INTERNATIONAL JOURNAL OF MARITIME TECHNOLOGY IJMT Vol.9/ Wter 018 (33-40) Avalable ole at http://mt.r/browse.php?a_code=a-10-194-1&sd=1&slc_lag=e Dowloaded from mt.r at 5:56 +0430 o Wedesday July 11th 018 [ DOI: 10.95/mt.9.33 ] Resstace Predcto for a Novel Trmara wth Wave Percg Bow Karm Abar Valabad 1*, Mohammad Reza Khedmat, Abbas HasaAbad 3, Alreza Mohammad 3 1 Mare Faculty of Imam Khome Martme Uversty, Nowshahr-,Ira, Assstat Professor, Abar.arm@gmal.com(Correspodg Author) Departmet of Martme Egeerg of Amrabr Uversty of Techology, Tehra, Ira, Professor, Khedmat@aut.ac.r 3 Mare Faculty of Imam Khome Martme Uversty, Nowshahr-, Ira, Lecturer, Msc,alreza.or.mohammad@gmal.com, hasaabad74@gmal.com ARTICLE INFO Artcle Hstory: Receved: 13 May.017 Accepted: 6 Feb. 018 Keywords: Trmara Resstace Percg Bow Expermet ABSTRACT 1. Itroducto There s a creased terest trmara vessels due to ts advatages ad applcatos (Elc 003). Because of the stablty gaed from the sde hulls, the trmara ca use sleder hulls that reduce resduary resstace. As a cosequece, the trmara reduces fuel cosumpto compared to a equvalet moohull. The trmara s three hulls have the flexblty to accommodate may propulso plat arragemets. A mportat feature of the trmara form s the addtoal upper dec ad upper shp space that s created. For the same dsplacemet or volume as a moohull, the trmara form wll geerate a shp wth a greater legth ad, the useful cetral rego, greater upper dec beam that s extreme breadth betwee the two sde hulls, gvg the possblty for may potetal uses. The trmara may offer desrable motos performace. The log, sleder waterle of the ma hull provdes excellet seaeepg performace, beeft from the added collso protecto ad damaged stablty, the use of the sde hulls as armor for crtcal machery ad cotrol spaces the case of war vessels. The trmara hull form offers maor advatages sgature reducto to warshp desgers. Dyamc behavour of a trmara vessel s vestgated ths study. The body of the trmara s composed of a cetre hull wth a qute sleder wave percg bow profle (a legth-to-wdth rato of 1.96) ad two outrggers wth Wgley mathematcal body. Trmara hull form ad moto have bee extesvely studed due to the developmet of umercal ad aalytcal methods as well as the explotato of expermetal setup. I ths artcle, we vestgate the possblty to move the sde hulls logtudal ad trasversal wth respect to the ma hull order to fd the optmum stuato for mmum drag. The mathematcal approach s umercal method CFD wth the help of VOF. Moreover the expermetal measuremet was provded for some cases. The smulato results dcated good agreemet wth the expermetal results. The vestgatos udertae wth the scope of ths artcle provde a startg pot to vestgate the flow patter ad performace of such shps. 33 Hebblewhteetals. (007) vestgated the effects of the logtudal stagger of the sde hulls (outrggers) wth respect to the ceter hull o the motos heave ad ptch of a represetatve trmara hull. K. A. Valabad et al.(014) Ivestgated the Dyamc behavour of a trmara vessel. The lterature survey dcates that, to date, vestgatos o trmara hull forms have bee cofed to determg the effects of trasverse ad logtudal postos of the sde hulls maly o the resstace ad powerg characterstcs. Javamardetals. (008) vestgated the hydrodyamc resstace ad maeuverg of a trmara wth Wgley body form usg a CFD code. The results showed that for trmara cofgurato whe the three bow hulls are alged, as the speed creases, the rate of total drag growth wll decrease, because the legth of teracto betwee the waves created by the ma hull wth outrggers decreases. Resstace decreases wth creasg trasverse dstace where three hulls bow are alged, but creasg trasverse dstace does ot affect where three bodes ster are alged. The wor also uderled that hydrodyamc resstace s a mportat factor for trmara desg, but factors such as maeuverablty ad seaeepg are also cosderable.
Karm AbarValabad et al. / Resstace Predcto for a Novel Trmara wth Wave Percg Bow Dowloaded from mt.r at 5:56 +0430 o Wedesday July 11th 018 [ DOI: 10.95/mt.9.33 ] Outrggers posto has great effect o trmara maeuverablty. Whe the bow of three bodes are alged, the maeuverg qualty s ot good, because ths case, vessel trm causes outrggers to come out from water. Therefore moto stablty decreases. Other cofguratos have almost the same turg crcles dameter. But from resstace pot of vew, whe the ster of three hulls are alged, less thrust force s ecessary, so t s more effectve tha other cofguratos. I. Mzeetals. (009) studed a large Trmara shp - Heavy Ar Lft Support Shp (HALSS) showg a large chage resstace (70%) due to a moderate (15% from legth of ceter hull) shft the logtudal sde hull posto. The wor also focused o the fluece of the segs o the ster flow, uderstood wth the ad of several Computatoal Flud Dyamcs calculatos performed wth varous computatoal codes ad compared to model test data. N etals. (011) otced that sce trm ad sage are sgfcat whle vessels are advacg forward wth hgh speed, the predcted vessel resstace based o restraed model theory or expermet may ot be real resstace of vessels durg voyage. They foud t ecessary to tae the fluece of hull gesture to accout for predctg the resstace of hgh-speed shp. They treated the resstace problem of hgh speed shp wth the vscous flow theory, ad adapted the dyamc mesh techque to cocde wth varato of hull gesture of hgh speed vessel o voyage. The smulato of the models of S60 shp ad a trmara movg towg ta wth hgh speed correspoded to the expermetal data, dcatg that the resstace predcto for hgh speed vessels should tae hull gesture to cosderato ad the dyamc mesh method proposed was effectve calculatg the resstace of hgh speed vessels. H. Zeraatgar et al.(011) studed a squat for vessels wth Seres-60 hull forms shallow water. Whe a shp moves the shallow waters, the velocty of the flud flow at the bottom of the shp creases ad the pressure decreases whch tur leads to the decrease of buoyacy force ad the crease of the resstace by creasg shp draught. The scope of the preset wor s to move the lateral hull X (logtudal) ad Y (trasversal) drecto (Y1 ad Y) to fd the best posto regardg the least drag. The trmara velocty vares wth the o-dmesoal Froude umber(fr): 0.15, 0.3, 0.45, 0.6, 0.75, 0.9 ad 1. The smulato was performed wth the VOF method. Descrpto of the Model Wave percg bow profle (Fgure 1) has two advatages: mprovg the hydrodyamc performace as well as smplfyg the costructo process [1-]: The smplfyg costructo process cludes %15 decrease labour egagemet, %50 decrease assembly, weldg ad bedg expeses (due to ts smplcty%15 decrease algmet process operato ad evetually there s a potetal of beg automatcally welded [1-]; The sgfcat mprovemet of wave percg bow profle cludes hgher eergy-effcet characterstc waves, hgher trast speed, reduced power cosumpto, mproved fuel effcecy, creased operatoal tme, creased schedule-eepg, elmato of slammg ad bow mpact, soft etry waves, less spray, low accelerato levels, reduced vbrato levels, creased comfort ad avalable crew rest tme, safer worplace due to smoother motos ad protecto provded by hull [1-3]. To fabrcate the model the fbre reforced plastc was exploted. The model was made wth a scale factor of accordg to ITTC 7.5-01-01-01. The hull form was modelled up to the ma dec level ad o appedages were ftted. Legth betwee perpedcular ad servce speed of the vessel are equal to 14 m ad 5 ots, respectvely. These features correspod to the Froude umber of 0.368. Fgure shows trasverse sectoal vew of the ma hull as well as the supportg sde hulls; Table 1 presets the prcpal dmesos of the prototype vessel ad ts scaled modelwth scale factor λ=80, whle the body les are show Fgure 3. The model has bee bult up to the ma dec omttg shaft, propeller, steerg ad propulso systems. I order to separate erta forces from hydrodyamc forces, before each test, draft ad trm values must be adusted to compesate the dstrbuto of weght ad erta forces the model. Thus, locato of cetre of gravty ad the values of gyrato rad must be ow. The model s loaded ad ballasted such a way that the values of Vertcal posto of Cetre of Gravty (VCG), Logtudal posto of Cetre of Gravty (LCG) ad also rad of gyrato for both ptch ad roll motos ca be easly reached. Locato of cetre of gravty for the model was determed usg suspeso method, Fgure 4(a). Moreover, Bfflar method [1] was used to determe the rad of gyrato ar, Fgure 4(b). Radus of gyrato s foud to be equal to 0.387 m for ptch moto (about 5 percet of water le legth) ad 0.095 m for roll moto (about 35 percet of overall beam). Fgure. 1 The cetre (ma) hull s wave percg bow profle 34
Karm AbarValabad et al./ IJMT 018, Vol. 9; 33-40 Dowloaded from mt.r at 5:56 +0430 o Wedesday July 11th 018 [ DOI: 10.95/mt.9.33 ] Fgure. Trasverse sectoal vew of the ma hull ad ts supportg sde hulls Fgure. 3 Body les ad geeral layout of the trmara vessel ad ts scaled model cetre hull sde hull trmara model (a) (b) Fgure. (a) Applcato of the suspeso method to determe the model s cetre of gravty, (b) Applcato of Bfflar method for determato of rad of gyrato Fgure. 3 Towg ta facltes of the Mare Research Cetre (MRC) at the Sharf Uversty of Techology (SUT) Table 1. The prcpal dmesos of prototype trmara ad ts scaled modelwth scale factor λ=80 Characterstc[ut] Model Legth overall [m] 1.55 Legth o waterle [m] 1.54 Beam overall [m] 7.x10 - Beam o waterle [m] 1 x10 - Depth [m] 14.7 x10 - Draught [m] 5.48 x10 - Legth of sde hull [m] 45 x10 - Beam of sde hull [m].95 x10 - Depth of sde hull [m] 10.17 x10 - Draft of sde hull [m] 0.93 x10 - Clearace betwee cetrele of 1.15 x10 - ma ad sde hull [m] Dsplacemet [to] 4.39 x10-3 3. Expermetal Set-Up The expermetal program was performed explotg the towg ta facltes of Mare Research Cetre (MRC) at Sharf Uversty of Techology (SUT), Fgure 5. The towg ta cludes three basc parts: the ta, the computerzed towg system ad the wave geerator. Legth ad wdth of the ta are 4 m ad.5 m, respectvely (see Table ). Wave geerator s able to produce ether regular or rregular waves wth legth of 0.3 m to.8 m ad maxmum ampltude of 0.1 m. I order to damp the waves a wave damper s cotrved at the ed of the ta. The Labvew software was developed to acqure the measured hull s motos. Table 1. Ma partculars of the towg ta of MRC at (SUT) Characterstc Value Legth 5 [m] Wdth.5 [m] Depth 1. [m] Maxmum speed of carrage 6 [m/s] Maxmum accelerato of carrage [m/s] Towg system Electromotor [4w] 35 4. Expermetal Program A seres of resstace tests calm water s coducted o the trmara model order to detfy the total
Karm AbarValabad et al. / Resstace Predcto for a Novel Trmara wth Wave Percg Bow Dowloaded from mt.r at 5:56 +0430 o Wedesday July 11th 018 [ DOI: 10.95/mt.9.33 ] resstace. The dsplacemet of the model s determed cosderg the dsplacemet of the prototype vessel (48 to). Other codtos such as trm ad draft are also establshed so that the real desg codtos of the vessel are fulflled. Maxmum speed of the model s equal to m/s correspodg to the speed of 35 ots of the prototype vessel. Fgure 6 shows a typcal testg stuato. Fgure. 6 Model durg resstace test uder head sea codto (model speed=0.5 m/s) Every test s repeated 3 tmes to assure the valdty of the test results. I addto to vsual cotrol of water surface, tests are carred out wth 15 mutes delay for the water surface to calm dow. 5. Numercal Model The Reyolds average Naver stoes equato were used wth ths study to umercally model the flow characterstc aroud the trmara: ( u ) 0 ( 1,,3) (1) t x ( u ) ( uu ) ( ) u u u u u p t x x x x 3 x x x 1 () (3) (4) 1 Where t s tme, s the desty, s the dyamc vscosty, s the flud phase umber, s the phase fracto ad uu s the turbulet Reyolds stress ( ). u u u uu t t x x 3 x (5) Where t s turbulet vscosty, s the turbulet etc eergy. To solve such problem the stadard model s used wth ths study through the followg equatos: ( ) u t x x x t P S (6) 36 u t x x x t C1 P C S Where the dsspato of turbulet etc eergy s, P s the producto of turbulet etc eergy, S ad S are source terms ad s the dyamc turbulet vscosty. P Ad t are as follow: t C (8) u P uu (9) x Where: C1 1.44, C 1.9, C 0.99, 1, 1.3 These set of equatos are solved va Fluet code. The terpolato methods used are as follow: SIMPLE method for Pressure-Velocty Couplg, Gree-Gauss cell based for Gradet, PRESTO! For pressure, secod order upwd for Mometum, QUICK for Volume Fracto, Secod order Upwd for Turbulet Ketc eergy ad turbulet dsspato rate. For the smulato of the free surface ad also capturg the wave patter a volume of flud method (VOF) s used. Through ths method every cell s cosdered to be occuped wth two fluds: water ad ar wth a volume fracto whch satsfes the followg equato: 1 t (7) (10) 1 (11) Every trasport varable ( ) s represeted by the phase fracto through the followg equato: (1) 1 5.1 Boudary Codto ad Mesh Desty Aalyss The trmara was modelled a umercal doma cosstg of water ad ar. The ar ad water have a commo surface at the level of 4.5 m above the lowest part of the trmara. The let s dvded to two let codtos: ar let velocty ad water let velocty, the outlet s thoroughly defed as outflow. The two phases of flud, ar ad water s treated wth multphase mxture model Fluet. The volume of flud (VOF) approach s resposble to capture the two phase flud behavour specfcally at the terface level. Grd sestvtes were performed to esure the relablty of the umercal model. Namely, the most mportat parameter of ths study.e. the drag force was adopted as cotrolled varable. The mesh desty was progressvely creased but the quattes chaged less
tha 3%. Accordg to the sestvty aalyss, a fal mesh of approxmately 450K elemets was adopted for the smulatos. Karm AbarValabad et al./ IJMT 018, Vol. 9; 33-40 Dowloaded from mt.r at 5:56 +0430 o Wedesday July 11th 018 [ DOI: 10.95/mt.9.33 ] 6. Results ad Dscusso The expermetal tests were doe o the trmara model to vestgate the drag force the rage of low to moderate Fr umber: 0.1 to 0.51. To ths am, the sde hulls are located at the mddle part of the ma hull ad the trasversal postos were vared wth two cofguratos, 15 mm (cofgurato 1) ad 150 mm (cofgurato ) away from the ma hull (see table 3 ad 4). Table. Drag force measured for the trmara wth cofgurato 1 for the Fr 0.1~0.51. Cofgurato 1 Fr 0.1 0.6 0.31 0.36 0.41 0.46 0.51 Drag(N) 99 NA 13 6 45 375 411 Table 3. Drag force measured for the trmara wth cofgurato for the Fr 0.1~0.51. Cofgurato Fr 0.1 0.6 0.31 0.36 0.41 0.46 0.51 Drag(N) 41 86 10 151 189 6 51 Accordg to table 3 by creasg the Fr umber the drag force creases. Moreover eve a slght crease the trasversal posto of the sde hull (cofg. 1 to cofg. ) causes a reducto o trmara drag force. The reaso mght be based o the fact that by creasg the dstace betwee sde hull ad ma hull the wave teracto produced by each hull decreases; more over by approachg the hulls to each other (cofg. 1) the trapped waes betwee the hulls wll have less space to be damped ad thus geerate aother source of drag cremet. The umercal smulato was valdated by comparg wth the expermetal results. To ths am a parameter: the rato of the drag of varous velocty to the drag of the lowest velocty related to Fr = 0.1 s troduced as crtero factor. For ths reaso two cases of trmara cofgurato were studed: case I, the sde hulls are at 9.6 meter trasversal dstace ad 18 meter logtudal dstace (correspodg to model trmara wth 00 mm logtudal ad 15 mm trasversal sde hull posto) ad case II, the sde hulls are 1 meter trasversal dstace ad exactly at the rear posto of the ma hull (correspodg to model trmara wth 0 mm logtudal ad 150 mm trasversal sde hull posto). The result of such comparso s provded below (Fgures 7 ad 8): 37 Fgure. 7 The Drag rato of case I for the data derved from the umercal approach ad resulted from the expermetal setup Fgure. 8The Drag rato of case II for the data derved from the umercal approach ad resulted from the expermetal setup The drag rato s defed as C d C d0, whle C d0 s the total drag at Fr= 0.1, the avalable expermetal results are up to Fr umber 0.51. There s a good agreemet betwee the treds of the two dagrams. At case I, the umercal approach shows a bt of overestmato however both dagrams show pea ad valley, though the umercal results s more flatteed relatvely ad the valley value s see hgher Fr umber. The reaso for the more scattered type data of the expermetal result s due to the fact that t also cocludes the wave pheomeo, coversely the umercal approach may poorly capture such evet. As see case II whe the sde hull s postoed at the rear part of the ma hull together wth the hgher trasversal dstace, the expermetal result has a ascedg tred wth almost costat slope whch s also repeated the umercal approach result. Here however the umercal approach uderestmates the Drag rato. The almost costat slope at case II compared to a slghtly slope fluctuato at case I reveals the effect of postog the sde hull at the mddle part of the ma hull, that s, the effect of wave mag, wave breag ad wave teracto may play a role; specfc the logtude postog of the sde hull s the source of wave mag or wave breag ad the trasverse closeess s the source of the wave teracto. Thus due to further trasverse dstace of the sde hull to the ma hull as well as postog at the rear part of the ma hull at case II caused less fluctuato over the drag rato. As of the am of the curret study, our vestgato was focused
Karm AbarValabad et al. / Resstace Predcto for a Novel Trmara wth Wave Percg Bow Dowloaded from mt.r at 5:56 +0430 o Wedesday July 11th 018 [ DOI: 10.95/mt.9.33 ] to optmze the logtudal posto of the sde hull for two ma cases, say, sde hull trasverse posto: Y1= 9.6 m ad Y= 1m. The sde hull accordgly advaces step by step toward the frot of the ma hull ad utl t reaches to the mddle of the ma hull of the trmara. More advacg the posto of the sde hull was ot the purpose of ths study. More precsely several trmara were modeled whle the sde hulls are moved from the very rear part of the ma hull to 40% of the legth of the trmara. The optmzato parameter s the total drag cossts of the pressure ad vscous drag. Here the results based o the total drag are provded. It ca be see that how the trmara behaves sometmes wth radcal drag varatos wth respect to the trmara sde hulls posto ad the Fr umber. A wde rage of Fr umber from very low to very hgh value were examed through the umercal approach; Fr umber equal to 0.15, 0.30, 0.45, 0.60, 0.75, 0.90 ad 1. Fgures 9 depct the varatos of total drag versus logtudal posto of the sde hull for varous Fr umber whe the trasversal dstace s Y1= 9.6 m A overall loo o the total drag dagram wth varatos of Fr umber dcates that geeral the total drag creases by creasg the Fr umber however some Fr umbers such as 0.15, 0.45, 0.6 ad 1 the slope of the dagram turs dow whe the sde hulls get close to the mddle part of the ma hull. By movg the sde hull from the rear part to the frot part of the trmara, the total drag vares three stages; at frst ad the last stage the total drag varato slope s low whle betwee those stages the varato slope s very hgh. Thus movg the sde hull from the rear part to somewhere aroud 5% of the legth of the ma hull causes the hghest level of total drag most of the cases. I partcular at Fr umber 0.15 ad 0.6 at the frst stage the drag ether decrease or does ot crease. At the last stage aga there s a reducto drag force. Fr umber 0.3 ad 0.75 show a always ascedg dagram. At Fr umber 0.45 the total drag dagram s ascedg utl close to the mddle of the trmara at whch the total drag slghtly decreases. Fgures 10 depct the varatos of total drag versus logtudal posto of sde hull for varous Fr umber whe the trasversal dstace s Y= 1m. Fgure. 10 The varato of total drag vs. x posto of the sde hull at Fr umber whe the trasversal dstace s Y1= 1 m Whe the trasversal dstace s Y=1 m, the case of Fr umber 0.15 behaves dfferet way comparg to the rest of the Fr umbers, that s, at Fr umber 0.15 there s a crease, decrease ad aga crease total drag level versus advacg the sde hull, though t should be cosdered that the total chage Fr umber 0.15 s ot so sgfcat. For the rest of Fr umbers there s almost smlar behavor: there s a crease of total drag followed by two stages of decrease total drag wth hgher ad lower slope respectvely. By creasg the Fr umber the varato of total drag versus sde hull movemet creases. Moreover the total drag value creases by creasg the Fr umber. Fgure. 11 Vscous to Pressure force rato vs. Fr umber for varous sde hull logtudal posto at Y1= 9.6 m. Fgure. 1 Vscous to Pressure force rato vs. Fr umber for varous sde hull logtudal posto at Y= 1m. Fgure. 9 The varato of total drag vs. x posto of the sde hull at Fr umber whe the trasversal dstace s Y1= 9.6 m 38 Fgures 1 ad 13 dcate the varato of Vscous to Pressure Force rato versus Fr umber based o the logtudal ad trasversal posto of the sde hull
Karm AbarValabad et al./ IJMT 018, Vol. 9; 33-40 Dowloaded from mt.r at 5:56 +0430 o Wedesday July 11th 018 [ DOI: 10.95/mt.9.33 ] (logtudal postos are here appled as X1=0 m, X= 18 m, X3= 31 m ad X4= 49 m away from the very rear part of the ma hull). The vscous to pressure force rato has a dfferet behavor for the case of Y1 ad Y. At Y1 the varatos of Vscous to Pressure Force rato for varous X do ot dffer very much. For both cases of Y1 ad Y the dagram of the vscous to pressure force rato s descedg. The dfferece betwee the cases wth dfferet logtudal values (X) at Y1 s much less tha Y. At Y although the tred of the dagram for the cases wth dfferet logtudal values (X) are more or less smlar the X1 has a dfferet behavor terms pf dcatg more fluctuato. Moreover for X to X4 there s a crease o the level of vscous to pressure force rato whle ths tred s ot applcable cosderg for X1 to X. Geerally speag the vscous to pressure force rato s always bgger tha 1 dcatg that the vscous force trmara s bgger tha the pressure force. Y= 9.6 m ad X1 Y= 9.6 m ad X Y= 9.6 m ad X3 Y= 9.6 m ad X4 Y= 1 m ad X1 Y= 1 m ad X Y= 1 m ad X3 Y= 1 m ad X4 Fgure. 13Volume of water fracto at plae of water/ar tal level for trmara dfferet cofguratos Fgures 13 dcate thetypcally volume of water fracto at the tal posto of water/ar level Fr0.45. These cotours actually represet the pea ad valley of the water as a cosequece of wave producto. A very sleder shape of the ma hull as well as the sde hulls prevets ay sgfcat perturbato at the frot sde of the trmara whle coversely at the aft part of both the ma hull ad sde hulls lots of perturbatos are created. Thus for the cofguratos of whch the sde hull s located closer to the aft, the total area affected by such perturbato patter s wdeed ad lmted to the aft part, coversely by movg the sde hull toward the frot part of the ma hull the affected area s legtheed but also arrowed whch attached to the ma hull. Moreover by creasg the trasversal dstace of the sde hull, the perturbato wdeed ad also legtheed toward the aft of the trmara ad affected far doma beyod that of closer trasversal sde hull case (Y=9.6 m). 39
Karm AbarValabad et al. / Resstace Predcto for a Novel Trmara wth Wave Percg Bow Dowloaded from mt.r at 5:56 +0430 o Wedesday July 11th 018 [ DOI: 10.95/mt.9.33 ] 7. Cocluso I ths study a expermetal setup as well as umercal approach (CFD) was exploted order to predct the flow patter ad total drag level based o the varous cofgurato of sde hulls o a trmara wth a ew hull profle: wave percg bow. The results of the CFD study had a good agreemet wth those of expermetal setup. Va curret study t was cocluded that the varous cofgurato shows dfferet flow patter ad more mportatly dfferet total drag value. More specfcally the tred ad value of total drag chages based o the Fr umber ad so the trmara velocty. Ths fact partcular suggests that ay ewly modfcato of the trmara should be appled cosderg the desred velocty. Furthermore the total drag umber creases rapdly by creasg the Fr umber dcatg more desg effort for the trmara modfcato at hgher speed. The flow patter ad the produced wave s also depeds o the sde hull at whch by approachg the sde hull to the ma hull the affected area arrowed ad became smaller, coversely the hgher trasversal dstace causes the affected area stretched to the aft of the trmara although the wave teracto may reduce. Furthermore, movg the sde hull toward the frot part of the ma hull causes the affected area stretched toward the frot sde however t arrowed ad somewhat lmted aroud ad attached to the hull wall area. 8. Refereces 1-Elc, Z.; (003), Wave mag resstace characterstcs of trmara hulls: Ms Thess; Naval Postgraduate School, Moterey, Calfora, Avalable from Iteret: www.dtc.ml/dtc/tr/fulltext/u/a40575.pdf - Ma, K.J. et al.; (007),Resstace Predctos for a Hgh-Speed Sealft Trmara, 9th It. Cof. o Numercal Shp Hydrodyamcs A Arbor, Mchga, Aug. 5-8. www.dtc.ml/dtc/tr/fulltext/u/p039.pdf 3- Hebblewhte, K.; Sahoo, P. K.; Doctors, L.J. (007),A case study: theoretcal ad expermetal aalyss of moto characterstcs of a trmara hull form, SAOS Vol. No. pp. 149 156. http://dx.do.org/10.1080/174453007014304 4- Fag, M.C.; Che, T.Y. (008),A parametrc study of wave loads o trmara shps travelg waves, Ocea Egeerg 35: 749 76. http://dx.do.org/10.1016/.oceaeg.008.0.001 5- Javamard, M.R.; Jahabahsh, E.; Sef, M.S.; Sayyaad, H. (008),Hydrodyamc Aalyss of Trmara Vessels, Polsh Martme Research 1(55) Vol 15; pp. 11-18. DOI: 10.478/v1001-007-0046-5 6- Valabad K. A.; Khedmat, M.R.; Sef, M.S. (014),Expermetal Study o Heave ad Ptch Moto Characterstcs of A Wave-Percg Trmara, Trasactos of FAMENA 38 (3), 13-6. http://hrca.srce.hr/19609 7- Mze, I.; Karafath, G.; Queutey, P.; Vsoeau, M. (009),Iterferece Pheomeo Desg of Trmara Shp, 10th Iteratoal Coferece o Fast Sea Trasportato, FAST, Athes, Greece. 8- Chog-be, N.; Re-chua, Z.; Guo-pg, M.; Ju, F. (011),Hull Gesture ad Resstace Predcto of Hgh-Speed Vessels, J. of Hydrodyamcs, 3():34-40. DOI: 10.1016/S1001-6058(10)60108-4 9- Bo, Y.; Zuo-chao, W.; Mg, W. (01),Numercal Smulato of Naval Shp s Roll Dampg Based o CFD, The Secod SREE Coferece o Egeerg Modellg ad Smulato, Proceda Egeerg 37: 14 18, Elsever. do:10.1016/.proeg.01.04.194 10- Zeraatgar, H.; Valabad, K.A.; Yousefead, R. (011),Parametrc Aalyss of Shp Squat Shallow Water by Model Test, Brodograda 6 (1), 37-43. 40