Ocean Engineering 53 (2012) 38–47

Contents lists available at SciVerse ScienceDirect

Ocean Engineering

0029-80

http://d

n Corr

E-m

fg.david

luis.per

journal homepage: www.elsevier.com/locate/oceaneng

Experimental assessment of interference resistance for a Series 60 catamaranin free and fixed trim-sinkage conditions

Antonio Souto-Iglesias n, David Fernandez-Gutierrez, Luis Perez-Rojas

Model Basin Research Group (CEHINAV), Naval Architecture Department (ETSIN), Technical University of Madrid (UPM), 28040 Madrid, Spain

a r t i c l e i n f o

Article history:

Received 24 February 2012

Accepted 3 June 2012

Editor-in-Chief: A.I. Incecikmore extensively with a Series 60 catamaran. The influence of the testing condition (fixed or free)

together with the influence of hull separation has been analysed. The relevance of these experimental

Available online 10 July 2012

Keywords:

Interference resistance

Interference factor

Series 60

Catamaran

Free trim

Fixed trim

Fixed sinkage

Free sinkage

Free model

Captive model

18/$ - see front matter & 2012 Elsevier Ltd. A

x.doi.org/10.1016/j.oceaneng.2012.06.008

esponding author. Tel.: þ34 913367156; fax

ail addresses: antonio.souto@upm.es (A. Sout

@gmail.com (D. Fernandez-Gutierrez),

ezrojas@upm.es (L. Perez-Rojas).

a b s t r a c t

The interference resistance of multihulls taking into account the test condition (fixed or free model) is

experimentally studied. Experiments have been carried out with a commercial catamaran model and

results in the separation optimisation techniques based on slender body flow solvers is discussed.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

A significant body of literature analysing multihulls hydro-dynamics (Chen et al., 2003; Insel and Molland, 1992; Migaliet al., 2001; Molland et al., 1996; Turner and Taplin, 1968; Yeunget al., 2004), mainly considers slender body simplifications andfocus on moderate and high speed regimes. Broglia et al. (2011)and Zaghi et al. (2011) use instead a Navier–Stokes solver tosimulate multihulls, finding a good agreement for the resistancevalues and describing complex interference effects at high Froudenumbers regimes.

Most of these analyses assume a fixed model conditionconsequently reducing the computational effort. This, combinedwith the slender body assumption, allows for the simulation of awider range of configurations in terms of separation and velocityfor a reasonable computational effort. With these types of codes,it is therefore feasible to set up a separation optimisation frame-work in early design phase (Moraes et al., 2007; Yeung and Wan,2007).

In Souto-Iglesias et al. (2007), the interference resistance ofmultihulls was analysed by assessing its relationship with the

ll rights reserved.

: þ34 915442149.

o-Iglesias),

shape and amplitude of the wave train between the hulls for aspecific commercial vessel design. The free model condition wasthen considered making it more difficult to identify interferenceeffects due to substantially different dynamic trims and sinkagesbetween the monohull and the catamaran. This case study isherein revisited by considering the fixed model condition.

In addition to the commercial vessel, a Series-60 (S60) cata-maran has been experimentally studied. Its hull shape signifi-cantly changes from the former, expanding the geometry typesanalysed. Although the S60 is a well known hull for experimentaland computational analyses (Todd, 1964; Kim and Jenkins, 1981;Toda et al., 1988, 1992; Nakatake and Takeshi, 1994; Tarafder andSuzuki, 2008), to the authors’ knowledge, its behaviour as amultihull has not yet been experimentally described and suchknowledge may be useful for CFD practitioners working onmultihull hydrodynamics.

In Yeung et al. (2004) the interference resistance of a S60catamaran was numerically studied neglecting trim and sinkageinfluences. They provided the value of the interference factor for awide range of separations and speeds and a significant insightinto the complexity of the multihull wave interference phenom-ena. Their predictions have been contrasted with experimentalresults in the present paper.

The paper is organised as follows: first, aiming at presentingthe problem and the notation, the interference resistance isdefined. Second, the commercial vessel case that was studied

Nomenclature

cat catamarancF friction resistance coefficientcT total resistance coefficientcw wave resistance coefficientDzbow variation of bow draft in free model condition (m)Dzstern variation of stern draft in free model condition (m)g gravity (m/s2)Fn Froude numberIF interference factorL length between perpendiculars (m)

mh monohulln kinematic viscosity (m2/s)RF flat plate friction resistance (N)RT total resistance (N)Rw wave resistance (N)RWmh wave resistance of monohull (N)RWcat wave resistance of catamaran (N)Re Reynolds numberS60 Series 60s separation (m)V velocity (m/s)

A. Souto-Iglesias et al. / Ocean Engineering 53 (2012) 38–47 39

under the free trim condition in Souto-Iglesias et al. (2007) isrevisited, this time, considering the fixed trim condition effect oninterference resistance. Third, a S60 catamaran is analysed com-paring the experimental data under fixed and free trim testconditions with the existing data found in the previously men-tioned literature. Finally, a summary of the drawn conclusionstogether with future works are provided.

Table 1Main dimensions of the case studies.

Main features Commercial vessel S60 Units

Length between perpendiculars (L) 2.208 2.500 m

Beam (mh) 0.238 0.333 m

Draft 0.120 0.133 m

Wetted surface (mh) 0.885 1.062 m2

Displacement (mh) 84.35 65.70 kg

Block coefficient 0.653 0.600

Length–beam ratio 9.28 7.51

Beam–draft ratio 1.98 2.50

Fig. 1. Commercial vessel model geometry and reference system.

2. Interference resistance

In multihulls, there is usually a strong interference betweenthe wave systems generated by each hull. This interference caneither be favourable or unfavourable to the global resistance ofthe hull. To properly characterise this effect, the interferencefactor IF is defined as the ratio of the difference between the waveresistance of the catamaran, RWcat , and twice the wave resistanceforce of a monohull, RWmh :

IF ¼RWcat�2RWmh

2RWmhð1Þ

Ideally, the value of the interference factor should be kept assmall as possible, negative if achievable (Yeung and Wan, 2007).

To correctly calculate the interference factor, the frictionresistance has to be subtracted from the total resistance obtainedin the experiments. Air drag and correlation allowance areconsidered negligible in the present analysis. The wave resistanceis obtained via the Hughes (Lunde et al., 1966) decomposition.

RT ¼ RWþð1þkÞRF ð2Þ

where k is the form factor, assumed identical for both themonohull and the catamaran cases. RF is the friction resistanceof a flat plate with equivalent wetted surface, computed from thefriction drag coefficient (CF) obtained via the ITTC 1957 correla-tion line formula:

cF ¼0:075

ðlog10ðRe�2ÞÞ2ð3Þ

There is a strong dependence between the wave resistance andthe value set for the form factor. This significantly affects theextrapolation procedure but moderately influences the value ofthe interference factor IF while maintaining its sign, the reasonbeing that the frictional components of the resistance cancel outin the numerator of Eq. (1). Therefore, establishing whether theinterference effects are favourable or unfavourable does notdepend on eventual uncertainties of the form factor computationprocedure.

The interference factor is sometimes defined considering thetotal resistance (Zaghi et al., 2011). According to the Hughesresistance decomposition, using the total resistance instead of the

wave resistance implies changing the denominator of Eq. (1) tothe total resistance, since as aforementioned, friction componentscancel out in the numerator.

The value of the interference factor is investigated in thepresent paper by looking at the influence of the testing conditionfor two vessels, namely a commercial vessel and a Series 60 (S60).The characteristics of both models are presented in Table 1.

3. Commercial vessel

3.1. General

This vessel is commonly used in the transport of goods and fishto and from a sea farm. The main dimensions of the model arepresented in Table 1. The reference system considered, thenotations describing the hull separation and the vessel geometryare shown in Fig. 1. The separation (s) is defined as the distancebetween each hull’s centreline, and is made nondimensional withthe length between perpendiculars (s/L).

The free model condition studied in Souto-Iglesias et al. (2007)was aimed at finding the relationship between the interference factor

A. Souto-Iglesias et al. / Ocean Engineering 53 (2012) 38–4740

and the amplitude of the wave system in between the two hulls.The present study completes the previously mentioned work byperforming tests in fixed model condition using this geometry, thuseliminating the effects of sinkage and trim movements. A photographtaken during the tests of this paper’s experimental campaign isshown in Fig. 2. Further information about this hull is included inSouto-Iglesias et al. (2007) including its 3D geometrical definition asan IGES file, provided as a supplementary material.

The following tests were carried out:

�

Monohull, free model � Monohull, fixed model � Catamaran, s/L¼0.388, in free model condition � Catamaran, s/L¼0.388, in fixed model condition

The separation (s/L¼0.388) was chosen for having the mostinteresting interference effects, as found in Souto-Iglesias et al.(2007). A test matrix comprising of the speeds shown in Table 2was initially devised. The speed range of main interest corre-sponds to Froude numbers between 0.2 and 0.4. For the Froudenumber 0.375 the experiment was repeated 5 times in order toassure that measurement uncertainties remain considerablysmaller than the interference effects to analyse. A collection ofextra velocities was run for the range 0.3oFno0.4 in order to

Table 2Froude numbers and velocities

considered for the commercial

vessel tests.

Point Fn V (m/s)

1 0.100 0.465

2 0.150 0.698

3 0.200 0.931

4 0.250 1.164

5 0.300 1.396

6 0.350 1.629

7 0.375 1.745

8 0.375 1.745

9 0.375 1.745

10 0.375 1.745

11 0.375 1.745

12 0.400 1.862

13 0.450 2.094

14 0.500 2.327

15 0.550 2.560

Fig. 2. Picture of commercial vessel-model test.

properly characterise the resistance hump. Videos of theseexperiments, provided as supplementary material, can be foundonline at http://canal.etsin.upm.es/ftp/2012/S60/

3.2. Results

The resulting experimental curves are presented in Fig. 3.It can be observed that there is a significant difference in theresults for the fixed and free model conditions, with the freemodel resistance being larger than the fixed model in all cases, asin Kim and Jenkins (1981) for a S60 monohull and Moraes et al.(2004) for the Wigley hull. With regard to the differencesbetween monohull and catamaran, the tendency in the monohullresistance is monotonic whilst a clear hump can be appreciatedfor the catamaran configuration. Focusing on the hump region,these characteristics are discussed in detail in what follows next.

In order to adequately estimate the interference factor for acontinuous range of Froude numbers, the resistance curves werefitted with NURBS (Fig. 4 left and right). In these figures, themarkers correspond to the raw experimental data. The interfer-ence factor refers to a comparison between wave resistanceswhich have been obtained from the total resistance following theprocedure described in Section 2 and considering a form factor of0.24. The form factor has been taken as the same for thecatamaran and the monohull. Fig. 4 left and right show thedifferences in wave and total resistance in the hump region(0.3oFno0.4) between the monohull and the catamaran forthe free and fixed model conditions respectively. It can be seenthat the wave resistance and the total resistance follow a similartrend, although as previously mentioned, the values remain lowerfor the fixed trim condition. Favourable interference regionscorresponding to those where the catamaran resistance is smallerthan twice that of the monohull can also be observed.

The interference factor is calculated from these data with theresults shown in Fig. 5. While it is apparent that the values aredifferent for 0.3oFno0.34, a very similar pattern is obtained forFn40.34. Overall, the tendency of the interference factors for thefree and fixed model conditions is similar, with some differencesin the IF values for the Froude numbers between 0.3 and 0.34.This fits with what was expected from analysing the trim anglesof the monohull and catamaran configurations in free modelcondition, as discussed in Souto-Iglesias et al. (2007).

Results regarding sinkage and trim are presented in Fig. 6.They are made nondimensional using the typical length V2/g(Eqs. (4) and (5)), as in Kim and Jenkins (1981).

Trim¼�ðDzbow�DzsternÞ2g=V2ð4Þ

Sinkage¼�ðDzbowþDzsternÞg=V2ð5Þ

Fig. 3. Total resistance of commercial vessel, s/L¼0.388.

Fig. 4. Total and wave resistance, commercial vessel, free (left) and fixed (right) conditions.

Fig. 5. IF of commercial vessel for test case s/L¼0.388.

Fig. 6. Sinkage and trim, commercial vessel.

Fig. 7. S60 catamaran model.

Fig. 8. S60 (Todd, 1964) body plan (black) and present study (red). (For interpretation

of the references to colour in this figure legend, the reader is referred to the web

version of this article.)

A. Souto-Iglesias et al. / Ocean Engineering 53 (2012) 38–47 41

This typical length is the characteristic wave length over 2p.Although the sinkage is significant (o10% of the draft), its behaviouris very similar for both the monohull and the catamaran. If we look atthe trim, absolute trim angles remain small (between �0.31 and 0.31,equivalent to 70.06 in the nondimensional trim from Fig. 6) withsmall variations. The trim angle reduction around Fn¼0.37 for thecatamaran may help in explaining the favourable interference foundin the free model condition for this velocity.

4. Series 60

4.1. General

The tests have been carried out with a Series 60 (Todd, 1964)catamaran (fig. 7). The model characteristics have been presentedin Table 1 together with those of the commercial vessel test case.The dimension ratios are fairly similar for these two vessels but

the hulls are significantly different:

1.

The S60 has no cylindrical section compared to a long one forthe commercial vessel.

2.

The S60 has a conventional cruise type aft body and thecommercial vessel has a transom stern.

3.

The S60 has no knuckles while the the commercial vessel has ahard chin.

Prior to the milling of the models, the hull geometry wascomputationally redefined starting from the IGES definition used

A. Souto-Iglesias et al. / Ocean Engineering 53 (2012) 38–4742

as benchmark in the Tokyo 1994 CFD Workshop. The reason forthis refairing is that too many surface patches with not enoughquality matching were used in the latter. Furthermore, a verticalextension of the model was required to cope with the generatedwaves from high Froude number tests. The matching of theupdated geometry with the original S60 definition (Todd, 1964)is good, as can be appreciated in Fig. 8. The IGES file used here isprovided as a supplementary material at http://canal.etsin.upm.es/ftp/2012/S60/, with the aim to serve as a standard digitaldefinition for further studies.

The following separations have been tested:

a)

s¼0.565 m, s/L¼0.226 b) s¼0.768 m, s/L¼0.307 c) s¼0.971 m, s/L¼0.388 d) s¼0.1174 m, s/L¼0.470

Fig. 9. Picture of S60 model test.

The rationale behind this selection is that, according to thecomputational analysis of a Series 60 catamaran by Yeung et al.(2004), s/L¼0.226 was determined as the separation ratio forwhich the largest favourable interferences take place. s/L¼0.388is the separation ratio with the largest favourable interferenceeffects for the commercial vessel case studied in the previoussection. s/L¼0.307 is the mean value of 0.226 and 0.388.s/L¼0.470 is larger than 0.388 and chosen to evenly space the4 separations. Results are presented and discussed for each ofthese 4 separations.

The form factor used for the computation of the wavecomponent of the resistance is taken as 0.0673. This value wasdeduced by Min and Kang (2010) who undertook a very thoroughstudy on the dependence between the form factor and theReynolds number. As for the commercial vessel, it is assumedthat the form factor for the monohull and the catamaran isthe same.

The velocities presented in Table 3 were run for the monohulland for the catamaran with all four separations in both free andfixed model conditions. On top of the points presented in Table 3,a total of 5 extra runs were done for the regions of convexitychange in the resistance curves. These extra points are shown inthe resistance curves in the next section. Since it was previously

Table 3Froude numbers and velocities for the S60 catamaran tests.

Point Fn V (m/s)

1 0.15 0.743

2 0.20 0.990

3 0.25 1.238

4 0.26 1.288

5 0.27 1.337

6 0.28 1.387

7 0.29 1.436

8 0.30 1.486

9 0.31 1.535

10 0.32 1.585

11 0.33 1.634

12 0.34 1.684

13 0.35 1.733

14 0.36 1.783

15 0.37 1.832

16 0.38 1.882

17 0.39 1.931

18 0.40 1.981

19 0.41 2.030

20 0.42 2.080

21 0.43 2.129

22 0.45 2.229

23 0.50 2.476

24 0.55 2.724

unclear where the strongest interference effects would take place,the range of Froude numbers is wider than the one used for thecommercial vessel (Table 2). The videos of these experiments,provided as a supplementary material, can be found online athttp://canal.etsin.upm.es/ftp/2012/S60/. A photograph taken dur-ing the experiments is presented in Fig. 9.

4.2. Resistance curves for all separations

The resistance curves for the monohull and the catamaranwith all 4 separations in fixed and free model conditions arepresented in Figs. 10 and 11. There is a slight hump in theresistance curves for both fixed and free model conditions for0.3oFno0.4. In both conditions and as a general trend, theresistance diminishes as the separation increases, tending to thatof the monohull. Let us point out that the monohull resistance hasbeen doubled for the comparison. The translation of these resultsin the interference factor is later discussed.

Fig. 10. S60, total resistance in free model condition.

Fig. 11. S60, total resistance in fixed model condition.

A. Souto-Iglesias et al. / Ocean Engineering 53 (2012) 38–47 43

4.3. Resistance curves in free and fixed model conditions

The graphs in Fig. 12 show the resistance curves for eachseparation in fixed and free model conditions, and compare them

Fig. 12. S60, total resistance in fixed and free model conditions. Top left: s/L=

Fig. 13. S60, total and wave resistance in free model condition. Top left: s/L=0

with the monohull ones. As a general trend, it can be observed thatthe resistance is greater in the free model condition than in the fixedone for each separation. This is best appreciated when comparing thedata for the greatest speed. In Section 3.2, a similar effect is described

0.226, Top Right: s/L=0.307, Down left: s/L=0.388, Down Right: s/L=0.470.

.226, Top Right: s/L=0.307, Down left: s/L=0.388, Down Right: s/L=0.470.

A. Souto-Iglesias et al. / Ocean Engineering 53 (2012) 38–4744

for the commercial vessel. As can be appreciated in Fig. 12, thedifferences are larger for the catamaran than for the monohull andeven larger for small separations compared to large ones. This effectwas also described for the Wigley hull by Moraes et al. (2004).

Fig. 14. S60, total and wave resistance in fixed model condition. Top left: s/L=

Fig. 15. IF for the S60. Top left: s/L=0.226, Top Right: s/L=

For the catamaran in free model condition, with s/L¼0.226, thegreatest speeds could not be reached due to the generated wavesentering the model. For s/L¼0.307 in free model condition,the planning range for the catamaran configuration is reached.

0.226, Top Right: s/L=0.307, Down left: s/L=0.388, Down Right: s/L=0.470.

0.307, Down left: s/L=0.388, Down Right: s/L=0.470.

A. Souto-Iglesias et al. / Ocean Engineering 53 (2012) 38–47 45

This can be deduced by looking at the flattening of the resistancecurve for Fn¼0.55. For s/L¼0.388, the difference in resistancevalues between the monohull and the catamaran grows smallerfor large Froude numbers both in fixed and free model conditions.This tendency is made clearer with the largest separation(s/L¼0.470).

4.4. Wave resistance

In order to calculate the interference factor for a continuousrange of Froude numbers, the resistance curves have been fittedwith NURBS. For each case, wave resistances have been obtainedfrom the total resistance following the procedure described inSection 2. The curves representing these results are shown inFigs. 13 and 14 for free and fixed model conditions respectively.In these figures, the markers correspond to the raw experimentaldata. Data are presented for Fn40.3, where the first behaviourdifferences between the monohull and the catamaran start to takeplace. We can conclude that for the free model condition andsmallest separation, there is no favourable interference region.For the largest Froude numbers the catamaran and the monohullresistances tend to converge. In the mid part of the graphs thetrends are more intricate and described through the IF in the nextsection.

4.5. Interference factor

Using the wave resistance curves presented in the previoussection, the interference factors for both fixed and free modelconditions and for all separations are presented in this section.

Fig. 16. Contour plot as function of Fn and s/L of the IF for the S60. Top: Y

Results are compared with Yeung et al. (2004) and Yeung (2005),who considered a thin-ship potential approximation to model theproblem, with a fixed model hypothesis.

Interference factors for free and fixed model conditions arepresented for all separations in Fig. 15. Focusing on s/L¼0.226, itcan be appreciated that the free model and fixed model inter-ference factors are significantly different. Although according toYeung et al. (2004), where this last separation with Fn¼0.33produces the most favourable interference effects, this does notoccur in the present experiments. For Fn¼0.33 the interference isunfavourable and the minimum is shifted to around Fn¼0.38. Thefree model condition presents overall a more unfavourablebehaviour than both fixed condition and theoretical model. Thisis relevant since in real applications, the free model conditionapplies. For the largest velocities there is a convergence betweenthe fixed model condition results and those of Yeung et al. (2004).

For s/L¼0.307, it can be appreciated that the free modelinterference factor significantly differs from the fixed model onein the range 0.35oFno0.4. With regards to the comparison withYeung et al. (2004), it is noticeable that the peak value of theinterference coefficient is shifted to 0.05 (from 0.38 to 0.43 in theexperimental results). This shift is also present in the minimumvalue of the interference factor. For the largest velocities there is aconvergence between the experimental results and those fromYeung et al. (2004) in free and fixed model conditions. Further-more, the interference effects diminish and the IF tends to zero, asis the case in Zaghi et al. (2011).

Analogously to what happened for the commercial vessel, inthe S60 case, the strongest favourable interference effects arefound for s/L¼0.388. With regards to the comparison with Yeung

eung et al., (2004), Down left: Free model, Down right: Fixed model.

Fig. 17. Sinkage for the S60.

A. Souto-Iglesias et al. / Ocean Engineering 53 (2012) 38–4746

et al. (2004), the peaks and valleys in the experiments are delayedwith respect to the model. For the largest velocities, the conver-gence of the experimental results found in this paper to those ofYeung et al. (2004) is clearly appreciated. More attenuated trendsare observed for the largest separation, s/L¼0.470.

An interesting global representation of these effects across thedifferent separations is given. To do this, a contour projection ofthe 3D graph for the IF is presented in Fig. 16. The tendenciesobserved in the individual graphs for each separation (Fig. 15) arenow clearer. The colour scale in each graph is individualised dueto the range of the interference factor data from Yeung et al.(2004) being significantly shorter than the one found experimen-tally. Globally there are some similitudes in the interferencepatterns but some differences can be appreciated.

Comparing the free model experimental data (which is therealistic configuration to be found in full scale) with those ofYeung et al. (2004) shows that the most favourable interferencetakes place at a similar Fn (0.33) and with a similar IF (around�0.2) but at a larger separation (0.4 instead of 0.226). This Fn issimilar to that found by Zaghi et al. (2011) with a slenderermodel. The unfavourable interferences are stronger in the experi-mental case with a maximum of the order of 0.7 instead of thetheoretically calculated 0.3. It is significant that this maximumdoes not take place for the smallest separation, as is the case inZaghi et al. (2011). Also, in experiments, there is a smoothertransition between the favourable and unfavourable regionscompared to the theoretical model.

Now comparing free and fixed model condition tests, otherdifferences can be appreciated:

1.

Fig. 18. Trim for the S60.

The transition between favourable and unfavourable regions issharper for the fixed model case. Such a sharp transition in thefixed model case is predicted by the theoretical model.

2.

For the smallest separations and contrary to what happens inthe free model condition, there are favourable, although quitemild, interference regions in the fixed model condition results.

3.

Although the unfavourable interference regions are similar insize, the free model ones are more intense.

4.

The most favourable interference factor in fixed model condi-tion is smaller than the free model one.

Summarizing, the free model condition tends to enhance thefavourable and unfavourable interference effects.

4.6. Sinkage and trim

The object of this section is to analyse the relationshipbetween the IF differences in free and fixed model conditionsand the dynamic position (sinkage and trim) in free modelcondition. It is also relevant to analyse differences in sinkageand trim in free model condition between the monohull and thecatamaran; such values are presented in nondimensional form inFigs. 17 and 18, following the definitions by Kim and Jenkins(1981) presented in Eqs. (4) and (5).

When comparing the S60 data with those of the commercialvessel (Fig. 6), sinkage seems to be of the same order but trim issignificantly larger for the S60. Pending future work, we believethis may have an influence on the IF behaviour change betweenfixed and free model conditions.

When comparing the S60 monohull and the S60 catamaran infree model condition, large differences in sinkage can be appre-ciated for 0.3oFno0.42 (Fig. 17). For the shortest separation(s/L¼0.226) the sinkage for the catamaran is around 50% greater.Also for s/L¼0.226, as can be seen in Fig. 15, the differences in theIF between free and fixed model are significant but not mono-tonic, unlike the sinkage differences, which are monotonic.

Looking at the trim (Fig. 18) and in all cases, the differences aremore patent for larger Fn. Between Fn¼0.38 and Fn¼0.45 asignificant trim increase is appreciated. This shift requires furtherinvestigation in order to evaluate a possible relation betweendifferences in the IF in free and fixed model condition.

5. Conclusions

The interference resistance of multihulls taking into accountthe testing condition (fixed model or free model) has beenexperimentally studied. Experiments have been carried out witha commercial catamaran model and more extensively with aSeries 60 catamaran. For the commercial vessel, the influence ofthe model condition has been analysed for the separation inwhich the strongest interference effects take place. In this case ithas been shown that the influence of the model condition (free-fixed) is not substantial. This is consistent with the experimentspresenting moderate dynamic trim-sinkage values and smalldifferences in dynamic trim and sinkage between the monohulland the multihull configuration in free model condition.

For the Series 60 model a range of separations has been studiedand compared with the fixed model slender body theoretical results.The differences between the free and fixed condition experimentalresults are significant, with the free condition providing moreextreme cases in the favourable and unfavourable interferenceregimes. The optimum interference factor (�0.2) appears at a Froudenumber of 0.33, agreeing with theoretical results. Nonetheless, thisoptimum interference occurs for a substantially larger separationratio (0.40) than the theoretically predicted (0.226). The transitionbetween favourable and unfavourable regions is sharper for the fixedmodel case. Such a sharp transition is in accordance with thetheoretical model predictions. For the smallest separation and

A. Souto-Iglesias et al. / Ocean Engineering 53 (2012) 38–47 47

contrary to what happens in the free model condition, there arefavourable, although quite mild, interference regions in the fixedmodel condition. It has been described that for each separation thereis a shift in the maximum favourable and unfavourable interferenceFroude numbers as compared to the theoretical model. In general, thefree model condition tends to enhance the favourable and unfavour-able interference effects.

As a final conclusion, we believe that the differences describedin this paper between experimental results and theoretical pre-dictions and between the wave resistance in fixed and free sink-trim conditions may be relevant at the decision-making level inearly multihull hydrodynamic design. In addition, and since thehulls that have been treated are a standard and a fully definedone, we hope this paper will be useful as benchmark data fornumerical analysis of multihull hydrodynamics.

Acknowledgements

The research leading to these results has received funding fromthe Spanish Ministry for Science and Innovation with the ‘‘Programa

de Acceso y Mejora de las ICTS’’, which provided funding for carryingout the experimental campaign in CEHIPAR model basin. We thankElkin Mauricio Botia-Vera, Luise Draheim, David Feijoo de Azevedo,Carlos Ariel Garrido Mendoza, Francisco Perez-Arribas, RoqueVelasco-Sopranis, Hugo Gee all from our research group, and LiborLobovsky from University of West Bohemia for their support indifferent tasks during the research that has led to this paper.

References

Broglia, R., Zaghi, S., Di Mascio, A., 2011. Numerical simulation of interferenceeffects for a high-speed catamaran. J. Mar. Sci. Technol. 16, 254–269.

Chen, X.N., Sharma, S.D., Stuntz, N., 2003. Wave reduction by S-Catamaran atsupercritical speeds. J. Ship Res. 47 (2), 145–154.

Insel, M., Molland, A.F., 1992. An investigation into the resistance components ofhigh speed displacement catamarans. R. Inst. Nav. Archit. 134, 1–20.

Kim, Y.H., Jenkins, D., 1981. Trim and Sinkage Effects on Wave Resistance withSeries 60; cb¼0.60. Techical report. David W. Taylor Naval Ship Research andDevelopment Center, Bethesda, Maryland.

Lunde, J.K., Shearer, J.R., Wieghardt, G.W., Lap, A.J., Landweber, L., Inui, T.,Weinblum, G., Brard, R., 1966. Report of Resistance Commitee. Technicalreport. International Towing Tank Conference (ITTC).

Migali, A., Miranda, S., Pensa, S., 2001. Experimental study on the efficiency oftrimaran configuration for high-speed very large ships. In: Proceedings of theFAST Conference, 2001, pp. 1–5.

Min, K.-S., Kang, S.-H., 2010. Study on the form factor and full-scale ship resistanceprediction method. J. Mar. Sci. Technol. 15, 108–118.

Molland, A.F., Wellicome, J.F., Couser, P.R., 1996. Resistance experiments on asystematic series of high speed displacement catamaran forms: variation oflength–displacement ratio and breadth–draught ratio. R. Inst. Nav. Archit. 138,55–71.

Moraes, H.B., Vasconcellos, J.M., Latorre, R.G., 2004. Wave resistance for high-speed catamarans. Ocean Eng. 31 (17–18), 2253–2282.

Moraes, H.B., Vasconcellos, J.M., Almeida, P.M., 2007. Multiple criteria optimisationapplied to high speed catamaran preliminary design. Ocean Eng. 34 (1),133–147.

Nakatake, K., Takeshi, H., 1994. Review of program 2, inviscid flow around series60 with free surface. In: CFD Workshop, vol. 2. pp. 130–159.

Souto-Iglesias, A., Zamora-Rodrıguez, R., Fernandez-Gutierrez, D., Perez-Rojas, L.,2007. Analysis of the wave system of a catamaran for CFD validation. Exp.Fluids 42 (2), 321–332.

Tarafder, M., Suzuki, K., 2008. Numerical calculation of free-surface potential flowaround a ship using the modified Rankine source panel method. Ocean Eng. 35(5–6), 536–544.

Toda, Y., Stern, F., Longo, J., 1992. Mean-flow measurements in the boundary layerand wake and wave field of a series 60 CB¼ .6 model ship—part 1: Froudenumbers .16 and .316. J. Ship Res. 36 (4), 360–377.

Toda, Y., Stern, F., Longo, J., 1988. Mean-flow Measurements in the Boundary Layerand Wake and Wave Field of a Series 60 Cb¼ .6 Model Ship—Part 1: FroudeNumbers .16 and .316. Technical report. IIHR report no. 352. The University ofIowa, Iowa City.

Todd, F.H., 1964. Series 60 Methodical Experiments with Models of Single-screwMerchant Ships. Technical report. David W. Taylor Model Basin.

Turner, H., Taplin, A., 1968. The resistance of large powered catamarans. Trans.SNAME 76, 180–213.

Yeung, R.W., Wan, H., 2007. Multi-hull configuration design: a framework forpowering minimization. In: Proceedings of the ASME 2007 26th InternationalConference on Offshore Mechanics and Arctic Engineering (OMAE2007), vol. 4,pp. 833–842.

Yeung, R.W., 2005. Interference resistance of Multi-hulls per thin-ship theory. In:Proceedings of the International Workshop on Water Waves and FloatingBodies.

Yeung, R.W., Poupard, G., Toilliez, J.O., 2004. Interference-resistance prediction andits applications to optimal multi-hull configuration design. Trans. Soc. Nav.Archit. Mar. Eng. 112, 142–169.

Zaghi, S., Broglia, R., Mascio, A.D., 2011. Analysis of the interference effects forhigh-speed catamarans by model tests and numerical simulations. Ocean Eng.38 (17–18), 2110–2122.