A new method for developing hull forms with superior seakeeping qualities

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A NEW METHOD FOR DEVELOPING HULL FORMS WITH SUPERIOR SEAKEEPIIIG QUAL ITI ES

C. J. Grigoropoulos and T. A. Loukakis

Department of Naval Architecture and Marine Engineering, NationaL Technical University of Athens, 42 October 28th, Athens 10682, Greece.

ABSTRACT

A new method for anaLyticaL seakeeping optimization is

described. The method is based on a computer code which

pre-dicts seakeeping performance when the ship profile, the design waterline, the sectional area curve and the distribution aLong the ship of the centroid, KB(x), of the cross sections are pre-scribed. The code can automatically generate variant hull forms

differing frOm a parent in the main dimensions and ir one or

more parameters such as C, LCF, LCB, KB distribution, C etc.

When appropriate ranges for the principal characteristics

and parameters of

the hull

form under investigation are

prescribed, a formal optimization procedure is used to obtain

the variant with the best seakeeping behaviour. The

optimiza-tion procedure uses as objective funcoptimiza-tion the weighted average

of a number of peak ship responses in reguLar waves for a

num-ber of ship speeds and headings and determines the optimum hulL form using the Hooke and Jeeves Algorithm.

To investigate the validity of this approach, the hull

farm of a reefer vessel was selected and optimized in head seas

'th respect to vertical acceleration and relative motion. The

variant huLL form had the same main dimensions and displacement

as the parent, but a considerably improved seakeeping behaviour

as analytically predicted. Two-meter moods of the parent and e optimized hull forms were subsequently built and tested for

resistance and in regular and random head seas for verticaL

sip responses and added resistance.

The experimentaL results verified the analytical

predict-ions with respect to the seakeeping performance, whereas only

minor differences between the two huLl forms in calm water

I NTRODUCT ION

The

incorporation

of

superior

seakeeping qualities

in

a new

ship design

is obviously desirable, although seakeeping is not

usually a

dominant parameter

In the design process, especially

for

merchant

ships.

However,

recent

studies

have shown

that

seakeeping considerations can and should be incorporated from

the beginning

in the design procedure but

that

there

is

also

room

for

considerabLe

seakeeping

improvements

even when

the

displacement and the principal characteristics of

a new design

have been determined without any seakeeping considerations.

Seakeeping experiments are lengthy, tedious and costly and

hence can not be of general use for feasibility or optimization

deSign work,

àlthough some helpful systematic testing has been

reported1'2'3 for naval type hull forms. Nevertheless

the

ber

of pertinent hull

form parameters,

which can be examined

experi.entatty is very Limited.

Thus,

seakeepirtg optimization

work has

to

be done

using

numerical

computational

methods,

which shouLd be both efficient and sufficiently accurate.

The

time

efficiency

requirement precludes

the use

of

three-dimensional methods and all work

is

done using either

of

the

two prevalent

forms

of

strip theory4'5.

Now,

the results

of

strip theory for ship motions are

in general accurate enough,

even

for

hull

forms

and

ship

speed-wave Length

variations,

which violate basic assumptions of the theory.

This

is

a

curious but welcome result. For strip theory to be implemented,

the

two-dimensional

hydrodynamic

characteristics

of

the

ship

sections should be known. This

iS difficult

in an optimization

probLem,

because the different hull

forms under consideration

are.

not

known

in adequate geometrical detail.

Thus,

either

a

two-6

or three-parameter7 Lewis-form representatTon of the ship

sections

is used. This is not the case when a sfp motion data

base

is constructed using analytical calculations for existing

ships of similar type, then a close-fit8 representation for the

ship Sections can also be employed. When

a

two-parameter form

representation

is

employed,

the

principal

dimensions

of

the

ship together with the sectional area curve, rie waterline and

the

profile suffice

to describe the ship for

se;akeeping

cal

culaticris.

For

a three-parameter Lewis-form representation the

verticaL

centroid

of

the

ship

sections

sould also

be

presc r i bed.

However,

the

term "accurate"

to describe

iTotion

predict-ions is used traditionally in

a

loose sense and therefore

care-ful

experimental verification of

the actual

advantages

of

op-timized hull forms is stiLl necessary9. Only one such

verifica-tion has been reported until now by Bales and DaY10,

A second

one is presented in the sequel.

Computational methods have been used since 1970 to predict

seakeeping

performance

and

relate

it to hull form

parameters,Refs 11 to 15, but the first complete seakeeping

op-timization method is due to Bales16. Bates used computations

for 20 existing destroyer-type huLl forms and Linear regression

analysis techniques to correlate averaged seakeeping

perfor-mance, in head seas and at various ship speeds, to certain

em-piricaLLy selected hull form parameters.

He then used the

resulting optimum combination of these parameters and

conven-tional Lines drawing methods to design an "optimum seakeeping"

hull form. A model of this ship was tested1° and found to

ac-tually possess superior seakeeping characteristics, along with

some Inferior caLm water resistance. Bales' method was Later

extended to mere huLl parameters by Walden17 and Mc Crelght'8

always for the same type of ships. Wijngaarden19 used Bates'

methodoLogy to develop an optimum small hull form for the North

sea area, taking account of both seakeeping and calm water

resistance. Bates' method depends on a precalculated data base

and its results apply to similar ships.

A different approach was used by Qile et a12° and Walden

et aL21 to derive hulL forms with optimum seakeeping

perfor-mance. Both construct hulL

forms analytically using

the

aforementioned two-parameter Lewis-form representation and

after adopting appropriate seekeeping criteria, see e.g. Ref.

22, they calculate a "limiting wave height" for each hull form. The optimum hull form, defined as the one for which the highest value of the Limiting wave height is possible. before any of the

adopted criteria is violated,

is determined using various

search methods. The analytically cOnstructed hull forms and the

directly computed ship responses, make these methods

indepen-dent of a data base and more general in. their area of

applica-tion. Walden et al include calm water resistance calculations

in their Optimization scheme.

The present method to develop hull forms with superior

seakeeping qua(ite.s, baSed on work done in Ref. 23, is similar

in principle to the methods of QiLe and WaLden but. it is also

different from the above in several aspects. Thus:

It uses a three-parameter Lewis form representation for the ship sections

Using a parent hull form, actual or generated from prelini-

-nary design considerations, it can generate variant hull

forms, differing from the parent in only one or more pre-scribed hull form parameters.

C) The seakeeping performance is assessed from regular wave

response operators.

d) The final seakeeping "measure of merit" is determined a

pos-tenon, taking also into account the propulsive performance

in waves.

V

be discussed Later.

CaLm water resistance is not Included In the optimization

scheme. The reason for this omission is that available

anatyti-cat tools for calm water resistance estimation are not thought

to be accurate enough for optimization purposes, in particular

when only secondary hull form parameters are altered. For

in-stance the method used in Ref. 21 overpredicts the Towing Tank

resistance results for the reefer ship by 25%. In addition,

hull forms with

Less calm water resistance do not always

possess better propulsive performance in waves or even in caLm

wet e r.

SEAKEEPING PERFORMANCE AND SHIP DESIGN

As every Naval Architect knows,

a

ship can very well

be

designed without any considerations of her seakeeping perfor-mance, especially during the preliminary design phase. This im-plies that seakeeping performance Is seLdom important enough to

significantLy affect the main design parameters. Therefore an

inclusion of seakeeping considerations In a structured design

methodology24 should be done in a decisive but inobstructive

manner.

Following this reasoning It was decided that seakeeping

optimization should have

a

parent hull form as

a starting point, a huLl form designed to meet the "owner's requirements",

which at

most might

Include a call

for "good seakeeping

qualities". Such a hull form, for which not even the existence

of faired ship lines

is necessary,

is amenable to Limited

modifications in its principal dimensions and hull form

parameters, which might nevertheless significantly improve the

seakeeping performance.

A brief discus.sion is now in order about the relation of

the hull geometrical parameters to its seakeeping

characteris-tics. A Study of recent works on the subject shows that

Different researchers propose different sets of parameters as mainly affecting seakeeping performance.

The same parameter is shown to affect the seakeeping

be-haviour of different types of Ships in a different manner.

To briefly illustrate

the above points

we note that

Bales16 used in his original work six parameters, which were

Later extended by Walden17 to seven, to accOunt for the effect

of displacement. However,

when Mc Creight18 extended the

original data base from 20 to 180 hull forms, he obtained ten

significant parameters only two of which were the same

as

Bales'. Similarly, Wijngaarden1 used six parameters, only one

of which was the same as Bales' and none belonged to the Mc

Creight group.

With regard

to the effect of

the various

parameters Bales concluded that a large waterplane area coeffi-

-cient and a smalL vertical prismatic coefficient are beneficial

for destroyer type huLL forms, _{whereas Wijngaarden reaches the}

oppOsite conclusions for small hull forms in the North Sea.

SimiLarly, Loukaks et 5125 _{have shown that}

a Large value for

the (LCB-LCF) separation is beneficial for Series 60 ships,

whereas the Opposite is true for a frigate hull form.

In view of the above, the method of directLy computing

hull forms and their responses seems to be more useful for

design purposes.

As mentioned in the introduction, If the principal

dimen-sions of the hull form L, B, T, the sectional area curve S(x),

the waterline curve B(x), _{the longitudinal profile curve Z(x)}

and the Longitudinal distribution curve of the _{centroids of the}

ship Sections KB(x) are specified, seakeeping _performance

cal

-culations can be readily and accurately performed. _{At the same}

time aLL traditional ship design variables, _{can be derived from}

these curves i.e _{CB, CM, Cup,} LCB, LCF, KB. In addition other

design variables as , 'Ce, etc. can be obtained from the

above.

The present method correlates the seakeeping performance

of a hull form to the values of the set CL, _{8, 1, C8,}

CM,

LCB, LCF, KB(x)} and searches for an optimum _Solution.

To obtain variant hull forms from the parent, Lackenby's26

method was extended so that Waterlines and sectional

area

curves of any shape can be accommodated and, more important,

that any of the six form parameters LCF, C8, LCB, _CM,

KB(x)} can be independently varied. Thus, variant hull forms

differing in one parameter only can be generated and _by

succes-sive applications of the method, hull forms with prescribed

values 0f these parameters are obtained.

To obtain an optimum solution a measure of merit should be

specified. As such,

the averaged values

of several ship

responses, e.g. heave, pitch, ro(l, absolute vertical

accelera-tion, reLative vertical motion, sLamming incicence etc., over

several _{ship speeds and sea states have been commonly used in}

"seakeeping rank estimator" methods like Bales'. In direct cal-

-culation methods, like Qile's, a service spee for optimization

is specified and the aforementioned limiting wave height is

used for optimization in conjunction with prescribed criteria

for the ship responses. Both of these methods require time

con-suming computations to determine the

necessary Response

Amplitude Operators CR.A.0), whose squared magnitude times the

sea state spectrum determines _{the response spectrum, for each}

hull form examined during the optimization process.

catcuta-tion of the ship responses in sea states nor the determination

of the complete R.A.O. is necessary to perform seakeeping

op-timizatioñ. Instead the optimization can be done using only the

peak values of the R.A.O. of a few ship responses, _basically

absolute vertical acceleration and relative vertical motion.

Thus the required computer time for the optimization is _greatly

reduced. The rationale behind this proposaL is that any

altera-tion of the hull form Is going to affect the R.A.O. curves,

which have the umimodal shape shown in figs. 1 and 2. The same

is true for the response spectra and, as it _{can be seen from}

the figures,, the frequency of the peak response shifts only

slightly for fully developed sea states ranging from _{sea state}

5 to sea state 9. _{Thus the magnitude of the peak value of the}

R.A.O. is the dominant factor determining the magnitude _{of the}

ship response and It Is therefore postulated that

"ship responses at sea are minimum when the

corre-sponding peak value of their R.A.O. is minimum".

Nu.erical computations have shown that this assertion Is true

for ships with displacement and dimensions close to those of the parent hull form.

However, the magnitude of the peak value of the relative

vertical motion R.A.O. Is not adequate to describe seakeeping

events related to the underwater part of the hull, as bottom

slamming and propeller emergence. Thus, these events can not be

explicitly included in the optimization process and the

cor-responding performance of the optimum hull form can be

estab-lished only a posteriori. This is a slight shortcoming when

draft Is kept constant or is _{changed only a little from the}

parent, _because

_{the minimization of}

_the

_{relative motion}

provides a strong indication that the corresponding seakeeping

events wilt also be reduced. THE OPTIMIZATION PROBLEM

With the previous discussion in mind, the optimIzation problem

can be stated as folLows

Find the variant with the optimum seakeeping performance

of

a parent

huLl

form, described by the

set of

four curves

S(x), B(x), Z(x) and KB(x) and identified by the, set of

de-sign variables (L, B, 1, _{CB, CM, Cup, LCB, LCF, KB) under}

given constraints.

Seakeeping performance is expressed as :he weighted sum of

the peak vatues of

a prescribed set of ship responses in

regular waves, for various ship speeds and headings. Optimum

performance corresponds to the minimum value of this _{sum, which}

is the object function of the problem.

The constraints to be included in the optimization problem are classified in the following two categories:

Equality conditions established by hydrostatic and stability considerations or economical reasoning.

InequaLity constraints imposed by common design practice Ii-ml tat ions.

In the first class of constraints the following relations are included

The relation between the displacement, the main dimensions

and the block coefficient:

= CB L B T = constant

Geometrical relations that hold between the various form

parameters,

i.e.

CB = CtJp * C,J

CB C * _CHP

In the second class of constraints the following

In-equalities should be taken into account for reasons shown In parentheses

LCB1 LCB LCB2 (trim)

CHP CHPO

(caLm water resistance)

GM _{GNMIN Ctransverse stability)}

C1

C2

(deck space, calm water resistance)

The following characteristics of the optimization problem

can help In selecting the appropriate optimization method the non-linearity of the constraints

the existence of both, equality and inequality constraints

the unimodality of the object function, experimentally veri-

-fied by setting up the optimization procedure from different starting points and arriving at the same result

the continuous character of all decision variables.

On the basis of the above the direct optimization method

proposed by Hooke and Jeeves27, in conjunction with the

Exter-nal Penattry Function Method28 has been selected. The External

Penalty Function Method is used to convert the constrained

op-timization problem to an unconstrained one and is more

effi-cient than the Internal Penalty Function Method. The method of

Hooke and Jeeves is simple to program and has found to be very

effective for the particular optimization problem in comparison to other direct search methods.

ANALYTICAL AND EXPERIMENTAL VERIFICATION

The proposed method has been successfuLly appLied to several

hull forms, both of merchant and naval ships. For its initial

experimental verific-ation, the hull form of a modern 93.4 _in

long reefer ship was selected and it was decided to optimize

The object function in this case was chosen as the sum of

peak R.A.O. _{values for vertical acceleration and relative}

mo-tion at a point 0.1 *

LBp behind the forward perpendicular. The

principal dimensions and

bull

form parameters of the parent and

the optimum huLl forms are shown in Table 1. the respective

body plans are shown in Fig. 3 and 4.

Table 1 :

Principal dimensions and form parameters of the

parent and the optimum hulL form.

Two meter models of the ships were subsequently built and

tested for resistance and in regular waves and in sea states _at

14 and 17 knots ship speed. The EHP curves for the two huLl

forms at three different drafts, Fig. 5, indicate a quite

simiLar performance. The theoretical and the experimental

results for heave, pitch, vertical acceleration at x37.36 m

and x=-45.00 m, relative motion at x37.36 m and x-45.00 m and

added resistance are shown In Figures 6 to 21. Comparing the

experimentaL to the anaLytical results we deduce that, although

theory underpredicts, the analyticaLLy predicted differences

are verified by the experiment and that the optimum hull form has ifldeed a significantLy improved seakeeping performance.

In addition, optical observations of the random sea

ex-periments indicate as much as 65 % reduction in deck wetness

occurrences for the optimum hulL form.

DISCUSSION AND CONCLUSIONS

When a ship operates in _{waves her performance} is degraded by

either an involuntary Or

a

voLuntary speed reduction. The

former Is due to the added resistance and the loss of propul-

-sive efficiency in waves whereas the later is decided by the

captain when ship motions anc/or the occurrence of seakeeping

events become excessive. An approximate method to evaluate the

involuntary speed reduction is to superimpose the added

resis-tance in waves to the calm water resisresis-tance and, using the calm water propeLLer-hull interaction coefficients and the propeller and engine characteristics, to determine the maximum attainabLe

ship speed at e.g. constant engine revolutions. This curve

defines the upper Limit of the operabiLity region of a ship as

HULL FORM _{LRP,m 8, a T,m} , nit C8 _- C1 C LCS,m LCF,m

PARENT 9340 17.00 6.50 6103 0.575 0.752 0.770 -3.23 -5.04

OPTIMUM 93.40 17.00 6.50 61C8 0.575 0.728 0.790 -1.67 -1.44

LCB, LCF and

KB(x),

in order to demonstrate the applicability

a function at sea state and heading. However, when the seas get

rough and various ship responses exceed specified leveLs or

criteria, then an additional voluntary speed reduction curve

can be calculated, representing the most restrictive criterion.

These calculations for the parent and the optimum reefer

ships are shown

in fig. 22

for operation

In head, fuLly

developed seas. From this figure it can be concluded that the

reduced added resistance of the optimum ship compensates in higher sea states her slightly higher calm water resistance. In

addition, the

improved seaworthiness of

the optimum Ship

results in a much greater limiting wave heght, 6.55 in instead

of 4.11 in, after which ship operations become lotion limited.

If the involuntary speed reduction is neglected, the difference

In limiting wave heights becomes, erroneously, significantly

smaller. The pair (limiting wave height - corresponding ship

speed) represents a "measure of merit" for _seakeepirig

perfor-mance. This example demonstrates the usefulness of performing

seakeeping optimization after the preliminary design process

has adequately progressed.

The main advantages of the proposed optimization method

can now be summarized as folLows

The use of the three-parameter Lewis-form representation of the ship sections alLows the desirability of U forms or V

form to be investigated. In Ref. 7 is demonstrated that the

KB(x)

effect

can be significant.

The method is suitable for immediate incorporation in the preliminary design spiral and it can readily accommodate alt necessary design constraints.

The method is very efficient so that it can run on a

per-tonal computer as it circumvents the need for computing

both

the full R.A.O. and the perforrnance at sea for all hull form variants.

The method does not depend on empirically imposed seakeeping en terla

The method is complemented by by the suggestion that the fi-

-naL assessment of seakeeping performance

should

incLude

pro-pulsive performance in waves.

Finally, it should e noted that seakeeping optimization

with respect to vertical motions only seems adequate as roll

response can be treated by bilge keel de.sign, anti-rolling

devices and change-s in GM.

Naturally, a total design procedure should include more

accurate calm water resistance and propulsion estimates than

presentLy available. In the meantime, it seems that any adverse

effects on

propulsion from

seakeeping imposed hull form

r

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