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Practical evaluation of resistance of high-speed catamaran hull forms—Part IIP. K. Sahoo a; S. Mason b; A. Tuite b

a Australian Maritime College, Launceston, Australia b Incat Crowther Pty Ltd, Sydney, Australia

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To cite this Article Sahoo, P. K., Mason, S. and Tuite, A.(2008)'Practical evaluation of resistance of high-speed catamaran hullforms—Part II',Ships and Offshore Structures,3:3,239 — 245

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Ships and Offshore StructuresVol. 3, No. 3, September 2008, 239–245

Practical evaluation of resistance of high-speed catamaran hull forms—Part II

P.K. Sahooa∗, S. Masonb and A. Tuiteb

aAustralian Maritime College, Launceston, Australia; bIncat Crowther Pty Ltd, Sydney, Australia

( Final version received 21 May 2008)

This study attempts to extend the analysis of several resistance prediction procedures based on experimental work carriedout by researchers and, subsequently, wave resistance estimation as illustrated in Part I of this study by Sahoo et al. (2007).All the methods used have been analysed and compared with results obtained from towing tank tests, CFD analysis by use ofSHIPFLOW and a computational analysis is software package CATRES, whose operation is based around thin ship theory.The results obtained from each of the resistance prediction methods have been investigated, and the limitations and areas ofeffectiveness for each of the resistance methods have been determined in relation to the vessels tested. Throughout this study,the primary objective of validating the resistance equations developed in Part I of this study has been achieved. The level towhich the resistance prediction tool can be utilized during the designing of high-speed catamarans was further determinedthrough the analysis of the results.

Keywords: catamaran; resistance; wave resistance; computational fluid dynamics

Nomenclature

At Immersed transom areaB Demi-hull beam at the waterlineBT Beam-draught ratioCB Block coefficient CB = ∇/LBT

CF International Towing Tank Confer-ence ’57 ship model correlation lineCF = 0.075/ (Log10Rn − 2)2

CT Total resistance coefficientCWCAT Wave resistance coefficient for cata-

maran configurationCR Residuary resistance coefficientFn Froude number (based on length)Fn∇ Froude number based on volumetric

displacementg Acceleration due to gravity,

9.81 m/s2

iE Half waterline entry angle in degreesKpi partial form factor as used in

catamaran resistance prediction toolCATRES

L or LWL Waterline lengthL/B or LWL/BXDH Length/beam ratio (demi-hull)L/∇1/3 Slenderness ratioRT/� Total resistance to displacement ratios Separation (measured between demi-

hull centre planes)s/L Separation ratio (between demi-hull

centre planes)

∗Corresponding author. Email: [email protected]

S Wetted surface area1 + k Form factor1 + γ k Viscous form factor for catamaransy Vertical coordinateα A correction factor dependent on type

of sternβM Deadrise angle at amidships in de-

greesδW Transom wedge angle� Displacement∇ Volumetric displacement

Introduction

In current practice, there are three generally accepted meth-ods for the determination of the resistance characteristicsof any vessel, as follows:

� Statistical analysis of experimental data, in which resis-tance data for a range of Froude numbers are analysedfor geometrically similar models with varying L/B, B/T ,CB and/or L/∇1/3 values, such that resistance parame-ters such as CT or RT/� could be estimated with somedegree of accuracy for any model existing within theparameter space.

� In computational fluid dynamics (CFD) method, whichbehaves as a numerical towing tank, wave resistance datacould be obtained more readily since rapid transforma-tion of hull form parameters (within parameter space)

ISSN: 1744-5302 print / 1754-212X onlineCopyright C© 2008 Taylor & FrancisDOI: 10.1080/17445300802263831http://www.informaworld.com

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240 P.K. Sahoo et al.

can be undertaken easily and data harvested within ashort span of time. SHIPFLOW and CATRES are exam-ples of CFD analysis tools used in determining the waveresistance of marine vessels.

� Application of amended Michell’s integral or slenderbody (thin ship) theory to high-speed marine vessels.

All three methods have their advantages and disadvantages,which are primarily concerned with accuracy, cost and time.Although CFD and analytical methods are becoming moreaccurate and are being recognized as legitimate sourcesfor the calculation of ship resistance and, thereby, optimis-ing hull forms, there still remains the necessity to validatethe results. Results obtained from these sources need tobe validated for accuracy and any potential sources of un-certainty so as to have a degree of confidence in theseresults.

It is the purpose of this study to provide a comparison ofa variety of resistance calculation methods, and ultimatelyto validate a series of resistance regression analysis equa-tions previously developed in Part I. This will be achievedby determining the resistance characteristics of three dif-ferent catamaran hull forms that are currently in operationin the high-speed ferry industry.

By comparing the results obtained from these varioussources, it is possible to compare, both graphically and nu-merically, the characteristics of each resistance prediction

method and the accuracy of the total resistance obtainedat various Froude numbers. By doing this, the effective-ness and accuracy of the resistance prediction methods, inparticular the regression equations, could be achieved.

Summary of various methods

Molland et al. method (1994)

Table 1 depicts the summary of range of parameters and itsuse in the regression model, as illustrated in Part I of thisstudy.

CATRES

CATRES is a resistance prediction method, utilizing thinship theory, which was developed by the Maritime ResearchInstitute Netherlands for use on semi-planing catamaranswith symmetrical hull forms.

The total resistance of the vessel is determined throughthe summation of four separately determined resistancecomponents:

RW = Twice the wave resistance of a single demi-hullRWi = Wave interference resistanceRHS = Hydrostatic resistance for the drag of an immersed

transomRFR = Viscous resistance.

Table 1. Range of validity for catamaran configuration.

Molland et al. Zips Pham et al. Schwetz and Sahoo et al.Parameters (1994) (1995) (2001) Sahoo (2002) (2004)

L/B 7.0–15.1 7.55–13.55 10.40–20.80 8.80–15.0 10.0–15.0L/∇1/3 6.27–9.5 6.30–12.60 6.30–9.56 8.04–11.2B/T 1.5–2.5 1.5–2.5 1.47–2.31 1.5–2.5CB 0.397 0.50–0.60 0.46–0.68 0.40–0.50LCB/L (%) 43.6 40–49Deadrise angle at 16–38◦ 16–27◦ 23–44◦

amidships βM

Half angle of iE 2.1–38 5.4–10.71entrance indegrees

1 + γ k 1.41–1.48Equation 7

and Table 7 ofPart I

CWCAT Equation 8 Equation 13 Equation 17 Part I Equation 21 Part Iand Table 8 of and Table 11 of and Table 20 of and Table 25 of

Part I Part I Part I Part IResiduary

resistance ofcatamaran, CR

Table 17 of Part I

Transom wedge, δW 0–12◦

Type of hull form NPL round bilge Chine Chine Round bilge, semi-swath and chine Round bilge

Note: LCB indicates longitudinal centre of buoyancy, reference from the transom; NPL, National Physical Laboratory.


Ships and Offshore Structures 241

Table 2. Vessel’s operating locations.

Vessel Yard built Area of operation

Seastreak New York Gladding Hearn Shipbuilders Manhattan—Central New JerseyNew York Water Taxi Gladding Hearn Shipbuilders New YorkJet Cat Express (Catalina) Nichols Bros Boat Builders Long Beach—Catalina Island

The values of the wave resistance and the wave interfer-ence resistance are both determined using thin ship theory.Due to the slenderness of the hulls, they can be representedby a distribution of Kelvin sources in their centre planes.When combined, the sources produce a flow field that satis-fies the hull boundary condition. Numerical differentiationis used to determine the perturbation velocities (velocitydifferences with respect to the ship speed), obtained fromthe velocity potentials induced in the Kelvin sources. Theresistance is then found by integrating the perturbation pres-sure over the hull, obtained from the linearised Bernoulliequation.

The wave interference resistance is calculated in a simi-lar manner, where the effect of the second hull is accountedfor by the addition of another plane of Kelvin sources.The viscous resistance (RFR) is approximated by CATRESthrough the following formula:

RFR = 1

2ρSV 2(1 + αKpi) (CF + CA) . (1)

For an immersed transom, CATRES introduces a correctionfor the resistance incurred due to the hydrostatic pressureof the flow, clear of the transom not being equal to zero, as

per Equation (2):

RHS = −ρg

∫At

ydAt, (2)

where At = immersed transom area.

Test models

The three vessels chosen to undergo analytical and ex-perimental testing are all Incat Crowther-owned and IncatSydney-designed passenger ferries that are currently oper-ating in the United States of America as shown in Table 2.The vessels were chosen because of their high speed, ferrynature and the fact that towing tank tests on these three ves-sels had been conducted previously. The vessel particularsare shown in Tables 3 and 4. The line plans of the vesselsare shown in Figures 1, 2 and 3.

Results

The hull forms of the three vessels have all undergone calmwater resistance tests at the Australian Maritime College

Table 3. Main particulars of three chosen catamarans.

Particulars of vessels, name (ID)Parameters

Seastreak New York Water Taxi Jet Cat Express (Catalina(2352) (2602) Express) (2621)

Waterline length (m) 37.838 20.781 39.117Displacement (t) 182.636 57.304 206.003Draft (m) 1.934 1.642 2.033Beam waterline (m) 10.34 8 10.31Beam waterline (demi-hull) 2.64 2.2 2.61CB 0.461 0.372 0.49Service speed (knots) 37 26 37.5Model scale 1:26.5 1:14 1:40

Table 4. Hull form characteristics of three chosen catamarans.

Parameters Seastreak New York Water Taxi Jet Cat Express (Catalina express)

Length/beam ratio L/B 3.66 2.60 3.79Slenderness ratio L/∇1/3 6.73 5.44 6.68Beam/draft ratio B/T 1.37 1.34 1.28Block coefficient CB 0.461 0.372 0.49



Baseline

Figure 1. Line plan for vessel 2352—Seastreak.

Ship Hydrodynamic Centre. The results obtained from thetowing tank tests were non-dimensionalised so that thesecould be presented and compared with the regression mod-els developed in Part I of this study. The results for all re-sistance methods have been plotted together (RT/� againstFn∇) to provide a simple graph that could be easily inter-preted.

Discussion

As can be seen from Figure 4 (Seastreak), the results ob-tained from the regression equations provide a relativelyeven spread of precision in relation to the results obtainedfrom the towing tank results, which have been taken tobe the datum for all comparisons as towing tank tests areconsidered to be the basis of any comparative analysis.

Baseline

Baseline

Baseline

Figure 2. Line plan for vessel 2602—New York Water Taxi.

Baseline

Baseline

Figure 3. Line plan for vessel 2621—Catalina Express.



Figure 4. RT/� against Fn∇ for various methods (Seastreak, 2352).

The method of Schwetz and Sahoo (2002) can be seen tofollow the trend of the towing tank results, almost identi-cally, while constantly producing results with a higher valueof total resistance. It can be seen that the percentage dif-ference obtained from the method of Schwetz and Sahoo(2002) in comparison to the towing tank results is approx-imately 10–15%. The methods of Sahoo et al. (2004) andPham et al. (2001) can be seen to be slightly more ac-curate than that of Schwetz and Sahoo (2002), althoughboth these methods underpredict the results of the towingtank data, with the method of Pham et al. (2001) fallingaway from both the towing tank results and the Sahoo etal. (2004) results at both low and high volumetric Froudenumbers. Throughout the speed range, CATRES comparesfavourably whereas SHIPFLOW consistently overpredictsthe experimental data.

As can be seen from Figure 5 (New York Water Taxi),the methods of Pham et al. (2001) and Schwetz and Sahoo(2002) greatly underpredict the total resistance right acrossthe speed range, with both resistance curves increasing ata decreasing rate, whereas the curve of towing tank resis-tance values is almost linear in nature. The results obtainedfrom the Sahoo et al. (2004) and SHIPFLOW methods showcurves that are almost identical in form as that of the tow-ing tank curve, yet both underpredict the total resistanceby a considerable amount. The curve obtained from theCATRES results does not match any of the other methodsrising far sharper than the other predictions and levellingto eventually underpredict the towing tank results above avolumetric Froude number of approximately 2.5.

As in both the previous cases, the data from variousmethods seem to fluctuate appreciably from experimental

Figure 5. RT/� against Fn∇ for various methods (New York Water Taxi, 2602).



Figure 6. RT/� against Fn∇ for various methods (Catalina Express, 2621).

data as shown in Figure 6 (Catalina Express). The total re-sistance data obtained from CATRES overpredicts the totalresistance of the towing tank values by approximately thesame margin as Schwetz and Sahoo (2002). SHIPFLOWand Sahoo et al. (2004) produce results with almost thesame error in comparison to towing tank values, whereSHIPFLOW slightly overpredicts the total resistance in thelower speed range, eventually underpredicting the total re-sistance above a volumetric Froude number of 2.8. Thetotal resistance curve of Sahoo et al. (2004) underpredictsthe total resistance throughout the same speed range as whatSHIPFLOW overpredicted the total resistance. The total re-sistance obtained from the method of Pham et al. (2001) issufficiently accurate, although the curve underpredicts thatof the towing tank throughout the speed range.

Conclusions

In this article, the authors have attempted to validate thevarious methods against three randomly chosen vessels,which are already in operation. Some conclusions that canbe drawn are as follows:

(1) There are some notable differences in the total resis-tance curves obtained from the differing resistance pre-diction methods, both between methods for a particularvessel and compared with the different vessels.

(2) In general, SHIPFLOW returns higher values of totalresistance compared with towing tank data except forNew York Water Taxi. The overprediction could bedue to overcompensating for the interference effectsbetween the hulls or an inability to model the effect offollowing waves.

(3) The curve of RT/�, obtained from the regression meth-ods, seems to maintain similar accuracies comparedwith towing tank results for different vessels. The re-

gression models for resistance equations are determin-ing fairly accurate values for the tested vessels, bearingin mind that the regression models were developed onthe basis of certain types of hull form, as illustrated inPart I of this study.

(4) CATRES, considering the age of the program and thetheory it is based on, performs extremely well. In thecase of New York Water Taxi, the majority of the re-sistance prediction methods fail to produce accurateresults. This is thought to be due to a slightly morepronounced chine than what is present on the othertwo vessels, and a general form of the hull that is moresuited to these two methods. However, this does not ex-plain the extent to which the other regression methodand SHIPFLOW underpredict the total resistance ofthis vessel.

1. It may, however, be remembered that the regressionequations were developed on the basis of a systematicseries of specific hull forms that are totally unrelated tothe randomly selected hull forms used for comparativeanalysis.

Final remarks

The purpose of this study is to provide a comparison ofa variety of resistance calculation methods, and ultimatelyto validate a series of regression analysis equations previ-ously developed and presented in Practical Evaluation ofResistance of High-Speed Catamaran Hull Forms—Part I.

It has been shown through this study that the developedregression equations are able to give reasonably accuratepredictions of resistance, with little input data about thehull form and minimal time for the calculation process. Itis, therefore, determined that with some refinement and op-timisation of the regression equations, the equations could



provide viable first estimates of the resistance character-istics of hull form in early design stages. The regressionmodels are to be used with due care with regard to thetype of hull form (round bilge or chine) used in catamaranconfigurations.

Acknowledgements

The authors express their sincere gratitude to The Aus-tralian Maritime College, Australia (specialist institute ofUniversity of Tasmania) and Incat Crowther Pty Ltd, Syd-ney, Australia for their support and encouragement through-out the course of this study.

ReferencesMolland AF, Wellicome JF, Couser PR. 1994. Resistance exper-

iments on a systematic series of high speed displacementcatamaran forms: variation of length–displacement ratio andbreadth–draft ratio. Ship Science Report No. 71. Southamp-ton, UK: University of Southampton.

Pham XP, Kantimahanthi K, Sahoo PK. 2001. Wave resistanceprediction of hard-chine catamarans through regression anal-ysis. Proceedings of the 2nd International Euro Conference onHigh Performance Marine Vehicles (HIPER’01). Hamburg,Germany. p. 382–394.

Sahoo PK, Browne NA, Salas M. 2004. Experimental and CFDstudy of wave resistance of high-speed round bilge catamaranhull forms. Proceedings of the 4th International Conferenceon High-Performance Marine Vehicles (HIPER’04). Rome,Italy. p. 55–67.

Sahoo PK, Salas M, Schwetz A. 2007. Practical evaluation ofresistance of high-speed catamaran hull forms–part I. J ShipsOffshore Struct. 2(4):307–324.

Schwetz A, Sahoo PK. 2002. Wave resistance of semi-displacement high speed catamarans through CFD and regres-sion analysis. Proceedings of the 3rd International Euro Con-ference on High Performance Marine Vehicles (HIPER’02).Bergen, Norway. p. 355–368.

Zips JM. 1995. Numerical resistance prediction based on resultsof the VWS hard chine catamaran hull series ’89. Proceedingsof the 4th International Conference on Fast Sea Transportation(FAST ’95). Vol. 1. Luebeck, Germany. p. 67–74.


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