The effect of some hull form parameters on the sea-keeping behaviour of surface ships

rATZCHIEF

KOHOEPERDIR.

no

MOPEXOL.HbIM KA4ECRIAM MOB

FIAABT,IMX TEXHAMECKNX

COOPDKEHWA-Ceurnsapb 1983

13apslo

The prediction of the seakeepihg performance

of surface ships has been possible since the

mid-1950's, the analytical tools are being continuously

'refined and digital computers are becoming

general-ly available. Correlation with experimental results

is satisfactory both for regular waves and

seawa-yes. Therefore,' it is evident that analytical

meth-ods could be used not only to predict but also to

relate ;a prfOri hull geometry to teakeeping

behav-iour-in a manner suitable for the design process.

The most sucessful effort so far in this

field was presented by Bales (1980), who developed

an analytical model relating ship hull geometry to'

an index of seakeeping merit and quantified it

using destroyer-type hull forms of a specified

displacement. Bale's seakeeping rank factor R

depends only on a small number Of conventional hull

parameters and it has been recently extended by

Walden (1983) to incorporate the effect of

displa-cement.

Using his Method, Bales (1982) designed an

"optimum" Kull form and tested a 4m 'model to

vali-date his procedure. The superior seakeepihg

cha-racteristics of the design were experimentally

demonstrated, along with some interior resistance

Characteristics.

Prior to Bales, a number of authors, namely

Bales and CuMmins (1970), Loukakis and

Chryssosto-midis (1975), Beukelman and Huijser (1977) and

Schmitke (1982) have used analytical methods to

predict seakeeping performance and to relate it

,

THE EFFECT OF SOME HULL FORM PARAMETERS ON THE

SEAKEEPING BEHAVIOUR OF SURFACE SHIPS

Theodore A. Loukakis

Anastassios N. Perakisa Fotit A. Papoulias

Te

ool

e

ft

CONFERENCE

on

SEAGOING

OUALJTIES OF SHIPS

AND MARINE STRUCTURES

seomixr 1983

licerio

undo

Bale's seakeeping rank factor was assumed to

have a simple functi,.al relationship to the hull

parameters

R

o0so1(C1.1y)iu2tCliA)+o (T/Oso4(c/04.

1.(15(CVPF)'36(CVPA)

(1)

where the six paraimAers are:

.1.

Waterplane coefficient ferward of amidsnips,

WF

Waterplane coefficient aft of amidthips,Cw.

Draft-to-lengtn ratio, T/L, where T it draft

and L

is ship length

Cut-up ratio, c/L, where c is the distance

from the forward perpendicular to the

cut-up point

5_

Vertical prismatic- coefficient forward of

-amidships, Cor

and

Vertical prismatic coefficient aft of

amid-ships, C

VPA

The hull

for-in parameters were selected on

the basis of experience and intuition and it is

noteworthy that Length was excluded. However, the

sevencoefficients01' -1-0,6 were determined

for

ships of conttant displacement L.4300 tons.

To quantify the coefficients Bales used

ana-lytically computed stakeeping responses (pitch,

heave, relative motion at, stations 0 and 20',

this paper station 0 signifies thE

bottom slamming at station 3, acceleration at

sta-tion 0, heave accelerasta-tion and accelerasta-tion

station 20) of twenty destroyer-type hulls for a

nunherof ship speeds and sea states. The responses

were averaged over the speed and sea'state'ranges,

normalized with respect to their minima and again

averaged for each hull to determine a Value for R.

These twenty values were then used to quantify the

seven coefficients of relation (1) using

linearre-gression'analysis techniques. Later, Walden (1983)3

using" a similar methodology, added a term in

rela-tion (1) expressing theeffect of displacement A

on R:

04:7.

(A-4300)

4300

(2)

from its experimental validation,Bales'

Apart

method. has been used for several design exersises

resulting each time'in hull forms with superior

seakeeping qualities, leading to the conclusion

that Indeed-the effort to relate hull form

para.-meters to seakeeping behaviour can be o useful

endeavour.

The main purpose.of this paper is to propose

that, may be, other hull form parameters than

the ones selected by Bales, which describe better

the hull form relatively to her behaviour in

we-yes, might be more appropriate for the definition

of a teakeeping rank indicator. The selection of

these parameters was again based on the ,experience

of the authors. However, a tedious and

time-consum-ing effort has been undertaken toAemonstrate the

effect of some of the proposed parameters on

sea-keeping,both quat_itatively and gOontititavely,

by independently varying one only parameter at a

time. This approach is novel. In addition added

resistance was included in the responses studied.

The hull form parameters, to he studied in

the sequel are.

(LCB+LCF)/2, (LCB-LCF), Cw and KB(X)

(3.),

where.: LCB and LCF are the longitudinal location

of the centrpids of the waterplane area and the

sectional area curve

from Midship, Cw the

water-plane coefficient and KB(x) the distribution of

the centroids of the cross-section t of the ship

:along its length from the keel line.

That. is, we will examine hull form parameters

that can be varied for a hull form with given

.

principal dimensions and displacement of the

_nip.

The results to

presented include 'merchant

marine type ships from tne Series 60 and two naval

ships of the destroyer-type.

2.

ANALYTICAL TOOLS

The computer program used for the seakeeping

calculations was first developed at M.I.T. by

the first of the authors and is based on the strip

theory developed by Salvesen.Tuck and faltinsen

(1970), The added resistance calculations are baud

on the method of GerritsMa and Beukelman (1971)for

head seas and on the method of Loukakis-Sclovou,

.nos (1978) for oblique seas,and all degrees of

freedooL

The program was originally using Lewis-form

-representation for the cross-sections. It has

been since modified at NJ.U.A. to indlude,amonq

others, the Frank close-fit representation for

the dross-sections ,:nd the extended, three

para-meter, Lewis-form r,,iresentation oeveloped by

Athanassoulis and Lc..Jkakis (1983). The last

ana-lytical tool is useiul in synthesizing the hull

forms necessary for Ene present investigation.

An extendea Lewis-form representation of a

cross-section reseN,bles in general Closely the

actual cross section, since it prossesses the

same beam, draft, sectional area and vertical

-centroid position 0(x).

The form of the new family is

W=f()=C1+C3

+C5 3+C1C

(4)

mopping conforMally the unit semi-circle c=eXp(i0),

-11<ecO, to the cross-section w(0).

The four coefficients of relation (4) can be

calculated from the four aforementioned properties

of the ship section. The usual Lewis form

repre-sentation of ship sections neglects the vertital

position of the centroid of the ship section. In

Fig.1 the Lewis form representation of a ship

.

A(x)

section with A = -IT- -0.8 and o =

- 0.6

is shown, together with the two extreme members

of the new family. The KB/T values are 0.637 for

the Lewis-form and 0.597 and 0.669 for the extend

ed Lewis forms.

The added mass and damping properties of

these sections differ considerably and the same

is true for the exciting force that surface n-aves

exert on them.

-2-I(s/7 =0.66 ci

KB/T= 0. 63-3

LEM.ti5FoRM

113/T.--=0.5c33-Lewit,fOrm and Extended Lewis-Jbem .

. representation of a cross section

A hull form can now be readily represented,

in a form suitable for quick seekeeping computa-tions, if one specifies;

a). The main dimensions L,B,T

The sectional area curve A(x)

The waterline y(x)

The profile z(x)

el The vertical centroid distribution along the length of the ship KB(x)

Variants of this hull form, -with the same

main dimension, disOlacement, 6= jrA(X)dx and

profile can be synthesized as follows: With only the.centroid of the sectional

area Curve A(x) shifted, that is the LCB position. This is done by using standard

methods of the ship designer, described by Perrakit (1977), on the sectional area

curve. Then, each cross section has the

original beam, a hew,cross-sectional area

and an appropriate

Ka(x)

so that KB remains

constant, and it can easily be represented

by a member of the extended Lewis-form family.

With only the centroid of the waterline y(x)

shifted, that is the LCF position. Then the same procedure as previously is used with

each section having a new beam and the

origi-nal cross-s area dnd

KB(x)

position.

With botn the LCii and LCF positions shifted,

while the KB position is kept constant

With only the wateeplane coefficient changeth

In this case each section has a different

beam and the original crost-sectiOnal area

and KB(x)

With only the 1(3(x) distribution modified.

With regard to the last variant it can noted

that, with constant beam, draft and cross-sectional -area, Moving 101(x) upwards makes the sections more

and downwards more LI-like,Fig..1*

PARAMETER SENSITIVITY RiitiS

The effect of the selected parameters on sea-

-keeping behavibur has been investigated both for cruiser stern ships and navaLdestroyertype ships.

3.1 Cruiser-Stern Ships

The initial work on the cruiser stern ships

is older., Perrakis In that work the scope

of the Seakeepinq Stal;oard Series of Loukakis and

Chryssostomidis (197) was extended to include:

Results

for head Seas at zero speed Extention to oblique seaways

t) Sensitivity analysis of the original Series,

with respect to the hull form parameters LCB, LCF, Cw and CB

During the sensitivity analysis

it

was

detect-ed that Cw was an impOrtant parameter, CB was of minor importance, especially if the displacement was kept constant and that the effect of the loca-tion of the longitudinal centers LCB and LCf was

very important, especially if treated in terms of

their difference (LCB,LCF)..

At that time the effect of the aditional

parameter (LCKCF)/2,which also depends on the

longitudinal centroids, was not understood and in

addition the Extended Lewis-form representation was not available to examine the effect of the

po-sition of the vertical dentroids.

The influence of the two longitudinal centroib

parameters will be demonstrated in graphical form

for

the following two basic

hull

forms from the

Table 1. Principal Characteristics

of the Series 60 Ships

Perakis (1977) created variants of the two

basic hull forms by shifting LCB and LCF by 1.2%1_

and (LCB-LCF) by -.1-1.5%L. Thus, in terms of the two

longitudinal centroid parameters, the seven hull

forms of Table 2 were treated analytically.

Table 2. Variants of the Series 60 Hull Forms

Since Perakis work was intended to extend

the usufulness of the original.Seakeeping Standard

Series, the hull forms were run for the same speed

and sea state ranges (Fr.No4.1,0.2 and 0.3 and

H-1/3/L=0.015, 0.020, 0.025, 0.030, 0.040, 0.050,

0.075 and 0.1 where H-113 is the significant wave

height and the sea states are taken to be fully

developed) and for the same responses as the S.S

Series.

From Perakis' results the following hull

responses:Heave, Pitch,Relative motion and

Rela-tive Velocity at Station 1, Acceleration at

Sta-tion 1, AcceleraSta-tion at StaSta-tion 20 and Added

re-sistance are plotted in Figures 2 to 15 for Fr.

No=0.2 and H-1/3/L=0.03 (head seas). The

select-ed speselect-ed is near the design speselect-ed for such ships

and the selected sea state, with

H-1/3=12ft or

Sea State 5, can be considered as moderate to

heavy for the 400ft long ships.

The results are plotted in a non-dimensional

forum with respect to the responses of the basic

ships.

Before commenting on the results one should

stress a) that all hull forms for each CB have the

same principal dimensions, displacement, waterline

area and profile b) that the selection at thd'basie

ships is accidental, from the point of view of

their'seakeeping qualities and c) that the ratios

of their principal dimensions are quite different..

With regard now to the effect of the

longitu-dinal centroids on the various seakeeping responses:

Heave (Figs 2 and 3) is almost not affected by the

position of (LCB+LCF)/2

but,is greatly

influen-ced by the magnitude of the (LCB-LCF)

separation,

increasing with an increase of the parameter and

vice-versa.

It is rather surprising that a change

in (LCB-LCF) by +0.02L results approximately in

an +20% change in heaving motion.

From the same

figures we conclude that the effect of both

parameters on heave is monotonic, but linear

for (LCB+LCF)/2 and slightly non-linear for (LCB-LCF)

Pitch (Figs 4 and 5)is affected somewhat

by

(LCO+LCF)/2, decreasing as the centroids move

tow-ards the bow. The effect of the parameter is linear.

The effect of (LCB-LCF) is opposite than on heave.

An increase of the parameter results in a decreasing

response. The effect is significant for the more

slender hull form and not as pronounced for C6=0.7.

Again the effect is non-linear but monotonic,

espe-cially for the fuller hull form.

Bow Relative Motion (Figs.6 and 7) is moderately

affected by (LCB+LCF). 2, decreasing as the centroict

move forwards. The ef:,ct is linear. The effect of

(LCB-LCF) is also seric..is, non-linear and slightly

non-monotonic for C6=u.6' for which the relative

motion decreases in general with increasing centroid

separation. This trend is reversed for CB=0.7,fOr

which relative motion increases with increasing cerr

troid separation. For this hull form the effect of

(LCB-LCF) is monotonic and slightly non-linear.

Bow Relative Velocity (Figs 8 and 9) is also

mode-rately affected by (LCB+LCF)/2

and decreases as

the centroids move forwards in a linear manner.

This response decreases considerably with

increas-ing centroid separation monotonically and slightly

non-linearly for C6=0.6. For CB=0.7 the results

are mixed because the smallest (LCB-LCF) results

In the smallest response, but the largest

(LCB-LCF) is better than the intermediate, that is the

effect of the parameter is monotonic and

non-linear,

-4-Hull form

C8=0.6

LCB+LCF

LCB-LCF ---7---

LCB-LCF CB=0.7 LCB+LCF 2 1

4.65

-2.825

4.23

-1.15

2

4.65

-0.825

4.23

0.885

3.

.2.65

-3.325

2.23

-1.615

4 '

2.65

-1.825

2.23

-0.115

2.65

-0.325

2.23

1.385

6 .

. 0.65

-2.825

0.23

-1.115

7

0.65

-0.825

0.23

0.885

CB

0.60

0.70

L(ft)

400 400

L/B

₈₅

7.0

BIT

.

2.0

3.0

Cw

0.713

0.788

LCB(U)

+1.0

LCF(U)

-3:15

-1.23

ILCB-LCFI(U)

2.65'

2.23

ILCB+LCF10,0

_-1.825

-0.115

r---

CB=06. 1.48 1.28 1.48

0

_1.28 UI Lei 1.08 .88 .60 .88 HEAVE

4.65

2.65

-4.0

-3.8

-2.0

-1.8

8.8

"FIG.21 (1.MIXF)/2

LOP]

PITCH

0.65

2. G5

-.4.8

-3.8

-2.8

-1.8

8.8

FIG.4 : (1..C13+La)12 [% LOP]

-4.8

-3.8

-2.8

-1.8

0.8

FIG.6 t

(.C8+LCF)/2 LOP]

-4.8

-3.8

-2.8

-1.0

0.0

(LCB+LGF)/2 11. LP]

ABS. VERT. ACCELERATION

II I STA

0.6s

2.65

4.65

-4.8

-3.8

-2.8

-1.8

8.8

FIG.10: (1.G8+LGF)/2 10A, LOP]

1.08 1.03 .98 .93 .88 1.20 .80 CB.0.7 PITCH

0.2'3

2.23

4.25

2.0

-1.8

0,8 1.8 2.8 FIG.: CLCB11.GF)/2 (2/0

LP]

2.0

-1.0

8.8 1.0 2.8 : (LC8sLCF)/2 (14 LOP]

ABS. VERT. ACCELERATION

STA 1 -9.13 2.25

-2.8

-1.0

0.0 1.8 2.8 FIC.11: (LCE4LCF)12 1.13P7 HEAVE 1.48

.1.23

1.20 1.80

2.23

.00

0.2:3

.68 . PT

-2.8

-1.13 8.8 1.8 2.8

Fic.3

1.0341..CF W2C/o LOP)

REL. VEi-.T VELOCITY

SIA I

0.25 4.212.1-3

-2.2

-1.0

0.2 1.8 2.8

Bow. Acceleration (Figs 10 and 11) is reduced li-nearly and appreciably.at both centrbids move,

for-wards. For C =0.6 the response decreases seriously

with increasing (LCB-LCF) in.a slightly non-linear

, monotonic manner. For CB=0.7 althiYUghthe

largest-1LCB-L.CF)'results in the smallest acceleration,

the smallest (LCB-LCF) is second best, that is

the effect non-monotonic and non-linear,

-. Stern Acceleration (Figs 12 and 13) is slightly -increased as bdth Cehtroidt move forward. The

effect

of

(CCB,LCF) is similar As with the bow

acceleration.

Added Resistance (Figs 14 And 15) is only slightly

, affected by (LCB+LCF)/2 . On the contrary it is

seriously affected by (LCBACF) decreasing, for both hull fOrms, with an increase of the centroid

' separation. Jaw effect is monotonic and non-linear

etpecitlly-for the fuller hull form.

One can try to summarize the aforementioned

comments as follows:

The average longitudinal location of the

cetroids, expressed as (LCB11.Cf)/2, affectt,

considerably

all

kinematic responses. The results

vary in general linearly with the parameter. All

motion responses are reduced with a forward mo-tion of the centroidt, except the stern accelera-tion which is slightly increased. Added resittance

is only slightly affected by (tCB+LCF)/2.

The separation of the location of the

longi-tudinal tentroidt, expressed as (LCB-LCF), affects Seriously all kinematic responses and the added

resistance.

For the slender hull, CB=0.6, all kinematic

responses decrease with increasing tentroid

se-paration, except heaving motion and added resistoft

ce which increase. The effect of the parameter

is notr-linear but in general monotonic.

The results for the fuller hull fort,C6=0.7 are more mixed. Heaving motion, pitching Motion

and added resistance behove similarly as

f6r

C8=0.6, On the contrary, relative motion and

relative Velocity are minimum for the smallest value Of the parameter and the results for bow and

stern acceleration are non-linear and non,-monotonit

although the largest value of the parameter results

in the minimum responses'.

The effect of the position of the longitudinal centroidt LCB and LCF was demonstrated for two hull forms, one ship speed and one sea state. Much more investigation is required before one can decide

.how to proceed, in an educated way., to include the

(LCBACF)/2 and (UCB-LCF) parameters in a function expressing a seakeeping rank factor.

Another method used to investigate the effect

of a hull form parameter will be demonstrated now

in conjuction with the waterplane coefficient

_C.

For this investigation two variants of the basic Series 60 hull form with C0=0.70 were generated

with the value of C1 _{by +0.02.}

The response results for the three hull

forms-.

were used to measure the rate of change of each

response with respect to changes in C. This was

done by plotting for each response the tins value,

non-diMensionalized with respect to the correspond-ing value for the basic hull form, versus Cw. A

straight line was then fitted, using linear

regres-sion, through the three points and the slope of this line was considered to express the desired

rate (see for example Fig.24). The hUterical values of the resulting slope 6(rits1/5(Cw) express per cent change in response tIRS per 0.01 change in C.

In Figs. 16 to 21 the slope of the responses

is plotted for all speeds and dl sea states

examin-ed.

Heave (Fig.16) is seen to .decrease substantially

and consistently

with

increasing C. The decrease is in general greater for the higher Fr.Uot and

the lower sea states

Pitch (Fig.)7) also decreases consistently with

increasing Cw but co,-%iderably less than heave,. For Pitch the effecl. of speed and sea state is not

Pronounced but it is stronger for an intermediate

speed and weaker' for low or high speeds.

Bow relative motion (Fig.18) at station 1 decreases.

consistently with increasing Cw and the effect of speed and sea state is similar as for pitch Bow relative velocity (Fig.19) behaves as bow re-lative motion

Bow acceleration (Fig.20) also decreases with in-creasing Cw, there is an intermediate speed for

which the effect is strongest and, except fbr the Very low sea states sea state does not affect much

the result

Added resistance (Fig.21) increases with increasing.. C for:low speeds and low sea states and otherwise

w

7

.75 1;13 C_, .1 ul -3 LI sca

C0=0.7

lit.mo.

.0 .1 .2 .3 4/3 I 1 1 10 .20

lo

'4o so .60

lu -30

ob .100 I I

1- -1

1 3

/3

3

HI13/

STA 1 I I I I

il). 20

30 40 51) E0 70 no 4. In

Fig. 18: Rel.moZion rate of change vs Cw

FR.NO: =0 0 0.1 0.2 0.3 STA-1

174-113/L..

I I 1 I 1

10 20 30 40 sn En 71 an 10:1

Fig. 20: Acceleration rate of change vs Cw

.95 .05 .75 1.13 7 .93

ABS. yRT. ACCELERATION

STA 20

-2.0

-1.8

8.8 1.8 2.8 FIG.13: (LCBM.CF)/2 1,ve 1.8123

Cs=07

C8'7

vilh/L

T1 V3 I t lo 2n 31, 4n I,' tu 70

Fig_ 21: Added Reo,Ltence rate of change

_{vs Cw}

C =0.6

ABS. VERT. ACCELERATION

STA 20

0.65

2.G5

1.65

1 I 1

--4.0

-73.8 -=2.0

-1.8

8.8 FIG.12: (LCBtl..CF)/2 I.m. LOP]

Fig. 16: Heave. rate of change vs Cw

_{Fig. 17: Pitch rate of change vs C}

.

Jo

20 '30 ;o so CO 70 80 90 100

Fig. 19: Rel. velocity rate of change Vs CW

2.1.1

ii_i_IIII

20 3n .0 51 co 70 20 JO

MERN ADDED RESISTANCE

2.6 5

A.G5

1 I

-4.8

-3.8

-2.8

-1.8

0.8

FIG.19; (.CIMLCF)/2 I 'V. LOP]

MEAN ADDED RESISTANCE

4:23

2.23

0.23

111

-2.0

-1.0

8.0 1.0 2.8

F1G215: (_CEMLCF)/2 f'Ve LOH

PI

r3.2

Destroyer-type SHips

As it has been mentioned earlier, the main purpose of the present investigation is to study the effect of important hull form parameters for seakeeping'behaviour by generating and computing the responses of variant hull forms.differing from

a basic by one only parameter. This was not fully ' possible when the cruiser stern ships were

investi-- gated using Lewis-form representation of the cross

' sections. Since each Lewis-form has a unique posi:

tion of its vertical centroid KB(x), the variants used for all preceeding calculations did not pos-sess exactly the same 1(I3(x) 'distribution or KB value as the basic.

This shortcoming was overcome with the

deve-lopment of the extended Lewis-form representation and Papoulias (1983) used the new capabilities to Study the effect of changes in Cw,(LCB+LCF)/2, (LCB-LCF) and KB(x) on the seakeeping performance

of naval ships of the destroyer-type.

Two hull forms were selected for this investi-gation. A frigate size hull form and a corvette size, with main particulars shown in Table 3.

Table 3. Main ParticularSof the Parent Ships

Shi Particular FRIGATE CORVETTE

tons 310

From the basic frigate hull form 21 variants were generated, 19 related to variationsof the.

longitudinal centroids and .with two different Cw,

and computer tested for a range of speeds and

sea states, always for head seas. All important responses for such naval ships were included in the investigation. In the sequel some of these re-sults will be presented in graphical form to

illus-trate the effect of the hull form parameters under

' investigation.

In Table 4 the grid of the 19 variant hull forms,with respect to the (LCB+LCF)/2 ana

(LCB-LCF), is shown. The Cw variations were done by

Table 4. Grid cf variant hull fonns

AFT FORE

(LCB+LCF) (basic)

p-0.015L P u+0.015L

changing the waterplane coefficient by +0.02.

In Figs. 22, 23 and 25 results for pitch, heave

and added resistance are shown for the 20 hull

forms of the (LCB+LCF)/2, (LCB-LCF) grid. The results are for a characteristic cruising speed of FrAo.=0.268 and a cnaracteristic sea state with modal frequency (frequency of the spectral peak) w =0.62sec-1 or T =10.20sec.

The following coments are now in order: Heave (Fig.22) decreases consistently as both cen-troids move forwards. The effect is linear and

va-ries from'significan: to moderate with the correspon-ding value of (LCB-L_ )/2.Heave increases

with(LCB-LCF) and the effect significant, non-linear and

monotonic.

Pitch (Fig.23) also decreases linearly as LCB

and LCF move together fcr..Ards but less than heave.An

increase in (LCB-LCF) causes pitch t6 increase also

appreciably.The effect is non linear ananionotonic

Added Resistance (Fig.25) decreases in general as

both centroids move toward the stern. The effect

is non-linear and (except one case) monotonic.The

value of the (LCB-LCF) parameter, for a constant value of (LCB+LCF)/2, causes added resistance to increase for negative values and again to

increa-se for large values. An optimum value exists for

small positive values. The effect is non-linear and

non-monotonic. .

Altering the waterplane coefficient by +0.02

causes the expected results shown in Fig.24, that is

-8-.1-(m) 120 80 L/B 8.57 7.27 BIT 3.50 3.14 Cw 0.70 0.77 LCB(%L) -2.88 -1.68 LCF(%L) -5.91 -6.32 KB IT 0.59 0.57 ILCB-LCF1(n) 3.03 4.64 LCB12LCF.

lot)

-4.40 -4.00 6+0.02L FL6 FL4I FL8 IFL]

17L71

I FL2 FL? IFL5I FL9 FL17 FL10 FL16 FL18 FL11 FL13 FL19 FL20 FL14 FL12 FL15 . 6 (basic) 6-0.02L 0 -(6-0.02L) -6 -(6+0.020

1.30

1.20 1.10

-1.5

-.5

.5

1.5

FIG:22: CHANGE OF (LCBtl_CF)/2 [°,0 LOP]

-2.8

8.8 7.0

F1G.124: CHANGE OF Cw 1/.1

FIG.26: FRIGATE BODY PLAN (FL3) LEWIS-FORM REPRESENTATION -FIG.28:VARIANT FL1 FIG.30:VARIANT FL4 FIG.32:VARIANT FWI .94 .92

-1.5

-.5

\-5

1.5 F1G.23: CHANGE OF (LCB+LCF)/2 LOP) -4 -2 2 2 4 11..03-LCF1 LOP] .

\

'-I--

-'-..---1---,

i

l I

."

FIG.27:FRIGATE BODY PLAN (FL3) EXTENDED LEWIS-FORM .. FIG.29:VARIANT FL2

.'---..1

'

'

. . , FIG.31:VARIANT FL5 .. FIG.33:VARIANT FW2

both heave and pitch decrease mocerately and

li-nearly with increasingCw.

To demonstrate further the effect of the two

centroid parameters four variant hull fOrms were

selected, with parameters differing from the basic

by 9.,9151..fbr the value of (LC0+1,CF)/2 and DY

+0.02L for the value of (LCB-LCF). These variants

are designated by the codes FL1,FL2,FL4 and FL5

and are shown in Table 4.

In Figs 26 to 31 the Lewis and extended Lewis,

fort representation of the basic hull form and the

four variants is shown: In Figs 32 and 33 the

ex-tended Lewis form representation of the Cw Variants

FW1 and FW2, is shown.

The results to be presented were obtained for

the same ship speed, Fr.No=0.268 and for a range

of sea states with modal frequency w

,

non-dithen-sional modal frequency Lar=w,

and

Correspond-ing modal 'period

P wo

lrad/Sec11.09 0.94 0.83 0.73

Q.2

0.545

0.49.

3.84 3.31 2.92 2:57

2.18

1.92

1.72

T

Isecl

5.76 6.65 7.57 8..59 10.20

11.52

12.82

The results for pitch, relative vertical

tionland relative vertical velocity at the"slamminn"

station(0.1L from the bow)and Acceleration at the

bridge (0.25L aft from the bow) are shown in Figs

34 to 41. The results are not-dimensionalized with

respect to the basic hull form. In addition the

dimensional results for the basic

hull-form,express-_

Ed as significant double amplitude per signigicaht

wave height are shown.. All results are plotted vs.

non-dimensional modal frequency W.

By examining the pertinent figures we can

remark:

Pitch (Fig 34 and 38) decreases consistently for

all sea states as the tentroids move forwards and

their separation decreases and Vice versa. The

effect is appreciable and of the same order of

magnitude for all sea states.

Relative Motion (Figs 35 and 39) decreases

appre-ciably for all but the very low sea states as the

centroids move forwards and their separation

de-creases and vise versa. For the very low sea

sta-tes the effect is insignificant and reversed.

Relative Velocity (Fig 36 and 40) behaves

similar-ly to relative motion.

Vertical 7..ctelerati.

(fis 37 and .41) beraves as

pitch except for ti,

hiyheSt w' (the lowest sea

state). The effect j% significant and more So for

changes in (LCB-LCF).

Apart for heave and pitch, all responses exa,

mined to far were for the fort...ard part'of.the Ship.

To complete the picture we will examine now what

'

happens along the length of the ship for the basic

ship and the four centroid variants in a sea state

-1

with w =0.62 sec

and with a Fr=0.628. The

cor-responding results for absolute motions, velocities

and accelerations are shown in Figs 42 to 47.

When both centroids move forward (Figs 42;43

and 44) all absolute kinematic responses are re-.

duced, by approximately the same aMmount, for the

forward half of the snip and vice versa, After the

midship section the rate of decrease decreases,

becomes zero for a location near the LCF and

nega-tive, that is the reLponses increase, for the aft

part of the ship.

When the centroid separation (Fig 45, 46, 47)

decreases, all absolute kinematic responses

decrea-se for most length of the ship, except near tne

stern and vice versa. The decrease is larger near

the midship section. Near the stern this trend is

reversed but the effect on the responses is

intig-nificant.

We will now inVstigate the effect of the

waterpla.ne coefficiert in more detail by examining

hull forms FW1 and Ft.:2

(Figs .48 to 51) at FrAo.

0.268 in all sea sta:es..

Pitth. (Fig 48) decrases appreciably with an

in-crease in Cw and vise versa. The effect is of the

same order for all s,a states.

.RelatiVeion and ;:elative velocity (Figs 49 and

50) at the "slaMming'slation 2 are also moderately

reduced as Cw increi.es but the effect 'becomes

negligible for the very low sea states.

Acceleration. (Fig

uehaves as pitch.

Returning to tLe tentroid parameters, we will

examine their effect on added' resjstance

.

When both centrJidS move forward (Fig 53)

ad-ded resistance is appreciably decreased for all

sea states and vice-versa. The same holds true

in general for a decrease in centroid separation

(Fig 52) exceot for Ine very low sea states, where

the trend is reversei.

-10-a

." FRIGATE

1.76

2.47

.3.17

3.89 FIG:4: NON-DIM. MODRI. FRED.

1.76

2.47

3.17

3.68

FIG:36: NON-DIM. MODAL FREQ.

1.76

2.47

3.17

3.8E FIG59: NON-DIM. MODAL FREQ.

1.76

2.47

3.17

3.86

FIGIO: NON-DIM. MODAL FRED.

-.5

-.3

-.1

D2 .1 .3

4.60

3.08

3.00

2.28

1.813 FRIGATE 1.76

2.47

3.17.

3.89

FIG:35:.NON-DIM. MODAL FRED.

1.76

2.47

3.17

3.88

F107h NON-DIM. MODAL FRED.

1.76 2.47

3.17

3.69

FIG:39: NON-DIM. MODR1.: FRED.

ABS. VERT.

RCCELER.

2.08

1.60 1.20 .80

2.40

2.00

1.60 1.20 .ea

3.0

2.4 1.8

12

.6 I ./

g

/..,

1

z.: ci In m Li m

2

o

a

Li

=

2

1 1.12 1.06 1.00 .94

.89

1.76. 2.47

3.17

N0N-01M. MODRL FRED. 3.88 3.0

2.4

1.8 1.2

.6

V In

ABS. VERT. VELOCITIES

F

Li

FL5

,..

-/

\

F

1 I I

.5

-.5

-.3

-.1 Di

.1 .3 .5 1.12

0

Ill 1.06 In Li In . 1.80

2

.94 .88 1.12 111 Li In 0. 1.86 1.88 6.1 .94 .89 u, 1.12 1.8$ cc

1.88

171

0

.88

4.68

3.66

3.138

2.28

1.12 1.06 1.88 .94

.ie

1.08 1.12 JIB 1.12 -88 .68 FRIGATE .

-.5

-.3

-.1)1

.1 FIG. 341X LBP .3 .5

-.5

-.3

-.1 El

.1

rio.6

x/ LOP

.3 1.76

247

3.17 3.88

FIG:98; NON-DIM. MODAL FRED.

1.76 2.47 3.17 3.88

FIG.510; NON-DIM. MODAL FRED.

1.76 2.47 3.17 3.68

FIG.52: NON-DIM. MODAL FRED. .5 3.8 3.8

a

2.4 LB

L2

.6

¢

4.6 3.8 3.8 2.2 900 700 500 300 1.25 1.15 1.05 .95 .85 .94 .88 FRIGATE

ABS. VERT. MOTIONS

-.5

-:3

-.1 pl

.1 .3 .5 FIG.A5: X / LOP

-.5

-.3

-AD1

1IG:47: x / LOP .3 1.76 2.47 3.17 3.138

FIGA5: NON-DIM. MODAL FRED.

1.76 2.47 3.17 3.88

FIG.51: hOU-D1M. MOLAL FREO.

1.76 2.47 3.17 3.811

FIG:53: NON-DIM. MODAL FRED.

.5 3.0 2.4 1.8 1.2 .s 3.0 2.4 2.0 1.6 1.2 1.8 1.4 1.0 .6 900 708 500 308

-12-1.40 1.20 -J M 1.88 -

.as

.68 1.88 1.84 1.88 .56 .92 1.25 1 . 1:15 .95 .85

MEAN ADDED RESISTANCE

FRIGATE

1.176 2.47. 3.17 3.138

FIG.5q; NON-Dill. HODRLFRED.

CORVETTE

1.76 2.47. 3.17 3.88

11056: NON-Dirt. NODALFRED.

1.76 2.47 3.17 3.88

FIG58; NON-DIN. HODRL FRED.

1.76 2.47 3.17 3.88

110.60; NON-DIN. NODAL FRED.

500 708 5138 380 2.6 2.2 1.8 1.4 4.2 800 608 4130 200 1.25 .55 .E5 1.70 2.47 3.17 3.88

1I0.55: NON-01M. m06111. FRED.

IL 1

REL. VERT. NOTION

STA 2

-1.16 2.17 3.17 3.88

mori-olm. HOD& FRED.

AliS. VERT. ACCELERATION

_F

CO'r4V

.F b2

S TA 5

-1.76 2.47 3.17 3.88

FIG.55; h3u-D1m. MODAL FRED.

2.6 2.2 1.8 1.4

/s-x,

ke440-4,:e

cli44A-,Zet4)4%,

CORVEI.TE 1.9 HEAVE 1.12 1.80

- -

F131 1.1 1.80 CORV. 1.0

F42

-.94 .6 .88 BBO

NER:i F,CDEE RESISTANCE

F 33_7:

441"84"")

408

244.0

208

1.76 k.-17 3.17 3.69

/-ap 4. DISCUSSION

The analytical results presented here are part of a continuing investigation at N.T.U.A. for the determination of a seakeeping rank factor R along the lines followed by Bales (1982) in his

pioneer-ing work. it is our opinion that, poamiblY. an Im-proved seakeeping rank factor can be established by including more and different hull form

parame-ters, having a functional relationship not necessa-rily linear. In addition, the use of the R factor

The effect ortw on added resistance is

examin-ed in Fig.54. It can be seen that the effect is small for the moderate and heavy sea states. For the lower sea states an increase ip Cw results in ap-preciably increased added resistance.

We have left last the investigation of the ef-fect of the vertical centroid parameter KB(x) on the seakeeping behaviour of destroyer-type ships. The corvette hull form will be used for this

in-vest igation

4

Two variants of this hull form were generated with all hull parameters constant except that the

centroids of the sections were-moved upwards or

downwards with end result the overall KB to change

by 1.2% up (FBI) and 3.16% down (FB2). The results

for the kinematic responses are plotted in Figs 55 to 59 for Fr.No=0.268 and all sea states. From the examination of these figures, without getting into details, one can conclude that moving the position of the vertical center of buoyancy upwards increases appreciably all responses for all sea states. The opposite is true for a. downwards movement of KB but the effect is much weaker. The effect of the position of KB on added resistance is shown in Fig. 60. The results are mixed and both variants have

in general greater added resistance than the parent.

However, one can alter the vertical centroid of the ship sections differently for the forward and the aft part of the ship, in such a way that

the overall KB remains constant. To investigate

-this possibility two more variants of the corvette hull form were generated, FB3 with KB(x) increased

for the-tow sections and decreased for the stern

ft

sections and FB4 with the opposite changes.

On Fig.61 the effect of these changes on ad-ded resistance is shown. It can be seen that FB3

is uniformly and considerably worse than the parent and FB4 is uniformly better but to a smaller extent.

.should be eAtunded to other classes of snips, e.g.

Merchant Marine-type cruiser stern ships.

The form of the R factor presently under inves-tigation is:

R = f ( L, 9/L34 T/L, B/L. Cw.(LCB+LCF)/2,

(LCB-LCF), KB(x)) ( 5 )

In this form 8 hull form parameters will be

neces-sary for the determination of a seakeeping merit rank instead of the 6 used by Bales or 7 after Walden's (1983) extension.

Actually there is no difference in the number of required parameters: because Bales included

implicity L in his ranking by choosing the longest

hull form in his sampl,! for the optimization exer-site.

The new formulation for R includes the ship length

L.and in addition:

Three parameters ICw,(LCB*LCF)/2,(LCB-LCF)]

replace four of Bales [CwF, twA, CwpF, Cvpp]

Aditional work,not presented here, has established

the equivalefice of these two set of parameters.

91L3 replaces (L-4300)/4300, the new

parameter being more general

T/L is used as in Bales' work

B/L replaces c/L, which was found to be of

no particular importance for destroyer-type hull

form and which is not meaningful] for other classes

of ships. On the contrary L/B is known to affect

seakeeping behaviour and wave bending moments, Lou-kakis and Grivas (1980).

KB(x) is included. This parameter is well knovn to affect seakeeping behaviour by making the sec'-tions shape-more U-form or V-form.

The foregoing conaents do not signify, that Ba-les' seakeeping rank factor is not successfull

enough. On the contrary, the calculation of the R

factors for the frigate hull form and her 19 variants,

Fig.62, shows the same general trends with the heave

and pitch responses, Figs 22 and 23.

A general conclusion from the present

investi-gation is

thet

two of thO parameters investigated,

(LCO*LCM) and Cw, affect imakeeping behaviour in

approximately the same manner for both Series 60

hull forms and the'frigate. (The same is true for

the Corvette, although the corresponding results

are ript presented.)

-14-Fig.62. Bales' Seakeeping Rank

vs (LCB+LCF) /2 and _(LCB-LCF)

Moving both centroids forward is beneficial

. for all kinematic responses for

most part of the

. ship and vice-versa. There is however a mild trend reversal near the stern of the ship. The effect of

(1CB+LCF)/2 _{on added resistance is mixed and of}

mi-. nor importance for the Series 60 hull forms but strong and non-linear for the frigatte.

Increasing Cw is beneficial for all kinematic responses but.it can result in increased added re-. sistance.

' The effect of both (LCB+LCF)/2 and Cw on the

kinematic responses is in general linear.

The centroid separation parameter affects dif-ferently.the.Series 60 hull forms and the frigate (or the corvette). Decreasing the value of (LCB-LCF) 'decreases both heave and pitch for the frigate and

heave for the Series 60 hull forms, but in the

-later case pitch is increased. Generally speaking,

decreasing the value of (LCB-LCF) is detrimental fcr

the performance of the C8=0.6 hull form, except for the added resistance, which decreases along with heave. For CB=0'7 the effect is mixed. A decrease

in (LCB-LCF) results in decreased heave, relative motion, relative velocity and added resistance and

in increas-ed.pitch and acceleration along the _ship.

The effect of (LCB-LCF) on the kinematic

res-ponses is non-linear and can be non-monotonic.

Finally; moving the vertical centroid of all

stations upwards

is in

_{general detrimental on}

sea-keeping performance and vice-versa. If we consider

that movinii the vertu:el

centroids upwards results

in more V-form sections,

the present result can be

different than traditional

knowledge. However, one

should keep in mind that in _{the present}

investiga-tion KB(x) was the only _{parameter varied, which}

was not the case in previous

investigations. The

KB(x) distribution can also be changed by moving the centroids in the opposite sense for the forward and the aft part of the ship,

while keeping the overall KB value constant. The _{effect of KB on the}

responses is non-linear.

Finally, with regard to the dependence of the effect of the parameters from the ship speed and the sea state, we can observe that, _{in general,a} beneficial effect is conserved for _{all sea states} of importance and all Fr.Nos, although the magni-tude of the effect can vary _{significantly and}

non-monotonically.

In addition, as it is obvious from _the present-ed results, each class _{or sub-class of ships will}

require a separate ifivestigation for the

determina-tion of the constants of the funcdetermina-tional

relation-ship determining a seakeeping rank _{factor among its}

members.

To conclude, we should mention that seakeeping

performance, cannot be optimized independently _from

other design cosiderations and in particular from

the resistance characteristics _{on the resulting hull}

forms.

References

Athanassoulis,G.a(Jd !Dukakis T.A., "An Extendei

Lewis-form Ship-Section _{Family.and'its} Ap-plication to Seakeeping Calculations", Report No 10-83, Dept. of N.A.M.E., N.T.U.A., ₍₁₉₈₃₎

Bales O.K., "Optimizing tne Seakeeping Perfor-mance of Destroyer-Type Hulls", Thirteenth Symposium on Naval Hydrodynamics, Tokyo,

(1980)

Bales, O.K. and Cummins, "The Influence of Hull Form on Seakeeping", Transactions,

S.N.A.M.E., Vol.78 (1970)

.Beukelman,li..and Huijser,A., "Variation of

i

Parameters DetenAining Seakeepihg"I.S.P.,

Gerritsma,J. and Beukelman,v., "Analysis of the Resistance Increase in Waves of a Fast Cargo Ship", Report No.334, Laboratory for Ship Hydrodynamics, Delft, The Netherlands, (1971)

Loukakis T.A. and Chryssostomidis C.,

"Sea--. keeping Standard Series for Cruiser-Stern Ships';

.Transactions, SNAME, (1975

.7) Loukakis,T.A.and Sclavounos P.D., "Some

Ex-tensions of the Classical Approach to Strip Theory of Ship Motions, Including the Calcu-lation of Mean Added Forces and Moments'; J.S.R., Vol.22, No 1, (1978)

Loukakis,T.A. and Grivas S.B., "A Method for Establishing Ship Design Wave Bending Moment and its Comparison with Classification So-cieties' Rules", Ocean Engineering, yo1.7,

(1980)

Papoulias,F., "Sensitivity Analysis of the Dynamic Behaviour of Naval Ships", Diploma Thesis, Dept. of Naval Architecture and Mari-ne EngiMari-neering, N.T.U.A.., 1983 (In Greek)

Perakis, A., "Seakeeping Standard Series IP: Diploma Thesis, Dept of Naval Architecture and Marine Engineering, N.T.U.A., (1977) Salvesen,N., Tuck, E.O. and Faltinsen O., "Ship Motions and Ship Loads", Transactions,

S.N.A.M.E., Vol.73, (1970)

Schmitke,R.T., "Seakeeping Algorithm for the DREA Monohull Frigate Destroyer Concept

Explo-ration Model", D.R.E.A.,Technical Memorandum

. 82/K, (1982)

Walden D.A., "Extension of the Bales_Seakeepinq

' - Rank Factor Concept", DTNSRDC, (1983)

. Prof. T.A. Loukakis

Dept. of Naval Architecture and Marine Engineering National Technical University of Athens 42,.281s Octovriou Athens, Greece Ass.Orof. A,N.Perakis Grad.Student F.A.PapouliaS Dept.of N.A.M.E.

The University of Michigan Ann Arbor, Michigan U.S.A.