Seakeeping Analysis of two Medium-speed Twin-hull Models

Journal of Ship Production and Design, Vol. 31, No. 3, August 2015, pp. 192 200 http://dx.doi.org/10.5957/jspd.31.3.140020 Seakeeping Analysis of two Medium-speed Twin-hull Models George Zaraphonitis, Gregory J. Grigoropoulos, Dimitra P. Damala, and Dimitris Mourkoyannis School of Naval Architecture and Marine Engineering, National Technical University of Athens (NTUA), Athens, Greece The use of twin-hull ships for high-speed passenger and car-passenger transportation is widespread, whereas their potential use for high-speed cargo transportation was estimated as limited. The present article discusses the seakeeping performance of two twin-hull models of an innovative medium-speed container ship design. Their hull form was the result of a thorough hydrodynamic optimization performed at the School of Naval Architecture and Marine Engineering of NTUA aiming to minimize the calm water resistance within the EU-funded project EU-CargoXpress. The seakeeping analysis was performed by applying numerical tools and also by performing a series of experiments in the towing tank of NTUA and MARINTEK. The obtained results are presented and discussed. Keywords: seakeeping; twin-hull; containership; numerical analysis; model tests 1. Introduction TWIN-HULL SHIPS are extensively used for high-speed passenger and car-passenger transportation. Many designers and shipbuilders investigated the possibility to operate them also as fast cargo ships without much success yet. Within the research project EU-CargoXpress of the European Union Seventh Framework Program, an alternative potential use of the twin-hulls concept as medium speed twin-hull container ships has been investigated. After an extensive hull form optimization aiming to minimize calm water resistance, the seakeeping analysis of the resulting hull forms was performed by applying numerical tools and also by performing a series of experiments in the towing tanks of NTUA and MARINTEK. More specifically, calculations have been performed using three different approaches of varying complexity and theoretical consistency. The first one is based on strip theory adapted to twin-hull vessels. The second is a fully three-dimensional (3D) approach based on the distribution of pulsating Green sources over the wetted surface to calculate the velocity potential using appropriate correction terms to account for the forward speed. The third also fully 3D approach is based on the distribution of Rankine sources over the wetted and the free surface to satisfy the linear free surface condition. The numerical results are compared with each other and with experimental measurements. The validity of the applied approaches is discussed. Manuscript received by JSPD Committee July 14, 2014; accepted August 19, 2014. 2.1. Strip theory method 2. Numerical tools Among the various codes implementing strip theory for twin-hulls, the codes MOT35 and MOT246 (McCreight & Lee 1976) were selected to calculate the dynamic response in regular waves. The codes use the modified strip theory of Salvesen et al. (1970), disregarding the transom stern terms, coupled with the close-fit hull form representation proposed by Frank (1967), as extended by Lee et al. (1971) to twin-hull sections, to solve the two-dimensional potential flow problem. They also take into account the viscous components applying appropriate semiempirical correction terms and can incorporate the effect of foils, although this capability has not been used in our evaluations because the vessel is not quite fast. The theoretical background of MOT codes is presented in detail by Lee (1976). 2.2. Three-dimensional Green source panel method The second approach is a fully 3D panel method for the evaluation of the responses of marine structures at zero speed, subject to incident regular waves, developed by Papanikolaou (1985) and based on the distribution of zero-speed pulsating Green sources over the wetted surface to express the radiation and diffraction potentials. This procedure was extended by Papanikolaou et al. (1990) for the case of a vessel advancing with forward speed based on a simplification of the exact free 192 AUGUST 2015 2158-2874/15/3103-0192$00.00/0 JOURNAL OF SHIP PRODUCTION AND DESIGN

surface boundary condition, enabling the use of the zero-speed pulsating Green source for the solution of the resulting boundary value problems. A computer program (NEWDRIFT) based on this procedure was developed and extensively used and validated against available experimental results for a series of vessels traveling in general with low to moderate forward speed (at Froude numbers up to 0.35). The software has been also extended to treat multihull vessels and in particular catamaran and SWATH ships. 2.3. Three-dimensional Rankine source panel method The third approach refers to the 3D time-domain, panel code SWAN2 (2002). The general formulation is described by Sclavounos (1996), whereas the specific time-domain solution was presented in detail by Kring (1994). The software implements a fully 3D approach based on the distribution of Rankine sources over the wetted and the free surface. The linear free surface condition is satisfied, whereas it has the capability of taking into account the nonlinear Froude-Krylov and hydrostatic forces. This option, however, was not activated in the calculation presented here, because it led to some diverging dynamic responses. Furthermore, in the use of SWAN2, an iterative procedure was added to converge to the actual dynamic draft and trim of the vessel at each speed. A sensitivity analysis was conducted to define a suitable extent of the free surface grid in the longitudinal and lateral directions as well as the respective number of panels fitted on the wetted surface of the vessel. Table 1 Main particulars of twin-hull EU-CargoXpress Main Characteristic, Symbol, Hull A Hull B Displacement, D (mt) 3000 2514.2 Length at waterline L WL (m) 77.610 82.648 Breadth overall B (m) 21.000 21.000 Breadth, demihull (m) 7.130 6.160 Draft, T (m) 4.680 4.096 Trim by stern t, (m) 0.334 0.520 LCG fwd of AP (m) 37.310 38.789 VCG above BL (m) 12.540 12.100 Metacentric height, GM (m) 5.080 11.130 Hull separation, S (m) 13.870 14.840 Service speed (knots) 15.000 13.000 Roll Radius of Gyration, R XX (m) 6.500 7.800 Pitch Radius of Gyration, R YY (m) 17.800 19.750 3. The test cases The studied hull forms are the result of an extensive optimization performed in the framework of the EU-funded research project EU-CargoXpress. The objective of this project was to deliver a small innovative container ship for coastal operation based on the twin-hull configuration. The hull form optimization has been performed using an innovative procedure developed by NTUA based on the integration of suitable software tools, i.e., the ship design software NAPA for the design of hull forms, an in-house computational fluid dynamics code for the evaluation of resistance in calm water and a general purpose multiobjective optimization software (modefrontier) to set up the optimization problem and to control the overall process. The core of the procedure is a parametric model developed within NAPA for the completely automatic generation of alternative hull forms based on a set of design parameters. A series of parametric models has been developed, each one of them being adapted to diverse design requirements, as defined during the evolution of the project. Using these parametric models, 15 different optimization studies have been performed; from each one of them, several hundreds of alternative hull forms have been automatically Fig. 1 Seakeeping test in NTUA with hull form A derived and evaluated. Among them two different hull forms have been finally selected based on their favorable hydrodynamic characteristics to be further investigated and model-tested. The main particulars of the two hull forms are tabulated in Table 1. The two hull forms have been model-tested by NTUA and MARINTEK. Three models have been constructed, one based on the first hull form and two based on the second one (Figs. 1 3). NTUA performed resistance and seakeeping tests in head seas for the first hull form (Zaraphonitis et al. 2011) and resistance tests in upright and heeled condition for the second hull form. MARINTEK performed self-propulsion and seakeeping tests in head seas for the second hull form (Rambech 2012). Seakeeping calculations applying numerical tools have been performed for both hull forms by NTUA. As can be seen from Fig. 1, a hull form with a relatively large bulbous bow was selected for model A, whereas a rather H 1/3 ¼ significant wave height (m) RAO ¼ Response Amplitude Operator RMS ¼ root mean square RVM ¼ relative vertical motion RVV ¼ relative vertical velocity Nomenclature g ¼ gravitational acceleration T P ¼ modal period (seconds) U ¼ forward speed w 0 ¼ wave frequency w ¼ encounter frequency a w ¼ wave amplitude k ¼ wave number b ¼ wave heading (b ¼180 for head waves) S w (w) ¼ spectral density of incident wave S i (w) ¼ spectral density of response i AUGUST 2015 JOURNAL OF SHIP PRODUCTION AND DESIGN 193

The derivation of the responses in irregular seaways in the cases of the strip theory code MOT and the 3D Green Source Panel Method software NEWDRIFT was carried out as follows for the response i: S i ðwþ ¼ S w ðwþraoi 2 ð1þ Fig. 2 Resistance tests in NTUA with hull form B In the case of the time-domain code SWAN2, the statistical results were derived by applying fast Fourier transform on the respective time histories. Head (b ¼ 180 ), bow-quartering (b ¼ 135 ), and beam (b ¼ 90 ) waves were considered. The following responses were evaluated during the numerical analysis: heave, pitch, roll, vertical acceleration at the bow, at the Center of Gravity (CG) and at the stern. Model tests at the same sea states have been conducted in the Towing Tank of the Laboratory for Ship and Marine Hydrodynamics of NTUA. As a result of budgetary limitations of the CargoXpress project, it was not possible to include tank tests in regular waves in the test program. The dimensions of the facility, with a length of 91 m, breadth of 4.56 m, and a depth of 3.00 m, allow only for testsinheadwaves. In the following, the numerical predictions in regular waves are presented followed by the respective results in random seaways. The latter will be compared with the respective experimental results. 4.1. Regular wave results Fig. 3 The model of hull form B used for the seakeeping tests in MARINTEK unconventional bow shape with a reverse profile inclination at and above the waterline was selected for model B. 4. Seakeeping results for hull form A The first hull form was optimized for a service speed of 15 knots. However, the seakeeping tests and calculations have been performed for a comparatively reduced speed of 13 knots. This is because it was anticipated that a vessel of such a small size would not be able to sustain its design speed at the sea states under consideration. The dynamic performance of hull form A was numerically evaluated at a set of regular waves with periods in the range from 2 seconds to 15 seconds. Furthermore, the seakeeping behavior of the vessel was investigated in three realistic seaways, modeled according to the Bretschneider formulation. The corresponding significant wave heights and peak periods are listed in Table 2. In Figs. 4 11 the Response Amplitude Operator (RAO) curves for heave, pitch, and roll responses of hull form A are plotted on the basis of the numerical results using all three methods described in Section 2. All RAO curves are made nondimensional following the guidelines of ITTC (1984). Heave has been nondimensionalized by the wave amplitude (a w ), whereas pitch and roll by the product of the wave amplitude times the wave number (a w.k). Accelerations are divided by (g.a w /L WL ) to become nondimensional. The horizontal axis in all the plots presented here corresponds to the wave period. Following these figures, NEWDRIFT predicts a more acute peak for the heave motion, whereas all three codes estimate quite well the heave resonant period. The first of the twin peaks of the heave motion that may be observed in the results of NEWDRIFT code both in head and bow-quartering waves corresponds to the heave resonance, whereas the second one is a Table 2 Tested wave spectra for hull form A Sea State H 1/3 (m) T P (seconds) A 2 7.7 B 3 8.6 C 4 10.3 Fig. 4 Heave Response Amplitude Operator (RAO) curves, head waves 194 AUGUST 2015 JOURNAL OF SHIP PRODUCTION AND DESIGN

Fig. 5 Heave Response Amplitude Operator (RAO) curves, bowquartering waves Fig. 8 Pitch Response Amplitude Operator (RAO), bow-quartering waves Fig. 6 Heave Response Amplitude Operator (RAO), beam waves Fig. 9 Pitch Response Amplitude Operator (RAO), beam waves Fig. 7 Pitch Response Amplitude Operator (RAO), head waves Fig. 10 Roll Response Amplitude Operator (RAO), bow-quartering waves result of the heave and pitch coupling. The pitch RAO curves derived by SWAN2 do not present any peak, whereas a sharp peak is observed in the predictions of the two other codes. In contrast to the heave motion, the pitch responses around resonance, predicted by the strip theory code MOT, are quite higher than those predicted by NEWDRIFT both for head and bow-quartering waves. The numerical predictions for the RAO curves of the roll response are plotted in Figs. 10 and 11. MOT takes into account viscous damping components in the calculations using appropriate empirical formulae. However, a roll resonance is observed in the MOT predictions; whereas even without damping components, the results obtained with SWAN2 do not exhibit any peak at all. AUGUST 2015 JOURNAL OF SHIP PRODUCTION AND DESIGN 195

Fig. 14 Stern vertical acceleration, head waves Fig. 11 Roll Response Amplitude Operator (RAO), beam waves The numerical predictions for the vertical acceleration at the bow and stern of hull form A are plotted in Figs. 12 15 for head and bow-quartering waves using all three prediction codes. A relatively better agreement among the three codes may be observed in the acceleration results for the bow area than those for the stern. A sharp peak is predicted by NEWDRIFT at the bow area, whereas SWAN2 gives the smaller peak responses with the MOT35 results being generally in between the other two curves. For the stern area, the higher responses are predicted by MOT35 with the lower results once again predicted Fig. 15 Stern vertical acceleration, bow-quartering waves by SWAN2. Two distinct peaks are predicted by NEWDRIFT, corresponding to the heave and pitch resonant periods. 4.2. Dynamic responses in seaways Fig. 12 Bow vertical acceleration, head waves Fig. 13 Bow vertical acceleration, bow-quartering waves To compare the numerical predictions, derived by the three methods under consideration, with the experimental measurements obtained with a scale model of hull form A, the root mean square (RMS) dynamic responses in the three sea states listed in Table 2 have been calculated. The RMS predictions for the heave and pitch responses as well as for the vertical acceleration at the ship s bow, stern, and at the center of gravity, obtained numerically (for head and bow-quartering seas) and experimentally (only for head seas), are listed in Tables 3 and 4. In addition, the predicted RMS values for sway, roll, and yaw motions, derived by MOT 246 and SWAN2 for oblique seas (bow-quartering and beam seas), are presented in Table 5. According to the results presented in Table 3, for the head sea case, the numerical predictions of heave motion by MOT35 are in better agreement with the model tests than the other two codes. In the case of the pitch motion, better agreement with the experiments is shown by NEWDRIFT. The results obtained by SWAN2 are smaller than those obtained by the other two codes and by the tank tests, whereas MOT35 gave the larger pitch predictions. In bow-quartering seas (Table 4), MOT35 and SWAN2 are predicting similar results for the heave motion, whereas the 196 AUGUST 2015 JOURNAL OF SHIP PRODUCTION AND DESIGN

Table 3 Comparison of results in head waves Table 5 Sway RMS, bow-quartering and beam waves (m) Sea State Experimental MOT35 NEW-DRIFT SWAN2 MOT35 SWAN2 Heave RMS predictions, head waves (m) SS A 0.389 0.399 0.517 0.354 SS B 0.647 0.609 0.802 0.576 SS C 0.880 0.965 1.075 0.842 Pitch RMS predictions, head waves (degrees) SS A 1.563 2.000 1.803 1.209 SS B 2.490 2.735 2.714 1.925 SS C 3.018 5.208 3.307 2.505 Vertical acceleration RMS at bow, head waves (g) SS A 0.221 0.221 0.305 0.182 SS B 0.319 0.315 0.438 0.269 SS C 0.333 0.552 0.487 0.313 Vertical acceleration RMS at CG, head waves (g) SS A 0.069 0.072 0.102 0.066 SS B 0.099 0.103 0.146 0.096 SS C 0.099 0.174 0.163 0.111 Vertical acceleration RMS at stern, head waves (g) SS A 0.127 0.279 0.191 0.119 SS B 0.185 0.379 0.272 0.170 SS C 0.210 0.763 0.301 0.198 RMS, root mean square; SS, sea state; CG, center of gravity. Table 4 Comparison of results in bow-quartering waves Sea State MOT35 NEWDRIFT SWAN2 Heave RMS predictions, bow-quartering waves (m) SS A 0.384 0.527 0.386 SS B 0.618 0.801 0.617 SS C 0.812 1.064 0.883 Pitch RMS predictions, bow-quartering waves (degrees) SS A 1.766 1.472 1.069 SS B 2.677 2.147 1.633 SS C 3.672 2.534 2.025 Vertical acceleration RMS at bow, bow-quartering waves (g) SS A 0.209 0.249 0.156 SS B 0.311 0.343 0.221 SS C 0.431 0.367 0.245 Vertical acceleration RMS at CG, bow-quartering waves (g) SS A 0.062 0.099 0.066 SS B 0.090 0.136 0.096 SS C 0.129 0.147 0.111 Vertical acceleration RMS at stern, bow-quartering waves (g) SS A 0.241 0.156 0.106 SS B 0.368 0.213 0.148 SS C 0.499 0.229 0.164 RMS, root mean square; SS, sea state; CG, center of gravity. NEWDRIFT predictions are comparatively higher. The smaller pitch motions in bow-quartering seas are predicted again by SWAN2 and the larger ones by MOT35 with the NEWDRIFT predictions being somewhere in the middle. The predictions of the vertical acceleration at the bow, stern, and at CG derived with SWAN2 for the head seas case are generally in good agreement with the experimental measurements. NEWDRIFT is uniformly overpredicting the experimental results, whereas MOT35 is in good agreement at lower sea states but gives Sea State 135 90 135 90 Sway RMS, bow-quartering and beam waves (m) SS A 0.130 0.337 0.106 0.267 SS B 0.235 0.570 0.195 0.444 SS C 0.268 0.739 0.322 0.725 Roll RMS, bow-quartering and beam waves (degrees) SS A 0.708 2.276 0.326 0.969 SS B 1.052 3.333 0.737 1.964 SS C 1.225 4.895 1.709 3.537 Yaw RMS, bow-quartering and beam waves (degrees) SS A 0.313 0.086 0.283 0.165 SS B 0.458 0.129 0.452 0.283 SS C 0.608 0.179 0.611 0.501 RMS, root mean square; SS, sea state. the higher predictions at the higher sea state, especially at the stern. In the bow-quartering seas, SWAN2 gives the smaller predictions of the vertical acceleration among the three codes. The MOT35 predictions are close to SWAN2 at CG but much higher at the ends (particularly at the stern). The NEWDRIFT predictions are higher at CG but somewhere between the other two codes at the ship ends. Regarding the lateral motions, reasonable discrepancies are observed in all three cases (sway, roll, and yaw) as depicted in Table 5. In particular, the roll motion RMS predictions in beam seas derived with SWAN2 are significantly smaller than those derived by MOT35 (in beam seas, the difference is up to by 57% at the smaller sea state and by 28% at the highest sea state). The only exception is the case of bow-quartering waves at the highest sea state, where the SWAN2 prediction of the RMS roll motion is 40% higher than that of MOT35. The already observed discrepancies in the case of regular waves among the three numerical prediction codes are therefore apparent also in the case of the dynamic behavior in seaways, although the results in this case perform better because they are integrated over the respective spectra. 5. Seakeeping results for hull form B The second hull form was optimized for a service speed of 13 knots. A scale model of hull form B equipped for selfpropulsion was tested by MARINTEK at the following combinations of sea state and speed: SS A: H 1=3 ¼ 2:0 m and T P ¼ 7:7 sec at U ¼ 11:4 knots SS B: H 1=3 ¼ 3:0 m and T P ¼ 8:6 sec at U ¼ 10:7 knots The measured speed during the experiments with the selfpropelled scale model was reduced in comparison with the design speed to account for the added resistance of the ship in waves. The numerical seakeeping analysis has been performed applying the computer code SWAN2 (2002) both in regular and irregular incident waves at the 75% payload departure condition for AUGUST 2015 JOURNAL OF SHIP PRODUCTION AND DESIGN 197

five wave headings (0,45,90, 135, and 180 ). Calculations in irregular waves have been performed at the same sea states and forward speed as those of the tank tests. 5.1. Regular wave results The seakeeping behavior of the second hull form in headto-beam regular waves was calculated with the 3D panel method, time-domain code SWAN2. The calculation encompasses a range of periods within the Bretschneider spectra, corresponding to the listed two sea states. Because the two speeds that were used during the tank tests with sea states A and B (11.4 and 10.7 knots, respectively) are quite close to each other, plots of the RAO curves are provided only for the lower speed. The numerical predictions derived with SWAN2 are presented in Figs. 16 19 for surge, heave, pitch, and roll motions. The translational motions are nondimensionalized by the wave amplitude (a w ), whereas the rotational motions are divided by the product of the wave amplitude times the wave number (a w.k) to become nondimensional. Some differences may be observed in the behavior of the two hull forms in regular waves. A sharp heave resonance for the three headings tested is observed in Fig. 17 for hull form B, which is not present in the results obtained by SWAN2 for Fig. 18 Nondimensional pitch motion Fig. 19 Nondimensional roll motion Fig. 16 Fig. 17 Nondimensional surge motion Nondimensional heave motion hull form A. The pitch responses of hull form B in head and bow-quartering waves are quite smaller than those of hull form A, whereas in beam seas, the pitch response of both hull forms is very small. The roll responses of hull form B in bow-quartering and beam waves are relatively larger than those of hull form A, exhibiting a resonant peak, which is not present in the results of the first hull form obtained with SWAN2, presented in Figs. 10 and 11. 5.2. Dynamic responses in seaways Using the SWAN2 time-domain code, the time histories of the dynamic responses of hull form B were derived for a period of 1800 seconds (30 minutes) for five headings from head seas (180 ) to following seas (0 )in45 steps. The time step was 0.05 seconds, corresponding to sampling frequency of 20 Hz. The numerically derived time histories were analyzed using fast Fourier transformation and the RMS values were calculated. A comparison of the obtained numerical results with the results of the tank tests conducted by MARINTEK for the heave and pitch motions and for the vertical acceleration at CG and at the ship s bow is presented in Table 6. As may be observed from this table, the numerical predictions are in good agreement with the experimental measurements. Heave motion is underestimated 198 AUGUST 2015 JOURNAL OF SHIP PRODUCTION AND DESIGN

Table 6 Comparison of predictions in irregular head seas 6. Conclusions Sea State A B Prediction method Experimental Numerical Exp. Num. RMS heave (m) 0.238 0.221 0.388 0.370 RMS pitch (degrees) 1.047 0.926 1.547 1.433 RMS acceleration at bow (g) 0.148 0.147 0.195 0.192 RMS acceleration at CG (g) 0.044 0.044 0.057 0.058 RMS, root mean square; CG, center of gravity. by 7.1% at sea state A and by 4.6% at sea state B. Pitch motion is underestimated by 11.6% at sea state A and by 7.4% at sea state B. The differences in the vertical accelerations both at the bow and at the vessel s CG are in all cases less that 2%. The full set of the obtained numerical results for the five different headings is summarized in Table 7. The maximum heave response is obtained at beam seas (90 ), whereas the maximum pitch motion occurs at head (180 ) and bow-quartering (135 ) waves. The maximum values for the vertical accelerations are exhibited in the bow area of the vessel in head and bow-quartering waves. In comparison to the bow vertical accelerations, those in the stern area are reduced by approximately 30% 35% when sailing in head or bow-quartering waves, whereas the vertical accelerations amidships are reduced by approximately 70% in head or bow-quartering waves. According to the original plans, the wheelhouse was to be located in the forward part of the ship, quite close to the bow. In this case, the vertical accelerations at the wheelhouse are expected to be quite high with the vessel failing to fulfill the corresponding operability criterion for merchant ships established by the Nordic Project in head or bow-quartering incident waves of sea state B, whereas the criterion is marginally fulfilled in sea state A. The roll response is marginal in beam seas with sea state B (H 1/3 ¼ 3 m, T P ¼ 8.6 seconds); hence, it might be useful to consider fitting some kind of active stabilizing fins to the hull form. The results from the analysis of the seakeeping performance of two variants of an innovative medium-speed container ship design of the twin-hull configuration are presented and discussed. The two hull forms resulted from a thorough hydrodynamic optimization performed at the School of Naval Architecture and Marine Engineering of NTUA aiming to minimize the calm water resistance within the EU-funded project EU-CargoXpress. The seakeeping analysis was performed by applying numerical tools and also by performing a series of experiments in the towing tank of NTUA and MARINTEK. The Laboratory for Ship and Marine Hydrodynamics is a member of ITTC since its establishment and participates in all uncertainty evaluation studies organized by ITTC. A 5% error in the dynamic responses is considered reasonable in the experimental evaluation of the regular and random wave results using models with a length exceeding 2 m. The results for hull form A were obtained by three different numerical codes of varying complexity and theoretical consistency. These results have been compared with each other and with the tank tests measurements and the accuracy of the used numerical procedures has been discussed. One of these codes, i.e., SWAN2, was selected to be used for the numerical evaluation of the second hull form. By comparison of the available experimental results, it may be observed that the second hull form exhibits significantly lower vertical responses in head irregular waves by 30% 40% in comparison with the first variant. The same conclusion may be derived from the comparison of the results derived by SWAN2 for the RMS responses in head and bow-quartering irregular seas for the heave and pitch motions and the vertical accelerations at CG and at the bow area. With respect to the roll response, however, as a result of the much higher GM value of the second hull form (Although the demihull breadth of hull form B is smaller than that of hull form A, its waterplane area at equal displacement is approximately 8% larger. In addition, hull form B is tested at a reduced displacement, Table 7 Responses in irregular waves from head seas (1808) to following seas (08) Heading 180 Heading 135 Heading 90 Heading 45 Heading 0 Heading Sea State A B A B A B A B A B H 1/3 (m) 2.0 3.0 2.0 3.0 2.0 3.0 2.0 3.0 2.0 3.0 T P (seconds) 7.7 8.6 7.7 8.6 7.7 8.6 7.7 8.6 7.7 8.6 RMS surge (m) 0.210 0.373 0.223 0.372 0.053 0.080 0.337 0.540 0.318 0.505 RMS heave (m) 0.221 0.370 0.251 0.435 0.354 0.575 0.180 0.354 0.143 0.268 RMS pitch (degrees) 0.926 1.433 0.916 1.351 0.184 0.241 0.643 0.978 0.579 0.940 RMS sway (m) 0.000 0.000 0.096 0.196 0.362 0.617 0.309 0.551 0.000 0.000 RMS roll (degrees) 0.000 0.000 0.653 1.244 2.625 3.809 0.569 0.875 0.000 0.000 RMS yaw (degrees) 0.000 0.000 0.283 0.493 0.239 0.350 0.934 1.360 0.000 0.000 RMS acceleration at bow (g) 0.147 0.192 0.138 0.178 0.031 0.042 0.013 0.028 0.007 0.027 RMS acceleration at CG (g) 0.044 0.058 0.037 0.050 0.040 0.051 0.005 0.009 0.003 0.010 RMS acceleration at stern (g) 0.093 0.134 0.090 0.123 0.059 0.069 0.014 0.029 0.008 0.035 RMS RVM at bow 1.017 1.423 0.867 1.151 0.305 0.384 0.621 0.844 0.422 0.695 RMS RVM at stern 0.659 0.994 0.510 0.737 0.568 0.737 0.925 0.960 0.364 0.424 RMS RVV at bow 0.498 0.652 0.432 0.544 0.132 0.154 0.111 0.154 0.051 0.088 RMS RVV at stern 0.395 0.514 0.276 0.367 0.237 0.294 0.170 0.198 0.043 0.080 RMS, root mean square; CG, center of gravity; RVM, relative vertical motion; RVV, relative vertical velocity. 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resulting in an increased BM value. Considering also its relatively reduced VCG, hull form B has a significantly increased GM value (11.130 m) in comparison with a GM value of 5.080 m of hull form A.), the situation is reversed and, according to the numerical results, the second hull form exhibits considerably higher roll responses in bow-quartering and beam irregular waves by 70% 170% in comparison with the first hull form, whereas in the stern quartering seaways, its roll response is smaller by approximately 50%. It should be stressed, however, that the derived numerical seakeeping results for the two hull forms are not directly comparable, because they correspond to different loading conditions (according to the light weight and payload specifications provided by the designer) and different sailing speeds. Acknowledgments The research leading to these results has received funding from the European Union s Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 233925. References FRANK, W. 1967 Oscillation of Cylinders in or Below the Free Surface of Deep Fluids, DTNSRDC, Report No. 2375, Washington, DC. ITTC. 1984 Report of the Seakeeping Committee, Proceedings, 17 th International Towing Tank Conference, September 8 15, Gotebörg, Sweden. KRING, D. C. 1994 Time Domain Ship Motions by a Three-Dimensional Rankine Panel Method, PhD thesis, MIT, Cambridge, MA. LEE, C. M. 1976 Theoretical Prediction of Motion of Small Waterplane Area Twin Hull (SWATH) Ships in Waves, DTNSRDC, Report No. 76-0046, Bethesda, MD. LEE, C. M., JONES, H., AND BEDEL, J. W. 1971 Added Mass and Damping Coefficients of Heaving Twin Cylinders in a Free Surface, DTNSRDC, Report No. 3695, Bethesda, MD. MCCREIGHT, K. K. AND LEE, C. M. 1976 Manual for mono-hull and twinhull ship motion prediction computer program, DTNSRDC, Report No. SPD-686-02, Bethesda, MD. PAPANIKOLAOU, A. 1985 On integral equation methods for the evaluation of motions and loads of arbitrary bodies in waves, Ingenieur-Archiv, 55, 17 29. PAPANIKOLAOU, A., SCHELLIN, T., AND ZARAPHONITIS, G. 1990 A 3D method to evaluate motions and loads of ships with forward speed in waves, Proceedings, 5 th International Congress on Marine Technology, IMAEM 90, May, Athens, Greece. pp. 452 457. RAMBECH, H. J. 2012 Model Tests, CargoXpress, MARINTEK Report MT53 F12-042-Rev. 1-530775.00.01, April 17. SALVESEN, N., TUCK, O. E., AND FALTINSEN, O. 1970 Ship motions and sea loads, Transactions of the Society of Naval Architects & Marine Engineers, 78, 250 287. SCLAVOUNOS, P. D. 1996 Computation of Wave Ship Interactions, Advances in Marine Hydrodynamics, Edited by M. Qhkusu, Computational Mechanics Publications, Southampton, UK. SWAN2. 2002 User Manual: Ship Flow Simulation in Calm Water and in Waves, Boston Marine Consulting Inc., Boston, MA. ZARAPHONITIS, G., GRIGOROPOULOS, G., DAMALA, D., AND MOURKOYANNIS, D. 2011 Seakeeping analysis of a medium-speed twin-hull containership, Proceedings, 11 th International Conference on Fast Sea Transportation, (FAST 2011), September 26 29, Honolulu, Hawaii. 200 AUGUST 2015 JOURNAL OF SHIP PRODUCTION AND DESIGN