On the great trimaran-catamaran debate

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 mul-tihulls

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

min-imize 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 demon-strate 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 = B= CA = cB = Cp = F = Fv = L– j5/@/3 : Nhull = R= RA = RF = RH = RT z RW = T= u = u= w= 9=

Waterline beam

x

=

Correlation

allowance

Y=

Block coefficient

z

=

Prismatic

coefficient

Froude number

A=

Volumetric Froude number

v=

Waterline length

Slenderness coefficient

P

=

Number of subhulls

6

=

Resistance

Correlation

resistance

liMctional resistance

Hydrostatic

resistance

Total resistance

Wave resistance

Draft

Speed

Mean speed

Weight

Acceleration

due to gravity

Dedication

Longitudinal

stagger of sidehulls

Longitudinal

coordinate

Transverse coordinate

Vertical coordinate

Displacement

mass

Displacement

volume

Trim

Stern wedge angle

The author would like to dedicate this paper to the

late Sir Christopher

Sydney Cockerell (1910 to 1999),

the inventor

of

that remarkable form of high-speed marine transportation, the hovercraft, or air-cushion vehicle. The first large person-carrying machine, the SRN1, was launched forty years ago in May 1959. Be-cause the hovercraft possesses virtually no frictional resistance and low wave resistance, it is still the marine vehicle which can claim the highest transport factor or efficiency for calm-water operation.

1 Introduction

1.1 Background

In recent years, considerable interest has been shown in reviving the trimaran concept. The justifica-tion for the expenditure of research and development effort on this type of vessel is as follows: the essential claim is that a very slender monohull would exhibit the lowest overall resistance, particularly at high speeds, when compared with either the traditional monohull or the catamaran, However, the optimal monohull is so slender that it would be laterally unstable. Hence, the design must be slightly compromised by adding sidehulls with a displacement which is relatively small compared with the displacement of the main hull.

To better understand the philosophy of the de-velopment of vessels with more than one hull or sub-hull, it is worthwhile to consider some of the literature on the most ‘traditional” of modern multihull vessels, the catamaran. An example of research in this area is the work of Everest (1968), who reported results of both towing-tank resistance experiments and compu-tations. He expounded on the matter of interactions between the wave systems generated by the two demi-hulls, as well as viscous interactions between them. Good agreement was achieved between the predictions and the measurements.

Turner and Taplin (1968) did their experiments on a catamaran whose demihulls were laterally asymmet-ric. It is thought that this feature was selected in order to minimize vortex shedding at the demibows due to cross-flow effects. Laterally symmetric demihulls were also tested and these were found to be better in terms of resistance at lower speeds only,

The importance or otherwise of demihull asymme-try was also the subject of work by Yokoo and Tasaki (1969a and 1969b). Their conclusions appear to be somewhat different in that asymmetric hulls were sig-nificantly bet t er over the entire speed range, with re-spect to the total resistance. Pien (1976) studied both catamarans and smrdl-waterplane twin-hull (SWATH) ships in his work. Unozawa and Shimizu (1977) con-centrated their efforts on other design aspects, such as seakeeping and structural loads — rather than on the resistance alone. Kusaka, Nakamura, and Kunitake (1980) analyzed a SWATH, with a view to minimiz-ing the wave resistance. They developed optimal hull forms, based on the wave-resistance theory of Michell (1898).

More recently, Doctors (1991) did a series of calcu-lations for both resistance and motions of catamarans. In that work, he showed that by increasing within rea-son the slenderness of the demihulls, one could gener-ally reduce both the overall resistance of the

catama-ran as well as its response in head seas. Following that effort, Doctors, Renilson, Parker, and Hornsby (1991) presented the results of an investigation into a modern ferry catamaran, the RiverCat, which is characterized as having very slender hulls. They demonstrated that the traditional thin-ship theory could be used to good effect to predict the resistance behavior of this full-size vessel.

The monohull has not escaped the attention of latter-day researchers in the quest to discover im-proved forms, but now in much slenderer forms in or-der to minimize its resistance. It has been been gener-ally shown that as the length of the vessel is increased beyond that traditionally considered acceptable, so the wave resistance is reduced and the frictional increased is increased, as would be anticipated if the displace-ment is to be maintained constant during this stretch-ing process. The optimal length for the minimal total drag is much greater than that normally chosen. Un-fortunately, such optimal lengths lead to vessels which are laterally unstable, It has been suggested that this problem can be solved by using small outriggers; a cu-rious example is the Super Outrigger vessel proposed by Daniel and Daniel (1990). This vessel would employ a single outrigger on one side, which has the advantage of possessing less resistance than the more obvious lat-erally symmetric layout requiring two such outriggers. Slender monohnlls were also the subject of research by Jullumstr@, Leppanen, and Sirvi6 (1993), who con-firmed the necessity for large values of the slenderness coefficient in order to reduce the resist ante.

In recent years, considerable interest has been dis-played in trimaran designs. The general philosophy supporting this investment of research effort,

as

noted above, is that from a purely hydrodynamic-resistance point of view, the slender monohull appears to be the best choice. The outriggers are added only to provide lateral static stability. Therefore, the ques-tion is how one can minimize the severe drag imposed by the sidehulls, which is caused by their large wet-ted surface in relation to the gained buoyancy. An early paper following this path was written by Wil-son and Hsu (1992). Different longitudinal positions of the sidehulls were considered,

as well as

different hull forms. These concepts were analyzed within the framework of linearized ship-resistance theory, with the aim of gaining favorable wave interferences be-tween the hulls. Towing-tank experiments were also conducted and these verified their theoretical predic-tions. Similar work was done by Suzuki and Ikehata (1993), in which five different positions for the two sidehulls were examined.

Summers and Eddison (1995) carried out a care-ful investigation on a trimaran frigate which not only

z z z

A

Z-kA’-

I

I

Figure

1: Definition

of the

Problem

(a) Principal

Dimensions

z

_{Blended-stern parent}

_hull

&

Figure

1: Definition

of the

Problem

(c) Blended-Stern

Parent

Hull

included the matter of resistance, They were also concerned about motions and safety after a specified amount of damage, They demonstrated distinct re-sistance advantages in comparison with conventional monohulls as well as reduced pitching in head waves. Work on the same project was reported by Pattison and Zhang (1995) and Andrews and Zhang (1995). The last two papers included a brief history behind the trimaran concept and mention was made of one of the early examples in recent times, the Ihm Voyager. Trimarans with slender main hulls were also studied by Li, Tieli, and Huang (1993). Not unexpectedly, their theoretical predictions also indicated a lower resistance for the trimaran compared with that of a standard monohull. Furthermore, they showed that the relative position of the sidehulls was not a major factor in the design. A similar investigation was done by Lindstri5m,

Pointed–stern parent hull

Figure

1: Definition

of the

Problem

(b) Pointed-Stern

Parent

Hull

%

A Transom-stern parent

hull

Figure

1: Definition

of the

Problem

(d) Transom-Stern

Parent

Hull

Sirvio, and Yli-Rantala (1995).

A very extensive experimental study was reported by Ackers, Michael, Tredennick, Landen, Miller III, Sodowsky, and Hadler (1997). In this study, a sys-tematic set of towing-tank tests was conducted, in which the sidehulls were positioned in several locations both longitudinally and laterally at different Froude numbers. They supplied a number of contour plots providing data on the interference effects on the re-sist ante. For one particular configuration, they too demonstrated the superiority of this trimaran in com-parison to the equivalent frigate, at the higher speeds being contemplated.

One of the most mathematical optimization stud-ies was that of Lazauskas and Tuck (1998). They con-sidered a number of layouts of the subhulls. These lay-outs included laterally symmetric catamarans,

Item Condition

Trim

Stern wedge angle

Waterline length

Displacement

mass

Block coefficient

Prismatic

coefficient

Slenderness coefficient

Length-to-beam

ratio

Symbol P 6 L A cB Cp L/V~/3 L/B

Units

degrees degrees ; 3 0.0 6 1.771 10.84 0.5696 0.7483 8.000 12,94 Values 6 0.0 6 1,754 7.949 0.5238 0.7230 8.784 13.05 9 0.0 6 1.731 5.059 0.4485 0.6758 10.08 13.18

Table

1: Geometry

of the

Test

Demihull

in Three

Conditions

Item

Parent

Type of stern

Waterline length

Waterline beam

Draft

Displacement

mass

Block coefficient

Prismatic

coefficient

Slenderness coefficient

Symbol L B T A cB Cp L/@/~ Length-to-beam ratio \ LIB

units

m

m

m

t

Values

1

Pointed

30.0 2.000

1.631

50.0 0.4984 0.6174 8.210 15.0 2 Blended 30.0 2.000 1.527 50.0 0.5325 0.6671 8.210 15.0 3 Transom 30.0 2.000 1.353 50.0 0.6011 0.7630 8.210 15.0

Table

2: Geometry

of the

Three

Parent

Monohulls

bium catamarans (in which the two demihulls are stag-gered longitudinally), and tetramarans (where the sub-hulls were positioned in a diamond pattern). Some very impressive reductions in wave resistance at quite specific speeds of operation were demonstrated; these hulls would show promise in river operations provided their unorthodox appearance would be acceptable to the public.

A novel idea was proposed by Gee, Dudson, Marchant, and Steiger (1997). Their pentamaran in-volves a total of four sidehulls, with two of these side-hulls normally just clear of the water. The displace-ment of all four of the sidehulls is very low, so that the drag penalty for the first two sidehulls in normal operation is very low for this concept. The additional two sidehulls only become immersed during large an-gles of heel, when an additional margin of stability is required.

The underlying purpose in all of this research, of course, is the drive to improve the so-called transport efficiency oft he vehicle. The hydrodynamic transport efficiency is essentially the ratio q = W/R, where W is the weight of the vessel and R is its resistance. Thus, over three decades ago, Lackenby and Slater (1968) compared the advantages of different types of

mono-hulls, catamarans,

and trimarans.

They were able to

demonstrate

advantages

of the trimaran

with respect

to resistance,

at Froude numbers

of around 0.4.

Nu-merical optimization of the hull forms has been done by a number of researchers. Recent examples include Pal and Doctors (1995) and Pal, Peacock, and Doctors (1999). Doctors and Day (1995) employed the genetic algorithm (GA) combined with an efficient representa-tion of the wave resistance, wherein most of the actual computation could be effected separately from the op-timization procedure. Gawan-Taylor (1996) presented resistance comparisons of monohulls and catamarans in which the basis of comparison was an equal payload capacity.

Day, Doctors, and Armstrong (1997) did an ex-haustive genetic-algorithm comparison between mono-hulls, catamarans, SWATHS, semi-SWATHs, hover-craft, and surface-effect ships. The calculations, which were applicable to calm water only, clearly showed that the hovercraft was superior, because of the absence of hydrodynamic frictional resistance. For similar rea-sons, it was shown that the monohull was better than the catamaran. The subject oft ransport efficiency was the core topic of the workshop, whose proceedings were reported by McKesson (1997). It was re~eatedlv noted

that the key to high-speed long-range efficient trans-portation lay in improving this quantity; if a vessel possessed a low transport efficiency, it simply could not carry a sufficient quantity of fuel to reach its des-tination.

1.2 Current Work

The work to be reported on here is devoted to a large set of parametric calculations in which the three basic displacement-ship concepts, the monohull, cata-maran, and the trimaran, are to be evaluated. Thus, it can generally be stated that the present aim is to recompute the cases considered by some of the above-mentioned researchers. However, the additional int en-tion here is to systematically analyze a large range of lengths of the vessel types. Moreover, the methods to be used here will enable transom-stern hull forms to be studied — as well as hulls with a pointed stern.

The computations are carried out on vessels of two displacements. The first vessel has a displacement of 50 t and may be considered to be a generic river ferry with a size similar to that of the RiverCat. This ves-sel operates on the Parramatta River leading to Syd-ney Harbor and was described by Doctors, Renilson, Parker, and Hornsby (1991). The two main concerns here are the wave generation (because of the question of wave damage to the river banks) and the total re-sistance (because it affects the powering). The second vessel has a displacement of 10,000 t. This vessel rep-resents a possible candidate for a SeaLift ship in which the total resistance only is the quantity to be reduced.

2

Theoretical

Techniques

2.1 Thin-

Ship Analysis

Figure l(a) depicts a hull at the free surface of the water. There will be a hollow in the water behind the vessel in the case of a transom stern. The thin-ship theory of Michell (1898) will be employed in the analy-sis. Improvements by Lunde (1951) which incorporate restrictions of the width of the canal and the depth of the water are also included. The method of modeling the flow in the region of the transom, which was devel-oped by Doctors and Day (1997), will also be utilized here. Further details of the computer representation of the hull were described by Doctors (1993).

For the purpose of this exercise, a typical modern high-speed transom-stern parent hull was chosen. This is shown in Figure 1(d). This hull is characterized by possessing a single chine and having a transom stern, A fore-aft symmetric vessel was created by re-using the bow section at the stern. This vessel is known here as the pointed-si?ern parent hull and is shown in Fig-ure 1(b). Finally, a vessel, which is midway between

these two extreme cases, is depicted in Figure l(c). This is referred to as the blended-dern parent hull. It was created using the method of Doctors (1995). 2.2 Verification of Theory

We start by presenting some data for the model hull shown in Figure l(d). This was tested in the tow-ing tank as a catamaran. The geometric details of the test model demihull are presented in Table 1. The vessel was run in a total of nine conditions. Varia-tions included differing displacements, differing static trims, and differing amounts of transom-stern wedge. The computer program described by Doctors (1995) was used to merge the original vessel with either 070, 100%, or 150?lo of the angle of a 4° standard wedge. The three principal loading conditions are presented in Table 1.

In addition, the beam of the catamaran model was specified through the centerplane-to-centerplane spac-ing of 0,4133 m, while the towing tank had a width of 3.50 m and was filled to a depth of 1.5 m. Fig-ure 2(a) shows the components of resistance for the catamaran model tested in Condition 6. The curves show respectively the experimental data for the total experimental resistance, the wave resistance, the hy-drostatic drag (due to the lack of water pressure on the transom), the frictional resistance, and the total theoretical resistance. It is seen that the correlation at Froude numbers greater than about O.4 is excellent. The Froude number is defined as F = U/~, where U is the speed of the vessel, g is the acceleration due to gravity, and L is the waterline length of the ves-sel. In these calculations, the frictional resist ante was calculated according to the 1957 International Towing Tank Committee (ITTC) formula, described by Lewis (1988, Section 3.5). The correlation allowance CA was zero.

Figure 2(b) compares the total resistance for all of the three loading conditions shown in Table 1. The predictions are seen to be too high at low speeds due to the fact that the stern has been assumed to be “run-ning dry”. For this work, the low-speed theoretical model of Doctors ( 1998b) was not employed, as it has little bearing on the predictions at the Froude num-bers of interest. In the same vein, correction factors for the wave resistance and for the frictional resistance, such as promoted by Doctors (1998a), were not ap-plied, because there is more than sufficient accuracy here without their use.

2.8 Parent Hull Forms

The three principal parents are depicted in the last three parts of Figure 1, The corresponding geometric data is shown in Table 2.

0.2

Curve Comp L= 1.75 m 000 0 T,E

L/Vi/s =

a78

---

_w

_{tine = I’Tl’C}

o.15- _______

_H

_CA

₌

_o

0 ~ ———. — F w

0.1– stirn

=’TmmOm

Nbd

=

2 / / 0.05-/ <--- ,---#.,. -~.% wc-7fi ---0 _{I I} I 1

0

0.2 0.4 0.6 0.8 1 F 0.2

Curve

L/Vi/8

Comp

0000 8 T, E o ❑ 00 / a 8.78 T, E o

0.15-

0000 _{10.1 T, E o 04} ~ ---.._--- _{B T} w ---—-—— _{8.78 T} 0 ~&&”” 0.1

10.1

T

_,.

_--

/:.%-0

0.2 0.4 0.6 0.8 1 F

Figure2:

Test

of Computer

Program

(a) Resistance

Components

Y Y 4r— z “t===”

=l==-x=l

--”

Y Y

Figure

3: Layout

of Multihulls

(a) Identical

Subhulls

2.4 Generation of Hulls to be Analyzed

Six different chdd hulls were created from each of the three parent hulls in Table 2, by simply scal-ing the beam and draft in unison. By this is meant that the beam-to-draft ratio of the subhulls B/T is

kept fixed during this stretching

process. In this way,

these

hulls, or subhulls, could be employed to construct monohulls, catamarans, trimarans, tetramarans, pen-tamarans, and hexamarans, while maintaining the dis-placement A constant at 50 t for use as the river ferry. The layouts of the regular multihulls are shown in Figure 3(a). The overall centerplane-to-centerplane spacing for the multihulls was chosen to be 10.0 m. That is to say, the overall spacing-to-length ratio for the parent-hull configuration is 0.3333. Also shown, in Figure 3(b), are sidehull trimarans, which will be discussed in detail later.

Figure

2: Test

of Computer

Program

(b) Comparison

of Three

Hulls

‘-

1-‘ I c z x

Figure

3: Layout

of Multihulls

(b) Sidehull

Arrangement

3

Numerical

Experiments

9.1 River

Vessel

The two parts of Figure 4 show the wave resistance Rw

and

the total resistance RT for the pointed-stern river vessel with a displacement of 50 t. The results have been computed for six values of the speed given by U =

10.0( 1.0)15.0 m/s.

That

is, the mean value

~ is 12.5 m/s and the range AU is 5.0

m/s. The plotted data represents the mean of the corresponding resistance values.

One can see the very favorable effect on wave re-sistance by increasing the length. This is true for all the multihulls shown. On the other hand, Figure 4(b) indicates that the total resistance drops as the length increases only for the monohull, where one can observe that the optimum length is at least 50 m. The

multi-288

0.06

Stern = Pointed I Curve INh Fixed = B/T ---

1

0.04

1

A

.

6ot

u

—-——.—-

2 Line = I’ITC ————— s

CA

=

0.0004

4

k“”og ‘“..

u=

125

m/s ‘.\ ~ ‘.. AU = 5 m/a 0.02 – ‘.. =.

0.01-o~

B()

95

40

46 60 66 60 Lm

Figure

4: Length

for Pointed-Stern

River

Vessel

(a) Wave

Resistance

----m

Curve

N

---

₁

0.04 ---——

2 ——. .— ₃

r

4 %00S ,, ‘. ‘1 ‘. w ‘. 0,02 ‘., Stern = Blended Fixed = B/T A . 60t Line = Ill’(l CA = 0.0004 u= 126 m/s AU = 6 m/a

30

36

40

46

60

66 60 Lm

Figure

5: Length

for Blended-Stern

River

Vessel

(a) Wave

Resistance

hulls all show greater total resistance than that of the monohull. The total resistance of the multihulls usu-ally increases with the length. This outcome follows from the fact that the large wetted-surface area is the essential deficiency of a multihull.

Similar conclusions can be drawn for the blended-stern vessels in Figure 5 and the transom-blended-stern vessels in Figure 6,

By way of summary, Figure 7 represents a cross plot of the influence of the number of subhulls Nhull on the wave resistance and the total resistance for the thirty-meter river vessel. There is no doubt that the catamaran is superior to the monohull, because the wave resistance is less and there is little penalty in terms of the total resistance. On the other hand, if other factors (structural and operationrd) permit, the sixty-meter vessels in Figure 8 are seen to be much

0.08 –_{.—— ——————__} ——-—- __ ———-— — ;

I--n:----. -_.___-.---j

1

----~“”w

---4

---Stern = Pointed %; 04 Fixed = B/T A . 6ot Curve N Line = ITTC --- 1

0.02- CA

= 0.0004

—----—-

2

u=

126

m\e ————. _s o AU = 5 mle 4 I I I I I

30

S6

40

46 60 66 60 Lm

Figure

4: Length

for Pointed-Stern

River

Vessel

(b) Total

Resistance

0.1

0.08-

—--—————

.——

————————————-0.02- CA = 0.0004 ———---- 2 u=

126

m\s ————. 3 0 AU = 6 m/s 4 I I I I I

so

96

40

46 so 65 60 Lm

Figure

5: Length

for Blended-Stern

River

Vessel

(b) Total

Resistance

superior in terms of the wave resistance, while only a small pemdt y in total resistance is apparent.

3.2

SeaLift

Ship

We now proceed to a larger vessel in order to

illus-trate the question of scale. As an example, we assume

the vessel to have a displacement

of 10,000 t, implying

that the length and the other linear dimensions should

be greater by the factor 5.8480. The operational

speed

U and the speed range AU have been Froude-scaled

from the values pertinent

to the river ferry. Figure 9

shows the effect of varying the length on the total

re-sistance for two of the parent

hulls.

As

in the case of the (smaller) river vessel, we observe that if the resis-t anresis-te were resis-the only criresis-terion in the design of a ship, then the monohull is best — provided that there is no 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} ‘k -t -.. AU = 5 m/8 @o.02 ‘“..

o~

30

3s

40

4s

50

65

60

Lm

Figure

6: Length

for Transom-Stern

River

Vessel

(a) Wave

Resistance

0.06

Cuwe St.arn Fixed = B/T

--- Pointed L . SOm

0.04- ---– Blended A .

50 t

Tranmm Line = ITTC

CA

0.03- ;.

= 0.0004

&

\’.

u=

12.5

m/e AU = 6 m/n . --.- . . . ..-. C

0.01

1

Figure

7: Number

of Subhulls

for Thirty-Meter

River

Vessel

(a) Wave

Resistance

that the catamaran or the trimaran can compete.

3.3 Calculation

of Friction

Because the frictional resistance is such an

impor-tant factor, it was decided to recompute some of the

re-sults

using the 1947 American Towing Tank Commit-tee (ATTC) formula, which was developed by Schoen-herr (1932). In a separate numerical experiment, the correlation allowance CA was set to zero, rather than the more usual value of 0.0004.

The two parts of Figure 10 pertain to the monohull and the cat amaran, respectively. It can be seen that there is no discernible difference between the ITTC and the ATTC computations. On the other hand, the importance of the correlation allowance is clear. These results show that an excellent improvement in the performance of around 23?40for the monohull and

~ Stern = Transom %; 04 Fixed = B/T A . 60t Line = ITTC

0.02- CA

=

0.0004

u=

126

m/n o AU = 5 m/e 1 I I

d

Curve N --- ₁ ---

₂

.—.

——

₃

4

so

36 40 46 60 66 60 Lm

Figure

6: Length

for Transom-Stern

River

Vessel

(b) Total

Resistance

~O’M

1

Fixed = B/T $Ow L = 90 m A .

50 t

Line = ITTC

0.02 CA

= 0.0004

-u=

126 m/e --- Blended 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

River

Vessel

(b) Total

Resistance

25% for the catamaran (for a length of 350 m) could be achieved, simply by maintaining vessels with a hy-draulically smooth surface finish.

9.4 Comparison of Sidehull Trimarans

It would seem certain from the above comparisons and discussions of the resistance qualities of the multi-hulls, that sidehull-trimaran arrangements wilJ exhibit a behavior that can be anticipated in a simplistic man-ner and that there are unlikely to be any surprises. That this is indeed so will now be demonstrated.

Some sidehull trimarans patterned after the con-figurations depicted in Figure 3(b) were evaluated. In all cases, the sidehulls were each assigned a displace-ment equal to 107o of the total, while the main, central, hull supported 80% of the total. To simplify this in-vestigation, the three linear dimensions of the sidehulls

““””

Fixed = B/T L . 60 m 0.04- ii= 50t Line = ITTC = 0.0004 k0.09- := 125 m/s ‘k AU = 5 m/s @

0.02-0.01

i

——. ——

0

I I I I I

1

1

2

s

4

6

6

Figure

8: Number

of Subhulls

for Sixty-Meter

River

Vessel

(a) Wave

Resistance

0.1

Stern = Pointed Fixed = B/T

‘“081

~

ILine

.—— ————.— ——___ ——-— ——-

-1

---u=

-d

.--_

_----

-___________-_—

_---

_---

---.

1000Ot

Cuwe N . ITIC --- 1

0.02- CA

= 0.0004

———--—- 2

t?=

S0.29m/s

.—— —.

s

o

AU = 1209 m/sI I I 4 160 200 260 800 S60 Lm

Figure

9: Length

for SeaLift

Vessel

(a) Pointed-Stern

were made equal to 50% of the corresponding linear di-mensions of the central hull. That is, all three subhulls were geosims of each other. The sidehull centerplane-to-centerplane spacing was chosen to be the same as that for the two outer subhulls in the previous calcu-lations.

Figure 11 shows the wave resistance and the total resistance for four concepts, as follows: the monohull, the catamaran, the sidehull t rimaran (with the sterns of all the subhulls aligned with each other, r/.L = O), and the sidehull trimaran (with the sterns of the side-hulls shifted forward 25% of the length of the central hull, r/L = 0.25). Regarding the wave resistance in Figure 11(a), we see that the two sidehull trirnarans differ very little from each other in terms of their wave resistance, indicating that wave-interference effects be-tween the three subhulls certainly exist but are not

0.1

008-~“’w

Fixed = B/?’ &iw L . _{60 m} A . 50 t

“f=3=LE%

1

2

3

4

s

6

Nhti

Figure

8: Number

of Subhulls

for Sixty-Meter

River

Vessel

(b) Total

Resistance

0.1

Stern = Blended Fixed = B/T OIAU = 12.09 m/m 4 I I I I

1s0

2(io

260

800

S60

Lm

Figure

9: Length

for SeaLift

Vessel

(b) Blended-Stern

overly significant. One can detect a small improvement for the sidehull trimararis compared to the monohull, but the catamaran is still better. Turning now to the total resistance in Figure 1 l(b), one sees that the fric-tional resistance component results in the generally poorer behavior of the sidehull trimarans. Inciden-tally, the difference between the two

aidehull

trimarans is the same for both parts of Figure 11. This is be-cause there are no interferences between the frictional effects on the three subhulls according to the theory used here.

Finally, Figure 12 shows the corresponding com-parison for the blended-stern sidehull trimaran and Figure 13 shows the same results for the transom-stern sidehull trimaran. Once again, the calculations show that sidehull trimaran suffers from excessive frictional resistance — at least in the present case.

01..- 01 0.0s Stern = Blended r Curve Fixed = B/T ---Nbti =

1

. . . .

Line ITI’C A’Tl’C 11”1’C

1

c 0.0004

0.0004

0

002- A= 1000O t

u=

90.23

m/8 o AU = 12.09 m/s I I 1 150 200 2s0 300 Sso Lm

Figure

10: Calculation

of Frictional

Resistance

0.1

0.08

~o.od

+04

0.02

0

(a) Monohull

Stern = Pointed Fixed = B/T A . 100CX3t Line = ITTC CA = 0.0004 u= S0.2S m/a AU = 1209 m/a Curve

I

Nhd

I

r/L ---—--. —--.—— —— 1 0

2

0

3

0

s

0.26

<. -.. --- ---—-.=-==

m-150

200

250

Soo

360

Lm

Figure

11: Comparison

of Pointed-Stern

Concepts

(a) Wave

Resistance

3.5 Importance

of Scale

Because the SeaLift vessel has been Froude-scaled from the river vessel, it may be stated that the di-mensionless wave resistance for these two sizes will be the same when plotted as a function of the volumetric Froude number Fv = U/~~.

On the other hand,

the specific, or dimensionless,

total resistance

R~/W

for the larger

vessel will be less. This is because the frictional-resistance coefficient drops as the Reynolds number increases.

This feature is illustrated in Figure 14(a), for the monohull and the catamaran, and in Figure 14(b) for the trimaran and the tet ramaran. The reduction in total drag-to-lift ratio is substantial. At a volumet-ric Froude number of 2.5, the reduction is respectively 1370, 19’Yo,17Y0, and 2070 for these four vessels. Fur-thermore, these calculations emphasize the fact that

1

‘“

IEEE

‘-- Stern = Blended Fixed = 00s Nhw =

~“’w

1.

---

---

---

---hi:~

1

0.02 A

=

1000Ot

v=

90.2S

m/e o IAU

_I

=

12.09m/e

_I

_I

_I

160

200

260

Soa

360

Lm

Figure

10: Calculation

of Frictional

Resistance

(b) Catamaran

Cuwe -.---——— —---—————

T1

N r/L 1 0 2 0 9 0 9 0.2s

P----:

‘. ____

~“’m

--.-

-=.---___________=

_----

~

_

——

k4:04

--- ---

---AL

160

200

2s0

900

350

Lm

Figure

11: Comparison

of Pointed-Stern

Concepts

(b) Total

Resistance

improvements

in performance

can be derived purely

by increasing the size of the vessel. It

that Templeman and Kennell (1999) conclusions.

4

Concluding

Remarks

4.1 Current

Work

should be-noted came to similar

The present research allows us to conclude the fol-lowing points:

1. Increasing the length of the vessel beyond that normally considered appropriate is beneficial, if the intention is to reduce wave generation at volu-metric Froude numbers of around 2.088. The cor-responding slenderness coefficient for the mono-hull is 16.38;

0.1

0.08 0.06 k 3 @ 0.04 0.02 0 Stern = Blended

I

curve

I~h~

I

r/L Fixed = B/T --- 1 0 A .

1000Ot

I

---I 2 I 0 Line = ITTC ————— 9 0

CA

=

0.0004

9

I026

u=

30.23m/e

AU =

1209 m/s

~. --- ---150 200 250 Soo

950

Lm

Figure

12: Comparison

of Blended-Stern

0.1

0.08

~o.od

GO04

0.02

0

—

Concepts

(a) Wave

Resistance

Stern = Tranaom Fixed = B/T A .

1000Ot

Line = ITTC CA = 0.0004 u= S0.29 m/a AU = 1209 m/a Curve INhti Ir/L

---1

1 I 0 —-—--—— _{2 0} ---+

3 /

o

s I 025 ----

--150

200 250 900 Sso Lm

Figure

13: Comparison

of Transom-Stern

2.

3.

4.

Concepts

(a) Wave

Resistance

For the range of lengths considered, the catama-ran is superior to the monohull in terms of wave generation. This has important implications when selecting a ferry type for operation in rivers; If the vessel must be restricted in length to cur-rently accept ed values, then the t rimaran offers a reduced wave resistance of around 19!Z0compared to the catamaran and 53% compared to the mono-hul. At somewhat greater lengths, trimarans, tet ramarans, pentamarans, and hexamarans per-form no better than catamarans in terms of wave generation;

Regarding total resistance, the monohull is almost always superior to any of the multihulls. Possible exceptions would occur only at the lower lengths, when the catamaran is marginally superior.

---I

2 I c .—— —— _{3 (}

1=

‘.

3 ] o.2f

-..

_

~“”m

.-.~.- -- ________-_=

————

—-

----4;.04

--- --- ---

.

L

ALine =

.

0.02 CA = u= o AU =

1000Ot

ITTC 0.0004 302S m/a 12.09 m/s I I I

150

200

2s0

300 950 Lm

Figure

12: Comparison

of Blended-Stern

0.1

0.08 jkO”M GO~ 002 0

293

Concepts

(b) Total

Resistance

:-~ ~ -.--: -- ___ ---G -- .--— =-—.= _—_--— Stern= Transom --- ---Fixed = B/T A . 1000Ot Line = ITTC ~

CA

=

0.0004

—---

2

0

u=

90.29

m/a —— —.. _{3 0} AU = 1209m/s 3

0.26

I I I

150

200 250 SOo S50 Lm

Figure

13: Comparison

of Transom-Stern

5.

6.

7.

Concepts

(b) Total

Resistance

The sidehull trimaran

is marginally

superior

to

a monohull in terms of wave resistance,

but its

performance

at the same length is not as good as

that of the catamaran;

Regarding

total resistance,

the sidehull trimaran

is inferior to both the monohull and the

catama-ran at currently

acceptable

lengths.

If greater

lengths

can be tolerated,

one might be able to

make a case for sidehull trimarans

over

catama-rans.

Frictional

resistance is seen to be a major

stum-bling block if the intention

is to obtain ~ransport

factors exceeding

20 at high volumetric

Froude

numbers of around 2.088. Large reductions in

to-tal

resistance can ideally be achieved by maintain-ing a hydraulically smooth hull surface.

4.2 Future Work

Future work can be concentrated on the details of the hull shape, more along the lines of traditional hull-optimization techniques. However, it would seem difficult to achieve any remarkable gains, given the re-quirement to travel at the abovementioned high volu-met ric Froude numbers.

The wave resistance is a weak function of the cross-sectional shape for slender hulls, so it would seem nec-essary to aim for semicircular sections that will mini-mize the wetted-surface area for any given volume of displacement.

Because of the clear superiority of the monohull at the higher speeds, one can make a strong case for avoiding the multihull concept altogether, if total re-sistance, rather than wave resistance, is the key design consideration. Because such slender monohull vessels are laterally unstable, one must also argue the merit of artificially stabilized slender monohulls, as a means of improving the transport efficiency for displacement vessels,

Acknowledgments

This work was supported by the Australian Re-search Council (ARC) Large Grant Scheme through grant number A89917293 and The University of New South Wales (UNSW). The author wishes to express his gratitude to both of these institutions for this sup-port.

The author would also like to thank various naval architects working in the Australian high-speed ferry design and construction industry for their valuable dis-cussions which provided the background ideas for the work presented in this paper.

References

ACKERS, B. B., MICHAEL, T. J., TEEDENNICK, O.w,, LANDEN, H. C., MILLER III, E, R., SODOWSKY, J. P., AND HADLER, J. B.: “An In-vestigation of the Resistance Characteristics of Powered Trimaran Side-Hull Configurations”, Truns. Society of Naval Architects and Marine h’ngineers, Vol. 105, pp 349-368, Discussion: 369-373 (1997) ANDREWS, D.J. AND ZHANG,

J.-W.:

“Considera-tions in the Design of a Trimaran Frigate”, Proc.

International

Symposium on High-Speed Veaaela for ZYansport and Defence, Royal Institution of Naval Ar-chitects, London, England, pp 15- 1–15-21 (November 1995)

DANIEL, N,I. AND DANIEL, H. E.: “SuperOutrigger: Less Pitch, Less Roll, Less Drag, Less Cost, Less

Com-plex”, Proc. Seventh International High-Speed Surface Craft Conference, London, 19 pp (January 1990) DAY, A. H., DOCTORS, L. J., AND ARMSTRONG, N. A.:

“Concept

Evaluation

for Large

Very-High-Speed Vessels”,

Proc. Fourth International Confer-ence on Fast Sea Transportation (FAST ‘97), Sydney,

Australia,

Vol. 1, pp 65-75 (July 1997)

DOCTORS, L. J.:

“Some Hydrodynamic

Aspects

of

Catamarans”,

Thans. of Mechanical Engineering,

In-stitution

of Engineers,

Australia,

Vol. ME 16, No. 4,

pp 295-302 (December 1991)

DOCTORS, L. J.:

“HYDROS: Integrated

Software for

the Analysis

of the Hydrostatics

and

Hydrodynam-ics of Marine Vehicles”,

Proc. Tenth International Maritime and Shipping Symposium (ShipShape 2000),

University of New South Wales, Sydney, New South Wales, Vol. 1, pp 373-392 (November 1993)

DOCTORS, L. J.: “A Versatile Hull-Generator Pro-gram”, Pmt. Twenty-Fimt Century Shipping

Sym-posium, University of New

South

Wales,

Sydney,

New South Wales, pp 140-158, Discussion:

158–159

(November 1995)

DOCTORS, L. J.:

‘Intelligent

Regression

of

Resis-tance Data for Hydrodynamics

in Ship Design”,

PTOC.

Twenty-Second Symposium on Naval Hydrodynamics, Washington, DC, 16 pp (August 1998)

DOCTORS, L, J.: “An Improved Theoretical Model for the Resistance of a Vessel with a Transom Stern”, PTOC. Thirteenth Awtmlasian Fluid Mechanics Con-ference (19 AFMC), Monash University, Melbourne, Victoria, Vol. 1, pp 271-274 (December 1998) DOCTORS, L,J.

AND DAY, A. H.: ‘Hydrodynamically

Optimal Hull Forms for River Ferries”,

Proc. Interna-tional Symposium on High-Speed Vessels for Thmwport and Defencej

Royal

Institution of Naval Architects, London, England, pp 5-1-5-15 (November 1995)

DOCTORS, L.J.

AND DAY, A. H.:

“Resistance

Pre-diction for Tkmsom-Stern

Vessels”,

Proc. Fourth In-ternational Conference on Fast Sea fiansportation (FAST ‘97),

Sydney, Australiaj

Vol. 2, pp 743-750

(July 1997)

DOCTORS, L.J,

RENILSON, M. R.,

PARKER, G.,

AND

HORNSBY, N.: “Waves and Wave Resistance of a High-Speed River Catamaran”, PTOC. First International Conference on Fast Sea l%ansporta-tion (FAST ‘91), Norwegian Institute of Technology, Trondheim, Norway, Vol. 1, pp 35-52 (June 1991)

EVEREST, J. T.:

“Some Research

on the

Hydrody-namics

of Catamarans

and

Multi-Hulled

Vessels in

294

0.1

Stem = Blended Fixed = B/T i

0.08 Nhti =

1 _--- ---i L-l- --- . -@-z=-0.06 ------- --- --y _.---:-2:-2---:-z:-- --w ---

---0.04

---s

--Curve L A ---1 SO m I 60t

0.1

Stern =Blended _/ Fixed = B/T 0,08 – Nhti = 2 0.06-~ % Curve L A ---.-- _SOml

_{60 t}

0.02- Line =

ITTC

–––--–-

175

10000

cA

=

0.0004

.—— —.

60

60

0

COmp= T

861

1000O

I

I

I I I I 1.7

1.8

1.9

2

21

22

2.9

2.4

2.5

FV

Figure

14: Importance

of Scale

of Vessel

(a) Monohull

0.1

0.08

0.02

0

,/- ----,/’ ,,~ ,/~- --- A==---.-% Stern = Blended Curve L A Fixed = B/T --- mom 60t Nhw = ?3

- –---– 17s 1000O Line = ITTC ————— _{60 60 CA =}

_0.0004

361

1000O

Camp = T I I I I I I

1.7

1.8 1.9 2 2.1 2.2 2s 2.4 2.5 FV m!—--—- .4- v--- , *“. *-..

E lgure

A*: ~pormnce

01 scale

01 (c)

‘lkimaran

Calm Water”, fiana. North Ewt Coast of Engineers and Ship budders,

Vol. 84, No.

vessel

Institution 5, pp

129-148, Discussion: D29-D34 (May 1968)

GAWAN-TAYLOB, P,: “Catamaran versus Mono-hull — Not the Final Word”, PTOC. Au8Marine ’96,

Fremantle, Western Australia,

5 pp (November 1996)

GEE, N.,

DUDSON, E,,

MARCHANT, A,, AND STEIGER, H.:

“The Pentamaran:

A New Hull Concept

for Fast Freight and Car Ferry Applications”,

Proc. Thirteenth Fast Ferry International Conference, Sin-gapore, 21 pp (February 1997)

JULLUMSTR@, E,, LEPPANEN, J., AND SIRVIO, J.: “Performance and Behaviour of the Large Slender Monohull”, PTOC. Second International Conference on Fast Sea l%anaportation (FAST ‘93),

Society of

0.02- Line =

rrrc

––––-–-

175

10000

C*

=

0.0004

————.

60

60

~

Comp = T 961

10000

I

I

I

I

I

I

I 1.7 1.8 1.9 2 21 22 2S 2.4 2.5 FV

Figure

14: Importance

of Scale

of Vessel

(b) Catamaran

0.1

/“

0.08- ,/’ -- ---- /-<---~b~- -H 0.06-w

0.04

Stirn = Blended

Cuwe

L A Fixed = B/T --- _30m

_{60 t}

_{Nhw =}

₄

().02- ---

175

1000O

Line = ITTC ——.—— _{60 60 CA = 0.0004} 0 I I961 I 1000OI I Comp =I I T

1.7

1.8

1.9

2

2.1

2.2

FV

Figure

14: Importance

of Scale

(d) Tetramaran

Naval Architects of Japan, Yokohama, pp 1477-1488 (December 1993)

2S 2.4 2.6

of Vessel

Japan, Vol. 2,

KUSAKA, Y., NAKAMURA, H., AND KUNITAKE, Y.: ‘Hull Form Design of the Semi-Submerged Catamaran Vessel”, PTOC. Thirteenth Symposium on Naval Hy-drodynamic, Tokyo, Japan, pp 555–565, Discussion: 566-568 (October 1980)

LACKENBY, H. AND SLATER, C.: “The Case for Mul-tihull Ships with Particular Reference to Resistance Characteristics”, PTOC. Diamond Jubilee International Meeting,

Society of Naval Architects

and Marine

En-gineers (SNAME), New York, 15 pp (June 1968)

LAZAUSKAS, L. AND TUCK, E. O.:

“Wave

Cancella-tion by Weinblum-Type

Catamarans

and

Diamond-Shaped

Tetrahulls”,

PTOC. Third Biennial

Engi-295