ADDED RESISTANCE AND PROPULSIVE PERFORMANCE
OF SHIPS IN WAVES
S. Nakamwui
Oct!zz Unve4Ltj
Jctpin
INTERNATIONAL SEMI NAR ON WAVE RES ï STANCE
February 3 - 5, 1976
TOKYO
THE SOCIETY OF NAVAL ARCHITECTS OF JAPAN
7;(
V
- -
J1j iLab. y.
ARCHIEF
Technische Hogescho
L INTRODUCTION
Following the traditional design pro-cedure, ship dimensions and hull form have been determined by considering mainly the calm water performance, and the engir.e power required to maintain the ship speed in a seaway is obtained from the calm
water resistance by applying a mean service margin. However, it has been recently considered to be important to improve the accuracy for predicting the added resis-tance and propulsive performance in waves, and to establish the rigorous method for determining the power margin.
For this purpose, the theoretical and experimental studies on the added
resis-tance, propulsive performance and power prediction in waves have been performed actively in Japan. Especially, for high speed container ship form, methodical and synthetic investigations were conducted by the 108th and 125th Research Committee of the Shipbuilding Research Association of
Japan. This paper is intended to describe the results obtained frote these investi-gations as well as the recent works and developments on this field.
ADDED RESISTANCE AND PROPULSIVE PERFORMANCE OF SHIPS IN WAVES
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2. DESCRIPTION. OF CONTAINER SHIP MODELS
Three different hull forms of single screw high speed container ship are chosen for the theoretical and experimental investigations. The principal particulars of the three ships and propellers arid the considered models are given in Table 1.
The container ship model No.1 is a model with CB = 0.559, L/B = 6.89 and
13/d 2.99, which is chosen as a prototype
for the Research works of the 108 Research Conunittee of the Shipbuilding Research Association of Japan (SR 108) . The body
plan of the model ship is shown in Fig.l. Model No.2 has the same values of CB and B/d as those of model No.1, only the
Length-breadth ratio being changed to L/B
= 8.0. Model No.3 has almost the same form as model No.1, but is different slightly in CB, L/B and B/a, which was used for the study on seakeeping qualities by Tasai et al.
(l
9 1/2 9 3/ Fp
Fig. 1. Body plan and bow and stern profile of single screw container ship model No.1.
Table l.Principal particulars of container ships and propellers.
Propeller
Diameter
Pich ratio
Expanded blade area ratio
Blade thickness ratio
Boss ratio
Number of blades
3. ADDED RESISTANCE IN WAVES
3.1 Added Resistance in Regular Head Waves
Resistance tests in regular head waves
were conducted with container ship models
No.1, No.2 and No.3 ab the Experiment Tank
of Osaka University (100 in x 7.8 in)
(21 [3]
[4]. The measurements were carried out with
constant tow forces by a gravity type
dynamometer, and the model was free to
heave, pitch and surge.
The added
resis-tance of restrained model in regular head
waves was also mesured with model No.3
by a differential transformer type
dynamo-meter.
The wave height of regular waves
was
maintained at a constant value of Lpp/5O
and the wave length was varied from 0.5
Lto 2.0 or 2.5 Lpp.
Ship speed was selecte
as follows
Fn = 0.15, 0.20, 0.25, 0.30
for models No.1 and No.3
Fn = 0.20, 0.25, 0.30
for model No.2
The results of measurement are
present-ed in the form of the nondimnensional addpresent-ed
resistance coefficient defined by,
-
/
2 20AW - RAW pg T3 L
as a function of the wave length / ship
-2-6. 56310.150
1.007
0.6935
0.0530
0.1848
5length ratio, and are shown in Figs.2-. 4.
In the above definition, RAW is the added
resistance in regular waves,
P the density
of water, g the gravitational acceleration
and
the wave height of regular waves.
In Fig.2, the results of experiments
which were carried out with a 3.5 in length
model similar to the model No.1 at the
Sea-keeping Basin of Nagasaki Technical
Insti-tute, Mitsubishi heavy Industries (160 in x
30 in) [5] are also presented by black spots.
In evaluating the added resistance in
regular head waves, it is general in Japan
that the calculations are carried out on
the basis of Maruo's theory
[6] [7] [8] (9]
[10].
According to Maruo's theory, the
deter-mination of hydrodynamnic singularities
which replace the ship hull is essential
in the computation of the added resistance.
There are several approximate methods of
determining the hydrodynamic singularities
as follows
original Maruo's method [6]-[l01
ModIfied Maruos method by Nakamura
and Shintani [11] [12]
Method using the slender body theory
by Fujii and Takahashi [13]
Improvement using the Isolated
Singularity ]ethod (I.S.M.) by
Takagi and Hosoda [14]
Model No.
No.i
No. 2
No. 3
Ship
ModelShip
Model
Ship
Model
Length between
perpendiculars
L(mn)
175.00
4.500
240.00
5.225
175.00
4.000
Breadth moulded
B (in)25.40
0.653
30.00
0.653
25.70
0.5874
Draft, Fore
dF (m)
8.00
0.2057
9.148
0.2057
8.54
0.1952
Aft
d (nI)9.00
0.2314
10.626
0.2314
9.62
0.2199
Mean dA (in)
8.50
0.2186
10.030
0.2186
9.08
0.2076
Trim by stern
(in)1.00
0.0257
1.180
0.0257
1.08
0.0247
Displacement volume
V (in3)21,222
0.3608 40,606
0.419
23,188
0.2769
Block coefficient
CB0.559
0.559
0.568
Prismatic coefficient
C0.580
0.580
0.592
Waterplane area cceff.
C0.686
0.686
Midship section coeff.
C0.966
0.966
0.959
Longitudinal center of
buoyancy from F.P.
0.5l8L
0.514L
0.520L
Height of center of
(in)
gravity above base line
9.39
0.200
11.111
0.242
7.78
I0.1778
Longitudinal radius Qt
kgyration
yy
0.24L
0.24L
0.24L
Length-breadth ratio
L/B6.89
8.00
6.81
Breadth-draft ratio
B/d
2.99
2.99
2.83
D (in)6.50
I0.1672
P/D1.055
1.055
0.73
0.73
0.0446
0.0446
5 5Other various methods for calculating the added resistance in regular head waves are developed by various researchers as follows 5) Joosen's method [15] G) Boese''s method [16] 3.0 2.0 ¡ .0 o 3.0 20 z10 o 30 2.0 1.0 Fo 020 Fn025 Exprirnenr o .- Calculation
/ \ - Tokagi(tS,tT)
/ O- '
Ger,iisn-a s/
Conto,n, Ship Nodol No.2 C=0.55q 8.0B/dqq
\O
\
Fig.2. Comparison of added resistance coefficients in regular head waves between experiments and calculations(Container ship model No.1)..
o
05 10 ¡5 2.0 /L 25
ig.3. Comparison of added resistance coefficients in regular head waves between experiments and calculations
(Container ship model No.2).
30 20 1.0 20 1.0 o
Fig.4. Comparison of added resistance
coefficients in regular hca waves between experiments and calculations (Container ship model No.3).
Wahab's method [17]
Ankudinov's method [16] [19]
Gerritama and Beukeirnan 's method
[20) [21)
Shintani's method [221 Salvesen's method [23]
Kholodili-n and Yurkov's method [24)
Detailed studies of the different added resistance theories and their accuracy
have been made by Shintari.i[22]
and Strom-Tejsen et al. [25]. According to Shintani's study, it is found that the results of calculation roughly explain the experimental results, but usually they seem to be smaller than the experimental values in fat ships and
larger in slender ships.
In this paper, the
ex-perimeutal results of contai-ner ship models No.1 and No.2 are compared with the
calcu-lations by Tak,'s method
[14] and Gerritsma's method
[20], an&'ìor t'su1ts of
experiments with model No.3, Gerritsma's method and Boese's method[l6] are applied.From Figs.2 and 3 it can be said that the calculations by Takagi's method (I.S.N.) show fairly good coincidence with the experimental results.
e; Fn 015 Experiment Fnr 020 / Ca/cu.' otion \ Corri.' smcJs mc.'hd
j' \
Mot ion (ree -o'- /\
MdlOfl 11Cc -J\
Restrained Restrained-\&eses
meThod'\
- -,.
e; .
. - FnrO2S Frieû'30 -s \\\ ' .i
\
I Iji
ii
'I /1 1/'l'_-_
30 0/5 faper.'r,u,O. CQÑkurn,uo 0.20 Conrcr.ie, Shiphadal No, /
e,,,'011, Calcule rica IClrie(iS'1)
- -
09 20L/fi-q
C0 - 0. 55Q\
5/d-'2,gq 4\
fr "f . I.0 ,",\
e.-,' IIu\
\\
o.
s., F,, 0.2.5 F0-0.30'\
I..
cf\
.11Ï
II\\
\,\
20 Li c\jl /1 of
ciljI
\\
10 G.. .' Q.. .1 O 5 / A/j 2. ¿.5 20 ¿l: 30 2.0 1.0., o
p' 2 F. 1.5 2D 5 1.0 15Figs.2--4 show that the calculated re-sults by Gerritsma's method agree well with the experimental results for models No.1 and No.3 (L/B 7), but they give larger values at the peak of response curves for model No.2 (L/B = 8), especially at high
speed. The calculated results by Boeses method for model No.3 are smaller than the
experimental results in case of short wave length, and give larger peak values at low
speed.
As another example of the comparison of added resistance in regular head waves between experiments and calculations, the
results for a Series 60, C3 0.70 parent form are shown inFig.5, and those for a Series 60, CB = 0.30 parent form are shown
w /5 Se,,os 50 C0 0,70 L/3= 70 Bld 2. 5 S Fn= 0.20 o
'
o o I. O ¡5 2.0 A/LFig.5. Comparison of added resistance coefficients in regular head waves between experiments and calculations
(Series 60, CB = 0.70 model). F, OIS Se,es 60 Cs=0s0.L/s6s. B/d -2.5 o Srrom.Tojsen A SS,çroni A Cctcu'c o 2.5 01ro0'5 rr'1hod t.j ¡ricin Te;eir) 6e,,,rmo ( -jons,,, I O88
1/
A° 11/
rZ,
05 1.0 1.5 A 20 25 Nc,00 (bj .Shrnrcn,) Pfod'»Od MOruO C - ) M,uo(b,j F.,j,,) oFig.6. Comparison of added resistance coefficients in regular head waves between experiments and calculations
(Series 60, C8 = 0.80 model).
.4..
in Fig.6. In these figures, ths experimen-tal results are obtained from the date by Strom-Tejsen et al. [25] and Shintani[26]. In Fig.5, the calculated results are quoted from the data calculated by Strom-Tejsen
et al. [251 , Shintani [26) and Loukakis [27)
using the methods of Maruo, Joosen and
Gerritsma. In Fig.6, the calculations are quoted from the data calculated by
Strom-Tejaen et al. [25], Shintani[23] and Fujii et al. [291 by applying the methods of Maruo, Joosen and Gerritsma.
The values calculated by Strom-Tejsen using Joosens method are very small com-pared with other calculations as well as experimental results. It is found that even the calculated results by the same method do not always coincide with each other due to the difference of computation
program.
It is a general tendency that the cal-culated results are considerably small compared with the experimental results for the range of shorter wave length, particu-larly in case of a full ship. Fujii et al.
[29] proposed an approximate calculation method considering the added resistance due to the wave reflection at the blunt model on the basis of the formula of
drift-ing force. It was shown that the total added resistance of a full ship in waves can be evaluated approximately as the sum of the added resistance due to the wave reflection at the bow and the one due to the ship motions.
In order to investigate the effect of wave height on the added resistance,
re-sistance tests in regular head waves were carried out with container ship model No.3, varying the wave height from Lpp/l00 to
00 50 40 ¡5 20 (_ ,ns 5 ¡0 th so ID 20 C. k") 20
Fig.7. Effect of wave height on ad,ded resistance coefficients in regular head waves (Container ship model No.3).
CclCuIOtin bWSrrom.TI')0r, yShnrni byLoakckis
PScwo rr,erhod Joosensmfhod Gerirsmo
-Eipc'Iimnr o a Y.02O.'fL.O9 Centone, ¡h.p ilopeS #0 3
.;nne,,,,,
- F,,025. A/.O9 -Fo-020.'YL.15 . .. 20 '5 'o 0.5Lpp/20, at the conditions of A/L= 0.9, 1.5 and Fn 0.20, 0.25. Added resistance coefficients for the pitching and heaving model and for the restrained model are plotted on a base of wave height in Fig.7.
It is shown that the linear relationship between added resistance due to waves and wave height squared is valid approximately for the range of the wave height of Lpp/50
Lpp/30, but it has a tendency to be larger than the squared wave height law for the range of lower wave height and smaller for the ronge of higher wave
height.
3.2 Added Resistance in Regular Oblique
Waves
Experimental, approaches for obtaining the added resistance in regular oblique waves have almost never been carried out,
'o n AIL Cs Fn = 020 A
/80° r'
¡
t, Il Ii/
Consoner Ship Node f No. / 202\
,Drz,9,cos '5 ¡.0 05 '5 sFig.8. Comparison of added resistance coefficients in regular oblique waves between experiments and calculations
(Container ship model No.1).
Fn 020
Z /500
/
Dec 2500 005 E-._..
because the testing techniques are so diffi-cult. Recently resistance tests in regular oblique waves with a container ship model were carried out at the Seakeeping Basin of Nagasaki Technical Institute, Mitsubishi Heavy Industries, usisg a newly designed
gravity type resistance dynarnometer by
Fujii at cl. [29). The container ship model is similar to the model No.1 with length of 3.5 m and the experimental conditions
are as follows
Wave length = 0.5-2.0
Wave height = 1/50 (constant) Wave direction : X = l80°= 00 at
inter-val of 30° (X= 180° corresponds
to head waves)
Ship speed : F = 0.15, 0.25
Results of the experiment are shown in Fig. 8.
Fundamental formula for calculating the added resistance in regular oblique waves is given in Maruo's theory[l0). Hosoda[30] has applied the Isolated Singu-larity Method, which was developed by Takagi and Hosoda[14) for the calculation of added resistance in regular head waves, to the determination of the distribution of hydrodynarnic singularities in case of lateral ship motions, and obtained a method for calculating the added resistance in regular oblique waves.
Numerical calculations were performed for the container ship model No.1. The results of calculations are shown in Fig. 8 and are compared with those of experiments.
In bow waves (X= 150°, l20°),the cal-culated results of the added resistance are in good agreement with the experimental re-sults in case of Fn = 0.15, but in case of F = 0.25, the calculated values are small at the peak of the response curves.
1.0 X/j, 2.0
Fig. 9. Components of added resistance coefficients in regular waves (Container ship model No.1).
1.0 20 Z - /50' 05° I
\
Co,,io,,,, SP nod,! NS i Esp,,,m,n( O -go' u CO((oin,,n 0 H,i000FO_ii
-02$ .1 F,- OiS 0 o 025°o,
/
\\
u ° u°\
,X-60° B O ,I '---°"'-
C 5-i202'
,
¡.0 2.0 2. 2In beam, quartering or following wa.res the qualitative tendency of the calculated results gives fairly good agreement with the experimental ones, but there is not always in good agreement quantitatively between them.
According to Hosoda's method, the add-ed resistance coefficients in regular oblique waves are expressed as
= RAW / (B2/L) 01IH
0pp6+ DS
+ Dj4C z0C0SEz+ DHSZOSinEZ + Dp cosE+ DpsB0sin.fe + Dpc ;0cosE9z+ Dpps z0e0sinE8 + D1y02+ : + DRIP02 + DA+ ¡)y
o Dy5 sinE+ Dsc V0C0SE7+
Dss Y03Ex
+ DRc cosf,,+ DR5 (p,,
S1fl(
+ DyÇt,,y0
cosEy+ DyssÇ4,y),
SiflEy
+ DyRc1/)cosE
+ DyRSb9,sin,
+ DsRCy0c,,cosEP+ DSRSY,9, sinE
where, z0
= za/a :(heave), G
= a/kÇa ¡(pitch)
= y/
a (sway) s =(Pa/1Ça : (yaw), (p (p/k a (roll)
¡ wave amplitude, k ; wave number,
suffix a denotes the amplitudes of
ship motions, and E, E. are the phase differences between the inci-dent waves and heave, pitch, /
is the phase difference between
heave and pitch, ...
In order to evaluate the relativo im-portance of the individual components of added resistance in regular head and bow waves, the corresponding values are calcu-lated for the model No.1. The results of calculation at F = 0.20 are presented in
Fig.9. It is shown that the longitudinal ship motions, pitch and heave, mainly con-tribute to the added resistance and the contributions due to lateral ship motions are negligible small in regular head or bow waves. The calculations of added
resis-tance due to only the longitudinal motions are carried out, and it is confirmed that the contributions of lateral ship motions are very small.
According Lo this conclusion, the added resistance in regular oblique waves are easily calculated on the basis of exten.ion of the calculation method for regular head waves and by using the values of longitudi-nal ship motions in regular oblique waves, as shown by Fujii et al. [5) [29] or Reukelman et al.(3l). Salvesen's method for calcula-ting the added resistance in waves is also applicable to the case of regular oblique waves.
-6-.3.3 Average Added Resistance in Irregular Waves
Resistance tests for the container ship model No.3 were carried out in irregular waves with eight different wave spectra
(Sequence Nos.l-'-8) which are shown in Fig.
lO[32]. Wave spectra of sequence Nos.l-4 are the series of mean wave period, the significant wave height being maintained 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 and the mean wave period T0 for each of the wave spectra are given in
Fig. 10.
The values of average added resistance obtained from the model experimeñts in irregular waves are divided by the squared significant wave height and are presented in Fig.l1 as a function of the significant wave height and the mean wave period.
6.0 4.0 2.0 o 6.0 4.0 2.0 Sc C w) (cmec) Seq. fic No. cc") I /078 2 gqq 3 /0.56 4 /0.04 . /4/3 1.552 5c(W) (cmi sec) Seq.8 S.q. 7 Seq/Ia T. St. cm, (S?c, 5 6.35 /.40/ 2 qçq 4i3 6 1/54 /,3q0 7 13.40 L3q5 8 /3/2 /3Ç ,/Seq 6 ,Seq. 2 Seq 0 2.0 4.0 60 8.0 i (seC) Fig.l0. Wave spectra used for model
experiments in irregular waves.
Seq. 4 Seq. I Seq. 3 Seq.2 2.0 4.0 6.0 8.0 e) (sec)
Con tomer Ship Model No 3
e
/2 1.4 1.6 f8
0.5 075 f25
Fig. 11. Coioparison of average added resistance in irregular waves
between experiments and predictions
(Container ship model No.3).
In this figure, X5is the wave length of regular waves corresponding to the mean period of irregular waves.
The measured average added resistance are compared with the values whicli are pre-dicted from the response curves obtained by the model experiments in regular head waves and the wave spectra by applying the linear superposition method. It is shown from Fig.l1 that the measured values of added resistance in irregular waves are nearly proportional to the squared significant wave height and give fairly good agreement
with the predicted ones.
t.
PROPULSIVE PERFORMANCE IN WAVES 4.1 Added Thrust, Torque and Number ofRevolutions of Propeller in Waves Self-propulsion tests in regular head waves were conducted with container ship models No.1, No.2 and No.3 at the
Experi-ment Tank of Osaka University (2] [3)
[41.
The testswere carried out at the
self-propulsion point of the model and the mean
values of thrust, torque
and numberof
revo-lutions of model propeller were measured. In the self-propulsion tests, the model was free to heave, pitch and 'surge. The test
conditions are the some as those for
resistance tests in regular heid waves,
which are stated in 3.1.
As an exampic, the experimental results
of added thrust, torque and number of
revo-lutions for the model No.3 are presented in
the form of nondinsensional coefficients, as
shown in Fig.12.
The effect of wave height on the added
thrust, torque and number of revolutions
were investigated by self-propulsion tests
in regular head waves,varying tho wave
height from Lpp/lOO to L/20
t the
condi-tions of
,X/L
0.9, 1.5 and Fn
=0.20,
0.25.
The measured results are presented
in Fig.l3.
The variations of the added
thrust and torque with wave height show a similar tendency to those of the added resistance, but the added number of revolu-tions of propeller shows somewhat different
tendency.
Self-propulsion tests in irregular waves were also carried out with the con-tainer ship model No.3 [32]. The wave spectra used for the model experiments in irregular waves are the same as those used fer the resistance tests that are shove in
Fig.l0.
The measured values of average
thrust, torque and
numberof
revolutionsdivided
by thesquared
significant waveheight of irregular waves
are presented inFig. 14 and are compared with the predicted values by the linear superposition method.
30 20 n-,-n 0 05 n co n.j Ç, o
Contoinrr Ship NodI No.3
-
'
Thrust increasc FI) 0.15 --0.20 -d-0.25 0.30 -=---Torque increase IL 20Fig.l2, Added thrust, torque and
number of revolutions of propeller
in regular head waves (Container
ship model No.3).
¡.5 Exp. Predict. 0.2í o 025 80 030 A a 60 40
-A..-- n__A.
.-A 20 I Q) e H,, (c'o) o I 12 14 16 18 ¿050 40 25 L//-/,,3 Fn Exp. f',ethct. 05 O 0.20 0.25..i.. '-.
-oo----80 60 40 20 o0 20 '5 a o o 0.2 C; 0, O
Conrane, Shin hlode! No.3
S W (cm) 20 5 C- (cm) 1(1
80 50 0 L/ 20 80 50 40 20
Fig.13. Effect of wave height on added thrust, torque and number of
revolu-tions in regular head waves (Container ship model No-3).
4.2 Propeller Open-Water Characteristics in Waves
In order to investigate the propulsive performance in waves and to analyse the
pro-pulsion factors, it is necessary to clarify the propeller open-water characteristics in
waves.
Taniguchi[33] and -McCarthy [34] carried out the propeller open-water tests in regu-lar head waves and compared the measured results with those in still water. The
results show that the mean values of thrust and torque in waves are identical with those
'in still water.
The authors carried out th propeller open-water tests with a five-bladed propel-ler of 0.15 m diameter ab the
conditions
of torced oscillations of pitch, heave and surge in still water as well as in regular and irregular head waves (35]. The propel-ler model used for the experiments is th one which is equipped for the container ship model No.3 and the main particulars are shown in Table 1. A summary of test conditions is given in Table 2.The mean values of the fluctuating propeller thrust and torque are compared with the open-water characteristics in uni-form flow of still water, and the results
-8-Conrc,ner Ship 1-1cd( /Io.3
T4u/H5 (AV/,n)
- (kç.m/m)..
A -/
i--../
-
,'/---.. V - I_ca
o o (//sec.m').
0.5Fig.14. Comparison of average added thrust, torque and
number
ofrevolu-tions of propeller n-4equìar waves
between experiments and predictions (Container ship model No.3).
of experiments are shown in Figs.l5---l8. It is confirmed from these figures that the time averages of 'the propeller open-water characteristics in waves are considered to be identical with those in still water when
a propeller is sufficiently immersed.
FnoO2O Thrist increose Fri c025 Thrust ,rcrec3 0 Torque 'crease 0 o o Targue u,,crease 00 0 'W 00 0 t -- Reo1ut;an r..reas.e oo o e - °8_Reyc1uf,cn rcreose - ssN.,,..._í..ìui_ìì ii TAi,/H,'J (i'g/,) 60 40 e -° 00 20 o 0AW/HC?(Ag.m/m5) 1.2 £ 1.0 o.& 0.6 0.4 NAv/H, (I/5c.m') /00 50 H,,3 (cm) O á IO /4 16 /8 50 40 30' o o (sec) 1.4 1.6 1.8 60 40 20 O 1.2 1.0 0.8 0.6 0.4 100 SC
0.6
0.4
0.2
o
Table 2. Test conditions of propeller open water tests.
Freq. (Hz; 0.5/ O 57 0.66 0.88 0.4 Forced Heo(jo K K0
000
s e ea av
£ A Y 0.5 ¿3ir, uniform /Iow
06 0.7 08
Fig.15. Propeller open-water character-istics at forced heave oscillation.
Fig.].6. Propeller open-water character-istics at forced pitch oscillation.
Oß 0.4 02 FrqjHz Kr K0 q in uniform fioul Forced Surge FreqJHz) Kr K0 7 0.5/ 0 0 0 0.57 0 0 0.66 a A V ÛR8 A A Y in uniform /Iouî In Regular k'oves 0.4 .0.5 0.6 0.7 0.8
Fig.l7. Propeller open-water character-istics at forced surge oscillation.
Freq.Hz) Kr K0 70 0.5/ 0
0 0
-. 0.57 e or
0 56 a a o ¡n uniform flaw 08P3 A L V 0.4 0.5 0.6 0.7 0.8Fig.l8. Propeller open-water chracter-istics in regular head waves.
Freq. of Advance coeff. Advance speed No.Of revol.
Kind of tests
oscil-lation J V N (Hz) (m/sc) (1/sec) Forced heave oscillation Double amp. : 8 cm 0.51 0.57 0.66 0.88 0.4 0.8 0.6 1.2 10 con st Forced pitch oscillation 0.51 0.57 0.4 0.6 10 Double amp. 3 deg. 0 66 0.88 0.8 1.2 const. 0.51 1.55 0 57 0.4 1.40 7.5 o6c 0.88 -0 8 1.20 0.90 20 Forced surge 0.60 10 oci11ation 0 88 0.4 cOnst. 1. 08__ Double amp. : 0.6 0. 8 8 cm 0.88 const. 1.44 16 0.88 0.4 0.8 0 1.2 10 con st. In regular head waves 0.51 0.57 0.4 0.6 10 Wave height : 0 66 0.8 1.2 cOnst. 8 cm 0:88 Forced heave oscillation in regular head waves 0.88 0.4 0.9 15 Double anip.of heave: 8 cm 0.8 7.5 Wave height: 8 cru In irregular head waves 10.91 cm 0.954sec 0.7 0.525 5 0.5/ 0 0 0 0.57 e e e 0.66 a a V 0.85
A AY
0.6 0.7 as 0.4 0.5 0.6 0.4 0.2 o 0.6 0.4 0.24.3 Self-Propulsion Factors in Waves
As mentioned above, it may be confirmed that the mean values of propeller open-water characteristics in waves are identical with those in still water, so the effective wake
fraction w0, relative rotative efficiency and propeller open-water efficiency r in waves are analysed from the measured values of thrust, torque and number of revo-lutions of the propeller and the mean ship speed in waves by applying the thrust iden-tity method using the propeller open-water characteristics in still water. The thrust deduction factor in waves is obtained from the values of resistance and thrust at the saine ship speed measured in resistance and self-propulsion tests.
The self-propulsion factors in waves had been considered to be almost the same values as those in still water[33] [36]. However, it has been considered to be neces-sary to study the detail of the character-istics of self-propulsion factors in waves in order to improve the accuracy for pre-dicting the propulsive performance in waves.
For this purpose, resistance and self-propulsion tests in waves have been carried out carefully with a ship model of Series
60, C0 = 0.70 parent forrn[37] [38] and con-tainer ship models Nos.l-3[2] [3] [41 [32],
and the self-propulsion factors are obtained from the above mentioned procedure.
As an example, the variations of self-propulsion factors in regular head waves
with the wave length-ship length ratio for the container ship model No.3 are presented
in Fig.l9. 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-propul-sion factors in regular head waves vary considerably in the region that the wave
length- ship length ratio,À/L 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 propeller open-water efficiency decreases remarkably inthe 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 (i-we) arid (l-t) are larger than those in still water, while the vari-ation of relative rotative efficiency with wave length is comparatively smail and the value is nearly equal to that in still
water. The similar results were obtained from the experiments by Moor et al. [39].
The effect of wave height on the self-propulsion factors in regular head waves
is also studied with the container ship model :o.3, and the results are presented
in Fig.20. In this figure, the values of
- 10
-'5
1.0
1.0
0.5
C&nciner Sfrp tlodc.1 No. 3
Fig.19. Self-propulsion factors in regular head waves (Container ship model No.3).
Cc.m,ne, Ship 1odel N. 3 -/'ZR
\L
- --t F,O20'YL'09 I-". C. tc'n2000si
b L/C_ 20 FtO25."iL'Q9-.
iTL--Fn025 'IL7$ i- ? 70 (J k-tn) 00 500 LIC.. 20Fig.20. Effect of wave height on self--propulsion factors in regular head waves (Container ship model No.3).
--
---Fe0i5
-T
Fn020---TT
Fn.tO30:=
Fm025 .----
---05 10 15 20 0.5 1.0 1.5 2'/L l0 70 05 '.5('4 I. 1. C. 8 8 10 /2 14 16 /8 ò1b 4 2Cr 25 L/H 6 8 10 /2 14 /6 / i0 40 .0 )s L. /1,,.
self-propulsion factors in still water are shown by the horizontal broken unes.
From this figure, it can be said that the propeller open-water efficiency de-creases considerably, while the value of
(l-w0) has a tendency to increase with the increase of wave height. On the other hand, thevariations of and (l-t) with wave height aro comparatively small.
Fromthe results of the resistance and self-propulsion tests which were carried out for the container ship model No.3 in
irregular waves with the wave spectra as shown in Fig.lO, the self-propulsion factors are analysed by the saine procedure as
mentioned above and are presented in Fig. 2]. as a function of significant wave height and of mean wave period.
It is 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 efficiency in irregular waves decreases with the in-crease of significant wave height, and the values of (lWe) 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 clarify the above mentioned characteristics of self-propulsion factors in waves, the radial distribution of inflow velocity in the propeller disc in regular head waves were measured by using circular ring typo wake meter with the container ship model No.3. Furthermore, the wake measurements on restrained model in regular
head waves and on the conditions of forced pitch oscillation in still water were
per-formed. A summary of test conditions are
12 I.0 08 0/i 0. I. 1. 0. 0.
Fig.2l. Self-propulsion factors in irregular waves (Container ship model No.3).
/6 1.8
10A,/L
Table 3. Test conditions of wake measure-ments in propeller disc.
Ring No. 4 5 6 7 8 9 10
r/S 0.897 0.789 0.681 0.576 0.467 0.362 0.254
shown in Table 3 [32].
The measured results are presented in the form of the ratio of the mean inflow
velocity in the ring plate in regular head waves (l_wn)w to that in still water (l_wn)s as a function of the ratio of radius of the ring to that of the propeller,r/R and are shown in Fig.22.
As shown in this figure, it becomes clear that the values of
are larger than unity as a whole. Especial-ly, the closer the measuring position is to the center of propeller, the larger the values become, and this means that the dis-tribution of the mean inflow velocity in the propeller disc in waves approaches that in uniform flow. Furthermore, the values become much larger in case of A/L =1.1, where the ship motions are very severe. When ship model is restrained in regular
F wOtCt
8-
r
0.20 ConrOirlSJiip -0./i- n Still
1-r.. . I-S.-ek
£:
:
70 70 L £-
A £ L £ . 0.25 F,= 0.30 g Z -4---Ir
»-ccc,, o I-w-r p .L_...J-
-*
-'/0 'rF, = 0./S -- in it/Il wolOt , 0.20 C tOrnì, Ship
flodl 1/ej e ca ca
1L
a h j. A F,- 0.25r,- ojo
t 9, Z ---.'-r.
e[-5V
S'..r
-9 . 2o...I,",)
* 4- 4 AKind of tests Fn Ring Wavelength Wave height
In regular head 4, 5, 6, 7 0.5. 0.8, 0.20 8, 9, 10 1.]., 1.5, CL/SO) waves 4 20 0.20 7 0.9, 1.5 CL/laO L/20) waves 2.0, 2.5 Restrained model 05, 0.6, 8 in regular head 0.20 7 1.1, 1.5, (L/50) Forced pitch in 4 6 7 8 Freq. of pitch
Double amp. :3deg 0.88, 1.09 Nz
still water 0.20 ' ' ' 0.52, 0.60, 0.72, Freq. : 0.52 Hz Forced prtch in Double amp. 1, 2, 3, still water 0.20 6, 10 4 dec 1.2 .4 1.6 1.2 1.4 05 0.75 ¿0.i,,4 oí
(6 .4 1.2 (1 -W,,)ij (j - W,,)0 Propeller boss of No 3
Container ship mod
- Wo). ir, regular wo ves
F0 = 0.20 (/-w,, in still um?e, i-' N" N'. 00.5 0.8 a 1.1 ALS o 2.0 2.5 1.6 12 -(.2 loo 1.05 1.00 I / 2.0 2.5 A/L
Fig.23. Ratio of (l-w) in propeller disc in regular head waves to that in still water with restrained model (Container ship model No.3).
'.3
1.2
Fig.24.Ratio of (l-w) in propeller disc in forced pitch oscillation test to that in still water
(Cohtainer ship model No.3).
I.' I. Ca o
--
o OSO 0.72N
A 0.88 N\\. N
°\
(i /Otced pitch (1 ¡t, still watetNN N.
0.2 0.4 0 5 0.8 (I W,,)p forced pitch in still caterContainer ship model, Restrained
F= 0.20 r/' = 0.576 r/R o 0.254 A 0.68/ IO 2.0 3.0 e0lde9) 4.0
Fig.25. Effect of amplitude ors ratio of (i-w1) in propeller disc in forced pitch oscillation test to that in still water (Container ship model No.3).
Though the calculated results of thrust and torque coefficients by two methods give ccnsiderably large values compared with the experimental ones, those of propeller open-water efficiency as a ratio of thrust coef-ficient to torque coefcoef-ficient agree fairly well with the experimental values. And the propeller characteristics at behind condi-tion in regular waves are also calculated by the same methòds as mentioned above using the measured distribution of inflow
1.00 0.2
0.4 0.6 0.8 r/R 1.0
Fig.22. Ratio of (lwn) in propeller disc in regular head waves to that in still water (Container ship model No.3). head waves, the values of (lWn) are not so much larger than those in stiIl water, as shown in Fig.23. However, the mean values of inflow velocity at the condition of forced pitch oscillation, (l-w10), aro much larger then those in still water,
especially at a radius closer to the center of propeller, as shown in Fig.24. And it is shown from Fig.25 that the larger the amplitude of forced pitch oscillation is, the larger the values of (l-wn)p become. It is concluded, therefore, froto these facts that the increase of (l-w) in waves com-pared with that in still water is mainly due to the magnitude of ship motions.
It has been said that the propulsive performance in waves is explained fairly well by the overload effect on the propeller due to the added resistance in waves [40]. As mentioned above, however, the self-propulsion factors are affected consider-ably by ship motions, so lt is considered that the results of t1e overload tests in still water are not always coincide with those of self-propulsion tests in waves.
This fact is proved experimentally by Moor
al. [39) and the authors[37] [38].
In order to investigate the character-istics of self-propulsion factors in waves, an attempt was made to calculate the self-propulsion factors by ising the propeller
characteristics obtained from the blade element theory [32]..
The propoller open-water characteris-ti.cs in still water are calculated by the following methods.
Calculation method A : Simple blade
element theory
Calculation method B : Blade element
theory considering the drag-lift ratio of blade section
Consoner ship model Nc3 Forced pitCh F0 = 0.20 Froq. (HZ) o 053 1.4 Propeller 5 oS S
Container ship model NQ3 Forced pitch
Freq. 0.52Hz
F0= 0.20
_ç i - uit,»
075
070
Fig.26.. Comparison of self-propulsion factos irs regular head waves between experiments and calculations
(Container ship model No.3).
06 velocity in the propeller disc and the mean
values of number of revolutions measured by the self-propulsion tests in waves. Then the effective wake fraction Wer relative rotative efficiency and propeller open-water efficiency fl0 in regular head waves are obtained by applying the thrust identi-ty method using the propeller open-water characteristics in still water calculated as mentioned above.
The comparison between the results thus calculated and those obtained from the ex-periments is shown in Fig.26. In the figure the mean nominal wake fraction w in the propeller disc which are obtained by means of volume integral method using the measured - distribution of inflow velocity, is also
presented. The calculated value of n by
the method A is always equal to 1.0, but
the one by the method B gives a similar ten- 1K1
dency to the experimental results. It can K7
be said that the qualitative tendency of 0.3
the calculated self-propulsion factors,(l-w0),
02
R and no shows fairly good agreement with
the experimental ones, though there are some differences between them quantitatively.
4.4 Propeller Load Fluctuations in Waves
0.3
The fluctuation of propeller load in
waves has been considered important to eva- 0.2 luate the propeller racing, propeller excit-ing vibration and strength of propeller and 0.f
shafting.
o
To investigate the characteristics of
the fluctu.etioas of .prcpeller...thrust and
torque, measurements were carried out at the propeller open-water tests as mentioned
in 4.2 [35], and at the self-propulsion tests in regular and irregular waves with
the container ship model No.3 [4] [35].
At the measurements of propeller load fluctuations, the apparent fluctuations caused by the oscillation of self-propul-sion dynamometer arc considered to be included in the measured values, so they are corrected by using the resilts of calibration tests
(1) Propeller load fluctuations at the
065
propeller open-water tests
060
In case of the propeller open-water tests with forced heave and forced pitch oscillations, the propeller load fluctu-ations do not appear, except the apparent fluctuations due to the mechanism of
dyna-mometer.
The measured double amplitudes of pro-peller load fluctuations in the open-water
10- AK,
Fig.27. Thrust and torque fluctuations at propeller open-water tests with forced surge oscillation.
Fig.28. Ratio of thrust and torque fluctuations to mean thrust arid torque at propeller open-water tests with forced surge oscillation.
CsrTcin,, sap 'd1! No.3 2,
--
F 0.20 stilt wore, - u',____T-z____.
Cc, 'cu . C fa CO AIlethod
-. E -?C (n Still watE' Forced ca.opnf(t,
06-- ¿Kf co daring pep..
(0)01. /(uctLaotwft_ -'0.4-Surqe 0.57z Ez;e:,mon, o u1K7 ° 'Ç O -066Hz _'..V20:.,2
04. 0.68 ni - v-o.qo,,,,c _.a-TTK 0.5/az Forced K0 V/55,cv5 /0.3 -dTuIO,dol jSeors/utc. i -Du. cems,o°rnt C'SP.i
racl./iaictJfo,t/02
- ::j cr.
.- /0
Suge 057HZt
V/.4Om/oeo 'j.
/
Expaomeitt7,'
.Q 4K7'Krz'' /
A ¿4/K0/
1T-i , i i' 0.88 lIZe0/
0.5 IO 20 L'O 0.6 j 0.8" 0.4 0.6 j 08 0.4 0.6j
0.8 0.4 0.6 0.8 I IO I.05 IC: o oc 055 055 0.45 0.4 02 o 00 0.4 02 oFig.30. Ratio of thrust and torque fluctuations to mean thrust and torque at propeller open-water tests in regular head waves.
Lests with forced surge oscillation are ?resentod in the form of nondimensional
officients,
AKT = AT/pn2D, AKQ = AQ/pn2D5 es a function of advance coefficient J = IA/nD, and are shown in Fig.27. And the ratio of the measured fluètuations of
pro-ieller thrust and torque to the mean values DE total thrust and torque, that is
T/T and aKQ/KQ, are presented in Fig.28. The measured results of propeller load fluctuations at the open-water tests in
egu'Lar head waves are shown in Fig.29, dth the form of AKT and AKQ versus 3, and in Fig.30 wih the form of AKT/KT and
Q/KQ. - 14 -o 0.2 Fn 0 20 0.!. 0.1 o o 0 0:5 1.0 I 20 05 À4 2:0
Fig.31. Ratio of thrust fluctuation to mean thrust at self-propulsion tests
in regula: head waves (Container ship model No.3).
Fig.32. Ratio of torque fluctuation to mean torque at self-propulsion tests in regular head waves (Container ship modal No.3).
(2) Propeller load fluctuations at self-propulsion tests
The measured double amplitudes of pro-peller thrust and torque which are obtained from the self-propulsion tests irs regular head waves, are divided by the mean values
of total thrust and torque, and are
presented in Fig.3l and Fig.32 as a Ounction
of A/L. In these figures, circular spots are the measured values and the dotted lines the mean line of corrected values.
The effect of wave height on the fluc-tuations of thrust, torque and number of revolutions of propeller at the self-propul-sion tests in regular head waves is also studied and the results are shown in Fig.
33. In this figure, the measured values 05/Hz 8
---
---_--
... (ri. (S,'pç open -In Regsi-...
00.6 'moncO 0.4- 0,2-orVatjes 057Hz -A o---...
R...A
E:c,ei,rnenr - 066Hz$_'o:
- 0.2-088Hz_-..
F-=0.l5 ,.-'- .
TorqueSOQ3
9/
....o>.
F7ucturmon in Regular Voues
Fn=020
o
o----_O ..
o.-
0.1 ; ...O (opensmem °
---cal
So-oro' /unc:OASoon Irre cf op. - cOrrocrd "
Fn0.25 0.3-_..._ ,, pro mLol fluor rCrO ¡sorChi Iou ron
0.2-
.- -.
FnO30 Kr as/Hz In Regular Vaues 0.57 Hz 06 -4T4 ¿Q. CJ b Soars !L'nC. 06 0.4 -«-'Do,, rcnS,d9r,r, prop.J.
,'O1 /luc1,atoo-
JT(CUI bj prop. cl 0.4 ---JJ mWs,r ..-Expor,roon oAje/e
0.2 02 A o 0.66 r 0.88 'e 0.6 06 0.4 0.2 _- 0._,,9' A Q___..-__ .- ----o 0.4 06 04 0.6 as 0.4 0.6 ,, 08 a4 0.6 08 Fig.29. Thrust and torque fluctuationsat propeller open-water tests in regular head waves.
lr/r[ Fo= 0.15
- -
Thrust F7uctu,crs in Regidor Vaves0.21 02
0.3
0l
Li
o
-
Cs! tv S.rs' f cor,fl.o, !,ro Ql erp col,e('Od
- csvs,a',
Fn=025
---
,'
ur 0.5 i.0 '5A/L Rd k4 2.0 '0 iK 06 04 0.2 0.8 06 0.4 0.2 .jQ,f) 04 0.3 o. 0.1 o 0. 0. 0.g 0.10
'r
Ci'
005 04 0. o 0.5 0. 0.0 Ct.,aro,n0r Shsp fr/ada! No 3Fig. 33 Effect of wave height on fluctuations
of propeller thrust, torque and number
of revolutions in regular head waves. are divided by the
wave
height, and are presented as a function of wave height.It is said that the amplitude of propeller
load fluctuation is approximately
propor-tional to the wave height, except the case
of
excessive high wave height.
From the results of self-propulsion tests in irregular waves with the wave spectra as shown in Fig.lO, the significant values of fluctuation of propeller thrust
and torque,
and
are obtained.These values are divided by the significant wave height of the corresponding irregular
waves, and are presented in Figs.34-37 as
a function of significant wave height and of mean wave period.
5, 10 ¡.1 /8 6
50 4) X 25 60 0 40 .50 25 H/L
'4 I8
Fig.34. Effect of significant wave height
on thrust fluctuation at self-prouision
tests in irregular waves.
/.0 0.8 0.6 0,4 02 o 1.2 1.0 08 0.6 0.4
Fig.35. Effectof mean wave period on thrust fluctuation at self-propulsion tests in irregular waves.
rhrul( Fluctual,on
0.6-
---.04--Cal
bj SOp.opals CFSCCiCF.cxss,e, pis seta! flJCr. - - -'Po, c0151Set p;5p retO! flurs. ?
was-c ,r.
in Irro;ular kves
F,s=O.2
e
-
P55's) c r. ¿ej 1,-scar Srp5'100S'trinìus,G ,ea,afre amp acal
F=0.25
06-
--. 04 T0(5CC) -Fe" 0.33 Exp ,Ccuec:cd r . -5/L. 09--/
.e__A___.!__f_L_'-- '--r
'
2 5VL'15 --e-1'
-t--025 ¿p. CalE Cal.0£
-- -- -- __,--
- 'íía,
- ;____ . a.-
OSO- -rl
--L--7
rIO4O, Torque Flucruo non
0.6 in Irregular Waves ¿'IP. FnO.20 £ - ¡iva F0015
-*--- Cal. Nsj pmp, opon chofac(
£ CGtlS0,'f P'op. resp!. f!SJC'
-- --Da. cons der. p--OP. recidI, j!rsc 5.401-' P'C$ICF. N.J (moot SUPO'pQSit,ois
wale lSCsgIsr reuCrrC.1 ¿15500 espCi.se amp. cspc-rG:O(
Fo"0.25 FrrO.30 1.4 N ' 12
2--'-
t - t -. £ £ L IO £-- _____--L-_î
0.6-IO,.ir Thruil F(uctuct,cn
H F00.J5 ¿'1 IlreçfJIor Wcves F0"O,20 -0.4- 4
-,---- -,----Ce' Oj a-,----or. ors-,----s
(lt's _-'- '
----Oscios ' '..c,
flu i -.- Prej N.j 1,rmcr 5rsperO;,rcr, us ng vespa se amp ope ator
- -
-Fn030 0.6 ¿"P ,COrre.rd Qs-:
11va 10)7 Ih9-rfl/Ns) Torque Fluctuation F=O15 ---foin lue guIar Waver
--:j::---&o_s.
- ---0.6- -- 4 N' taj :p-5r5 Ol,a,acr - - -0 j:t' resa!J!siCt 044 - P'ej,cr b,, ¡siseas ssiperces,r,cv,
uttig reSpaiss? amis orcec rot
-.'_e
A ¡.0 ',,'
a - A--
LL 08-4."
'
£ - -'A £ L £--
EXp. £ ¿"P.CO('ccilcd -rociad ¡0 14 ¡8 6 IO 14 Is 60 50 40 25 H,,,,7_ 60 50 40 33Fig.35. Effect of significant wave height
on torque f].uctuation at self-propulsion
test
in irregular waves.
¡.2 ¡.4 1.6 1.8 ¡.2 1.4 1.6 1.8
05 075 1.0 )4 F25 0.5 1.25
Fig.37. Effect of mean wave period on
torque fluctuntio, at self-propulsion
tests in irregular waves.
J 2 ' (ein) C,v (cm) 80 5060 L'C 20 50 b ¡.2 .4 ¡.6 I.8 I? 05 0.75 À./ 5.25 05 1.6 1.8 0.75 / 0 125 0.4 0.? O 06 0.4 0.2 I.0 as 0.6 0.4 02 o f2 1.0 0.8 0.6 0.4
Ship rrotion (calCulated2j Fluctuation
of J
L
Fluctuationof J
Fig.38. Calculation methods of propeller load fluctuations in regular head waves;
"Calculation A"is a method using the ship motions calculated by the strip method and the orbital motions of incident waves. "Calculation B" is a method taking the fluctuation of number of revolutions of propeller into consideration in addition to the 'Calculation
A'.
"Calculation C" is a method using the ship motions obtained from the experiments and the orbital motions of wavesconsidering
the wave heightreduc-tion at the stern.
The wave height reduction of the incident waves at the stern was measured with the restrained model No.3 of container ship in regular head waves, and the results are preented in Fig.39 in the fçrm of the ratio of the wave eight at the stern to that of incident waves, In the
figure, an approximate formula,
'/
= O,2(\/L)+O.5 [4], which is obtained from the analysis of the experimental results with mathematical ship forms by Jinrsaka[441, and the calculation by using the threedimenosional periodic sources as the
repre-- 16
-fFluctuation
of JFig.39. Ratio of wave height at the stern to that of incident wave (Container ship model No.3).
sentation of ship hull based on Jinnaka's method[45] are presented.
The results of calculation of propellèr load fluctuations using the propeller open-water characteristics are shown in Fig.27 and Fig.29,for the condiLion of propeller open-water tests with forced surge and irs regular head waves, respectively. It seems that the calculated fluctuations of thrust considering the fluctuation of number of revolutions of propeller agree well with the measured ones, while those of torque show some difference. The same tendency is obtained fronthecomparison of propeller load fluctuations at the self-propulsion tests in regular head waves, and it can bo said that by considering the wave height reduction at the stern, it shows better
agreement.
The calculated results by "Calcula-tion B" and "C" for the effect of the save (3) Calculations of propeller load
fluctu-ations and comparison with measurements The propeller load fluctuations are predicted from the propeller open-water characteristics in still water by using the fluctuation of axial inflow velocity in the
propeller disc, which are calculated from
Ship
inotiobs and orbital mo Lions of waves. This calculation method is used by McCarthy et al. [34] , Ilyin et al. [42] and Sluijs [43].The ?rocedure of calculation is shown in Fig. 38. 1.0 0.8 06 0.4 0.2 0
-V
02(A/L)f05 Cal b2 3-dim. priod,c source ExpFriment o F5 = 0.15 A 0.20 0.25 D 030 ¡.0 1.5 2.0 2.5 Propeller opencharacteristics
characteristics
Propeller operi Propeller opencharacteristics
À 8 C FluctuatiOn ° K1,K0 Fi uct Cation of K6K0 Fluctuationof Fluctuat ion of T,O Calculation L
cl
T,Q Fluctuat ion of Calculation Calculation ave height reductionat stern
Orbital motion Ship irCtiofl Orbital motion Ship motion Orbital nitticri
of wave (calculated of wave (measured) of wave
Fluctut ion Fluctuation
height of regular head waves on the pro- REFERENCF:S
peller load fluctuations are shown in Fiq.
33. in this case, too, the results of thrust fluctuation by 'Calculation C" show closer agreement with the measured results, but for the torque fluctuation the agreement
is not always good.
Another method by using the Sears' non-stationary airfoil theory are applied
to the calculation of propeller load fluc-tuations and exciting vibratory forces in regular oblique waves by Yuasa[46]. The
results by this method are shown in Figs. 25,30 and Figs.31,32. 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.
It is concluded from these figures that the wave height reduction of the incident waves at the stern and the fluctuation of number of revolutions of propeller based on
the response characteristics of the prime mover should be taken into consideration
for predicting the propeller load
fluctu-tions.
The calculation method for predicting the significant values of propeller load fluctuations in irregular waves are develop-ed by applying three different methods as follows [35]
Method A using the propeller open-water characteristics
Method B : using the Sears' non-stationary
airfoil theory
Method C : using the linear superposition
principle
The calculated results by Method A and Method C are shown in Figs.34-.-37, and are compared with the experimental values.
It can be said that the calculated results by the method using the propeller open-water characteristics show closer agreement by considering the wave height reduction of incident wave at the stern and the fluctuation of number of revalu-tiens of propeller. The significant values of propeller load fluctuations divided by the significant wave height of irregular waves have a tendency to increase with the increase of wave height, arid this can be explained by the Method A. On the other
hand, the predicted values by linear
superposition principle using the response amplitude operators obtained from the ex-perimerits in regular waves and the wave spectra give a constant value with the change of wave height.
Tassi, F., Takagi, M., Canne, M.,
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