Propulsive Performance of a Container Ship in Waves

3. Propulsive Performance of a Container Ship in Waves

Shoichi NAKAMURA*, Member, Shigeru NAITO*, Member

(From J.S.N.A. Kansai Japan, No. 158, Sep. 1975: No. 159, Dec. 1975and No. 162, Sep. 1976)

Summary

With a model of single screw high speed container ship, resistance and self-propulsiontests in regular and irregular waves are carried out in the Experimental Tank of OsakaUniversity.

The experimental results of ship motions in regular head and following waves andmean increase of resistance in regular head waves are compared with the results obtainedfrom the theoretical calculations.

The effects of wave height and propeller diameter on ship motions, mean increases ofresistance, propeller thrust, torque and revolutions, self-propulsion factors and propellerload fluctuations are investigated.

The significant amplitudes of heave, pitch and the mean increases of resistance, propellerthrust, torque and revolutions measured in irregular waves are compared with the valueswhich are predicted from the response operators obtained from the experiments in regularwaves and the wave spectra by applying the linear superposition method.

The self-propulsion factors in regular and irregular head waves are analysed by assum-ing that the mean characteristics of propeller in waves are identical with those in stillwater. Furthermore, to investigate the characteristics of self-propulsion factors in waves,the inflow velocity into the propeller disk in regular waves are measured by using a ringtype wake-meter, and the wake fraction, relative rotative efficiency and propeller open-water efficiency in regular waves are calculated by using the measured inflow velocitydistribution, the propeller revolutions and the propeller open-water characteristics.

The measured amplitudes of propeller load fluctuations are compared with the theoreticalcalculations by using the propeller open-water characteristics in uniform flow.

* Osaka University

1. IntroductionContainer ship is strongly required to main-

tain the rigid time schedule and to ensure thesafe navigation. High speed ship, however,will experience larger ship motions in roughseas which can result into high power increase,severe acceleration, deck wetness, slammingand propeller racing etc. Therefore, it isimportant for such a ship to investigate theship motions, resistance increase and propul-sive performance in waves. Power increase ornominal speed loss of a ship in waves isusually estimated by using the theoretical or

24

experimental results of increase of resistanceor propeller thrust and by assuming that thetime averaged values of propeller open-watercharacteristics and self-propulsion factors inwaves are nearly equal to those in still water.

However, the hydrodynamic forces actingon a ship hull and propeller are varying withtime due to wave and ship motions, and theflow field around the ship in waves should bedifferent from those in still water. Therefore,it is considered that the detailed studies onship motions, resistance increase and propul-sive performance in waves are necessary inorder to improve the accuracy for predictingthe power increase in rough seas.

L

Propulsive Performance of a Container Ship in Waves 25

For this purpose, with a model of singlescrew high speed container ship, resistanceand self-propulsion tests in regular and ir-regular waves were carried out.

Furthermore, in order to clarify the char-acteristics of self-propulsion factors in waves,it seems to be necessary to measure the inflowvelocity into the propeller disk, and makinguse of a circular ring type wake meter, theradial distribution of inflow velocity in pro-peller disk was measured and also the theo-retical approach about self-propulsion factorsin waves was performed.

The fluctuation of propeller load in waveshas been considered important to evaluatepropeller racing, propeller exciting vibrationand strength of propeller and shafting. Toinvestigate the characteristics of the fluctua-tions of propeller thrust and torque, measure-ments were carried out at the self-proplusiontests in regular and irregular waves and themeasured results were compared with thetheoretical calculations..

24 Ship .Model and Experimental 'Conditions.1 Model ship and PropellerThe experiments have been carried out with

.a model of single screw high speed containership, which is the same model as the oneused for the study on seakeeping qualities byTasai et al." The principal particulars ofthe model ship and propeller are given inTable 1. The model is made of wood and

Table 1 Principal Particulars, ,of model ship and,propeller

Ship model

BASE LINE

B A AP 1/4 1/2 CC 93/4Fig.. 1 Body plan and bow and stern profile of isingle screw container ship

BASE LINE

Length betweenperpendiculars L" (m) 4.. 000

Breadth B (m) 0.5847Draft fore dF (IT) 0.1952

aft dA (n1) 0.2199mean dM (IT) 10.2076

Trim (m) 0.0247Displacement volume IF (m3) 0.2769Block coefficient CB 0.568Waterplane area coeff. Cwp . 0.709Midship section coeff. CM 0.959Longl. center of

buoyancy from F.P., FB 0 .,520.L,

Longl. center offloatation from F.P. 0.5343 L

Longitudinal radius,of gyration k55. 0.24 L

Height of C.G. abovebase line KG (m),

Length-breadth ratia LIB0.1778

6.81Breadth-draft ratio Bid 2.83

Propeller model A

Diameter D ,(m) 0.15 0.112Pitch ratio 1.007 1.009Expanded blade area ratio 0.6935 0.670Blade thickness ratio 0.0530 0.05Boss ratio 0.1848 0.180Number of blades 5 5

Direction, of turning Right Right

t

the body plan of the model ship is shown inFig. 1.

The vertical position of the center of gravityand the longitudinal radius of gyration of themodel are adjusted by an oscillating tablemethod.2.2 Experimental Conditions

The following experiments were carried outat the Experiment Tank of Osaka University(100 m x 7.8 m).

(1) Resistance and self-propulsion tests instill water as well as in regular waves

A summary of conditions of resistance and

Table 2 Test conditions of resistance and self-propulsion tests in regular waves

Effect of wave length and ship speed

Effect of wave height

self-propulsion tests in regular head and fol-lowing waves are shown in Table 2. The shipmotions of heave, pitch and surge were meas-ured by low friction potentiometers. Whenthe model was free to heave, pitch and surge,the measurement of resistance was carried outwith constant tow force by a gravity typedynamometer, but at the test of restrainedmodel in regular head waves the resistancewas measured by a differential transformertype dynamometer. The self-propulsion testswere carried out at the self-propulsion pointof the model and the mean values and fluctua-

97. CFI, A/L Measuring items

Motion free0.15 0.5, 0.6, 0.7, 0.8,

Pitch, Heave, Surge,Relative stern motion

Resistance 0.20 L/50 0.9, 1.0, 1.1, 1.2, Resistance, Wavetests 0 25 (8 cm)

Head wavesRestrained

model0.30

1.3, 1.5, 1.7, 2.0Resistance, Wave

0.15 Pitch, Heave, Surge,Self-propulsion

test0.200.25

L/50(8 cm)

0.5,0.9,

0.6,1.0,

0.7,1.1,

0.8,1.2,

Relative stern motion,Propeller thrust, torque,

Propeller: A, B0.30

1.3, 1.5, 1.7, 2.0revolutions, Wave

Followingwaves

Self-propulsiontest

0.200.25

L/50(8 cm)

0.4,0.8,

0.5,0.9,

0.6,1.1,

0.7,1.3,

Pitch, Heave, Surge,Propeller thrust, torque,

Propeller: A 1.5, 2.0, 2.5 revolutions, Wave

F. Cw RI L Measuring items

Pitch, Heave, SurgeMotion free

Resistance 0.20 L/100 L/20 0.9 Resistance, Wavetests 0.25 1.5

Restrainedmodel

(4 cm) (20 cm)Resistance, Wave

Head wavesSelf-propulsion

test0.200.25

L/100 L/20

(4 (20 cm)cm)

0.9

1.5

Pitch, Heave, SurgePropeller thrust, torque,

Propeller: A revolutions, Wave

Self-propulsion1,1100 L126.7

Pitch, Heave, Surge,test

Propeller: A, B0.20

(4 cm) (15 cm)1.0 Propeller thrust, torque,

revolutions, Wave

26 Shoichi NAKAMURA, Shigeru NAITO

60

4.0

2.0


Irregular waves

2.0 4.0 6.0 8.0 0 2.0 4.0 60 8.0W (sec') I, (sec')

Fig. 2 Wave spectra used for model experiments in irregular waves

Table 3 Test conditions of resistance and self-propulsion tests in irregular waves

Table 4 Test conditions of wake measurements in propeller disk

4.0'

2.0

5,1w1tare- sec)

Seq.8

Seq.7

s, 6

Ss, 2

599 5

Seq. Ho

5 536 1.4082 9.99 1.4136 11.54 )3907 13.40 13958 16.12 1.399

Measuring items

Resistance test:Resistance,Pitch, Heave, Surge,Ship speed,Wave (encounter and fixed point)

Self-propulsion test:Propeller thrust, torque, revolutionsShip speed

Wave (encounter and fixed point)

0.9, 1.5

8 9 10

0.467 0.362 0.254

Wave height (cm)

8

(L/50)

4-20(L/100-L/20)

Freq.: 0.52, 0.60, 0.72, 0.88,1.09 Hz

Double amp. 1, 2, 3, 4 deg.

Kind of tests Ring No.

In regular head waves0.20

4,

9,5,

10

6, 7, 8,

0.20 7

Restrained model in regularhead waves 0.20

4, 6,

7

Forced pitch in still waterDouble amp.: 3 deg. 0.20 7, 8, 10

Forced pitch in still waterFreq.: 0.52 Hz 0.20 6, 10

70.576

Ring No. 4

rIR 0.8975

0.7896

0.681

FmSeq. No. 111/3 (CM) 7'0 (sec)

1 10.78 1.159

Mean wave period 2 9.99 1.413series 3 10.56 1.562 0.15

4 10.04 1.694 0.205 6.36 1.409 0.252 9.99 1.413 0.30

Significant waveheight series 6 11.54 1.390

7 13.40 1.395

8 16.12 1.399

(cm' sec)1

234

10789.99

/05610.04

1.1581.4131.5621.694

60

0.5, 0.8, 1.1, 8

1.5, 2.0, 2.5 (L/50)

Wave length AIL

0.5, 0.8, 1.1,1.5, 2.0, 2.5

Sep 2

Sep

Seq. 3

28 Shoichi NAKAmURA, Shigeru NAITO

tions of propeller thrust and torque weremeasured by a differential transformer typedynamometer. The mean values of the propel-ler revolutions were measured by an electroniccounter and recorded by a digital printer,while the fluctuations of revolutions weremeasured analogically by a low inertia gen-erator attached to the motor shaft.

Resistance and self-propulsion tests inirregular waves

The experiments were carried out for eightdifferent wave spectra (Sequence Nos. 1-8)which are shown in Fig. 2. Wave spectra ofsequence Nos. 1-4 are the series of meanwave period, the significant wave height beingmaintained at an almost constant value of 10cm, and those of sequence No. 2 and Nos.5-8 are the series of significant wave height,the mean wave period being kept at an almostconstant value of 1.4 sec. The significantwave height 11113 and the mean wave periodTo for each of the wave spectra are given inTable 3.

Wake measurements in propeller diskThe radial distribution of inflow velocity in

the propeller disk were measured by using acircular ring type wake meter. A summaryof test conditions are shown in Table 4.

3. Ship Motions in Waves3.1 ship Motions in Regular Head Waves

The measured amplitudes of heave, pitchand surge motions obtained from the resistanceand self-propulsion tests in regular head wavesare shown in Fig. 3 in the non-dimensionalform as a function of wave length/ship lengthratio AIL.

The amplitudes of heave and pitch are cal-culated by the ordinary strip method (0.S.M.)and those of surge are calculated by theuncoupled equation of motion on the assump-tion that the surge force is considered to beonly the Froude-Kriloff force and the dampingforce for surge can be neglected. The resultsof calculations are shown in Fig. 3 and com-pared with those of experiments.

It is shown in Fig. 3 that no significantdifferences appear in the measured amplitudes

Heave

ei .

Pitch

Surge

,

Fn.0.15

_.

He

4

Fn.:0.20

o

Pitch o

Calculation

e

Exp.Resrstance test o

Sell-prop. test

Heave

Pach

g o

Fn .0-25

Heove

.

'-e-NN---8 %

Fn. 0.30

Retch

e

,

0 -

,

e

Surge .__..-o- Surge ----c.--

10 IS An. 20 IS 75 zo

Fig. 3 Comparison of ship motions in regularhead waves between experiments andcalculations

of heave and pitch between the towed modeland the self-propelled model. The calculatedresults of pitch motion by the O.S.M. showfairly good agreement with the experimentalresults, while those of heave motion are slightlylarger than the experimental results for therange of AIL> 1.0 and the difference is largerat high speed. The measured amplitudes ofsurge at the resistance tests agree fairly wellwith the calculated results by the above men-tioned method.

The amplitudes of relative motion to thewave surface at the position of propeller weremeasured by the resistance type wave heightprobe attached to the model, and the resultsare compared with the calculations accordingto the 0,S.M. as shown in Fig. 4. There is

05

to

05

05

LI?

to

KT as

JO

5

005

(2)

0.5

5.0

0

1.5

ol0

0.5

1,5

0.5

0 05

5 Eep.Resistance test oSell-prep. test

Fn. 0.15

Fe. 015


0.S. Fn. 0.20

75 x4.20 0.5 10 1.5 20

Fig. 4 Comparison of relative stern motions inregular head waves between experimentsand calculations

no significant differences in the measuredvalues between the towed model and the self-propelled model. The measured amplitudesof relative stern motion are higher than thecalculated values for the range of long wavelength, while smaller for the range of AIL< 0.7and the difference is considerably large. Thisfact may be explained from the reasons thatthe wave height reduction of the incidentwave at the stern is larger for the range ofshorter wave length and that the differenceof phase lag of pitch to heave between experi-ments and calculations is comparatively largein case of short wave length.3.2 ship Motions in Regular Following Waves

The measured amplitudes of heave, pitchand surge motions obtained from the self-propulsion tests in regular following wavesare shown in Fig. 5, and the results are com-pared with those of calculation by the samemethod as the case of regular head waves.The arrow marks on the abscissa show thevalues of AIL that the phase speed of waveis equal to the ship speed. The values ofAIL is equal to 0.251 for the ship speed ofF=0.20 and 0.393 for F=0.25. Therefore,all of the experiments were carried-out at theconditions that the phase speed of wave isfaster than the ship speed.

As to the amplitudes of heave and pitch, the

0 .3

0.4

0.2

00.8

0.6

4 0.4

.02

20

1.0

00.5 2.0 2.5

x/L

Fig. 5 Comparison of ship motions in regularfollowing waves between experiments andcalculations

calculated values are slightly larger than themeasured ones, but the calculated amplitudesof surge are considerably larger. It seemsthat the further study on the disagreement ofsurge motion in following waves should benecessary.3.3 ship Motions in Irregular Head Waves

From the results of resistance tests and self-propulsion tests in irregular waves with thewave spectra as shown in Fig. 2, the significantamplitudes of heave, pitch and surge are ob-tained by the spectral analysis. These resultsare divided by the significant wave height ofthe corresponding irregular waves, and arepresented in Fig. 6 as a function of significantwave height and in Fig. 7 as a function ofmean wave period. In the Fig. 7, 20 is thewave length of regular waves correspondingto the mean period of irregular waves.

The measured values are compared with thevalues which are predicted from the responseamplitude curves obtained by the model ex-periments in regular head waves and the wavespectra of corresponding irregular waves, ap-plying the linear superposition method. It isshown from Figs. 6 and 7 that the measuredvalues give fairly good agreement with thepredicted ones,

1.0 1.5

7.0

0.30

30

o.

0.

o.

0.6

a0.4

5.

Pi-gt. 6 Comparison of ship motions in irregularhead waves between experiments and cal-culations (effect of significant wave height)i

0

02

lb o 6 / 14 1 lb

60 50 40 30 2.5 um03 [60 50 40 30. 25 L/Nsis

Shoichi NAKAMURA, ,Shigeru NAITO

0 075 1.0 1.25 0.5 075 1.0 44 025

Fig. 7 Comparison of ship motions in 'irregularhead waves between experiments and cal-culations (effect of mean wave period)

3.4 Effect of Wave Height on ship MotionsThe effect of wave height on ship motions

Was investigated by resistance tests and self-propulsion tests in regular head waves, vary-ing the wave height from L/100 to L/20 atthe conditions of A/L.0.9, 1.5 and F..0.20,0.25. The measured double amplitudes ofheave, pitch and surge are presented in Fig. &as a function of wave height Cp

It is shown from the figure that the lintarrelationship between the ship motions and thewave height is satisfactory. In this experi-

Fn 020./L v0 9,15

-0-1r*

Pitch

70

:,*

Surge

Pitch

Heave Resist. testSelf-prop, I.

C, 1 (cm) 20

20

'Fig: 8 Effect of wave height on ship motions inregular head waves

ments, no significant differences appear in themeasured amplitudes of heave and pitch be-tween the towed model and the self-propelledmodel, while some difference appear in theamplitude of surge.

4. Mean Increases of Resistance, and Thrust,Torque and Revolutions of Propeller inWaves

4,1 Mean Increases of' Resistance, and Pro-peller Thrust, Torque and Revolutions inRegular Head Waves

The measured results of meah resistanceincrease obtained from the resistance tests inregular head waves are presented in the formof non-dimensional coefficient as a function ofAIL, and are shown in Fig. 9. In the figure,the calculated results by Gerritsma's method"and Boese's method') are also shown to com-pare with the experimental results,. The cal-culated results by Gerritsma's method agreewell with the experimental ones. The cal-culated results by Boese's method are smallerthan the experimental results in case of shortwave length, and give larger peak values atlow speed.

The mean increase of resistance for therestrained, model in regular head waves wasmeasured by a differential transformer typedynamometer and the results are shown inFig. 9. The calculated results by Gerritsma's

A'

C3P4riftuorResist:rest Sell.potess

Pitch 0znik, Heave

PrecOcrioni

4,5443 SU Ige 0 ----F0= 0.15 F. = 0.20

%Ai,.4.0.46

,,, s--a -IA,-, 77 es ,.,

ey dri,,,-O.- - -gi-4,271,,- 0* - 5,- 3_ 411.21.'1 ,..-

F.= 0.25 1 Fn 0.3041444,,,____,_a..--,0- ° 7'4'41![",___A,__.

1

,z-..--,-4----'-% 0 LAI,,

-

4'1,41--.1-- -ra--2,-. - t[40,,,,.,)t

-,0"--,9 0

,,,XVuth* o ,o

H,,

Res; .11.Ztirirli[PrPitch

2[./Ily HKaie a'rd., Surge 0

r6P.tesr P'edic1iGn

-.-- - - -

Fn = 0.15

s ra,,,/14,13 __-t ......-.. co--'

--- Ovs/Hvs__,3---Q--"...-.-151:'1,0Pa ---

-

a 0 20-A-

.

.-4-1--/H.ly24.13',__

.

100--

Fe= 0.25...6.-Z.M.4-0r.

..."-.0.0A1'S."

.4 e sec). I

Fe = .230

0,-

t?"1:.7 e,M4 ---t-

-B.H , _ _ a IL --u-do--- ,4( sac! ,t t .

1.2 1.4 1.6 1.4

0.

_

0.

0

0

3,0

-

Propulsive Performance of a Container Ship, in Waves

,Fig. '9 Comparison of resistance increase coef-ficients in regular head waves betweenexperiments and, calculations

Thrust increase

Fn0150200.25030

V,

Torque increase

Revolution increase

5 AA 2

_

Fig. 10 Coefficients of mean increase of propellerthrust, torque and revolutions in regularhead waves,

method show a good agreement with the ex-perimental results.

The self-propulsion tests in regular headwaves were carried out at the self-propulsionpoint of the model and the mean increases ofpropeller thrust, torque and revolutions arepresented in the form of non-dimensional coef-ficients, as shown in Fig. 10.4.2 Mean Increases of Propeller Thrust,

Torque and Revolutions in Regular Fol-lowing Waves

Non-dimensional coefficients of the meanincreases of propeller thrust, torque and revo-lutions obtained from the self-propulsion testsin regular following waves are shown in Fig.11. These values are smaller than the valuesobtained from the self-propulsion tests in regu-lar head waves.4 3 Mean Increases of Resistance, and Pro-

peller Thrust, Torque and Revolutions inIrregular Head Waves

The values of mean increases of resistance,and propeller thrust, torque and revolutionsobtained from resistance and self-propulsiontests in irregular head waves are divided bythe squared significant, wave height and areshown in Fig. 12 as a function of the signifi-cant wave height and in Fig. 13 as a functionof the mean wave period.

Each of the measured mean increases arecompared with the values which are predictedfrom the response curves obtained by modelexperiments in regular head waves and the.wave spectra by applying the linear superpo-

0.4

0.2

0.4

0.4

0,2

Fig. 11 Coefficients of mean increase of propellerthrust, torque and revolutions in regularfollowing waves

045

1-s.\I \

II ,\

Experiment(

Motion free -e-Restrained

,Fe -020

nt \- I

....-c-7-4÷-

I

Calculation

Gerritsmds method\ Motion free - -\ Restrained\Lipase's method.

\\..

Fn 025

I-\\.\

I

\\

ir'

Fn .0.30'

IP

'II

i/

TA./p9C.:18%1-1Thrust Increase

.... -0-. . .

°'"if5PC:018'/L1Torque Increase

Fe Exp.,020 -a-025 --e--

t''''D'i 9 cx.f (S'L)

o .i, 7 .

Revolution irrrease

1.0 7.5(3./L 2' 5 .5 An 20

0.5 l0 7.5 2.0 Ai L 5

3 0

2.0

140

20

20

05

2.0

10

31

0

0

-

0

10


/0 12 /4 16 18

60 50 40 30 25 L/FL

Fig. 12 Comparison of mean increases of resist-ance, propeller thrust, torque and revo-lutions in irregular head waves betweenexperiments and predictions (effect ofsignificant wave height)

sition method which is expressed as follows:

H4w=2 HAW(W) Sc(coOda), ( 1 )0

where

HAW: mean increases of resistance orpropeller thrust, torque or revolu-tions

HAW/2: response curve in regular wavesSc(a).): spectrum of encounter wave

C.: wave amplitude

It is shown from Fig. 12 that the measuredvalues of mean increases are nearly propor-tional to the squared significant wave height.Although the agreement between the experi-mental values and the predicted ones is notso good as the ship motions, it can be saidthat the linear superposition method seems tobe useful for predicting the mean increasesof resistance or propeller thrust, torque or

L2

0

0

0.

100

50

05 On '00/L 1 25

Fig. 13 Comparison of mean increases of resist-ance, propeller thrust, torque and revo-lutions in irregular head waves betweenexperiments and calculations (effect ofmean wave period)

revolutions from the viewpoint of practicalpurpose.4.4 Effect of Wave Height on Mean Increases

of Resistance and Propeller Thrust, Torqueand Revolutions

In order to investigate the effect of waveheight on the mean increase of resistance,resistance tests in regular head waves varyingthe wave height from L/100 to L/50 werecarried out at the conditions of A/L=0.9, 1.5and F.=0.20, 0.25, and the results are shownin Fig. 14.

The experimental results for the restrainedmodel are also presented in Fig. 14. It isshown that the linear relationship betweenthe resistance increase due to wave and thewave height squared is valid approximatelyfor the range of the wave height of L/50L/30, but it has a tendency to be larger thanthe squared wave height law for the range

Fn Exp. Pr.d,cr.0(5 0020025 .5

- 030

--a, ---,

o a do .go

o

,0 0 0

'0A1.44,e hg o'n/in',

i ... "'Le_A ._. ..._ _;-___. -

8

"'------"0-7,---

Al,./11,-; (v.'')7 7 . , fit.,-;,,. TA_

11 ,,, (cm ,

RA1144 Fn Exp. Predicr

-0 /5 0(4,,,,,)025 A030

1 . I-- a--).. ....,....,--" p II -.......

'-Z-------'-'or-';'--"-;t7.-66

,41/41,%3

, .../....-. _74:-..---,,,..."--.--- °

, o°o

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OA/43/0"/"," "--- -,// ,' k *4' \N

.4 / ...--"Er. .----,-.!-

8

-..........

aNA,AL,,,, .r i/...', G.

--.-..---- ---.....-...,0 ._--

---(sec)

14 16 18

3

6

2

6

4

8

6

4

2

4'

05

/00

50

0.

(

-

6

20

0.0

of lower wave height and smaller for therange of higher wave height.

The effect of wave height on the mean in-creases of propeller thrust, torque and revolu-tions are investigated by self-propulsion testsin regular head waves at the same experi-mental conditions as mentioned above. Themeasured results are presented in Fig. 15.

'a- az4-1

Propulsive Performance of a Container Ship in Waves

0- "I /5C. (c2m01 /5 Cv.50 ab 20 so so 40 L cw-10

Fig. 14 Effect of wave height on resistance in-crease in regular head waves

Fig. 16 Effect of wave height on mean increasesof propeller thrust, torque and revolu-tions in regular head waves (effect ofpropeller diameter)

The variations of the mean increases of thrustand torque with wave height show a similartendency to those of the resistance increase,but the mean increase of propeller revolutionsshows somewhat different tendency.

Self-propulsion tests with the propeller mod-el A and B of different diameter were carriedout in regular head waves, varying the waveheight from L/100 to L/26.7 at the conditionof AIL=1.0 and F=0.20. The measured val-ues of mean increases of propeller thrust,torque and revolutions are shown in Fig. 16as a function of the squared wave height.

The region of wave height at which themean increases are proportional to the squaredwave height are affected by wave length.When the ship motions are severe, for examplein case of AIL= 1.0, the region is narrow andwhen the ship motions are moderate, theregion is comparatively wide.4.5 Effect of Propeller Diameter on Mean

Increases of Propeller Thrust, Torqueand Revolutions

Making use of the propeller A and B, self-propulsion tests in regular head waves werecarried out for the speed of F-=0.20. At thistests, the wave height was maintained at a

4-0,azo

T000sr increase

-

F0 .azsThrust increase

A/L

...- ,5

Torque Increase

- ' ^

Torque increase

o "' . oo

Revolts/son increase

o

NL,-...,________._.

Revolution increase

0

2.0

1 0-

05 -

Fn.020,,/, 09

Resistance test-0-

Ft, 0 25 , ./L n 0 9

Motion freeRestrained

/. - 020 ,A/ L =1.5

as

$ 10 Cw 15 fr, 20 5 10 C, 15 km, 20

80 50 40 L/ c. 20 80 iO 40 L icw 20

Fig. 15 Effect of wave height on mean increasesof propeller thrust, torque and revolu-tions in regular head waves

20

1,5

113

1,1 0

05

1.5

0.5

0.150.1/2

020

Fir.

.


Fig. 17 Effect of propeller diameter on mean in-creases of propeller thrust, torque andrevolutions in regular head waves

constant value of L/50 and the wave lengthwas varied from 0.5L to 2.5L. The mainparticulars of two propellers are shown inTable 1. The measured results of the meanincreases of propeller thrust, torque and revo-lutions are presented in Fig. 17 as a functionof AIL. In order to show the effect of pro-peller diameter on the mean increases of pro-peller thrust, torque and revolutions, the fol-lowing non-dimensional coefficients in whichthe propeller diameter is not included are used.

Thrust increase coefficient:

714w1pg;w2(B2IL)

Torque increase coefficient: QmvlpgCw2B2

Revolutions increase coefficient:N AwVL'IgCw2(B21L)

The thrust increase is hardly affected bythe propeller diameter. On the other hand,in case of smaller propeller diameter, the meanincrease of propeller revolutions is larger as

a whole, and those of torque is somewhatsmaller at the peak of response curve. Theexperimental results of the mean increases ofpropeller thrust, torque and revolutions incase of varying the wave height are shownin Fig. 16 and show the same tendency.

5. Self-propulsion Factors in Waves5.1 Analysed Results of Self-propulsion Fac-

tors in WavesIt may be confirmed that the time averaged

values of propeller open-water characteristicsin waves are identical with those in stillwater' '5).6, so the effective wake fractionw relative rotative efficiency 7)R and propelleropen-water efficiency 77o in waves can be an-alysed from the measured values of thrust,torque and revolutions of the propeller andthe mean ship speed in waves by applyingthe thrust identity method using the propelleropen-water characteristics in still water. Thethrust deduction factor t in waves is obtainedfrom the values of resistance and propellerthrust at the same ship speed measured inresistance and self-propulsion tests.

The self-propulsion factors in waves hasbeen considered to be almost the same valuesas those in still waterl'. However, it seemsto be necessary to study the detail of the char-acteristics of self-propulsion factors in wavesin order to improve the accuracy for predictingthe propulsive performance in waves.

For this purpose, resistance and self-propul-sion tests in waves were carried out and theself-propulsion factors are obtained from theabove mentioned procedure. The variationsof self-propulsion factors in regular head waveswith the wave length-ship length ratio arepresented in Fig. 18. The values of self-propulsion factors in still water are shown inthe figure by the horizontal broken lines.

It becomes clear that the self-propulsionfactors in regular head waves vary consider-ably in the region that the wave length-shiplength ratio AIL is smaller than 1.5, and tendto the still water values with increase of AIL.The amount of these variations is larger incase of the low ship speed. Especially, the

Propulsive Performance of 4 Container Ship in Waves

other hand, the variations of )2R and (1-0 withwave height are comparatively small.

From the results of the resistance and selfpropulsion tests in irregular waves with thewave spectra as shown in Fig. 2, the self-propulsion factors are analysed by the same'procedure as mentioned above and are pre-sented in Figs. 20 and 21 as a function ofsignificant wave height and of mean waveperiod, respectively. It can be said that theself-propulsion factors in irregular waves donot vary so much with the mean wave periodand give almost the same values as those instill water. The propeller open-water effi-ciency in irregular waves decreases with the

00 I-C

/1,3

fiR

o 8 10

dais 40

12 la

JO

Fr,.020,

1 1

25 LA.

IR

F.025 , M.1.5

1-10

6 810, C) 40

- () 20'

14.-w 20 80 50 40 6/C,, 20

Fig. '19 Effect of wave height on self-propulsionfactors in regular head waves.

12 14 16

20 25 0/H,a

Fig, 20. Self-propulsion factors in irregular headwaves (effect of significant wave height)

1

Fn ;,0.15

11

-r---\-7----1;?

,,6

Fn

rii

-.- -----C.T--

-1-w----025

/lN

Fn,r 0.30.

----\--:-----;1,0

-----'-------- -------- --'<'----

,

_

---------- /9

F. . 0,15 in still water F,,.5

020

,----.--42--..-- 4-i-r, a 0, coI- l

. . .i.- ute na

...:__1 - w. . s.

4,,,,_____,.-AI 4a ..,

Fn - 0.25 1Fnft 0.30

n"

I.''t 2e ' - u4

'.` ^ H,taro.

fv. )

0 L 2.0 05 1.0

,Fig, 18 Self-propulsion factors in regiflar headwaves

propeller open-water efficiency decreases re-markably in the region of A/L-,-0.9-1.3, whereship motions are severe and resistance increaseis large. And in this range of wave length,the values of (1w) and (1t) are larger thanthose in still water, while the variation ofrelative rotative efficiency with wave lengthis comparatively small and the value is nearlyequal to that in still water. The similarresults were obtained from the experimentsby Moor et al.".

The effect of wave height on the self-propulsion factors in regular head waves isalso studied and the results are presented inFig. In this figure, the values of self-propulsion factors in still water are shown bythe horizontal broken lines. From this figure,it can be said that the propeller open-waterefficiency decreases considerably, while thevalue of (1 w,) has a tendency to increasewith the increase of '.wave height. On the.

Fn. 020 1,09 fn-025,2/L.09

5

1 01

05

,15

0.5

1.2

0.61

Co

C.

Co

C.4

1.0

Fn

35

020

05

4

19. 10I - I I


increase of significant wave height, and thevalues of (1-w.) have a tendency to increaseslightly with that, but these tendencies arenot so remarkable as those in regular headwaves. And when the significant wave heightof irregular waves is low, the self-propulsionfactors have almost the same values as thosein still water.

In order to study the effect of propeller

as

0.

0.8

0.

0.0

0.5

0.-5 1.0 1.25 05 0.75 10 A0A (.25

Fig. 21 Self-propulsion factors in irregular headwaves (effect of mean wave period)

10 15

C. (cm)

Fig. 23 Effect of wave height on self-propulsionfactors in regular head waves (effect ofpropeller diameter)

diameter on the self-propulsion factors inwaves, self-propulsion tests with the propellermodel A and B of different diameter werecarried out in regular head waves varying thewave length and the wave height for the speedof F.-=0.20. The analysed results of themeasurements are presented in Fig. 22 as afunction of wave length and in Fig. 23 as afunction of wave height. The relative rotativeefficiency s is hardly affected by the propellerdiameter and by the wave length. In caseof propeller B of smaller diameter, both thevalues of (1-w8) and 720 are smaller than thoseof propeller A, but this is due to the reasonsthat the propeller of smaller diameter givessmaller values in still water. The differencesbetween the values in waves and those in stillwater is not so large. In Fig. 22, the calculatedresults of (1 - we), r IR and )20 obtained by themethod mentioned in 5.3 are shown and givefairly good agreement with the qualitativetendency of the measured results.5.2 Wake Measurements in Propeller Disk

in WavesIn order to clarify the above mentioned

characteristics of self-propulsion factors in

Prop,dm .Ex pertment

in waves in sit!! water0,15 m 00.112m

Fn z 0.20_

Xnt_

18 = 1.0

_

_ _

1 -040

0.

vo- 0

"1..

° u.

- in still ware, Fn 0.20

2--e----9-,6-6i - t

0. /-4, , 7 /.....-

,2, 2, ____

Fn. 0.25

4F, 0.30

R

13

- r - ,

So

I - We -2,

ro I' st.c). .

a'

T".6.). .

Prop.dm .

0,10 rn0.tr?rn

Experimentin 051,// unarm

0 -. _Cola*, ton- -

7.4- ....--- a-a- -",-- f '',Pe

-7- .. . --- -...=-_:: i:

Fns 0 20

InA--,s-7...1 tFti

- -.-s2 CI

-0

Li ,,,....,_

-I,.,

' 6 Ei

o

$ ..

ce $-0.....8 o

a,

O.-

ti

A a ..,..'

°a 0

0

8 .

8-0- -

a 5 1.0 1.5 2025A/C

Fig. 22 Self-propulsion factors in regular headwaves (effect of propeller diameter)

1.2 14 1.6 1.0 1.2 /4 1.6

12

1.0

0.

0.6

0

1.2

1.0

0.

0

0.

0.

0.

o.

0.8

0.7

0.6

0.6

0.5

0.4

03

0

r

0.15

(-7

-..

-

Propulsive, Performance of a Container Ship in Way' ,37

waves, the radial distribution of axial inflowvelocity into the propeller disk in regular, headwaves were measured by using the circularring type wake meter. The outline of thecircular ring type wake meter and the attach-ing to the ship model are shown in Fig. 24.The force acting on the ring is measured bya strain gage as the displacement of cantilever.Making use of the relation between force andvelocity, the inflow velocity into propeller'disk can be obtained.

The statical calibration of this wake meterin uniform flow was conducted at the towingtank varying the speed for each of the rings,and it was confirmed that the force acting onthe ring was proportional to the squared speed.The dynamical calibrations of wake meterwere also conducted at the conditions of forcedpitch oscillation in still water and of the re-strained model in regular head waves at theconstant speed. Both the mean values andthe fluctuations obtained from the dynamicaltests agreed well with the predicted valuesusing the results of statical calibrations. Asummary of test conditions of wake measure-ments are shown in Table 4.

The measured results when the model isfree to heave, pitch and surge, are presentedin the form of the ratio of the mean inflowvelocity in the ring plate in regular headwaves (1w)w to that in still water (1w,0$as a function of the ratio of radius of thering to that of the propeller, rIR and areshown in Fig. 25.

As shown in this figure, it becomes clearthat the values of (1w0w1(1w7,)s are largerthan unity as a whole. Especially, the closerthe measuring position is to the center ofpropeller, the larger the values become, andthis means that the distribution of the meaninflow velocity in the propeller disk in wavesapproaches that in uniform flow, as shown inFig. 26. Furthermore, the values becomemuch larger in case of 2/L=1.1, where theship motions are very severe.

In order to make clear these phenomena,wake measurements were carried out for thefollowing conditions.

.(1) Restrained model tests in regular headwaves.

Forced Pitch oscillation tests in stillwater changing the frequency of pitch motion.

.56I (I -taniv

(1- viOs

14

Propellerboss

.A2

0.8

0.6

02

0.2

Container ship model

fn= 0.20

0.4 0.6

Fig. 24 Circular ring type wake-ineter

(1 -Lan)", . m regular wavesSi - ahosirs sr//I water

540.50.81.11.52.0-- 2.5

----0-- 0

0,8


Fn = 0.20

A/t

1 5--- 2.0in Stillwater

az 0,4 0:5° 8 r/R 50

Fig. 26 Distribution of (1w0) in propeller taskin regular head waves and in still water

1.0r/R

Pig. 25 Ratio of (1w,.) in propeller disk inregular head waves to that in still water

0.4

Propelleboss

/.0

3'81 Shoichi NAxAmURA, Shigeru NAITO,

Forced pitch oscillation tests in still'Water changing the amplitude of pitch motion.

The model is free to ship motions inregular head waves changing the wave height.

When the ship model is restrained in regularhead waves, the values of (1-w)w are not'So much larger than those in still water, asshown in Fig. 27. However, the mean valuesof inflow velocity at the condition of forcedpitch oscillation, (1-w0)p, are much largerthan those in still water, especially at a radiuscloser to the center of propeller and higherfrequency of forced pitch oscillation, as shownin Fig. 28. And it is shown in Fig. 29 thatthe larger the amplitude of forced pitch oscil-lation is,. the larger the values of (1-w0)pbecome near the propeller center. And it isalso shown in Fig. 30 that the larger the waveheight is, the larger the values of (1- w)wbecome. It is concluded, therefore, from thesefacts that the increase of (1-w5) in waves

Fig. 27 Ratio of (1-w.) in propeller disk in.

regular head waves to that in still water -with restrained model

4.6

1.4

8.2

100

4.15

405-

(1- wa)iiuta),s

0

Container ship model 0. Remained

"Fe= 0.20r/R= 0.576

,t0 1.5 2.0 2.5 AA

N

NNNNA

NN Nas,

H.1,-11.1e)p forced pitch,in still water

Fig. 28 Ratio of (1-w.) in propeller diskforced pitch oscillation test. to thatstill water

P.O

in

1.31 (1- 1110P( I -1.11n)5

Container ship modelForced pitch

&ea...0.521kFa= 0.20

II -urn), : forced PitchII (1-ura)sS instill water

2.0 0, (4e5)

Effect of pitch amplitude on the ratio of(1-w0) in propeller disk in forced pitchoscillation test to that in still water.

41- wah, in regular waveswah in still water

00.q1.5

10 " cu (cm) 2P

Fig. 36 Ratio of (1-w.), in propeller disk inregular head waves to that in still water(effect of wave height)

compared with that in still water is mainlydue to the magnitude of ship motions.

It has been said that the propulsive per-formance in waves is explained fairly well bythe overload effect on the propeller due to theresistance increase in waves". As mentionedabove, however, the self-propulsion factors areaffected considerably by ship motions, so itis considered that the results of the overloadtests in still water are not always coincidewith those of self-propulsion tests in waves..This fact has been proved experimentally byMoor et al.' and the authors".5.3 Theoretical Investigations on Self-propul-

sion Factors in WavesIn order to investigate the Characteristics

of self-propulsion factors in waves, an attemptwas made to calculate the self-propulsion fac-tors by using the propeller characteristicsobtained from the blade element theory andthe results of measured wake distribution inthe propeller disk in waves.

Vector diagram of inflow velocity into pro-

,111

11

II

It

Propene!boss

\= 0.20 Freq.

(Hz)0 0.53-- 0.60

0.72--- 0.88o 1.0q

(I - W0)5

Container shlp modelForced pitch

-- -

0.2 0.4 0.6 0.8 VR

Eiln)s


FA = 0.20r/R = 0:576

1.00

-

(1-

0

13

1.2

1.0

0 0.254A

1.0 3.0 4.0

Fig.

in

(I-

0.5

12

p pitch ratio'0 : propeller diameterR D/2V : ship speed

: chord length


419.= 2 N r

Fig. 31 Flows into a. blade ,element at radius of r

peller blade element at radius r is shown inFig. 31. We consider only the time averagedmean values of Inflow velocity. Accordingto the two dimensional blade element theory,the lift acting on a blade element is givenby

dL=n-pcV.Vdr ( 2 )

where V and V are the parallel and perpen-dicular components of inflow velocity to thechord of blade, respectively, and are expressedas follows::

V.=Vo cos /34+ Vz sin /36 1

V=V0 sin Po V cos po

Writing the number of revolutions of pro-peller as N, we get

tan tEla =pD/27r(p: pitch ratio) ,V0=27cNr , V.= V(1-0

( 4 )

The thrust and torque due to the lift ofeq. (2) are given by

IdT=dL cos /30dQ=dL sin po r ( 5)

Integrating dT and dQ from boss to tip ofthe propeller and multiplying by the numberof blades z, we can get the thrust and torqueof the propeller.

If the thrust and torque coefficients Kr. andKQ of the propeller open-water characteristicsare presented by a quadratic equations foradvance coefficient J as follows:

KT= T/PN2D4=a+bJ+cjaKQ=Q1pN2D5=d+6+fr

( 6 )

°The constant coefficients a,, b c are givenby

3

22(dr

cos Po sin /30(r4 R R )R

b=1-32-(L-)(cos2 19, sin° AY4 R

X cospo(r\(drR )Rc=-- H sin po

4 , R )TrZ C -

cos 130(dr\I

In case of' constant pitch propeller, therelation between a, b, c and d, e, f is

d=(p127r)a ,e:-.-=(p127)b, f=(1)127r)c (.8')

The values of coefficients for this propellermodel become

a =2.166 , b= 1.567 , c= 0.580( 9 )d=0.345 , e=O.250, f=O.092

and the propeller open-water efficiency No isgiven by

0=(ICTIKe)(.1127r)JIP no)

If the pitch ratio p is equal to 1, )25=J.According to this method,

KQIKT=P12r (constant) , (11)

and the relative rotative efficiency 7iR is alwaysequal to 1.0, In order to avoid this fact, weintroduce the drag-lift coefficient Si. Using

dL and .dD are expressed as follows:

dD=6,4L , e:,=tan-i (V21170)dL=n-pc(V02+ Vx2) sin (Po-- dai)dr

(12)

Then,

dT=dL(cos ,8i ei sin A)}(13)

dQ=dL(sin pi + ei cos Pi)r

In the same way as mentioned above, thecoefficients of the quadratic equations of KTand KQ are given by

dr= 7r4 (i) sin Pp(i)2(C)

ZZC

4

412(i)(zi. sin po + cos po(i)(9)

(i), cos po(A;)

(7)

C

V,-V(I-ur)

( 3 )

,

(


r )( dr\= (--c-.) cos tio(8 R R R

(14)

and the values for this propeller model are

a'=2.753, = 3.021 , c'=0.285 (15)d'=0.188, e'=0.252, = .435

Denoting the former method as A, the latermethod as B, the calculated results of pro-peller open-water characteristics by the twomethods are expressed in Fig. 32, where si isassumed to be 0.2 and constant. Though thecalculated results of thrust and torque coef-ficients by the two method give considerablylarge values compared with the experimentalones, those of propeller open-water efficiency

as a ratio of thrust coefficient to torquecoefficient agree fairly well with the experi-mental results. And the propeller character-istics at behind condition in regular waves arealso calculated by the same methods as men-tioned above using the measured distributionof inflow velocity into the propeller disk andthe mean values of number of revolutionsmeasured by the self-propulsion tests in waves.

2,

0

0.6

0.4

0.2

Calcu lotionMethod A

Ever 'men

0.2 04 6& 0.8 1.00

K,

10,K0

10

2.0

(0

Fig. 32 Propeller open characteristics calculatedby blade element theory

075

070

ass

060

Fig. 33 Comparison of self-propulsion factors inregular head waves between experimentsand calculations using propeller opencharacteristics by blade element theory

Then, the effective wake fraction w relativerotative efficiency 72 n and propeller open-waterefficiency 7;0 in regular head waves are obtainedby applying the thrust identity method usingthe propeller open-water characteristics in stillwater calculated as mentioned above.

The comparison between the results ofcalculation and those of experiments is shownin Fig. 33. In the figure, the mean nominalwake fraction w in the propeller disk whichare obtained by means of volume integralmethod using the measured distribution ofinflow velocity, is also presented. The cal-culated value of iR by the method A is alwaysequal to 1.0, but the one by the method Bgives a similar tendency to the experimentalresults. It can be said that the qualitativetendency of the calculated self-propulsion fac-tors (1 U) g), VR and r,o, shows fairly good agree-ment with the experimental ones, though thereare some differences between them quantita-tively.

The properties of wake fraction, relativerotative efficiency and propeller open-waterefficiency in regular head waves became evi-dent considerably, but the property of thrustdeduction factor in waves is not investigatedin this study.

2,Comcmet V, MO.

_------

1 to. 0.20

. .-

-s-srill ware,

---- -- --Cooper ornent

.......7 -....__.

I - tu

__

Calculi, r oonMethod A

_.77- -- ---.

_...........--- ...--o,

2 4I - tut,

2o

m 5011 warer

.

-./...

...-----

Z

8(C )c. sin po( )

R RdrR

)1.1

7I22e =-8

(C .

R)(sina cos

r dr\0)(R )R 1.0

0.5 1.0 1.5 2.0

0.6

05

0.5

0.4

f'

-'1.0

6. Propeller Load Fluctuations in Waves6.1 Inflow Velocity Fluctuations into Pro-

peller DiskInflow velocity fluctuations at the propeller

center in regular head waves which are neces-sary to investigate the propeller load fluctua-tions are expressed as follows:

S Upv U m t

VpilVw+Vmf

.= Caw exp (kh){c°s }.(w,tkl)sin

+we{VE2+F21 S cos I f.t)

t 'V G2 + H2 j- (sin )\ 1192 f

where

Up, V p: Axial and vertical components ofinflow velocity fluctuations at thepropeller center in regular headwaves

Uw, Vw: Components of Up, Vp due to or-bital motion of waves

UM, V2: Components of Up, Vp due toship motions

h, Vertical and horizontal distancesfrom the center of gravity of shipto the propeller conter

E= x sin oh80 sin enF=x0 cos oz: h0 a cos enG= za sin E4 +10a sin enH= za cos o+100 cos Eoc

131= tan" (FIE)132= tan' (GIH)

Surge motion : x = xa cos (0)J + E.c)

Heave motion: z=- z cos (wet + E,c)

Pitch motion 0 = 0 0 cos (a, et + 2 0 c)

Calculated results of Up andV p by eq. (16)for four Froude numbers are shown in Fig.34 and Fig. 35, respectively. The componentsof Up and Vp due to orbital wave motionsand ship motions are also shown in the figures.

Next, we consider the spectra of U1 andVp in irregular waves. Let S(w6) denote thewave spectrum, and Hx(we), &w0), and 110(w c)


(16)

05[

0.4

0.3

02

0.1

7:.

1.0

05

Fn. ars0.20,

025030

Fn. 015\020025030

r'cr

Inflow velocityby ship motionby orbital motiontotal

=

Fig. 34 Calculated axial component of fluctuationof inflow velocity into propeller disk

Inflow velocityby ship motionby orbital motiontotal

Fn

20 A., 2$

25

the response amplitude functions of surge,heave and pitch motions, the spectra of Upand Vp, Sur and S, p, can be expressed asfollows:

Sp(w)=.34.-(a),)[{0) exP (kh))2

+0)e2{11.2(a))+112142(0),)

+2h1I(co,)H,(co0) cos (o.cs))+201(00 exp ( kh)f1102 (E00)+ H02(w,)

+2h11(c. e)Ho(co,) cos (swc Eec)}1 2

X cos (131-141)] (17)

Svp(we)=Sc(w,)[{w exp (kh)}2

e2{I102 (0) e) + H ,2(a),)

+21112(w0)Ho(w0) cos (s:Eoc))

20twe exp (kh){H02(we)+121-1o2(0)0)

21110(we)110(o)0) cos (s,c coc)}112

X cos (132+1z1)} (18)

0 05 to 15 20 X/ L

Fig. 35 Calculated vertical component of fluctua-tion of inflow velocity into propeller disk

1:

025

0-30025

02

15


The spectra of inflow velocity fluctuationsat the propeller center in irregular waves canbe obtained by using these formulae.

However, the calculated values of the pro-peller load fluctuations by using Up of eq. (16)are larger than the measured ones. It is wellknown that the wave height at the stern islower than the incident wave height becausethe incident wave is deformed by the ship.This fact must be considered to calculate thepropeller load fluctuations because U5. occupieslarge part of Up. In this study the waveheight reduction of the incident wave at thestern with a restrained model is calculated byusing the three dimensional periodic sourcesas the presentation of the ship hull based onJinnaka's method').

The wave height reduction of the incidentwave at the stern is measured with the re-strained model in regular head waves forfour Froude numbers and the results arepresented in Fig. 36 in the form of the ratioof the wave height at the stern to that ofthe incident wave, Cw'/w, as a function ofAIL. In the figure an approximate formula,Cw'/Cw=0.2(A/L)+0.5, which is obtained fromthe analysis of the experimental results withthe mathematical ship forms by Jinnakalland the calculated results by the above men-tioned method are shown. The approximateformula agrees fairly well with the experi-mental results.

The fluctuation amplitudes of effective wakeare obtained by using the time histories ofthe fluctuations of propeller thrust and revolu-tions measured at the self-propulsion tests inregular head waves and the propeller open-water characteristics. The results are pre-sented in Fig. 37 in the form of the ratio ofUp to the ship speed V, and are comparedwith the calculated results by eq. (16). Thecalculated results of Up by taking into accountthe wave height reduction of the incidentwave at the stern show closer agreement withthe experimental results.

It is confirmed from the above mentionedresults that the fluctuations of propeller thrustand torque are mainly caused by Up and can

Calculationwith wave height correction

- without wave height correctionExperiment

Wake fractionFr) 045 0

020 A

025 0

030 o

2.2)=010

1.0

0.8

0.5

Experiment0.4 o Fn = a/5

--- 0.2 (X4.)÷ 0.5 0.20

0.2 --- Cal by 3-dim.period. source

C' 0.250 0.30

0.5 1.0 1.5 2.0 A/L 2.5

Fig. 36 Ratio of wave height at the stern to thatof incident wave with restrained modelin regular head waves

o 510 15 20 x L. 25

Fig. 37 Comparison of fluctuation on inflow ve-locity into propeller disk between experi-ments and calculations

be predicted by using the propeller open-watercharacteristics, considering the wave heightreduction of the incident wave at the sternand the fluctuation of revolutions of the pro-peller due to the response characteristics ofthe prime mover.6.2 Calculation Method of Propeller Load

FluctuationThe fluctuations of propeller thrust and

torque in regular head waves, JT and 4Q,can be expressed from the propeller open-water characteristics in still water by usingthe fluctuation of axial inflow velocity intopropeller disk JU and that of revolutions ofpropeller JN, as follows:

44QT =p.1U4JI.(19)

where

' 0.5

0.4

03

02

0.1

0,20

p..(PTU PT N)PQU PQN

and indicates the propeller characteristics.If the propeller open-water characteristics

are approximated by the quadratic equationsas shown by eq. (6), P is given by

pD2(bDN-E2cU), pDs(2aDN+bU)),(21)

' p.D3(eDN+2fU) pD4(2dDN+,eU)

AT, GIQ and AN are affected by the charac-teristics of prime mover. Supposing that 462is input and AN is output of the prime moverand phase difference between IQ and AN isabout 180 degrees,, AN is expressed by ../Q asfollows:

AQ (22)

where H is the characteristic value of theprime mover.

The solution of eq. (19) is obtained by usingeqs. (20) and (22) as follows,:

4T4PTU PTN'PQH)4U1-I-PQN

4QPQU AU1-1-PQN-H

AN,- PQU AU1+PQNH

Making use of these equations, the fluctua-tions of propeller thrust and torque can beobtained by considering the characteristics ofthe prime mover and the fluctuation of axialinflow velocity at the propeller center.

The value of H used in this calculationa constant value of 44.31/kg m sec, which isobtained from the result of the dynamic cali-bration test of the prime mover.

In case of irregular waves with the spectrumof S(o), the spectra of AT, 4Q and ANS47-(01.), SJe(w.) and -S4u(04)can be expressedas follows:

S 4T(W e)=PTN 'PQU 2

PTU 1+PQN'IlH) SUP(W'e)

iSjg(0e)= (1 +PP:. HY-Sup(f0) 1(24)-

Sjw(a),)=/ H.PQu )\2 Sup(04)\1+ PqN

Propulsive Performance of a Container Ship in Waves. 43

(20)

(23)

This result is obtained by neglecting themoment of inertia of the prime mover. Asthe revolutions of propeller at the self-propul-sion test are usually kept constant by control,the moment of inertia of the prime movercan be neglected, but when the torque iscontrolled to be kept constant the effect ofmoment of inertia must be exactly taken intoconsideration.

Next, let us define the response amplitudefunctions of AT, AQ and AN obtained by theexperiments in regular waves as follows

1-147,(0))-= ATI pgB2Cw

H4Q(o))=4Q1pgB2a:w (25)

114N(v)=21N-D3V1gB2Cw

where

breadth of shipD: propeller diameter

Cur: wave height of regular waveV: ship speed

Making use of the wave spectrum S(co) andI I Jr(C0), 114Q(W), 114N(W), each of the spectraof propeller load fluctuations in irregularwaves is given by the linear superpositionmethod as follows:

Sj7-(0))=(pgB2)2Hdr(qSc(0))S.,Q(0)),(pgB2D)2HJQ(0.)2Sc(w) (26)

S4N(c0)=(gB21D3V)2H4N(w)2St(w)

The significant values or other statistical'values of propeller load fluctuation can bepredicted from these spectra.6.3 Results of Experiments on Propeller Load'

Fluctuations(1)1 Propeller load fluctuations at self-pro-

pulsion testsa) In regular head wavesThe propeller thrust and torque at self-pro-

pulsion tests in waves are measured by usingthe self-propulsion dynamometer which is at-tached in the ship model. At the measure-ments of propeller load fluctuations, the ap-parent fluctuations caused by the movementof self-propulsion dynamometer due to theship motions are considered to be included in

(

JN= H.

is

B:

44 ,Shorchi NAKAMURA, Shigeru NAITO

'the measured values. It seems to be necessaryto take into account the following two factors.

The inclination component of the weightof propeller and shaft due to pitch motion ofthe ship model.

The component caused by surge motion,of the ship model.

Statical inclining test and forced surge oscil-lation test of the self-propulsion dynamometerwere carried out anti the correction valueswere obtained.

The measured 'double amplitudes of pro-peller thrust and torque are divided by themean values of total thrust and torque, andare presented in Figs. 38 and 39 as a function

ilT/T

0.

0.

0

0.

a

0.

4010a

0.

0.

0.

0.

0.5 1,0

0

a

10

0.

0.

0.

Of AIL. In the figure, circular spots are the,measured values and the dotted lines are themean line of corrected values. It seems thatthe calculated results of thrust fluctuation byeq. (23) taking into account the fluctuation ofpropeller revolutions and the wave heightreduction at the stern agree well with themeasured results, while those of torque fluc-tuation show some discrepancy.

Another method for calculating the propel-ler load fluctuations in regular waves by usingthe Sears' non-stationary airfoil theory hasbeen developed by Yuasa12). The results bythis method are shown in these figures. Thecalculated fluctuations give considerably largevalues compared with the measured ones, butthe ratio to the total thrust or torque showfairly good agreement.

b) In irregular head wavesFrom the results of self-propulsion tests in

Irregular waves with the wave spectra asshown in Fig. 2, the significant values offluctuations of propeller thrust and torque,47.113 and 4Q113, are obtained by the spectralanalysis. These values are divided by thesignificant wave height of the correspondingirregular waves, and are presented in Figs.40 and 41 as a function of significant waveheight and in Figs.. 42 and 43 as a functionof mean wave period. The calculated resultsby eq. (24) and eq.. (26) are also shown in

Fr= W5 ...--'-------.., Thrust-...

'-..-&---o0.3

Fructuation in, Regular ayes

'-'-'- ......----- '-------

, ''.111- -I. 0.2 0-9J't1=-----zr -

. '. .

C Expewnent -'- Cat by Sews' function

--Mean tine of. erp,, corrected - Da., c.n.diVagcS,.

Fr =0.25 a3 rconjer.---Dc, woe. ,eval iiirrio.---, ...,.......------_,

01-

wave height reauctian

..- ,..,...1 9 '

-... ---___---- ..._ ...... :7:7.0-O-0---oo-6 o 1

.104Ti, Thrust Fluctuation.._

thg.:21.:2,.. 025_,_--

- -CC.ILAV prppr.,open characr,

-- -D'a,'Z'rfZi,ng.f e`f.' ,..11`Areh 0.2um. height reduction

in lttegulat,,Waves

Fr ..------'

t .3_4- sP-"I

--- PrZnIts4cfgr-amp. operator

0.6

si A a

- -

Fr =G.30

EIP.,eorrecred6

t

fr,.05 --------,. Torque--..

Fluctuation in Regular Waves

Fr =0.20

c.°Z00,/

'

I.....-'6 0 ..=0.1.5c.w....1,9_. . :,,,,,.....:1-:,..,

0 Loeurnen I

- - neon tine C/ 900 ,.corrected '- Do..ird.diarmodc,,,

- Fr =0.25--.---._ .--.... --- DigtVeltrfagr'''-....._ ',........---- -'"- n.--. --...,...

----------i-a).--,'Bp crce--..-.12---,,--.

.

R.- 0.30 --o--o_ 1

0" - L6-64O-2 ' ---- --::31 '

2.0 05 i.0 LS A/L 2'0

Fig. 3& Ratio of thrust fluctuation to mean thrustat self-propulsion tests in regular headwaves

660 50 40 30 n's H,3/1 60 50 40 30 25 Hte34_

14 18 6 10 .14 18

15,4

Fig. 40 Effect of significant wave height on thrustfluctuation at self-propulsion tests in it--regular head waves

as 10 1. .2.0 0.5 1.0 /.5 AA .

Fig. n Ratio of torque fluctuation to mean torqueat self-propulsion tests In regular headwaves

0.4

0.

0.1-

'

G.30

- 0,4-

8

0.2

0.I

A, 2

Irt

Figs. 40-43, and are compared with the ex-perimental results.

It can be said that the calculated results bythe method using propeller open-water charac-teristics show closer agreement by taking intoaccount the wave height reduction of incident'wave at the stern and the fluctuation of pro-peller revolutions.

The significant values of measured fluctua-tion of propeller revolutions in irregular wavesare shown in Figs. 44 and 45 as a functionof significant wave height and of mean waveperiod, and these values are used for the

LO

0.8

0.6

0.4'

0.2

1.2

1.0

0.8

0.6

0,4

6 0 14 18 6 10 14 1860 50 40' 30 25 1-1,A. 60 50 40 25 Ri434.

Fig. 41 Effect of significant wave height on torquefluctuation at self-propulsion tests in ir-regular head waves

112 1:4 L6 1.3 1.2asa.75 1.0 A.4. (.20

Fig., 42 Effect of mean wave period on thrustfluctuation at self-propulsion tests in ir-regular head waves

PropulSive Performance Id a Container Ship in Waves

3

2

2

fi

6.6050

10 1418 6 '10 14 18

4i) 36 25 11,, 60 SO 40 30 25 H,,.4

Fig. 44 Effect of significant wave height on fluc-tuation of number of revolutions at self-propulsion tests in irregular head waves

calculation of fluctuations of propeller thrustand torque.

(2) Effect of wave height on propeller loadfluctuations

'The relationship between wave height andpropeller load fluctuations are given by usingeq. (23). Assuming that the fluctuation ofpropeller revolutions is equal to zero, the pro-peller thrust fluctuation is given by

zIT=PruilU= pD2(2c U+ bDN)al U

pV1Ns(2ci

b)Ns(i+ NAW1(27)

40, Torque Fluctuation in Irregular Waves

Fn= 0.2010--3L,'''', Fn= 0.150.3.m.,m) ....------, ------- - 1.0m 2,,

..,.....-

0,8-4,..

open charact.' - Cgisby:iferi9:0Prop. revol. /NC, 0.41

' -Do, consider, prop, revol. 'tut,. a- Wee e helm reduCtiOn

----_-_-------t......,--

...-'' -- - - -

Predict. by linear ouPer67gigHusing response 0,77P. OP.

1,1

,Fn-0.254.2

Fn- 0.30 A

...._.,;;;

1.0

.------L,.

, 0.8',A

1,..,.., 0-6..ii

,.... 0,4

...-t,f: , ---,-"' Exp.1. ....----- Exp.,coir=c-red

T., (SKI

1040, Torque Fluctuation1-11/3 Fn= 0.15

(kgrronJ - /.0

0.8r.......,....

0 6--

-Cgnitlierro.PbroepPe:;eff07:11. /PFiC' , 40.4---Os. consider. prop. rev 10 .wave height reductiOn

in Irregular Waves,

Exp. Fe- 0.20ExO. , corrected

_----------1--i.-.

Predict. by linear Su erpositionusing response amp.Peperoior

Fn=0;25

al'2-o

' - ' - ----- IV'

H,,3(cm) 0.61

Fn=030

r - ,' 11 I, A

_.___ _ _ r --",:

'Ho(cm), ,

Atha Revolution FluctuationHI/3

(Vsec.m ) Fn= 0.-15 n 31-

-8re- -6- -01 2

aon

o Experiment,1

'Plesf 1(4' iiesVpjtirieamsg.Pg,>:?csilz.P"

in irregular Waves

Fn= 0.20

8 ,,

- lc

Fn =025

C

0rs

tP 0 0 1

- ..

Hp-11an)

mo

1Fr==-0.301

do

a0 000

Hp.,(cm)

1 id.dTvl Thrust Fluctuation- Hv Fn=0. /5 0.6'(kg/m

..-- - --------------- ---,

1 1--____ Cal. by prop open choracr.

.conspiet prop. reiVtuCt,' -- -DP, consider, plop r 1.14,C s 0.2.

in Irregular .Woyes

Fn=0.20

waveheight reditCri n

r 4---s.......:-.-

...t ''''''

PuIV;4Tp,i,,,i.gr,;,nspuPg,,LHgiln. .

=0.25

6

, 0.4,Iero-,c ,

.

Fn= 0.30

5Pc---.-------

o Exp. rExp.,corrected

8_......

-- ----..-"-- 11-1

--

- ----------- - rp tsec )

14 1.,6 18 1.2 54 /;6 1.

0,75, 1.0 AA., 25 AS 0.75 1,0 A,A 1.25,

:Fig. 43 Effect of mean wave period on torque.fluctuation at self-propulsion tests in ir-regular head waves

1.6 /,8015 50 44425

0.8

0.6

0.4

0,2

0112

0.8

0.6

0.4

0.4

02

0

0.

0.4

1.4

-

0.2

/.0

-

04

-

45

1.2

0514

3

Fig. 45 Effect of mean wave period on fluctua-tion of number of revolutions at self-propulsion tests in irregular head waves

2

0.10

505

-ruzt

6

09

1-10 , 15 kr,lir e'o. 20

6

lo

ab so 4b

>vb.'s 10,

CpJ

uc,,, "Fig. 46 Effect of wave height on fluctuations of

propeller thrust, torque and revolutionsin regular head waves

where

N: mean value of propeller revolutionsin waves-=-Ns+NAW

Ns. number of revolutions of propellerin still water

NAW mean increase of propeller revolu-tions in waves

We can consider that the amplitude offluctuation of axial inflow velocity into pro-peller disk JU is proportional to the wave

amplitude, NAW is proportional to the squaredwave amplitude and the mean value of ad-vance coefficient in waves I does not changewith the increase of wave height.

Putting I U= k, NAw=k2C.2, 9D3(2cJ+b)Ns=k, eq. (27) becomes

4T,--k1k3(1+ (28)Ns

When N Aw is equal to zero, IT may beproportional to the wave height. On the otherhand, if N AW is proportional to the squaredwave height, IT becomes slightly larger thanthe values obtained from the linear relationbetween IT and wave height, because thevalue of NAWINS is usually smaller than 1.

The effect of wave height on the fluctua-tions of propeller thrust, torque and revolu-tions at the self-propulsion tests in regularhead waves is studied and the results areshown in Fig. 46. The measured values aredivided by the wave height and are presentedas a function of wave height. In this figure,"Calculation B" is a method using the shipmotions calculated by the strip method andthe orbital motions of incident waves takinginto consideration the fluctuation of propellerrevolutions. "Calculation C" is a methodusing the ship motions obtained from theexperiments and the orbital motions of wavesconsidering the wave height reduction at thestern.

It is generally said that the amplitude ofpropeller load fluctuation is approximatelyproportional to the wave height, except thecase of excessive high wave height. As tothe effect of wave height on the propellerthrust fluctuation, the above mentioned tend-ency is shown in Fig. 46. The relation be-tween the measured fluctuations of propellerthrust in irregular head waves and the sig-nificant wave height is also show the sametendency as shown in Fig. 40.

7. ConclusionsFrom the analysis of the experiments and

calculations the following conclusions may bedrawn:

Revolution FluctuationHo

,//Sec, Fn =0. /5 3

in irregular Waves

Fn=0.20

2z 2 --------- 9---- D rii

D &pet, In.( I----- Predict, by linear superposition

using resDcnse amp. Operator

' 10

Fn=025 Fn 0.304

? -------- .. ----- - - 3 E

a° 2 .,--1 ----------- ---c

.,.. /lo (SE, ) ro (sec)


1.2 4 1.6 1.2 1.4 1.6

0 5 /I. 1.0 I e5 25

3

2

4

2

0:5 1.0

5

5

0

2

Measured pitch motion in regular headwaves agree well with the calculated resultsaccording to the 0.S.M., while as to the heavemotion the calculated results is larger thanthe measured ones in the range of A/L=1.01.5, and the difference is large at the higherspeed.

Measured heave and pitch motions inregular following waves agree comparativelywell with the calculation according to the0.S.M., but the surge motion is considerablylarger than the calculation using the Froude-Kriloff force.

Amplitude of heave, pitch and surgemotions is proportional to the wave height ofregular waves and the linear superpositionmethod is valid for predicting the ship motionsin irregular waves.

Measured results of resistance increasein regular head waves agree fairly well withthe calculated ones by Gerritsma's methodfor the ship model used in the present study.

Mean increases of propeller thrust,torque and revolutions in regular followingwaves are considerably smaller than those inregular head waves.

For predicting the mean increases ofresistance or propeller thrust, torque and revo-lutions i5 irregular head waves, the linearsuperposition method seems to be useful fromthe view point of practical purpose.

Linear relationship between the meanincreases of resistance and propeller thrustand torque and the squared wave height isvalid for the range of the wave height ofL/50-L/30.

Self-propulsion factors in regular headwaves vary considerably with wave length,especially in the range of 2/L=1.0 1.5 whereship motions are severe.

Propeller open-water efficiency in ir-regular waves decreases with the increase ofthe wave height, and the values of (1we)have a tendency to increase slightly with theincrease of wave height.

Time averaged mean values of (1w,)in waves become larger than that in stillwater due to the ship motions, and the radial

distribution of the mean inflow velocity intothe propeller disk approaches that in uniformflow and 72R approaches unity.

Properties of (1w,), )2R and 720 inwaves are fairly clarified by the measurementsof flow field at the stern.

Fluctuations of propeller thrust andtorque are mainly caused by the fluctuationof axial inflow velocity into propeller disk andcan be predicted by considering the waveheight reduction of incident wave at the sternand the fluctuations of propeller revolutions,using the propeller open-water characteristicsin still water.

Propeller load fluctuations in irregularwaves can be predicted by using the propelleropen-water characteristics.

The present study was carried out as a partof the research works of the 125th ResearchCommittee of the Shipbuilding Research As-sociation of Japan. The authors should liketo express their gratitudes to the committeemembers by whom many fruitful guidanceand discussions were given. The authors alsoexpress their appreciations to Dr. R. Hosodaand Messrs. M. Inoue, R. Inoue, A. Inouefor their cooperation.

ReferencesF TASAI, M. TAKAGI, M. GANNO, H. ARAKAWAand M. KURIHARA: "A Study on the Seakeep-ing Qualities of High Speed Single Screw Con-tainer Ships," Jour. of Soc. of Naval Arch. ofWest Japan, No. 41 (Mar. 1971) P. 45, (in

Japanese)J. GERRITSMA and W. BEUKELMAN: "Analysisof Resistance Increase in Waves of a FastCargo Ship," Appendix 5 of Report of theSeakeeping Committee, Proc. 13th I.T.T.C.,Vol. 2 (1972) p. 902; I.S.P. Vol. 19, No. 217(Sept. 1972) p. 285P. BOESE: "Fine einfache Methode zur Bere-chnung der WiderstandserhOhung eines Schiffesim Seegang, Schiffstechnik, Bd. 17, Heft 86(1970) p. 29K. TANIGUCHI: "Propulsion of Ships in Waves,"Bulletin of Soc. of Naval Arch. Japan, No. 383(Aug. 1961) p. 315, (in Japanese)J.H. MCCARTHY, W.H. NORLEY and G.L. OBER:"The Performance of a Submerged Propeller


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in Regular Waves," DTMB Rep. 1440 (May1961)

S. NAKAMURA, S. NAITO and R. INOUE: "Open-water Characteristics and Load Fluctuations of 10)a Propeller in Waves," Jour. of Kansai Soc.of Naval Arch. Japan, No. 159 (Dec. 1975) p.41, (in Japanese)D.L. MOOR and D.C. MURDEY: "Motions andPropulsion of Single Screw Models in HeadSeas," Part II, Trans. RINA, Vol. 112 (1970)p. 121J. GERRITSMA, J.J. van den BOSCH and W. 12)BEUKELMAN: "Propulsion in Regular and Ir-regular Waves," I.S.P., Vol. 8, No. 82 (June1962) p. 235S. NAKAMURA, R. HOSODA and A. SHINTANI:"On Propulsive Performance of a Ship in

Regular Head Waves," Jour. of Kansai Soc.of Naval Arch. Japan, No. 134 (Dec. 1969) p.23, (in Japanese)T. JINNAKA: "Periodical Source and Its Ap-plications (continued)," Jour. of Soc. of NavalArch. Japan, Vol. 108 (Dec. 1960) p. 1, (inJapanese)T. JINNAKA: "Some Experiments on the Excit-ing Forces of Waves Acting on the Fixed ShipModels," Jour. of Soc. Naval Arch. Japan,Vol. 103 (July 1958) p. 47, (in Japanese)H. YUASA: "Calculation of the Fluctuationsof Propeller Load Induced by Ship Motions inOblique Wave (Part 1)," Jour. of Soc. of NavalArch. Japan, Vol. 136 (Dec. 1974) p. 69 (inJapanese)

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Propulsive Performance of a Container Ship in Waves

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