Dynamic Performance of the National Technical University of Athens Double-chine Series Hull Forms in Random Waves

Journal of Ship Production and Design, Vol. 3, No. 2, May 214, pp. 1 8 http://dx.doi.org/1.5957/jspd.3.2.142 Dynamic Performance of the National Technical University of Athens Double-chine Series Hull Forms in Random Waves Gregory J. Grigoropoulos and Dimitra P. Damala School of Naval Architecture and Marine Engineering, National Technical University of Athens, Athens, Greece A systematic series of double-chine, wide-transom hull forms with warped planing surface has been developed at the Laboratory for Ship & Marine Hydrodynamics (LSMH) of the National Technical University of Athens during the last two decades. The series are suitable for medium and large ships operating at high but preplaning speeds and consist of five hull forms. Two scaled models for each hull form have been constructed and tested in calm water and in waves. In this article, systematic experimental results in random waves are presented. More specifically, the parent hull form with L/B ¼ 5.5 was tested in three-level keel displacements, whereas the two corner hull forms with L/B ¼ 4. and 7. were tested at the central displacement. Thus, the effects of both the displacement and the L/B ratio on the seakeeping responses are investigated. All tests were performed at two speeds corresponding to Fn ¼.34 and.68 using the Bretschneider spectral model with nondimensional modal periods ¼ / p (L/g) ¼ 2. 5. at steps of.5 and model significant wave heights H 1/3 in the 8- to 16-cm range to represent moderate waves. Assuming linearity, the results for heave, pitch, acceleration, and added resistance are divided by H 1/3 (i.e., they refer to H 1/3 equal to unity). Keywords: seakeeping; systematic series; random waves; semiplaning hull; model tests 1. Introduction Manuscript received by JSPD Committee January 14, 214; accepted January 22, 214. A SYSTEMATIC series of double-chine, wide-transom hull form with warped planing surface has been developed at the Laboratory for Ship & Marine Hydrodynamics (LSMH) of the National Technical University of Athens (NTUA) during the two decades. The series, inspired by a proposal of Savitsky et al. (1972), provide a handy and suitable base for the design of medium and large modern monohull ships and pleasure craft, which operate at high but preplaning speeds. The series consist of five hull forms with L/B ratios equal to 4., 4.75, 5.5, 6.25, and 7.. The nondimensional displacement length coefficient C DL ¼r= ð:1l WL Þ 3 where r is the displaced volume and L WL the waterline length at rest is used to represent the loading condition. Two scaled models for each hull form have been constructed and tested in calm water at six displacements, including very light ones. The resistance characteristics of the series were presented by Grigoropoulos and Loukakis (22). Furthermore, their seakeeping behavior was found to be attractive on the basis of comparative model tests of the parent hull of the series and four other competitive hull forms (Grigoropoulos & Loukakis 1995). The experimental results were in agreement with the full-scale observations of Blount and Hankley (1976) on the design of Savitsky et al. (1972) many years ago. Thus, it was decided to carry out a systematic investigation of their dynamic performance in regular and random (irregular) waves. One year ago, Grigoropoulos et al. (21) presented the experimental results for regular waves. However, as Grigoropoulos and Loukakis (1995, 1998) concluded, carefully conducted random wave experiments are a much better yardstick for the comparative study of seakeeping behavior of high-speed semiplaning and planing hulls than regular waves. This is also supported by the fact that some nonlinearities on the estimation of the Response Amplitude Operators (RAOs) were mainly observed only around the peak of the respective RAO curves. In addition, Fridsma (1971), who provided the only existing systematic experimental study for the MAY 214 2158-2866/14/32-1$./ JOURNAL OF SHIP PRODUCTION AND DESIGN 1

seakeeping performance of planing boats in random waves, recommended these tests. However, Fridsma (1969, 1971) used quite small (1 m long) models with constant deadrise angle and parabolic finishing in the bow region. Thus, an ambitious and time-consuming experimental investigation was initiated at the LSMH of NTUA to test the hull forms of the series in random waves. Furthermore, the experimental results of tests in random waves provides a handy quantifier of the performance of hull forms in rough waters and they can be easily compared with available seakeeping criteria to identify whether a vessel is operable in a region or along a specific route (Grigoropoulos et al. 1997). In this respect, a similar systematic series for the preliminary prediction of the seakeeping performance for merchant ships has been numerically developed at the LSMH of NTUA (Grigoropoulos et al. 2). In this article, experimental results using three of the five hull forms of the series in random waves are presented. More specifically, the parent hull form was tested in three-level keel displacements corresponding to C DL ¼ 1.61, 3., and 4.23. Furthermore, the two corner hull forms with L/B ratios equal to 4. and 7. were tested at the level keel displacement with C DL ¼ 3. to investigate the effect of L/B ratio on the dynamic behavior. All tests have been performed at two speeds corresponding to Fn ¼.34 and.68. The Bretschneider spectral model with nondimensional modal periods ¼ / p (L/g) ¼ 2. to 5. with steps equal to.5 was used to model the sea states. The significant wave heights H 1/3 were selected in the 8- to 16-cm range to represent moderate waves. On the basis of the discussion earlier in this section, the root mean square (RMS) values of ship responses and the mean added resistance are assumed to vary linearly with H 1/3 and H 1/3 2, respectively. Thus, the RMS values of heave, pitch, and accelerations are divided by H 1/3, whereas mean added resistance is divided by H 1/3 2. 2. Review of past experimental works There are only limited data published on the seakeeping performance of high-speed hull forms, especially for hard-chine ones. In this section, the available experimental results referring to hardchine planing and semiplaning hulls are reviewed. The respective results for round bilge, semidisplacement hulls were reviewed by Grigoropoulos et al. (21). The only systematic experimental research for hard-chine hull forms was the one published by Fridsma (1969, 1971). He tested three prismatic models with deadrise angles of 1,2, and 3 and L/B ¼ 5.. For the intermediate deadrise angle, two additional L/B ratios of 3. and 4. were tested. Finally, for the same deadrise angle, a warped bow was fitted. In the first of his reports, he presented results for the performance in calm water and in regular head waves, whereas in the second one he reported on their dynamic behavior in fully developed head sea states. Savitsky and Brown (1976) used the experimental results of Fridsma (1971) to devise prediction formulae for the acceleration at the bow and at the longitudinal center of gravity (LCG) and the added resistance. Because the prismatic hull forms are not very realistic, they propose to use the maximum breadth over chines B PX to represent the breadth, the deadrise at amidships, and waterline length L WL for the length. Blount and Hankley (1976) also comment on the proper application of results derived on the basis of prismatic hull forms in actual warped vessels. In their evaluation of a double-chine hull tested, they conclude that the L/B ratio varies significantly (from 6.8 to 7.8) if B PX is replaced by the mean breadth over the 8% of the length from the stern B P.8. The authors compare the formula proposed by Savitsky and Brown (1976) with model and full-scale results for a double-chine and a single-chine hull form. However, they provide only limited information about the testing parameters for the model and full-scale tests. Van den Bosch (197, 1974) presented detailed experimental results for two and four planing hull forms, respectively. In the former paper, two boat models, similar to Series 62 with deadrise angles 12 and 24, are compared for their performance in calm water and in regular head waves. In the latter, on the basis of the experimental results for four motor boat models in calm water and in irregular head waves, he concluded that a wide transom is beneficial. Finally, Serter (1993) presented results of various deep-vee hull forms in random seaways (chapters 1, 2, and 6). The hull forms are nonstandard. Limited information about their geometry is provided. 3. The models of the National Technical University of Athens series The hull forms of the NTUA series have two successive chines running forward of the transom up to 7% of the hull length. U ¼ forward speed a ¼ vertical acceleration A ¼ wave amplitude B ¼ breadth molded B WL ¼ maximum breadth at waterline B PX ¼ maximum breadth over chines C B ¼ block coefficient C DL ¼ displacement length ratio at rest Fn ¼ Froude number F nv ¼ volumetric Froude number FP ¼ fore perpendicular g ¼ acceleration of gravity H 1/3,H S ¼ significant wave height (m) Nomenclature H 1/3M ¼ H 1/3 at model scale (m) H 1/3MFD ¼ H 1/3M for fully developed seas (m) k ¼ wave number, k ¼ 2p/l LCG ¼ longitudinal center of gravity L, L OA ¼ length overall L WL ¼ length at waterline at rest RAO ¼ Response Amplitude Operator R AW ¼ mean added resistance RMS ¼ root mean square R YY ¼ pitch radius of gyration T ¼ draft ¼ modal period (seconds) M ¼ modal period at model scale S ¼ modal period at full scale ¼ nondimensional modal period ¼ / p (L/g) WS ¼ wetted surface b ¼ wave heading (b ¼ 18 for head waves) r¼volume of displacement at rest D ¼ displacement at rest l ¼ wave length x 3 ¼ heave response x 5 ¼ pitch response r ¼ density of water 2 MAY 214 JOURNAL OF SHIP PRODUCTION AND DESIGN

Fig. 1 Lines plan of the parent hull form of the National Technical University of Athens series (the body plan is scaled up by a factor of three) Fine highly flared lines form the bow region. Among the five hull forms of the series with L/B ratios ranging from 4. to 7. in.75 steps, the one with ratio L/B ¼ 5.5 is the central (parent) one. Its lines plan is shown in Fig. 1. The hull lines end at the stern on a wide transom, whereas the deadrise angle varies from 1 at the transom to approximately 7 at the bow. The angle of entrance is small for all cases tested. The series members with different values of L/B were derived from the parent by keeping the same midship section and altering appropriately the station spacing. The nondimensional displacement length coefficient C DL is used to represent the loading condition. Although the calm water characteristics of the series were evaluated at six values of C DL ¼ 1., 1.61, 2.23, 3., 3.62, and 4.23, their seakeeping performance is evaluated at only half of them, i.e., at C DL ¼ 1.61, 3., and 4.23. The lower values of C DL correspond to the operating conditions of large ships, whereas the higher values to smaller passenger ships and pleasure craft. This fact, coupled with higher values of L/B for larger ships and lower values for smaller vessels, defines in rough terms the more valuable portion at the grid of the experimental results. In this article, results for the central hull form at the aforementioned C DL values and for two more hull forms with L/B ¼ 4. and 7. at the central C DL value (C DL ¼ 3.) are presented. The model lengths were determined using the 21st I.T.T.C. High Speed Marine Vehicles Committee suggestion (1996), that at least 2-m models should be used for such craft. However, the smaller values of C DL, corresponding to the lighter displacements, could not be achieved with these model lengths, because they correspond to model displacements less than the sum of the weights of the bare model and the dynamometer pod. Thus, for each member of the series, a larger model was also built. The scale of the smaller models was 6% that of the larger. Depending on the displacement to be tested, either the small or the large model was used. The relative position of the chines with respect to the waterline at rest ranges from both of them being submerged at the larger L/B ratios and the heavier displacements to both being emerged at the other end. 4. Experimental setup Three strap-down accelerometers with a - to 1-g range recommended for use in the.1- to 1-Hz band were fitted along the tested models of Table 1 at the FP, the LCG, and the AP to record the vertical accelerations. The wooden models were ballasted to a pitch radius of gyration R YY ¼.25 L WL and were attached to the carriage through a heave rod, pitch bearing, resistance measuring assembly and were tested in head waves. Thus, the models were free to heave and pitch and these responses were recorded. Furthermore, the total resistance was measured, and the added resistance in waves was derived. No turbulence stimulators were fitted. White noise, produced by a digitally simulated shift register with feedback, was filtered by the impulse response function corresponding to the specified wave spectrum and was used to generate the time histories of the pseudorandom waves (Golomb 1967). The model responses as well as the waves in the tank were sampled at a rate of 2 Hz. Fast Fourier Transform was used to estimate the RMS values of the responses. To investigate the presence of sharp peaks in the time histories of accelerations, a sampling rate at 1 Hz was used in some indicative runs at both tested speeds. However, the data did not reveal any indication of sharp bow-down impact accelerations, necessitating the use of special data acquisition and analysis techniques. Such a technique proposed by Zseleczky and McKee (1989) encompasses the use of buffers instead of filters in the peak-trough identification technique to throw away local minima and the application of a probabilistic approach using the P% probability level, i.e., the observed L/B L OA C DL Table 1 4. small (113/95) 2.292 m Characteristics of the tested models 5.5 big (118/96) 3.82 m 5.5 small (97/94) 2.292 m 3.497 1.635 1.61.59 69.13.511.97 2.19.88 2.145.728 3..488.362 28.174 29.615.35.297.8.83 2.175.834 4.23.368 43.53.28.16 7. small (116/96) 2.917 m 2.783 1.13.37 64.618.345.116 Notes: 1. Each cell of the table contains the following characteristics of the model: L WL (m) WS (m 2 ) B WL (m) D (Kgr) LCG (m) T (m) 2. Longitudinal center of gravity (LCG) from amidships, positive forward. The characteristics of the tested models are presented in the shaded cells of Table 1. MAY 214 JOURNAL OF SHIP PRODUCTION AND DESIGN 3

Table 2 Tested sea conditions for the small model with ratio L/B ¼ 4. and C DL ¼ 3. (scale 1:5) 2. 2.5 3. 3.5 4. 4.5 5. S (seconds) 6.557 8.197 9.836 11.475 13.114 14.754 16.393 M (seconds).927 1.159 1.391 1.623 1.855 2.86 2.318 H 1/3M (m).8.9.1.11.12.14.16 H 1/3MFD (m).34.54.77.15.138.174.215 H 1/3 /L WL *1 2 3.793 4.267 4.742 5.216 5.69 6.638 7.587 Table 3 Tested sea conditions for the large model with ratio L/B ¼ 5.5 and C DL ¼ 1.61 (scale 1:3) 1.5 2. 2.5 3. 3.5 3.5 4. S (seconds) 4.95 6.54 8.175 9.811 11.446 11.446 13.81 M (seconds) 1.117.837.67.558.479.479.419 H 1/3M (m).1.1.1.12.13.15.15 H 1/3MFD (m).32.57.89.128.175.175.228 H 1/3 /L WL *1 2 2.86 2.86 2.86 3.432 3.717 4.289 4.289 Table 4 Tested sea conditions for the small model with ratio L/B ¼ 5.5 and C DL ¼ 3. (scale 1:5) 2. 2.5 3. 3.5 4. 4.5 5. S (seconds) 6.613 8.266 9.919 11.573 13.226 14.879 16.532 M (seconds).935 1.169 1.43 1.637 1.87 2.14 2.338 H 1/3M (m).8.9.1.11.12.14.16 H 1/3MFD (m).35.55.79.17.14.177.219 H 1/3 /L WL *1 2 3.73 4.196 4.662 5.128 5.594 6.527 7.459 Table 5 Tested sea conditions for the small model with ratio L/B ¼ 5.5 and C DL ¼ 4.23 (scale 1:5) 2. 2.5 3. 3.5 4. 4.5 5. S (seconds) 6.659 8.324 9.989 11.653 13.318 14.983 16.648 M (seconds).942 1.177 1.413 1.648 1.883 2.119 2.354 H 1/3M (m).8.9.1.11.12.14.16 H 1/3MFD (m).35.55.8.19.142.18.222 H 1/3 /L WL *1 2 3.678 4.138 4.598 5.57 5.517 6.437 7.356 value that is exceeded by no more than P% of the observed data. The absence of impact accelerations may be attributed to the relatively low speeds of the tests along with the very high deadrise angles in the bow region of the models. Regarding the linearity of the responses, Van den Bosch (197) stated that it is important to know if tests in irregular waves will give results that will predict the true order of quality of two models; that is to say, when Model A appears to be better than Model B in regular waves, the same should follow from tests in irregular waves with a sufficiently wide frequency range. This follows automatically when the motions can be described by a set of linear differential equations. It seems even probable that quite a lot of nonlinearity can be introduced before this will invalidate the comparison. The first impression of the linearity can be obtained from optical observation of the recorded accelerations. Only scarce, steep rises when the bow hits the water surface were counted. Thus, it is seen that this evidence of nonlinearity appears to have a relatively small influence on the sine character of the pitch motion. Furthermore, the motion amplitudes for different wave amplitudes were recorded (linearity tests). The nonlinearity noticed was not significant and it was mainly concentrated around the peak of the RAO curve. Thus, it is significantly alleviated when spectral integration is carried out to derive the RMS values. This result is in agreement with the findings of Van den Bosch (197) who noticed a nonlinearity of some importance only at the highest speed of his tests i.e., at F nv 3 corresponding to Fn 1.3, which is outside the range of speeds under consideration for the NTUA series (results for Fn ¼.34 and.68 are provided here, whereas a higher speed of Fn ¼ 1.32 may be considered in the future). Furthermore, the preliminary experimental results presented here were faired through polynomial best fit curves with reasonable residuals. On the other hand, the operation at high speeds in severe sea conditions is of no practical interest, because the captains of passenger ships, when they encounter excessive sea waves, either slow down their engines or change their route to circumvent them. The derived experimental results for the heave, the pitch, and the accelerations are plotted in terms of the respective nondimensional RMS values. The following ratios have been selected to provide scale-insensitive quantities (pertinent recommendation of any ITTC Seakeeping Committees could not be found): RMS x 3 ¼ RMS x3 H 1=3 ð1þ RMS x 5 ¼ RMS x5 1 2 L WL H 1=3 ð2þ Table 6 Tested sea conditions for the small model with ratio L/B ¼ 7. and C DL ¼ 3. (scale 1:5) 1.5 2. 2.5 3. 3.5 4. 4.5 5. S (seconds) 5.649 7.532 9.416 11.299 13.182 15.65 16.948 18.831 M (seconds).799 1.65 1.332 1.598 1.864 2.131 2.397 2.663 H 1/3M (m).7.9.1.11.12.14.16.16 H 1/3MFD (m).26.45.71.12.139.182.23.284 H 1/3 /L WL *1 2 2.515 3.234 3.593 3.953 4.312 5.31 5.749 5.749 4 MAY 214 JOURNAL OF SHIP PRODUCTION AND DESIGN

RMS a ¼ RMS al WL gh 1=3 ð3þ On the other hand, added resistance is the difference between the mean total resistance of the model in a sea condition and the calm water resistance at the same speed. Contrary to the other responses, the added resistance is proportional to the square of the significant wave height. On the basis of this remark, and taking into account the recommendation of 17 th ITTC (1984) for the respective RAO, the added resistance AR in random waves is expressed by the following nondimensional quantity: AR ¼ AR L WL rgb 2 WL H2 1=3 ð4þ Among the quantities provided by equations (1) to (4), only RMS x 5 for pitch response is dimensional (in degrees), whereas the remaining ones are nondimensional. In the following Tables 2 6, the tested conditions are listed. On the tables the modal periods at the model scale as well as extrapolated at an assumed full scale are provided. The scale is 1:3 for the large models (Table 3) and 1:5 for the small models (Tables 2, 4, 5, and 6) to correspond to the same ship size. The tests have been carried out at selected significant wave heights. For comparison the respective significant wave heights corresponding to fully developed seas (Pierson-Moskowitz spectrum) are also provided. The tests were conducted by repetitive runs of the carriage until a total measuring period of 5 6 minutes at model scale was accumulated. This time interval corresponds to half an hour to 1 hour sampling period at the assumed full scale, as recommended for sufficient statistical accuracy, when stationary stochastic processes are analyzed. Sufficient time (5 15 minutes) was allowed between successive runs for the water in the towing tank to calm while its energy was continually checked. The recorded signals are passed through a low-pass filter with a cutoff frequency of 5 Hz and they are carefully inspected for any spurious noise content before their analysis. Fig. 3 Heave and pitch responses for the model with L/B ¼ 5.5 and C DL ¼ 1.61 Fig. 4 Heave and pitch responses for the model with L/B ¼ 5.5 and C DL ¼ 3. 5. Results and discussion In Figs. 2 6, the scale-insensitive dynamic responses for heave and pitch, as defined by equations (1) and (2), are given, for the tested sea conditions of Tables 2 6, respectively. Fig. 5 Heave and pitch responses for the model with L/B ¼ 5.5 and C DL ¼ 4.23 Fig. 2 Heave and pitch responses for the model with L/B ¼ 4. and C DL ¼ 3. In Figs. 7 11, the respective case-insensitive vertical accelerations at the bow, the LCG, and the stern of each model, as defined by equation (3), are plotted. Finally, in Figs. 12 16, the respective added resistance, as expressed by equation (4), are provided. The probability distributions of the dynamic responses were found to fit quite well within the normal distribution. Thus, the presented MAY 214 JOURNAL OF SHIP PRODUCTION AND DESIGN 5

Fig. 6 Heave and pitch responses for the model with L/B ¼ 7. and C DL ¼ 3. Fig. 9 Vertical accelerations at the bow, the longitudinal center of gravity, and the stern of the model with L/B ¼ 5.5 and C DL ¼ 3. Fig. 7 Vertical accelerations at the bow, the longitudinal center of gravity, and the stern of the model with L/B ¼ 4. and C DL ¼ 3. Fig. 1 Vertical accelerations at the bow, the longitudinal center of gravity, and the stern of the model with L/B ¼ 5.5 and C DL ¼ 4.23 Fig. 8 Vertical accelerations at the bow, the longitudinal center of gravity, and the stern of the model with L/B ¼ 5.5 and C DL ¼ 1.61 RMS values can be used to derive any other statistical value (e.g., 1/3 rd or 1/1 th significant values). Furthermore, on the basis of the linearity assumption, the results of Figs. 2 16 can be used directly to evaluate any response at a sea state by picking up the respective value of pertinent figure for the modal period of the sea state and deriving the respective dimensional response RMS value. Following these figures, the derived curves on the basis of the available results are quite smooth, even in the case of the mean Fig. 11 Vertical accelerations at the bow, the longitudinal center of gravity, and the stern of the model with L/B ¼ 7. and C DL ¼ 3. added resistance in waves, which is more sensitive being proportional to the square of the incident significant wave height. Some minor possible discrepancies, which affect also the final shape of the best-fit curves, will be crosschecked through additional testing on the way to evaluate all five hull forms of the NTUA series. For this reason, these results are characterized as preliminary. The complete campaign aiming at the derivation of the aforementioned 6 MAY 214 JOURNAL OF SHIP PRODUCTION AND DESIGN

Fig. 12 Mean added resistance in waves for the model with L/B ¼ 4. and C DL ¼ 3. Fig. 15 Mean added resistance in waves for the model with L/B ¼ 5.5 and C DL ¼ 4.23 Fig. 13 Mean added resistance in waves for the model with L/B ¼ 5.5 and C DL ¼ 1.61 Fig. 16 Mean added resistance in waves for the model with L/B ¼ 7. and C DL ¼ 3. 1.61, 3., and 4.23) at a grid of three modal periods in the given range and two additional significant wave heights. It should be noted here that as it can be noted on Tables 2 6, for the lower periods (respective ¼ 1.5 2.5), the selected significant wave heights for the tests were higher than the respective ones corresponding to fully developed seas (Pierson-Moskowitz spectral model). This was decided because the latter were too low to receive reliable experimental results (very small waves with decreasing energy content along the towing tank). However, this correlation was reversed at the higher periods. 6. Conclusion Fig. 14 Mean added resistance in waves for the model with L/B ¼ 5.5 and C DL ¼ 3. seakeeping responses for the two selected speeds encompasses 1 more cases including sets of testing sea conditions analogous to those described on Tables 2 6 of Section 4. Some additional linearity tests to further document the experimental results are also in the plan. They will constitute full sets of runs of the parent hull form at the three loading conditions (C DL ¼ This article presents the first preliminary results of the investigation of the seakeeping qualities of the double-chine, widetransom hull forms of NTUA series in random waves. More specifically, the experimentally derived seakeeping responses of the parent hull form of the series, at three loading conditions and the respective ones of the two corner hull forms at their central loading condition, are presented in graphic format. In this way, the effects of the loading condition on the parent hull form as well as of the L/B ratio at the central loading condition of the hull forms of the series are investigated. Finally, by testing at a MAY 214 JOURNAL OF SHIP PRODUCTION AND DESIGN 7

displacement speed (Fn ¼.34) and a semidisplacement one (Fn ¼.68), the effect of speed is derived. On the basis of the experimental results, the increase of the L/B ratio, for the same C DL, results in higher pitch, vertical accelerations, and added resistance, whereas heave is less sensitive to it. On the other hand, the increase of speed leads to reduced pitch and increased heave, whereas the vertical accelerations are increased in most of the cases and the mean added resistance is increased except for the low L/B ratio and the light displacement of the central hull form. Furthermore, the increase of the displacement, for the same L/B ratio, results in higher pitch at the lower speed only and slightly increased heave, whereas the vertical accelerations are reduced and the added resistance is increased. Finally, the values where the highest responses are observed are affected by all of these parameters without a clear trend. The aforementioned conclusions drawn on the basis of the tests in random waves are consistent with the respective results derived on the basis of the model tests in regular waves, as presented by Grigoropoulos et al. (21). Following a comparison with other transom-stern round-bottom systematic series of hull forms, the seakeeping behavior of the NTUA series is fully competitive. Becase the series depicts a satisfactory performance in calm water too, as demonstrated by Grigoropoulos and Loukakis (22), it offers an attractive design source for vessels 2 15 m long operating at the preplaning regime. Acknowledgments This extensive and time-consuming work was supported by the contribution of many students during their diploma theses. Furthermore, the technical personnel of the Towing Tank, Messrs Dionisis Synetos, Fotis Kasapis, and Giannis Trachanas are responsible for the good quality of the measurements. The authors are heavily indebted to them. References BLOUNT, D. L. AND HANKLEY, D. W. 1976 Full-scale Trials and Analysis of High-performance Planing Craft Data, Transactions of the Society of Naval Architects & Marine Engineers, 84, 251 277. FRIDSMA, G. 1969 A systematic study of the rough-water performance of planing boats, Davidson Lab. Rept. 1275, Stevens Institute of Technology, November. FRIDSMA, G. 1971 A systematic study of the rough-water performance of planing boats, Irregular Waves, Part II, Davidson Lab. Rept. 1495, Stevens Institute of Technology, March. GOLOMB, S. W. 1967 Shift Register Sequences, Holden-Day Inc, San Francisco, CA. GRIGOROPOULOS, G. J., DAMALA, D. P., AND LOUKAKIS, T. A. 21 Dynamic performance of the NTUA double-chine series hull forms in regular waves, Proceedings, 2 nd Chesapeake Power Boat Symposium, March 19 2, Annapolis, MD. GRIGOROPOULOS, G. AND LOUKAKIS, T. 22 Resistance and seakeeping characteristics of a systematic series in the pre-planing condition (Part I), Transactions of the Society of Naval Architects & Marine Engineers, 11, 77 113. GRIGOROPOULOS, G. J. AND LOUKAKIS, T. A. 1995 Seakeeping performance assessment of planing hulls, Proceedings, International Conference ODRA 95, Wessex Institute of Technology, September 2 22, Szczecin, Poland. GRIGOROPOULOS, G. J. AND LOUKAKIS, T. A. 1998 Seakeeping characteristics of a systematic series of fast monohulls, Proceedings, International Conference on Ship Motions and Manoeuvrability SMM 98, February 18 19, London. GRIGOROPOULOS, G. J., LOUKAKIS, T. A., AND PEPPA, S. 1997 Seakeeping operability of high-speed monohulls in Aegean Sea, Proceedings,8 th International Congress of International Maritime Association of the Mediterranean, November 2 9, Istanbul, Turkey. GRIGOROPOULOS, G. J., LOUKAKIS, T. A., AND PERAKIS, A. 2 Seakeeping standard series for oblique seas (A synopsis), Ocean Engineering Journal, 27, 111 126. ITTC. 1984 Report of the Seakeeping Committee, Proceedings, 17 th International Towing Tank Conference, June 1984, Göteborg, Sweden. ITTC. 1996 Final Report and Recommendations to the 21 st I.T.T.C. of the High-Speed Marine Vehicles Committee, Proceedings, 21 st International Towing Tank Conference, September 15 21, Trondheim, Norway. SAVITSKY, D. AND BROWN, P. W. 1976 Procedures for hydrodynamic evaluation of planing hulls in smooth and rough water, Marine Technology, 13, 4, 381 4. SAVITSKY, D., ROPER, J. K., AND BENEN, L. 1972 Hydrodynamic development of a high speed planing hull for rough water, Proceedings, 9 th Symposium on Naval Hydrodynamics, Office of Naval Research, August 2 25, Paris, France, p. 419. SERTER, E. H. 1993 Naval Architecture and Hydrodynamics of Deep-Vee Hull Forms, Naval Engineers Journal, 15, 85 85. VAN DEN BOSCH, J.J. 197 Tests with two planing boat models in waves, TH Delft, Report 266. VAN DEN BOSCH, J.J. 1974 Comparative tests of four fast motor boat models in calm water and in irregular head waves and an attempt to obtain full scale confirmation, Netherlands Ship Research Centre TNO, December, Report 196 S. ZSELECZKY, J. AND MCKEE, G. 1989 Analysis methods for evaluating motions and accelerations of planing boats in waves, Proceedings, 22 nd American Towing Tank Conference, August 8 11, St. John s, Canada. 8 MAY 214 JOURNAL OF SHIP PRODUCTION AND DESIGN