A consideration of model ship correlation of wake fraction

(1)

HITACHI ZOSEN TECHNICAL REPORT

by Sudo

Tanirnoto

February, 1968

NO.3

A Consideration of Model-Ship

Correlation on Wake Fraction

HITACHI ZOSEN

TECkNICAL RESEARCH LABORATORY: OSAKA, JAPAN.

(2)

A Consideration of Model-Ship Correlation no Wake Fraction

By Shoichi SUDO(Menther), Takaaki TANIMOTO (Member)

125'J

(3)

U.D.C. 532. 5. 011 629. 12. 011 629. 121. 56

A Consideration of Model-Ship Correlation on Wake Fraction S. Sudo, T. Tanimoto

H.Z.T.R. No. 3, February 1968, 9pp

6 tables, 3 illustrations

This paper studies wake data of large tankers arranged in order depending on

a statistical method of analysis; this study is preparatory to investigations into

model-ship correlation on wake fraction.

An accurate correction for the scale effect, between models and ships, on wake fraction is a subject of practical and scientific importance. Wide scatter of wake data which have been so far assembled makes us confused when

con-sidering model ship correlation. Accordingly, the character of the scatter was

examined first, and great efforts were exerted to eliminate sources of systematic

errors. The data thus put in order were analyzed by the Product Formula on

the basis of several parameters which represent the characteristics of hull form and hull-psopeller interaction.

The form parameters finally adopted are as follows.

Cs : Aftbody block coefficient.

Lg/B : Ratio of length of run to breadth. Lg/d Ratio of length of run to draught.

(4)

..

.

--

-

-w.,

- - .

--..-r.rr-rr.fl

r-.-.r--

- fD Area ratio of immersed midship section to propeller disk. vt'8/D Ratio of 2/3 power of displacement to square of propeller diameter. The analytical results are presented in the formulae. i -w,a= (CBA)2°28 X X (LR/d)°-55° X (Ag/f D X i -w = (CB.4Y°-981 X X (Ln/d)a x (Ag/

f

D) -o.00 X (v2'3/D2)0-155 For practical purposes the following formula has been derived from above- mentioned formulae for the model-ship correlation. 1 -to./1-ws (CBA) 1.04S (LR/B)o.4tS x (LR/d0-'6 < (Ag!

f

D x Moreover, this is simplified as follows for convenience in the approximate use. 1-w/ i we (CBA2 \

(5)

A Consideration of Model-Ship Correlation on Wake Fraction'

By Shoichi SUDO** (Member), Takaaki TANIMOTO** (Member) Summary

This paper studies wake data of large tankers arranged in order depending on a statistical method of analysis; this study is preparatory to investigations into

model-ship correlation on wake fraction.

An accurate correction for the scale effect, between models and ships, on wake fracJon is a subject of praclical and scientific importance. Wide scatter of wake data

which have been so far assembled makes us confused when considering model-ship cor-relation. Accordingly, the character of the scatter was examined first, and great

efforts were exerted to eliminate sources of systematic errors. The data thus put in

order were analyzed by the Product Formula on the basis of several parameters which represent the characteristics of hull form and hull-propeller interaction.

The form parameters finally adopted are as follows.

CBA Aft body block coefficient.

L5/B Ratio of lengih of run to breadth.

LR/d : Ratio of length of run to draught.

Area ratio of immersed midship section to propeller disk.

2/°/D2 : Ratio of 2/3 power of displacement to quare of proeller diameter.

The analytical results are presented in the formulae.

i -w,, =(Cn42°2 X (Le/B)O486 X (La/d)°550X (_4H/D2 )_o.107 X (2/3/D2 )0.aso i -w=(Ca.e)°.951 X (L,/B)0.06t X (LR/d)-°'44 X (Aa/ D2 )_O.029 X (2I3/D2 )5.135

For practical purposes, the following formula has been derived from above-mentioned formulae for the model-ship correlation.

i -m/ i -w,,, = (CBA)'°42 X (LR/B)°425 X (Le/d)0446 X (Aa/ )O. o7sx (2/3/.D2 )_D.052

Moreover, this is simplified as follows for convenience in the approximate use.

i-w/ iw,,,,=(C8A2 xB/d)0.415

I. Introduction

It is well known that the wake fraction of

a model is greater than that of the ship

because of the scale effect. In the case of

ordinary seagoing cargo vessie, however, the

scale effect is so small that the wake

fraction of a model is directly applied to the ship design in the usual way. It is because a

little low pitch ratios of ships' propeller are

* _{Presented at the Associated Meeting of Three}

Societies of Naval Architects of Japan, May

lO, 1967

* Technical Research Laboratory, Hitachi Shipbuilding and Engineering Co. Ltd.

7

-preferably used by taking the wake fraction somewhat great; their main engines are thus

in the safe side when the increase of resistance due to wind and waves at sea, and fouling of

hull and propeller are considered.

In the case of large tankers, the ecale effect on wake fraction becomes considerably great. Model results are to be corrected when

they are applied to actual ship design,

otherwise some mistakes, such as

underesti-mation of required power or an excess of

propeller revolutions will result. An accurate

(6)

fraction, therefore, is a subject of practical

and scientific importance. Many investiga-tions and theoretical studies have been conduc

ted, but pure theoretical studies are not yet

satisfactory for practical application. It is

anticipated that any practical conclusions

should finally depend on the comparison of

model and ship results.

Wake data which have been assembled up

to date are widely scattered, and it is very difficult to put them in order. In the case of

model-ship correlation factors, as 1-m/1-w,..

usually used, the scatter of the values of the

factors is specially great. Generally speaking,

even no principle of arranging the data in order exists at present. The most common way of finding a conclusion is to draw an

assumed mean line based on some theoretical

consideration in this scatter('). There must

be some reasons for the scattering, but

studies into these reasons seem to have been

neglected until now. In this paper, the state

of the scat ter was carefully examined, and a

statistical method of arranging the data in order was taken. The study is preparatory to investigations into the scale effect of the

wake fraction.

2. Concerning scatter of wake data

2.1 Character of the wake data

Data in this paper were taken from trial results of ships which were built by Hitachi

Shipbuilding & Engineering Co. Ltd., and

the results of the model experiments.

Let the character of the wake data be

considered first.

Values of the model wake fraction were

obtained from the results of self-propulsion tests conducted all in the same method in the

Mejiro Model Basin of Ship Research Institute,

the Ministry of Transportation. Accordingly,

the scatter of the model results is supposed only due to accidental errors. Values of the ship wake fraction were obtained from analytical results of sea trials of the ships;

8---if1

the results are those which are correted for wind and tidal current, assuming still water

and no wind conditions. The corrected results

correspond to the model results in tank.

Terefore, it can be said that the scatter of the ship data is also caused only by

acci-dental errors.

In all cases of arranging any kind of data in

order, errors contained in the data should be

only accidental ones. Especially in the case of

the wake data, this is essential because their

scatter is great and how to put them in

order is a main problem. Systematic errors

possibly contained in the data should be eliminated first of all, and consideration should begin with examination into sources which cause the scatter.

2.2 Scatter in various load conditions

Ships in the full load condition are

com-paratively in simple conditions for this study,

as they have the designed draught of even

keel and displacement. It is rather easy to

consider the effect of hull form on wake fraction

on the basis of some ordinary parameters like

coefficient of fineness. Whereas, ships have

random displacements, draughts and trims in

ballast conditions. Therefore, there seem to

be many unknown factors in the influence of hull form on wake fraction, relation between hull and propeller, and flow around the stern.

In the present state mentioned above, it is difficult to know whether the excess scatter

is due to arranging the data improperly or due

to errors, as data come from various condi-tions from the full load to the ballast condition. Moreover, there are a number of

cases in which model and ship were tested in conditions different each other. The difference

of test conditions between model and ship must be a source of the scatter.

At first, results of the full load conditions alone are taken up into the study, excluding those of the ballast conditions.

2.3 Separate considerations of model and ship each

(7)

the Reynolds Number, and this fact certainly

causes the scale effect between model and ship. When the results of model or ship are considered separately, the region of the Reynolds Number when tested is confined

within certain limits respectively. The

variance of the Reynolds Number in each case of models or ships can be considered

negligible in comparison with the difference between all the Reynolds Number of models and those of ships.

It is understood that the wake fraction does not substantially vary with speed in this case;

one value of wake fraction was adopted for one model or ship. According to the most usual way, the _{average values} of wake

fraction in the speed range corresponding to

that of ship trials were adopted at first.

These values were plotted as shown in Fig. I

on the basis of displacement-length ratio of aftbody VA/() one of the most typical form

parameters. The scatter of the plots is pretty

great, and it

suggests the importance of

selecting parameters for the basis of the

analysis. I - W .7 .6 .5 .7 _{¡ - w} .6 .5 20 25 30

f

Fig. 1. Results of wake fraction.

9-3. Numerical analysis

3.1 Principle of analysis

Values of the wake fraction are affected by various factors, not to speak of the Reynolds

Number. In other words, the values are represented

in the form of a

function of

several variables. Now, let factors which

affect the values of the wake fraction be

xi, x,

and z,,, and the following relation

is given.

lw=f(x, z2

x)

(i)

The determination of the function is actually

difficult, so the values of (1 w) have been

represented in diagrams on the basis of some parameters. In the case of

diagram-represen-tation, the selection of appropriate parame-ters is a trouble, as can be realized in Fig L

Nowadays, electronic computers have come

into use in daily works, and it becomes

possible to determine the form of the function, even when a number of parameters are taken

in the function. Thereby, the effect of each

parameter on the wake fraction is easily

judged. The method of so-called Product

Formula is suitable for this kind of analysis. Accordingly, Eq. (i) can be changed in

practice as follows

1w=x

.3:42 _xn' (2)

Then we have,

log (1w) =ailog xi+a2log z2+

+a,,logxn (3)

Eq. (3) is linear with respect log z (i= 1

2, n), and it is rather simple in

mathematical treatment. Moreover, the

coefficient ai indicates the effect of each parameter on the waka fraction. It can be

said that Eqs. (2) and (3) are appropriate to wake analysis.

Actual values, from the data, of the

parameters xi and wake fraction w are used in Eq. (3). When the number of the data

is the same as

that of the parameters, the coefficient al can be apparently determined. However, in this study, the number of the data is greater than that of the parameters,

(8)

as in usual cases, and values of the coefficient a cannot be definitely determined only their mean values can be obtained by the method of least squares. Especially in the case of

wake data containing various errors, the use

of the method of least squares is rather desirable. In this case, it is necessary that the selection of parameters is appropriateand

data are as many as possible.

3.2 Selection of parameters 3.2.1 In relation to hull form In the case of wake behind a flat plate,

the result much depends upon the Reynolds

Number, and secondly upon the edge effect,

effect of aspect ratio. Concerning flows around

three dimensional bodies like ship hulls,

pressure gradient along the bodiesis consi-dered to play a main role in the growth of the

boundary layer. The effect of the Reynolds

Number greatly differs according to ship

form it is better to forget the Reynolds

Number in this case. Therefore, the effect

of the Reynolds Numder was disregarded, as mentioned in Sec. 2.3, by considering model

or ship separately. That is to say, the

inclination of hull surface to the directionof motion is most important, and it has relation

to fullness of hull, ratios of hull dimensions

and so on. Block coeffient Ca, length-breadth ratio LIB, breadth-draught ratio Bld, longitudinal position of center of buoyancy

¿GB, etc. are suitable for the factors. In

the case of large tanker hulls with long

parallel body, actual results have shown that

the change of bow shape has no marked

influence on the wake fraction. Accordingly,

it is sufficient only to consider the charac-teristics of after half body. The parameter

ICB is thus eliminated, and aftbody block

coeffierit CSA is introduced instead ofCa.

Strictly speaking, the shape along stream lines is important. The data now under

consideration belong to the ordinary

single-screw form of tanker, and the difference of

shape of frame lines, and other minor differences are thought insignificant the coefficient of fullness and ratios of hull

di 10 di

-mensions are sufficient for this study.

3.2.2 In relation to working

propeller

What is discussed here is effective wake

fraction, and it should be considered in

connection with the working propeller.

Im-portant factors relating to the propeller are

the amount of thick wake region occupied by

propeller disk, propeller load factor and so

on. Ratio of the height of shaft center

from the bottom of a ship to draught Hid, area ratio of immersed midship section to

2

propeller disk Ag/ -i-D- , ratio of power of

displacement to square of propeller diameter

Vu/3/D, etc. closely relate to the

above-mentioned important factors. Longitudinal

position of propeller, rake angle of shaft center line and some other factors were taken

up, but they do not much affect the values of wake fraction for the same reason as the

forgoing paramelers of hull form ; they are disregarded in this study.

3.2.3 Basis of selection of parameters

In Eq. (2), if the selection of the

parame-ters is appropriate, the coefficient a will

have a trend which can be reasonably

illustrated according to theoretical expla-nation or experimental results. In addition,

it is considered that the still remaining scatter is caused by accidental errors and

wrong arrangement of the data. Accordingly,

it can be aassumed that

the better the

selection of the parameters is, the smaller

the scatter becomes.

The data were obtained from 15 models

and 43 ships (actually 15 ship-forms

corres-ponding to the models, as there are sister

ships). The study is in an experimental

stage, and the effect of each parameter or

the order of errors is still unknown. Moreover, the number of the data obtained is not great enough. In this study,

parame-ters simultaneously taken in each calculation

were limited to five or less in order to avoid confusion, and the calculations were tried

(9)

with various combinations of various parame-ters. The values of thrust deduction fraction

are closely related with the wake fraction,

and similar calculations were carried out also

on the thrust deduction fraction. A few examples of the results of the calculations

are shown in the following paragraph.

3.3 Results of calculations (i) CßA, LIB, Bld, H/d, VZ/3/D

The following five parameters were used

as they are most common in practical use. Aftbody block coefficient. A general index of aftbody mass directly

affect-ing the wake, and pressure gradient

along the aftbody.

L/B: Length-breadth ratio, an index of

inclination of aftbody water line to the center line.

Bld : Breadth-draught ratio, indicating the rate of effect of bottom and side of

a ship, and the effect of the free

surface on the wake.

Hid : if = height of the shaft center line from the bottom of a ship. Indicating

the rate of linear amount occupied by propeller diameter in vertical direction

and the effect of the surface on pro-peller.

y = displacement volume, D=propeller diameter. An index of propeller load factors.

The results of the calculations are as follows. i w = (CBA)-°.436x(L/B)°'27 x(B/d)-O.584 x (H/d)0.106 x (y2/3/D)-O099 i w = (CB4)O.961 x (L/B)°a x (B/d)-°'86 x (JTI/d)0.897 x (.2/3/D)O.343 i t = (C84)O.O8O x(L/B)0.054 x (B/d)-°.1'4 x (JI/d)o.139 x (y2I3/D)-0.019

In Eqs. (4), the power indices of V2!3/D

have the opposite sign for model (1 w,)

and ship (1 we). In addition,

results of many experiments have shown that the values of (1 t) decrease as the coefficient

of fullness increases, but the power index of

UBA in the formula (1 t) has the positive sign. These facts suggest that the selection

of the parameters is not proper.

The standard deviations and distributions of the results of the models or ships on the

basis of mean values obtained by Eqs. (4) are

in the table.

Table i . Standard deviation and distribution by Eqs. (4).

(2) Cn.i, LIB, Lid, Aa/.-D2,

Lid : Length-draught ratio, adopted in

place of Bld. A general index of the inclination of aftbody buttock lines to the level. It is supposed that the

effect of Bld could be separated and

taken into LIB and Lid.

Area ratio of immersed midship sec-tion to propeller disk, adopted in place of Jf,/d. This parameter places

em-phasis on the degree of effect of thick

wake region on the propeller. The

effect of propeller immersion, repre-sented by lf/d, is indirectly included

in this parameter.

The results are shown in the formulae.

i w = (CBA)-118x (L/B)°.59° x (Lld)0.563 x (A/D2)-0045x(v2/3/D)_O.134

i w = (UBA)O.322 x(LIB)°4°9 x(LId)_O.214 x(Ag/D0.113 x(V2/3/D2)0238

= (CBA)-O.532x(LIB)-O.129x(L,fd)o.014

X (Aa/D)0084 X (V2/3/D)O.0O2

In Eqs. (5), the power indices of CBA and have the opposite sign for model and ship. Values of the wake fraction will increase as the coefficient of fullness

in-creases, and the power index of CBA has the

posiLive sign in the formula (1 we), which cannot be reasonably illustrated. When

(5)

Standard

deviationbelow 4% dey,No. of data below 3% dey.No. of data

iw

0.023 (4.3%) 79% 0.021 (3.5%) 83% 76% 0.026

-

(3.3%) 77% (4)

i t

(10)

large part of a propeller is working in the

thick wake region, or A/D2 is great, the

value of the wake fraction should be great; the trend of the power index of is

hard to explain properly. The selection of the

pa rameters in this case must be also

im-proper.

Though some questions still remain about

the character of the power indices as men-tioned above, the standard deviations and

distributions were also examined, and the

results are obtained as follows.

Table 2 . Standard deviation and distribution

by Eqs. (5).

(6)

12-Values of the wake fraction will become greater as CHA increases or LB/B decreases;

their indices have the negative sign or the positive sign respectively. Flow around a ship with great CB and small LIB seems to

be rather two-dimensional, and Ln/d is not so significant as LB/B concerning the flow gradient. The effects of flat bottom and free surface are more important, and the wake

fraction will become great when the draught

is comparatively small, or LR/d is great; its power index must be in the negative sign. Moreover, it is a proper trend that the effect

of parameters having relations with the

Reynolds Number, except v2/3/D, is greater

in the case of models than in the case of

ships.

Standard deviations and distributions based on Eqs. (6) are shown in the following table.

Table 3 . Standard deviation and distribution by Eqs. (6)

(4) C'BA, LR/r. Áw/D2. v213/D2

Ln/r: r=Aa/U, where U is girth length

of immersed midship section. Namely,

r is the so-called hydraulic radius. In Eqs. (6), as mentioned before, the

power indices of Ln/B and LR/d were in the opposite sign each other. Flow phenomenon was deduced from these

facts, but its reason could not be cleared. The parameter LR/r was

adopted in place of Ln/B and LR/d in order to synthesize their effects in

a factor, and to make clear

the general trend.

The recuits of the calculations are shown

in the formulae. Standard deviation No. of data below 4% dey, No. of data below 3% dey.

i

W» _(3.4%)0.0 18 87% 73% 0.020

-

(3.3%) 86% 79% 0.017 (2.2%) 100% 86% Standard

deviationbelow 4% dey.No. of data

No. of data delow 3% dey.

1w,,'

_(34%)0.018 80% 73%

iw,

0.021 (35%) 86% 76%

1 -

0.015 (1.9%) 100% 86% (3) CBA, LB/B, Ls/d, Ac/-D2, V2/3/D2

Ln/B: Ratio of length of run to breadth,

adopted in place of LIB which roughly

represents the inclination of aftbody water line. This definitely represents

the inclination of run water line to the center line.

LR/d : Ratio of length of run to draught, adopted in place of L/d in the similar

reason mentioned above.

The results of the calculations are shown

in the formulae.

i w, =

(CBA)2.023 X (LR/B)04 X (L/d)-O.590 x (A / _D2 )-0107 x (?2/3/D2)O.O83

i

Ws = (CBA)-Q981X(LI/B)0°6' X(L,/d)-0.1 x (A/_D2)-0029 X

(vzì/D2)-1 t

= (CBA)0.247X(LR/B)0.126X (LR/d)0060 x(Â/_D2)0056 x(v2/3/.DZ)-O.126

The power indices of the same parameters

in the equations for model and ship have the

same sign, and they seem to have a reasonable trend.

(11)

i -w,,= (CDA)3.631X(LR/r)-°.379

x(A/_D2 )_O.213x(v2f3/D2)_O.O&9

i -w, =

X (A/ D2 )_O.073x(v/3/D2)_O.017

1 - t =

(CB4)°.509X(LR/r)°°9°

X (A/ ...D2)O.004 _{X (72/3/D} )_O.046

The power indices of the same parameters

in these equations have the same sign in

both cases of model and ship, and they are considered reasonable, just like the case of

Eqs. (6). The index of LR/r has the negative

sign, and it suggests that LR/r affects the

wake fraction as something like the effect

of aspect ratio rather than as the effect of the inclination of water lines or buttock

lines. This fact was also presumed from Eqs.

(4), in which the effect of B/cl is much

greater than that of LIB. Thus, the reason-ing about the effects of LR/B and LR/d on wake fraction in the preceeding paragraph

has been ascertained.

The standard deviations and distributions are shown in the following table.

Table 4. Standard deviation and

distribution by Eqs. (7).

(7)

3.4 Examination of the results of

calculations

Calculations with various combinations of

the parameters were carried out, and the

standard deviations from the mean values

based on Eqs. (5)-(7) are 3.3-3.5%, or about

0.02 in absolute value. The distributions in all cases are similar each other. Regarding

the extent of the scatter of the data, there

is no remarkable difference among the

vari-ous combinations of the parameters. For the results of model self-propulsion tests and

ship speed trials, it is inevitable and granted

to include 2-3 % errors ; this extent of the

scatter might be unavoidable.

13

-It is essential that the character of such

a function is easily understandable, and Eqs.

(6) and (7) are appropriate as explained before. It is considered expedient for the

examina-tion of wake character to use Ln/B and .Ln/d

separately. Thus, Eqs. (6) have been finally

adopted in the study.

Differentiating Eqs. (6) with respect to an optional parameter, the variation of wake fraction produced by unit variation of the

parameter can be found. As an example, when

a typical large tanker recently built is

picked up, her actual values of the parameters are as follows:

CBArO.775, La/B=2.448, Ls/d=6.788

A5t/.D2i5.15, v2/3/D2=49.46

When these values of the parameters are increased by 1% one by one, the variation of the wake fraction in each case is shown in the table.

Table 5. Variation of wake fraction produced

by unit variation of the parameters.

As shown in Table 5, the wake variation

based on USA is greatest when each parameter

varíes at the same rate. In other words, the effect of Us. is most important, and is followed by the effect of La/B and Lp/d.

The parameters, however, take random values

independent of each other, so the maximum and minimum values of each parameter in the data are shown in Table 6.

Effects of A/.D2 and V2/3/D2 on wake fraction are comparatively small, but these

parameters vary most widely, for the tankers

are nowadays getting larger and larger. Accordingly, if such data are put in order Standard

deviationbelow 3% dey.No. of data below 3% dey.No. of data

i _(4.2%)0.021 80% 67% w _{(3 5%)}0,021 _81% 71%

-

0.0 14 (1.8%) 100% 86% xi Models Ships Ax (6w/Oxi). GsA 1. 2753 0.0096 0.7458 0.0056 LR/B -0.0946 -0.0023 -0.0142 -0.0003 LR/d 0.0414 0.0028 0.0122 0.0008 0.0034 0. 0005 0.0011 0. 0002 ID 0.0008 0.0004 0.0016 0.0008

(12)

Table 6. Upper and lower limits of each

parameter.

disregarding the effects of Aa/D2 and V2/3/D2, it will become the source of the

scatter.

For purpose of reference, two model ships

having the greatest Cs and the smallest LIB

were taken up from systematical models

tested by the 61st. Research Committee of the Japan Shipbuilding Research Association,

and the results of the calculations based on Eqs. (6) were compared with the results of

the experiments on the two models.

Ex. 1 Model A (Cs=0.84, L/B=6.0, B,/d= 2.76) CSA=0.808, La/B=1.800, Ls,'d=4.968, Az/iD2=14.92, v2/3/D2= 48.75 1 w,,(calculatjon)=0.431 - 1 w(experiment)=0. 395

Ex. 2 Model B (Ci=0.22, LIB=5.5,

B/d=3.06)

CRÁ=0.794, LR/B=1.980, LR/d=6.058,

A/.D2=16.58, v2'3/D2= 52.18

1 w,,(calculation)=0.409 1 w,(experiment)=0.380

In both cases, the calculated values are higher than the results of experiments by

about 0.03 in absolute value.

4. Practical method of

model-ship correlation

In this manner, the wake data are widely scattered, and it is difficult at present to

draw final conclusions on the model-ship correlation. A practical and reliable method

of correlating model and ship, however, has been urgently required, and an attempt has been made to obtain a practical formula on

the problem.

14

-A model-ship correlation factor in the form of i w,,1 J. w,,, can he obtained directly from

Eq. (6).

j w,,1 I w,,=(CBA)'°42 X(L/B)-0425

x (L5/d)0446 X (_4/--D2 )O.078 X 2I3ID2 )_O.052

(s)

The data used to derive this equation were obtained from all kinds of tankers built

after World War II, that is, from D.W.

20,000 t tankers to super-large tankers

re-cently built; the values of Ae/2D2 and y213! D2

are in the wide range as mentioned before, but the values of the parameters will have

not much difference when the application of

the formula is limited only to such

super-large tankers to be built in near future.

The effects of these parameters seem to be small in Eq. (8), and they can he made constants by giving representative values. Then, Eq.(8) becomes a function of CBA,

LR/B and L5/d.

The power indices of L5/B and LR/d are nearly equal in absolute value, and have the opposite sign. Moreover, they are nearly

half of the power index of USA. For practical

purposes, an approximation is permissible; thus, Eq. (8) will be approximately

trans-formed into the following practical formula.

1 w/ 1 W=K(CBA2 XB/d)' (9)

As standard values for super-large tankers

to be built in the present and near future,

it is determined

that Ae1/D2=16, and

y2Ì3/D7=55, and the other parameters are varied in the range as follows:

CBA=0.72-0.80, Ls/B=1.8-2.6,

L/d= 5.5-7.5

Calculations based on Eq. (8) were carried Out in various combinations of the parameters

as mentioned before. The results of the calculations were plotted on the abscissa of (CBA2XB/d) as shown in Fig.2. The figure shows that the plots came close together in

a narrow zone, and the results can he

represented by a simple curve for an

approxi-C, La/B L5/d A/D2 V213/D2 Max. value 0.777 2.979 7.757 18.70 58.96

Min. value 0.732 2.265 6.036 7.62 25.48 Max./Min. 1.061 1.315 1.285 2.454 2.314

(13)

1.03 102 1.01 LOO 099 0.98

Fig. 2 Model-ship correlation factor.

5a55.5f taedrd 52111e

1.5 20

Fig. 3. Correction cofficients for

and V2'3/D2

mate use. When the values of AN/D2 and

2/3/D cannot he used due to deviation from

the standard ones, correction factors for the deviation are given in Fig. 3.

In actual cases, the value of v213!!)2 becomes

great when that of AR/--D2 is great, and

their power indices have the opposite sign there is an actual relation that the product

of the fourth and fifth terms in Eq. (8) is

always nearly equal to 1.0. For example, the

products or 10 of the 15 ship-forms, which

were actually analyzed, have values from 0.99 to 1.01, and maximum and minimum of the 15 values are 1.015 and 0.986 respectively.

Accordingly, putting )V= i in Eq. (9), the

power index p is determinable from Fig. 2. It was finally found from the values

calcu-lated by Eq. (8) that Eq. () substituting 0.415

for the index p can approximate the zone in

Fig.2. Thus;

1 ws! 1 -w,s=(CEA2 xB/d)0.415 o)

In Fig. 2, the actual results of the ships

examined are additionally plotted.

5. Conclusion

In order to investigate the model-ship

15

-correlation on wake fraction, the scatter of the wake data was examined, and the data

were put in order in the first place. It is

important for investigations into wake

phenomena to select appropriate form para-meters which arrange the wake data in order, because the effect of hull form or

hull-pro-peller interaction is more important than

that of the Reynolds Number when

consi-dering the model-ship correlation. The most important form parameters affecting the wake fraction are USA, LR/B and L5/d, followed

by

A/D2 and V2/3/D2.

In the separate

consideration of model or ship, the mean valuse of ( 1. w) have been able to be deter-mined by empirical formulae based on the form parameters mentioned above. Furthermore, a model-ship correlation factor in the form

of

1 w/ i w,, has been presented in an

approximate formula for practical use. The appropriate selection of form parameters proposed in this paper will be useful in future

studies. Especially in the relation between model and ship, it is an interesting fact that the effect of LIB, which has usually

been thought important, disppears ; it

sug-gests that the effect of the Reynolds Number

among models or ships is not so important as the effect of hull form, as discussed in the beginnig of this paper.

This study will be extented to ballast

conditions, and finally intends to establish a

general rule which is applicable to all the loaded conditions of both model and ship,

simultaneously taking the effects of the

Reynolds Number and hull form into

consi-derat ion.

Reference (for example)

K. Taniguchi Model Ship Correlation Mothod

in the Mitsubishi Experimental Tank, Jour. of the Socioty of Naval Archiocts of Japan No. 113

Reporta of the 41st. Research Committee and tho 61st. Research Committee of the Japan Shipbuil-ding Research Association.

(14)

71J

_1___*

Some Experiments on Anti-rolling Tank for Tankers

By Yukiharu NEKADO (ilfember)

This paper deals with comparative tests on the performance of an anti-rolling

tank of the modified "Flume" type when a large oil-tanker is equipped with it. The purpose of the tests is to get good design data of the tank.

The stabilizing action of the tank is derived from remarkable dissipation of energy. The dissipation is caused by the nozzle effect of holes in the longitudinal bulkhead, when the liquid in the tank oscillates through the bulkhead holes according to rolling. When this type of anti-rolling tank is installed on a tanker, one or two cargo tanks of the tanker are utilized for the purpose.

For the tests an anti-rolling tank model with two bulkheads was used and many

kinds of bulkheads were prepared for change.

The tank model was tested on a "Navipendulum", a rolling simulator and its angle

was recorded over an assigned frequency range.

As the results of the tests, two cases are successful for roll damping : one is a bulkhead with many small holes, and the other is a bulkhead with a vertical weir. Their frequency response curves show that the roll magnification factor becomes nearly constant and it is around 2.5. Some other cases are thought relatively good. Their response curves show that the magnification factor is relatively low and its peak value is about 3.0, while in the unstabilized condition it shows a much greater

value at resonance.

It is concluded that the ratio area of opening in the bulkhead/area of the bulkhead is 0.20-024 for effective damping.

The liquid level is also an important parameter and its most effective height is