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. 1975
and No. 162, Sep. 1976)
Summary
With a model of single screw high speed container ship, resistance and self-propulsion
tests in regular and irregular waves are carried out in the Experimental Tank of Osaka
University.
The experimental results of ship motions in regular head and following waves and mean increase of resistance in regular head waves are compared with the results obtained
from the theoretical calculations.
The effects of wave height and propeller diameter on ship motions, mean increases of
resistance, propeller thrust, torque and revolutions, self-propulsion factors and propeller
load fluctuations are investigated.
The significant amplitudes of heave, pitch and the mean increases of resistance, propeller
thrust, torque and revolutions measured in irregular waves are compared with the values
which are predicted from the response operators obtained from the experiments in regular waves 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 still
water. 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 ring type wake-meter, and the wake fraction, relative rotative efficiency and propeller open-water efficiency in regular waves are calculated by using the measured inflow velocity
distribution, the propeller revolutions and the propeller open-water characteristics. The measured amplitudes of propeller load fluctuations are compared with the theoretical calculations by using the propeller open-water characteristics in uniform flow.
* Osaka University 1. Introduction
Container ship is strongly required to main-tain the rigid time schedule and to ensure the safe navigation. High speed ship, however, will experience larger ship motions in rough
seas which can result into high power increase,
severe acceleration, deck wetness, slamming and propeller racing etc. Therefore, it is
important for such a ship to investigate the ship motions, resistance increase and propul-sive performance in waves. Power increase or nominal speed loss
of a ship in waves
isusually estimated by using the theoretical or
24
experimental results of increase of resistance or propeller thrust and by assuming that the time averaged values of propeller open-water characteristics and self-propulsion factors in waves are nearly equal to those in still water.
However, the hydrodynamic forces acting on a ship hull and propeller are varying with time due to wave and ship motions, and the flow field around the ship in waves should be
different from those in still water. Therefore,
it is considered that the detailed studies on ship motions, resistance increase and propul-sive performance in waves are necessary in order to improve the accuracy for predicting the power increase in rough seas.
L
Propulsive Performance of a Container Ship in Waves 25
For this purpose, with a model of single screw high speed container ship, resistance and 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 inflow velocity into the propeller disk, and making use of a circular ring type wake meter, the radial distribution of inflow velocity in pro-peller disk was measured and also the theo-retical approach about self-propulsion factors in waves was performed.
The fluctuation of propeller load in waves has been considered important to evaluate propeller racing, propeller exciting vibration and strength of propeller and shafting. To
investigate the characteristics of the fluctua-tions of propeller thrust and torque, measure-ments were carried out at the self-proplusion tests in regular and irregular waves and the
measured results were compared with the
theoretical calculations..24 Ship .Model and Experimental 'Conditions .1 Model ship and Propeller
The experiments have been carried out with .a model of single screw high speed container
ship, which is the same model as the one
used for the study on seakeeping qualities by
Tasai et al."
The principal particulars ofthe model ship and propeller are given in
Table 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
93/4
Fig.. 1 Body plan and bow and stern profile of isingle screw container ship
BASE LINE
Length between
perpendiculars L" (m) 4.. 000
Breadth B (m) 0.5847
Draft fore dF (IT) 0.1952
aft dA (n1) 0.2199
mean dM (IT) 10.2076
Trim (m) 0.0247
Displacement volume IF (m3) 0.2769
Block coefficient CB 0.568
Waterplane area coeff. Cwp . 0.709
Midship section coeff. CM 0.959
Longl. center of buoyancy from F.P., FB 0 .,520.L, Longl. center of floatation from F.P. 0.5343 L Longitudinal radius, of gyration k55. 0.24 L Height of C.G. above base line KG (m),
Length-breadth ratia LIB
0.1778 6.81 Breadth-draft ratio Bid 2.83
Propeller model A
Diameter D ,(m) 0.15 0.112
Pitch ratio 1.007 1.009
Expanded blade area ratio 0.6935 0.670
Blade thickness ratio 0.0530 0.05
Boss ratio 0.1848 0.180
Number of blades 5 5
Direction, of turning Right Right
the body plan of the model ship is shown in Fig. 1.
The vertical position of the center of gravity
and the longitudinal radius of gyration of the model are adjusted by an oscillating table
method.
2.2 Experimental Conditions
The following experiments were carried out at the Experiment Tank of Osaka University (100 m x 7.8 m).
(1) Resistance and self-propulsion tests in still 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 ship
motions of heave, pitch and surge were meas-ured by low friction potentiometers. When the model was free to heave, pitch and surge, the measurement of resistance was carried out
with constant tow force by a gravity type
dynamometer, but at the test of restrained model in regular head waves the resistance was measured by a differential transformer type dynamometer. The self-propulsion tests were carried out at the self-propulsion point of the model and the mean values and
fluctua-97. CFI, A/L Measuring items
Motion free 0.15 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, Wave
tests 0 25 (8 cm) Head waves Restrained model 0.30 1.3, 1.5, 1.7, 2.0 Resistance, Wave
0.15 Pitch, Heave, Surge,
Self-propulsion test 0.20 0.25 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, B 0.30 1.3, 1.5, 1.7, 2.0 revolutions, Wave Following waves Self-propulsion test 0.20 0.25 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 itemsPitch, Heave, Surge Motion free
Resistance 0.20 L/100 L/20 0.9 Resistance, Wave
tests 0.25 1.5
Restrained
model
(4 cm) (20 cm)
Resistance, Wave
Head waves Self-propulsion
test 0.20 0.25 L/100 L/20 (4cm) (20 cm) 0.9 1.5
Pitch, Heave, Surge
Propeller thrust, torque,
Propeller: A revolutions, Wave
Self-propulsion
1,1100 L126.7 Pitch, Heave, Surge,
test Propeller: A, B
0.20
(4 cm) (15 cm)
1.0 Propeller thrust, torque,
revolutions, Wave
60
4.0
2.0
Propulsive Performance of a Container Ship in Waves 27
Irregular waves
2.0 4.0 6.0 8.0 0 2.0 4.0 60 8.0
W (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 5,1w1 tare- sec) Seq.8 Seq.7
s,
6 Ss, 2 599 5 Seq. Ho 5 536 1.408 2 9.99 1.413 6 11.54 )390 7 13.40 1395 8 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, revolutions
Ship 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 waves
0.20 4, 9, 5, 10 6, 7, 8, 0.20 7
Restrained model in regular
head waves 0.20
4, 6, 7
Forced pitch in still water
Double amp.: 3 deg. 0.20 7, 8, 10
Forced pitch in still water
Freq.: 0.52 Hz 0.20 6, 10 7 0.576 Ring No. 4 rIR 0.897 5 0.789 6 0.681 Fm
Seq. No. 111/3(CM) 7'0 (sec)
1 10.78 1.159
Mean wave period 2 9.99 1.413
series 3 10.56 1.562 0.15 4 10.04 1.694 0.20 5 6.36 1.409 0.25 2 9.99 1.413 0.30 Significant wave height series 6 11.54 1.390 7 13.40 1.395 8 16.12 1.399 (cm' sec) 1 2 3 4 1078 9.99 /056 10.04 1.158 1.413 1.562 1.694 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
28 Shoichi NAKAmURA, Shigeru NAITO
tions of propeller thrust and torque were
measured by a differential transformer type dynamometer. The mean values of the
propel-ler revolutions were measured by an electronic
counter and recorded by a digital printer,
while the fluctuations of revolutions were measured analogically by a low inertia gen-erator attached to the motor shaft.
Resistance and self-propulsion tests in irregular waves
The experiments were carried out for eight different wave spectra (Sequence Nos. 1-8) which are shown in Fig. 2. Wave spectra of
sequence Nos. 1-4 are the series of mean
wave period, the significant wave height beingmaintained at an almost constant value of 10 cm, 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 almost constant value of 1.4 sec. The significant wave height 11113 and the mean wave period To for each of the wave spectra are given in
Table 3.
Wake measurements in propeller disk The radial distribution of inflow velocity in the propeller disk were measured by using a circular ring type wake meter. A summary of test conditions are shown in Table 4. 3. Ship Motions in Waves
3.1 ship Motions in Regular Head Waves
The measured amplitudes of heave, pitch
and surge motions obtained from the resistance and self-propulsion tests in regular head waves
are shown in Fig. 3 in the non-dimensional form as a function of wave length/ship length ratio 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 the
uncoupled equation of motion on the assump-tion that the surge force is considered to be
only the Froude-Kriloff force and the damping
force for surge can be neglected. The results
of calculations are shown in Fig. 3 and com-pared with those of experiments.
It is shown in Fig. 3 that no significant
differences 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 regular
head waves between experiments and
calculations
of heave and pitch between the towed model
and the self-propelled model. The calculated
results of pitch motion by the O.S.M. show fairly good agreement with the experimental
results, while those of heave motion are slightly
larger than the experimental results for the range of AIL> 1.0 and the difference is larger at high speed. The measured amplitudes of surge at the resistance tests agree fairly well with the calculated results by the above
men-tioned method.
The amplitudes of relative motion to the wave surface at the position of propeller were measured by the resistance type wave height probe attached to the model, and the results are compared with the calculations according to the 0,S.M. as shown in Fig. 4. There is
05 to 05 05 LI? to KT as JO 5 0 05 (2) 0.5 5.0 0
1.5 ol0 0.5 1,5 0.5 0 05 5 Eep. Resistance test o Sell-prep. test Fn. 0.15 Fe. 015
Propulsive Performance of a Container Ship in Waves 29 0.
S. Fn. 0.20
75 x4.20 0.5 10 1.5 20
Fig. 4 Comparison of relative stern motions in
regular head waves between experiments and calculations
no significant differences in the measured
values between the towed model and the
self-propelled model. The measured amplitudes
of relative stern motion are higher than the calculated values for the range of long wave
length, while smaller for the range of AIL< 0.7
and the difference is considerably large. This
fact may be explained from the reasons that
the wave height reduction of the
incidentwave at the stern is larger for the range of shorter wave length and that the difference of phase lag of pitch to heave between experi-ments and calculations is comparatively large in case of short wave length.
3.2 ship Motions in Regular Following Waves
The measured amplitudes of heave, pitch and surge motions obtained from the self-propulsion tests in regular following waves are shown in Fig. 5, and the results are com-pared with those of calculation by the same method as the case of regular head waves. The arrow marks on the abscissa show the values of AIL that the phase speed of wave is equal to the ship speed. The values of AIL is equal to 0.251 for the ship speed of F=0.20 and 0.393 for F=0.25. Therefore,
all of the experiments were carried-out at the conditions that the phase speed of wave is faster than the ship speed.
As to the amplitudes of heave and pitch, the
0 .3 0.4 0.2 0 0.8 0.6 4 0.4 .02 20 1.0 0 0.5 2.0 2.5 x/L
Fig. 5 Comparison of ship motions in regular following waves between experiments and
calculations
calculated values are slightly larger than the measured ones, but the calculated amplitudes of surge are considerably larger. It seems that the further study on the disagreement of surge motion in following waves should be
necessary.
3.3 ship Motions in Irregular Head Waves
From the results of resistance tests and self-propulsion tests in irregular waves with the
wave spectra as shown in Fig. 2, the significant
amplitudes of heave, pitch and surge are ob-tained by the spectral analysis. These results are divided by the significant wave height of the corresponding irregular waves, and are presented in Fig. 6 as a function of significant wave height and in Fig. 7 as a function of mean wave period. In the Fig. 7, 20 is the wave length of regular waves corresponding to the mean period of irregular waves.
The measured values are compared with the values which are predicted from the response amplitude curves obtained by the model ex-periments in regular head waves and the wave spectra of corresponding irregular waves, ap-plying the linear superposition method. It is shown from Figs. 6 and 7 that the measured values give fairly good agreement with the
predicted ones,
1.0 1.5
7.0
30 o. 0. o. 0.6 a 0.4 5.
Pi-gt. 6 Comparison of ship motions in irregular
head waves between experiments and
cal-culations (effect of significant wave height)i
0
02
lb o 6 / 14 1 lb
60 50 40 30 2.5um03 [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 'irregular
head waves between experiments and cal-culations (effect of mean wave period) 3.4 Effect of Wave Height on ship Motions
The 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 at the conditions of A/L.0.9, 1.5 and F..0.20,
0.25. The measured double amplitudes of heave, pitch and surge are presented in Fig. & as a function of wave height Cp
It is shown from the figure that the lintar relationship between the ship motions and the wave height is satisfactory. In this
experi-Fn 020 ./L v0 9,15 -0-1r* Pitch 70 :,* Surge Pitch
Heave Resist. test Self-prop, I.
C, 1 (cm) 20
20
'Fig: 8 Effect of wave height on ship motions in regular head waves
ments, no significant differences appear in the measured amplitudes of heave and pitch be-tween the towed model and the self-propelled model, while some difference appear in the amplitude of surge.
4. Mean Increases of Resistance, and Thrust, Torque and Revolutions of Propeller in
Waves
4,1 Mean Increases of' Resistance, and Pro-peller Thrust, Torque and Revolutions in Regular Head Waves
The measured results of meah resistance increase obtained from the resistance tests in regular head waves are presented in the form
of non-dimensional coefficient as a function of
AIL, 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 agree well with the experimental ones. The cal-culated results by Boese's method are smaller than the experimental results in case of short wave length, and give larger peak values at low speed.
The mean increase of resistance for the
restrained, model in regular head waves was measured by a differential transformer type dynamometer and the results are shown in Fig. 9. The calculated results by Gerritsma's
A' C3P4riftuor Resist:rest Sell.potess Pitch 0 znik, Heave PrecOcrioni 4,5443 SU Ige 0
----F0=0.15 F. =0.20%Ai,. --a 4.0.46-IA ,,,
s
,-, 77 es ,., ey dri,,, -O.- - -gi-4,271,,- 0* - 5,- 3_ 411.21.'1 ,..-F.= 0.25 1 Fn 0.30 41444 ,,,____,_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[Pr Pitch 2[./Ily HKaie a 'rd., Surge 0 r6P.tesrP'edic1iGn
. . . . -Fn = 0.15 s ra ,,,/14,13__-t
...-.. c o--' --- Ovs/Hvs __,3---Q--"...-.-151:'1,0 Pa -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 03,0
-Propulsive Performance of a Container Ship, in Waves
,Fig. '9 Comparison of resistance increase
coef-ficients in regular head waves between
experiments and, calculations
Thrust increase Fn 015 020 0.25 030 V, Torque increase Revolution increase 5 AA 2 _
Fig. 10 Coefficients of mean increase of propeller
thrust, torque and revolutions in regular
head waves,
method show a good agreement with the ex-perimental results.
The self-propulsion tests in regular head waves were carried out at the self-propulsion point of the model and the mean increases of propeller thrust, torque and revolutions are
presented 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 mean increases of propeller thrust, torque and revo-lutions obtained from the self-propulsion tests in regular following waves are shown in Fig. 11. These values are smaller than the values
obtained from the self-propulsion tests in
regu-lar head waves.
4 3 Mean Increases of Resistance, and Pro-peller Thrust, Torque and Revolutions in Irregular Head Waves
The values of mean increases of resistance, and propeller thrust, torque and revolutions obtained from resistance and self-propulsion tests in irregular head waves are divided by the squared significant, wave height and are shown in Fig. 12 as a function of the signifi-cant wave height and in Fig. 13 as a function of the mean wave period.
Each of the measured mean increases are compared with the values which are predicted from the response curves obtained by model experiments 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 propeller thrust, torque and revolutions in regular following waves 045 1-s.\ I \ II ,\ Experiment(
Motion free
-e-Restrained ,Fe -020 n t \ - I ....-c-7-4÷-I Calculation Gerritsmds method \ Motion free -\ Restrained \Lipase's method. \\ .. Fn 025 I-
\
\ .\ I \ \ ir' Fn .0.30' I P 'II i/ TA./p9C.:18%1-1 Thrust Increase .... -0-. . . °'"if5PC:018'/L1 Torque Increase Fe Exp., 020 -a-025 --e--t''''D'i 9cx.f(S'L) o .i,
7 . Revolutionirrrease 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 1032 Shoichi NAKAMURA, Shigeru NAITO
/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 between
experiments and predictions (effect of
significant wave height)
sition method which is expressed as follows:
H4w=2 HAW(W) Sc(coOda), (1 )
0 where
HAW: mean increases of resistance or propeller thrust, torque or
revolu-tions
HAW/2: response curve in regular waves Sc(a).): spectrum of encounter wave
C.: wave amplitude
It is shown from Fig. 12 that the measured values 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 not so good as the ship motions, it can be said that the linear superposition method seems to be useful for predicting the mean increases of 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 between
experiments and calculations (effect of
mean wave period)
revolutions from the viewpoint of practical
purpose.
4.4 Effect of Wave Height on Mean Increases
of Resistance and Propeller Thrust, Torque and Revolutions
In order to investigate the effect of wave height on the mean increase of resistance, resistance tests in regular head waves varying
the wave height from L/100 to L/50 were
carried out at the conditions of A/L=0.9, 1.5 and F.=0.20, 0.25, and the results are shown in Fig. 14.
The experimental results for the restrained model are also presented in Fig. 14. It is
shown that the linear relationship between the resistance increase due to wave and the wave height squared is valid approximately
for the range of the wave height of L/50
L/30, but it has a tendency to be larger than the squared wave height law for the range
Fn Exp. Pr.d,cr. 0(5 0 020 025 .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
- (4,,,,,) 0/5 0 025 A 030 1 . I-- a--).. ....,....,--" p II -... '-Z---'-'or-';'--"-;t7.-66 ,41/41,%3 , .../....-. _74:.. --,,,..."--.--- ° , o °o I 1 OA/43 /0"/","
/
"----,
/ ,' k
*4' \N .4 / ...--"Er. .----,-.!-8 -... a NA,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 0.0of lower wave height and smaller for the
range 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 tests in regular head waves at the same experi-mental conditions as mentioned above. The measured results are presented in Fig. 15.
'a- az
4-1
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 increases
of propeller thrust, torque and revolu-tions in regular head waves (effect of
propeller diameter)
The variations of the mean increases of thrust and torque with wave height show a similar tendency to those of the resistance increase, but the mean increase of propeller revolutions shows somewhat different tendency.
Self-propulsion tests with the propeller
mod-el A and B of different diameter were carried out in regular head waves, varying the wave height from L/100 to L/26.7 at the condition of AIL=1.0 and F=0.20. The measured val-ues of mean increases of propeller thrust, torque and revolutions are shown in Fig. 16 as a function of the squared wave height.
The region of wave height at which the
mean 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 and
when the ship motions are moderate, the
region is comparatively wide.
4.5 Effect of Propeller Diameter on Mean Increases of Propeller Thrust, Torque and Revolutions
Making use of the propeller A and B, self-propulsion tests in regular head waves were carried out for the speed of F-=0.20. At this
tests, the wave height was maintained at a
4-0,azo T000sr increase -F0 .azs Thrust increase A/L ...- ,5 Torque Increase - ' ^ Torque increase o "' . oo Revolts/son increase o NL,-...,________._. Revolution increase 0 2.0 1 005 -Fn.020,,/, 09 Resistance test -0-Ft, 0 25 , ./Ln0 9 Motion free Restrained /. - 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 increases
of propeller thrust, torque and revolu-tions in regular head waves
20 1,5 113 1,10 05 1.5 0.5 0.15 0.1/2 020 Fir. .
34 Shoichi NAKAMURA, Shigeru NAITO
Fig. 17 Effect of propeller diameter on mean
in-creases of propeller thrust, torque and
revolutions in regular head waves
constant value of L/50 and the wave length was varied from 0.5L to 2.5L. The main particulars of two propellers are shown in Table 1. The measured results of the mean increases of propeller thrust, torque and revo-lutions are presented in Fig. 17 as a function of AIL. In order to show the effect of peller diameter on the mean increases of pro-peller thrust, torque and revolutions, the fol-lowing non-dimensional coefficients in which
the 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 by the propeller diameter. On the other hand,
in case of smaller propeller diameter, the mean
increase of propeller revolutions is larger as
a whole, and those of torque is somewhat
smaller at the peak of response curve. The experimental results of the mean increases of propeller thrust, torque and revolutions in case of varying the wave height are shown in Fig. 16 and show the same tendency.
5. Self-propulsion Factors in Waves
5.1 Analysed Results of Self-propulsion Fac-tors in Waves
It may be confirmed that the time averaged values of propeller open-water characteristics
in waves are identical with those in
stillwater' '5).6, so the effective wake fraction
w relative rotative efficiency 7)R and propeller
open-water efficiency 77o in waves can be an-alysed from the measured values of thrust, torque and revolutions of the propeller and the mean ship speed in waves by applying the thrust identity method using the propeller open-water characteristics in still water. The thrust deduction factor t in waves is obtained from the values of resistance and propeller
thrust at the same ship speed measured in
resistance and self-propulsion tests.
The self-propulsion factors in waves has been considered to be almost the same values as those in still waterl'. However, it seems to be necessary to study the detail of the char-acteristics of self-propulsion factors in waves
in order to improve the accuracy for predicting
the propulsive performance in waves. For this purpose, resistance and self-propul-sion tests in waves were carried out and the self-propulsion factors are obtained from the above mentioned procedure. The variations
of self-propulsion factors in regular head waves
with the wave length-ship length ratio are presented in Fig. 18. The values of self-propulsion factors in still water are shown in the figure by the horizontal broken lines.
It becomes clear that the self-propulsion factors in regular head waves vary consider-ably in the region that the wave length-ship length ratio AIL is smaller than 1.5, and tend to the still water values with increase of AIL. The amount of these variations is larger in case of the low ship speed. Especially, the
Propulsive Performance of 4 Container Ship in Waves
other hand, the variations of )2R and (1-0 with
wave height are comparatively small. From the results of the resistance and self propulsion tests in irregular waves with the
wave 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 of
significant wave height and of mean wave
period, respectively. It can be said that the
self-propulsion factors in irregular waves do not vary so much with the mean wave period and give almost the same values as those in
still 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,, 20Fig. '19 Effect of wave height on self-propulsion
factors in regular head waves.
12 14 16 20 25 0/H,a Fig, 20. Self-propulsion factors in irregular head
waves (effect of significant wave height)
1 Fn ;,0.15 11 -r---\-7----1;?
,,6
Fnrii
-.- ---C.T---1-w ----025/lN
Fn,r 0.30. ----\--:---;1,0---'---
---
--'<'----, _ --- /9 F. .0,15 instill water F,,. 5 020 ,----.--42--..-- 4-i-r, a 0, co I- l . . . i.- ute na ...:__ 1 -w. . s. 4 ,,,,_____,I.-A a4 .., Fn - 0.25 1 Fnft 0.30 n" I.' 't 2e ' - u4 '.` ^ H,taro.
fv. ) 0 L 2.0 05 1.0,Fig, 18 Self-propulsion factors in regiflar head
waves
propeller open-water efficiency decreases
re-markably in the region of A/L-,-0.9-1.3, where ship motions are severe and resistance increase
is large. And in this range of wave length, the values of (1w) and (1t) are larger than those in
still water, while the variation of
relative rotative efficiency with wave length is comparatively small and the value is nearly
equal to that in still water.
The similarresults were obtained from the experiments by Moor et al.".
The effect
of wave height on the
self-propulsion factors in regular head waves is also studied and the results are presented inFig.
In this figure, the values of
self-propulsion factors in still water are shown by
the horizontal broken lines. From this figure,
it can be said that the propeller open-water efficiency decreases considerably, while the value of (1 w,) has a tendency to increase with 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 0.6 1 Co C. Co C.4 1.0 Fn 35 020 05 4 19. 10 I - I I
36 Shoichi NAKAMURA, Shigeru NAITO
increase of significant wave height, and the values of (1-w.) have a tendency to increase slightly with that, but these tendencies are not so remarkable as those in regular head waves. And when the significant wave height of irregular waves is low, the self-propulsion factors have almost the same values as those in 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 10A0A(.25
Fig. 21 Self-propulsion factors in irregular head waves (effect of mean wave period)
10 15
C. (cm)
Fig. 23 Effect of wave height on self-propulsion
factors in regular head waves (effect of
propeller diameter)
diameter on the
self-propulsion factors inwaves, self-propulsion tests with the propeller model A and B of different diameter were carried out in regular head waves varying the wave length and the wave height for the speed of F.-=0.20.
The analysed results of the
measurements are presented in Fig. 22 as a function of wave length and in Fig. 23 as a function of wave height. The relative rotative efficiency s is hardly affected by the propeller
diameter and by the wave length. In case of propeller B of smaller diameter, both the
values of (1-w8) and 720 are smaller than those
of propeller A, but this is due to the reasons that the propeller of smaller diameter gives smaller values in still water. The differences between the values in waves and those in still water is not so large. In Fig. 22, the calculated results of (1 -we), r IR and )20 obtained by the
method mentioned in 5.3 are shown and give fairly good agreement with the qualitative tendency of the measured results.
5.2 Wake Measurements in Propeller Disk
in Waves
In order to clarify the above mentioned
characteristics of self-propulsion
factors in
Prop,dm . in wavesEx pertmentin sit!! water
0,15 m 0 0.112m Fnz0.20 _ Xnt _ 18 =1.0 _ _ _ 1 -04 0 0. vo - 0 "1.. ° u
.
-
in still ware, Fn 0.20 2--e----9-,6-6
i -t 0. /-4, , 7 /...-,
2, 2, ____ Fn. 0.25 4 F, 0.30 R 13 - r - , So I We -2, ro I' st.c) . . a ' T".6.) . . Prop.dm . 0,10 rn 0.tr?rn Experiment in 051,// unarm 0 -. _ Cola*, ton-7.4- ....--- a-a- -",-- f ' ',Pe -7- ...--- -...=-_:: i: Fns 0 20 In A--,s-7...1 tFti - -.-s2 CI -0 Li ,,,....,_ -I,., ' 6 Ei o $ .. ce $-0... 8 o a, O.-ti A a ..,.. ' a 0 ° 0 8 . 8 0 -a 5 1.0 1.5
2025
A/CFig. 22 Self-propulsion factors in regular head
waves (effect of propeller diameter)
1.2 14 1.6 1.0 1.2 /4 1.6 12 1.0 0. 0.6 0 1.2 1.0 0. 0 0. 0. 0. o. 0.8 0.7 0.6 0.6 0.5 0.4 03 0 r 0.15 (-7 -..
-Propulsive, Performance of a Container Ship in Way' ,37
waves, the radial distribution of axial inflow
velocity into the propeller disk in regular, head
waves were measured by using the circular ring type wake meter. The outline of the circular ring type wake meter and the attach-ing to the ship model are shown in Fig. 24. The force acting on the ring is measured by
a strain gage as the displacement of cantilever.
Making use of the relation between force and velocity, the inflow velocity into propeller' disk can be obtained.
The statical calibration of this wake meter in uniform flow was conducted at the towing tank varying the speed for each of the rings, and it was confirmed that the force acting on
the ring was proportional to the squared speed.
The dynamical calibrations of wake meter
were also conducted at the conditions of forced
pitch oscillation in still water and of the re-strained model in regular head waves at the
constant speed. Both the mean values and
the fluctuations obtained from the dynamical tests agreed well with the predicted values using the results of statical calibrations. A summary of test conditions of wake measure-ments are shown in Table 4.
The measured results when the model is free to heave, pitch and surge, are presented in the form of the ratio of the mean inflow
velocity in the ring plate in regular head
waves (1w)w to that in still water (1w,0$
as a function of the ratio of radius of the
ring to that of the propeller, rIR and are
shown in Fig. 25.
As shown in this figure, it becomes clear that the values of (1w0w1(1w7,)s are larger than unity as a whole. Especially, the closer
the measuring position is to the center of
propeller, the larger the values become, and this means that the distribution of the mean inflow velocity in the propeller disk in waves approaches that in uniform flow, as shown in Fig. 26. Furthermore, the values become much larger in case of 2/L=1.1, where the ship motions are very severe.
In order to make clear these phenomena, wake measurements were carried out for the
following conditions.
.(1) Restrained model tests in regular head waves.
Forced Pitch oscillation tests in still water changing the frequency of pitch motion.
.56 I (I -taniv (1- viOs 14 Propeller boss .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 waves
Si - ahosirs sr//I water
54 0.5 0.8 1.1 1.5 2.0
--
2.5----0
-- 0
0,8Container ship model
Fn = 0.20 A/t 1 5
--- 2.0
in Still water az 0,4 0:5 ° 8 r/R 50Fig. 26 Distribution of (1w0) in propeller task
in regular head waves and in still water
1.0
r/R Pig. 25 Ratio of (1w,.) in propeller disk in
regular head waves to that in still water
0.4 Propelle
boss
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 in regular head waves changing the wave height.
When the ship model is restrained in regular
head waves, the values of (1-w)w are not
'So much larger than those in still water, as
shown in Fig. 27. However, the mean values
of inflow velocity at the condition of forced pitch oscillation, (1-w0)p, are much larger than those in still water, especially at a radius closer to the center of propeller and higher
frequency of forced pitch oscillation, as shown
in Fig. 28. And it is shown in Fig. 29 that the larger the amplitude of forced pitch
oscil-lation
is,. the larger the values of (1-w0)p
become near the propeller center. And it is also shown in Fig. 30 that the larger the wave
height is, the larger the values of (1- w)w
become. It is concluded, therefore, from these
facts 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 10 0 4.15 405-(1- wa)ii uta),s 0 Container ship model 0. Remained
"Fe= 0.20 r/R= 0.576 ,t0 1.5 2.0 2.5 AA N NN NNA
NN N
as,H.1,-11.1e)p forced pitch,
in still water
Fig. 28 Ratio of (1-w.) in propeller disk
forced pitch oscillation test. to that
still water
P.O
in
1.31 (1- 1110P
( I -1.11n)5
Container ship model Forced pitch
&ea...0.521k
Fa= 0.20 II -urn), : forced Pitch
II (1-ura)sS instill water
2.0 0, (4e5)
Effect of pitch amplitude on the ratio of (1-w0) in propeller disk in forced pitch oscillation test to that in still water.
41- wah, in regular waves
wah in still water
00.q
1.5
10 " cu (cm) 2P
Fig. 36 Ratio of (1-w.), in propeller disk in
regular head waves to that in still water
(effect of wave height)
compared with that in still water is mainly due to the magnitude of ship motions.
It has been said that the propulsive
per-formance in waves is explained fairly well by the overload effect on the propeller due to the resistance increase in waves". As mentioned
above, however, the self-propulsion factors are
affected considerably by ship motions, so it is considered that the results of the overload
tests in still water are not always coincide
with those of self-propulsion tests in waves.. This fact has been proved experimentally by Moor et al.' and the authors".
5.3 Theoretical Investigations on
Self-propul-sion Factors in Waves
In order to investigate the Characteristics of self-propulsion factors in waves, an attempt was made to calculate the self-propulsion
fac-tors by using the propeller characteristics
obtained from the blade element theory and the results of measured wake distribution in the 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---
0.88 o 1.0q (I - W0)5 Container shlp model Forced pitch -- -0.2 0.4 0.6 0.8 VR Eiln)sContainer ship model FA= 0.20 r/R = 0:576 1.00 - (1-0 13 1.2 1.0 0 0.254 A 1.0 3.0 4.0 Fig. in (I-0.5 12
p pitch ratio'
0 : propeller diameter
R D/2
V : ship speed : chord length
Propulsive Performance of a Container Ship in Waves 39
419.=2 N r
Fig. 31 Flows into a. blade ,element at radius of r
peller blade element at radius r is shown in Fig. 31. We consider only the time averaged mean values of Inflow velocity. According
to the two dimensional blade element theory,
the lift acting on a blade element is given
by
dL=n-pcV.Vdr ( 2 )
where V and V are the parallel and perpen-dicular components of inflow velocity to the
chord of blade, respectively, and are expressed
as follows::
V.=Vo cos /34+ Vz sin /36 1 V=V0 sin Po V cospo
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 of
eq. (2) are given by
IdT=dL cos /30
dQ=dL sinpo
r
( 5)Integrating dT and dQ from boss to tip of the propeller and multiplying by the number of blades z, we can get the thrust and torque of the propeller.
If the thrust and torque coefficients Kr. and KQ of the propeller open-water characteristics are presented by a quadratic equations for advance coefficient J as follows:
KT= T/PN2D4=a+bJ+cja
KQ=Q1pN2D5=d+6+fr ( 6 )
°The constant coefficients a,, b c are given by 3 2 2(dr cos Po sin /30(r 4 R
R )R
b=1-32-(L-)(cos2 19, sin° AY 4 R X cospo(r\(dr
R )R
c=--
H sin po
4 , R)
TrZ C -cos 130(dr\IIn case of' constant pitch propeller, the
relation 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 propeller
model 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 is
given 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 always
equal to 1.0, In order to avoid this fact, we introduce 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, the coefficients of the quadratic equations of KT and KQ are given by
dr= 7r4
(i) sin Pp(i)2(C)
ZZ
C
4
412(i)(zi. sin
po +cospo(i)(9)
(i),
cospo(A;)(7) C V,-V(I-ur) ( 3 ) , (
40 Shoichi NAKAMURA, Shigeru NAITO
r )( dr\
= (--c-.) costio(
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, = .435Denoting the former method as A, the later method as B, the calculated results of pro-peller open-water characteristics by the two methods are expressed in Fig. 32, where si is assumed to be 0.2 and constant. Though the
calculated results of thrust and torque coef-ficients by the two method give considerably large values compared with the experimental ones, those of propeller open-water efficiency as a ratio of thrust coefficient to torque coefficient agree fairly well with the experi-mental results. And the propeller character-istics at behind condition in regular waves are also calculated by the same methods as men-tioned above using the measured distribution of inflow velocity into the propeller disk and the mean values of number of revolutions
measured by the self-propulsion tests in waves.
2, 0 0.6 0.4 0.2 Calcu lotion Method A Ever 'men 0.2 04 6& 0.8 1.00 K, 10,K0 10 2.0 (0
Fig. 32 Propeller open characteristics calculated by blade element theory
075
070 ass 060
Fig. 33 Comparison of self-propulsion factors in
regular head waves between experiments
and calculations using propeller open
characteristics by blade element theory
Then, the effective wake fraction w relative
rotative efficiency 72 n and propeller open-water efficiency 7;0 in regular head waves are obtained
by applying the thrust identity method using the propeller open-water characteristics in still water calculated as mentioned above.
The comparison between the results of
calculation and those of experiments is shown in Fig. 33. In the figure, the mean nominal wake fraction w in the propeller disk which are obtained by means of volume integral method using the measured distribution of inflow velocity, is also presented. The cal-culated value of iR by the method A is always
equal to 1.0, but the one by the method B
gives a similar tendency to the experimental
results.
It can be said that the qualitative
tendency of the calculated self-propulsion fac-tors (1 U) g), VRand r,o, shows fairly good agree-ment with the experiagree-mental ones, though there are some differences between them
quantita-tively.
The properties of wake fraction, relative
rotative efficiency and propeller open-water efficiency in regular head waves became evi-dent considerably, but the property of thrust deduction factor in waves is not investigated in this study. 2, Comcmet V, MO. _-- ----1 to. 0.20 . .--s- srill ware,
--Cooper ornent ...7 -....__. I - tu __ Calculi, r oon Method A
_.
77- -- ---. _...--- ...--o, 2 4 I -tut, 2o m 5011 warer . -./... ...---Z 8 (C )c. sin po( ) R R dr R ) 1.1 7I22e
=-8 (C . R)(sin a cosr
dr\
0)(
R )R
1.0 0.5 1.0 1.5 2.0 0.6 05 0.5 0.4f'
-'1.06. Propeller Load Fluctuations in Waves
6.1 Inflow Velocity Fluctuations into Pro-peller Disk
Inflow 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 whereUp, V p: Axial and vertical components of inflow velocity fluctuations at the propeller center in regular head
waves
Uw, Vw: Components of Up, Vp due to or-bital motion of waves
UM, V2:
Components of Up, Vp due to
ship motions
h, Vertical and horizontal distances from the center of gravity of ship to the propeller conter
E= x sin oh80 sin en
F=x0 cos oz: h0 a cos en
G= za sin E4 +10a sin en H= 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 0c)
Calculated results of Up andV p by eq. (16) for four Froude numbers are shown in Fig.
34 and Fig. 35, respectively. The components
of Up and Vp due to orbital wave motions
and ship motions are also shown in the figures.
Next, we consider the spectra of U1 and Vp in irregular waves. Let S(w6) denote the
wave spectrum, and Hx(we), &w0), and 110(w c)
Propulsive Performance of a Container Ship in Waves 41
(16) 05[ 0.4 0.3 02 0.1 7:. 1.0 05 Fn. ars 0.20, 025 030 Fn. 015\ 020 025 030 r'cr Inflow velocity byshipmotion by orbital motion total =
Fig. 34 Calculated axial component of fluctuation of inflow velocity into propeller disk
Inflow velocity byshipmotion by orbital motion total Fn 20 A., 2$ 25
the response amplitude functions of surge, heave and pitch motions, the spectra of Up and Vp, Sur and S, p, can be expressed as
follows:
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 0-30 025 02 15
42 Shoichi NAKAMURA, Shigeru NAITO
The spectra of inflow velocity fluctuations at the propeller center in irregular waves can be 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 well known that the wave height at the stern is lower than the incident wave height because the incident wave is deformed by the ship. This fact must be considered to calculate the
propeller load fluctuations because U5. occupies
large part of Up.
In this study the wave
height reduction of the incident wave at the stern with a restrained model is calculated by using the three dimensional periodic sources as the presentation of the ship hull based on Jinnaka's method').
The wave height reduction of the incident wave at the stern is measured with the
re-strained model in regular head waves for
four Froude numbers and the results are
presented in Fig. 36 in the form of the ratio
of the wave height at the stern to that of
the incident wave, Cw'/w, as a function of AIL. In the figure an approximate formula,
Cw'/Cw=0.2(A/L)+0.5, which is obtained from
the analysis of the experimental results with the mathematical ship forms by Jinnakall and the calculated results by the above men-tioned method are shown. The approximate formula agrees fairly well with the
experi-mental results.
The fluctuation amplitudes of effective wake
are obtained by using the time histories of the fluctuations of propeller thrust and revolu-tions measured at the self-propulsion tests in regular head waves and the propeller open-water characteristics. The results are pre-sented in Fig. 37 in the form of the ratio of Up to the ship speed V, and are compared with the calculated results by eq. (16). The calculated results of Up by taking into account
the wave height reduction of the incident
wave at the stern show closer agreement with
the experimental results.
It is confirmed from the above mentioned results that the fluctuations of propeller thrust and torque are mainly caused by Up and can
Calculation
with wave height correction
- without wave height correction
Experiment Wake fraction Fr) 045 0 020 A 025 0 030 o 2.2)=010 1.0 0.8 0.5 Experiment 0.4 oFn=a/5 --- 0.2 (X4.)÷ 0.5 0.20 0.2 --- Cal by 3-dim.period. source
C' 0.25 0 0.30
0.5 1.0 1.5 2.0 A/L 2.5
Fig. 36 Ratio of wave height at the stern to that of incident wave with restrained model in regular head waves
o 5
10 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-water
characteristics, considering the wave height reduction of the incident wave at the stern and the fluctuation of revolutions of the pro-peller due to the response characteristics of the prime mover.
6.2 Calculation Method of Propeller Load
Fluctuation
The fluctuations of propeller thrust and
torque in regular head waves, JT and 4Q,
can be expressed from the propeller open-water characteristics in still open-water by using the fluctuation of axial inflow velocity into propeller disk JU and that of revolutions of propeller 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 equations
as 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 462 is input and AN is output of the prime mover and phase difference between IQ and AN is about 180 degrees,, AN is expressed by ../Q as
follows:
AQ (22)
where H is the characteristic value of the
prime mover.The solution of eq. (19) is obtained by using
eqs. (20) and (22) as follows,:
4T4PTU PTN'PQH)4U
1-I-PQN4QPQU AU
1-1-PQN-H AN,- PQU AU 1+PQNHMaking use of these equations, the fluctua-tions of propeller thrust and torque can be obtained by considering the characteristics of the prime mover and the fluctuation of axial inflow velocity at the propeller center.
The value of H used in this calculation a constant value of 44.31/kg m sec, which is obtained from the result of the dynamic cali-bration test of the prime mover.
In case of irregular waves with the spectrum
of S(o), the spectra of AT, 4Q and AN
S47-(01.), SJe(w.) and -S4u(04)can be expressed as follows:
S 4T(W e)= PTN 'PQU 2
PTU
1+P
QN'IlH) SUP(W'e)iSjg(0e)= (1 +PP:.HY-Sup(f0)
1(24)-Sjw(a),)=/ H.PQu )\2Sup(04)
\1+ PqN
Propulsive Performance of a Container Ship in Waves. 43
(20)
(23)
This result is obtained by neglecting the moment of inertia of the prime mover. As the revolutions of propeller at the self-propul-sion test are usually kept constant by control,
the moment of inertia of the prime mover
can be neglected, but when the torque is
controlled to be kept constant the effect of moment of inertia must be exactly taken into
consideration.
Next, let us define the response amplitude functions of AT, AQ and AN obtained by the experiments in regular waves as follows
1-147,(0))-= ATI pgB2Cw H4Q(o))=4Q1pgB2a:w (25) 114N(v)=21N-D3V1gB2Cw where breadth of ship D: propeller diameter
Cur: wave height of regular wave
V: ship speed
Making use of the wave spectrum S(co) and I I Jr(C0), 114Q(W), 114N(W), each of the spectra
of propeller load fluctuations in irregular
waves is given by the linear superposition
method 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 be
predicted from these spectra.
6.3 Results of Experiments on Propeller Load'
Fluctuations
(1)1 Propeller load fluctuations at
self-pro-pulsion tests
a) In regular head waves
The propeller thrust and torque at self-pro-pulsion tests in waves are measured by using the 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 movement of self-propulsion dynamometer due to the ship motions are considered to be included in (
JN= H.
is
44 ,Shorchi NAKAMURA, Shigeru NAITO 'the measured values. It seems to be necessary
to take into account the following two factors.
The inclination component of the weight
of propeller and shaft due to pitch motion of the 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 dynamometer were carried out anti the correction values were obtained.
The measured 'double amplitudes of pro-peller thrust and torque are divided by the mean values of total thrust and torque, and are presented in Figs. 38 and 39 as afunction
ilT/T 0. 0. 0 0. a 0. 4010 a 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 the mean line of corrected values. It seems that the calculated results of thrust fluctuation by eq. (23) taking into account the fluctuationof
propeller revolutions and the wave height
reduction at the stern agree well with the
measured results, while those of torque fluc-tuation show some discrepancy.
Another method for calculating the propel-ler load fluctuations in regular waves by using the Sears' non-stationary airfoil theory has
been developed by Yuasa12). The results by
this method are shown in these figures. The calculated fluctuations give considerably large values compared with the measured ones, but
the ratio to the total thrust or torque show
fairly good agreement.
b) In irregular head waves
From the results of self-propulsion tests in
Irregular waves with the wave spectra as
shown in Fig. 2, the significant values of
fluctuations of propeller thrust and torque,
47.113 and 4Q113, are obtained by the spectral
analysis.
These values are divided by the
significant wave height of the corresponding irregular waves, and are presented in Figs. 40 and 41 as a function of significant wave height and in Figs.. 42 and 43 as a function of mean wave period. The calculated results by eq. (24) and eq.. (26) are also shown in Fr= W5 ...--'---.., Thrust
-...
'-..-&---o0.3
Fructuation in, Regular ayes
'-'-'- ...---
'---,11- -I.''.1 0.2 09J't1=zr
-. ' . .
C Expewnent -'- Cat by Sews' function
--Mean tine of. erp,, corrected
-
Da.,c.n.diVagcS,.Fr =0.25 a3---Dc,rconjer.woe.,evaliiirrio. ---, ...,...---_,
01-wave height reauctian
..- ,..,...
1 9 ' -... .0-O-0---oo-6___---- ..._ ... :7:7--- o 1
.104Ti, ThrustFluctuation.._
thg.:21.:2,..
025_,_--- 025_,_---CC.ILAVprppr.,open characr,
---D'a,'Z'rfZi,ng.f e`f.' ,..11`Arehum. 0.2
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.°Z 00,/ '
I...-
'6 0 .. =0.1.5c.w....1,9_. . :,,,,,...:1-:,.., 0 LoeurnenI- -neon tineC/ 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 thrust
at self-propulsion tests in regular head
waves
6
60 50 40 30 n'sH,3/1 60 50 40 30 25 Hte34_
14 18 6 10 .14 18
15,4
Fig. 40 Effect of significant wave height on thrust fluctuation at self-propulsion tests in it--regular head waves
as 10 1. .2.0 0.5 1.0 /.5AA .
Fig. n Ratio of torque fluctuation to mean torque
at self-propulsion tests In regular head
waves 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 by the method using propeller open-water charac-teristics show closer agreement by taking into account 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 revolufluctua-tions in irregular waves
are shown in Figs. 44 and 45 as a function of significant wave height and of mean wave
period, 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 18 60 50 40' 30 251-1,A. 60 50 40 25 Ri434.
Fig. 41 Effect of significant wave height on torque
fluctuation at self-propulsion tests in
ir-regular head waves
112 1:4 L6 1.3 1.2
asa.75
1.0A.4. (.20Fig., 42 Effect of mean wave period on thrust fluctuation 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 onfluc-tuation of number of revolutions at self-propulsion tests in irregular head waves calculation of fluctuations of propeller thrust and torque.
(2) Effect of wave height on propeller load
fluctuations
'The relationship between wave height and propeller load fluctuations are given by using
eq. (23). Assuming that the fluctuation of
propeller revolutions is equal to zero, the pro-peller thrust fluctuation is given by
zIT=PruilU= pD2(2c U+ bDN)al U
pV1
Ns(2ci
b)Ns(i+ NAW1 (27)
40, Torque Fluctuation in Irregular Waves Fn=0.20 10--3L, '''', Fn= 0.15 0.3.m.,m) ....---, --- -m 1.0 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 ouPer67gigH
using response 0,77P.OP. 1,1
,Fn-0.25 4.2 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 Fluctuation 1-11/3 Fn=0.15 (kgrronJ - /.0 0.8r ...,.... 0 6- --Cgnitlierro.PbroepPe:;eff07:11./PFiC' , 40.4---Os. consider. prop. rev10 .
wave height reductiOn
in IrregularWaves ,
Exp. Fe-0.20
ExO. , corrected
_---1--i.-.
Predict. by linearSuerposition
using response amp.Peperoior
Fn=0;25 a l'2-o ' - ' - --- IV' H,,3(cm) 0.61 Fn=030 r -
,'
11 I, A _.___ _ _ r --",: 'Ho(cm) , ,Atha Revolution Fluctuation
HI/3 (Vsec.m ) Fn=0.-15 n 31--8re- -6-01 - 2 a on o Experiment ,1 'Plesf 1(4' iiesVpjtirieamsg.Pg,>:?csilz.P" in irregular Waves Fn= 0.20 8 ,, - lc Fn =025 C 0 rs tP 0 0 1 - .. Hp-11an) mo 1Fr==-0.301 do a 0 000 Hp.,(cm)
1 id.dTvl Thrust Fluctuation
-(kg/mHv Fn=0. /5 0.6'
..-- - --- --- ,
1
1--____ Cal.bypropopen choracr. .conspiet prop. reiVtuCt,
' ---DP,consider,plopr 1.14,C s 0.2.
in Irregular.Woyes
Fn=0.20
wave
height reditCri nr 4---s. ...:-.- . ..t '''''' PuIV;4Tp,i,,,i.gr,;,nspuPg,,LHgiln . . =0.25 6
,
0.4,Ie
ro-,c , . Fn=0.30 5Pc---.---oExp. r Exp.,corrected 8 _... -- ----..-"-- 11-1 --- --- - rptsec ) 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 /,8 015 50 44425 0.8 0.6 0.4 0,2 0 112 0.8 0.6 0.4 0.4 02 0 0. 0.4 1.4
-0.2 /.0 -04 -45 1.2 05 14 3Fig. 45 Effect of mean wave period on
fluctua-tion of number of revolufluctua-tions 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 revolutions
in regular head waves
where
N: mean value of propeller revolutions
in waves-=-Ns+NAW
Ns. number of revolutions of propeller in still water
NAW mean increase of propeller revolu-tions in waves
We can consider that the amplitude of
fluctuation of axial inflow velocity into pro-peller disk JU is proportional to the wave
amplitude, NAW is proportional to the squared
wave amplitude and the mean value of ad-vance coefficient in waves I does not change with 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 be proportional to the wave height. On the other hand, if N AW is proportional to the squared wave height, IT becomes slightly larger than the values obtained from the linear relation
between IT and wave height, because the
value 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 regular head waves is
studied and the results are
shown in Fig. 46. The measured values are divided by the wave height and are presented as a function of wave height. In this figure, "Calculation B" is a method using the ship motions calculated by the strip method and the orbital motions of incident waves taking into consideration the fluctuation of propeller
revolutions. "Calculation C" is a method
using the ship motions obtained from the
experiments and the orbital motions of waves considering the wave height reduction at the
stern.
It is generally said that the amplitude of propeller load fluctuation is approximately
proportional to the wave height, except the case of excessive high wave height. As to
the effect of wave height on the propeller
thrust fluctuation, the above mentioned tend-ency is shown in Fig. 46. The relation be-tween the measured fluctuations of propeller thrust in irregular head waves and the sig-nificant wave height is also show the same tendency as shown in Fig. 40.
7. Conclusions
From the analysis of the experiments and calculations the following conclusions may be
drawn: Revolution Fluctuation Ho ,//Sec, Fn=0. /5 3 inirregular Waves Fn=0.20 2 z 2 --- 9---- D rii D &pet, In.( I
--- Predict,bylinear superposition using resDcnse amp. Operator
' 10 Fn=025 Fn 0.30 4 ? --- .. --- - - 3 E a° 2 .,--1 -- ---c .,.. / lo (SE, ) ro (sec)
46 Shoichi NAKAMURA, Shigeru NAITO
1.2 4 1.6 1.2 1.4 1.6 05 /I. 1.0 I e5 25 3 2 4 2 0:5 1.0 5 5 0 2
Measured pitch motion in regular head waves agree well with the calculated results according to the 0.S.M., while as to the heave motion the calculated results is larger than the measured ones in the range of A/L=1.0
1.5, and the difference is large at the higher
speed.
Measured heave and pitch motions in regular following waves agree comparatively well with the calculation according to the
0.S.M., but the surge motion is considerably larger than the calculation using the
Froude-Kriloff force.
Amplitude of heave, pitch and surge motions is proportional to the wave height of regular waves and the linear superposition
method is valid for predicting the ship motions
in irregular waves.
Measured results of resistance increase in regular head waves agree fairly well with the calculated ones by Gerritsma's method for the ship model used in the present study.
Mean increases of propeller thrust, torque and revolutions in regular following waves are considerably smaller than those in
regular head waves.
For predicting the mean increases of resistance or propeller thrust, torque and revo-lutions i5 irregular head waves, the linear superposition method seems to be useful from the view point of practical purpose.
Linear relationship between the mean increases of resistance and propeller thrust and torque and the squared wave height is
valid for the range of the wave height of
L/50-L/30.
Self-propulsion factors in regular head waves vary considerably with wave length, especially in the range of 2/L=1.0 1.5 where ship motions are severe.
Propeller open-water efficiency in ir-regular waves decreases with the increase of
the wave height, and the values of (1we)
have a tendency to increase slightly with the increase 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 into the propeller disk approaches that in uniform
flow and 72R approaches unity.
Properties of (1w,),
)2R and 720 inwaves are fairly clarified by the measurements
of flow field at the stern.
Fluctuations of propeller thrust and torque are mainly caused by the fluctuation
of axial inflow velocity into propeller disk and
can be predicted by considering the wave height reduction of incident wave at the stern and the fluctuations of propeller revolutions, using the propeller open-water characteristics in still water.
Propeller load fluctuations in irregular waves can be predicted by using the propeller
open-water characteristics.
The present study was carried out as a part of the research works of the 125th Research Committee of the Shipbuilding Research As-sociation of Japan. The authors should like to express their gratitudes to the committee members by whom many fruitful guidance
and discussions were given. The authors also
express their appreciations to Dr. R. Hosoda
and Messrs. M. Inoue, R. Inoue, A. Inoue for their cooperation.
References
F TASAI, M. TAKAGI, M. GANNO, H. ARAKAWA
and M. KURIHARA: "A Study on the
Seakeep-ing Qualities of High Speed SSeakeep-ingle Screw
Con-tainer Ships," Jour. of Soc. of Naval Arch. of
West Japan, No. 41 (Mar. 1971) P. 45, (in
Japanese)
J. GERRITSMA and W. BEUKELMAN: "Analysis of Resistance Increase in Waves of a Fast Cargo Ship," Appendix 5 of Report of the Seakeeping Committee, Proc. 13th I.T.T.C.,
Vol. 2 (1972) p. 902; I.S.P. Vol. 19, No. 217
(Sept. 1972) p. 285
P. BOESE: "Fine einfache Methode zur
Bere-chnung der WiderstandserhOhung eines Schiffes
im Seegang, Schiffstechnik, Bd. 17, Heft 86
(1970) p. 29
K. 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
Propulsive Performance of a Container Ship in Waves 47
