Tests and design data of tank stabilisers of the free-surface type

1.Z DEC197Z- .

I

A

Lab. Y. xneepsvouw.unu.e

Technische

Uogeschool

HELSINKI UNIVERSITY CF TECHNÖLOGY

SHIP STRUCTURAL LABORATORY

OTANIEMI

FINLAND

Report No. 6

ibIioheék van d sbouwkunde. n,sc!'e Hogeschoo, DOCUMEN fAlle _I: D A-T U M: DOCUMENJATI

TISTS AND DESIGN DATA OF

TANK..

STABILISERS OF THE'

FREE-SURFACE TYPE

by

Max Honk'anen

Max .Honkanen

TESTS AND DESIGN DATA OF TANK

STABILISERS OF THE

FREE-SURFACE TYPE

CONTENTS PREFACE

...

r INTRODUÖTI.OÑ ... Page. 6 1. THEORY . lo

i i Linear Theory of Rolling in Regular Waves 10

1.2. DeterminatiOn of the Coefficients 12

l.3.Ro11inginIrreu1arSeas

114

2 . THE MODEL TESTS 16

2.iLawsofSimiiar.ity ...

2.2. The Testing Apparatus .16

2.3. Analysis of the Test Results 17

2 . 14.. The Test Program 19

3. THE RESULTS OF THE TESTS . 22

3.1. The Wave Phenomenon of the Tank ... 22

3.2. The Effect of the Damping 214.

3.3. The Effect of the Amplitude of Roil 26.

3.1!. The Effect of the Height of the Water Leve]..., 27

3.5. The Effect of thê Distance from Center of Roll 29

LI.. ON THE DESIGN OF FREE-SÜRFACE TANKS ... .30 14.1. Generai Remarks ... .

30.

14.2. The Dimensioning of the Tank

14.3. The TankerStabiliser ...' 314

5 EXAMPLES 36

5.1. Compárison of the FreeSurface Tanks ... 36

.5.2. The Tanker Stäbiliser Perförrnance ... 141

6. CONCLUSIONS . . . 145

6.1. Summary of the Results . 145

6.2. Cornment on the 9esearch of Tank Stabilisers 146

LIST 0F SYMBOLS . 148

LIST OF REFERENCES ...i . . . . ... . . ...

.

50

Helsinki University of Technalogy on the subject of passive tank stabilisers. Professor J-E. Jansson has been the initiator às well as the head of this pro-gram, and the testing apparatus has been designed by Proféssor V. Kostilainen and. Mr. J. Sukselainen,

Lic.Techn. both from the Ship Hydrodynamics Laboratory at the Helsinki University. Qf 'rechnology.

The results of

this

paper are thainly based on the wo'k of Mr.. K. Levander,M.r. O. Salminen and Mr. T. Bragge, who have. Ínade the practióal test ihg and analing the results as their Diploma Thesis.

The original reearch work was cärried out already in 1967-1968. Since that time further stabiliser testing has been made at the Helsinki University of Technology. The. intention was originally to bring ail the material between two covérs, but when ttie author started this work, it became quite obvious that such a paper would become too extensive. Therefore, only results of these three Diploma Thesis Works are published here because they could be con'eriientiy combined to one homogenous work. It is the. author's intention to publish more of

.the reults.of the Helsinki University of Technology as

soon as some of his complementing stüdies are completèd.

In this paper philosophy an notations of paper's written by Mr.. J.J. van den Boschand Mr. J.H. Vug.ts of the

Technicàl U.rv.rsi.ty of Deift has been followed. They have tested a number of free-surface tanks without any damping device, and they give the resülts as sets of

coefficients as functions of a non-dimensional frequency parameter, the ratio of the water level height to the tank breadth and the. ratio of the tank bottom's distance

from the center of roll to the tank breadth. In this

paper data for different kind.s of damping arrangements are pÌ'esented in asimilar way.

The author has collected, and, united the data. He has also made some completing calculations and simplificat ions in prescnting the data. The author wishes to express his gratitude to all mentioned above as well as to those' numerous persòns who have given valuable advice either in form of conversatiön or correspöndence.

Otaniemi, September the 30th, .1971

Max Honkanen, Naval 'Architect

problem in Naval Architecture since sailing vessels lost their dominant part at' sea. Especially after the WOrld War II, when the hull form of the ship is determined

rather by economical reasons than by good seamanship,'

and on the other hand,' increased efficiency, speed 'and comfort are requested for even in severe weather

conditions, the ship motion stabilisation has become more and more important. A 'stabilised'ship öffers many advantáges: the ship's speed can be maintained even in bad weather thus allowing för a more accurate'

scheduling, the comfort of,the crew a'nd the passengers is increased resulting in bet±er efficiency of the wOrk atid a göod 'reputation ¿f the ship, cargo and other damages due t'o violent motions are reduced, and

ships, espécially military vessels,' become more

independent of the weather conditions. These advantages should be weighed against i'nstal,Jation costs, driving and maintenance'costs and costs due to lost loading capaöity. Inmany'cases of today, a stabilised ship offers abetter economic result than a ship löaded with seasick passengers.

The rolling motion has fréguently been object to,stabil ising 'efforts 'because the forces involved are relatively small compared with forces caused by other motions. The stabilisation Of roll is today mainly achieved either

by anti-rolling tanksor fin stabilisers This paper'

is merely concerned with anti-rôlling tanks of 'the free-surface type. '

rectangular open basin placed transversely in the ship. The rolling motion generates a borè in the tank which tends to counteract the motion. This is the si.tuatio

if the tank is properly tuned, Which means that the natural period of the tànk '1uid is sufficintly close to the rölling périod of the ship to cause a phase lag

to themotion. When the ship isrolling at resonance,

thé ship motion lags the waves by 90 degrees and the tank fluid lags the, motion by approximately 90 degrees,

so the böre lags thé sea by about half â cyóie thus acting asa sort of negative wäve tending to reduce the

foróe of the sea. Thesé purefree-surf'ace tanks are discussed in detail in a series of papers by Messrs. J.J. van den Bosch, J.H. Vugts and A.P. dé Zwaan of the Technical University of Deift.

The rolling of the ship is not usually regular. It is affected by the iPregularity of the sea and the course and the speed of the ship. Thé tuning of' the tank is therefore cnstantly altered and the performance

impaired. In fact, in very unfavourable conditions the roll .tnplitudes may éven increase because of the acti9n

of thé tank. In the philosophy of the Utanks first suggested by Frahm, this most inconvenient phenomenòn i.s satisfactorily eliminated by applyftig a proper amount of damping to the tank. This same ideà has been used in the Flume Stabilisat ion System, which consists of a free-surface tank fitted with proper damping pieces or bulkheads. It should, however, he poitited out that physically it is of minOr significance how the damping has been generated, only the totál damping coefficient is the determining factor of the behavioÌ" .of the system. Therefore, the great variety of existing damping systéms should be looked upon as a whole.

The natural period of a frêe-urface tank is .propor-tiona.l tO thé breadth of the- tank änd inversely pro-portional to the square root of the water depth in the tank. To obtain a sufficiently long natu'a1 period for the tank, maximum breadth should be used. Thi.s is

usually restricted by the vessèls beam, so in. most casés of pract.ioal tank design, the corréct tuning of

the tank requrê ¿ relatively low water level. This

in turn leads to a dec.reásed stabilising moment, whichmay require an installation of severaltanks abovè each other.. increased damping results in an increased natùral period nd a brOader effective frequency band thus improving the performance of the tank up to a certain point, after which it is impaired again because of the great etergy. losses of the flow. The optimal damping, as it can be seen, is not a

simple question tÖ be answered, and therefore much effort i.s madé to investigate this problem.

-An interesting appliáation of the free-surface tank is found in the tankér practice, when the cargo itself -. could be used as tank flUid. It has been investigated

whether properly shaped and dimensioned holes in the longitudinal bulkheads còuld replace the double bottom otherwise needed to create the shallow water effect.

t has been fund out t.hat the design really acts as an orthodox free-surface tank in essentials. The impaired efficiency may very well be compensated by a longer tank; a whole tank group could be used as a stabiliser. Most part. of this paper is concerned with the

stabil-isatiOn of tankei's with the aid of free-surface tanks with and without ä double bottom. Both designs are discussed and compared, and as an example, roll

have been worked out..

In this paper a linear theory of stabilised rolling is first given foilöwing the. philosophy of the papers óf the Technical University of Deift. 'he testing apparatus and the 'model test prögram are then described in Chapter

2. The various effects found out in the model tests are

presented and discissed in Capter 3. In Chapter 4 some

aspects of the design of free-surface tanks are discussed and the use of the daca of the model tests is explained. 'Ì'hree examples are then worked out in Chapter 5.

Conclusions are drawn in Chapter 6 and sòme comments on the reseárch of tank stabilisers are discussed. The results of the model tests are finally preséntéd as a set of curves giving non-dimensional tank moment compón-ents as a function of a nön-dimetisional fréquency

panameter and different parameters describing the tank geometry.

1. THEORY

Li. Liñéar Theory of Rolling in Regular Waves

The theory of a rolling ship with a tank stabiliser is presented in accordancé with the papers of the Technical University ofbeift.

The fbllowing assumptions have béen made in order to approach the. problem in a. reasonably rational wà:

The only motion of the ship tb be consideréd is:

roiing round

_a longitudinal, axis that passes

through the ship's center of gravity

The amplitudes of the motions are so small that linear theory can be applied.

- The ship!s °wn résistance to roll or damping is proportional to the angular velocity of roll The mornetit exerted on the ship by' the wave is

sinusoidal.

The equations of motion with and without a stabiliser can now be written.:

+ N0 + R _Mw

(1.1..)

Iø+ N0

+R00

Mw + M,1 where (l...2..)

10 maO moment of inertia of ship aM surrounding

'fluid with respect to thè axis of röll, N0 = linear damping coefficient of ship,

R0 linearized righting moment'of ship per unit heel,

MW

exctingmoment due to waves,

M.. exciting moment due to tank st'abiiier and

The exciting moments were asume. to be of the harmonic type:

Mw 4wa5in1t + ew)

MT;

MTaSlrl(Wt + CT)

MWa= amplitude of wave moment, MTa= amplitude of tank moment,

= phase lag of ship's motion to the wave, CT phase lag of tank fluid to motion of ship,

t = time, the time derivative operator is denoted

by a dot above the quantity in question, and

w angular frequency.

The solution of the equations of motion is of the type:

a similar solution for (1.2.) is found as for

alinear

second degree differential equation:

tanc w2)2 + (N0 - N0) where 11 (1.9.)

.0

(1.5.)

By differentiating (1.5.), substituting (1.3.) into (1.2.) and adopting notations

and (1.14.) MTCOSCT

(1.6.)

a

MTsInCT

(1.7.) Mw (1.8.)

hesolution of (1.1.), the ship without

a stabi.1iser,

is simply found by writing AR0

AN0

0.

The natural angular frequency

,

defined as the. frequency

when tat

=

_{ör LW}

900

is

0ac

At this frequency the resonant amplitude becomes

M

Wa

(M0 - AN0)w0

Itshould bé pointed out that etitions(L8.) to .(i.i.l..)

hve to be solved by iterative methods, becausé their

liriearity is destroyed by the terms AR0 and ANØ. These

terms depend on the amplitude of the motion and the

frequency, but the iterative, process i

fortunately

strongly convergênt.

Theoretically the linearization

of this non-linear system is not correct, but results

obtained in practice justify that the system as a

whöle acts reásonably well äs a linear oné.

Determination, of the Coefficients

Theparameters of the equations of motion can be determined

in accordance with literature; pnly sorne rèmarks are

discussed here.

The thass tnothént of inertia

The mass möment of inertia can be written

i

A..2(1

_{+ k)}

where

(1.12.)

j

_{radius of gyratior of ship,}

displacement of ship,

g acceleration of gravity= 9.81 rn/s2 and corretiOn factor foi' the added virtual mass, 0.10 ...

The radius of gyration may be presented iP

form--j CB %ji-.

()

where (1.13.)

B beam

of'

ship,

H depth of ship and

c coefficient deendin on the type and the Ioadin

of thé ship, c 0.29 . .. 0»40. The damping coefficient N0

The damping coefficient can bé expressed with the aid of-a non-dimensional damping coefficient

V0 (l.1'4.)

= non-dimensional damping coefficient 0.07-0.20.

The linearized righting moment per unit heel R. This coefficient can be written

R09

where

= metacentric height of ship.

The wave moment amplitude Ma

The wa\e moment amplitude òan be expressed as

13

(1.15.)

=

RØWeXP(-

_2g where (1.16.)

= maximal wave slope and

-T = draft

of'

ship.

The exponential term makes allowance for the Smith-effect assuming that the centroid of the pressure distributiön is located at one half of the ship's dräft, T/2.

1.3.

o11ing inIregular.Sças

In practice the ship very seldom rolls in regular waves. The actual seaway is more or less irregular, and thereforé a method is needed. to tranform the: data obtained bytests in regular wàves to a

prediction of the b?haior of the ship in an actual seaway. This is most conveniently done by the use of the energy spéctrum.

Equatin (1.8.) can be rewritten after substitution of (1.16.) and making follOwing notations:

X

_{tning factor}

and

%''ø

-

1/R)2

-

v)2A2

The ratio øa/'W is termed th roll amp1ification factor.

This factor squared gives the response amplitude operator which enables the computation of thé roll sectrum Of

the ship:

12

Ø(W)

()

_Sw(u)

whére (1.18.) = ordinate of roli spectrum and

ordinate of wave slope spectrum.

Thewave s1oespectrum can b

dèrived from the eñergy

spectrum by thultipiyingte ordinates with the wave number squared:

w2T

0a 2g

Sw(w) :.k2S(w)

S,(W)

k wave number

w2/g

and

Sr(W) = ordinate of energy spectrum.

The significant roll amplitude o.r the mean value of one third highest roll amplitudescan now be computed:

(1.20.)

15

The significant roll athplitude is a much mòre reliable criterion of the stahiliser's performance than a

percentage roll reduction factor based on regular wave tests. It may happen that the energy spectrum of the

ship's operating areà has its maximum at such a frequency where the tank stabiliser does not act satisfactorily. This leads to a poor performance of the stabiliser in spite of a gOod percentage roll redüction factor.

THE MODEL TESTS

2.1. Laws of 'Smi1arity

The stabiliin:Pibmént öf the tank f1u!d i.

Òaused by

a wave phenôñienon, so the gravity forces are the most

imÒrtänt :òn. Thêt'e also' é.its internal fiictiorä1

dampingof thé tank fluid, büt forces düe to this type

of damping aré relatively

rnal.l compared with the Others.

Therefore the Froudets law of similarity can be used.

The tankmoment amplitude of (1»4.). may now be written

in a non-dimensional form:

= PPgb31

.

where

nondimnsionaI tank moment amp1itde.,

density of tank fluid,

b

= breadth of tank and

i

= length of tank..

A non-dimensiónal frequencypararneter is defined as

=

(2 2

By representing the in-phäse and. out-of-phase components

.1asir1cT and ]JaCOSCT as functions of .t.he frequency

parameter

one has obtained a non-dimensional set

of curves which is independent of the scale.

.2 .The T?sting Apparatus

The testingapparatus is shown in figure 1.

Figure

-iDriving mOtor

2' Excentric flywheel

with gear box.

3 Driving cam

14 Frame

Inductive dynamomet er Position indicator Amplifiér Universal counter Figure. 2

2.3. Analysis of the.. Test Results

The oscillograph. record contained followin information: - the total moment curve of' the tank fluid and the

testing apparatus,

- a time scale at intervals of one second, and

neutral position inication of' the tank.

Oscillograph 17

The tank model was attached to a frame where its vertical position could be varied. The frame.perforthed forced oscillations generated by an excentr,c cam. The ratio

of the excentricity to the length öf the. cam did not exceed 1:28, so the oscillations were harmonic to a

sufficient degree. The excentricity of the cam could be

variedgivingalterd amplitudes to the motion.

The

system was driven by an electric motor coupled to the cam by a gear bOX. By altering the speed of the motor different Írequencies could be obtajned.

The tank moment was registered by ari inductive, dynamo-meter and measured by an AC-bridge. The signal was

amplified arid recorded by an öscillograph. A universal counter was also connected. together with the oscillograph to give signals at proper intervals of time. An inductive indicator was installed to the excentric flywheelS to record the position of the tank; its signal was also recorded by the oscillograph. The whole system was calibrated with weights of known magnitude. The instrumentation, is illustrated in figure 2. ,

The periOd of thé thötiòn

as meaured from the record

and the nondimensional frequency parameter of (2.2.)

wa

théncalculatéd:

-

-

/Ç,2rr/

ëonstiant

WV

-

p'eriòd

The. phase lag betweén thé tOtal momént and thé motiOn

wá

determined with the aid of the neutral position

marks.

Aftér thê moment. Of thé testing apParatus hd

been separately determined with an empty tank, the

components and.phase lag of the tank moment could be

còfputed iñ áccordancé with figure 3

MTCOSCT

Figurer 3

Ma5flCT

r42asin2

MTa'cOSCT

M2cosc2 - Mla

Mm 5].fl

äìctan

_TaT

(2.l.)

moment amplitude of testing apparatus with

an emptytank,

M2

moment amplitude with a filled tank,

MTa

moment amplitudé caused by the tank fluid,

C2

phase lag between total motnènt and motion and

CT

phase lag between tank moment and motion.

It should be nöted that thé tnorñents in question aré

vectorial quantities and shouidbe accordinly computed.

(2.3.)

2.14. ThTest_Program

A rectangular free-sürface tank, preèntèd in figure 14,

was tested with different darPping arrangements.

Damping 'a I bulkheads 0000 0000 ò000 0000 0000 0000 Type A Perforàtion 1/2 Figure 5 Type B Perforation 1/2 19 Type C Perforation 1/3 The dimensions of the model tank were:

b 1.500 m breadth of tank,

i 0.200 fri length oftank,

pm 1000 kg/rn3 denity of tank fluid,

h height of water level was varied,

e height òf he tight part Of the bulkhead, s = height of tarilç bottom above center of roll,

0a amplitude of roll.

Three types of damping bulkheads were used, the geometry and the perforation ratios are to be seen in figure 5.

Three types Of constriction pieces were also tested.

The geometry of these piece.s is to be seen in figure

6.

_{The pieces were locaed at one half}

f

_{the tank}

breadth and. they restricted the cross section area by

50 per cent.

i

2

b/3

CP I

Figüre .6

A third type of damping was produöed with the damping

bülkheads but they were placed above a tight part of

the.longitudînalbulkheäd, sée figure LI.

The tests.

were run at various heights of the tight part of the

bulkheads, e. The effective heightofthe water levél

was then h - e.

Each variation was tested at twelve.frequencies ranging

from

_{0.2 t:o}

2

1.3.

The effective height of the

water level was varid h/b

0.02.. .0,10, five values

weré used.

Three arñpiitude.s of roll were used:

0.033, 0.067 and 0.100 radians.

Four values òf the

distance of the tank bottom from the center of roll

wêrè used: s/b

-0.LI0, -.0.20, 0 and 0.20.

As it would not have been, meaiingful to test. all

cdmbin-ations, oniy the most interesting ones were studied.

The tested combinations are to be seen in table Ï on

he next page.

Th

test is indicated by an x and the

numbers refer to the set of curves at the end of this.

paper; all of the curves are not published.. The type

of damping is denoted by number.of datnper times type

of damper, and distance between the damping devices.

Table i

e

Damping

p1ate

s/b

+0 20

s/b

O

s/b

-0 20

s/b

-O 14Q

0a

033

067

100

033

067

100

033

067

100

033

067 100 o 0

!X

1

lxA,O

-r

2xA,b/3

x

2xA,b/2

x 9 x

lo x

11 x

12 x

13 x

l4

2xB,b/2

x 17

2xC,b/2

x 18

2xA.,3bR

X L 3xA,b/14 x o O

'x

5 x

2x

6 .,

CPI

x

23x

CPu

X214x

CPIII

x x

19 x

x

20 x

'x

x

21 x

X

22

'0

2x'A,bt2

r x

15i x

16

0 06 2xB,b/2

x

25

x 2E x 27

0.12

2xA,b/2

2xB.,b/2

x x x 28.

2xC,b/2

x

0.25 2'XB,,b/2

H X

X. 29

3.1

o 375 2xB,b/2

X X 30 32 o

2xB,b/2

x x O O x

3x

7 x 8

3. THE RESULTS OP THE TESTS

3.1. The Wave Phenomenon of the Tank

The bore generated in a free-surface tank mày be compared with a shallow water wave. The celerity of

such a wave is

c _{where (3.1.)}

ô celerity of wave and

h depth o,f watér.

The wavetravelsthe breadth of the tank in one half of the cycle, so the theoretical natural, angular. frequency of the tank fluid becOmes: I

(32. )

The observed natural Írequencies were slightly higher than the theoretical Ones. The difference between these two was decreased with an increased daniping andan

increased height of the water level but with a decreased amplitude and a decreased distance of the tank bottom from the center of.roll. In most cases the discrepancies were not significant. This philosophy is not directly applicable to the tank with partially tight bulkheads. The tests indicate that an effective.depth of water should be used in computations which contains the whole part of the free water above the tight prt of the

bulkheads h - e added with about 18 percent ofe:

he

h- (1

- Ce)e

ceO.l8

(3.3.)

This philosophy seems justified because the water below the level determined by. the 1ol in the bulkheads is only partly set into motion by the movement of the ship.

The tank moment amplitude may in this case be divided into three components:

= MT2 + M where

(3iL)

MT1 inertial moment of the "frozen" fluid, MT2 statical moment of the "frozen" fluid and MT3 stabilising moment of tank fluid.

The inertial moment can be written:

MTl = '- i w2i00 Where (3.5.)

= virtual mass moment of inertia of "frozen" fluid.

he statical 'piornent can be approximated by the expression

+ )sinø

P(s +

)Ø (3.6.)

mass of "frozen" fluid.

As it can be seen from (3.5.) and (3.6.) these tank, moment components are actually in phase with the motion. They could therefore be regarded as a part of the moment of the testing apparatus, Mia in figure 3. However, there

arisés difficulties in defining the "frozen" fluid. In accordance with (3.3..) only about 80 per cent of. the fluid defined bythe lòwe.st part of the holes in the bulkheads

shàuld be counted for.' In this paper, the components. have not been' separated because of the uncertainties mentioned

above.

The generation of the bore had a iffrent nature than

the normal free-surface tanks. The phenomenon was more sharply tuned and the wave was, not as steep as the bore. This was due to the eddy generation in the wing tanks. However, the system as a whole acted reasonably similar to an orthodox free-surface tank.

3.2. Tte Effect of the.Damping

The. different damping bulkheads had only a small influ ence on the natural period of the tank; the more damping the smaller the natural angular freouency. The shape of the holes had no significant influence on the tunthg of the tank.

The stabilising moment was, however, greatly influenced by the damping. The following results can bé looked. upon as mean values of the measurements, table 2:.

Table 2

In this case, too., the shape ofthe holes had no

significant effect on the moment. It seems therefore obvious that the perforation rat.io should exceed 50 percent in order to avoid considerable loss of the stabilising moment. On the other hand, too small an. internal damping leads. to a narrow, sharply tuned moment curve which will result in an unfavourable performance in irregular seas. An other aspect to be taken IntO consideration wheii designing holes

into the lòngitudinal bulkhead.is the strength. Perforation ratio,

per cent

. Relative stabilising

moment, per cent, 100 100 %

50%

. .

86%

.33%. .

..

67%

The effect of the distance betweeñ two symmetrically attached damping bulkheáds was tested with damping bulkheads A.. The results did not significantly depend on the height of the

water level, therefore they can be represented by a single

curve shown in fIgure

7.

The definitions are to be seen from figure 7. The value of the relative tank moment amplitude is related to the value of the tank without any

damping, i.e. the distance y/b = 0. When one bulkhead is

attached at the. plane of symmetry of the tank, thèn y/b

0.5. 1.0 0.9 0.8 0.7 0.6

0.5

o

= relative stabi.lising tank moment amplitude Figure 7

When a longitudinal bulkhead of a tanker is used as a damping bulkhead as well, it is very unfortunate. that the

effect of the distance between the bulkheads, which is usually about b/2, tends to reduce the stab,ilising moment by 21 per cent. If the djstance between the bulkheads were increased to 0.6b, i.e. y/b = 0.20, the reduction

would only amount about 1.2 per cent.

25

Some interesting results were found with the constriction pieces. The effective frequency band of CF I and CF III

was considerably narrower than the one of CF il. On the

other hand, the tank moment amplitude of CP I.Ì was the best of all, in fact, it always reached the level of the tank with no damping at all, especially, when, the reduced amount of water is taken into account. The damping

bulkhead was also compared with the coìstrictiOn pieces but its performánce was found to be worsé. The natural frequency of the tank was slightly reduced by the effect of the constriction pieces; the same result was obtained with the damping bulkheads. Also the position of the tank with respect to the axis of roil had similar influence on

the natural frequency than the damping bulkheads.

The constriction piece CF III was considered the most

interesting one, and therefore the effects of different

parameters were quantitatively determined with CP III

and only qualitatively with the others.

3.3.

The Efct of. th,e Amplitude of, Roll

When the ar!iplitude of roll increases, the fluid motion becomes more violent giving an increased stabilising moment. If the equations of motion were linear, the tank momeflt amplitude should vary linea.rly with the amplitude of roll. However, the energy losses of the tank fluid ar,e approximately proportional to., the linear velocities squared, which means that at larger

ampli-tudes of roll the losses are relatively larger than at

smaller amplitudes. Therefore the tank marnent amplitude is proportional to a power of the roll amplitude less than one. A square root law has often been mentioned,

and in fact, tests made with damping bulkheads and'

constriction pieces indicate, that the maximal values of the

a5

Tcu

may be approximatéd in the

form:

(3.7.) Ua51r1T(øa) _{_-}

_/0a

This, howevèr, is far away from the truth at the ends

of the effective frequency range.

The UaTlS

are also shifted towards higher frequencies with an

increàsing amplitude of roll; a somewhat surprising

result.

The tank with partially tight bulkheads showed a

some-what different behavior.

Over à. non-dimensional

fre-quency range

2

0.5 ..

1.0 the correlation was almost

linear although not starting from the origin.

This

indicates that a power 2/3 would perhaps be nearer the

truth than 1/2, but this should be more thorol4ghly

investigated,.

Therefore, caution and experieticed júdgeieñt

hould be

used when trying to apply results obtained at a certain

amplitude of roll to other amplitudes.

3.11. The Effect Qf t.hHeight of the Water Level

1he propörtion of the height of the water level to the

tank breadth is the main factor determining, the tuning

and the. effective frequency band of the tank.

The tank

moment amplitude is also affected by the height of the

water; the more water, the larger the moment.

For the free-suraòe tank with damping bulkheads the

correlation between the maximum value of the quadrature

compónent aSIT of the tank moment amplitude arid the

relative height of the watet' level was déterrm4ned, and

thé result is' as follows:

lsir1T

)

h

7.9

+ 0.21

27

The same correlation for the constriction piece CF III was nò longer 'lineai:

h

1h

P'as1r1cT(& .-'

I

h -= .1) (3,9.)'

Hbwever, no matter of what form thé tÍuth may be, bOth expressions clearly indicate the fact that the produced stabilislng moment per unit mass of the stabiliser fluid isthe'larger the lower the water' level is.

Unfortunately, the absolute stabilising moment may not be sufficientj enough, so several .stabilisêrs' above each

other nay be needed.

When the dampirig bulkheads are partially tight the qUestion of the height of t'he water level gets a somewhat different meaning. We shall 'at first consider the effect of the free water ieìe'l hêiht and then' the effect of the height of the tight part of the bulkhead's.

At values (h e)/b < 0.01 no wave was generated at all.

When.(h - e)/b was O.0l...0.09, the tank moirent amplitude

was nearly proportional 'to (h - e)/b at c2 >

0.8

but at lower values of 2 the correlation becomesdegressive,afld

at' 2 '0.4 a squàre root law was validi WheP considering the quadrature component of' the tank mortient'amplitude.,

it was found out that at (h é)/b = 0.10' ... 0.15 the decrease of the phase angle overcame the increase of the tank moment amplitude resulting into a decreased' out-of-phase component. Therefore, t fling he tank to 'its theoreticàl natural frequency does nOt give the best

posible performance as à stabiliser. Thé t'ñk shöii]?d

always be subcritically tuned, that means, 'the natural

frequency should always be somewhat above the operating

.29

The height of the. tight part of the bulkhéads häd a very small effect on the behavior of the free water except at very low vahes of é/b, when the inflUénce of the tank bottom was considerable. When the totl moment of the tank was studied it was noted, thatthe moment amplitude was increased and the phase angle decreased wth an.

increasing e/b. This is because o' the increased virtual

mass moment of inertia of the Ìfrozeh fluid.. This, in

urn, leads to a decreased,quadature component of. the tank moment amplitude with its macrnum shifted to higher frequencies. The moment amplitudè curVes are also

flatter.

3.5.

The Eff&tof the Dis.tance from Center of Roll

It cán generally be stated that the higher the tank is placed the more favourably it acts. Almost a linear .

increase f thé tank moment amplitude was discovered

with an iceasi

s/b combined with a broader

effect-ive. frequency band. An interesting result was 'fötind out

- ith the conStrictiön pieces. The increase of' the tank

moment amplitude with an. increasing s/b was not as strong with the con.tr.iction pieces as it was with a tank without

any damping. This explaine the peculiarity, that at s/b : -0.140, i.e.. the tank bottom well. below the center

of roil, the tank with constrict.idn'pieces showed better stabilising characteristics thàn an ordinary frée-surface

tank..

The tank with partially tight bulkheads acted reasonably similary with respect to the effect of s/b, although thé phase angles were nöt as much affected. The

quadrature compçnent of the tank momeìit athplitude there-fore varied linearly With s/b.

ON THE DESIGN OF .FREESURFACE TANKS

11.1. General Bernarks

When a f±'ee-su'faóe trik i considered for a vesel several aspects should be taken. into account. 'First

of all, it should be stUdied, whether the general arrangement of the ship permits the installation of a tank stäbiliser. As it has been pointed Out arlier,

the tank should be placd as high as possible. If'

this is possible frrn the general arrangement's point of view, the ÏèStion Of the stability of the ship arises. The mass 6f the tank fluid is in the range of 0.5 to 2 per cent of the shipTs displacement, so it is capable of lifting the center of gravity of the ship considerably. The free surfa.öe also reduces the rnetacentric height, consequently the stability

of the ship may become critical. The tank shoild' be

a bi'oad as possible, therefòre in most casés, the

location of: the tank is restricted to the. midship region. Also another fact speaks in favour of this: the disturbing effects of.heaving and pitching are then at their minimum.

When considering the capacity, of the tankstabiliser, the tank moment arnplitude may be compared with an

eual'moment to produce a static heel. This angle.

may be termed as tank capacity, and experience, has shown that values of about 2 degrees give satisfactory 'stabilsing performance:

p

2°

or' if water is used,

PaSirlCTlb

57.140

31

When a tanker should be stabil.isèd, . tank with

part-ially tight bi lkheads is the obvious solution.. tn this case it s.not meaningful to express the amount of whole tank fluid as a percentage of the displacement, because the cargo or the ballast òan serve as tank fluid. The

loss bI deádweight is here the dornihant factor, and the

reduced efficiency f the stabiliser by usina a high

water level may be compensated by i.engthening the tank.. However, this should not be exaggarated because too

long a tank leads to structural difficulties and great losse.s of deadweight without giving actual improvement to the behavior of the ship in waves. Therefore., the length of the tank is both a technical and an economical problem of optimisation.

Another question. to be answered when choosing a tank stabiliser for a ship is the. optimum damØing of the tank. It can be stated that a tank without any damping is

rather an exeption than a rule. Such a tank usually cuts off very well the resonance peak of the roll amplitu4e òurve but gives ari increased amplitude outside the

resonant region. This situation can be improved by proper damping. Too much damping will, of course, totally prevent

the flow ot the fluid. The amount of damping may be afected by thè Use of proper damping pieces, perforated bulkheads or br rPanging the stiffener's inside the tank. On the other hand, to avoid tòo exessive eddy making in the wing tanks of a tanker, fairing p1ate. thay have to be used. At the present state of the art, it is not possible to give accurate quanttative data about this, and therefore model tests are still needed to obtain an optimum solutioh in each individua] case.

11.2. The Dimensioning pXthe Tank

The dimensioning of the pure free-surifacé tatik is first considered and the modifications from this when

desigtiin a tahker stabiliê'r' is discUssed in the next paragraph.

It is assumed that the breadth, the height of the tank bottom above center of roll and the lehgth of the tank are determined in accordance with the philosophy of

11.1. There remains to be deterrnind the optimal hight

of the water level in the tank. At first, the natural frequency of the ship should be evaluated from (1.10.):

pwv

As well as AR0 is not 'yet known, it can be approximated with the aid of the lost metacëntric height due to thé

free surface:

-' where (14.2.)

MG

T1

'AMG =

moment of inertia Of the free surface, for a rectangular shape i. = 1b3/12.

The non-dimensional frequency parametèr can now be determined:

0 = ø

From the siñe-diagrams optimum' h/b is' now determinèd to give the quadrature component 11SiflCT best possible values at frequencies

o.7

. ...

l.25Ç20.

When h/b has been choosen, IIaCOSCT i

read.from the.

curves for

0.100 at a frequency Q

Q0. AR0

can nowbe determined from (1.6.):

1 COSCr1,

LR0=

a

0a

Pgb3l

If this differs essentially, say about more than 5 per

cent of the value given by (1L2.), the calculation. should

be repted with the new

R0.

The first or second step

usually gives sufficient accuracy.

The next step is to determine the roll response curve

for different frequencies from (1.17.).

As this is not

a linear expression with respect to

and

it has

to be solved by iteration.

The ma:ximurn amplitude of

roll is computed and cOMpared, with the 0a

0.100 which

was assumed.

If there is a difference, the calculation

should be repeated either by using a córrection from

(3.7.) or by using linear interpolation in diagrams

for

different amplitudes.

When this proôeduxe is completed, the roll spectrum

Mày

be computed from (1.18.) and the significant aip1itude

of roll from (1.20.).

This is then compared with the

significant amplitude of roll of the. unstabilised ship.

If the design is succesful, reductions thörê than 50 per

cent shouldbe achieved by the tank stabiliser.

Ït.i.s

once again pointed out that a percentàgé redtiction of

the maximum aniplitude of roll derived from

regular sea

tésts i. not a reliable criterion of the performance

of

the tank stabiliser.

case, the great amount of the stabiliser fÏuid is not a disadvantage if the cargo is used as stabiliser fluid. The more fluid in the tank, the less deadweight _{is lost} and the better is the economical result.

It is quite obvioUs, as stated before, that the tank should be designed as broad as possible. The, height

of the tank bottom from the'center of roll cannot be

freely. choosen as it is rather constant for tankers in loaded conditlbn, average values of s/b _-0.30..

.-0.35

may be used. Curves for s/b = =0.20 and' -0i0 are

introducèd, so a linear interpolation between these car'i be used.

T:he

paraîneters to be determined ar-thente ratios e/b änd (h - e)/b and the length of the tank, 1.

The test results showed that the ratio of the height of. the. tight part o.f thel bulkhead.s to the breadth of the tank, e/b, should be choosen as large as possible. This is luckyly in áccòrdance with the economicál requirements of.the tank operation. The wave in the

tank should ót hit the deck girders. Within the limits

of the classification rules, a value of e/b0.3Ô can be

räched.. With the aid of air holes in the girders and fairing plate arrangements this ratio could still be slightly increased. . .

The holes in the longitudinal bulkheads detérmined.. by t:he optimum height of th free water level and the required degree of damDing Pest stabiliing moments were obtained When the ratio (h.- e)/b was 0.05...0.07.

35

As. the height of the wave scarcely exceeded 0.03b, the height of the hoe.s is not to exceed Ó.lOb or the upper

edge of the holes shOuld not extend above the lower edge

of the side girders of the dêck. The perforation rati.o

of the perforated area should exceed 50 per cent.

Structural consideràtionS, however, bring an upper limit

to the incrésê of the perforation ratio.

The upper limit of the increase of the tank length is

detèrmined by the loss of stability due to the free

surfäcè. The length of an individual tank compartment is also limited by rules. If the stabiliser is very

long, transverse splash bulkheads iiay

beneededto prevent

distuí'bance caused by pitching. The best result in

choosing the length of the tank is obtained by computing the significant arnlitudes of roll at the desired state of the sea for different lengths of the tank. From this computation an optiuial length of th tank can be choosen

when the achieved stabiliser performance is in aP

5. EXAMPLES

5.1.

Comparison of the Free-Surface Tanks

To compare the tank with constriction piece CP III with the tank w.thout any: damping, calculations were

carried, out ör a Liberty-replacement ship, the British S.D.114 with the following principal dimensions:

Length between perpendiculars, L _1314.13 rn

Molded beam, B. 2,Q.142, rn

Depth to upperdeck .

11.7M rn

Depth to second deck .

8.69

.m

Drught at DWL,

: .

'

8.69

m

Dispiabement at 'DWL, A . 181482 ts

The tank had a length of 5.145 meters and a breadth df

.20.20

meters.

Three loading conditions were studied:.

Table ₃

The loading condition C. corresponds to the ballast

loading condition. The other two have been selected to give the ship as different natural periods as possible..

A B C

Displacement, tons . .

17575

16500

7870

Metacentric height, /m .

1.38

070

3.62

Loss of stability, A/m

. 0.21 0.22 . 0.146

Damping coefficient V0

_0.135

0.192

'0.0835

Mass moment of inertia,10/kgms2.106

113.5

_106.5

50.81.

Stiffness coefficient R0/kprn.1b6 _214.25

1.1.60

28.50

Damping coefficient N0/kgms.l06

7.06

6.66

3.18

Nàtural frequency w0/sT1 0.146

0.33

0.71

Natural period T0/'s .

13.6

19.0

8.85

The calculations were. carried out with the aid of formula (1.8.). The maxima.l wave slope was taken as 0.025. The tank was located on the double. bottori corresponding to à value of s/b -0.20. Also the effect of chöosing à higher location for the. tank corresponding to s/b 0.20 was studied in loading condition A. The results of these calculations in regular waves are presented in figures 8.. .11.

The loading condition A is studied in figure

8.

The optimal

h/b for the tank with CF III is seen, to. be about h/b 0.06 compare th the value. h/b = 0.014 of the tank without

damping. The stabiliser fluid arf'ourts are àccordingly

0.65

and 0.5 per cent of the displacement, and the maximum amplitudes of r011 14.0° and 14.2°. 1though the

tank with CF

ÏII

shows à slight àdvantage compared with the tank without damping, its ecotiomical performance is

much ithpaired by the fact that it needs about 20 per cent more stabiliser fluid than the other alternative

0a _Lo co ading nd i t co adin d i t y i on Figure 8 3.7 0.5 1.0

C)/S1

O _0.5 1.0 w/s

The favourable effect of a high 1oc.tion f the tank

i. clearly seen from figure 9, Wheré the Ôading condition A is studied with a value of s/b 0.20. Overall perormance of both tanks has been improved., the tank without damping giVes a better re1ative improvement than the tank with constriction pieces

CP.III. . . £

II

P.1 jon A I O t

__

-

(SMeLl

w

_____

_o.o;

-

1 c ond j

Si '

_k 0.5

Figure 9

The advantage Of the greatêr.darnping is to be seen in figure 10, where the loading conditiOn B is studied. The ship has now a large natural period of roll. The optimum height pf the water level has been reduced, significantly in the tank With CF III. It. istherefor

L

a.1 g . No CP ... cindi ion A s b +0. .0 _{No tank} h/b

002---006

-. ii - ..o. 08-.0.5 1.0 w/s-'

50 50 CF_III B No tan h/b 0.2 b. 4 0.6 co dit ion Lo a B No din t an

D2

Nb C h/b D.6 39

superior to the tank without darriping in this case It

is to be noted that large periods of' roll are also met when the ship is sailing in quartering seas, which case

is often the wòrs.t one with respect to ship motions. This indicates that a good average performance of' a tank stabiliser requires a proper amount of internal damping

0.5

1.0 wTs'

Figure Ï0

The ballast loading condition C in figure 11 seems to bê quite impossible tobe stabilised with any reasonable filling of the tank1 The. Water leve].s.required are so

high that theycànnot be realised in practice. This

implies that bilge keels should also be fitted, especially

if the vessel is to sail a large part of' the tne in ballast cöndition.

.5

ion Loading co CF .II1 .0.014 0.06 -. h / b 0.û ... nd i t o.:o I' N0 tank

Lt

IC No uank Loading condit Ón NO CF Pa.ble t; -Beaufort number Wind velocity, knots Significant .iave height H113,meter Significant wave length X113,meters 6 25 14 ₀ 50 7 30

70

78 o

_0.5

1.0 w/s1

Figure 11

The rolling of the ship in irregular seas was studied in loading condition A. The state of the sea was:

The heights of the water levels were choosen in accordance

dth figure

8.

The following significant amplitudes of

roll were computed:

Tablê 5

It is interesting to note that the esonánt roll mplitude

reuctions from figure

8,

regular seas, of over 50 per

cent have shrunk to about 30 per cent in irregular seas. In this case, the tank with CF III did not show

significant superiority but its relative performance would be improved with increasing periods of roll.

5.2.

The Tanker Stabiliser Performance

Optimal tank stabilisers of the free-surface and thè

per-forated bulkhead type were designed. for a

₂₀₀₀₀

_{tdw tanker} and cornparison.s were made both in regular and in. irregular

Wind velocity knots Ship without stabiliser, degrees Stabiliser with CP III degrees Stabiliser

WhOU

damping,

derees

25

512

385

395

30

_13.20

'

8»45

'

8.70

seas. _{The characteristics of the ship are:} Length between perpendiculars :

165

m

Molded beam . 22 m

Drought at full load .

.

9.5

m

H

Molded depth . 12.2 m

Displacement at full load . 26000 t

Metacen.tri.c height .

2.3

m

Sti.ffness coefficient/kpm . 60.106

Mass, moment of inertia/kgms2 205.106

Natural angular frequency . ..

o.L

e_1.

The tank was placed in a tank group in the middle portion of the ship., Longitudiràl bulkheads were used as damping bulkheads with a perforation ratio

of 50 per cent. The tank bottom was at

7.10

meter's

Lost metacentric height, 0.23M . 0.53 rn

Tank capasity static 'héel .

. 1.6

°

The calculations were cärried Out only for the full loading condition. The wave slope was 0.02.5.. he

tahk bottom was then omitted, and the same càlculations ierecarred out' for two heights of the tight part of the bulkheads. he results in regular seas are

presented in figure.l2. . . . .

loo

Tanker stabilisér

Figure .12

height over the base piane. corresponding to s/b .0.

The dimensions of thé tank were:

Lengthöf tañk, 1 . 114.14 m

Breadth of tahk, b 22.0 r

Density of tank fluid,

T 900 kg/rn3

Height of water level, h/b = 0.08

1.76

m

Mass of'ank Íluid,

_1.93

per cent of A 503 t

143

As It can be seên, the: design.with a firm tank, bottom is supèrior to the others. In this case, however, i.t should be rernembered that the tank length has been the same for

all a1ternatives namely one half òf the length o ttê tank group.

The perfórnane of the' stabilisers was also predicted in irregular seas. The state of the sea was the same as in table 14 The results ofthis study are presented in

table 6. '

Table 6

As it can be seen, the stabiliser with a bottom gives an average reduction of .roll of about 5Ò per cent. On the other hand,, only 70 pêr cent of the cargo capacity, of the tank section can be used. Wheh the bottom is omitted,

the efficiency of.the stabiliser is reducéd 10 .... 20

per cent. However, it would not produce any difficulties

to

compensate this by lengthening the tank. It is inter-estingto note, that the filling of 80 per cent did not impair the performance more than about. 10 percent

compared with the optimùm filling of 60 per cent. There-fore, stabilisers with perfOrated bulkheads should bè filled as high as posible to give the best economical performañcé. Wind velocity knots -Unstablished ship, roll degrees

Sabiliser

OttOTTI 7 io U eg ees Stabiliser with holes, e/b = 375, 80 % full, degrees Stabiliser with holes, e/b 25, 60 % full, degrees 25

906

14.82 5.27 ''. 14.87

-47%

-142%

-46%

30 18.140 '8.10 19.66 9.37

-56%

-142%

-49%'

There has been differences in opiniön, whèther bilge keels hou1d be fitted to a ship with a stabiliser or

not. To illustrate this, 0.5 meters high bilge keels

extending One half of the length of the ship wre assumed to be fitted on the tanker, and calculations

were carried out for the wind velocity of ₂₅ knots.

The resulting significant ròll angles are below:

Table ₇

The improved behavIor ofthe ship due to the bilge keels should be weighed against the ircreased resist-ance.. of the ship acting all the time., not only during

bad weather'.. It seems to be quite óbvious, that bilge keels. together wi.th a tank stabiliser is not a just-ified solution for slow vessels. When fast going passenger liners are. concerned,, the answer to thi.s problem may become different. If the bilge keels themselves substantially reduce roiling, they may give a certàin security margin for those cases, when the tank stabiliser does not act satisfactorily or even falls out for some reason. . .

No bilge keels empty tank . Bilge keels, empty tank Ño bilge keéls . full tank Bilge keels, full tank

9.06°

7.52°

.

-.

14.82°

. . - 147% . 14.320

- 53%

6 CONCLUSIONS

6.1. ummary. of _t.heResults

he results obtained at these tests are summarized in this chapter. Some problêm which are not yet satisfactorily solved are also brought up for discussion.

The damping, of the different systems had only a Small influence on the natural frequency of the tank. The

effective frequency band was affected by the damping to a cèrtain degree, and the tank moment amplitüde always

decreased with an increase in damping. At low frequencies thé decreased taflk moment amplitude due to increased

damping was compensated bi the broadér effective frequency

band leading to an improvèd performance of the tañk. So

if the ship is to sail in quartering seas from astern when

large periods Of encounter are to be expected, the internal

damping of the tank has to be detérmined to give an optimum performance to the stabiliser.

The testéd damping arrangements were perforated bulkheads and constriction pieces of different geometry. The shape of the holes in the bulkheads had no significant effect on thé tank performance. A. disadvantage of the bulkheads was the extensive éddy formatioi in the wing tanks,.

especially in the tank with partially tight bulkheads.

The actual free-Surfàce tank òan be replaced by a design with partially tight bulkheads up to a height of 25a.!30 per cent of :the breadth of the tank and f.jlledup to a

levél of 30 ... ¡40 per cent of the breadth. The efficiency of such a tank compared with an orthodox free-surface tank is reduced by about lO..20.per cent, but as this design is intéñded for tankers, no problems should arise in

competisating thi.s reduct4on of efficiency by lengthening the tank. When the cargo itself were used as stabiliser fluid, the installation of the stabiliser would not

cause any great losses of the cargo capacity. The wave phenomenon in a tank of this type reminds the bore of a free-surface tank, but it is not as sharp crested as the böre. The tank walls are therefore subjected to smaller impact forces than the walls of an.orthodox free-surface tank.

Design diagrams for thé tested stabilisers are given in this paper and the use of the diagrams is explained, Methods of predicting a ship's behavior both in regular and in irregular seas are discussed. The main idealisa-tions of this paper are: linear theory has been applied, the fluid has assumed to be non-viscous and the effects of other ship motions on the rolling have been neglected.

6.2. Comments on the esearchof Tank Stabilisers

A seriou.s problem inthe field of tank stabiliser model tests is the extensive amount of information that is gatheì'ed with numerous tested alternatives. Effort should bernade to investigate, how small changes in the tank moment curves obtained with bench tests affect the behavior of thé whole system ship and tank. It is the author's opinion, that by a clever choie'of parameters the presentation of the results could be simplified

without seriously violating the validity of the prédiction of a ship's behavior. This should however be studied

by comparing model test predictions and theqretical calculations with full scale trial data.

Thé effect of other ship motions on the performance of the stabilise' should be investigated. It is obvious that the efects of pitching and heaving can be reduced

147

by proper transverse fairing plates. Thè influence of swaying could be studied by using the theory of coupled rölling end swaying. The yawing motion could have some effect on the behavior of the tank if it were situated far away from the midship ectión.

In order to carry out these ineCtigations, some promising experience has been gathered at the. Helsinki University of Technology by the use of an analogue computer to simulate the rolling ship equipped with a:stabiliser..

Some interesting results have been btained with U-tanks

of the controlled-passive tpe. It is the intention of

the author to extend this field of research to cover the free-surface tanks as well. It is belived that in this way valuable information is gathered to direct research workers towa'dC a generalized theöry of ship motion stabilisers.

B Beam of ship

CR Center of rotation

G _{Center of gravity of ship}

H _{Depth of ship, height of wave}

H113 _{Significant wave height}

10 Mass moment of inertia of ship with added mass

L Length of ship

Metacentrjc height of ship

Roll exciting moment due to waves

M

Amplitude of M

MT Exciting moment due to tank stabiliser

4Ta Amplitude of MT

N0 _{Linear damping coefficient of ship} R0 _{Linear restoring coefficient of ship}

Ordinate of wave slope spectrum

S _{(w) Ordinate of roll spectrum}

SR (w) Ordinate of energy spectrum T0 _{Natural period of roll}

T Draft of ship

b Breadth of tank

c Celerity of wave

e Height of the tight part of the bulkheads

g Gravity constant 9.81 rn/s2

h _{Water depth in the tank measured from the bottom}

j Ship's radius of gyration

k Wave number

1 Length of tank

s _{Distance of tank bottom from center of roll}

t Time

Maximum wave slope

V CT ew

X'

0 0al/3 øác w Völume of displacement

Phase lag between fluid motion and ship Phase lag between ship and wav

Tuning factor, wavé length

Non-dimenionàl ailiplitude of tank moment N on - d im en s ion al damping öòefficient

Mass density of water

Na' density Òf tank' flUid

Roll angle Roll athplitUdè'

Significant roll amplitude Resònant rôlI amplitude

Non-dimensional angular frequency Value of at resonance

Angular freauency

Nätural angular frequency

LIST OF REFERENCES

'Levander, K. : Undersökn-ing av passiva ,stabiiiserings-tankar med olika dmpningsarrangemarig. Diploma Thesis

Work, Helsinki University of TechnOlogy, Otaniemi

_1967.

Salminên, O.: Passilviset va.imennustankit eriÏai.silla supistuskappaleilla. Diploma Thesis Work,, Helsinki

University of Technology, Otaniemi

_1967..

Bragge, T.: Eräs passiivisen vaimênnust'ankin tankki-laivasovellutus. Diploma Thesis Wörk,. Helsinki

University of Technology,

_1967.

van den Bosch, J.J. and Vugts., J.H.: Roll Damping by Free-Surface Tanks. Report no 83S, NètherÏand.s Ship Research Centre, Delft 1966.

van den Bosch, J.J. and Vugts, J.H.: Some Notes on the Perfòrmance of Free-Surface Tanks as Passive Anti-rolling Devices. Report No 119, Technological University,

Delft 19614.

van den Bosch, J.J. and de Zwaan., A.P.: Roil Damping by Free-Sürfaöe Tanks with Partially Raised Bottom..

Report No 28Ó, Teähnological University, Deift 1970.

Vossers, G.: Resistance:, Propulsion and Steering of Ships, Part C. The .echnical Publishing Company H. S.tam N.y., Haarlem

_1.962.

Nekadö, Y.:' SQme Experiments on Anti-roiling Tank for Tankers. Technical Review No 60, Hitachi Zosen News, VoI. 11, No 5, December 19.68. . .

2.0

1.5

1.0

0. .5 O

_____

pi1VAII-_IL

-'

/

le

0.5

a'102

-=

= +Ó.20

No dampng

067

DIAORAM i h b. 51

___J,.

105

1.0

0.5

=

No ap

Uah102

PaCOS Lt

a

t

0 0 DIAGRAM 2

°°

1.0

0.5

Ua/102

-

UaslflCt

---: UaCO5Ct

0.110

0m

o dam p i

DIACRAM 6

ô. lo

_

fLV

- o

. o

i .. 5

1.0

0.5

_____

o

__

u

___=

___

ììUII

a

- 1w_

55

PaCOt

= -0.20

No damping

0 = . 00

1.0.

0.5

1.5

1.0

0.5

-

u1c DIAGRAM 9

-UCOSC DIAGRAM 10

Pa/'102

asjn1c

s

0.ln

'J

0.10

Damping 2xA,b/2

.033

0.06

'u

-__

-

I

1.

+0.20

Damping 2xA,b/2

.067

2.0

1.5

1.0

0.5

0.5

o

1.0

AM 12

_{= bio}

2

e

3:

DIAGRAM 11 u

/10

a = +0.20 Damping 2xA,b/2 .100

ampig 2xA,b/2

.033 57

Pan1ct

5

1.0

0.5

n

E_ L

-

'p

_____

1M.ì1

_

\

_-i

z QQ

z _O Damping 2xA,b/2 0.10 b

A

08

__

I

' ''_

-0.5

s b Damping 2xA,b/2 0a z .100 z

_.067

UaCOSCt

1.5

1.0

0.5

DIAGRAM a/'102 14 O 0 0.02

--__ N

__4_

0A T

\

O 5

Ua5Ct

0.10

-0.20

-

_{4I...____}

Dampiig 2xA,b/2

..o67 -0.20 Damping 2xA,b/2 .100 b b = 0.10 5

- =pcoset

1.5 1.0 DIAGRAM p

/10_2

a 16

0.5

N 0.02

59 DIAGRAM 15

Pa1102

1.0

1.5

1.0

0.5

+0.20

Damping 2xC,b/2

.067

0.

5

1.5

0.

1.5

1.0

0.5

= +0.20

Damping CPIIÏ

0a

.067

s b

Damping CPIII

DIAGRAM 20 10

-

,-

ooLf

0

.067

61

_____ - Pa51t

-DIAGRAM 19

_0.10

1.0

o.

-- 002

__Í&4I

h. DIAGRAM 2].

1ahh102

DIAGRAM 22

1a/'102

-

P.aX1

PaCOt

b

-0.20

Damping, CPIII

-0.L0

Damping CPIII

.067

5

-0.10

b

A

" '

-

_0.o

DIAGRAM 2

1SflEj;

h

___

0..10

A

0 02

4I

63

-0.20

Damping CPu

.067

2

+0.20

Damping 2xB,b/2

.100

.15

-

_aCOt

1.5

1.5

1.0

0.5

-DIAGRAM 27

1-1/10_2

PaC0t

0.5

DIAGRAM 28

-0.20

Damping 2xB,b/2

0

.100

.0.12:

1.0

-0.20

Darning 2xB,b/2

.100

0.06

65

1.0

0.5

1.5

1.0

0.5

29

Ua/102

± 0.25

DIAGRAM 30

-0.20

DamDing .2x8,b/2

0_a

.i0Ô

0,375

0.5

-0.2d

Damping 2xB,b12

.100

Ua5lflCt

PaCOSCt -

aSt

0.5

1.0

1.5

'

..' O.31 DIACRAM 31 J

/10_2

a

-PCOSC;

DIAGRAk 32 U

/ i 0-'

-O.40

Damping 2xB,b12

100

0.25

-o.';o

o

Damping 2xB,b/?

.100

e

0.375

67

9

5

.5