Seakeeping assessment of fishing vessels in conceptual design stage

ARTICLE IN PRESS

0029-8018/$ - see

doi:10.1016/j.oc

�CorrespondiE-mail addre

(A.D. Alkan), n

(A.O. Uysal).

Ocean Engineering 34 (2007) 724–738

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Seakeeping assessment of fishing vessels in conceptual design stage

Ayla Saylia,�, Ahmet Dursun Alkanb, Radoslav Nabergojc, Ayse Oncu Uysala

aDepartment of Mathematical Engineering, Yildiz Technical University, Davutpasa Campus 34010, Istanbul, TurkeybDepartment of Naval Architecture, Yildiz Technical University, 34349 Besiktas, Istanbul, Turkey

cDepartment of Naval Architecture, University of Trieste, 34127 Trieste, Italy

Received 30 December 2005; accepted 20 May 2006

Available online 25 September 2006

Abstract

The main idea of this paper is to identify functional relations between seakeeping characteristics and hull form parameters of

Mediterranean fishing vessels. Multiple regression analysis is used for quantitative assessment through a computer software that is based

on the SQL Server Database. The seakeeping attributes under investigation are the transfer functions of heave and pitch motions and of

absolute vertical acceleration at stern, while the ship parameters influencing motion dynamics have been classified into two groups:

displacement (D) and main dimensions (L,B,T), coefficients that define the details of the hull form (CWP, CVP, LCB, LCF, etc.).

Four multiple regression models having different parameter combinations are here investigated and discussed, giving way to the so-

called ‘Simple Model’, ‘Intermediate Model’, ‘Enhanced 1 Model’ and ‘Enhanced 2 Model’. The obtained results are more than

satisfactory for seakeeping predictions during the conceptual design stage.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Fishing vessels; Conceptual design; Ship motions; Data analysis

1. Introduction

Several methods of incorporating seakeeping assessmentinto the conceptual design of fishing vessels have beenproposed, since it is ascertained that rational considerationof potential seakeeping behaviour from the real beginningof the design process is economically sound. They arebased either on direct computations over pre-designed hullforms, or they rely on results from systematic seriesanalysis.

Whichever method, computer code, and/or approach areused through the design process, it is well known that therelative requirements for seakeeping and other hydrody-namic issues are often in conflict. For instance, whilstresistance and powering are sensitive to changes in localhull geometry, seakeeping performance generally dependson primary geometric characteristics (main dimensions,

front matter r 2006 Elsevier Ltd. All rights reserved.

eaneng.2006.05.003

ng author.

sses: [email protected] (A. Sayli), [email protected]

[email protected] (R. Nabergoj), [email protected]

hydrostatics and weight distribution) and is slightlysensitive to small changes in the hull form, both generaland local. Therefore, it should be mandatory to considervessel’s behaviour in a seaway from the very initial(conceptual) stage, since the related improvements aredifficult and expensive to obtain afterwards.It is generally accepted that conceptual design proce-

dures require simplicity in use while assuring sufficientaccuracy in prediction. This is also true for seakeepingevaluation that implies a specialisation in terms of the classof vessels as well as of realistic operating environment. Tothis end, the transfer functions for a set of medium-sizeMediterranean fishing vessels are here assessed to buildgeneral regression formulae, suitable to predict the shipbehaviour in regular waves and, moreover, in irregular seaby means of the well known superposition technique. Sincethe seakeeping ability of a fishing vessel drives theeffectiveness of the fishermen and the operability of thefishing systems in rough weather, the present analysis hasbeen carried out with the main scope of investigating theeffect of different hull forms and loading conditions onship motions and vertical accelerations on board. In this

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ARTICLE IN PRESSA. Sayli et al. / Ocean Engineering 34 (2007) 724–738 725

respect, the present paper represents a natural extensionand completion of previous contributions (Trincas et al.,2001; Nabergoj et al., 2003).

2. Design strategy

Among different approaches in conceptual design, themost promising strategy to model vessel hydrodynamics isto employ approximating functions, which describe specificship responses. Statistical techniques are widely used indesign to build approximate formulae, based on expensivecomputer analysis, since they are much more efficient torun and easier to integrate. At the same time, they yieldinsight into the functional relationship between designvariables and performance responses (screening testspreliminary to sensitive analysis).

Seakeeping prediction methods basically rely on linearhydrodynamic theory for estimating vessel motions andcorresponding induced effects. This is more than sufficientat conceptual design stage, where extensive use of CFDcodes is certainly unpractical. In fact, the results of striptheory for ship motions are in general accurate enough,even for hull forms and vessel speed to wavelengthvariations that do not respect the basic assumptions ofthe theory.

Here, the very scope is to develop an efficient seakeepingprediction model to be included in a fast and comprehen-sive evaluation procedure of several alternative designs.The functions employed for seakeeping trade-offs andfeasible for design modelling are polynomial responsesurfaces. The coefficients of the approximating polyno-mials are calculated using a least-squares regressionanalysis to fit the response surface approximation toexisting data, which have been previously generated off-line through simulation/analysis routines and stored in thedesign database. The approximating functions can then beused for design predictions and/or to build a meta-modelfor the class of fishing vessels considered. In this respect,seakeeping modelling can be carried out at different levelsof interest, from transfer functions (Moor, 1967) to short-term statistics (Nabergoj et al., 2003; Moor and Murdey,1968; Loukakis and Chryssostomidis, 1975) and further upto ship response ranking (Trincas et al., 2001; Bales, 1980;Wijngaarden, 1984; Nabergoj et al., 1989; Alkan et al.,2003).

In any regression procedure, seakeeping modellingrequires the previous building of a design databasecomprising geometric variables and parameters of vessels(Hull Form Database) as well as their responses in specificseaways (regular and/or irregular waves) and differentoperating conditions (Seakeeping Database). A linearmultivariate regression analysis was here performed withthe main scope of identifying the independent variablesthat mostly affect the considered responses in regularwaves, i.e., heave, pitch and vertical acceleration at givenlocation. As the analysis was restricted to a specific class offishing vessels, it has been assumed that the response

surface is approximated by a simple mathematical modelwhere underlying equations are linear (polynomial re-sponse surface).

3. Design databases

3.1. Hull form database

The lines plans for a set of 13 medium-sized Mediterra-nean fishing vessels have been faired and stored to build therelational geometric database (Hull Form Database). Hullforms of the vessels are shown in Fig. 1 while their maingeometric particulars are given in Table 1. The populationincludes a large variety of single-screw hull forms, rangingfrom ‘U’ to ‘V’ sections forward, from rounded sections tounderwater chines, and from large bulbous bows to theremoval of bulb.The locations of the longitudinal centres are given

relative to after perpendicular and normalised by shiplength. For example, LCF/L and/or LCB/L values lowerthan 0.50 denote that the longitudinal centre of flotationand/or the longitudinal centre of buoyancy are located aftof amidships and vice versa. Static stability was checked indetail by considering geo-mechanical properties of thevessels at different loading conditions.Each fishing vessel has been evaluated at three different

loading conditions, denoted by the last digit of the label inthe first column of Table 1. In particular, digits 1–3, refer,respectively, to: LC1—leaving to the fishing ground (100%consumables); LC2—leaving from the fishing ground (fullholds and 40% consumables); and LC3—arrival to port(full holds and 10% consumables).In Table 1, we also show the ranges of the geometric

variables and hull parameters, thus providing all basicinformation to ascertain if a candidate design of givenvariables and parameters is within the region of the presentdatabase. The database capability to implement reliableregression formulae can be highlighted by checking thenormal distribution of geometric descriptors. For somevariables the correspondence is not so fair.

3.2. Seakeeping database

A total population of 39 cases (13 hull forms times threeloading conditions) is used to build the SeakeepingDatabase. To this aim, the seakeeping computations havebeen carried out by means of a two-dimensional computercode based on Frank close-fit method. A very accurate hullgeometry description has always been used, both forsectional offsets and number of stations. The pitchgyradius was held constant and fixed at 26 percent ofvessel length for whichever vessel.The seakeeping responses in head sea are generally the

most important responses for mono-hulls and constitutethe starting point for the evaluation of seakeepingperformance of a vessel. Thus, all calculations were carriedout for vertical motions and related kinematics. Roll is

https://www.researchgate.net/publication/298345147_SEAKEEPING_STANDARD_SERIES_FOR_CRUISER-STERN_SHIPS?el=1_x_8&enrichId=rgreq-badfbb0d480715150d5a55dfb44b1169-XXX&enrichSource=Y292ZXJQYWdlOzIyOTM1MzkzMDtBUzoxMTQ5NjM3NzEzMDE4OTFAMTQwNDQyMDkwNzk4MQ==

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Vessel 01 - LC2 (Dinko)T = 2.775 m

Vessel 02 - LC2 (Cost08)T = 2.775 m

Vessel 03 - LC 2 (Flori)T = 2.410 m

Vessel 04- LC 2 (Gemma)T = 2.647 m

Vessel 05 - LC 2 (Genova)T = 2.810 m

Vessel 06 - LC 2 (Greben)T = 2.687 m

Vessel 07 - LC2 (Ligny)T = 2.906 m

Vessel 08 - LC 2 (Tropesca)T = 3.049 m

Vessel 09 - LC2 (Aus25)T = 3.150 m

Vessel 10 - LC 2 (Mazara)T = 3.080 m

Vessel11 - LC2 (Nt28)T = 2.970 m

Vessel 12 - LC 2 (Russo)T = 2.885 m

Vessel 13 - LC2 (Ubcbig)T= 3.055 m

Fig. 1. Lines plans of the vessels.

A. Sayli et al. / Ocean Engineering 34 (2007) 724–738726

certainly an important ship motion, but the problemsrelated with non-linearity and accurate roll-dampingpredictions are outside the scope of the present work.

The computed ship responses include heave and pitchmotions, as well as vertical acceleration at aft perpendi-cular, which corresponds to a location in the stern workingarea. The vertical acceleration at stern is of particular

interest for establishing the working capability of thefishermen and is therefore useful to the designer. All theresults are given for regular waves in terms of non-dimensional transfer functions. They constitute the designinformation that is required to predict ship responses inconfused seas by means of the superposition technique.The calculations were performed at seven ship speeds, i.e.,

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Table 1

Hull form parameters

Vessel L (m) L/B (�) B/T (�) L/r1/3 (�) CWP (�) CVP (�) CWPA (�) CWPF (�) CVPA (�) CVPF (�) LCF/L (�) LCB/L (�)

V_011 21.38 3.171 2.582 3.955 0.857 0.490 0.965 0.621 0.513 0.583 0.392 0.463

V_012 21.38 3.171 2.458 3.827 0.874 0.505 0.979 0.635 0.535 0.589 0.393 0.456

V_013 21.38 3.171 2.846 4.234 0.807 0.468 0.909 0.591 0.479 0.570 0.400 0.479

V_021 25.74 3.677 2.646 4.200 0.841 0.574 0.846 0.663 0.608 0.670 0.406 0.488

V_022 25.74 3.677 2.541 4.103 0.864 0.576 0.871 0.673 0.613 0.701 0.399 0.482

V_023 25.74 3.677 2.769 4.312 0.796 0.587 0.804 0.654 0.611 0.696 0.426 0.494

V_031 25.00 3.472 3.158 4.216 0.832 0.610 0.834 0.698 0.635 0.689 0.436 0.494

V_032 25.00 3.472 2.988 4.091 0.853 0.617 0.868 0.703 0.638 0.701 0.427 0.488

V_033 25.00 3.472 3.398 4.386 0.770 0.630 0.744 0.690 0.675 0.674 0.468 0.499

V_041 26.35 3.513 2.914 4.144 0.813 0.621 0.852 0.666 0.626 0.715 0.427 0.489

V_042 26.35 3.513 2.833 4.083 0.823 0.625 0.868 0.668 0.628 0.720 0.423 0.486

V_043 26.35 3.513 3.158 4.327 0.771 0.624 0.789 0.659 0.635 0.698 0.447 0.497

V_051 25.00 3.125 2.835 3.692 0.875 0.628 0.882 0.668 0.710 0.757 0.397 0.472

V_052 25.00 3.125 2.752 3.634 0.890 0.629 0.890 0.674 0.719 0.763 0.393 0.468

V_053 25.00 3.125 3.000 3.802 0.819 0.651 0.800 0.658 0.753 0.760 0.423 0.477

V_061 20.50 2.941 2.766 3.852 0.804 0.521 0.845 0.559 0.511 0.614 0.435 0.492

V_062 20.50 2.941 2.585 3.691 0.834 0.533 0.879 0.574 0.530 0.622 0.429 0.484

V_063 20.50 2.941 3.066 4.117 0.742 0.512 0.769 0.536 0.495 0.597 0.451 0.503

V_071 25.00 3.125 2.835 3.631 0.898 0.644 0.891 0.690 0.719 0.746 0.398 0.467

V_072 25.00 3.125 2.753 3.576 0.903 0.651 0.894 0.696 0.732 0.747 0.398 0.463

V_073 25.00 3.125 3.001 3.739 0.860 0.652 0.852 0.679 0.723 0.743 0.413 0.473

V_081 27.25 3.733 2.547 4.118 0.782 0.650 0.799 0.669 0.661 0.747 0.440 0.501

V_082 27.25 3.733 2.394 3.989 0.818 0.642 0.836 0.679 0.657 0.750 0.426 0.495

V_083 27.25 3.733 2.700 4.243 0.753 0.654 0.746 0.661 0.674 0.740 0.452 0.507

V_091 21.00 2.770 2.627 3.514 0.861 0.540 0.844 0.672 0.515 0.652 0.424 0.481

V_092 21.00 2.770 2.406 3.332 0.887 0.563 0.881 0.697 0.556 0.663 0.424 0.472

V_093 21.00 2.770 2.756 3.619 0.831 0.537 0.816 0.660 0.572 0.643 0.433 0.486

V_101 30.80 2.962 3.870 4.061 0.766 0.662 0.873 0.544 0.718 0.695 0.388 0.424

V_102 30.80 2.962 3.402 3.811 0.783 0.688 0.884 0.567 0.759 0.688 0.392 0.418

V_103 30.80 2.962 4.132 4.199 0.756 0.648 0.862 0.533 0.700 0.689 0.386 0.428

V_111 20.00 3.061 2.633 3.967 0.799 0.495 0.734 0.666 0.495 0.509 0.428 0.486

V_112 20.00 3.061 2.455 3.787 0.824 0.514 0.754 0.691 0.527 0.520 0.430 0.478

V_113 20.00 3.061 2.901 4.239 0.738 0.484 0.667 0.636 0.474 0.487 0.447 0.497

V_121 27.30 4.015 2.729 4.275 0.884 0.636 0.831 0.784 0.663 0.651 0.447 0.485

V_122 27.30 4.015 2.484 4.072 0.915 0.648 0.866 0.806 0.679 0.663 0.444 0.480

V_123 27.30 4.015 2.941 4.447 0.841 0.642 0.785 0.765 0.665 0.642 0.461 0.490

V_131 28.00 3.060 3.386 3.825 0.854 0.663 0.903 0.699 0.658 0.770 0.428 0.488

V_132 28.00 3.060 2.995 3.599 0.885 0.680 0.939 0.707 0.685 0.788 0.416 0.477

V_133 28.00 3.060 3.704 4.003 0.823 0.657 0.859 0.694 0.650 0.755 0.442 0.496

min 30.80 4.015 4.132 4.447 0.915 0.688 0.979 0.806 0.759 0.788 0.468 0.507

max 20.00 2.770 2.394 3.332 0.738 0.468 0.667 0.533 0.474 0.487 0.386 0.418

A. Sayli et al. / Ocean Engineering 34 (2007) 724–738 727

Froude numbers Fn ¼ 0, 0.05, 0.10, 0.15, 0.20, 0.25, and0.30. The intention is to cover the whole range of vessel’sspeed profile including transfer from port to fishing groundand vice versa as well as catching and recovery activities.

4. Defining design variables

The most important problem for the designer whilecarrying out the synthesis of the seakeeping results is thatin the available literature the choice of the design variablesis arbitrary and does not generally align from one series,study or formula to another (Moor, 1967; Moor andMurdey, 1968; Loukakis and Chryssostomidis, 1975; Bales,1980; Wijngaarden, 1984). Therefore, it is preliminary towhichever modelling to take into account the common

attitude to substantially reduce the number of independentvariables to a few basic descriptors of the hull formaccording to personal practise and experience. This canhave serious implications for the visibility of the trade-offs,which occur in optimisation procedures where objectivefunctions are often based on methodical series data orregression ranking formulae. In this respect, Table 2 showsa brief summary of the principal models often used forseakeeping predictions at very initial design stages.It is known from seakeeping theory that, in addition to

wave excitation, a ship underway is subject to inertia,added mass, damping and restoring forces. The inertiaforces are related to the structural mass and its distribu-tion. On the other hand, the added mass and fluid-dampingforces depend on the displaced volume, as well as on the


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Table 2

Summary of the principal seakeeping models

Model description Regression variables Comments

(Moor, 1967) L/B, L/T, CWP, kyy/L, V/L1/2 Bending Moment Database Ships

(Moor and Murdey, 1968) L/r1/3, L/B, L/T, CB, CWP, LCB, kyy/L,

V/L1/2RMS Database Ships

(Loukakis and Chryssostomidis, 1975) L/B, B/T, CB, Fn RMS Series 60 Ships

(Nabergoj et al., 2003) L/r1/3, T/B, CVP, LCF, LCB, CVPF, BML RMS Mediterranean Fishing Vessels

(Bales, 1980) T/L, c/L, CWPF, CWPA, CVPF, CVPA Ranking Destroyers

(Wijngaarden, 1984) L/B, L/T, CP4, CWP, LCF, LCB Ranking Research Vessels

(Nabergoj et al., 1989) T/L, c/L, CWPF, CWPA, CVPF, CVPA Ranking Large Trawlers

(Trincas et al., 2001) L, T/B, L2/BT, AWP/r2/3, CPVF, CPVA,

BML/L3B, (LCB�LCF)r, LCBr1/3Ranking Mediterranean Fishing Vessels

(Alkan et al., 2003) L/B, L/T, B/T, CB, CP, CM, CVP, CWP,

L/r1/3, LCB, LCF

Table 3

Implemented seakeeping regression models and corresponding design variables

Model Description Non-dimensional ratios Hull form parameters Speed

I Simple L/r1/3, L/B, B/T Fn, Fn2

II Intermediate L/r1/3, L/B, B/T CWP, CVP Fn, Fn2

III Enhanced 1 L/r1/3, L/B, B/T CWP, CVP, LCF/L, LCB/L Fn, Fn2

IV Enhanced 2 L/r1/3, L/B, B/T CWPA, CWPF, CVPA, CVPF Fn, Fn2


longitudinal distribution of both the cross sectional areaand beam-draught ratio. The restoring forces are governedby the waterplane area and the longitudinal distribution ofbeam. In conclusion, the motions of a ship should begoverned by its main dimensions, the form of waterplanearea, the distribution of sectional area and draught, inaddition to her speed and heading.

In principle, as far as regression models are concerned,any choice of regression variables can be decided and, inparticular, different combinations of them can be allowed.However, in the present analysis, the attention is limited tothe influence of geometric, weight and speed character-istics. The parameters under investigation are grouped asfollows:

�
Displacement (D) and main dimensions (L,B,T), ortheir ratios. � Coefficients defining the hull form, in terms of long-
itudinal distribution of sectional area, beam or draught,e.g. CWP, CVP, LCF, LCB, etc.
� Centre of gravity and inertia of weights, e.g. LCG,
VCG, kyy, etc.
� Speed on course.
The first and second group of parameters is concernedwith the specification of the hull characteristics, while thethird group with the definition of the mechanical propertiesof the vessel. They are the principal parameters influencingthe ship motions and accelerations. For deck wetness and

water impact forces the above water form characteristics,such as freeboard and flare are most important, but theywill not be considered here. The weight distribution dataare similar for all the ships by assuming a fixed longitudinalradius of inertia (kyy/L ¼ 0.26).To develop sufficiently simple and reliable regression

models, it is convenient to start with very few regressionvariables and increase their number progressively as suggestedby the precision required for the approximating polynomialunder investigation. Therefore, the models are considered withdifferent levels of complexity, including both principal andsecondary form parameters, as shown in Table 3.

5. Multiple regression analysis

Multiple regression analysis is a logical extension of two-variable regression analysis. Instead of a single independentvariable, two or more independent variables are used toestimate the values of a dependent variable. The regressionequation is derived using the least-squares method. Themethod uses the following low-order polynomials:

Y ¼ A0 þ A1X 1 þ A2X 2þ ; � � � ;þAnX n, (1)

where Y is an estimated-dependent variable; X1, X2 ,y ,Xn

are the independent variables used to estimate thedependent variable Y and A0, A1, A2 ,y ,An are coefficientsthat reflect the dependency’s influences on the dependentvariables. Multiple regression analysis can be solved usingthe w2-test. It gets difficult to estimate the parameters

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Table 4

Coefficients for simple regression model

Coefficients of heave transfer functions za¼ A0 þA1

L

r1=3þ A2

LBþA3

BTþ A4FnþA5Fn2

l/L A0 A1 A2 A3 A4 A5 R2

0.50 �0.0487 0.0555 �0.0123 �0.0156 �0.5502 1.0330 0.6838

0.75 0.1354 �0.0618 0.0583 0.0441 �1.4327 3.0426 0.8495

1.00 �0.5461 0.3678 �0.1107 �0.0962 �0.0872 �2.3763 0.7565

1.25 �1.1381 0.5969 �0.0999 �0.1722 3.6513 �12.9446 0.8227

1.50 �0.8469 0.4967 �0.0443 �0.1605 4.4911 �9.7896 0.7724

1.75 0.2402 0.1930 0.0053 �0.1299 2.2373 2.0216 0.8949

2.00 0.9499 0.0168 0.0151 �0.1103 0.7934 6.2817 0.9205

2.50 1.0372 0.0112 �0.0049 �0.0769 0.4371 3.3637 0.9022

3.00 0.9891 0.0159 �0.0052 �0.0496 0.4236 1.2317 0.8896

Coefficients of pitch transfer functions ya ¼ B0 þ B1

L

r1=3þ B2

LBþ B3

BTþ B4Fnþ B5Fn2

l/L B0 B1 B2 B3 B4 B5 R2

0.50 0.0228 �0.0051 0.0097 0.0049 �0.2979 0.5015 0.8752

0.75 �0.0614 0.0954 �0.0407 �0.0204 �0.7397 1.3033 0.8052

1.00 �0.1758 0.1944 �0.0302 �0.0171 �1.0827 �0.3594 0.9368

1.25 �0.2990 0.2487 �0.0301 0.0159 0.9213 �6.3529 0.8553

1.50 �0.0236 0.2092 �0.0619 0.0451 1.9392 �5.4877 0.5522

1.75 0.6932 0.0580 �0.0757 0.0498 1.1895 0.7746 0.8581

2.00 1.1157 �0.0177 �0.0784 0.0299 0.7191 3.1494 0.9029

2.50 1.1391 0.0044 �0.0784 0.0095 0.6535 2.3557 0.9203

3.00 1.1094 0.0155 �0.0721 0.0069 0.5298 2.0278 0.9336

Coefficients of absolute vertical acceleration transfer functions avLga¼ C0 þ C1

L

r1=3þ C2

LBþ C3

BTþC4Fnþ C5Fn2

l/L C0 C1 C2 C3 C4 C5 R2

0.50 �1.6371 �0.1706 1.6461 0.3207 �0.4979 �26.5440 0.5258

0.75 �1.3229 4.1800 �1.6659 �1.9544 �6.8836 6.1558 0.5030

1.00 �14.5208 6.8680 �0.2903 �1.6383 31.6532 �119.7730 0.7518

1.25 �17.0380 5.5094 0.8831 �0.4738 61.2818 �131.1120 0.7290

1.50 �7.4445 2.5627 0.7124 0.1890 38.5132 22.3118 0.8829

1.75 5.1534 �0.6110 0.4263 0.3692 10.1442 124.8288 0.9667

2.00 8.0496 �1.0829 0.0775 0.1729 5.4764 103.1251 0.9650

2.50 4.4491 �0.1610 �0.1656 0.0091 8.3733 38.5484 0.9755

3.00 2.9537 0.0055 �0.1248 0.0052 7.2054 19.8967 0.9834


automatically when the variables and functions increase.For the general formulae, the matrixes used for theestimation of the coefficients in Eq. (1) are:

X ¼

1 x11 x12 :: x1k

1 x21 x22 :: x2k

:: :: :: :: ::

1 xn1 xn2 :: xnk

2666664

3777775

Y ¼

y1

y2

::

yn

2666664

3777775

A ¼

A0

A1

::

Ak

2666664

3777775. ð2Þ

Then the matrix of the regression coefficients can becalculated from the relation:

A ¼ ðXTX Þ�1ðXTY Þ. (3)

To carry out the regression, the Hull Form Databaseis built using Visual Basic programming language basedon SQL-Server database. The data analysis is donedynamically by using statistical techniques to analyserecords on a ship database and to automatically findout both the motion characteristics and their depen-dencies. These latter are described by linear functionsbetween seakeeping responses and geometrical character-istics. The system considers the database changes at anytime without any need of reconstructing the completesystem.

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Table 5

Coefficients for intermediate regression model


L

r1=3þ A2

LBþA3

BTþ A4CWP þ A5CVP þ A6FnþA7Fn2

l/L A0 A1 A2 A3 A4 A5 A6 A7 R2

0.50 �0.2601 0.1577 �0.0980 �0.0701 0.0783 0.3014 �0.5502 1.0330 0.6998

0.75 0.3460 �0.1795 0.1593 0.1111 �0.0551 �0.3730 �1.4327 3.0426 0.8585

1.00 �1.1055 0.6522 �0.3514 �0.2517 0.1868 0.8622 �0.0872 �2.3763 0.7675

1.25 �1.3240 0.8275 �0.3132 �0.3318 �0.1320 0.9058 3.6513 �12.9446 0.8348

1.50 �0.9694 0.7551 �0.2892 �0.3501 �0.2388 1.0813 4.4911 �9.7896 0.7848

1.75 �0.5593 0.6906 �0.4281 �0.4245 0.1369 1.6472 2.2373 2.0216 0.9040

2.00 �0.2764 0.5860 �0.4594 �0.4083 0.4868 1.6433 0.7934 6.2817 0.9265

2.50 0.4300 0.2585 �0.2060 �0.1971 0.2902 0.6567 0.4371 3.3637 0.9044

3.00 0.6851 0.1290 �0.0955 �0.1013 0.1606 0.2803 0.4236 1.2317 0.8906


L

r1=3þ B2

LBþ B3

BTþ B4CWP þ B5CVP þ B6Fnþ B7Fn2

l/L B0 B1 B2 B3 B4 B5 B6 B7 R2

0.50 �0.0224 0.0038 0.0041 0.0035 0.0352 0.0054 �0.2979 0.5015 0.8778

0.75 �0.2212 0.1974 �0.1298 �0.0813 0.0238 0.3406 �0.7397 1.3033 0.8246

1.00 0.0273 0.2232 �0.0722 �0.0652 �0.2561 0.2876 �1.0827 �0.3594 0.9453

1.25 0.2817 0.1967 �0.0185 �0.0155 �0.5408 0.2117 0.9213 �6.3529 0.8720

1.50 0.7385 0.1451 �0.0508 0.0006 �0.7157 0.2968 1.9392 �5.4877 0.6049

1.75 1.2534 0.0865 �0.1416 �0.0428 �0.6339 0.5621 1.1895 0.7746 0.8873

2.00 1.5471 0.0258 �0.1503 �0.0585 �0.5189 0.5310 0.7191 3.1494 0.9197

2.50 1.8652 �0.1165 �0.0092 0.0147 �0.5964 0.0102 0.6535 2.3557 0.9322

3.00 1.8252 �0.1410 0.0327 0.0416 �0.5347 �0.1598 0.5298 2.0278 0.9426

Coefficients of absolute vertical acceleration transfer functions avLga¼ C0 þ C1

L

r1=3þ C2

LBþC3

BTþC4CWP þC5CVP þ C6Fnþ C7Fn2

l/L C0 C1 C2 C3 C4 C5 C6 C7 R2

0.50 �22.3695 6.4871 �3.4716 �2.3666 12.4592 14.2935 �0.4979 �26.5440 0.5390

0.75 �34.7370 16.7501 �11.7171 �7.7444 17.4555 31.4095 �6.8836 6.1558 0.5604

1.00 �14.3417 10.8180 �4.1728 �4.7924 �5.8240 18.1115 31.6532 �119.7734 0.7961

1.25 �7.6815 6.8989 �1.1129 �2.7449 �11.8907 13.5438 61.2818 �131.1120 0.7548

1.50 1.1321 4.3234 �1.5944 �2.2790 �11.5944 14.6310 38.5132 22.3118 0.8967

1.75 5.6009 3.0759 �3.2167 �2.6099 �5.7331 17.1219 10.1442 124.8288 0.9760

2.00 6.2147 1.9822 �2.8014 �2.0278 �2.4289 12.5306 5.4764 103.1251 0.9715

2.50 6.9510 0.0839 �0.5752 �0.4977 �2.9988 3.0452 8.3733 38.5484 0.9799

3.00 5.1181 �0.0935 �0.1745 �0.1868 �2.1509 1.2199 7.2054 19.8967 0.9869


6. Regression models for seakeeping responses

An extensive set of ship response values correspondingto a set of points in the design space (wave length and speedof the vessel) was stored in the Seakeeping Database. Thisdesign database was used to estimate the correspondencebetween numerically and statistically derived values whilechanging the independent variables. The screening testswere enough satisfying as regards the control of statisticalparameters (R2, t-Student, etc.), thus confirming that linearregression analysis is feasible over fairly large intervals ofdependent variables. In this respect, the proposed linearregression models are defined as follows:

(I)
Simple Model
z

a¼ A0 þ A1

L

r1=3þ A2

L

Bþ A3

B

Tþ A4Fnþ A5Fn2,

ya¼ B0 þ B1

L

r1=3þ B2

L

Bþ B3

B

Tþ B4Fnþ B5Fn2,

avL

ga¼ C0 þ C1

L

r1=3þ C2

L

Bþ C3

B

Tþ C4Fnþ C5Fn2.

ð4Þ

(II)
Intermediate model
z

a¼ A0 þ A1

L

r1=3þ A2

L

Bþ A3

B

T

þ A4CWP þ A5CPV þ A6Fnþ A7Fn2,

ya¼ B0 þ B1

L

r1=3þ B2

L

Bþ B3

B

T

þ B4CWP þ B5CPV þ B6Fnþ B7Fn2,

ARTICLE IN PRESS

Table 6

Coefficients for enhanced 1 regression model


L

r1=3þ A2

LBþA3

BTþ A4CWP þ A5CVP þ A6LCF=Lþ A7LCB=Lþ A8Fnþ A9Fn2

l/L A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 R2

0.50 �0.1104 0.0739 �0.0348 �0.0288 �0.0674 0.1307 �0.3754 0.4942 �0.5502 1.0330 0.7205

0.75 0.2486 �0.1296 0.1213 0.0866 0.0352 �0.2716 0.2460 �0.3009 �1.4327 3.0426 0.8607

1.00 �0.7532 0.5051 �0.2365 �0.1804 �0.1072 0.5666 �0.9023 0.9379 �0.0872 �2.3763 0.7748

1.25 �0.5692 0.3950 0.0129 �0.1181 �0.8773 0.0229 �1.8888 2.5389 3.6513 �12.9446 0.8517

1.50 0.1830 0.2143 0.1274 �0.0859 �1.2593 �0.0128 �2.9287 3.3376 4.4911 �9.7896 0.8058

1.75 0.7940 0.1531 �0.0052 �0.1649 �0.9657 0.5695 �3.4756 3.4800 2.2373 2.0216 0.9213

2.00 0.7652 0.1974 �0.1510 �0.2216 �0.3371 0.8673 �2.6845 2.5651 0.7934 6.2817 0.9382

2.50 0.8747 0.1152 �0.0897 �0.1292 �0.0393 0.3735 �1.1548 0.9932 0.4371 3.3637 0.9116

3.00 0.8850 0.0787 �0.0528 �0.0780 0.0262 0.1828 �0.5243 0.3830 0.4236 1.2317 0.8959


L

r1=3þ B2

LBþ B3

BTþ B4CWP þ B5CVP þ B6LCF=Lþ B7LCB=Lþ B8Fnþ B9Fn2

l/L B0 B1 B2 B3 B4 B5 B6 B7 B8 B9 R2

0.50 �0.0332 0.0105 �0.0009 0.0002 0.0464 0.0191 0.0268 �0.0386 �0.2979 0.5015 0.8783

0.75 �0.1235 0.1516 �0.0945 �0.0589 �0.0626 0.2481 �0.2484 0.2826 �0.7397 1.3033 0.8291

1.00 �0.0482 0.1781 �0.0448 �0.0407 �0.2683 0.1883 0.2221 0.1439 �1.0827 �0.3594 0.9473

1.25 �0.0857 0.2692 �0.0834 �0.0478 �0.3136 0.3483 0.9712 �0.6139 0.9213 �6.3529 0.8796

1.50 0.3243 0.3115 �0.1815 �0.0798 �0.3764 0.6305 1.0630 �1.0733 1.9392 �5.4877 0.6188

1.75 0.9320 0.2832 �0.2890 �0.1403 �0.3043 0.9647 0.7995 �1.1375 1.1895 0.7746 0.8922

2.00 1.2724 0.2085 �0.2861 �0.1494 �0.2229 0.9061 0.6779 �1.0379 0.7191 3.1494 0.9227

2.50 1.6814 0.0306 �0.1169 �0.0591 �0.3740 0.3138 0.4442 �0.8062 0.6535 2.3557 0.9351

3.00 1.6855 �0.0120 �0.0609 �0.0234 �0.3488 0.1075 0.3312 �0.6903 0.5298 2.0278 0.9458

Coefficients of absolute vertical acceleration transfer functionsavLga¼ C0 þ C1

L

r1=3þ C2

LBþC3

BTþ C4CWP þC5CVP þ C6LCF=Lþ C7LCB=Lþ C8Fnþ C9Fn2

l/L C0 C1 C2 C3 C4 C5 C6 C7 C8 C9 R2

0.50 �22.5122 5.6740 �2.9252 �1.9419 11.7220 12.5602 0.6928 3.5507 �0.4979 �26.5440 0.5411

0.75 �29.9897 13.1928 �9.0978 �5.9650 11.9475 24.0794 �11.5651 19.7364 �6.8836 6.1558 0.5812

1.00 �19.2165 5.7251 �0.9203 �2.0743 �8.7489 7.0680 15.1566 19.1232 31.6532 �119.7734 0.8473

1.25 �19.6143 3.6825 0.5638 �0.8988 �9.9746 6.1524 33.6315 5.1493 61.2818 �131.1120 0.7923

1.50 �8.6192 1.8526 �0.3313 �0.8523 �9.8740 8.9254 27.4241 3.4983 38.5132 22.3118 0.9091

1.75 �1.3419 1.4825 �2.4300 �1.6803 �4.3456 13.4115 19.4633 1.7443 10.1442 124.8288 0.9818

2.00 �0.3493 1.4076 �2.6908 �1.6333 �0.2027 11.0015 18.0518 �2.5482 5.4764 103.1251 0.9777

2.50 2.6131 0.0242 �0.7196 �0.4033 �1.2136 2.7143 11.8098 �3.1255 8.3733 38.5484 0.9878

3.00 2.5434 �0.1584 �0.2402 �0.1154 �1.1203 0.9608 7.0207 �1.7222 7.2054 19.8967 0.9936


avL

ga¼ C0 þ C1

L

Bþ C2

B

Tþ C3

L

Tþ C4CB þ C5Fn

þ C6Fn2. ð5Þ

(III)
Enhanced 1 model
z

a¼ A0 þ A1

L

r1=3þ A2

L

Bþ A3

B

Tþ A4CWP þ A5CPV

þ A6LCF=Lþ A7LCB=Lþ A8Fnþ A9Fn2,

ya¼ B0 þ B1

L

r1=3þ B2

L

Bþ B3

B

Tþ B4CWP þ B5CPV

þ B6LCF=Lþ B7LCB=Lþ B8Fnþ B9Fn2,

avL

ga¼ C0 þ C1

L

r1=3þ C2

L

Bþ C3

B

Tþ C4CWP þ C5CPV

þ C6LCF=Lþ C7LCB=Lþ C8Fnþ C9Fn2. ð6Þ

(IV)
Enhanced 2 model
z

a¼ A0 þ A1

L

r1=3þ A2

L

Bþ A3

B

Tþ A4CWPA þ A5CWPF

þ A6CVPA þ A7CVPF þ A8Fnþ A9Fn2,

ya¼ B0 þ B1

L

r1=3þ B2

L

Bþ B3

B

Tþ B4CWPA þ B5CWPF

þ B6CVPA þ B7CVPF þ B8Fnþ B9Fn2,

avL

ga¼ C0 þ C1

L

r1=3þ C2

L

Bþ C3

B

Tþ C4CWPA þ C5CWPF

þ C6CVPA þ C7CVPF þ C8Fnþ C9Fn2. ð7Þ

The regression coefficients obtained from the equationsare given in Tables 4–7, which allow trade-off estimation ofresponses due to simultaneous variation of the relatedgeometric variables.

ARTICLE IN PRESS

Table 7

Coefficients for enhanced 2 regression model


L

r1=3þ A2

LBþA3

BTþ A4CWPA þA5CWPF þ A6CVPA þA7CVPF þ A8FnþA9Fn2

l/L A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 R2

0.50 �0.1542 0.1146 �0.0598 �0.0443 �0.0204 0.0179 0.0041 0.1669 �0.5502 1.0330 0.7250

0.75 0.2899 �0.1112 0.0873 0.0656 �0.0590 0.0424 0.0723 �0.2057 �1.4327 3.0426 0.8721

1.00 �0.9078 0.4944 �0.1853 �0.1558 0.1410 �0.1391 �0.1336 0.4920 �0.0872 �2.3763 0.7946

1.25 �1.5311 0.7578 �0.1934 �0.2510 0.0546 �0.2462 �0.3537 0.9272 3.6513 �12.9446 0.8678

1.50 �1.4183 0.7469 �0.1956 �0.2907 0.1368 �0.3661 �0.2646 1.0986 4.4911 �9.7896 0.8176

1.75 �0.7651 0.6362 �0.2998 �0.3537 0.2840 �0.2513 0.0813 1.1386 2.2373 2.0216 0.9284

2.00 �0.1863 0.4906 �0.3281 �0.3369 0.3298 �0.0192 0.2172 0.9405 0.7934 6.2817 0.9462

2.50 0.3796 0.2604 �0.1852 �0.1905 0.2314 0.0440 0.1281 0.4203 0.4371 3.3637 0.9215

3.00 0.6154 0.1492 �0.1006 �0.1089 0.1520 0.0313 0.0792 0.1935 0.4236 1.2317 0.9070


L

r1=3þ B2

LBþ B3

BTþ B4CWPA þ B5CWPF þ B6CVPA þ B7CVPF þ B8Fnþ B9Fn2

l/L B0 B1 B2 B3 B4 B5 B6 B7 B8 B9 R2

0.50 �0.0100 0.0108 �0.0056 �0.0019 0.0024 0.0371 0.0413 �0.0185 �0.2979 0.5015 0.8865

0.75 �0.1855 0.1648 �0.0926 �0.0570 0.0053 �0.0237 0.0343 0.1697 �0.7397 1.3033 0.8375

1.00 �0.0214 0.1948 �0.0342 �0.0297 �0.1703 �0.1034 �0.0505 0.2029 �1.0827 �0.3594 0.9450

1.25 0.2286 0.1401 0.0503 0.0404 �0.3067 �0.2672 �0.0713 0.0721 0.9213 �6.3529 0.8677

1.50 0.5532 0.0909 0.0372 0.0638 �0.2607 �0.4272 �0.0200 0.0418 1.9392 �5.4877 0.5805

1.75 1.0081 0.0287 �0.0368 0.0276 �0.1232 �0.4361 0.0563 0.1402 1.1895 0.7746 0.8741

2.00 1.2311 0.0011 �0.0763 �0.0044 �0.0457 �0.3328 0.0293 0.2114 0.7191 3.1494 0.9129

2.50 1.2795 �0.0187 �0.0425 0.0020 �0.0131 �0.2981 �0.0389 0.1293 0.6535 2.3557 0.9291

3.00 1.2522 �0.0237 �0.0247 0.0109 0.0072 �0.2609 �0.0437 0.0587 0.5298 2.0278 0.9417

Coefficients of absolute vertical acceleration transfer functionsavLga¼ C0 þ C1

L

r1=3þC2

LBþ C3

BTþ C4CWPA þ C5CWPF þC6CVPA þC7CVPF þC8Fnþ C9Fn2

l/L C0 C1 C2 C3 C4 C5 C6 C7 C8 C9 R2

0.50 �11.7464 4.3704 �2.4324 �1.5968 0.6156 7.9369 6.4530 1.7990 �0.4979 �26.5440 0.5698

0.75 �14.4271 10.3491 �6.8053 �4.7677 0.8327 5.7156 5.4905 8.4392 �6.8836 6.1558 0.5956

1.00 �7.5230 6.8386 �0.8605 �1.8732 �10.7580 0.4029 �5.2701 11.4861 31.6532 �119.7734 0.8321

1.25 0.3644 1.9500 2.9926 0.7337 �14.6318 �2.6617 �7.6542 7.6781 61.2818 �131.1120 0.7727

1.50 8.2361 �0.5448 2.6649 1.1192 �12.4662 �4.0737 �6.1139 6.7766 38.5132 22.3118 0.8989

1.75 13.4549 �1.5554 0.8262 0.4291 �8.1809 �2.3288 �3.0299 6.3489 10.1442 124.8288 0.9751

2.00 12.5896 �1.5308 0.1554 0.2286 �5.3475 �0.3556 �2.5518 4.6731 5.4764 103.1251 0.9715

2.50 8.0738 �1.0734 0.4227 0.3873 �2.9879 �0.4186 �2.4069 1.8816 8.3733 38.5484 0.9812

3.00 5.4183 �0.6809 0.3447 0.2975 �1.8339 �0.3799 �1.6446 1.0339 7.2054 19.8967 0.9881


7. Discussion

7.1. Behaviour of the coefficient of each regression variable

Behaviour of the coefficient of each regression variablein the models is compared in Figs. 2–4, together with thecorresponding R2 values.

In particular, a positive value of the coefficient impliesthe preference for a low value, while a negative coefficientindicates the preference for a high value of the correspond-ing variable. The results of the linear regression analysis arein agreement with the general trends of parameter influenceon good seakeeping of ships, which are summarised inTable 8.

In case of variable sign in Table 8, the guideline for thedesigner is not straightforward. It results that, for a given

volume of displacement, a shorter ship length with lowerbeam and lower draft should be preferred. A preference forhigher CWP, higher CWPF, lower CVP, and lower CVPF hasbeen obtained while the influence of LCF/L and LCB/L isquite contradictory. The role of the parameters shown withquestion marks is not clear. The above conclusions are inagreement with the general requirements for designing astable platform for ship operations at sea.In principle, they are applicable within the design

space domain identified by min–max values of the HullForm Database. Nevertheless, the validity of Eqs. (4)–(7)has to be verified by running examples even if the rela-tively high values of R2 suggest satisfactory predictioncapabilities in almost the whole interval of wave lengths.It is also shown that increasing the number of regre-ssion variables does not lead to significant improvements

ARTICLE IN PRESS

Heave Regression Coefficients

-2.0-1.5-1.0-0.50.00.51.01.5

0.5 1.0 1.5 2.0 2.5 3.0A

oL/

B c

oeffi

cien

t

-1.0

-0.5

0.0

0.5

0.5 1.0 1.5 2.0 2.5 3.0-1.0

-0.5

0.0

0.5

0.5 1.0 1.5 2.0 2.5 3.0

CW

P c

oeffi

cien

t

-1.5-1.0-0.50.00.51.0

0.5 1.0 1.5 2.0 2.5 3.0C

VP c

oeffi

cien

t

-0.50.00.51.01.52.0

0.5 1.0 1.5 2.0 2.5 3.0

LCF

/L c

oeffi

cien

t

-5

0

5

0.5 1.0 1.5 2.0 2.5 3.0

LCB

/L c

oeffi

cien

t

-5

0

5

0.5 1.0 1.5 2.0 2.5 3.0

CW

PA c

oeffi

cien

t

-0.5

0.0

0.5

0.5 1.0 1.5 2.0 2.5 3.0

CW

PF c

oeffi

cien

t

-0.5

0.0

0.5

0.5 1.0 1.5 2.0 2.5 3.0

L/∇

1/3

coe

ffici

ent

-0.5

0.0

0.5

1.0

0.5 1.0 1.5 2.0 2.5 3.0

B/T

coe

ffici

ent

CV

PA c

oeffi

cien

t

-0.5

0.0

0.5

0.5 1.0 1.5 2.0 2.5 3.0

CW

PF c

oeffi

cien

t

-0.5

0.0

0.5

0.5 1.0 1.5 2.0 2.5 3.0

Fn

coef

ficie

nt

-5

0

5

10

0.5 1.0 1.5 2.0 2.5 3.0

Fn2

coef

ficie

nt

-20-15-10-505

10

0.5 1.0 1.5 2.0 2.5 3.0

SimpleIntermediateEnhanced 1Enhanced 2

0.5

1.0

0.5 1.0 1.5 2.0 2.5 3.0

R2

λ/L

λ/L

Fig. 2. Heave coefficients for examined regression models.


ARTICLE IN PRESS

Pitch Regression Coefficients

CW

P c

oeffic

ient

-1.5

-1.0

-0.5

0.0

0.5

0.5 1.0 1.5 2.0 2.5 3.0C

VP c

oeffic

ient

-0.5

0.0

0.5

1.0

-0.5

-1.0

-1.5

0.0

0.5

1.0

1.5

-0.5

0.0

0.5

1.0

1.5

CW

PA c

oeffic

ient

-0.5

0.0

0.5

CW

PF c

oeffic

ient

L/∇

1/3

coeffic

ient

-0.5

0.0

0.5

-0.5

0.0

0.5

-0.5

0.0

0.5

0.5 1.0 1.5 2.0 2.5 3.0

-0.5

0.0

0.5

1.0

1.5

2.0

0.5 1.0 1.5 2.0 2.5 3.0B

o

B/T

coeffic

ient

L/B

coeffic

ient

LC

B/

L c

oeffic

ient

0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0

0.5 1.0 1.5 2.0 2.5 3.0

0.5 1.0 1.5 2.0 2.5 3.0

0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0

0.5 1.0 1.5 2.0 2.5 3.0

LC

F/L

coeffic

ient

-1.0

-0.5

0.0

0.5

CV

PA c

oeffi

cien

t

-0.5

0.0

0.5

CV

PF c

oeffi

cien

t

-0.5

0.0

0.5

Fn

coef

ficie

nt

-2.0-1.5-1.0-0.50.00.51.01.52.0

-10

-5

0

5

0.5

1.0

0.5 1.0 1.5 2.0 2.5 3.0

R2

SimpleIntermediateEnhanced 1

Enhanced 2

Fn2 c

oeffi

cien

t

λ/L

0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0

λ/L

0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0

Fig. 3. Pitch coefficients for examined regression models.


ARTICLE IN PRESS

Vertical Acceleration Regression Coefficients

-40-30-20-10

01020

0.5 1.0 1.5 2.0 2.5 3.0

CO

L/∇

1/3

coe

ffici

ent

-505

101520

L/B

coe

ffici

ent

-15

-10

-5

0

5

B/T

coe

ffici

ent

-10

-5

0

5C

WP c

oeffi

cien

t

-20

-10

0

10

20

CV

P c

oeffi

cien

t

-100

10203040

LCF

/L c

oeffi

cien

t

-20-10

010203040

LCB

/L c

oeffi

cien

t

-505

10152025

CW

PA c

oeffi

cien

t

-15

-10

-5

0

5

CW

PF c

oeffi

cien

t

-10-505

1015

0.5 1.0 1.5 2.0 2.5 3.0

0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0

0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0

0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0

0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0

CV

PA c

oeffi

cien

t

-10

-5

0

5

10

CV

PF c

oeffi

cien

t

0

5

10

15

Fn

coef

ficie

nt

-50

0

50

100

-150

-50

50

150

0.5

1.0

0.5 1.0 1.5 2.0 2.5 3.0

R2

SimpleIntermediateEnhanced 1Enhanced 2

λ/L

0.5 1.0 1.5 2.0 2.5 3.0

0.5 1.0 1.5 2.0 2.5 3.0

0.5 1.0 1.5 2.0 2.5 3.0

λ/L

0.5 1.0 1.5 2.0 2.5 3.0

Fn2

coef

ficie

nt

Fig. 4. Vertical acceleration coefficients for examined regression models.


ARTICLE IN PRESS

Table 8

Hull form requirements for good seakeeping

Variable Heave Pitch Vert. Acc. at Stern

L/r1/3 Low Low Low

L/B High High ?

B/T High ? High

CWP High High High

CVP Low Low Low

CWPF High High High

CWPA Low High High

CVPF Low Low Low

CVPA ? ? High

LCF High Low Low

LCB Low High Low

Fn=0.00

Fn=0.10

Fn=0.20

Fn=0.30

0.0

0.5

1.0

1.5

2.0

0.5 1.0 1.5 2.0 2.5 3.0

z/a

(-)

0.0

0.5

1.0

1.5

2.0

z/a

(-)

0.0

0.5

1.0

1.5

2.0

z/a

(-)

0.0

0.5

1.0

1.5

2.0

z/a

(-)

λ/L

0.5 1.0 1.5 2.0 2.5 3.0

λ/L

0.5 1.0 1.5 2.0 2.5 3.0

λ/L

0.5 1.0 1.5 2.0 2.5 3.0

λ/L

(a)

Fig. 5. (a) For each Froude number, comparison between computed and predi

(b) For each Froude number, comparison between computed and predicted pit

each Froude number, comparison between computed and predicted vertical

analysis.


of the approximation. This matter should be furtherinvestigated.

7.2. Comparison between computed and predicted transfer

functions

For each Froude number, Fig. 5a shows the comparisonbetween computed and predicted transfer functions ofheave for Vessel V_051. Fig. 5b and c illustrate thecomparison for transfer functions of pitch and absolutevertical acceleration of the same vessel.It can be seen from Fig. 5 that the transfer functions for

heave and pitch are predicted closed to the computed ones

Fn=0.05

Fn=0.15

Fn=0.25

0.0

0.5

1.0

1.5

2.0

z/a

(-)

0.0

0.5

1.0

1.5

2.0

z/a

(-)

0.0

0.5

1.0

1.5

2.0z/

a (-

)

SimpleIntermediate

Enhanced 1Enhanced 2Computed

0.5 1.0 1.5 2.0 2.5 3.0

λ/L

0.5 1.0 1.5 2.0 2.5 3.0

λ/L

0.5 1.0 1.5 2.0 2.5 3.0

λ/L

cted heave transfer functions (z/a) for Vessel V_051 by regression analysis.

ch transfer functions (y/a) for Vessel V_051 by regression analysis. (c) For

acceleration transfer functions (avL/ga) for Vessel V_051 by regression

ARTICLE IN PRESS

Fn=0.00

0.0

0.5

1.0

1.5

0.5 1.0 1.5 2.0 2.5 3.0

θ/α

(-)

0.0

0.5

1.0

1.5

θ/α

(-)

0.0

0.5

1.0

1.5

θ/α

(-)

0.0

0.5

1.0

1.5

θ/α

(-)

0.0

0.5

1.0

1.5

θ/α

(-)

0.0

0.5

1.0

1.5

θ/α

(-)

Fn=0.05

Fn=0.10 Fn=0.15

Fn=0.20 Fn=0.25

Fn=0.30 SimpleIntermediateEnhanced 1Enhanced 2Computed

λ/L

0.5 1.0 1.5 2.0 2.5 3.0

λ/L

0.5 1.0 1.5 2.0 2.5 3.0

λ/L

0.5 1.0 1.5 2.0 2.5 3.0

λ/L

0.5 1.0 1.5 2.0 2.5 3.0

λ/L

0.0

0.5

1.0

1.5

θ/α

(-)

0.5 1.0 1.5 2.0 2.5 3.0

λ/L

0.5 1.0 1.5 2.0 2.5 3.0

λ/L

(b)

Fig. 5. (Continued)


for the whole range of Froude numbers. In the case ofvertical acceleration, over estimation occurs at smallFroude numbers and close estimation appears at higherFroude numbers. The relatively similar trend is also foundfor the other vessels, but is not shown.

8. Conclusions

An attempt has been made to check the validity oflinear regression models for reproducing the transferfunctions of different design solutions stored in thedatabase. It is demonstrated that the very simple anddesign-oriented regression equations fit well the shipresponses of the Seakeeping Database. To this purpose,

the original transfer functions of Vessel V_051 arecompared with the estimated transfer functions throughthe Simple, Intermediate, Enhanced 1 and 2 regressionmodels, while taking into account also the influenceof the Froude numbers on the motion responses. Duringthe numerical experiments it has been observed thatthe Froude numbers play a serious role on the motionresponses. Simple, Intermediate, Enhanced 1 and 2models proved that increasing the number of indepen-dent variables do not give higher accuracy in the pre-diction of the responses, so that using Simple andIntermediate models would be more suitable at con-ceptual design stage. In general, the results enable thedesigner to predict the seakeeping behaviour of fishingvessels in the very initial design stages with a satisfyingapproximation.

ARTICLE IN PRESS

0.0

5.0

10.0

15.0

20.0

0.0

5.0

10.0

15.0

20.0

Fn=0.10

0.0

5.0

10.0

15.0

20.0

0.5 1.0 1.5 2.0 2.5 3.0

a vL/

ga (

-)a v

L/ga

(-)

a vL/

ga (

-)

Fn=0.20 Fn=0.25

Fn=0.30Simple Intermediate Enhanced 1 Enhanced 2 Computed

λ/L

0.5 1.0 1.5 2.0 2.5 3.0

λ/L0.5 1.0 1.5 2.0 2.5 3.0

λ/L

0.0

5.0

10.0

15.0

20.0

0.5 1.0 1.5 2.0 2.5 3.0

a vL/

ga (

-)

λ/L

0.0

5.0

10.0

15.0

20.0

0.5 1.0 1.5 2.0 2.5 3.0

a vL/

ga (

-)

λ/L

0.0

5.0

10.0

15.0

20.0

0.5 1.0 1.5 2.0 2.5 3.0

a vL/

ga (

-)

λ/L

0.0

5.0

10.0

15.0

20.0

0.5 1.0 1.5 2.0 2.5 3.0

a vL/

ga (

-)

λ/L

Fn=0.15

Fn=0.00Fn=0.05

(c)

Fig. 5. (Continued)


Acknowledgement

The research in this paper has been supported by theTurkish State Planning Organization under the name of theResearch Project 26-DPT-06-02-01.

References

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Seakeeping assessment of fishing vessels in conceptual design stage