Model ship correlation method in the Mitsubishi Experimental Tank

December 1963

Mitsubishi Shipbuilding & Engineering Co., Ltd.

Tokyo Japan

bth.

y.

Tch&

_Hogaschoo

Defft

MITSUBISHI TECHNICAL BULLETIN

MITSUBISHI TECHNICAL

BULLETIN MT&O1O1 2R

Model-Ship Correlation Method

in the Mitsubishi Experimental Tank

By

Kaname Taniguchi, Dr. Eng.

A paper presented at the Spring Meeting of

UDC 692. 12. 07. 001. 2: 533. 6. 07 Mitsubish;

1. Introduction

[t is not an easy matter to make a precise predic-tion of performance of an actual ship from the model

tests. Indeed, the higher the requirement of accuracy

of prediction is. the more the difficulty is. This difficulty

comes mainly from the lack of our knowledge of the scale effects on the resistance, propulsion factors and the characteristics of the propeller. The method for

correcting these scale effects, the so-called model-ship

correlation method is one of the most important pro-blems for our tank people.

It has been an ever hot

problem in the International Towing Tank Conference.

At the present stage of our knowledge. it is not possible to make a reliable prediction of performance of an actual ship from the model test results and the

pure theory only. We have to rely upon the actual ship data and to use the empirical correlation factors which

are analyzed from those actual ship data. Therefore.

it is essential to gather the reliable data of such

analy-sis as many as possible, in order to develop a reliable

model-ship correlation method.

The Mitsubishi Experimental Tank belongs to a shipyard. one of the most powerful shipyards in the world, and has been testing directly every new ship which was built in the shipyard with the large scale

model (7 meter as standard). SHP and the related data on the sea trials of these ships have also been measured by the experienced staff of our Experimental Tank. So

we are in the most favourable situation to investigate

the model-ship correlation problem.

The necessary conditions for a good model-ship cor-relation method are as follows:

The accuracy and reliability are sufficient for

the severe practical use.

The assumptions involved in the method are

reasonable and do not conflict with the theory. The method must be simple enough to he used in the routine works, and must be applicable to any type of ships, such as a high-speed planing

boat.

The method must be flexible to allow a necessary

improvement or modification in accordance with the development of our knowledge of the scale

effect.

Model-Ship Correlation Method

in the Mitsubishi Experimental Tank

Kaname Taniguchi*

The model-ship correlation method which is developed and used in the Mitsubishi Experimental Tank is presented. From the ship trial anal ,j.'is, two correlation factors, i.e. the so-called roughness allowance factor and a wake correction factor are analyzed. The analyzed data of these correlation factors are given for more than 50 vessels of

miscellaneous kinds. The power estimation of an actual vessel using these correlation

factors is the reverse process of the trial analysis. The detailed explanations of the

whole system of this method are given.

Strictly speaking, the method of model-ship

correla-tion involves so many complicated factors in details. that there are many, as many methods as the number of experimental tanks in the world. And the

interna-tional unification of the method is hoped eagerly.

Though our model-ship correlation method is not

perfect, it satisfies practically all the above conditions

and has been used satisfactorily for long years. The author presents this paper, hoping it will be of any service to the concerned circles and that he will be given some useful suggestions as to the further

im-provement of this method.

2. Model Test

Model test is perfoi'med with a large scale model, 7 meters in length as standard. Test procedure is con-formed to the I.T.T.C.A1B0C1 methods. i.e. the resis-tance test and the corresponding self-propulsion test are

carried out on the same day. As for a single-screw

ship, these tests are performed with full appendages bilge keels and rudder), but for multiple-screw ship

the resistance tests are performed both with and with-out appendages. The propeller open-tests are performed

immediately prior to the self-propulsion tests for the propeller to be used, at two kinds of revolutions. The

one corresponds to the standard Reynolds' number )R

=4.5 x l0) for standard use and the other corresponds

to the rated RPM of the ship. The latter characteristics

are used for the analysis of the self-propulsion tests.

There are, however, usually not so much differences in these two characteristics at two kinds of revolutions.

Resistance tests are extended to the low Froude

number as low as 0.1. from which Hughes' form factor K is also analyzed. The mean Reynolds number at 0.1 Froude number is approximately (5-7) x 10e.

From the resistance tests with and without

appen-dages (for multiple-screw ship), we analyze the total

appendage resistance coefficient. It is defined as follows: Total appendage resistance coefficient, c50

where,

.JR=(Resistance with all appi

(Resistance without app.)

F=Total wetted area of the appendages,

integrat-ing the girth length along ship length (not

along the water line).

Ass,sfarit Director of Laboratory & Chief, Experiniental Tank, Mitsubishi Shipbuilding & Engineering Co., Ltd., Dr. Eng.

Model-Ship Correlation Method in the Mitssthishi Experimental Tank 3 2 8 u-7 s

04

3 2 lo lo 3 2 4 5 6 7 8 910 3 4 5 6 7 8 91O V JF/2 V 2

Fig. I Examples of plotting of against

3 4

5678910

Fig. 2 Plotting of Cap,, against lLucy Ahtonl

2 3 3 4 5 6 7 8 910' 4 5 67 8910 I 'L...."

/

Quadruple-screw car-ferrY

-

' 's / High

\

Appendages: -speed torpedo-boat & triple rudders shafts,shaft-bkr

-- "

---Sub- chaser AppTripie

- -

_{shafts,Shaft-bkt.'} & rudders

u

Ad

-Twin- screw App: : shafts. soner dome destroyer shaft-bkt, rudders 0.455 /(log,R,)1

lii

W &

9-Model 12-Model 20-Model 2-Model

0.25

/

0.3 A

___

16' -Model / 1 0' -Model Actual ship 0.15

L

E

N1

UI.

0.455/(l0&,R)'' Lucy Ashton (Shaft-Bossing Series) 5 4 3 2 u-a ca o lo g 8 7 6 5

and the corresponding Reynolds' num'r. F!2 ¡.

c,pp

is plotted on the basis of R

and the general

trend of C against Rnapp conforms to that of usual friction line against R. From these plottings we analyze

the resistance ratio (corresponds to Hughes' r and

apply the same resistance ratio to ship calculation at

the corresponding of ship and Froude number. Fig. i shows an example of this plotting and Fig. 2

shows the similar plottings for the Lucy Ashton's

ex-periments2 including the actual ship's data.

From these figures. the validity of our practice to

calculate appendage resistance may be allowed. As for the self-propulsion test, we usually conduct

the test at the ship point of propulsion. In this case

the resistance coefficient of ship is calculated from the following formula:

C1= 0.490/(logi:Rn)258 = (1 + 0.0770) X 0.455/(log1oR (238 and the appropriate skin friction correction is applied.

But in a special case, e.g. in the case of high speed planing boat and of the self-propulsion test in waves. we conduct the test at the model point of propulsion.

From the self-propulsion test, we analyze the self-pro-pulsion factors by the thrust identity method using the above stated open-characteristics of the propeller at the

Reynolds' number corresponding to the ship's rated RPM. It is a generally recognized fact that the self-propulsion factors are practically independent of the

propeller loading within the practical limit. We calcu-late the DHP of ship from the residual resistance coef-ficient. propeller characteristics and the self-propulsion

factors with appropriate correlation factors as shown later and do not calculate directly from the DHP of model by the mechanical scaling up. Therefore, the propeller loading is not a substantial problem for us.

i.e.

in our self-propulsion test it is not a matter of

substantial importance for us which friction line is to

be used or how much the roughness correction is.

In the case of ship whose propeller is expected to

suffer severe cavitation, we conduct also the cavitation test for her model propeller and measure the cavitation characteristics in the homogeneous flow.

We use usually a current-meter to get a more

rea-sonable relative speed to water. The current-meter is

positioned in the centerline plane of model, one ship's length forward of F.P. of model and at 150mm below the water surface. It is 120mm in diameter and two-bladed windmill type, supported by one jewel bearing and one plastic bearing and its number of revolution is counted electronically without any geai' friction.

The wake velocity measured in the test jun is

ap-proximately +1° of the velocity of previous measuring

run.

3. Ship Trial Analysis

Sea trials are performed carefully in accordance

with the trial code almost same as that of the 41st

Re-search Committee3 of the Shipbuilding Research

As-sociation of Japan. The effects of the wind and tidal current are corrected to the tank test condition by the J.T.T.C.method' . This method. however, fails in the

case of athwartships wind,

then we use

a more

rigorous method5 of correction, taking the effect of small speed difference in the up and down runs into

consideration.

The torque of the propeller shaft is measured with a precision torsion-meter (electric type6 or optical type),

however, the rigidity of the propeller shaft is not usual-ly measured. We have already many such data. i.e. the

modulus of rigidity of 36 intermediate shafts were

measured by Dr. Togino and he got°

G=(8.31±0.081) X 10' kg/cmi.

We use this mean value, i.e. G=8.3lxlOSkg/cm2.

(Ap-I)efldix 1)

Zero line of the torque measurement is determined

as the mean of the both readings of the torsion-meter in the dead slow rotation of shaft in normal and

op-posite directions. From this measurement the stern

tube friction may be estimated, but we do not use this

value to estimate DITIP/SHP. because the stern tube friction at the normal running condition may not be

same as that at the dead slow turning condition. From thus measured and cori'ected data. we make a ship trial analysis as shown in Table I. In this

analy-sis, the assumptions as for the negligibleness of the

scale effect on the following items are made: relative rotative efficiency

thrust deduction factor propeller characteristics

residual or wave resistance coefficient

In Table I, in the step (4). we take e,=0.98 as standard.

irrespective of the value of' stern tube friction above

mentioned. However, it may be more reasonable to

deduce the constant torque loss corresponding to ap-proximately 2% of the normal rated torque.

In the

step (7). we calculate torque coefficient corresponding to

the open-condition in accordance with the thrust identity system. The propeller open-characteristics used in the

step 8) and (9) are derived from our standard propeller Table I. SHIP TRIAL ANALYSIS

vo N SHP K50

J

K, ws e fpv2V C. Cr C15' C1 log,0vLWL MIB 01012R DECEMBER 1963

measured and corrected for tidal

currents and wind

DHP DHP=e, x SHP/ (no. of propellers,

standard e, = 0.98

24668 DHP

R5 K5=

D5

from propulsion experiments

K00 = er,a X K5 = (6) X (5)

from propeller open-characteristics,

using 7 lw,=30.866 D 1 _-wm

e=-

_1w,

-T T=2.9028x 105D'N2K, x (no. of pro-pellers tm R0 R0 (1 - t01)T

R,0 R,,, =R, - (allowance for added air

resistance)

JN

3

(l5

(16

from reaistance experiments (17)(l8)

(19)x

Model-Ship Correlation Method in the Mitsubishi Experimental Tank charts R06=4.5x 10) with the appropriate correction

for area ratio, boss ratio and blade thickness ratio. We have found from our long experiences that the

much better consistency of the ship trial analysis can

be obtained by the use of the above mentioned charac-teristics than by the use of the individual

open-charac-teristics of the propeller used in the self-propulsion

tests.

In the step (15), we make the correction for the added air resistance (in still air) corresponding to the

difference of the still air resistance between the actual ship and the model.

From the ship trial analysis, we get two correlation factors, i.e. e9 (step 11)) and cj, (step (20)). The former

is the empirical correction factor for the scale effect on the wake and the latter is the similar factor for the

so-called roughness correction.

The steps (18)-(20) may be modified to follow Hughes'

method9 and of course, we may modify the step (20) to get 4e1 (roughness allowance) instead of c,.

In this analysis, the assumption of the negligible-ness of scale effects on e,, t, and C,. (or c,0.) is allowed practically. i.e. the scale effects on these factors are not

so much if any. And the K5-K0 relation of the

pro-peller suffers much less from the scale effects than the

-0.2 0. 8 0. 6

o

X 0.4 E 0,2 "0

r

'-vo

1 0.4 0.5 N, B.

Mean value line Mean value- standard deviation zone 0.5 06 0.7 0.8 019 10

0. 6 0. 7 0. 8

(All welded, commercial anti-fouling paint. Numbers indicate ship correlated)

0. 9 1.0

1.1 1.2 1.3 14 15

Reynolds no. R,=VL0./a X 10

case of K5-J or K5-J relations. Therefore, the analyzed

c,, (or 4c1) has a pretty clear physical meaning and universality, though it contains all the residuals from

the experimental errors and the assumptions made. But the wake correction factor, e9 (step (11)) suffers directly

from the scale effect on the K5-J relation. Therefore,

it depends upon the R0k of the propeller charts used and the Reynolds' number on which the model wake

fraction w,0 is measured.

It is essential to check carefully the propeller chart and w,0, in the case of utilizing the similar correlation factors from the different experimental tank or of com-paring such data from the different sources.

Figs. 3-6 show such analyzed results for about

50 single-screw ships built recently in our shipyards. These vessels are all welded and painted with usual

commercial antifouling paint.

In our trial analysis method, the problem as to which friction line is adopted as reference is not of substantial

importance. We use at present Prandtl-Schlichting's

formula. However, it is not difficult to convert the

re-sults into those corresponding to other friction formula.

Fig. 3 shows such a result for le1 using the I.T.T.C. 1957 model-ship correlation line as reference friction line and Fig. 4 shows a similar plotting for IC1 using

16

1.2 1.3 1.4 1.5 1. Reynolds' no. R,,=VL,j 10'

Fig. 4 Resistance correction factor Ic1 (Hughes' method) vs Reynolds' number

1,7 1. 8 9 2J 2. 1 22 23

2, 2 (A111 welded commercial anti.fouling

-aint. Nursbers inicate ship correlated)

,7 _"22.4 8 16 in ____ -- -¡6 ,.,, 6 . . 28 24 20 2 deviation N. B. -'-e---Mean value val ue± Mean line standard

'j

36 'SS' 40 deviation zone

I.

-Fig. 3 Resistance Correction factor .ic1 &I.T.T.C.) vs Reynolds' number

0.6 0.4 0.2 ' -0.2 -0.4 - 0. 6

1. 0 0. 9 0.8 ai 0.4 - 0.4 - 0.6

Single-ncrew mer chant Ship, all welded commercial ant i -foul ing paint. Numbers ndicate ship correlated.

o ...Full load condition o --.- Trial condition (' loath

load condition

'

Maximum cuntinunuo rating Mear salue line

Mean value- standard deviation

0.6 0.7 0.8 0.9 1.0 1.1 1.2 13 14 1.5 1.6 1,7 1.8 1.9 2.0 2 1 22 23 2.4 Reynolds no, R.=VL / Y 10

Fig. 5 Wake correction factor e1 vs _{Reynolds' number}

MIS 01012R DECEMBER 1963 Standard devatov 44 44 correlation L0210m line calculated S

it

for L=7m,

(full load coed)

F0 -0,20

3

7 10

b.

Sri 8

18 _02e io 24 ₂₂ S

i2I)?.:..

f 14 12

A

32 5 2; - - 21 3e

.

..,

S Sso..36,

!---s 39 S 37 0-0 40 0. 7 0. 8 ₀₉ 1. 0 e,

I W

I Ws

Fig. 6 Correlation between Jc1 and e single-screw ship)

0. 2 o X o I-o o 0. 2

Model-Ship Correlation Method in the Mitsubishi Experi?nental Tank Hughes' method.

Fig. 5 shows a plotting of e1 for

single-screw ships and Fig. 6 the correlation of the3e

e1 and 4e1 (I.T.T,C.(.

From Fig. 3 and 4, we can see a slight superiority

on the consistency of plotting in Fig. 4 (Hughes' method)

over Fig. 3 (I.T.T.C. friction line). A general reasonable-ness of Hughes' method is thought to be shown in this comparison, though the validity to use his form factor K got in the low Froude number into the higher speed region remains some questions.

In Fig. 6 we can see a correlation between Jej and

eI, i.e. the more the Je1, the more the e1 is. By the simplified assumptions that

(a) the velocity distribution in the frictional belt

around propeller obeys the 1/7th-power law and

is uniform in the depthwise direction,

h) the magnitude of the frictional wake can be

determined by the momentum equation so that

the drag due to the momentum loss is equal

to the frictional resistance of the model or the

ship,

we can calculate the approximate relation between Jej (I.T.T.C.) and e1 theoretically (Appendix 3. In Fig. 6, thus calculated line is shown for reference.

For twin-screw ships analyzed e1 is 0.95M.98 and

there can be seen no difference in Jej between the

multiple-screw ship and the single-screw ship.

4. Power Estimation

The power estimation is naturally a reverse process of the ship trial analysis. Our method of power

estima-tion is shown in Table II. It is thought that there

remains nothing to be added for detailed explanation

except some minor points.

In the steps (4).(7), the

modifications have to be made in accordance with the

analysis method and the reference friction line adopted. The step (10) is corresponding to the step (15) of Table

I. In the steps (l8)(20), we use the '/K1/J curve against

J from the estimated propeller characteristics. These

characteristics are also got from the standard series

charts of the propeller by correcting the effects of

dif-ference in area ratio, boss ratio and blade thickness ratio of the actual propeller from that of the standard

series propeller.

This process of power calculation is also program-med into the electronic Computer.

As seen from the Figs. 3-5, the standard deviation of 4e1 and e1 are approximately ±0.1 x 10 and ±0.04

respectively.

Therefore, the standard deviation (error)

of the

power estimation is approximately ±0.25 knots for the

same power. taking the correlation of Jcj and e1 (see

Fig. 6) into consideration. However, for usual cases,

in which some appropriate type ships Can be used. the estimation error of the speed can be expected to approach within ±0.15 knot. This has been proved

from many examples during a long period of time

(Appendix 2).

For special cases, in which the severe cavitation is observed, the trial analysis must be performed first in

the speed region in which no cavitation occurs. From

this analysis, ¿le,. and e1 are estimated and then we ex-tend the power calculation up to the higher speed zone using these 4c1 and e1, assuming that there is no

cavita-tion. From the actual difference of the measured SHP

and RPM and such calculated SHP and RPM at the

Table Il. POWER CALCULATION

V8 Ship speed, given v/V PLrL

vL0, standard condition, l5C, sea

log10

water

C18 _R1/--pV2S

_-

_{roughness correction}estimated, taking appropriate

CJih=Rf/+pv2v (4)xS/v

Cn8 from resistance experiments

C0=C18+Crn.

j-Pv2 V

R880 (7)x(8)

allowance for added air resistance, standard 1-(9)+(10)

(11)x(1)

145.79

from propulsion experiments (li) - to8 1wo8 from el,=

_lw,

mated properly 0.51444 X V0(1 w8) e0 is

esti-from propeller

open-charac-teristics. using (18)

1tilo

eH,=

_1w,

from propulsion experiments

transmission effici.ency,

stand-ard e,=0.98

71a=ep X e118 X e,.0, Xe1 (12)

(24)

N-6$"

60 (17)

-

D_DX(19)

same speed, we can analyze the cavitationeffects. from

which we get the correction factors K01 and K,.0 for

cavitation characteristics, including the effect of shaft inclination on the cavitation. The power estimations of such vessels are quite reverse of the trial analysis. We

calculate first the power and RPM for the assumed

condition of no cavitation and then correct them using K51. K,.5 and the cavitation characteristics of the

pro-peller used. The latter calculation of correction may

be performed by trial and error method easily. assuln-ing RPM of propeller at a given ship speed.

By this process of power estimation, we get satis-factory results for the naval vessels of Froude number more than 0.5 and also for the high speed planing boat up to about 50 knots.

For the calculations of power and revolution in the

regular waves, the same method may be applied. In

the waves which are met practically the time mean

characteristics of a propeller may be thought not to be

effected by waves.oloì And the time mean values of

the propulsion factors are also shownhl approximately equal to those in the still water condition. Therefore,

2 of (9) R8 EHP t, T /T/p w8 17) v v'T/p VK8/J-

_vD

J

e5J eg8 e0 7)a SHP N

(i)

it is only necessary to add the appropriate resistance

or thrust augmentation due to waves (and due to wind if necessary) to the step (11) or (14) of Table II.

In the case of irregular waves, approximate time

mean augmentation of thrust may be calculated as

fo11ows'2:

JT='Ft(w).[2r(w)]2.dw

= JT(w)/H2 Transfer function of thrust increase

The validity of this approximate method is shown in the analysis of the SS Nissei-Maru."3'

5. Acknowledgement

This model-ship correlation method has been de-veloped by the author in these fifteen years. In this

period of time, a lot of assistance and

cooperation

were given him by the shipyards and the staff of the

Mitsubishi Experimental Tank, especially Mr. K. Tamura

and Dr. K. Watanabe.

The author wishes to acknowledge the assistance

given by them and to thank the director of our

Labora-tory for the permission of publishing this papel. References

9th I.T.T.C., Report of the Propulsion Commitee. H. Lackenby: B.S.R.A. Resistance Experiments on the Lucy Ashton. Part IllThe Ship-Model

Correla-tion for Shaft-Appendage CondiCorrela-tions. T.1.N.A.. Vol. 97. No. 2, 1955.

The 41st Research Committee, Investigations into the Propulsive and Steering Performances of Super Tankers. The Report of the Ship-building Research

Association of Japan. No. 31. Nov.. 1960.

Miß 01012R DECEMBER 1963

7

J.T.T.C..Standardization Trial Analysis Code(Draft.

Bulletins of the Society of Naval Architects of

Japan. Jan.. 1944.

K. Taniguchi and K. Tarnura: On the New Method of Correction for Wind Resistance-Relating to the

Analysis of Speed Trial Results. Jour, of Seibu Zosen Kai (The Society of Naval Architects of'

West Japan). Vol. 18. Aug., 1959.

6) K. Taniguchi and K. Watanabe: A New Electric

Torsion Meter for High Speed Naval Craft. Jour. of Zosen Kiokai (The Society of Naval Architects

of Japan). Vol. 108. Dec.. 1960.

S. Togino: The Measurement of the Modulus of Rigidity of Intermediate Shafts. Jour. of Zosen

Kiokai. Vol. 59, Nov., 1936.

G. Hughes: Friction and Form Resistance in

Tur-bulent Flow, and a Proposed Formulation for Use in

Model and Ship Correlation. TINA. Vol. 96. 1954. K. Taniguchi and K. Tamura: On the Performance of a Propeller in waves. Mitsubishi Experimental

Tank. Report 221 (Apr.. 1955).

(10 JR. McCarthy. W.H. Norley and G.L. Ober: The Performance of a Fully Submerged Propeller.

D.T.M.B. Report 1440, May. 1961.

(11) K. Taniguchi: Lecture on the Performance of

Ship in Waves. J.T.T.C. Symposium on the Ships

and Waves (June. 1961).

12 Lectures on the above mentioned Symposium by

K. Taniguchi and by H. Maruo.

(13) K. Taniguchi and M. lizuka: On the Motion and

the Thrust Augmentation of a Ship in Waves-Comparisons between the Model Tests and the Actual Ship Expenments of the "Nissei-Maru ". Jour. of Seibu Zosen Kai (The Society of Naval

Mode i-Ship Correlation Method in the Mit.5ubishi Experimental Tank

Appendix

i

Modulus of Rigidity of 36 Intermediate Shafts by Dr. Togino's Measurements

Total mean of modulus of rigidity, 8.314±0.0808=8.314(1±0.00971)xlOt kg'mm

S. Togirto The Measurement of the Modulus of Rigidity of Intermediate Shafts. Jour, of Zosen Kiokai, VoI. 59, Nov., 1936

Appendix 2

Deviation of DHP and N due to the

Standard Deviation of JCI and e

Je5.

i .4('/K/J) i _f

i

Jc4e

e1, '' 3

'/K/J - 3

k 4 e,' e5

-'--0.6e

i Jc1je,

1. Calculation Formulo

J

4 C1 e, /

'l'he following are the established relations. Introducing these into equations (5) and (6), we obtain

RV i the following equations for calculation ot the deviation

DHP- (1) of DHP and N due to the standard deviation of 4c1

145.8 e5 e,

l-t

and e,,.

N-

V,(1-w,)_30.866JD (2) _JDHP

-

_{7 fJc\}

2

lie,

DHP 12 c1 ) 3 e, ) (7) Rp/2V2V3(Cr+Cui)=pI2V2S(CIr+Ci) (3) _{=O.I5

-0.4

(4e5"1 (8) lWm, k er / k e )

e,-

_1-w, (4)

Since we can assume Cr'FC! for an ordinary commercial 2. Calculation of the Deviation of DHP and ship at her normal speed, equations (1) through (4) yield _{N due to the Standard Deviation}

the following equations,

_{Of iCf and e,}

4DHP 1

4c14e54e,

DHP 2 c1 e5 From Figs. 3 and 5, the mean values of Cf and e,

iN

4e,

4J

and the mean standard deviations of c1,, and e may be

N - - e5 - J

taken as follows:

From actual examples, we can assume the following c15±ic1s=(1.4±0.l)X103(ITTC

relations: e,±Je,=0.9±0.04

Mark

Chemical comp,.ition % Material test rrvnilts _{Modulus of} rigidity x10' kg/moss Dia, of intermediate shaft mm C P S -Mn _Si. Tensile str. kg/mm' Elong. % A

-

-

-

-

-

-

-

_{8.84 432.0} B

-

-

-

-

-

4.5.5 36.0 8.17 344.9 C

-

-

-

-

-

-

8.28 424.1 D .21 .033 .025 .57 .14 48.6 36.0 8.36 455.0 E .80 .034 .020 .66 .16 50.0 30.0 8.36 455.0 F

-

-

-

-

-

--

-

8.29 405.0 G H

--

-

-

-

-

-

-

-

-

-

-

-

-

8.20 8.47 330.0 329.3 I .15 .022 .032 .53 .259 51.0 38.3 8.39 378.4 J .14 .025 .027 .59 .240 46.8 34.6 8.26 420.0 K .14 .022 .019 .49 .315 .51.3 34.0 8.18 419.9 L .19 .025 .080 .55 .228 49.8 34.0 8.29 378.4 M .15 .021 .022 .53 .306 50.7 37.0 8.31 419.9 N .19 .020 .018 .52 .212 49.4 34.0 8.32 315.0 0 .14 .024 .021 .50 .212 46.8 35.0 8.35 315.2 P .15 .031 .021 .57 .235 47.4 34.6 8.30 315.1 Q .15 .028 .023 .49 .172 49.8 36.8 8.18 378.0 R .17 .020 .022 .60 .181 50.0 30.6 8.31 437.9 s

-

-

-

-

-

-.

-

8.51 401.5 T

-

-

-

-

-

-

8.37 4.50.9 U

-

-

-

-

-

-

-

8.26 282.1 V

-

-

-

-

-

-

-

8.27 430.9 W

-

-

-

-

-

-

-

8.35 284.9 X

-

-

-

-

-

-

8.29 284.9 Y

-

-

-

-

-

46.1 37.0 8.26 420.1 Z

-

-

-

-

-

48.4 32.0 8.35 420.0 A'

-

-

-

-

-

-

-

8.3) 340.0 B' .24 .029 .031 .75 .26 46.1 34.8 8.53 430.1 C, .23 .034 .031 .65 .24 50.0 27.3 8.29 430.0 D'

-

-

-

-

-

49.8 33.0 8.33 335.0 E'

-

-

-

-

-

47.2 85.0 8.28 335.1 F'

-

-

-

-

-

51.0 ' 27.0 8.43 345.1 G'

-

-

-

-

-

-

8.32 423.9 H' .17 .019 .025 .48 .247 49.1 34.8 8.27 430.1 V

-

_. -_.

-

-

-

-

8.25 259.7

J'

-

-

-

-

48.5 38.0 8.28 3)5.0

And there is the correlation between ej and e as shown in Fig. 6, i.e.

Jc= ±0.1 x 10* *ie1= ±0.01

(double sign in same order)

Therefore, for the calculation of J DHP/DHP and j NI

N due to the standard deviation of Je1 and ej. we can

put

Jcj/c1±0.1/l.4

4ej/e=±0.030.9 (double sign in arbitrary order)

Introducing these relations into equations (7) and (g),

they become

I J DHPJDHPI =(7/12).(0.1/1.4) + (2/3). )0.03/0.9)=0.064

I J N/N =0.15. (0.1/1.4) +0.4.0.03/0.9) =0.024

From the actual examples we can assume

(JDHP\ /

DHP ) / 3V,4=0.029/0.1 kn

Therefore, the deviation of DHP. N and V (at same

DHP) due to the standard deviation of Je1 and ej shown in Figs. 3 and 5 are calculated as follows;

J DHP/DRP= ±6.4%

IV/V = ±0.22 kn(at same DHP) (9)

JN/N =±2.4%

3. Actual Examples

In usual case, however, we can rely upon the

suf-ficient data obtained from the

suitable prototypes.

Therefore, the actual estimation errors of DHP, V,4 and N (actual trial values corrected for winds and currents

minus estimated values before trial) are fairly smaller

than those calculated as shown in (9).

The estimation errors were actually calculated for 41 vessels recently built in our shipyard (Nagasaki

Works), and we obtained the following mean values: / j DHP ' (Actual power at the estimated

DHP)

-

MCR -speed for MCR)-MCR - 0.0293±0.0327 4V=(Actual spee at MCTh (Estimated at MCR=0.l0 kn±0.113 kn

(JN\

(Actual RPM)(Estimated RPM

N J -

Estimated

at the same speed)

00077±00145 RPM

MCR=Max. continuous rating of main engine)

These results show that, in the total mean of 41

examples, the power is 2.93% smaller, the speed is 0.10

kn higher and the RPM is 0.77% higher than those estimated before trial and the standard variations of

these actual estimation errors are 0.0327, 0.113kn and

0.0145 respectively. These actual standard variations are approximately half of those calculated as shown in 9i.

Appendix 3

Theoretical Calculation of e

1. Theory

If we assume that the stream at the position of the

propeller is equivalent to a stream along a vertical

plank having the depth equal to the draft at the posi-tion of the propeller and that the velocity distribuposi-tion

in the frictional boundary layer conforms to the 1/n th power formula, then we have

I

v'/v0=(z/.3)1, (1

MTB 0101 2R DEcEMBER 1963

where v0= general velocity at the position of the

pro-peller outside the boundary layer v'=local velocity inside the boundary layer

ö=thickness of the boundary layes' at the

position of the propeller

and z=distance from the ships surface. From the momentum relation, we have

Rj=p/2.v21Sct=p1° (v0v')v'dz, (2)

where v4=ship speed

S=wetted surface area of ship

e1=frictional resistance coefficient of ship R1=frictional resistance of ship

and 1=total girth length at the position of the

propeller.

Further, if we denote a effective frictional wake

frac-tion by w1. then we have

x2( xm)(e'0u')dr.dui/

1

v'/vo= (z/o)'

R.o

v'/v0=1 R>ô

where R=radius of propeller

and

z2)1x)=weight for the thrust distribution

to xr/R.

From (1) and (2), p/2'v4Sc1= p1òvo {i

-

(z/ò)} (z/ .d(z/ò) vo

/

/(n+1)(n+2) S

R - 'Cf y4 _i n 1D o where D=2R.

From 11 and (3). using the relation z=r.cosO,

1t2

x2(1x') [1 (

xcos

o) '}dx.d0 P CIt/I

x2(1x)dx.dO

IR

where

l1

x.cos =0 for R/o>1.

f) J

Integrating the denominator,

6 Im+3' rl rIt/2 r . x

w1= I I \ xt)lxtm) 1(R/ô) 44x 41.costO

V ?fl /.)o Jo _I

dx.dO (6)

where

l_(

-x.cosO)=0 for R/ò>1.

(1.11 Case: R/ò<1 Integrating (6), n+1

1

n2(rn+3) k 2n 3n±l)(3n+mn+l) k 2n (R/ô)* ₍₇₎ 1.2) _{Case: R/ò>l} From (6), 6 )m+3) _{X2(1_X}

_{{1(R/a)X*cos'Ì}

m L

J dxd O 8O(X)2(1Xtm) { 1 (R/ö) x cos J/R u dxdû]

where O0(x)=cos ö/r=cosl

x(R/ö)' x>ò/R.

In equation (8), the indefinite integration of the second term on the right hand side can not be

per-formed analytically. Hence, the following approxima-tion is made.

(8)

Mode l-S/ip Correlation ill ethod in the Mitsubi/,i Experimental Tank

cosO.dO (10)

If we denote the viscous part of the wake fraction

by w, and the remainder by w,, then the wake fraction w by Taylor's definition is represented as follows:

w=w1+w2 (il) or Wv.,=W1V,,+W,V, By definition V8-wv,=V0 (12) and w1v2Iv,=wj (13)

From the equations (11) and (13)

V0 W, w-w2 V1 _W! WI Using (12) y0 w-(1-vùv5) V1 W! Vn 1-Wi y0

i-w

(14)

From equations (14) and (4), we obtain

D of o C 6 ni-3 _f 1. 1 m x2U _xnn) 1- (R/ô)" x cos dxdO-

°0x2(1_xm) l-(R/ô)cos"(»

.38/Ro dxd (9)

The second integral of (9) is calculated as follows:

8Ox2(.n {l_)R/ò)x cosO} dxdO

m-(?n+3-3x'°0)x30 ° 3(rn+3) mn- {3n+mn+ 1- (3n + 1)xmal 23+# n _{(3n+1)(3n+mn+1)} cosO.d O Therefore equation (9) becomes

rl n+1 \

3 n2(m+3) 2n I

'

Wfl

)3n+1((3n+in+1)

(2n+l\

RIO)" \ 2n I 2

m(m+33x°',)x'0

o 3(m+3) 6 in+3 mn-{3n+inn+1-(3n+1)x",}x,,' n r m (3n+1)(3n+nn+l) 1-w I(n+1)(n+2( S

-- /

(R/o) (15) 1-w1 n 1D

In equation (14), the left hand side, vjv2 is independent of Reynolds' number. Hence, we can take the same

value of V/VS for model and ship at the same Froude

number. If we distinguish the ship from the model by

suffixing s and 25 respectively, then we have

V0

l-w

1w1

(16)

Vn lWf,n. 1w12

Therefore, the wake correction factor e, can be written

in the form as follows:

l-w,,, 1W10,

(17)

1-w5

lw15

and from (4)

(R/Ô)n,Cin,= (R/ö)0c1., (18)

Since the quantities S/iD, c and w,,, are known for a

certain model, we can solve the two unknown quantities W11 and (Rio)2 from a pair of equations (15) and (7) or

(15) and (10). Hence, if we assume y12, then (Rió), can

be calculated from (18) and w1, from (7) or (10).

There-fore, using (17) e, can be calculated from w10,, and w1,

and Wn can be estimated from W,,, and e,.

2. Calculation

Index n in power formula (i) depends upon the

Reynolds' number and the pressure gradient along the

stream. In the stream near propeller there is pressure

rise along the direction of stream. Hence, index n may

be taken smaller than 7. which is appropriate for the boundary layer along a flat plate. However, n=7 was

chosen, since we considered from our experiences on this method that it would be better to take n=7 rather than the smaller n value. Besides we take m=1 for

the index of the thrust distribution in equation (3).

Then equations (7). (10) and (15) are reduced as follows:

wj=l-0.8411(RJó)4,

(R/ô)i

(7')

w,= 1 -0.84l1(R/ô)+- 2 (1 -(4-3x0)x'01 iî

168 7-)'29-22x,(x,' 2. i

+

8 (R/o)1 cos1 O.dO,

(R/ò)>l . (l0' 2.0 1.8 1.6 1.4 1.2 n 1.0 0.8 0. 6 0. 4 0. 2 1-w

/72

/S

1-w1 J/

7 or 0.4 0.3 1.4 0.2 0. 1 1. 2 1.0 0 0.2 0.4 0.6 0.8 (1-w) o,

B. High Speed Liner ) ight condition. ?,,=0.25, L,,,=7" -0.4 MTB 01012R DECEMBER 1963 e 11

(i-w)ø

01 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.762 R/ö 0.0875 0.108 0.201 0.314 0.446 0.592 0.751 0.924 1.110 1.310 1.526 W! 0.4731 0.3880 0.3308 0.2870 0.2505 0.2199 0.1928 0.1684 0.1461 0.1263 0.1095 0.0959 20 25 30 35 0.9855 1.375 1.808 2.280 10'xcr(ITTC) 1.535 1.472 1.424 1.388 lO'4c1 0.4 0 -0.4 0.4 0 -0.4 0.4 0 -0.4 0.4 0 -0.4 10'c1, 1.935 1.535 1.135 1.872 1.472 1.072 1.824 1.424 1.024 1.788 1.388 0.988 (R/ò), 0.455 0.574 0.776 0.470 0.598 0.821 0.483 0.618 0.860 0.492 0.634 0.891 W1, 0.248 0.223 0.189 0.245 0.218 0.182 0.242 0.215 0.177 0.240 0.212 0.173 e, 0.942 0.912 0.874 0.939 0.908 0.868 0.935 0.903 0.862 0.933 0.900 0.857

Model data R,,,,,=1.445x 107, Cjm=2.817x 10-'. w,,,=0.275, (l-w,,,)0,, =0.6356, w1,,,=0.2014, (R/a),,,=0.695

20 25 R,,,. 10' 1.231 1.721 10.c1(ITTC) 1.492 1.431 10'.4c1 0.4 O -0.2 0.4 o -0.2 10cj, 1.892 1.492 1.292 1.831 1.431 1.231 (R/ö), 1.035 1.311 1.515 1.069 1.366 1.590 WI, 0.155 0.126 0.110 0.151 0.122 0.105 ej 0.945 0.914 0.898 0.941 0.909 0.893

Model data R,,,,,=1.155x lOE. C17,,=2.926x10-', w,,,=0.44, (lWm)0,m=0.39. w1,,,=0.291, (R/ö),,,=0.301

wj=1_(1_w)ø(RJô)?E, =0.4110 / (1/2)D )15)

The simultaneous equations (15') and (7') or (15') and

y Sc1

can see the correlation between e1 and Jc1 or the scale shown in the lower tables.

These results are shown in Fig. 2A, from which we (10') can be easily solved graphically. The solutions are

shown in the upper table and also plotted in Fig. IA

for practical use.

Then e1 can be calculated as follows, using Fig. lA. Calculate 0 from the model data, where 1/2 may be taken as d,,.

Read (R/ô),,, and wj-,,,, from Fig. lA against 1-W,,,)

Calculate (R/ò), by the equation. (R/6)=(R/ö)m.cjw,f i 0.2

(j,.

Read w1, from Fig. IA such as

w!,.

o

Finally calculate e1 by the equation, e;=(l-wjm,)/

(1- Wf,1.

3. Correlation between e and cf -0.2 From equations 17), (10), (17) and )18), it can he easily

shown that ei is chiefly dependent on cf,/cf,,,. Usually.

most self-propulsion tests are performed by use of the standard size models, whose Reynolds' number or c1,,,

are accordingly lying in a relatively narrow region of

value. Hence, we can consider that ej is chiefly

de-pendent on c13, i.e.. the scale ratio of model and Jr1. Therefore, there must be a correlation between e1 and Jr1 (and the scale ratio of modeli. To realize this correlation, some typical examples are calculated as

A. Super Tanker )fully loaded condition, F,,=0.20, L,,,=7'

Q

X

1 0.4

0.8 09

e.

Fig. 2A Correlation between 4c1 and

Model-Ship Correlation Method in the Mitsubishi Experimental Tank

ratio. i.e.. the value of e increases with the value of ..ICJ or L/LS. However, the effect of the scale ratio on

e

is not large as seen from Fig. 2A.

In Fig. 6, a

typical result of these calculation, i.e.. the result for a super tanker of 210" length (L/L=30) is plotted and

compared with the analyzed points of the actual trials.

We can see a reasonable agreement between the calcu-lated one and the actual data except the extremely low e1-zone. Therefore, we can conclude that this simplified theoretical method of calculating e1 is reasonably usable

for the evaluation or correction of w1 and the

under-standing of variation of w1 due to the scale ratio or Jcr.