A free surface tank as an anti-rolling device for fishing vessels

4

A Free Surface

_{as an A}

Vice for Fishing Vessels

by J. J.

vaiz den Bosch

Utilisatioii d'une citerne a carne liquide comme amortisseur de

roufls a bord des bateaux de pciie

L'auteur passe en revue divers systèmes d'amortissement du roulis pour voir s'ils satisfont aux besoins des bateaux de péche. I.e choi se porte stir une citerne constituée par un paralkIépipède rectangle, dans lequel l'énergie est fournie par un simple efTet de "mascaret".

Des equations mathématiques thCoriques de mouvement sont

formulCes pour un bâtiment roulant librernent dans un fluide, et

i'on étudie VinfJuence de divers paramétres sur Ic niouvernent.

L'équation est ensuite modifiCe pour tenir compte de linstallation a bord du bãtiinent d'une citerne simple a carCne liquide. La section qui suit est consacrée aux donnCes_{relatives a un reservoir} parallélC-pipédique et a i'effet des paramètres du reservoir sur Ic roulis.

L'auteur dCcrit une citerne concue pour un hãtiment particulier,

pour trois conditions de déplacement, et construit des courbes

théoriques qui sont comparées avec les résullats de quatre series d'essais sur modèle. Ii Ctudie les variations par rapport aux résultats théoriques, et termine en présentant diverses_suggestions.

TJHERE is no doubt that

_{many fishing vessels} would benefit from the installation of sonic means

It _{of roll damping to ease deck working conditions} and increase effective fishing time. The major types of

roll damping devicesnow in use are:

o Active fins

o Passive tanks based. on the U-tube principle

o Active tanks based on the U-tube principle

Passive free-surface tanks

This paper deals with the application of the passive free-surface tank in its simplest form.

Bilge keels are excluded from this _{discussion because} other roll damping devices are considered as supple-mentary rather than as an alternative _{to bilge keels.}

This is discussed more fully at the end of the paper. A fishing vessel's damping system should be:

o Effective even at low or zero speeds o Efficient for many conditions

o Inexpensive to install and maintain

Trouble-free in normal use

Active fins are not effective at low speed. Initial costs are relatively high.

Passive tanks based on the U-tube principle are often rather sensitive to differences in the natural roll period of the ship, and if designed to cover a wider frequency

range the overall efficiency falls.

Activated U-tanks are efficient over a wide range of

conditions. They seem _{good for large boats, but are} complicated and may be too costly for small boats.

Although passive free-surface tanks are less efficient

than activated U-tanks, they are simple to install and

perform satisfactorily in most conditions.

[159]

El tanque de balance con superficies libres corno cstabilizador para barcos de pesca

Se estudian y comparan varios tipos de estabilizadores, en orden a

los requisitos dc UflO adecuado_{para los barcos de pesca. Se elige} uii

simple tanque rectangular, de forma de caja, que aprovecha Ia energIa de Ia ola de marea. Se desarrollan _ecuaciones

teórico-matemáticas de movimiento de una embarcación que se balancea

lihrementc en un IIquido, cstudiándose el efecto de los diversos

parámetros sobre ci movimiento. La ecuación _{se modifica despuCs} para instalar en Ia emharcaciOn un simple tanque con superficies libres. La sección siguiente trata de _{los datos de un tanque}

rec-tangular y Ia intluencia de sus parãrnctros en el moviniiento de

balanceo.

Se expone Un ejemplo de diseño de_{tanque para un tipo} deter-rninado de emharcaciOn. con tres condiciones de desplazamiento, y se presentan cubiertas teOricamente calculadas, comparándolas con

cuatro series de ensayos de nodelos. Se _{discuten las variaciones}

de los resultados teóricos _{y se hacen, por ültimo, aigunas} suge-rencias.

= &siflwt

The solution of the above _{equation is expressed by:}

Ka

and:

ROLLING MOTION ACCORDING TO SIMPLIFIED TFIEORY

Roiling without tank in operation

The equation of motion. In recent years the theoretical

approach to ship motion

_{has been improved, and}

frequently a simplified mathematical model is used, such as the damped linear mass-spring system (Vossers, 1960).

For the calculation of the influence _{of the tank on the} ship's rolling motion this same method is used only considering the rolling motion. The equation of motion

is given by the expression:

I+N+R.,q=K

if the exciting moment K varies sinusoidally with time, the resulting motion would also be _{sinusoidal and of the}

same frequency. The moment, however, will always be in advance of the motion. The _{lihase angle between the} moment and the motion varies from zero, for very low

frequencies, to 1 80°, for high frequencies. If the moment is expressed by:

K = KCsin(a)t+CKO)

and the motion by:

/

\ (RI.w2)2+No2

Nco

tang CK

I

Often the amplitude is written in the form ofa

magni-fication factor, that is, the ratio of the motion amplitude at a certain frequency to the static angle of heel under influence of a heeling moment of the same magnitude. At the natural or resonance frequency:

IR

(O°

the phase angle becomes 900 and the magnification factor can become very large if the damping is relatively small.

A criterion of damping is the non-dimensional damping

coefficient:

N,

\7IR

At resonance the magnification factor amounts to:

The influence of the separate coefficients

Using the above expressions a qualitative analysis of the influence of the separate coefficients can be made:

An increase of I is accompanied by a decrease of

the natural frequency. At the

same time the magnification factor increases because of the in-fluence of I on

o An increase of R results in a shift of co towards

a larger value and also in an increase of the

magnification factor at resonance

o An increase of N results in smaller amplitudes

over the entire frequency range

These tendencies are illustrated in fig 1 Starting from

an amplitude characteristic with v0.l (a probable

15

5

Rft3INA

Fig 1. Influenceof coefficients ofequation of motion

[160]

value for rolling) and co= 1, the effect is shown ofa

doubling of one of the coefficients while the other two

remain unaltered.

Influence of the tank on rolling motion Fundamental behaviour of the tank

When a tank, partially filled with a liquid, say water, is forced to oscillate about a fixed axis, the water

move-ment creates a momove-ment acting about the same axis. When the motion of the tank is sinusoidal the_moment. appears to be mainly sinusoidal of the same frequency as the motion, with a phase lag ranging from zero to

180° depending on the frequency. The natural frequency

of the system is defined as the frequency at which _the

phase angle equals 90°.

The moment can be resolved in a component which is in phase with the motion and the quadrature coin-ponent which has a phase lag of 90° with the motion.

Expressed mathematically:

the motion is:

aS1110)t and the moment:

M =MaSfl(Wt+Cz)

= MaSin WI COS C + Ma COS Cot Sin E

The first term is the in-phase term and the second is the term with a 90° phase difference. In fig 2 the amplitude and the phase angle are shown as functions of the fre-quency, and in fig 3 the corresponding components are given. l3oth figures serve only as examples to illustrate

the tendencies. 180 -Et degrees go U Ci) sec

M3COSEt

W sec1

Fig 3. Components_oftankmoment

The equation of motion with the tank in operation

Consider the tank moment as an external moment

acting on the ship on a fore and aft axis through the centre of gravity of the ship. The equation of motion is:

I+NS+R

\Vith 4) = & sin wi this expression becomes:

/

_{- j}

M

+

M K

+

(N

co - -- sin cos cot = --- sin (cot + eK)

The reduced ui-phase component @fa/4)n)

cos e can

be considered as a reduction of RIw2. The reduced quadrature component (ilIi/4)a) sin e can he considered as an augmentation of the damping when sin r is

negative, i.e. throughout the entire frequency range

con-sidered.

Influence on amplitude characteristic

Utilizing the above, the influence of the components of

the tank moment (fig 3) can easily be combined with the curves in fig 1. Assuming that the natural frequencies of the tank and the ship differ little, it follows:

From fig 3 it appears that the in-phase component

of the tank moment is positive for frequencies below the natural frequency of the tank. For this range the amplitude characteristic of the ship. including the tank, tends to the curve on the left

in fig 1. The positive value of (Ma/4)a) cos i has

the effect that the vessel seems to have a longer natural period. (Reduction of R, or augmentation

of J.)

The quadrature component can be considerable

if compared to the ship's own damping and

because of this the reduction of the amplitude in the range around the combined natural frequency

can be very large

o For the range beyond the natural frequency of the tank the vessel obtains the character of a stiffer

ship due to the negative in-phase component

15 0 F-U Li 10 7 _{.W1T1.TANLJN.}

'

OPERTION

\

.' Fig 5 I

/

[161]

_r

0.5 L)

se'

1.5 20

Fig 4. Schematic pe,centation of tank iiiflueizce

Fig 4 shows a tentative curve of the amplitude versus frequency for the ship-pius-tank system. Notable is the

occurrence of tile two secondary peaks in tile curve. This

)

freedom, which are here the rolling of the ship, and the motion of the tank water. The flatter the phase charac-teristic of the tank, the wider the frequency_{range which} is covered by the quadrature component, and the more these two secondary peaks are smoothed.

If the natural frequency of the tank is higher than the natural roll frequency of the ship, the secondary peak in

the lower range is more accentuated, while the other one

can disappear completely.

RECTANGULAR TANK DATA

General

The free surface tank owes its damping characteristics to the development of a bore, a typical shallow water

wave. Fig 5 shows two photographs of this phenomenon

in two consecutive stages. Jt is evident that with every

roll work is done in raising the tank water, thus reducing

0020 0015 0005 0 -180 d.gr.es -50 0

the energy of motion. The theoretical natural frequency for small amplitudes can be derived as follows:

The velocity of propagation of this type of wave is:

C =\/gh

The distance travelled in one period is twice the breadth of the tank so the natural period is:

2b

=

'.,tgli

and the natural frequency is:

2ir

rr

-0)1 = - =

A series of tests shows that an increase of the amplitude

of the motion induces the actual natural frequency to

increase.

Fig 6. Non-dinien3iolzal amplitude and phase of tank Inonle/il for S/b =0

[162]

S/b=O

(i.O10

j

T

-/

'I-

_{hla' .f..}

-4 OS I0 Cs to wV7 is

O.O2 aois aoio a a - 1zo t-9

The data shown in fig 6,

7, 8 and 9 are results of

experiments with a model tank excited by an oci1lating mechanism. While the tank performed a swinging

motion the moment about the axis of rotation was

measured. In fig 6 and 7 the phase and the reduced moment amplitude are shown versus the reduced fre-quency c'/h/g and in fig 8 and 9 the sine and cosine components are given. The amplitude is made

non-dimensional by dividing by p1gb3 1.

Influence of parameters

There are six parameters which control the tank moment: The motion amplitude

11 & increases the moment amplitude does not increase at the same rate and so the tank is less

effective when the motions are large

[163 1

o The influence of the frequency of the motion co is evident from fig 6, 7, 8 and 9

The tank breadth b

The moment amplitude varies with the third

power of the tank breadth provided that the ratio of the water depth and the breadth is kept con-stant; (the breadth is measured across the ship)

o The tank length 1

The moment is directly proportional to the tank length (measured in fore and aft direction) o The water depth Ii

As is shown, the natural tank frequency depends on the breadth and the water depth. in addition to this influence on the phase relation, the depth of the water influences the total weight and

there-fore the moment

o The height of position s

The vertical height of the position of the tank is F2

s/b=O.20

of b.

\

_-

4

4

-r Os to t5 as to wV is

U

U Fig 8. Non-dimensional components of tank moment for S/b=0

measured from the axis of rotation to the tank bottom. A negative value means that the tank bottom is situated below the axis of rotation A comparison of fIg 6 and 7 or $ and 9 indicates that a more highly situated tank produces a larger

stabilizing moment

Considerations for application

The presented data can he used for ships with

values ranging from 0.03 to 0.18 B

The static reduction of GAi due to the free sur-face of the tank must be acceptable. The loss of static stability can demand a restriction of the tank dimensions. The reduction of GM, should not be taken into account while the ship's own

natural period is being calculated

@ A roll damping tank should, if possible, extend over the full breadth of the vessel because of the large influence of the breadth on the moment

amplitude

o The tank should be situated as high as possible

[164]

s/b= 020

Fig 9. Non-dimensional components of tank mnonzent for S1b = 0.20

o From experience it is known that the minimum depth of the tank should be approximately three times the water depth in the tank. This influences

the position of the tank in height. As a preliminary estimation for the tank depth the value D _{2 GAI} can be used

o The data which are shown in fig 6, 7, 8 and 9 are results of measurements with çf= 0.10 radians or about 6°. The calculation of the influence of the

tank on the rolling motion is based on the assumed

linearity of the system. When the results are

interpreted, it has to be borne in mind that this assumption is not strictly true

The diversity of conditions imder which a vessel has to fulfil its task makes it very difficult to

suggest an optimal design for the anti-rolling tank, and for that reason a compromise has to he found.

EXAIPLE OF APPLICATION

Ship and tank data

As an example the design of an anti-rolling tank for a

small trawler is discussed. The

_{7i/B values of this}

s/b=0

---Lt

S/b=-0.20

-I

4

Ii

\\

_'ii-i'

---//i ---

'-'

--t

()

ship are fairly high in order to comply with Rahola's stability criteria. Such a vessel, operating on the North

Sea or in comparable areas, often meets conditions which may cause it to roll heavily.

The main dimensions are: Loa=91.87 ft (28.00 m) Lpp=78.42 ft (23.90 m)

B =20.28 ft (6.18 m)

D = 11.36 ft (3.46 m)

From a variety of possibilities three tentative loading conditions were selected for further investigation. The

conditions are summarized in table 1.

TABLE 1: Considered loading conditions

The "fishing condition" (B in the table) was rather extreme. For the calculation of GM it was assumed that the consumption of fuel and stores was about 22 tons, that the fish hold contained about 15 tons catch and that

a new catch weighing about 30 tons lay on deck.

The values ofM, for the conditions A and C satisfied the criteria of Rahola, also if the reduction of GM due

to the free surface in the tank was accounted for.

The position of the tank was chosen approximately amidships taking up part of the bunker space between the engine room and the fish hold. It extended over the

full breadth of the vessel, so b=B=20.28 ft (6.18 m). The

length of the tank was restricted to 4.40 ft (1.34 m) in accordance with the mentioned values and the criteria of Rahola. The values of s/b in table 1 show

rounded-off values following from an assumed height of

the tank 6.56 ft (2.00 m) above the base line.

Determination of water depth and discussion of the tank

effect

The choice of depth of water in the tank is governed by the requirements of easy operation. it is important that the captain of a small fishing vessel is not burdened by such matters as adjusting the water level in the tank to the momentary value. Once it is filled to its pre-scribed level in port it should be unnecessary to give it

any attention, except in emergencies.

In fig 10 the curves of/2a sin e, and ia cos are given

for the vertical tank position s/b= -0.150. These curves

Were obtained by interpolation from the diagrams in the

figures. Although the ratio s/b varies slightly for the three loading conditions, the mean value was sufficient

15 10 n 10 5 -2 -2 1.0 x 13 - 1a NE l5aCt sE 0.5 x 10 sfb=-0 150 0.10

Fig 10. Components of tank inoineizt

CONDITION A

h/bOO8

9

WITH TANK EMPT

WtTBJA1JK IN OPERATION Conaition Quantity A Leaving port B .E'uring fishing C A verage of other conditions 4 tons (ton) 161.4 (164) 184.1 (187) 172.2 (175) GM ft (m) 2.75 (0.84) 1.87 (0.57) 2.36 (0.72) GM _{0.136 0.092 0.117} B K=O-4 B ft (rn) 8.11 (2.46) 8.11 (2.46) 8.11 (2.46) Tsec 5.39 6.55 5.83 c sec' 1.165 0.960 1.079 0.07 0.07 0.07 KG ft (m). 9.12 (2.78) 9.97 (3.04) 9.55 (2.91) s/b --0.125 -0.175 -0.150 0 0.5 10 1.5 20 C.) sec Fig 11. Results of calculation

to determine the desired water depth for all conditions. The appropriate quantities for these conditions are listed

in table 2.

The reduced frequency wv"b/g corresponding to the natural frequency of the ship with an empty

tank

165]

-0,lxlO

p

P 0 or tL 10 z 0 I-or 0 Li z 0 or 5 0 CONDITION B

WITH TANK EMPTY

,WIIH..IANKIN

hA0.08

_,1

OPERATION

0.5 1.0 15

L) Secl

The water depth ratio (h/b)th which was derived

from the consideration that the theoretical

natural frequency of the tank and the ship should

be equal

The water depth (/iJb)0 which was derived from fig 10 giving the largest sine component of the

moment at the stated reduced frequency

Evidently, as table 2 shows, the water depth for which

the largest damping effect at a given frequency was obtained, was somewhat larger than the theoretical value. To comply with the demand for simplicity, one value of h/h must be chosen. In order to make a correct choice, the effect of the tank on the amplitude charac-teristic was calculated for all three loading conditions, for their respective s/b ratios and for two water depths,

namely h/b=O.06 and h/h == 0.08. The tank was assumed to be filled with fresh water.

TABLE 2: Reduced natural frequencies of the ship and water-depth

ratios under consideration Condition

h/b 0.06

L_L_L I _LL.L_ I

20

The actual calculation is omitted from the paper. The

results are shown in fig 11, 12 and 1 3. Fig 11 represents

condition A. It was evident that with both depths the [166J 15 5 CONDITION C YIITH.JANK E1PTY 0 05 Jb0008 WITh TANIcJri QRERAJ ION 0O6 1.0 1.5 C.) sec 20

tank gave considerable damping. Although the peak

amplitudes of both curves were approximately equal, the largest water depth was to be preferred because, with the

peak occurring at a lower value of w, the accelerations of the vessel will be less. In fig 12 the results of the calculation are shown for condition B. In this condition the vessel was less stiff. The natural frequency of the ship was considerably lower than that of the tank for /i/b=0.OS, which accounted for a marked peak in the

lower frequency range. Although the curve for /z/b=0.08

was certainly an improvement in comparison with the original characteristic, the aniplitude characteristic for

h/b=0.06 was better. For the third condition fig 13 shows

a result which was somewhere between the other two

conditions as was to be anticipated.

The main conclusion from these figures was that, in spite of the different water depths in the tank and the different loading conditions, the calculated amplitude

characteristics were all very similar and all show a rather

large improvement over the amplitude characteristics of the ship without the tank operating. A sound choice was li/b = 0 07, which gave a water depth of h= 0.07 x 20.28

= 1 42 ft (0.433 m). The total amount of water was Lxbxh= 126.71 ft3 (3.586 m3). This was about 2 per

cent of the average displacement.

MODEL EXPERIIENTS

Purpose and performance

The large number of simplifications which had been introduced in the course of the calculation procedure

required checking. Item lb U)

/-A 0.925 B 0.762 C 0.856 Ag (/z'b)h 0.087 0.059 0.074 (h/b)0 0.094 0.070 0.082

Fig 12. Results ofcalculatioiz Fig 13. Results ofcalculation

The tests were carried out with a 1 : 1 5 scale ship

model in which a roll oscillator and a recording gyro-scope had been installed. In this model a tank was installed with dimensions according to those mentioned previously. Next, the model was ballasted and trimmed so its stability and natural roll period corresponded to

the condition A specified in table 1. By means of the roll

oscillator the model was subjected to a moment with a

sufficiently constant amplitude having any desired

frequency within the considered range. The gyroscope served to measure the roll angles.

The following test series were carried _{out with the} model with the tank empty, then filled to the level

corresponding with li/b = 0.08:

An oscillation test with the model subjected _to roll moments with a constant amplitude of 0.289 lb.ft (004 kg.m) but with different frequencies The object was firstly to determine an acceptable

value of v, for the ship with empty tank (the value

of i'=0.07 which was introduced in table

1), and secondly, to furnish a comparison with the

calculated curve for the stabilized ship

o A similar test but with a larger moment amplitude,

namely, M0=0.434 lh.ft (0.06 kg.m). The aim of this was to obtain an impression of the degree of the non-linearity of the system, both with and without the tank in operation

o The third series consisted of experiments in

regular waves. The model was held at zero for-ward speed and the waves on the beam, butwas

free to roll, drift and heave. The wave dimensions

and roll

angles were measured. From these measurements the ratio between the rolling amplitude and the wave slope amplitude has been calculated as a function of the frequency [a/k(W)]

The purpose of this

test series was twofold. Firstly, it should provide a comparison with the results of the oscillation tests and with the cal-culation from which it could be determined if the motions of drift and heave did have a significant influence on the performance of the stabilized ship. Secondly, these measurements should form

the basis for comparison with the results obtained in an irregular wave pattern

o The object of the fourth series was the measure-ment and analysis of the model rolling motion

with zero forward sl)eed in irregular beam seas. A

check on the correctness of the mathematical assumptions in this particular case was provided by a comparison between the experimentally

determined spectrum of the rolling motion and the

spectrum calculated from both the results of tests

in regular waves and the measured spectrum of the

waves

The results

In fig 14 the results of the first series of tests are shown.

The measured and calculated amplitude characteristics

for the ship without the tank closely resemble each other.

The curves with the tank in operation differ. The cal-culated curve appears to be a mean of the experimental

curve. The curve of measured roll amplitudes, presented

[167] 15 cc 0 U U-10 5 15 CONDITION A CALCULATED CURVE FOhLb0 1YtItLiTM4k EMPTY fLEXPERIMZNT WLTK MO289f1tbs. JLCAL CLLA I ED ACCORtIN T. LINE.AR 4. EQUATION OF lMQT ION IANKJt OPERATION E.X.PERIMENT WITH Ma

-

0299ft.tbs N 05 10 i15 20 (ii sec.

Fig 14. Results of oscillation tests compared with calculated cuimes

CONDITION A ALCULATED CVE FOR hLb0.08 LW1TJ±IANKMPLY \E XP EM EN I WITH I _MQ289ftWS 0

12.

EXFEfJ11ENLWJIH Mz0.434ftjbs. (a)mx 16.1.

1-\\

\j

I TANK IN [OPERATION EXPERIMENT WITH.: MQ2.8i.tt1bs. Ma043Left. Lbs. 0 0.5 1.0_{W sec 11.5} 20

Fig 15. Results of oscillation tests for different moment amplitudes in dimensionless form, shows two pronounced secondary

peaks. The reason for this discrepancy is the

non-linearity of the tank moment. The dimensionless pre-sentation obscures the fact that the measured values

were all considerably lower than the 0.1 radians (570) which was the basis of the calculation. For such small amplitudes the curve of e versus the frequency is much

steeper than for an amplitude of

_{0.1 radians, which}

results in a greater damping in the neighbourhood of the tank's natural frequency and _{a less damping}

else-where. These differences _{are not of practical importance} as the measured values are small.

In fig 15 the results for the largest moment amplitudes

are shown. The amplitude characteristic _{for the ship} without the tank is lower than _{in the previous case,} indicating that the damping _{coefficient increases with} in-creasing amplitude. The _{curve for the stabilized ship} shows the same tendency as has been described in the

-15 5 - çALc'JLATEO 1AGNFICATION -fACTORfQft b/bQ.O8 0 0.5 ItQDELWJTkE TANXMPJY amax2i0 OPERAT)ON \SURED \ALUES 10 U) sec

Fig 16. Results of tests in regular_it'ares

former section hut to a lesser degree. _{For the larger} (but still small) rolling angles, the measured values for the largest moment amplitudes show the least deviation

from the calculated curve.

In fig 1 6 the results of the tests in regular waves are

given. Tile non-dimensional roll amplitude curve for

the unstabilized ship seems to be shifted somewhat when

compared with the previously _{deterniined amplitude} characteristics, and the peak is _{considerably reduced.} This last point is undoubtedly partly due to tile larger rolling angles, for the deck entered the water; and probably there is also a decrease of the wave moment due to the orbital motion mentioned _earlier.

It is possible that part of this

_{larger damping and}

probably the slight shift of the curve are caused by the coupling of the rolling motion and other motions; i.e. sway and heave. This, however, is _{not yet clear. Tn any} case, this appears to be of no practical _{significance as is} shown by the good _{agreement between the measured}

20

[ 168)

and the originally calculated values, for tile stabilized

ship.

Before considering tile next figures some quantities have to be defined. The roll angles _{in regular waves are} given as ratios to the_{wave slope. Therefore, the spectral} density of the irregular wave pattern is presented by_a

wave slope spectrum which is defined by:

S(w) do) E

S:(W) dco

g

-The average value of the highest

_{third part of tile}

observed amplitudes of a random fluctuating quantity, say the roll angle, is often called the _significant

ampli-240 80 0 COND!TION A EXCLUSIVE TANK, 4 S,MEAURED

ii

05 -t cALcjJLA.T.Ep J FROMRESPONSE WAYES Il -fi \ A \xSkck \ 1.5 20 sec.

Fig .17. comparison of calculated and measured roll speclra,for the

s/zip alone

tude. Tile significant roil amplitude_{can be regarded as a}

measure of the impression the amplitude of the rolling motion makes on the observer. For _{a stationary time} series and a spectrum of small width tills quantitycan be calculated from the expression:

Pa1/3 2s/io

where:

?flo = JS(w)dw

0

In fig 17 the wave slope spectrum is shown with _two roil spectra, one measured, one calculated from the experimental results in regular waves with the tank not operational. The agreement is

_{good, as regards the}

significant roll amplitudes and the frequency range.

In fig 18 the spectra for the model with the tank in

operation are shown. One spectrum is measured, another

COND!flON A

LCALCVLALED

1 11AGNiF1CAiiLQN

(

is calculated from the results in regular waves, and a

third is calculated from the originally computed response shown in fig 14. The agreement is good.

A comparison of the significant roll angles for the

stabilized and the unstabihized ship reveals that an overall reduction of 50 per cent is achieved in this wave spectrum.

20 160 -x (.0 c '-I) 80 C0NDJT!0N A INCLUSIVE TANK. s,,cAcvj.ArEDfiwNi R$fQ1tE L TO R UA8W1E _a i/3-4-LLY''/ CQMftUTED AME1JTJDE HARACTEPISTJC

///

<' /_-'

/

a :656° S,J1EASURE

_±i:

0 05 10 1.1 U) sec:1

Fig 18. Gomparison of calculated and measured roll spectra for the S//ij) lilt/i tank

SUGGESTIONS Bilge keels

As has been mentioned, the omission of bilge keels is

not advised. There are two reasons for this. The first and most important is that there can be emergency situations

(i.e. icing up) when it will be necessary to empty the tank because of its negative influence on tile statical stability. If no bilge keels are fitted it will leave the ship

with extrenlely low roll damping.

The other reason is that the non-linear effect of the

tank is somewhat neutralized by tile bilge keels. When the

motion amplitudes become large because of bad sea conditions tile tank moment is not so effective. The damping of bilge keels, on tile contrary, increases

con-siderably with increasing motions. Dimensioning the tank

In the foregoing pages little is said about the amount of water a roll damping tank of this type should contain. In this case it was about 2 per cent of the displacement which is certainly not an insignificant amount. An. overall reduction of 50 per cent was achieved but it depends on the sea conditions what this reduction will

he. it is dependent on many factors, which roll amplitudes 2.0

[169]

and roll accelerations are found acceptable. and it is very difficult to define a basic criterion. The ultimate

answer can only be found by experience. It15tile author's

opinion that it does not pay to economize too much on

tile dimensions of the anti-rolling tank, especially ifone

has a free hand during the design stage of the vessel.

Posilion of the tank

If an anti-rolling tank is wanted, one has to provide space for it where it will work efficiently, and the same remarks hold as for tile dimensioning of the tank.

Obstructions in the tank

It is not always possible to avoid placing stiffeners in

the tank side. if the obstruction is snlall, say the stiffener

height is not more than about 10 per cent of the tank length, the influence, as has been shown by tests, is not

serious.

CONCLUSION

A free surface tank of the type presented here, that isa

rectangular tank with flush front and rear bulkheads and bottom, can provide an efficient means of roil damping. its simplicity of installation, ease of maintellance and

reliability nlakes it especially attractive for small vessels. Nomenclature

b Breadth of the tank measured athwartships

D Depth of the tank

f

Magnification factor

Magnification factor at the natural frequency of

roll

Ii Depth of water in tile tank measured from the

water surface at rest to the bottom of the tank

J,

Virtual mass moment of inertia of roll

k Virtual radius of gyration of roll

/ Length of the tank measured in fore and aft

direction

Al Moment produced by the anti-rolling tank M Moment amplitude produced by tile anti-rolling

tank

in

The integral of the roll spectrum over the

frequency from zero to infinity

Damping coefficient of roiling

R Stiffness coefficient of rolling S1(w) Spectral density of wave slope

S4,(w) Spectral density of roll

s Vertical distance of the axis of rotation to tile bottom of the anti-rolling tank

T1 _{Theoretical natural period of the water motion} in the anti-rolling tank

Phase angle between the rolling motion and the tank moment

&113 Significant roll amplitude Non-dimensional lank moment

Pa Non-dimensional tank moment amplitude

Non-dimensional damping coefficient of roll

w1 _{Theoretical natural frequency}

_{of the water}

motion in tile tank

c

V

U)

4(e)

11h1

lid

.A

II, !II__

II!iIlh

_JIL'L'L

0

-I

B

L1L

II

$

I,

A

15

2xJ0

L.0 _-1 1,5

sec

FIGURE 1.

INFLUENCE OF COEFFICIENTS

_{OF EaUATION}

W sec

FIGURE 2.

AMPLITUDE AND PHASE OF TANK MOMENT.

I

180

Ct

degrees

15

0

I-U

LI-10

z

0

U

U-z

CD

5

1

0

0

0,5

_{_11,0} (.4)

sec

FIGURE 4.

1,5

SCHEMATIC PRESENTATION OF TANK INFLUENCE.

Il

ii

Il

If

Il

I _I

'1

I

II

i

WITHOIJJT

I

LIANK

I I 1 I

I

'I

/

I

\

\

WITH TANK IN

//

ION

\

%PER

--2

1.4 x 10

-2

1.OxlO

-.L SINC

a

t

+L COSE

a

_t

-2

0.5x10

0

0.25

0.5

Wj

FIGURE 10.

COMPONENTS OF TANK MOMENT.

-s/b -0.150

(t)a0'0

-

Ia

C OS C

h'bO.lO

= =

".7

A,

...b/b=O.1O

-

4

SINC

t

..0Q6.0.08

I I I I - I I

0.75

1.0

15

1

0

0.5

1.0 1.5

Ci sec

FIGURE 11.

RESULTS OF CALCULATION.

2.0

CONDITION 1

WITH TANK EMPTY

h/b-0.08

WITH TANK IN

_{P ER A I I 0 N}

i

I I I

h/b= 0.06

I I I I I I ct:

0

C-) 1<

IL

10

z

0

I-1<

(J

IL

z

CD

I

I

5

15

4-0

I-U

LL

10

z

0

F-U

LL

z

0

15

1

0.5

1.0 1.5

L) sec

FIGURE 12.

RESULTS OF CALCULATION.

2.0

CONDITION 2

311TH TANK EMPTY

h/b-008

WITH TANK IN

OPERATION

I I I I

h/b =0.06

,

15

'4-1

0

_2.0

CONDITION 3

..WITH TANK EMPTY

h/b0.08

I I

WITH TANK iN

OPERATION

I I I

0.06

I I I I I I I I L_.._____i 0.5 1.0 1.5

sec

FIGURE 13.

RESULTS OF CALCULATION.

A

5

0

I-C-) LL 10

z

0

I-0

U-z

CD

15

10

z

0

F-U

Li

z

CD

I

I

5

1

0

0.5 1.0 1 1.5

W sec.

FIGURE 14. RESULTS OF OSCILLATION TESTS

COMPARED WITH CALCULATED CURVES.

2.0

CONDITION

-1

VITH TANK EMPTY

EXPER MENT WITH

I

M0.289ft.Lbs.

CALCULATED

ACCORDING

TO

-/

_\

110

EÜUATION OF

MOTION

CALCULATED CURVE

I I I

AJK

IN

FOR h/b0.08

I

OP-RATION

-I I I I

PERIMENT

ITH Ma

-.O.289ft.Lbs.

I I I I I I I I I

15

4-0

U

10

I

5

1

CONDITION

-1

tWITH TANK EMPTY

\\I\EXPERIMENT

WITH

\I

\

I\Mo2e9ftlbs

1-amax.

EXPERAMENT

12.3°

WITH

M -0434ft.lbs.

I I

a)max.16.1°

-CALCULATED CURVE

\

\/

I I

TANK IN

A .OPERATION

FOR h/b0.08

EXPERFMENT

-

/

/

-

,i

I I I I I I I I

WiTH:

,

1=s.2:ft.lbs.

\\

I I I

M0.434ft.

lbs.

. 0.5 1.0 CL)

sec15

2.0

FIGURE 15. RESULTS OF OSCILLATION TESTS

FOR DIFFERENT MOMENT AMPLITUDES.

0

0.5

1.0

1 1.5

(5*4)

sec

FIGURE 16.

RESULTS OF TESTS IN REGULAR WAVES.

2.0

CONDITION 1

I I

CALCULATED

I'

it

I 'i

MAGNIFICATION

FACTOR

i

it

/

/

I.

I

/ IS

I

I I I i I . I

MODEL WITH

TANK EMPTY

a)max.210°

TANK IN

CALCULATED

MAGNIFIC1ATION

5\

I

OPERATION

FACTOR FOR h/b0.08'

'V

'

,:

-I I I I

\MEASURED

VALUES

-I I I

15

a10

ka

I

5

1

240

C-) a) (I) (44 a) ci)

L

0)

a)

160

80

0

0.5

1.0 1 1.5 Li)

sec.

-2.0

FIGURE 17. COMPARISON OF CALCULATED AND

MEASURED ROLL SPECTRA FOR THE SHIP ALONE.

CONDITION

EXCLUSIVE

1.

TANK.

I /

CALCULATED

FROM RESPONSE

TO REGULAR

I

WAVES

ai/313.28

SMEASURED

I I I / I I

4OxSkk

ait.1372°

I I I I

/

I

/

I I

-

I

I

I

I

I

I I I I I,'

\.

_\

I I

2L0

e

cD

e

I

80

FIGURE 18.COMPARISON OF CALCULATED AND

MEASURED ROLL SPECTRA FOR THE SHIP WITH

_TANK.

CONDITION

INCLUSIVE

1.

TANK.

-.

S,CALCULATED

TO REGULAR

FR'i

S,J"1EASUR'

_a1/3&84

ONSE

WA VS

_°a1/366'

S ØCALCULAT a FsM

I

CMPUTED AMPLIT DE

\

CHARACTERISTIC

/

656°

0.5 1.0 1.5

2.0

It)

sec

-

KtaSIN Ct

)

KtaCOSCt

U)

s/b =0

h/b=0.04

a°0333

0.50

0.25

s/b=0

h/b=0.04

(

a0.10

a0.0667

7

0.25

0.50

0.75

1.00

1.00

0.75

1OLa

0.50

0.25

180

degrees

90

s/b=0

h/b =0.04

0.25

0.50

/

h

a0.10

a

=0.0333

075

1.00

0.25

0.50

0.75

1.00

2.0

1.6

w

z

ml.2

x

cs.J

D

0.8

01+

7

0.75

1.00

w\/b/g

1.25

s/b=0.10

0.10

_h/b=0.08

h/b=0.06

h/b=0Q1.

'I

,=0.87m

(JJ

0.75 W

=0.87m

V

DESIGN COND.

_=1.30

_{6 m}

0

0.25

0.50

1.6

01.

0

0.4

0.8

0.50

0.75

1.00

w\/b/g

1.25

s/b

= 0.10 0.10

/

-h/b=0.08

h/b=0.0.

=,4

-'h/b

Co cDII CD (-)

31

e-3

Lii

t.

c

0

31

TI

3

0

z

°E

ZD

(Ii"

wix

00

0.25

0

SHIP

TA N K

1'MEASURED

OSC.TEST

I

WITHOUTCALCULATED

=0.06

9-I I I

/

/

MEASURED

OSC.TEST

JTANK

SHIP

WITH

I

_\v=o.o69

CALCULATED

\\

0

0.25

0.50

0.75

1.00

1.25

wVB/j

0.75

1.00

W\JB/g

1.25

I'

I'

F

I

SHIP

TANK

MEASURED

[OSC.TEST

WITHOUTCALCULATE

4w)-

Ij

I

/

I

MEASURED

_1SHIP

JTANK

v=vIw)

I

IOSC.TESTWITH

_CALCULA

0

0.25

0.50

0.25

0.50

0.75

1.00

WB/g

1.25

E

I'l

SHIP WITHOUT

TANK

3697

SCALCULATED

I I

FROM OSC.TEST

I I I

_I

I I / I I

S1MEASURED

I

I

I

lOxS

/

28

24

lOXSk

20

16

12

8

4

U

0.25

0.50

0.75

1.00

W\[B/g

1.25

[c

SHIP WITHOUT

TANK

I J

IA

SCALCULATED

FROM OSC.TEST

SMEASURED

I____

lOxSk_

0.75

1.1.00

wV-

1.25

SHIP WITH TANK

lOxSk

SPECTR.1

S,MEAS URED

,SCALCULATED

1"

FROM OSC.TEST

0

0.25

0.50

tLi

0.75

1.00

WVB/g

1.25

SHIP WITH TANK

lOxS

SPECTR.2

ScI, MEASURED