On self-propulsion tests in waves with super tanker models

REPORT

OF

TRANSPORTATION TECHNICAL RESEARCH INSTITUTE

REPORT NO. 44

On Se1fPropu1sion Tests in Waves

with Super Tanker Models

by

Ryo TASAKI and Hiromitsu KITAGAWA

June 1961

Published by

TILE UNYU-GIJUTSU KENKYUJO MEJIRO, TOSIIIMA-KLT, TOKYO, JAPAN

RChT

Lab. y.

Çuwunde

On Self-Propulsion Tests in Waves

with Super Tanker Models

by Ryo Tasaki and Hiromitsu Kitagawa

Contents

Summary 1

Introduction 2

1-1 Model characteristics 3

1-2 Method of the tests 4

Results of Tests 5

2-1 Model motions and accelerations 5

2-2 Thrust, torque and revolutions of propeller 5

Discussion of Results 13

3-1 Self-propulsion factors 13

3-2 Effect of change of flare upon motions and propulsive performance 14

3 -3 Tank wall effect 15

3-4 Prediction of motions and propulsive performance under rough weather -.17

3-4-1 Ship motions 17 3-4---2 Propulsive performance 17 3-5 Conclusion 20 Acknowledgement 21 Nomenclature 21 References 23

Appendix 1 Resistance Increase in Irregular Waves 24

Appendix 2 Calculation of Power Increase of Ships under Rough Weather 29

Summary

This report deals with the results of the self-propulsion tests in waves

with two tanker models, which are either extreme from of the displace-ment length ratio group of the U-T Series, the tanker model series of the

TTRI. In addition to the results of the tests, which are the main purpose

of the tests, the authors discuss the self-propulsion factors, effect of the

change of flare upon motions and propulsive performance, and tank wall

effect.

At the end of the report, the authors give a method to predict

the propulsive performance of ships under rough weather and compare

the performances of the ships corresponding to the two forms tested.

1-1. Introduction

Recently several reports on the tank 'tests in waves were published,

but they were confined to the model tests with fine ship forms as cargo

ships and fishing boats. The present report deals with the results of the tests with two models of super tankers. These tests were carried out in

Model propeller

Model propeller number 1138

Diameter, D1, m 0. 158

Pitch ratio, H/D const. 0. 770

Developed area ratio, AnM 0.405

Boss ratio, d/DL 0.210

Blade thickness ratio, t/D,, 0. 050

Number of blades

Blade section Unken type

-2-Table 1. Characteristics of model and actual ships

Model ship

Model number 1319 1320

Length between perpendiculars, Lpp, m 4.500

Breadth, B, m 0.592 0.643

Depth, D, m 0.331 0.352

Draft, d, in 0.240 0.261

Displacement, v m3 0.512 0.604

Wetted surface area, m2 4. 131 4.467

Dipsplacement-length ratio, V/LPP3 x 10 5. 623 6. 628

Block coefficient, Ca 0. 800

Waterplane coefficeient, Cw 0. 868

Midship coefficient, CM 0.990

Longitudinal centre of buoyancy, % of Lpp from F.P. 48.50 Distance between L.W.L. and bowchock top line at bow, f, m 0. 202

Longitudinal radius of gyrationin air, Ka 0,25Lpp Natural pitching period afloat, Tpo, s 1. 16 1. 19

Actual ship

Length between perpendiculars, Lpp, m Breadth, B, m Depth, D, m Draft, d, in Displacement, r m3 Normal SHP Normal RPM 25.07 14.02 10. 18 38, 874 190. 50. 17, 000 105 27.21 14. 89 11. 05 45, 823

an attempt to obtain available data of ship motions and propulsive

perfor-mance in a seaway for such a full ship form as a tanker. In addition, as

the main difference between two ship forms is the displacement length ratio (abbreviated to the d-i ratio in the following), we can evaluate the

influence of the change of the d-1 ratio on ship motions and the propulisive performance of ships in a seaway for such a full ship form as the tanker.

It is needless to say that the d-/ ratio is one of the most important

factors for the propulsive performance of the ship in calm water.

Recently E.V. Lewis has pointed out this ratio is an available parameter

for evaluating the ship performance in heavy seas.' G. P. Stefun showed

the influence of ship form on motions in regular head waves, using this

ratio as a parameter to present the ship form.'

But the results were

confined to rather small d-/ ratio and dealt with only motions.

This

report deals with the propulsive performance in addition to ship motions and it will give an interesting knowledge for the initial design.

A preliminary experiment on the shipping water was carried out during

the tests with one of the models.

1-1 The model characteristics

The two models tested were either extreme form of the d-i ratiogroup

of the U-T Series (the Tanker Model Series of the TTRI

_{), and their}

characteristics are shown in Table 1. The bodyplans are presented in

Figs. 1-a and 1-b. Fig. 1-a shows M. No. 1319 (TTRI Ship Propulsion

Division Model Number) with smaller d-1 ratio v/L3 x 1O=5.60 and Fig.

1-b shows M. No. 1320 with larger d-1 ratio v/L3 x 10=6.6O. As the

two models have the same breadth-draft ratio, B/d=O.247, their bodyplans under the load water line coincide when comparing them in bodyplans of the same breadth.

The forms above the load water line were constructed under the

assump-tion that the length of the corresponding actual ship L

was 190.5m.

The list of the characteristics of the actual ships is given in the lower

part of Table 1.

The flare before S.S. No. 8l above the load water line was changed

in three types for the model with larger d-1 ratio (M. No. 1320) in an

attempt to investigate the effect of variation of the flare on the shipping

3

-__a.uaia,______

Fig. 1a Bodyplan and profile of b:)w and stern of M. No. 139

Fig. 1b Bodyplan and profile of bow and stern of M. No. 1320

water in waves.3 The profile of the bow was not changed for simplicity. 1-2 Method of tests

The tests were carried out in the No. i Towing Tank of the Ship

Propulsion Division of the TTRI. The models were self-propelled in head

regular waves by the propeller driven by an electric motor on board.

No friction correction was applied and the models ran at their own self

propulsion points. The mean thrust, torque and number of revolutions per second were measured by a strain-gauge type propeller dynamometer

and a revolution counter. Heave, pitch angle, surge, encounter marks,

wave profile relative to the towing carriage, and accelerations at the bow,

-,

JI

:::iii

-______________r -

--

L__

.. -

---

.4

midship and stern were simultaneously recorded on

the paper

of a

penoscillograph with time marks.

The wave length tested was of 50, 75, 100, 125, 150, 200 and 250 of

the model length.

_{The wave height was 0.lOm throughout the}

_tests.

In the present tests, the test conditions of wave length 50 _{and 250% of}

the model length were added to the conventional _{test conditions of the}

basin, as the shorter waves are important in the view of the _resistance

increase in waves for the ship of full form and the longer waves are to

he noticed when drawing response of motions of the ship to waves.

2. Results of Tests 2-1 Model motions and accelerations

Measured values of motions are plotted against speed in Figs. 2-a, 2-b,

2-c and 2-d. _{In these figures, the phase differences o. and O, are defined}

in the following. _{When we represent the elevation of the water surface}

by rW=rWe1TE t _{at the centre of gravity of the model, positive for surface}

rising, the heave and pitch are given by and

e1Etö)

positive for bow rising, respectively.

The results of _{the measurement of accelerations are given in Figs.}

3-a, 3-b, 3-c, 3-d, 3-e and 3-f.

The non-dimensional expressions of model motions _{are presented in} Figs. 4-a and 4-b.

2-2 _{Thrust, torque and revolutions of propeller}

The results of the measurement of thrust,

_{torque and number of}

revolutions per second are presented in Figs. 5-a and 5-b. The

self-propulsion factors are given in Figs. 6-a, 6-b, 6-c and 6-d.

The increments of thrust, torque and revolutions are given in Figs.

7-a and 7-b. _{The non-dimensional expressions of the increments are}

pres-ented in Figs. 8-a and 8-b.

5 -'t J.' N i, z,, o .6 7

r

2 /

// z.? z5. ti

,:_f /6 /7 J /1O'EL .YPErû , J _/.s

Fig. 2a Heave and its phase difference of M. No. 1319

c VL = '= o 7fZ . o A 7JOZ X /25Z

/4 =i2Ì

oo-'---______o 6 .7 .? r# ./..' 1.7 -'I /.6 .d ..7 /Y N'c.26Z 5p'.? Vos J i.J "/ Fig. 2b Pitch and its phase difference of M. No. 1319

6--7 A/i. 51Z i A/i.

f5Z

o 75Z A

77.

7fZ

z1# /uJ.Z

/4

o o

z,, r,, r

I

o /L 757. A /5L97. .80W C. //I O -o o _r 7 P .9

r E /' r

<E - r.? r .5 E d - 7 t /vIoL. SPEED Vi ,i

Fig. 2c Heave and its phase difference of M. No. 1320

£1 o' TP: ----0 -t A - t o E.?' -14'4S G 0 o -/L = 52Z 757. f 2fZ i *

t

.d 7 .F q

t

// .'<E t

/1 /5 tE r7rF

MODEL SEED VM ,

Fig. 2d Pitch and its difference of M. No. 1320

o

G A/L = Iz ìosx A/L Otf 6' V. ?6'fl/

j .5 xo o G _A/i. 5'r. = o 757. .t 7oZ O

I/#/

A 258% /25% 'Yje 8/8M o I I 0 .2 4. 4 .8 /8 /2 /4 /6 f8 Moc'CL p8EO, VM IN

Fig. 3a Bow acceleration (S.S. No. 9) of M. No. 1319

o A/i. = fOX /L /58%

o 75/. + 780%

o /087. A 73-87.

*

fZfi

//A- 8/2AY

,41orz ..YPEFO, IN 81/3

Fig. 3-- b Midship acceleration (S.S. No. 5) of M. No. 1319

1.0 O f4W.5

= 5'Z

À./L o /L0 A hoz X ¡757. _'4',v 00

/

i r t I I I i o .2 .4 .6 . 10 /2 14 ¡6 /8 MODEL SPE'EO V,'r ¡N "'/

Fig. 3c Stern acceleration (S.S. No. 1) of M. No. 1319

I14E'4S G

= )7

_/L a 75Z A ffzt'Z o

/T7

/Zf% ..DIV 8 ¡ fg. A

9-MODEL YPEED , ,._

Fig. 3d Bow acceleration (S.S. No. 9) of M. No. 1320

'k

-

f-Moofz Yeo iv '/c

Fig. 3e Midship acceleration (S.S. No. 5) of M. No. 1320

4t'4,e4S D 75Z 7hZ X ¡7hz

¡jg

.501V 2

I

o o o o + - .2 4 .6 if /6 12 f4 /6 17 /10/ML 5FEED E..

Fig. 3f Stern acceleration (S.S. No. 1) of M. No. 1320

10

-14?45 0

)JL = lZ t

)JL = 2Z D A ZuIZ o X

/ïlZ

5T4/ J7'v

û/.;'

2 o /6 '7 /4.

f'

f8

/1 /2 /4 .4 3

r'

70,1/Ns ForraR. /tp

Fig. 4a Non-dimensional expressions

of motions of M. No. 1319 .Y788 44/87 VI - 12f?: 5.0?: ì.5.0?: 75?: , Z,,?: o roo?: Zfo?: 8/8 * '4X55 .8 .4

s

i. "r . .8 .1 -4 .7 o f' /2 '.0 .4 b 6

,,/7/7/4 /5

- 7bn,aic Facrot, 4,

Fig. 4b Non-dimensional expressions

of motions of M. No. 1320 ÁIXPXL, 9 .57/1.1 1.547M' .01.1.- 78.0?: A/I - JI'?:. 751'?: o 7,7% o /007. ,aa/1S' 0 175?: . 34b' 2" /587. .4?:. ...O/8. o 't, .o1A4'A'3 o /.0-°. J/? b 75?: o , 74.07. a 75-"?: o .6 .7 .7 ,91.06,,f,J/4.J'to,?,,,.F M,00 Sopo.o, V" . /4 MAX 9# 4' i: 875. i0 _{5,/5. 8}

Fig. 5a Thrust, torque and revolu- Fig. 5b Thrust, torque and

revolu-tions per second of M. No. 1319 tions per second of M. No. 1320

.4 .4 .9 .3 .9 .0 ç, NS '.7 'P

Mo..o. Sposo b?:. a

5 .4 7 .7 9 to If fr '7 ?1 15

't,

i as 03 4/ 4f 9 09. Sfx 5,7 -: 1"° ;6t'0 .5 .0 -7 Z .0 (0 /4 /2 /3 0 (3 Moceo Ynro «Ip

Fig. 6a Self-propulsion factors of

M. No. 1319 (Thrust identity method)

V TiZ2 L10t A/I /75% A/I 14% ilZ 75% 1 7/IZ o 14171 754% e. -t I/4 03' o .5 -' .7 .1 .9 (0 4.1 /2 (9 f4 f9 Ii /7 17 Mopto SP,,,, 7.. .. S

Fig. 6c Self-propulsion factors of

M. No. 1320 (Thrust identity method)

12

-00 a 0 ₄ o0 47 aV'on oO a ', 05 44 'a 4.2 5 4 7 5 .9 (0 (1 /2 ( i 15 16 f.'f fo Mai00 Speie, -o

Fig. 6d Self-propulsion factors of M.

No. 1320 (Torque identity method) 77 M4.PXS o .30,717 Hi4f79 A/h - f 24C- 5471 71/3 0 75% p 414Z o IOIZ n 25,%

o'

°

:'

' 67591.0ff f213 lAIS 16171/ Moon 5,vec, 1.

Fig. 6b Self-propulsion factors of M.

No. 1319 (Torque identity method

:'

,0°n0o°°°° O 577/I 10172%' 0 A/c - /2,03 aS/h- ft'3 I3lX 0 71% 1 244% 0 /4/2 a ZYtZ 110 07' Q taZo. '5, 'f. wo 03 07 'o 45 43 02 0f fa S H,. .4/5,... 4.7 40 9 40 k 03 2. 42

'o',

°'

::°

12 2 L? 10 .0 'f.3 /.0 49 at 'a'. 07 -n on oan 1/4 - .O.'Z 75% n /44% a S o o,. 47 00 O ..,,&f - o : 07 Q.' i /5 .5 04 07 as 44 0.5 'a 42L .5 .7 S 0f

03 /22 'q 'n a2.0 6.0 o I1A4Ç5 SIL 585 SIL 755 + 74,82. /'85 A 754'S 8 /8, * * '4__-.--

.4 .

frf0r1. S00.¼. 'Ss

revolutions per second of M. No. 1319

- 13 -,

o

q io

3. Discussion of Results

As stated in the introduction, one of the purposes of the present tests

is _{to obtain data of the ship behaviour and propulsive performance in}

waves for such a

full

ship form as the tanker.

The results of the

foregoing section will give available materials for this purpose.

In this section, the authors discuss some of the remarkable facts concl-uded from the results of the tests and give a prediction of the propulsive performance of ships in a seaway as an example of the application of the

results of the tests.

3-1 Self-propulsion factors

Self-propulsion factors were calculated from the measured values of

Figs. 5-a and 5-b,

and are plotted against model speed in

Figs. 6-a,

revolutions per second of M. No. 1320

Fig. 7a Increment of thrust, torque and Fig. 7b Increment of thrust, torque and

SIL 505 4/4 6587. O 75% o 688% 758% /755 41_ 8i8 .5 6 7 .8 .6 .0 (.2 '3 4 (.5 (.6 /7 /2 2 .6 7 Z 9 1.0 I' 1.2 /3 /lo,'s Srr V,., w 'y0 /4 /5 06 /7

N

I

14

-Fig. 8a Non.dimensional expressions of Fig. 8b Non-dimensional expressions of

increments of thrust, torgue and revolu- increments of thrust, torque and

revolu-tions per second of M. No. 1319 sions per second of M. No. 1320

6-b, 6-c and 6-d. The propeller efficiency is, of course, dependent on the propeller load condition and takes lower values than values in still water. The calculated values of the wake fraction and relative rotative coefficiency

scatter about the values in still water, except in the case of short wave

length of O.50L. In these figures,

the values in still water are those

without friction correction, in other words, the values at the self-propulsion points of the model.

From these figures, it seems to be concluded, in the accuracy of the

experiment, that the wake fraction and relative rotative coefficiency take almost the same values as ones in still water.

3-2 Effect of change of flare upon motions and propulsive

perfor-mance

For M. No. 1320 with the larger d-1 ratio, the flare before S.S. No.

M.IRAS 171RK5 = JÛZ ° A/L= 107. o 717. S fIX o 1117. 8 f117. , : o S f1'#Z /717.

'z

1/ox

z

//8/ k _{25_Z} N k + 7.87. fox 4. -. 'J-4 + 4

8 above the load water line was changed in three types in an attempt

to investigate the effect of change of flare on the shipping water in waves.

The discussion on the shipping water was detailed in the other paper3.

In this

place, the authors discuss the effect on motions and propulsive

performance.

The data of the tests are plotted in Figs. 2-c and 2-d for motions

and Fig. 5-b for propulsive performance. From these figures, it is con-cluded that no remarkable effects are observed in this case.

This is expected from the comparatively small change of flare to the

voluminal form of the forebody. It is difficult to give the general

con-clusion from the present tests, but it can be said that the change of flare

to this extent does not have much influence on ship motions and

propul-sive performance for such a full ship form as in this case.

3-3 Tank wall effect

After the Eighth ITTC, the tank wall effect on the model tests in

waves of the conventional towing tank is one of the most important pro-blems for the tank test technique in waves4'. T. Hanaoka has calculated

the tank wall effect to be observed in the narrow tank3' and Reference 6

gives the relation among the tank width, wave length and the speed

influenced by the tank wall. Recently, a few experimental investigations are published concerning this problem7'8.

The authors had noticed that the regular scattering of the measured values of motions was observed in the lower speed range of the tests in

waves and they thought that it was caused by the tank wall effect. In

order to get

rid of the unreliability in this speed range, the number of

test running has been increased. Experiences of the tests with several

ship forms showed the fact that appearance of the tank wall effect was, of course, remarkably dependent on the model speed and seemed to be

influenced by the ship form, for instance, the shape of the bow. In the

present tests, the authors could test two models with the identical tendency

of the ship form. Therefore, if the appearance of the regular scattering

has the same trend for both models, they will become reliable data of the

phenomenon.

The remarkable appearance of the tank wall effect is shown in Figs.

9-a and 9-b, which is selected from Figs. 2-a through 2-d. The speed

V = - is inserted in Figs. 9-a and 9-b. The pattern of wave system

due to the model motions changes at this speed. The critical speed given

in Fig. 3 of Reference 6 is also presented in the figures. Appearance of

the tank wall effect is very complicated. The theoretical consideration

shows the fact that the speed range of occurrence of the tank wall effect

extends as far as the high speed with increase of wave length. But the

experiments show that the appearance of the tank wall effect for very

long waves, longer than 150 0/, of model length, is not remarkable. This

is because of the fact that model motions are small for very long waves,

in other words, the waves generated by the model motions are very small. For waves of 100 to 150 0 of model length, the tank wall effect appears

remarkably. From the authors experience, it seems that the tank wall

effect appears more remarkably for the fuller model.

'f /0 If Niwe, Spera /N 7/,

-

16 --f i, J L

f

A/I - ff8 % L /0 /5 O aNO 15f9 .5 /8 1f

Mami 5re8 t' "Is

Fig. 9a Tank wall effect on heave Fig. 9b Tank wall effect on pitch

2 1 cwr,ca YACED ¿V ¿VP 4) MODEL Lesern ₈₄₅ rom,- aqDr# /0 'J aL /00 ,VL -/08 %

3-4 _{Prediction of motions and propulsive performance under rough}

weather

One of the results expected from model tests in waves is a prediction

of the behaviour and propulsive _{performance in a seaway. At present,}

the method proposed by M. St. Denis, W.J. Pierson9 and E.V. Lewis' is

an available one to predict the behaviour of ship in_{a seaway. The authors}

have been using the similar method _{to evaluate the propulsive performance}

in waves'5, which is proved in the _{Appendix 1. In this section, firstly,}

the authors compare motions of the two models to investigate influence of

the change of the ship form on the behaviour in a seaway. _Secondly,

they calculate the power increase _{or speed loss under rough weather for} the corresponding actual ships _{presented in Table 1, using the method}

abovementioned.

3-4-1 Ship motions

The comparison between motions is given in Fig. 10, which does not

show much difference between _{the two models. It}

_{suggests that the}

behaviour of the corresponding actual

E.V. Lewis' method will give almost

same results and that the change of

the d-1 ratio in the _{range tested does}

not make much difference on the

behaviour of the ships in a seaway.

3-4 2 Propulsive performance

The increments of thrust, torque

and revolutions per second in waves

are compared in Fig. 11, which shows

some difference between two models on

the contrary to the

_{case of motions.}

To evaluate the effect of the difference

on the propulsive performance of the

actual ship in a seaway, the authors

calculated the power increase of the

corresponding actual ships under rough

weather. The method is presented in

17

-ships in a seaway predicted by the

.4 .2 o 1.4 55 NNO/n/9 #1/l./J2O /50 200 4/L .5 2507. oo ,f3C IO 55 .50 .5 .6 ;3 .5 q j.., ii 12 1.3 /4 /5 1.6 's., 53 .5 .6 . 8 q (.0 7.! _f2 1..3 (-0 (.5 1.6 tp 7t/,VtflG FACTOR, tSp

Fig. 10 Comparison of motions between two models in non-dimensional expression

Appendix i and 2. Characteristics

of the assumed actual ships

are

given in Table 1.

Power curves under rough

weather are presented in Fig. 12. '

-In the calculations, the following °

assumptions are made for simplicity.

In spite of the fact that

all the

wave components of the actual seas

are distributed over the hemicircie

-18

-7_50 -5 I ff/VÛ /3/9 ITAlO. /328 2g2 C

Erw(, x)=e

cosa Xw if

_J<Xw<j

= O otherwise.

.05

The assumptions abovementioned may make numerically unexact the

results of the calculation but may

be permissible to the comparative evaluation of the propulsive performance under rough weather.

.03

in front of the ship when she runs ' 02

against the wind, it is assumed that ot all the wave components come o

05

20

directly in front. This assumption

is, of course, too severe to estimate _/25

power increase due to waves but

the authors dare to take this assump-

'

10,%

7°

cf 3

2

o

I /o /5 20

Alsoe_SPEEL, V os Onors

presented versus ship speed in Fig. not much difference between two

forms.

Figs. 15-a and 15-b give the

percentage speed loss at constant

revolutions per second,

respec-tively. These figures show that

the ship with the greater d-i

ratio experiences the greater speed loss under rough weather.

The process of the calculation

gives the power increase due to

waves and one due to wind

se 19 se

-I lo -O /0/VO ,3iq MA/O /320 5 20 Mos.. PL,,V 22

Fig. 12 Power curves under rough weather _{Fig. 13 Power per unit displacement}

The power per unit displacement was calculated from Fig. 12 and

presented in Fig. 13. But Fig. 13 shows that there are little difference

between two ships when considering the power per unit displacement.

The ratio of the power under rough weather to one in still water is

14. This figure shows that there is

M 22 1320

Is 20

s Ssro, V,

Fig. 14 Power increase under rough weather

.35 .30 25 20

'5

t0 s

parately. The ratio of the power

increase due to waves to one

due to both waves and wind is

presented versus wind velocity in

L

Fig. 16. In this case, the ratio

is independent on the ship forms

and the ship speed. Fig. 16 shows

that the power increase due to Fig.

wind takes rather greater part of

the power increase under rough weather. The process of the calculation gives the power increase in a seaway for such

20

-04 -040.1315

04.140.1320

/0

16 Ratio of power increase due to waves

to one due to waves and wind

also the fact that in considering large ship forms as were tested,

the waves of shorter length than ship length is comparatively important,

since the ocean waves contain the components of such short wave length at the beginning of a storm.

3-5 Conclusion

As mentioned at the beginning of this section, the results of the tests

presented in Figs. 2-a through 8-b are one of the purposes of the report.

In addition to the results, the following is concluded.

The self-propulsion factors are regarded to be same as the values

of the tests in still water in the accuracy of the experiment.

The change of flare to the extent of the present tests does not

have much influence on ship motions and propulsive performance for such

a full ship form as in this case.

The tank wall effect appeared in the present tests.

W Vt,crrt. t i.. ,o70004 ToY

The ship with the greater d-i ratio experiences the greater speed

loss at the constant revolutions and power under rough weather.

For such full ship forms as the tested models with CB=O.80 the

change of the d-i ratio,

v/La in the range from 5.6 x 1O to 6.6 x 1O does not have much effect on ship motions, the power per unit displacement and the percentage increase of power under rough weather.

The power increase due to wind takes rather greater part of the

power increase under rough weather.

In considering power increase in a seaway for such full and large

ship forms as were tested, the wave of shorter length than ship length is

comparatively important, since the ocean wave spectrum contains

com-ponents of such short wave length at the beginning of a storm.

Acknowledgement

The authors wish to express their appreciations to Mr. K. Tsuchida,

Chief of the Ship Propulsion Division, and the staff of the towing tank,

especially, to Messrs M. Sasaki and N. Yokoo for helping obtain the

laboratory data.

The tests were conducted under contract to the Nuclear Powered Ship Research Association of Japan.

The authors thank the director of the

Association for his permission to publish this paper and the members of

the ship propulsion group of the Association for the co-operation in reducing

the data.

Nomenclature

The following nomenclature is used in the report. _{Where units are}

not given, any consistent system is intended.

Symbols L length of ship in m B breadth of ship in m D depth of ship in m d draft of ship in m V displacement of ship in m3

S,

wetted surface area in m2

a scale ratio, LiLM

C8 block coefficient

Cw waterplane coefficient

CM midship coefficient

lcb longitudinal centre of buoyancy in % of L from F.P.

k, longitudinal radius of gyration in air in m DM diameter of propeller in m

H/DM pitch ratio

b/DM boss ratio

t/DM blade thickness ratio

V ship speed in rn/s wave amplitude in m wave height in m wave length in m

wave number, 27r/A

z heave amplitude in m

pitch amplitude in deg.

phase difference in deg.

a8 bow acceleration in g

a midship acceleration in g

a8 stern accelation in g

T thrust in kg

Q torque in kg-m

N revolutions per unit time

L .

T

, non-dimensional expression of thrust

ICH

pgB2Hw2D21 non-dimensional expression of torque

DM3LV

gHw2B non-dimensional expression of revolutions per unit

time

4T increment of thrust in kg

4Q increment of torgue in kg-m

iN

increment of revolutions per unit time

U wind velocity in rn/s

E(w) energy spectrum, subscript shows concerning variable

22

-Subscripts

s ship u wind

M model z heave

w wave pitch

References

E.V. Lewis "Ship Speeds in Irregular Seas ". Trans. SNAME, Vol. 63, 1955.

G. P. Stefun "The Influence

of Ship Form in

Pitch and Heave Amplitude ".

TMB Report No. 1235, Sept. 1958.

Ryo Tasaki "On the Shipping Water in Head Waves ".

Journal of Z.K. Vol. 107, 1960.

Proceedings Eighth International Towing Tank Conference,

Madrid, Sept. 1957.

Tatsuo Hanaoka "Theoretical Investigation Concerning Ship Motions in Regular Waves ".

Proceeding Symposium on the Behaviour of Ships in a Seaway,

Sept. 1957, Wageningen.

"Brief Review of the Research Programme on Seakeeping of the

Netherlands Ship Model Basin ".

W.O. Report No. 33-15-1, NSMB, Oct. 1959.

Edward Numata "Influence of Tank Width on Model Tests in Waves ".

Davidson Laboratory, Stevens Institute of Technology, Note No.

551 Aug. 1959.

G.P. Stefun "Comparative Seakeeping Tests at the David Taylor

Model Basin, the Netherlands Ship Model Basin and Admiralty Ship Model Basin ".

TMB Report No. 1309, May 1960.

M. St. Denis and W.J. Pierson "On the Motions of Ships in Confused

Seas ".

Trans. SNAME, Vol. 61, 1953.

-Euch Kawashima, Minoru Sakao and Ryo Tasaki "On the External Force Acting on the Marine Reactor due to the Ship Motions in

Rough Seas ".

Journal of Z.K., Vol. 105, 1959.

Hajime Maruo "The Excess Resistance of a Ship in Rough Seas ". International Shipbuilding Progress, Vol. 4, No. 35, 1957.

Appendix

i

Resistance Increase in Irregular Waves

Assuming the linear superposition, we can calculate the resistance

increase in irregular waves as follows.

1. Mean resistance increase in irregular waves

T. Hanaoka and H. Maruo have introduced methods to calculate the resistance increase in regular head waves5'1. The assumption of the

linear superposition allow us to regard the velocity or acceleration potentials

representing the fluid motion due to ship motions in irregular waves as the summation of those due to the regular components of the irregular

waves.

In this place, we use T. Hanaoka's theory to calculate the component

potential. Following T. Hanaoka's expression, we take the moving

co-ordinate system which advances with a constant velocity V in the direction

of negative x axis and the ship travels with the system. x, y and z are

Cartesian co-ordinates with the origin o in the free surface of deep water

and oz vertically upwards. The ship's surface is presented by the equation,

Y,=f(x, z)

(a-l)

He presents the ship form oscillating in waves in the following.

Y,f(x, z)

(Z*_rw) _(a-2)

where Z*=_xçb+z (a-3)

the wave system travelling positive direction of z

r(t)=

r(n) cos (o),t- TX± )

-the pitch ('Rh R12 R18 R R2 I I?2 2 R28 K.R31 R32 R38

(t)=

() cos

the heave

z(t)=

z(n) cos (wt+ô2(n) + ).

For these expressions, the non-uniform wave resistance R (t) and the

drifting force D (t) become

R(t)=

(Z*_rw) dxdz

--dxdz.

D(t)=

af_az

(Z* r)

arw_ax

and the resistance increase is

R(t)+D(t),

(a-7)

where is the acceleration potential due to the ship motions and ocean waves of unit amplitude, and the integration extends over the

vertical-median plane of the ship. Put the acceleration potentials due to the pitch

motion, heave motion and ocean waves

_ç,

çb and ç respectively, the

elements of the non-uniform resistance and drifting force are written in

the following,

ççaf

j) ax

/ Xçb z

-

r,

(xçs \ ar D= D23 _ax

T. Hanaoka's expression for ç, provides the following representation for

ax =o

-

25

-ax (øI Ç2, ç5)_yOdxdz

(a-4)

Now,

cos (wt+ a1(n) + )

+5m

xsin (wt+,,)

, }

where P, F,

F3. are the functions of n, x and z, F1

(n; x, z),

F3(n; x, z).

Then the general term of (a-8) is given by

Fdxdz

cos (wt+ò(m)+

cos (wt+ô(n)+

)

a(m)b(n)

_{cosÇt+ò(m)+,,) sin (wt+ò(n)+)}

+F1 Sifl(wt+ôi(fl)+)}

_z(n)jF2

cos

+F2 sin (wt+2(fl)+)}

ax

_>r(n){F cos (wt+ )+F3, Sfl (oi,,t+

arw

_{=r(n)cos xcos (wt+)}

(a-9)

cos (o,,t+ò(m) + e,,,) cos (at+ Òb(fl) + e,,)

li

2 COS

t+o(m)òb(n)+ec)

+cos

cos (w,,t+ ò(m) + e,,) sin (w,t+ oo(n) +

=

sin (wwn t+(m) +òb(n) + e,, +

+sin (ww, t+(m)b(n)+

-and

w,+w,,(m+n) 4w>O,

ww,=(mn) 4a> O,

as m, n> 1.

When considering the mean values of R(t) and D(t) with respect to time, we have to count only the direct current components, i.e. the terms of w, w,,=O or m=n.

According to the common treatment of the random phenomena, the mean value of the general term with respect to time can be replaced by

the mean value with respect to the random phase

içç a!

R=22

.F(n; x, z)dxdz

a(n) b(n)cos

((n)òh(n) sin (ò(n)ò(n)).

(a-iO)

This expression shows the fact that the components of a and b with

different frequencies do not have any contribution to the resistance increase

In other words, it is the resistance increase due to the existence of the

n-component only. That is

R(t5=R(n),

D(i)=D(n),

(a-il) ,-1 where cos (ò1(n)ô1(n)) cos o(n) where 1=ç(n), 2(n)=z(n), 3(n)=r(n), ==O, K1(n)=r Fdxdz, L(n)r= cos(rx)dxdz, for _i=2,3.

We can write the mean resistance increase as follows,

27

3 ¡3

R(t)+D(t)=

ÇRi+Di8

i1 ¡=1

=1 [(Rii(n)+Diì(n))1

(a-13)

Then, it is said that the mean resistance increase in irregular wave system

is the summation of the resistance increases due to the regular waves of

the components of the system.

2. Relation between resistance increase and energy spectrum of waves We put the frequency response of the pitch and heave motions of the ship to waves A1(w) and A2(w) respectively.

The resultant motion in (a-12) is

(a-14) Then R1(w) = cos (òi(n) -D3(w,) = L(w)A(w)A3(w) cos o where A3=1. We put

R(w)±D(w)

_{K A 2+(K +K )A A cos(}

- r2 (c) +K22A22 + (K13 +L1) A1 cos ô --(K23+L3) A2 cos o2+(K33+L3) = AR(w) , or R(t) ± D(t) = AR(w,,)r(w,) . (a-17) r- i

We call the function AR(w,) the reponse of the resistance increase. Put

the energy spectrum of the irregular wave system E,(w),

r((o,,)=

()

_. (a-18)

Then,

-tD(= AR(w) E,()dw,

(a-19)

where we can obtain AR(w) from the expression (a-16) or the tests in

regular waves.

In addition, the expression (a-16) suggests an interesting fact that

we can evaluate the contribution of motions and waves to the resistance

increase in irregular waves. And this expression gives us an idea that

K. and L1 can be separately obtained by the forced oscillation of the

model, if we measure the mean drag during the oscillations and it will

give us an insight into the resistance increase in a seaway.

Appendix 2

Calculation of Power Increase of Ships under Rough Weather

a. Calculation of thrust increase Thrust increase due to waves

(1)

_{Draw '' )}

-

() curves for constant speed V1

The model speed V, corresponds to the ship speed V5 Vw.

(2) Assume the length of the corresponding actual ship, where we

put LS=ISLM.

Determine (2/L)M for the appropriate components of the wave

(A (À

_2g

1

\LI'M

LJs

L8 oj2

From the curves of (1), read

(4T)

for ₍ of (3)

Transform to

(4)

by the following formula,

f4T f4T _a.

Calculate the component thrust increase by the following formula,

E f

fJTv\

_\flirJS

TI 2E,,

Draw JT(w5)w curves, which are the spectra of the thrust

they can not have any significance like the spectra of the ocean waves and ship motions but the following integrals have only a meaning as the thrust increase.

(3)

spectrum

(7)

increase,

-Integrate the curves with respect to w., that is

= 4T

and get the thrust increase under the assumed condition, ship speed Vs and the ocean wave spectrum E,(w)

Thrust increase due to wind

Wind resistance IT, is calculated as follows

pk(U+ V)2,

U is the wind velocity and V is the ship speed, p is the density of air

and k is a drag coefficient, for example, given by Report of the Shipbuilding

Research Association of Japan No. 1, 1954. Thrust increase under rough weather

The thrust

increase under rough weather is

given by the

following

4T=4T,+4T.

b. Calculation of DHP

(1) We use the following subscripts,

i: presents the values at a certain speed in still water.

: presents the values at the same speed as above under rough

weather. Then,

DHP11 Tw(1-w)w

DHP1 rç

where the propeller efficiency

the relative rotative coefficient

(1 - w) : the wake fraction We assume that

and (1w)w=(1w)1

From (1), we get

DJ-IP1 = DHP1.

-.

T1

Then, we can calculate DHP by ussing DHPI, predicted from the results

of tests in still water, the results

of the propeller open tests and T1

calculated by the following

T1 = T1 + IT.

-Postscript

The calculations in this report were completed in

1959. But the

publication was delayed up to the present, as the authors could not have

enough time to retouch the figures for printing. Thereafter, the theoretical

investigation in this field has made remarkable progress. For instance, the authors must quote Dr. H. Maruo's "On the Increase of the Resistance

of a ship in Rough Seas" for a reference, which was presented at the

Annual Meeting of the Society of Naval Architects of Japan, November

1O-42, 1960. He investigated the fundamentals of the resistance increase in waves and established a generalized theory in irregular waves.