dynamic performance of the ntua double-chine series hull

11th International Conference on Fast Sea Transportation FAST 2011, Honolulu, Hawaii, USA, September 2011

Dynamic Performance of the NTUA Double-Chine Series Hull Forms in Random

Waves

Gregory J. Grigoropoulos1, and Dimitra P. Damala1

1School of Naval Architecture and Marine Engineering, National Technical University of Athens (NTUA), Athens, Greece

ABSTRACT

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 NTUA, during the last two decades. The series are suitable for medium and large ships operating at high but pre-planing 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 paper, systematic experimental results in random waves are presented. More specifically, the parent hull form with L/B = 5.50 was tested in three level keel displacements, while the two corner hull forms with L/B = 4.0 and 7.0 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 = 0.34 and 0.68, using the Bretschneider spectral model with non-dimensional modal periods TP’ = TP/√(L/g) = 2.0 to 5.0 at steps of 0.5 and model significant wave heights H1/3 in the 8 – 16 cm range to represent moderate waves. However, the results for heave, pitch, acceleration and added resistance presented refer to H1/3 = 1 m.

KEY WORDS

Seakeeping, systematic series, random waves, semi-planing hull, model tests.

NOMENCLATURE

U forward speed a Vertical acceleration A Wave amplitude B Breadth molded BWL Max breadth at waterline BPX Maximum breadth over chines CB Block coefficient CDL Displacement-length ratio at rest Fn Froude number Fnv Volumetric Froude Number FP Fore perpendicular g Acceleration of gravity H1/3, HS Significant wave height (m) H1/3M H1/3 at model scale (m) H1/3MFD H1/3M for fully developed seas (m) k Wave number, k=2π/λ LCG Longitudinal centre of gravity L, LOA Length overall LWL Length at waterline at rest RAO Response Amplitude Operator

RAW Mean added resistance RMS Root Mean Square value RYY Pitch radius of gyration TP Modal period (sec) TPM Modal period at model scale TPS Modal period at full scale TP’ Non-dimensional modal period TP’ = TP/√(L/g) β wave heading (β =180o for head waves) Volume of displacement at rest Δ Displacement at rest λ Wave length ξ3 Heave response ξ5 Pitch response ρ Density of water

1.0 INTRODUCTION

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 pre-planing speeds. The series consist of five hull forms with L/B ratios equal to 4.00, 4.75, 5.50, 6.25 & 7.00. The non-dimensional displacement-length coefficient 3

DL WLC 0.1L where

is the displaced volume and LWL the waterline length at rest, is used to represent the loading condition. Two scaled models for each hull from has been constructed and tested in calm water at six displacements, including very light ones. The resistance characteristics of the series were presented by Grigoropoulos & Loukakis (2002). 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 and Loukakis, 1995). The experimental results were in agreement with the full-scale observations of Blount & 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. (2010) presented the experimental results for regular waves. However, as Grigoropoulos & Loukakis (1995, 1998) concluded, carefully conducted random wave experiments are a much better yardstick for the comparative study of

© 2011 American Society of Naval Engineers 623

seakeeping behavior of high-speed semi-planing and planing hulls than regular waves. This is also supported by the fact that some non-linearities 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 seakeeping performance of planing boats in random waves, recommended these test. 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 provide 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. 2000).

In this paper, 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 CDL = 1.61, 3.00 and 4.23. Furthermore, the two corner hull forms with L/B ratios equal to 4.0 and 7.0, were tested at the level keel displacement with CDL = 3.00, in order to investigate the effect of L/B ratio on the dynamic behaviour. Al tests have been performed at two speeds corresponding to Fn = 0.34 and 0.68. The Bretschneider spectral model with non-dimensional modal periods TP’ = TP / √(L/g) = 2.0 to 5.0 with step equal to 0.5 was used to model the sea states. The significant wave heights H1/3 were selected in the 8 – 16 cm range to represent moderate waves. However, the results presented refer to H1/3 = 1 m. Results for heave, pitch, acceleration as well as added resistance are presented.

2.0 REVIEW OF PAST EXPERIMENTAL WORKS

There is 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 hard chine planing and semi-planing hulls are reviewed. The respective results for round bilge semi-displacement hulls were reviewed by Grigoropoulos et al. (2010).

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 10o, 20o and 30o and L/B =5.0. For the intermediate deadrise angle two additional L/B ratios of 3.0 and 4.0 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, while 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 LCG and the added resistance. Since the prismatic hull forms are not very realistic, they propose to use the maximum breadth over chines BPX to represent the breadth, the deadrise at amidships and waterline length LWL 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 BPX is replaced by the mean breadth over the 80% of the length from the stern BP0.8. 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 (1970, 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 12o and 24o 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 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 non-standard. Limited information about their geometry is provided.

3.0 THE MODELS OF THE NTUA SERIES

The hull forms of the NTUA series have two successive chines running forward of the transom up to 70% of the hull length. Fine highly flared lines form the bow region. Among the five hull forms of the series with L/B ratios ranging from 4.00 to 7.00 in 0.75 steps, the one with ratio L/B = 5.50 is the central (parent) one. Its lines plan is shown in Fig. 1. The hull lines end at the stern on a wide transom, while the deadrise angle varies from 10o at the transom to about 70o at the bow. The angle of entrance is very small for all waterlines tested.

Fig. 1. Lines plan of the parent hull form of the NTUA series (the body plan is scaled up by a factor of three).

624 © 2011 American Society of Naval Engineers

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 non-dimensional displacement-length coefficient CDL is used to represent the loading condition. While the calm water characteristics of the series were evaluated at six values of CDL = 1.00, 1.61, 2.23, 3.00, 3.62 and 4.23, their seakeeping performance is evaluated at only half of them, i.e. at CDL = 1.61, 3.00 and 4.23. The lower values of CDL 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 paper results for the central hull form at the aforementioned CDL values and for two more hull forms with L/B = 4.0 and 7.0 at the central CDL value (CDL = 3.00) are presented.

The model lengths were determined using the 21st I.T.T.C. High Speed Marine Vehicles Committee suggestion (1996), that at least two-meter models should be used for such craft. However, the smaller values of CDL, corresponding to the lighter displacements, could not be achieved with these model lengths, since 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 series a larger model was also built. The scale of the smaller models was 60% 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.

Table 1. Characteristics of the tested models.

L/B 4.00-small

(113/95)

5.50-big

(118/96)

5.50-small

(097/94)

7.00-small

(116/96)

LOA 2.292 m 3.820 m 2.292 m 2.917 m

CDL

3.497 1.635

1.61 0.590 69.103

-0.511 0.097

2.109 0.808 2.145 0.728 2.783 1.130

3.00 0.488 28.174 0.362 29.615 0.370 64.618

-0.305 0.080 -0.297 0.083 -0.345 0.116

2.175 0.834

4.23 0.368 43.530

-0.280 0.106

Notes:

1. Each cell of the table contains the following characteristics of the model:

LWL [m] WS [m2] BWL [m] Δ [Kgr] LCG [m] T [m]

2. LCG from amidships, positive forwards.

The characteristics of the tested models are presented in the shaded cells of Table 1.

4.0 EXPERIMENTAL SETUP

Three strap-down accelerometers with a 0 – 10g range recommended for use in the 0.1 to 100 Hz band were fitted along the tested models at the FP, the LCG and the AP, to record the vertical accelerations. Due to the relatively limited importance, it was decided to suppress the latter from the results presented in this paper. The wooden models were ballasted to a pitch radius of gyration RYY = 0.25 LWL and were attached to the carriage via 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.

The sampling rate was selected to 20 Hz. In order to investigate the form of the acceleration time histories sampling at 100 Hz rate was performed for 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 & McKee (1987) encompasses the use of buffers instead of filters in the peak-trough identification technique (PKT), to throw away local minima and the application of a probabilistic approach using the P% probability level, i.e. the observed 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 (1970) stated that it is important to know if tests in irregular waves will give results which 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 non-linearity 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 non-linearity 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 non-linearity 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 (1970) who noticed a non-linearity of some importance only at the highest speed of his tests i.e. at FnV ~ 3 corresponding to Fn ~1.3, which is


outside the range of speeds under consideration for the NTUA series (results for Fn = 0.34 and 0.68 are provided here, while a higher speed of Fn = 1.032 may be considered in the future). Furthermore, the preliminary experimental results presented herein were faired via 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, since 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 non-dimensional Root Mean Square (RMS) values. The following ratios have been selected to provide scale-insensitive quantities (pertinent recommendation of any ITTC Seakeeping Committees could not be found):

3

3

'

1/3

RMSRMS H

(1)

5

5

2' WL

1/3

RMS *10 LRMS H

(2)

' a WLa

1/3

RMS LRMS gH (3)

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 17th ITTC (1984) for the respective RAO, the added resistance in random waves is expressed by the following non-dimensional quantity:

' WL2 2WL 1/3

AR LARgB H

(4)

Among the quantities provided by relations (1) to (4) only

5

'RMS for pitch response is dimensional (in degrees), while

the rest ones are non-dimensional.

In the following Tables 2 to 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 1:30 for the large models (Table 3) and 1:50 for the small models (Tables 2, 4, 5 & 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 one hour sampling period at the assumed full scale, as recommended for sufficient statistical accuracy, when stationary stochastic processes are analyzed. Sufficient time (5-15 min) 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 and they carefully inspected for any spurious noise content prior to their analysis.

Table 2. Tested sea conditions for the small model with ratio L/B = 4.0 and CDL = 3.00 (scale 1:50).

TP' 2.0 2.5 3.0 3.5 4.0 4.5 5.0

TPS (sec) 6.557 8.197 9.836 11.475 13.114 14.754 16.393

TPM (sec) 0.927 1.159 1.391 1.623 1.855 2.086 2.318

H1/3M (m) 0.080 0.090 0.100 0.110 0.120 0.140 0.160

H1/3MFD (m) 0.034 0.054 0.077 0.105 0.138 0.174 0.215

H1/3/LWL*102 3.793 4.267 4.742 5.216 5.690 6.638 7.587

Table 3. Tested sea conditions for the large model with ratio L/B = 5.5 and CDL = 1.61 (scale 1:30).

TP' 1.5 2.0 2.5 3.0 3.5 3.5 4.0

TPS (sec) 4.905 6.540 8.175 9.811 11.446 11.446 13.081

TPM (sec) 1.117 0.837 0.670 0.558 0.479 0.479 0.419

H1/3M (m) 0.100 0.100 0.100 0.120 0.130 0.150 0.150

H1/3MFD (m) 0.032 0.057 0.089 0.128 0.175 0.175 0.228

H1/3/LWL*102 2.860 2.860 2.860 3.432 3.717 4.289 4.289


TP' 2.0 2.5 3.0 3.5 4.0 4.5 5.0

TPS (sec) 6.613 8.266 9.919 11.573 13.226 14.879 16.532

TPM (sec) 0.935 1.169 1.403 1.637 1.870 2.104 2.338

H1/3M (m) 0.080 0.090 0.100 0.110 0.120 0.140 0.160

H1/3MFD (m) 0.035 0.055 0.079 0.107 0.140 0.177 0.219

H1/3/LWL*102 3.730 4.196 4.662 5.128 5.594 6.527 7.459


TP' 2.0 2.5 3.0 3.5 4.0 4.5 5.0

TPS (sec) 6.659 8.324 9.989 11.653 13.318 14.983 16.648

TPM (sec) 0.942 1.177 1.413 1.648 1.883 2.119 2.354

H1/3M (m) 0.080 0.090 0.100 0.110 0.120 0.140 0.160

H1/3MFD (m) 0.035 0.055 0.080 0.109 0.142 0.180 0.222

H1/3/LWL*102 3.678 4.138 4.598 5.057 5.517 6.437 7.356


TP' 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

TPS (sec) 5.649 7.532 9.416 11.299 13.182 15.065 16.948 18.831

TPM (sec) 0.799 1.065 1.332 1.598 1.864 2.131 2.397 2.663

H1/3M (m) 0.070 0.090 0.100 0.110 0.120 0.140 0.160 0.160

H1/3MFD (m) 0.026 0.045 0.071 0.102 0.139 0.182 0.230 0.284

H1/3/LWL*102 2.515 3.234 3.593 3.953 4.312 5.031 5.749 5.749

5.0 RESULTS AND DISCUSSION

In Figs. 2 to 6 the scale-insensitive dynamic responses for heave and pitch, as defined by relations (1) & (2) are given, for the tested sea conditions of Tables 2 to 6, respectively. In Figs. 7 to 11 the respective case-insensitive absolute vertical accelerations at the bow, the LCG and the stern of each model, as defined by relation (3), are plotted. Finally, in Figs. 12 to 16 the respective added resistance, as expressed by equation (4) are provided.


0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

RM

S ξ

3/H

s, R

MS

ξ5*1

0-2

*LW

L/ H

s(d

eg

)

Tp'

L/B=4.00, CDL=3.00

Heave, Fn=0.34

Heave, Fn=0.68

Pitch, Fn=0.34

Pitch, Fn=0.68

Fig. 2. Heave and pitch responses for the model with

L/B = 4.0 and CDL = 3.00.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

RM

S ξ

3/H

s, R

MS

ξ5*1

0-2

*LW

L/ H

s(d

eg

)

Tp'

L/B=5.50, CDL=1.61

Heave, Fn=0.34

Heave, Fn=0.68

Pitch, Fn=0.34

Pitch, Fn=0.68


L/B = 5.5 and CDL = 1.61.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

RM

S ξ

3/H

s, R

MS

ξ5*1

0-2

*LW

L/ H

s(d

eg

)

Tp'

L/B=5.50, CDL=3.00

Heave, Fn=0.34

Heave, Fn=0.68

Pitch, Fn=0.34

Pitch, Fn=0.68


L/B = 5.5 and CDL = 3.00.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

RM

S ξ

3/H

s, R

MS

ξ5*1

0-2

*LW

L/ H

s(d

eg

)

Tp'

L/B=5.50, CDL=4.23

Heave, Fn=0.34

Heave, Fn=0.68

Pitch, Fn=0.34

Pitch, Fn=0.68


L/B = 5.5 and CDL = 4.23.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

RM

S ξ

3/H

s, R

MS

ξ5*1

0-2

*LW

L/ H

s(d

eg

)

Tp'

L/B=7.00, CDL=3.00

Heave, Fn=0.34

Heave, Fn=0.68

Pitch, Fn=0.34

Pitch, Fn=0.68


L/B = 7.0 and CDL = 3.00.

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

RM

S a

*LW

L/ (

Hs

*g)

Tp'

L/B=4.00, CDL=3.00

Acc @ Bow, Fn=0.34

Acc @ Bow, Fn=0.68

Acc @ LCG, Fn=0.34

Acc @ LCG, Fn=0.68

Acc @ Stern, Fn=0.34


Fig. 7. Absolute vertical accelerations at the bow, the LCG and the stern of the model with L/B = 4.0 and CDL = 3.00.

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

11.00

12.00

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

RM

S a

*LW

L/ (

Hs

*g)

Tp'

L/B=5.50, CDL=1.61

Acc @ Bow, Fn=0.34

Acc @ Bow, Fn=0.68

Acc @ LCG, Fn=0.34

Acc @ LCG, Fn=0.68




0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

11.00

12.00

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

RM

S a

*LW

L/ (

Hs

*g)

Tp'

L/B=5.50, CDL=3.00Acc @ Bow, Fn=0.34

Acc @ Bow, Fn=0.68

Acc @ LCG, Fn=0.34

Acc @ LCG, Fn=0.68





0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

RM

S a

*LW

L/ (

Hs

*g)

Tp'

L/B=5.50, CDL=4.23Acc @ Bow, Fn=0.34

Acc @ Bow, Fn=0.68

Acc @ LCG, Fn=0.34

Acc @ LCG, Fn=0.68Acc @ Stern, Fn=0.34


Fig. 10. Absolute vertical accelerations at the bow, the LCG

and the stern of the model with L/B = 5.5 and CDL = 4.23.

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

11.00

12.00

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

RM

S a

*LW

L/ (

Hs

*g)

Tp'

L/B=7.00, CDL=3.00

Acc @ Bow, Fn=0.34

Acc @ Bow, Fn=0.68

Acc @ LCG, Fn=0.34

Acc @ LCG, Fn=0.68



Fig. 11. Absolute vertical accelerations at the bow, the LCG

and the stern of the model with L/B = 7.0 and CDL = 3.00.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

Ra

w*L

WL/ (ρ

*g*B

WL

2*H

s2)

Tp'

L/B=4.00, CDL=3.00Added Res., Fn=0.34

Added Res., Fn=0.68

Fig. 12. Mean added resistance in waves for the model with

L/B = 4.0 and CDL = 3.00.

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

Ra

w*L

WL/ (ρ

*g*B

WL

2*H

s2)

Tp'

L/B=5.50, CDL=1.61Added Res., Fn=0.34

Added Res., Fn=0.68


L/B = 5.5 and CDL = 1.61.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

Ra

w*L

WL/ (ρ

*g*B

WL

2*H

s2

)

Tp'

L/B=5.50, CDL=3.00

Added Res., Fn=0.34

Added Res., Fn=0.68


L/B = 5.5 and CDL = 3.00.

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

Ra

w*L

WL/ (ρ

*g*B

WL

2*H

s2)

Tp'

L/B=5.50, CDL=4.23

Added Res., Fn=0.34

Added Res., Fn=0.68


L/B = 5.5 and CDL = 4.23.

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

Ra

w*L

WL/ (ρ

*g*B

WL

2*H

s2)

Tp'

L/B=7.00, CDL=3.00

Added Res., Fn=0.34

Added Res., Fn=0.68


L/B = 7.0 and CDL = 3.00.

Following these figures, the derived curves on the basis of the available results are quite smooth, even in the case of the mean 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 cross-checked 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 seakeeping responses for the two selected speeds encompasses ten more cases including sets of testing sea conditions analogous to those described on Tables 2 to 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 (CDL = 1.61, 3.00 & 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 to 6, for the lower periods (respective TP’ = 1.5 to 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.

6.0 CONCLUSION

This paper presents the first preliminary results of the investigation of the seakeeping qualities of the double-chine, wide-transom 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 graphical 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 displacement speed (Fn = 0.34) and a semi-displacement one (Fn = 0.68) the effect of speed is derived.

On the basis of the experimental results, the increase of the L/B ratio results in more severe seakeeping responses. The same holds true also for speed. The effect of loading condition is reverse, i.e. by increasing the displacement the dynamic responses are in general reduced.

Following a comparison with other transom-stern round-bottom systematic series of hull forms, the seakeeping behavior of the NTUA series is fully competitive. Since the series depicts a satisfactory performance in calm water too, as demonstrated by Grigoropoulos & Loukakis (2002), it offers an attractive design source for vessels 20 – 150 m long, operating at the pre-planing regime.

REFERENCES

Blount, D.L. & 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, pp. 251-277.

Fridsma, G. (1969). “A systematic study of the rough-water performance of planing boats”, Davidson Lab. Rept. 1275, Stevens Inst. 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 Inst. of Technology, March.

Grigoropoulos, G.J. & Loukakis, T.A. (1995). “Seakeeping performance assessment of planing hulls”, Proceedings of the International Conference ODRA’95, Wessex Inst. of Technology, Szczecin, Poland, September.

Grigoropoulos, G.J., Loukakis, T.A. & Peppa, S. (1997). “Seakeeping operability of high-speed monohulls in Aegean Sea”, 8th I.M.A.M. Congress, Istanbul, Turkey, November.

Grigoropoulos, G.J. & Loukakis, T.A. (1998). “Seakeeping characteristics of a systematic series of fast monohulls”, Proceedings of the International Conference on Ship Motions and Manoeuvrability SMM'98, London, February.

Grigoropoulos, G.J., Loukakis, T.A. & Perakis, A. (2000). “Seakeeping standard series for oblique seas (A synopsis)”, Ocean Engineering Journal, 27, pp. 111-126.

Grigoropoulos, G. & Loukakis T. (2002). “Resistance and seakeeping characteristics of a systematic series in the pre-planing condition (Part I)”, Transactions of the Society of Naval Architects & Marine Engineers, 110.

Savitsky, D. & Brown, P.W. (1976). “Procedures for hydrodynamic evaluation of planing hulls in smooth and rough water”, Marine Technology, 13(4), pp. 381-400.

Savitsky, D., Roper, J.K. & Benen, L. (1972). “Hydrodynamic Development of a High Speed Planing Hull for Rough Water”, 9th Symposium on Naval Hydrodynamics ONR, Paris, p. 419.

Serter, E.H. (1993). “Hydrodynamics and Naval Architecture of Deep-Vee Hull Forms”, Hydro Research Systems S.A..

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, Rept. 196 S, December.

Van den Bosch, J.J. (1970). “Tests with two planing boat models in waves”, TH Delft, Rept. 266.

Zseleczky, J. & McKee, G. (1987). “Analysis methods for evaluating motions and accelerations of planing boats in waves”, Proceedings of the 22nd A.T.T.C.

ACKNOWLEDGEMENTS

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 & Giannis Trachanas are responsible for the good quality of the measurements. The authors are heavily indebted to them.


dynamic performance of the ntua double-chine series hull

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