show promise in river operations provided Pal and Doctors (1995) and Pal, Peacock, and Doctors their unorthodox appearance would be acceptable to (1999). Doctors and Day (1995) employed the genetic the public. algorithm (GA) combined with an efficient representa- A novel idea was proposed by Gee, Dudson, tion of the wave resistance, wherein most of the actual Marchant, and Steiger (1997). Their pentamaran in- computation could be effected separately from the op- volves a total of four sidehulls, with two of these side- timization procedure. Gawan-Taylor (1996) presented hulls normally just clear of the water. The displace- resistance comparisons of monohulls and catamarans ment of all four of the sidehulls is very low, so that in which the basis of comparison was an equal payload the drag penalty for the first two sidehulls in normal capacity. operation is very low for this concept. The additional Day, Doctors, and Armstrong (1997) did an ex- two sidehulls only become immersed during large an- haustive genetic-algorithm comparison between mono- gles of heel, when an additional margin of stability is hulls, catamarans, SWATHS, semi-SWATHs, hover- required. craft, and surface-effect ships. The calculations, which The underlying purpose in all of this research, of were applicable to calm water only, clearly showed that course, is the drive to improve the so-called transport the hovercraft was superior, because of the absence of efficiency oft he vehicle. The hydrodynamic transport hydrodynamic frictional resistance. For similar rea- efficiency is essentially the ratio q = W/R, where W is sons, it was shown that the monohull was better than the weight of the vessel and R is its resistance. Thus, the catamaran. The subject oft ransport efficiency was over three decades ago, Lackenby and Slater (1968) the core topic of the workshop, whose proceedings were compared the advantages of different types of mono- reported by McKesson (1997).., It was re~eatedlv noted 286 - - that the key to high-speed long-range efficient trans- these two extreme cases, is depicted in Figure l(c). portation lay in improving this quantity; if a vessel This is referred to as the blended-dern parent hull. It possessed a low transport efficiency, it simply could was created using the method of Doctors (1995). not carry a sufficient quantity of fuel to reach its des- 2.2 Verification of Theory tination. We start by presenting some data for the model 1.2 Current Work hull shown in Figure l(d). This was tested in the tow- The work to be reported on here is devoted to a ing tank as a catamaran. The geometric details of the large set of parametric calculations in which the three test model demihull are presented in Table 1. The basic displacement-ship concepts, the monohull, cata- vessel was run in a total of nine conditions. Varia- maran, and the trimaran, are to be evaluated. Thus, tions included differing displacements, differing static it can generally be stated that the present aim is to trims, and differing amounts of transom-stern wedge. recompute the cases considered by some of the above- The computer program described by Doctors (1995) mentioned researchers. However, the additional int en- was used to merge the original vessel with either 070, tion here is to systematically analyze a large range of 100%, or 150?lo of the angle of a 4° standard wedge. lengths of the vessel types. Moreover, the methods to The three principal loading conditions are presented be used here will enable transom-stern hull forms to in Table 1. be studied — as well as hulls with a pointed stern. In addition, the beam of the catamaran model was The computations are carried out on vessels of two specified through the centerplane-to-centerplane spac- displacements. The first vessel has a displacement of ing of 0,4133 m, while the towing tank had a width 50 t and may be considered to be a generic river ferry of 3.50 m and was filled to a depth of 1.5 m. Fig- with a size similar to that of the RiverCat. This ves- ure 2(a) shows the components of resistance for the sel operates on the Parramatta River leading to Syd- catamaran model tested in Condition 6. The curves ney Harbor and was described by Doctors, Renilson, show respectively the experimental data for the total Parker, and Hornsby (1991). The two main concerns experimental resistance, the wave resistance, the hy- here are the wave generation (because of the question drostatic drag (due to the lack of water pressure on of wave damage to the river banks) and the total re- the transom), the frictional resistance, and the total sistance (because it affects the powering). The second theoretical resistance. It is seen that the correlation vessel has a displacement of 10,000 t. This vessel rep- at Froude numbers greater than about O.4 is excellent. resents a possible candidate for a SeaLift ship in which The Froude number is defined as F = U/~, where the total resistance only is the quantity to be reduced. U is the speed of the vessel, g is the acceleration due to gravity, and L is the waterline length of the ves- 2 Theoretical Techniques sel. In these calculations, the frictional resist ante was calculated according to the 1957 International Towing 2.1 Thin- Ship Analysis Tank Committee (ITTC) formula, described by Lewis Figure l(a) depicts a hull at the free surface of (1988, Section 3.5). The correlation allowance CA was the water. There will be a hollow in the water behind zero. the vessel in the case of a transom stern. The thin-ship Figure 2(b) compares the total resistance for all theory of Michell (1898) will be employed in the analy- of the three loading conditions shown in Table 1. The sis. Improvements by Lunde (1951) which incorporate predictions are seen to be too high at low speeds due to restrictions of the width of the canal and the depth of the fact that the stern has been assumed to be “run- the water are also included. The method of modeling ning dry”. For this work, the low-speed theoretical the flow in the region of the transom, which was devel- model of Doctors ( 1998b) was not employed, as it has oped by Doctors and Day (1997), will also be utilized little bearing on the predictions at the Froude num- here. Further details of the computer representation bers of interest. In the same vein, correction factors of the hull were described by Doctors (1993). for the wave resistance and for the frictional resistance, For the purpose of this exercise, a typical modern such as promoted by Doctors (1998a), were not ap- high-speed transom-stern parent hull was chosen. This plied, because there is more than sufficient accuracy is shown in Figure 1(d). This hull is characterized by here without their use. possessing a single chine and having a transom stern, 2.8 Parent Hull Forms A fore-aft symmetric vessel was created by re-using the bow section at the stern. This vessel is known here The three principal parents are depicted in the last as the pointed-si?ern parent hull and is shown in Fig- three parts of Figure 1, The corresponding geometric ure 1(b). Finally, a vessel, which is midway between data is shown in Table 2. 287 0.2 0.2 Curve Comp L= 1.75 m Curve L/Vi/8 Comp o 000 0 T,E L/Vi/s = a78 0000 8 T,E ------w tine = I’Tl’C ❑ 00 a 8.78 T,E o o.15- ______H CA = o 0 0.15- 0000 10.1 T,E o 04 ~ ———. — F ~ -----.._--- B T 0 ~&&”” w ---—-—— 8.78 T w /:.%- 0.1– stirn =’TmmOm 0.1 10.1 T ,. -- Nbd = 2 / / / 0.05- / <------,--- #.,. - ~.% wc-7fi ------

0 I I I 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 F F

Figure2: Test of Computer Program Figure 2: Test of Computer Program (a) Resistance Components (b) Comparison of Three Hulls

Y Y

4r— z ‘- “t===” 1-

‘ =l==-x=l--” c Y Y I x z

Figure 3: Layout of Multihulls Figure 3: Layout of Multihulls (a) Identical Subhulls (b) Sidehull Arrangement

2.4 Generation of Hulls to be Analyzed 3 Numerical Experiments

Six different chdd hulls were created from each 9.1 River Vessel of the three parent hulls in Table 2, by simply scal- ing the beam and draft in unison. By this is meant The two parts of Figure 4 show the wave resistance that the beam-to-draft ratio of the subhulls B/T is Rw and the total resistance RT for the pointed-stern kept fixed during this stretching process. In this way, river vessel with a displacement of 50 t. The results these hulls, or subhulls, could be employed to construct have been computed for six values of the speed given monohulls, catamarans, trimarans, tetramarans, pen- by U = 10.0( 1.0)15.0 m/s. That is, the mean value tamarans, and hexamarans, while maintaining the dis- ~ is 12.5 m/s and the range AU is 5.0 m/s. The placement A constant at 50 t for use as the river ferry. plotted data represents the mean of the corresponding The layouts of the regular multihulls are shown resistance values. in Figure 3(a). The overall centerplane-to-centerplane One can see the very favorable effect on wave re- spacing for the multihulls was chosen to be 10.0 m. sistance by increasing the length. This is true for all That is to say, the overall spacing-to-length ratio for the multihulls shown. On the other hand, Figure 4(b) the parent-hull configuration is 0.3333. Also shown, indicates that the total resistance drops as the length in Figure 3(b), are sidehull trimarans, which will be increases only for the monohull, where one can observe discussed in detail later. that the optimum length is at least 50 m. The multi- 288 0.06 Stern = Pointed Curve I Nh Fixed = B/T ------1 I __ ———-— — 0.04 A . 6ot 2 0.08–.—— ——————__ ——-—- Line = I’ITC —-——.—-————— ; s CA = 0.0004 4 I--n:----. -_.___-.------j u= 125 m/s ---- k“”og ‘“.. ‘.\ ~“”w ------1 AU = Stern = Pointed 5 m/a ~ ‘.. u ------%; 04 B/T 0.02– ‘.. Fixed = . =. A 6ot Curve N Line = ITTC ------1 0.01- 0.02-1CA = 0.0004 4—----—- 2 u= 126 m\e ————. s o AU = 5 mle 4 o~ I I I I I B() 95 40 46 60 66 60 30 S6 40 46 60 66 60 Lm Lm

Figure 4: Length for Pointed-Stern River Figure 4: Length for Pointed-Stern River Vessel (a) Wave Resistance Vessel (b) Total Resistance

---- 0.1 Curve N Stern = Blended ------1 Fixed = B/T -----—— 2 A . t —--————— 0.04 60 0.08-.—— ————————————- ——. .— 3 Line = Ill’(l m 4 CA = 0.0004 00S ,, % u= 126 m/s ‘. ‘1 ‘. AU = 6 m/a w ‘. 0,02r ‘., 0.02- CA = 0.0004 ———---- 2 u= 126 m\s ————. 3 0 AU = 6 m/s 4 I I I I I 30 36 40 46 60 66 60 so 96 40 46 so 65 60 Lm Lm

Figure 5: Length for Blended-Stern River Figure 5: Length for Blended-Stern River Vessel (a) Wave Resistance Vessel (b) Total Resistance

hulls all show greater total resistance than that of the superior in terms of the wave resistance, while only a monohull. The total resistance of the multihulls usu- small pemdt y in total resistance is apparent. ally increases with the length. This outcome follows from the fact that the large wetted-surface area is the 3.2 SeaLift Ship essential deficiency of a multihull. We now proceed to a larger vessel in order to illus- Similar conclusions can be drawn for the blended- trate the question of scale. As an example, we assume stern vessels in Figure 5 and the transom-stern vessels the vessel to have a displacement of 10,000 t, implying in Figure 6, that the length and the other linear dimensions should By way of summary, Figure 7 represents a cross be greater by the factor 5.8480. The operational speed plot of the influence of the number of subhulls Nhull U and the speed range AU have been Froude-scaled on the wave resistance and the total resistance for the from the values pertinent to the river ferry. Figure 9 thirty-meter river vessel. There is no doubt that the shows the effect of varying the length on the total re- catamaran is superior to the monohull, because the sistance for two of the parent hulls. As in the case of wave resistance is less and there is little penalty in the (smaller) river vessel, we observe that if the resis- terms of the total resistance. On the other hand, if tante were the only criterion in the design of a ship, other factors (structural and operationrd) permit, the then the monohull is best — provided that there is no sixty-meter vessels in Figure 8 are seen to be much constraint on the length. It is only at the lesser lengths 289 0.06 Curve NhU Stern = Treneom ------1 Fixed = B/T . 0.04- _—— —_— — 2 A 6ot .—. —— 3 Line = ITTC 4 C* = 0.0004 ~o.o.s- u= 12.6 m/s ~ Stern = Transom ‘k -.. AU = 5 m/8 %; 04 Fixed = B/T @o.02 -t ‘“.. A . 60 t Curve N Line = ITTC ------1 0.02- CA = 0.0004 ------2 u= 126 m/n .—. —— 3 o AU = 5 m/e 4 o~ 1 I I 30 3s 40 4s 50 65 60 so 36 40 46 60d66 60 Lm Lm

Figure 6: Length for Transom-Stern River Figure 6: Length for Transom-Stern River Vessel (a) Wave Resistance Vessel (b) Total Resistance

0.06 Cuwe St.arn Fixed = B/T ------Pointed L . SOm 0.04------– Blended A . 50 t Tranmm Line = ITTC CA = 0.0004 0.03-;. & \’. u= 12.5m/e ~O’M AU = 6 m/n Fixed = B/T $Ow L = 90 m A . 50 t . --.- ...... -. C Line = ITTC 0.01 0.02 CA = 0.0004 - 1u= 126 m/e ------Blended 1 o AU = 6 m/a Transom I I I I 1 2 3 4 5 6 Nh~

Figure 7: Number of Subhulls for Thirty-Meter Figure 7: Number of Subhulls for Thirty-Meter River Vessel (a) Wave Resistance River Vessel (b) Total Resistance

that the catamaran or the trimaran can compete. 25% for the catamaran (for a length of 350 m) could be achieved, simply by maintaining vessels with a hy- 3.3 Calculation of Friction draulically smooth surface finish.

Because the frictional resistance is such an impor- 9.4 Comparison of Sidehull Trimarans tant factor, it was decided to recompute some of the results using the 1947 American Towing Tank Commit- It would seem certain from the above comparisons tee (ATTC) formula, which was developed by Schoen- and discussions of the resistance qualities of the multi- herr (1932). In a separate numerical experiment, the hulls, that sidehull-trimaran arrangements wilJ exhibit correlation allowance CA was set to zero, rather than a behavior that can be anticipated in a simplistic man- the more usual value of 0.0004. ner and that there are unlikely to be any surprises. The two parts of Figure 10 pertain to the monohull That this is indeed so will now be demonstrated. and the cat amaran, respectively. It can be seen that Some sidehull trimarans patterned after the con- there is no discernible difference between the ITTC figurations depicted in Figure 3(b) were evaluated. In and the ATTC computations. On the other hand, all cases, the sidehulls were each assigned a displace- the importance of the correlation allowance is clear. ment equal to 107o of the total, while the main, central, These results show that an excellent improvement in hull supported 80% of the total. To simplify this in- the performance of around 23?40for the monohull and vestigation, the three linear dimensions of the sidehulls 290 0.1 ““”” Fixed = B/T L . 60 m 0.04- ii= 50 t 008- Line = ITTC = 0.0004 0.09- := k 125 m/s ~“’w Fixed = B/?’ ‘k AU = 5 m/s @ &iw L . 60 m 0.02- A . 50 t

0.01 i ——. —— 0 I I I I I 1 1 2 s 4 6 6 “f=3=LE%1 2 3 4 s 6 Nhti

Figure 8: Number of Subhulls for Sixty-Meter Figure 8: Number of Subhulls for Sixty-Meter River Vessel (a) Wave Resistance River Vessel (b) Total Resistance

0.1 0.1 Stern = Pointed Stern = Blended Fixed = B/T Fixed = B/T ‘“081~ .—— ————.— ——___ ——-— ——------1 -u= .--_------______-_—------1000Ot Cuwe N . ------ILine ITIC 1 0.02- CA = 0.0004 d———--—- 2 t?= S0.29m/s .—— —. s AU = 1209 m/s 4 OIAU = 12.09 m/m 4 o I I I I I I I 160 200 260 800 S60 1s0 2(io 260 800 S60 Lm Lm

Figure 9: Length for SeaLift Vessel Figure 9: Length for SeaLift Vessel (a) Pointed-Stern (b) Blended-Stern

were made equal to 50% of the corresponding linear di- overly significant. One can detect a small improvement mensions of the central hull. That is, all three subhulls for the sidehull trimararis compared to the monohull, were geosims of each other. The sidehull centerplane- but the catamaran is still better. Turning now to the to-centerplane spacing was chosen to be the same as total resistance in Figure 1l(b), one sees that the fric- that for the two outer subhulls in the previous calcu- tional resistance component results in the generally lations. poorer behavior of the sidehull trimarans. Inciden- Figure 11 shows the wave resistance and the total tally, the difference between the two aidehull trimarans resistance for four concepts, as follows: the monohull, is the same for both parts of Figure 11. This is be- the catamaran, the sidehull t rimaran (with the sterns cause there are no interferences between the frictional of all the subhulls aligned with each other, r/.L = O), effects on the three subhulls according to the theory and the sidehull trimaran (with the sterns of the side- used here. hulls shifted forward 25% of the length of the central Finally, Figure 12 shows the corresponding com- hull, r/L = 0.25). Regarding the wave resistance in parison for the blended-stern sidehull trimaran and Figure 11(a), we see that the two sidehull trirnarans Figure 13 shows the same results for the transom-stern differ very little from each other in terms of their wave sidehull trimaran. Once again, the calculations show resistance, indicating that wave-interference effects be- that sidehull trimaran suffers from excessive frictional tween the three subhulls certainly exist but are not resistance — at least in the present case. 291 01..- 01 Stern = Blended Curve Line c ‘-- Stern = Blended Fixed = B/T ------ITI’C 0.0004 Fixed = 0.0s Nbti = 1 ...... A’Tl’C0.0004 00s Nhw = 0 r 11”1’C1 1 ‘“ IEEE ~“’w ------hi:~

002- A= 1000Ot 0.021.A = 1000Ot u= 90.23m/8 1v= 90.2Sm/e o AU = 12.09 m/s IAU = 12.09m/e I I 1 o I I I I 150 200 2s0 300 Sso 160 200 260 Soa 360 Lm Lm

Figure 10: Calculation of Frictional Resistance Figure 10: Calculation of Frictional Resistance (a) Monohull (b) Catamaran

0.1 Stern = Pointed Curve INhd I r/L Cuwe N r/L Fixed = B/T ------1 0 -.------1 0 0.08 A . 100CX3t —--. —-- 2 0 ————--- 2 0 Line = ITTC .—— —— 3 0 ————— 9 0 ‘. CA = 0.0004 s 0.26 ____ 9 0.2s ~o.od --.- ~ u= S0.2S m/a ~“’m -=.---______=_ ——T1 ---- AU = 1209 m/a ------+04 k4:04P----:------<.

0.02 -.. ------—-.=-== m- 0 150 200 250 Soo 360 AL160 200 2s0 900 350 Lm Lm

Figure 11: Comparison of Pointed-Stern Figure 11: Comparison of Pointed-Stern Concepts (a) Wave Resistance Concepts (b) Total Resistance

3.5 Importance of Scale improvements in performance can be derived purely Because the SeaLift vessel has been Froude-scaled by increasing the size of the vessel. It should be-noted from the river vessel, it may be stated that the di- that Templeman and Kennell (1999) came to similar mensionless wave resistance for these two sizes will be conclusions. the same when plotted as a function of the volumetric 4 Concluding Remarks Froude number Fv = U/~~. On the other hand, the specific, or dimensionless, total resistance R~/W 4.1 Current Work for the larger vessel will be less. This is because the frictional-resistance coefficient drops as the Reynolds The present research allows us to conclude the fol- number increases. lowing points: This feature is illustrated in Figure 14(a), for the monohull and the catamaran, and in Figure 14(b) for 1. Increasing the length of the vessel beyond that the trimaran and the tet ramaran. The reduction in normally considered appropriate is beneficial, if total drag-to-lift ratio is substantial. At a volumet- the intention is to reduce wave generation at volu- ric Froude number of 2.5, the reduction is respectively metric Froude numbers of around 2.088. The cor- 1370, 19’Yo,17Y0, and 2070 for these four vessels. Fur- responding slenderness coefficient for the mono- thermore, these calculations emphasize the fact that hull is 16.38; 292 0.1 Stern = Blended curveI~h~Ir/L Fixed = B/T ------1 0 I ------0.08 A . 1000Ot ------2 0 2 c .—— —— Line = ITTC I ————— I 9 I 0 I 3 I ( CA = 0.0004 9 I026 ‘. 3 ]o.2f 0.06 -.. _ k u= 30.23m/e ~“”m .-.~.------______-_= ———— —- 3 AU = 1209 m/s ------@ 4;.04 ------. 0.04 1=A 1000Ot ~. Line .= ITTC 0.02 ---- 0.02 CA = 0.0004 ------u= 302S m/a AU = 12.09 m/s 0 o I I I 150 200 250 Soo 950 150L 200 2s0 300 950 Lm Lm

Figure— 12: Comparison of Blended-Stern Figure 12: Comparison of Blended-Stern Concepts (a) Wave Resistance Concepts (b) Total Resistance

0.1 0.1 Stern = Tranaom Curve INhti I r/L Fixed = B/T ------1 0 —-—--—— 0.08 A . 1000Ot 12 I 0 0.08 Line = ITTC -----+ 3 / o :-~ ~ CA = 0.0004 s I 025 -.--: -- ___ ------.--— =-—.=_—_--— ~o.od u= S0.29 m/a -G -- jkO”M ------= AU = 1209 m/a Stern Transom ------GO04 GO~ Fixed = B/T A . 1000O t Line = ITTC ~ 0.02 002 —------CA = 0.0004 2 0 -- u= 90.29m/a —— —.. 3 0 AU = 1209 m/s 3 0.26 0 0 I I I 150 200 250 900 Sso 150 200 250 SOo S50 Lm Lm

Figure 13: Comparison of Transom-Stern Figure 13: Comparison of Transom-Stern Concepts (a) Wave Resistance Concepts (b) Total Resistance

2. For the range of lengths considered, the catama- 5. The sidehull trimaran is marginally superior to ran is superior to the monohull in terms of wave a monohull in terms of wave resistance, but its generation. This has important implications when performance at the same length is not as good as selecting a ferry type for operation in rivers; that of the catamaran;

3. If the vessel must be restricted in length to cur- 6. Regarding total resistance, the sidehull trimaran rently accept ed values, then the trimaran offers a is inferior to both the monohull and the catama- reduced wave resistance of around 19!Z0compared ran at currently acceptable lengths. If greater to the catamaran and 53% compared to the mono- lengths can be tolerated, one might be able to hul. At somewhat greater lengths, trimarans, make a case for sidehull trimarans over catama- tet ramarans, pentamarans, and hexamarans per- rans. form no better than catamarans in terms of wave generation; 7. Frictional resistance is seen to be a major stum- bling block if the intention is to obtain ~ransport 4. Regarding total resistance, the monohull is almost factors exceeding 20 at high volumetric Froude always superior to any of the multihulls. Possible numbers of around 2.088. Large reductions in to- exceptions would occur only at the lower lengths, tal resistance can ideally be achieved by maintain- when the catamaran is marginally superior. ing a hydraulically smooth hull surface. 293 4.2 Future Work plex”, Proc. Seventh International High-Speed Surface Craft Conference, London, 19 pp (January 1990) Future work can be concentrated on the details DAY, A. H., DOCTORS, L. J., AND ARMSTRONG, of the hull shape, more along the lines of traditional N. A.: “Concept Evaluation for Large Very-High- hull-optimization techniques. However, it would seem Speed Vessels”, Proc. Fourth International Confer- difficult to achieve any remarkable gains, given the re- ence on Fast Sea Transportation (FAST ‘97), Sydney, quirement to travel at the abovementioned high volu- Australia, Vol. 1, pp 65-75 (July 1997) met ric Froude numbers. The wave resistance is a weak function of the cross- DOCTORS, L. J.: “Some Hydrodynamic Aspects of sectional shape for slender hulls, so it would seem nec- Catamarans”, Thans. of Mechanical Engineering, In- essary to aim for semicircular sections that will mini- stitution of Engineers, Australia, Vol. ME 16, No. 4, mize the wetted-surface area for any given volume of pp 295-302 (December 1991) displacement. “HYDROS: Integrated Software for Because of the clear superiority of the monohull DOCTORS, L. J.: at the higher speeds, one can make a strong case for the Analysis of the Hydrostatics and Hydrodynam- avoiding the multihull concept altogether, if total re- ics of Marine Vehicles”, Proc. Tenth International sistance, rather than wave resistance, is the key design Maritime and Shipping Symposium (ShipShape 2000), consideration. Because such slender monohull vessels University of New South Wales, Sydney, New South are laterally unstable, one must also argue the merit Wales, Vol. 1, pp 373-392 (November 1993) of artificially stabilized slender monohulls, as a means DOCTORS, L. J.: “A Versatile Hull-Generator Pro- of improving the transport efficiency for displacement gram”, Pmt. Twenty-Fimt Century Shipping Sym- vessels, posium, University of New South Wales, Sydney, New South Wales, pp 140-158, Discussion: 158–159 Acknowledgments (November 1995) This work was supported by the Australian Re- DOCTORS, L. J.: ‘Intelligent Regression of Resis- search Council (ARC) Large Grant Scheme through tance Data for Hydrodynamics in Ship Design”, PTOC. grant number A89917293 and The University of New Twenty-Second Symposium on Naval Hydrodynamics, South Wales (UNSW). The author wishes to express Washington, DC, 16 pp (August 1998) his gratitude to both of these institutions for this sup- port. DOCTORS, L, J.: “An Improved Theoretical Model for The author would also like to thank various naval the Resistance of a Vessel with a Transom Stern”, architects working in the Australian high-speed ferry PTOC. Thirteenth Awtmlasian Fluid Mechanics Con- design and construction industry for their valuable dis- ference (19 AFMC), Monash University, Melbourne, cussions which provided the background ideas for the Victoria, Vol. 1, pp 271-274 (December 1998) work presented in this paper. DOCTORS, L,J. AND DAY, A. H.: ‘Hydrodynamically Optimal Hull Forms for River Ferries”, Proc. Interna- References tional Symposium on High-Speed Vessels for Thmwport and Defencej Royal Institution of Naval Architects, ACKERS, B. B., MICHAEL, T. J., TEEDENNICK, London, England, pp 5-1-5-15 (November 1995) O.w,, LANDEN, H. C., MILLER III, E, R., SODOWSKY, J. P., AND HADLER, J. B.: “An In- DOCTORS, L.J. AND DAY, A. H.: “Resistance Pre- diction for Tkmsom-Stern Vessels”, Proc. Fourth In- vestigation of the Resistance Characteristics of Powered Trimaran Side-Hull Configurations”, Truns. ternational Conference on Fast Sea fiansportation Society of Naval Architects and Marine h’ngineers, (FAST ‘97), Sydney, Australiaj Vol. 2, pp 743-750 Vol. 105, pp 349-368, Discussion: 369-373 (1997) (July 1997)

ANDREWS, D.J. AND ZHANG, J.-W.: “Considera- DOCTORS, L.J, RENILSON, M. R., PARKER, G., tions in the Design of a Trimaran Frigate”, Proc. AND HORNSBY, N.: “Waves and Wave Resistance International Symposium on High-Speed Veaaela for of a High-Speed River Catamaran”, PTOC. First ZYansport and Defence, Royal Institution of Naval Ar- International Conference on Fast Sea l%ansporta- chitects, London, England, pp 15- 1–15-21 (November tion (FAST ‘91), Norwegian Institute of Technology, 1995) Trondheim, Norway, Vol. 1, pp 35-52 (June 1991)

DANIEL, N,I. AND DANIEL, H. E.: “SuperOutrigger: EVEREST, J. T.: “Some Research on the Hydrody- Less Pitch, Less Roll, Less Drag, Less Cost, Less Com- namics of Catamarans and Multi-Hulled Vessels in 294 0.1 0.1 Stem = Blended Stern = Blended / Fixed = B/T Fixed = B/T 0.08 Nhti = 1 0,08– Nhti = 2 ------i ------i ------. -@-z=------0.06 ------0.06- y _.---:-2:-2------:-z:-- ~ ------w --- % 0.04 ---s -- Curve L A Curve L A ------.-- L-l------1 SO m I 60 t SOml 60 t 0.02- Line = ITTC –––--–- 175 10000 0.02- Line = rrrc ––––-–- 175 10000 cA = 0.0004 .—— —. 60 60 C* = 0.0004 ————. 60 60 0 COmp= T 861 1000O ~ Comp = T 961 10000 I I I I I I I I I I I I I 1.7 1.8 1.9 2 21 22 2.9 2.4 2.5 1.7 1.8 1.9 2 21 22 2S 2.4 2.5 FV FV

Figure 14: Importance of Scale of Vessel Figure 14: Importance of Scale of Vessel (a) Monohull (b) Catamaran

0.1 0.1 ,/- ---- ,/’ /“ ,,~ ,/’ ------0.08 0.08- ---- /-<--- ,/~------~b~------H A==--- .-% 0.06-

w Stern = Blended 0.04 Stirn = Blended Curve L A Fixed = B/T Cuwe L A Fixed = B/T ------mom 60 t Nhw = ?3 ------30 m 60 t Nhw = 4 0.02- –-----– 17s 1000O Line = ITTC ().02------175 1000O Line = ITTC ————— 60 60 CA = 0.0004 ——.—— 60 60 CA = 0.0004 361 1000O Camp = T 961 1000O Comp = T 0 I I I I I I 0 I I I I I I I 1.7 1.8 1.9 2 2.1 2.2 2s 2.4 2.5 1.7 1.8 1.9 2 2.1 2.2 2S 2.4 2.6 FV FV

Em!—--—-lgure .4-A*: v-----~pormnce, 01*“. scale 01*-.. vessel Figure 14: Importance of Scale of Vessel (c) ‘lkimaran (d) Tetramaran

Calm Water”, fiana. North Ewt Coast Institution Naval Architects of Japan, Yokohama, Japan, Vol. 2, of Engineers and Ship budders, Vol. 84, No. 5, pp 129- pp 1477-1488 (December 1993) 148, Discussion: D29-D34 (May 1968) KUSAKA, Y., NAKAMURA, H., AND KUNITAKE, Y.: GAWAN-TAYLOB, P,: “Catamaran versus Mono- ‘Hull Form Design of the Semi-Submerged Catamaran hull — Not the Final Word”, PTOC. Au8Marine ’96, Vessel”, PTOC. Thirteenth Symposium on Naval Hy- Fremantle, Western Australia, 5 pp (November 1996) drodynamic, Tokyo, Japan, pp 555–565, Discussion: 566-568 (October 1980) GEE, N., DUDSON, E,, MARCHANT, A,, AND STEIGER, H.: “The Pentamaran: A New Hull Concept LACKENBY, H. AND SLATER, C.: “The Case for Mul- for Fast Freight and Car Ferry Applications”, Proc. tihull Ships with Particular Reference to Resistance Thirteenth Fast Ferry International Conference, Sin- Characteristics”, PTOC. Diamond Jubilee International gapore, 21 pp (February 1997) Meeting, Society of Naval Architects and Marine En- gineers (SNAME), New York, 15 pp (June 1968) JULLUMSTR@, E,, LEPPANEN, J., AND SIRVIO, J.: “Performance and Behaviour of the Large Slender LAZAUSKAS,L. AND TUCK, E. O.: “Wave Cancella- Monohull”, PTOC. Second International Conference tion by Weinblum-Type Catamarans and Diamond- on Fast Sea l%anaportation (FAST ‘93), Society of Shaped Tetrahulls”, PTOC. Third Biennial Engi- 295 neering Mathematics and Applications Conference PIEN, P. C.: “Catamaran Hull-Form Design”, .7. Soci- (EMAC ‘98), Adelaide, South Australia, pp 299-302 ety of iVaval Architects of Japan, Vol. 139, pp 185–198 (July 1998) (1976)

LEWIS, E.V. (ED.): Principles of Naval Architecture: SCHOENHERR, K. E.: “Resistance of Flat Surfaces Volume II. Resistance, Propulsion and Vibration, So- Moving through a Fluid”, Zkans. Society of Naval Ar- ciet y of Naval Architects and Marine Engineers, Jersey chitects and Marine Engineers, Vol. 30, pp 279–299, City, New Jersey, 327+vi pp (1988) Discussion: 299-313 (1932) LI, Z., TIELI, L., AND HUANG) D, L.: “A Study SUMMERS, A.B. AND EDDISON, J. F. P.: “Future of Performance Predictions for High Speed Slender ASW Frigate Concept Study of a ‘lXrnaran Variant”, Ship with Twin Wing Hulls (SSWWH)”, Proc. Sec- Proc. International Maritime Defence 1995 Confere- ond International Conference on Fast Sea !&ansporta- nce, Spearhead Exhibitions Ltd, London, England, tion (FAST ‘99), Society of NavaJ Architects of Japan, Vol. 1, 59 pp (March 1995) Yokohama, Japan, Vol. 1, pp 929–937 (December SUZUKI, K. AND IKEHATA, M.: “Fundamental Study 1993) on Optimum Position of Outriggers of Trimaran from LINDSTROM, J., SIRVIO, J., AND YLI-RANTALA, View Point of Wave Making Resistance”, Proc. Sec- A.: “Superslender Monohull with Outriggers”, ond International Conference on Fast Sea Transporta- Proc. Third International Conference on Fast tion (FAST ‘99), Society of Naval Architects of Japan, Sea Ykansportation (FAST ‘95), Schifl%autechnische Yokohama, Japan, Vol. 2, pp 12 19–1230 (December Gesellschaft, Travemiinde, Germany, Vol. 1, pp 295- 1993) 306 (September 1995) TEMPLEMAN, M. AND KENNELL, C.: “The Effect of LUNDE, J. K.: “On the Linearized Theory of Wave Ship Size on Transport Factor Properties”, Proc. First Resistance for Displacement Ships in Steady and Ac- International Conference on High-Performance Ma- celerated Motion”, Trans. Society of Naval Architects rine Vehicles (HIPER ‘99), Zevenwacht, South Africa, and Marine Engineers, Vol. 59, pp 25-76, Discussion: pp 210-219 (March 1999) 76-85 (December 1951) TKJRNER, H. AND TAPLIN, A.: “The Resistance of MCKESSON, C.B. (ED.): “Hull Form and Propulsor Large Powered Catamarans”, tins. Society of Naval Technology for High Speed SeaLift”, Proc. High Speed Architects and Marine Engineers, Vol. 76, pp 180-204, Sealijl Technology Conference, Naval Surface Warfare Discussion: 204-213 (December 1968) Center, Washington, 87 pp (October 1997) UNOZAWA, M. AND SHIMIZU, K.: “The Design of MICHELL, J. H.: “The Wave Resistance of a Ship”, Catamarans”, Proc. International Symposium on Philosophical Magazine, London, Series 5, Vol. 45, Practical Design in Shipbuilding (PRADS ‘77), So- pp 106-123 (1898) ciet y of Naval Architects of Japan, Tokyo, Japan, pp 403-410 (October 1977) PAL, P.K. AND DOCTORS, L. J.: “Optimal Design of High-Speed River Cat amaransn, Proc. Third in- WILSON, M,B. AND Hsu, C. C.: “Wave Cancellation ternational Conference on Fast Sea Ybansportation Multihull Ship Concept”, Proc. High Performance (FAST ‘95), Travemiinde, Germany, Vol. 2, pp 1379- Marine Vehicle Conference and Ezhibit (HPMV ‘92), 1390 (September 1995) American Society of Naval Engineers, Washington, pp MH26-MH36 (June 1992) PAL, P. K., PEACOCK, D., AND DOCTORS, L. J.: “Preliminary Design of High-Speed River Catama- YOKOO, K. AND TASAKI, R.: “On the Twin-Hull ran Ferries”, Proc. First International Congress Ship (No. l)n, University of Michigan, Department of on Maritime Technological Innovations and research, Naval Architecture and Marine Engineering, Report Barcelona, Spain, pp 523-535 (April 1999) 33, 20 pp (September 1969) PATTISON, D.R. AND ZEANG, J. W.: “Trimaran YOKOO) K. AND TASAKI, R.: ‘On the Twin-Hull Ships”, Trans. Royal Institution of Naval Architects, Ship (No. 2)”, University of Michigan, Department of Vol. 137, pp 143-153, Discussion: 153-161 (1995) Naval Architecture and Marine Engineering, Report 34, 10 pp (September 1969)

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