The main problems of high-speed ships operating in open seas are their insufficient seaworthiness and speed loss in high sea states. Small Water-plane Area Twin-Hulls (SWATH) are characterised by excellent seaworthiness, but the hull forms of a traditional SWATH are not suited for higher speeds. A new shape of underwater gondola has been developed for a semi-planing (S/P) SWATH. Additionally, hydrofoils can be applied to this ship to provide the optimal dynamic draught and trim, to mitigate motions in rough seas, and even to carry a part of the ship weight. The relative speed of this SWATH can be beneficially increased up to the displacement Froude number 3.
Several concept designs addressing naval and civil transportation needs are outlined in this paper

K. Matveev

V. Dubrovski

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32356(2005)4, 323-328HYDRODYNAMIC ASPECTS OF A HIGH-SPEED SWATH AND A NEW HULL FORM V. DUBROVSKY, K. MATVEEVUDC 629.57:532.5Victor DUBROVSKY 1Konstantin MATVEEV 2 Hydrodynamic Aspects of aHigh-Speed SWATH and a NewHull FormProfessional paperThe main problems of high-speed ships operating in open seas are their insufficient seaworthi-ness and speed loss in high sea states. Small Water-plane Area Twin-Hulls (SWATH) are charac-terised by excellent seaworthiness, but the hull forms of a traditional SWATH are not suited forhigher speeds. A new shape of underwater gondola has been developed for a semi-planing (S/P)SWATH. Additionally, hydrofoils can be applied to this ship to provide the optimal dynamic draughtand trim, to mitigate motions in rough seas, and even to carry a part of the ship weight. The relativespeed of this SWATH can be beneficially increased up to the displacement Froude number 3.Several concept designs addressing naval and civil transportation needs are outlined in this paper.Keywords: SWATH ships, high speed vessels, hull form, hydrodynamic analysisHidrodinamiËki aspekti dvotrupca minimalne povrπine vodne linije (SWATH) velike brzine inovog oblika trupaStruËni radGlavni problemi brodova velike brzine tijekom plovidbe na otvorenom moru su njihova nedovoljnapomorstvena vrijednost i gubitak brzine kod visokog stanja mora. ZnaËajka malih dvotrupacaminimalne povrπine vodne linije (SWATH) je njihova odliËna pomorstvena vrijednost, ali oblik trupatradicionalih SWATH-ova nije prilagoen za veÊe brzine. Razvijen je novi oblik podvodnog trupa(gondola) za poluglisirajuÊe SWATH-ove. Za takav brod se mogu dodatno rabiti i hidrokrila radipostizanja optimalnog dinamiËkog gaza i trima, smirivanja gibanja na uzburkanom moru i Ëak danose dio teæine broda. Relativna brzina ovih SWATH-ova se moæe korisno poveËati sve doistisninskoga Froudeovog broja 3. U ovom je Ëlanku prikazano viπe konceptualnih projekata ovihbrodova za potrebe vojnog i civilnog prijevoza po moru.KljuËne rijeËi: SWATH brodovi, brzi brodovi, oblik trupa, hidrodinamiËka analizaAbout authors:1 Independent ship designer, Russia2 Art Anderson Associates, USAReceived (Primljeno): 2005-07-05Accepted (PrihvaÊeno): 2005-09-08IntroductionThe main problems of high-speed ships (with the Froudenumber Fn = V / (gL)0.5 ≥ 0.5, where V- ship speed, m/s; L – thehull length at the water-plane, m; g – gravitational constant)  oper-ating in open seas are their insufficient seaworthiness and speedloss in high sea states. A Small Water-plane Area Twin-Hull Ship(SWATH) includes two submerged hulls (gondolas) and one ormore water surface piercing parts (struts) on each gondola. Suchships are characterised by excellent seaworthiness, comparable withthat of vessels having deeply submerged and automatically con-trolled hydrofoil systems. But hydrofoil boats are not as promis-ing as large ships due to the sharp increase in the foil system sizein comparison with ship dimensions and constant speed. Otherissues of hydrofoil vessels of this type are their cost and mainte-nance. In contrast, the SWATH type is less expensive and morereliable and can have large dimensions. Therefore, the increase inspeed of SWATHs can make them an attractive option for manyapplications, including high-speed oceanic transportation.However, the traditional hull forms of a SWATH are not in-herently suited for higher speeds. The main reason for a low waveresistance and for a superior seaworthiness of a SWATH is thesufficiently deep immersion of the main volume of the hulls. Allsurface craft, including SWATHs, drastically change their sin-kage and trim in the transitional speed regime. A traditionalSWATH with a blunt bow approaching the free water surface ina high-speed regime becomes inefficient. The subject of this pa-per is a new semi-planing (S/P) SWATH configuration designedfor high speeds.A typical dependence of the SWATH dynamic trim on theFroude number, Figure 1, shows a significant reduction in thebow immersion with increasing speed. On a traditional SWATH,a positive trim (bow up) is observed at small (< 0.3) and large (>0.45-0.5) length Froude numbers. A negative trim is not desir-able; it is usually counteracted by fins or by a special shape ofthe gondola. The initial (static) trim is approximately an additiveto the dynamic trim in the entire range of Froude numbers.The initial trim influences the residual resistance coefficients,depending on Froude numbers. An illustration of the influencecoefficient (defined as the ratio of the residual resistance coeffi-cients at non-zero and zero initial trims) is given in Figure 2 fora traditional SWATH. The negative static trim is favourable for324 56(2005)4, 323-328V. DUBROVSKY, K. MATVEEV HYDRODYNAMIC ASPECTS OF A HIGH-SPEED SWATH AND A NEW HULL FORMresidual resistance for relatively small Froude numbers (e.g. 0.3-0.4 in Figure 2); but it is not a reasonable method of resistancereduction because sailing with a negative trim is not a good seapractice. Only small positive initial trim seems permissible forhigh values of Froude numbers.A variation in the mean dynamic draught of a traditionalSWATH is usually negative (draught increases), but can be posi-tive either at very high relative speeds or if there is a significantinitial trim (Figure 3). The effect of the initial draught (variation)on the residual resistance coefficients of a traditional SWATHdepends on its relative speed (Figure 4). Smaller draught is obvi-ously favourable for relatively high speeds (Fn = 0.5-0.7 in Fig-ure 4), but this advantage remains only until the gondola is fullysubmerged. If draught becomes smaller than the gondola height,the residual resistance grows rapidly (e.g., the left part of thecurve Fn=0.9 in Figure 4). Larger draught is favourable for Froudenumbers 0.3-0.4.Figure 3 Example of the mean dynamic draught variation of a SWATHSlika 3 Primjer dinamiËkoga srednjeg gaza SWATH-aFigure 4 Example of the mean static draught influence on residualresistance coefficients of a traditional SWATH               (constant displacement)Slika 4 Primjer utjecaja poËetnoga srednjeg gaza na koeficijentepreostalog otpora tradicionalnog SWATH-a (konstantnaistisnina)  0.2 0.3 0.4 0.5 0.6 0.7 0.8-1.0-0.50.00.51.01.52.02.53.03.54.04.5Dynamic trim, degreesFroude number, FnStatic trim 0Static trim 1 deg.Figure 1 Typical dependence of the SWATH trim on the lengthFroude number, with positive and  zero static  trim (posi-tive trim corresponds to bow up)Slika 1 TipiËna ovisnost trima SWATH-a o duljinskom Froudeo-vom broju sa i bez poËetnog trima (pozitivni trim se od-nosi na uzdignuti pramac)                 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.91.01.11.21.31.41.5Fn = 0.30.40.50.7 0.9Initial trim influence coefficient0.50.90.7Static trim, degreesFigure 2  Example of the initial trim influence on the residual re-sistance coefficient CR of a traditional SWATHSlika 2 Primjer utjecaja poËetnog trima na koeficijent preostalogotpora CR tradicionalnog SWATH-a                 0.0 0.2 0.4 0.6 0.8 1.0 1.2-0.5-0.4-0.3-0.2-0.10.00.10.2Average draft changing, % of LFroude number FnZero initial trimPositive initial trim                0.85 0.90 0.95 1.00 1.05 1.10 1.150.70.80.91.01.11.2Fn = 0.30.30.40.40.50.50.70.70.90.9Initial average draft influenceRelative initial draft32556(2005)4, 323-328HYDRODYNAMIC ASPECTS OF A HIGH-SPEED SWATH AND A NEW HULL FORM V. DUBROVSKY, K. MATVEEVA partial exit from water of a blunt bow of the traditionalSWATH gondola, occurring at high Froude numbers due to vari-ations in the dynamic trim and/or draught, leads to several ad-verse effects: the increase in the wave-making resistance, theappearance of the wave-breaking resistance, the flow separationon a hull (accompanied by the resistance growth), and the in-crease of the longitudinal moment exerted on a hull. Besides,pitch and heave motions increase in rough seas if the gondolacrosses the water surface. Therefore, traditional shapes of under-water hulls are not acceptable for a high-speed SWATH.1 New hull formSome research efforts have been devoted to the study of un-conventional SWATH hull forms with reduced pitch moment athigh speeds [1]. In contrast to this approach, a positive pitchmoment can actually be utilised to reduce the wetted area of aSWATH, and consequently its towing resistance. To achieve thesegoals, the increase in the dynamic trim should be accompaniedby the decrease in the dynamic draught, so the dynamic wettedarea will be smaller than the static value.A special shape of the SWATH gondolas has been developedwith a purpose to operate at high speeds [2]. Hull lines of thenew form provide minimal drag at high speeds, when trim anddraught change significantly. An example of the new hull formis shown in Figure 5. The optimal dynamic trim and draught ofthe ship are ensured by a control hydrofoil system which canalso be applied for the motion mitigation in rough seas.Figure 5 Example of the new SWATH hull formSlika 5 Primjer novog oblika trupa SWATH-a1.1 ResistanceTable 1 Main characteristics of the towed modelTablica 1 Glavne znaËajke tegljenog modelaDesign draught, d,m 0.3 0.2Displacement, W, cub. m 2 x 0.175 2 x 0.130Waterline length, LWL, m 3.6 3.6Hull relative length, l = L / W1./3 6.44 7.1Overall beam, Boa, m 1.6 1.6Gondola beam, Bg, m 0.3 0.3Strut beam, Bst, m 0.2 0.2Wetted area, Sw, sq. m 6.43 5.0Bow foil area, Sf, sq. m 0.027 0.027Mass centre height, Zm, m 0.3 0.25Characteristics of the tested model are given in Table 1. Thetowed model was free to sink and to pitch. Turbulence stimula-tion by wires was applied at the first station of each hull. Themodel total towing resistance is shown in Figure 6. The residualresistance coefficient of the model with larger draught is presen-ted in Figure 7, where it is also compared with the same coeffi-cient of a common SWATH model. The new hull shape demon-strates lower residual resistance at the upper range of testedspeeds. The relative wetted area of the new-shape gondola atrest is only slightly larger than the wetted area of a traditionalhull form. Therefore, the new hull form can ensure higher achiev-able speeds in comparison with a traditional SWATH. The achiev-able speed of the new-shape SWATH can reach the displacementFroude number of about 3.Figure 6 Towing resistance of the model tested at two draughtsSlika 6 Otpor tegljenja modela izmjeren za dva gaza                  1 2 3 4 5 6 70100200300400500600Towing resistance, NModel speed, m/secd = 0.3 md = 0.2 m326 56(2005)4, 323-328V. DUBROVSKY, K. MATVEEV HYDRODYNAMIC ASPECTS OF A HIGH-SPEED SWATH AND A NEW HULL FORMFigure 7 Residual resistance coefficient of the model tested attwo draughtsSlika 7 Otpor tegljenja modela izmjeren za dva gaza1.2 Hydrofoil control systemAs noted above, the main objective of the control hydrofoilsystem is to ensure the optimal draught and trim. An additionalpurpose is the motion mitigation. The proper placement for the T-foil systems on the proposed ship is at the hull ends. The hydrofoilaspect ratio of 1.5-2 is recommended for this ship type to mini-mise vibrations and the probability of fatigue damage. The hydro-foil profiles should be chosen to maximise their lift-drag ratio un-der requirements for cavitation avoidance and strength. The hydro-foil area should be at least 5% of the ship water-plane area at rest.1.3 SeakeepingOne of the specific features of the new hull form is a consid-erable reduction of the longitudinal metacentric height with in-creasing speed (Figure 8). The relative water-plane area is alsosmall. This means that the natural pitch period is large, which isfavourable for longitudinal motions. A model with the new gon-dola shape was tested in regular head waves. The results for heaveand pitch amplitudes are shown in Figures 9 and 10, respectively.As any other SWATH, the new hull-shape model is characteri-sed by reduced motions with increasing speed. Besides, viscousdamping plays a significant role in sharp resonances typical forSWATH response amplitude operators. These experimental re-sults on sea-keeping allow us to estimate pitch and heave ampli-tudes for various ships of the proposed type.Figure 9 Response amplitude operator of pitch in head wavesSlika 9 Operator amplitude odziva kod posrtanja na valovimau pramacFigure 10 Response amplitude operator of heave in head wavesSlika 10 Operator amplitude odziva kod poniranja na valovimau pramac2 Possible realisations of an S/P SWATH2.1 Small-sized passenger ferry or motor yachtAn example of a relatively small variant of the new-hullSWATH is a ferry for 50 passengers, which can also be designedas a high-safety motor yacht. This ship will have the length of 15m, beam  of 7 m, depth of 4.5 m, displacement of 25 t, living areaof 50 sq. m, and engine power of 2x370 kW for the design speedof 30 knots. Living compartments, a wheelhouse, and enginerooms are arranged in the above-water platform. Power trans-0.2 0.4 0.6 0.8 1.0 1.2 1.401234567New shapeUsual shapeResidual resistance coefficient CR*103Froude number Fn             0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0152025303540Longitudinal metacentric height, % of LFroude number FnFigure 8 Example of the longitudinal metacentric height of theproposed SWATHSlika 8 Primjer uzduæne metacentarske visine predloæenogSWATH-a               2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.50.00.20.40.60.81.01.21.41.6Pitch angle relative to wave slope angle.Wave frequency, 1/secZero speedDesign speed                 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.50.00.20.40.60.81.01.21.4Heave amplitude relative wave heightWave frequency, 1/secZero speedDesign speed32756(2005)4, 323-328HYDRODYNAMIC ASPECTS OF A HIGH-SPEED SWATH AND A NEW HULL FORM V. DUBROVSKY, K. MATVEEVmission to propellers can be either mechanical or hydraulic. Theship can move even if one or both hulls are flooded. Figure 11shows an artist’s impression of a motor yacht. The living roomscan be transformed into one large cabin on a passenger ferry.Comparable mono-hull ships can operate only in the Sea Statebelow 2 (3%-exceeding wave height of 0.75 m). The proposednew shape of a SWATH can have the speed of up to 30 knots inthe Sea State 3 (wave height of 1.25 m) with a high level ofcomfort (Figure 12). For the 3%- exceeding vertical accelerationlevel of 0.25g, this ferry can ensure the speed of 22 knots with-out any motion mitigation system, and higher speeds are achiev-able with a control hydrofoil system.Figure 11 Example of a small motor yachtSlika 11 Primjer male motorne jahteFigure 12 Relative vertical acceleration a/g at 15%L from FP, 3%accidenceSlika 12 Relativno vertikalno ubrzanje a/g na 15%L od prednjeokomice, 3% premaπaja2.2 Fast corvettesCurrently, the main tendency in the development of surfacecombat ships is the increase in their speeds [3]. The new-shapeSWATH can ensure high speed and high seaworthiness for com-bat ships, such as patrol and attack corvettes (Table 2). An exter-nal view of the patrol corvette is shown in Figure 13. The pro-posed attack corvette can ensure the use of  helicopters in wavesup to the Sea State 5 (Figure 14). Pitch amplitudes within 4 de-grees define possible speeds for the helicopter operation without            5 10 15 20 25 300.050.100.150.200.250.30Sea State 32Sea StateSea State 1Relative acceleration at 15% L, a/g, 3-% accidence.Speed, knTable 2 Characteristics of a corvette-type S/P SWATHTablica 2 ZnaËajke poluglisirajuÊeg SWATH-a kao korveteShip type Patrol Attackcorvette corvetteThe full displacement, t, aprx. 400 1 200Full speed, knots 45 55Armament, t 50 100Useful area of decks, sq. m, aprx. 600 1 500Overall dimensions, m 40x16x9 55x28x12Design draught, m 3 4Main engine (GT) power, MW 2x8.5 GT2x22Design Sea State, Beaufort scale 4-5 5Helicopter weight, t 1x16 1 x 16Range, nm / Economy speed, knots 3 000 / 15 2 500 / 17Endurance, days 15 15Operability coefficient in NorthernAtlantic, %, aprx. 75 85               10 15 20 25 30 35 40234567Pitch amplitude, degrees, 3% accidence.Speed, knFigure 13 External view of a patrol S/P SWATH corvetteSlika 13 Vanjski izgled poluglisirajuÊe ophodne SWATH korveteFigure 14 Pitch amplitude in head waves of a patrol SWATH cor-vetteSlika 14 Amplituda posrtanja na valovima u pramac ophodneSWATH korvete328 56(2005)4, 323-328V. DUBROVSKY, K. MATVEEV HYDRODYNAMIC ASPECTS OF A HIGH-SPEED SWATH AND A NEW HULL FORMany automatic system of landing: from 20 to 40 knots inclusive.There is no other ship type that can provide such a level of speedand sea-keeping at so small displacement.2.3 Fast containershipAs shown in [2], the displacement of a SWATH with a newhull shape is excluded from above by the power of existing gasturbines. For example, a fast containership of this type (Figure 15)can carry a payload of 1 000 t at full speed of 60-65 knots over therange (at this speed) of 500 nm. Such a container-carrier can be analternative to the Japanese design of a Techno-Super-Liner, whichwas intended for similar initial data [4]. The proposed S/P SWATH,which is based on already conducted model tests, can ensure therequired characteristics and sufficiently high seaworthiness.Figure 15 A short-range fast container-carrierSlika 15 Brzi brod za prijevoz kontejnera maloga dosega2.4 Fast frigatesTable 3 Characteristics of a frigate-type S/P SWATHTablica 3 ZnaËajke poluglisirajuÊeg SWATH-a kao brze fregatePayload, t 200 400Usable area of decks, sq. m, aprx. 3 000 4 000Full displacement, t, aprx. 3 000 5 000Engine power, MW 4x22 4x50 / 4x65Full speed, knots, aprx. 55 50 / 65Design Sea State, Beaufort scale 6 6Number of helicopters 2 2Endurance, days 14 10Operability coefficient in NorthAtlantic, % 93 95Fast frigates can also be designed with the proposed shape ofgondolas (Figure 16). These battle ships should use gas turbinesfor the maximum available power. Two options of these frigateswere examined, with payloads of 200 t and 450 t. General char-acteristics of these ships are given in Table 3.Figure 16 External view of an S/P SWATH frigateSlika 16 Vanjski izgled poluglisirajuÊe SWATH fregateConclusionsBased on the conducted model tests, it is shown that the ap-plication of the new hull form can increase the speed of a SWATHup to the displacement Froude number 3 with a sufficiently highseaworthiness level. Combat ships of this type can ensure higherspeeds for the same (contemporary) engine power per ton of dis-placement. Estimations made for the new SWATH are given inFigure 17 over data available for traditional ships [4].Figure 17 The achievable speeds and corresponded relative po-wer of the new S/P SWATH (in the upper left part of thefigure). Other data are adopted from [4]Slika 17 Postizive brzine i odgovarajuÊa relativna snaga polu-glisirajuÊeg SWATH-a (u gornjem lijevom dijelu slike).                 Drugi su podaci uzeti iz [4]References[1] KRACH, A.M.: “SWATH–Hull Form with Low Destabilizing PitchMoment”, International Conference on High-Performance Marine Ve-hicles, Zevenwacht, South Africa, 1999, p. 124-135.[2] DUBROVSKY, V., LYAKHOVITSKY, A.: “Multi-Hull Ships”, Back-bone Publishing, Fair Lawn, NJ, USA, 2001.[3] KEANE, R.: “Naval Ship Design: High-Speed is Back Again”, 8th In-ternational Marine Design Conference, Athens, Greece, 2003.[4] BRICKNELL, D.J., CARLISLE, C.: “Propulsion for Fast Littoral Com-batants”, RINA International Conference SHIP 2004: Fare & Expedi-tionary Force, London, 2004.[5] KUSAKA, Y., et al.: “Research on Hydrodynamic Performance of TSL-A”, FAST-93, p.59-71,Yokohama, Japan.0 20 40 60 80 100 120 140 160 180 200 2200102030405060NavalAuxiliaries1 kW/tCoastalCraft 30 kW/t"Semi-planing"SWATH, 25-40 kW/tSpeed, knFast Attack Crafts,30-50 kW/tLittoral Combat Ships,20-30kW/tMain humpCorvettes,10-15 kW/tFrigates,10 kW/tDestroyers,5-10 lW/tShip length, m

Hydrodinamic Aspects of a High-Speed SWATH and New Hull Form

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