Experiments on a series 60, CB = 0.70 ship model in oblique regular waves

L

r*

1 'I

PAPERS

OF October 1966 Ship Research Institute

Tokyo, Japan

Tcnsd;e

t10.ch1

Detit

No. 18

SHIP RESEARCH INSTITUTE

Experiments on a Series 60, CB=O.70 Ship Modd

in Oblique Regular Waves

By

Experiments on a Series 60,

CB=0.70 Ship Model

in Oblique Regular Waves

By

Yasufumi YAMANOUCHI* and Sadao ANDO*

Abstract

The model ship motions and propulsive performance were measured

on the Todd series 60, block coefficient 0.70 hull, in oblique regular

waves. The tests were carried out at various wave length, course angle

to waves and model speed using a free-running model in the Mitaka No. i Ship Experiment Basin, the Ship Research Institute.

The frequency characteristics of the model ship motions and pro-pulsive performance on the basis of wave length at Froude number 0,

0.05, 0.10, 0.20 and 0.25 are shown in Figs. 2 to 4.

The results of the head sea tests are compared with those obtained at the three other tanks, with respect to pitch, heave, thrust and torque increase, as are shown in Figs. 5 to 8.

In the same conditions, the turning ability were also measured.

Introduction

Following the Recommendation of the Seakeeping Committee of the International Towing Tank Conference (I.T.T.C.), the model ship

motions and propulsive performance were measured on the Todd series

60, block coefficient 0.70 model, in order to compare the results with those obtained at other towing tanks, and also with the theoretically

computed ones. The tests were carried out not only in head seas, but

also in oblique waves.

The theoretical computations based on the strip theory are now in progress, and the results will be reported in near future.

Testing basin

The tests were carried out in the Mitaka No. i Ship Experiment Basin, the Ship Research Institute, which is 80 meters long, 80 meters wide, and 5 meters deep'1, the water depth being normally 4.5 meters. The wave maker of the flap type generates the tow-dimensional regular waves (two groups of oblique waves if necessary) as well as the irregular waves from one side of the basin.

Table 1. Principal particulars of ship model TODD SERIES 60, BLoCK COEFFICIENT 0.70 (Model 4212 W)

Length between perpendiculars 4.000m

Breadth B 0.571m

Draft T 0.229m

Displacement volume ç 0.3657 m2

Block coefficient CB 0.700

Prismatic coefficient Cp 0.710

Midship sectional area coefficient CM 0.986

Waterplane area coefficient Cp 0.785

Longitudinal center of buoyancy from F.P. FB/LPP 0.495

Lengthbreadth ratio LIB 7.000

Breadthdraft ratio BIT 2.500

Longitudinal radius of gyration k,,,, 0.25 L

Center of gravity above base line KG 0.222 m

Transverse height of metacenter GM 0.020 ni

tested

value-Natural circular frequency of pitch 5.49 sec'

Natural circular frequency of heave 5.19 sec-'

Natural circular frequency of roll w 2.86 sec-'

Dimensionless damping coefficient of pitch Ic,=aO/w, 0.107

Dimensionless damping coefficient of heave 0.115

Diameter D

Pitch ratio (0.7R) P/D

Expanded area ratio Ag/A0 Blade thickness ratio

Angle of rake

Number of blades Z

Direction of turning

Table 3. Principal particulars of rudder

4. Testing and measuring equipment

Since the tests were carried out by self-propulsive method, the

model ship was equipped with many kinds of instrument for measuring,

0.167m iioÓ 0.500 0.045 6.000 4 Right-handed 1.50 WL I.2SWL 1.0 OWL 0.75 WL 0.5OWL 025 NL 3 Since the basin is an open type without any guide or towing de-vice, the test of various kinds must always use the free-running model

ship, manoeuvered by radio control system. 3. Model ship, propeller and rudder

A wooden model of the length 4 meters was made following the

block 0.70 lines, a family of ship forms named as Todd series 60E2].

The principal particulars of the model ship and test conditions are listed in Table 1, the lines being shown in Fig. 1.

The propeller particulars of the Troost B 4-50 are listed in Table 2,

and the rudder particulars of the model are shown in Table 3.

Rudder area AR 0.0148 m2

Rudder area ratio AR/(L X T) 1/61.83

Aspect ratio 2.00

BL

20 1/2 FR

Fig. 1. Lines of series 60 parents, C0 0.70 (Model 4212W) Table 2. Principal particulars of propeller

4

powering and steering as well as controlling.

To measure motions and propulsive performance of the model, a vertical free-gyro for pitch and roll, a horizontal free-gyro for yaw,

an accelerometer for heave, a propeller dynamometer for thrust, torque

and shaft revolution, and a potentiometer for helm angle measurement

are installed on the model. The accelerometer was mounted on the top of a gimbal type pseude-horizontal plane setting equipment, which was

loaded about twenty centimeters abaft the center of gravity of the

Photo. 1. Arrangement of equipments in the model (series 60, block 0.70)

5 ship, as the transmitter of the position indicator was mounted just on the center of gravity.

To record these qualities, an electromagnetic oscillograph was used

on board the model, and was handled by radio control system. The

propelling power was given by a DC shunt moter connected with

bat-teries, and the revolution of the propeller was set by the voltage.

Other necessary equipments loaded on the model are a steering machine,

a wireless receiver, reduction gears, and a transmitter of the

ultra-sonic position indicator for measuring the course and speed of the model, and so on. Photo. i shows the set up of the model.

The wave was measured by a capacitance type probe.

The velocity and the course of the model was obtained from the trace of the position of the model at every second, given by two num-bers of four figures, that show the distances of the model from two

points on one side of the basin. Two ultrasonic receivers are placed

on these points and give the distance from the model receiving the

ultrasonic pulse from the transmitter mounted on the bottom of the

model.

5. Test program

The wave length and height, course angle to the waves and model

speed are listed in Table 4. Since the speed of the model was hard to control to the desired constant value, the speeds at the runs in a con-stant wave condition were taken rather closely from zero to high speed. The model was controlled through the radio-control system and steered

to keep her course at the desired angle of course to the waves.

The followings were measured.

motions: pitch, heave, roll, yaw and relative bow motion (did

not work good and was given up on the way)

propulsive performance: thrust, torque and shaft revolution

helm angle

wave height and length at a stationary point

model speed and course angle to waves

Table 4. Test program wave length i/ship length L (2/L):

Wave height w (nominal) (actual) (nominal) 0.40, 0.60, 0.80, 0.38, 0.58, 0.76, L/50=8.0 cm 1.00, 0.98, 1.20, 1.20, 1.50, 1.50, 1.90 1.90

Course angle to wave

Model speed y Vm 1800, 135°, 90°, o to 1.60m/s 450 _0°

The signals of (a) to (e) were recorded with time mark on the

os-cillograph on board the model and (d) and (e) was recorded on the shore.

The model going in waves is shown in Photo. 2.

1-hoto. 2. Experiment of series 60 muccI going in aves

6. Test results

The pitching, rolling and yawing amplitudes are shown in

dimen-sionless form divided by the maximum wave slope, and the heaving

amplitude obtained from the acceleration assuming the sinusoidal motion are divided by the wave amplitude.

The tested data of the ship motions in each course angle to the

waves are expressed for each wave length as functions of the circular frequency of encounter, except the data in the beam seas which were plotted as a function of the model speed, as in Figs. 9 to 12.

The propulsive performance are obtained by the following way.

The mean thrust increase at a certain speed may be found by

sub-tracting the thrust in still water from the mean of the thrust

fluctuat-ing in waves at the same speed, and the amount of increase of the

mean thrust is shown in dimensionless form divided by pgC.B2/L. The

mean torque and revolution increase of the shaft are obtained by the

same way, and divided by pgÇ,DB2/L and gB2/(LD3V) respectively. In Figs. 13 through 15 the propulsive data in each course angle are

presented in dimensionless form for each wave length as functions of

the circular frequency of encounter.

The thrust, torque and revolution of the shaft in still water are

shown in Fig. 16.

7

shown in each course angle to the wave. The fluctuations of the shaft revolution are negligibly small.

Through these experimental points the mean lines were drawn, from which the values at the circular frequencies of encounter corre-sponding to desired speed were read and represented in each course angle as functions of the wave length for each Froude number, as are shown in Figs. 2 to 4.

In Figs. 5 to 8 the results for head seas are compared to those

obtained at the Osak University Tank31, the Meguro Basin4 and the

Delft Technological University Tank (Gerritsma)

The experimental results for the turning ability are shown in Figs. 19 and 20. Fig. 19 shows the dimensionless angular velocity on the rudder angle and the ratio of the turning speed to the approach speed,

the Foude number 0.20. Fig. 20 expresses the advance, transfer and

tactical diameter at the same Froude number. 7. Discussions and Conclusions

Genenrally, good agreement are shown in the comparison of the

test results in head seas and the results obtained in three other tanks,

as are shown in Fig. 5 to 8.

Experimental test result obtained in

NSMB7, and the result of computation by Fukuda8 are available,

however, as the course angles were different from our experiments,

the comparison was not tried here in this report. That will be done

in the next report together with the comparison with the computation

now proceeding in our Division.

For most of the cases, the results of each run, plotted on the circular frequency of encounter, for each wave length, scatter rather little than expected, and accordingly the mean line was rather easy to

be drawn. The repeatability was also enough, for this kind of tests.

Pitching and heaving motion for each wave length in head and

bow seas has peak naturally in the vicinity of the synchronous

fre-quency of encounter. However, through detailed investigation we find

that for the waves longer than the ship length, the peak appears in

smaller frequency of encounter, namely a little slower speed than the

speed for synchronous encounter, for pitching, and in larger frequency

of encounter, a little faster speed than the speed for synchronous en-counter for heaving.

The difference of the response for F,, =0 in head and following

seas and also in bow and quartering seas comes from the geometrical

asymmetry of the ship form to the midship section.

Not because the course is not accurately 90°, but because the ship has a certain lee-way angle to keep the course angle of 900 to the

waves, the pitching motion appears even in beam seas.

By the way, attention should be recalled here again that the angle of encounter is expressed by the angle of ship course to the direction of propagation of the waves and is not the angle of ship centre plane

to the waves.

In following and beam seas, the response of pitch and heave

shows another hump and hollow or inflection point, the reason of them being unknown. In heaving response, the coupling of rolling exists surely, and these hump or hollow correspond to the peak response of

rolling.

The heaving motion in beam seas with rather short waves that

has synchronous period is rather large.

The longest waves tested (2/L= 1.90) has almost the synchro-nous period to the rolling, and thus produces a severe rolling in beam

sea.

Its amplitude reduces by the increase of the advance speed of the

model, and endorse the increase of damping by the increase of advance speed°.

In quartering seas, to all wave length tested here, rolling syn-chronus frequency of encounter was covered with the range of speed

tested. Rather a large non-linearity in the response of rolling was

re-cognized clearly, as the wave slopes changed widely from 2° to loo.

Even in head and following seas, a kind of coupled rolling motion expressed by the Mathew's equation was observed when the frequency of encounter, namely the frequency of pitching was about twice of the natural frequency of rolling. This is however a different kind of response, and was not expressed in this set of figures.

Yawing motion shows a similer tendency with the rolling, and

has peak response around the synchronous frequency of encounter of

rolling.

The patterns of the thrust and torque increase in head and

bow seas agree pretty well with that of the variation of heaving and pitching motion, and the amount of increase is highest when the syn-chronous motion appears in the waves with the length almost same with the ship length.

The rate of change of the amount of increase by the increase of

the advance speed is very high.

In quartering and following seas, both of the torque and

thrust decrease than those in still water, and the amount of decrease

is larger for longer waves mostly. For this type of ship, both do not show minus increase in beam seas.

In head, bow, beam and quartering seas, the revolution of

9 looking these results, attention should be paid on the fact that these variations in torque, thrust as well as in the revolution depend _pretty much on the character of the driving engine of the propeller, which is different from that of the main engine of the actual ship.

The values of torque, thrust and revolution in still water that were used as the basis for these analysis are pretty much higher than those obtained in the other tanks. The reason is the existence of the additive resistance of the transmitter of the position indicator (27çx

77 rn/rn) on the bottom, and also of a round pipe (145x5OO rn/rn) _{at the} stem to pick up the relative bow motion. However, these do not effect

on the increase of these amount in the waves.

The fluctuations of thrust and torque

_{are very large in the}

head seas when the mean value of the thrust and torque increase re-markably. _{Especially in the head seas, in the waves with the length}

equal to the length of the ship, the fluctuations _{are extraordinary large}

because of the racing of the propeller that comes from the severe

pitching and heaving.

In earring out the tests, the hardest _{cases to manoeuver the}

ship on course were the runs in beam and quartering seas with rather

short waves. _{This was especially the case when the model advances in} low speed. _{This comes from the relatively large yaw moment and}

sway force from the short waves and rather small correcting moment

by the rudder at low speed. The yawing has peak response near the

frequency of encounter of synchronous rolling, however, the _manoeuver is not necessarily hard around this frequency.

Concluding the remarks as above mentioned, now the authors be-lieve that the experimental set up, using the free-running radio

control-ed model in open basin, is reliable enough to get the _{reasonable data} on seakeeping quality as we do in the ordinary type experimental tank

with towing carriage.

References

H. Shiba, "On the Mitaka Ship Experiment Basin,' Report of _{Transportation} Tech-nical Research Institute, No. 12, Vol. 11, Feb. 1962.

F. H. Todd, "Some Further Experiments on Single-Screw Merchant Ship Forms-Series Sixty," S.N.A.M.E., Vol. 61, 1953.

S. Nakamura, "Experiments in Regular Head Waves (Series 60, C1=O.70 Parent Form)," Presented on the Experimental Tank Committee of the Society of Naval Architects of Japan, July 1966.

A. Shintani, "The Results of the Ship Motions Tested and Calculated in Regular Waves of Series 60 (Black 0.60 and 0.70)," Presented on the Experimental Tank Com-mittee of the Society of Naval Architects of Japan, July 1966.

J. Gerritsma, "Ship motions in Longitudinal Waves," I.5.P., No. 66, Vol. 7, Feb. 1960.

and Pitching Motions of a Series 60, C8=O.70 Ship Model in Regular Longitudinal

Waves," Report of Technological Univerity Deift, No. 139, 1966.

G. Vossers, W. A. Swaan and H. Rijken, Experiments with Series 60 Models in Waves," S.N.A.M.E., Vol. 68, 1960.

J. Fukuda, Computer Program Results for Response Operators of Ship Motions and Vertical Wave Bending Moments in Regular Waves (on Merchant Ship of 0.60 and 070 Block Coefficient)," The Faculty of Engineering, Kyushu University,Feb. 1966 (Unpublished).

Y. Yamanouchi. On the Analysis of the Ship Oscillations among WavesPart 1

I. : length between perpendiculars breadth T : draft D : propeller diameter AR rudder area V, Vm model speed

p mass density of water

g acceleration due to gravity

A : wave length

AIL _{wave length-model length ratio}

wave amplitude

Zw : wave height

k maximum wave slope k : wave number, 2r/A

We : circular frequency of encounter,

2r/ T,

w4, _{natural circular frequency of roll,}

2r/T

w _{natural circular frequency of pitch,}

22r/T,)

w, natural circular frequency of

heave, 2'r/Tz

rolling amplitude

O, : pitching amplitude

Z, heaving amplitude yawing amplitude

magnification factor of roll, ra/k,

pj magnification factor of pitch,

a, magnification factor of heave,

Z/Z,

Nomenclature

11

magnification factor of yaw,

çb,/kZa

z : course angle to wave F, : Froude number, V/(gL)'/2

44, tuning factor for roll, we/w4,

tuning factor for pitch, we/wo A, : tuning factor for heave, weIw,

TAW mean thrust increase or decrease QAW : mean torque increase or decrease

flAw revolution increase or decrease TAP thrust fluctuations

Q'

torque fluctuations

Dr dimensionless thrust increase,

YAW! (gZw°B2)/L)

ICr : dimensionless torque increase,

QAW/ {(pgZw2DE')/L)

dimensionless revolution increase,

(nAwD3 V)/ (gZw'B')/L}

Df dimensionless thrust fluctuations,

TAPI ((pgZ,2B2)/L)

¡Cf _{dimensionless torque fluctuations,} QAFI [(pgZw'DB')/L

V, : approach speed

V : turning speed

r' dimensionless angular velocity,

L/R

R turning radius

A : advance

Tr transfer

i'D : tactical diameter

I.O « o 5 1-o « .0

V:

d o o PIT C H Fn = O 180° I 35° 90° 45° 0 / L / L H E A V

¡

/

7 7

-

ç.-

-z ROLL

-0 0.5 iO 1.5 2.0

WAVE LENGTH / MODEL LENGTH

Fig. 21. Amplitudes of pitch, heave and roll as a function of wave length for each course angle to waves, F=0

0.5 .0 .5 2.0

IO s 0.5 o O S IO O PITCH o _HEAVE I-o .5 Li..

i

I

°:

ROLL Fn

0.05

IO L z

WAVE LENGTH / MODEL LENGTH , . / L

Fig. 2-2. Amplitudes of pitch, heave and roll as a function of

wave length for each course angle to waves, F=O.O5

13

.5 2.0

1.0 N Fn

OiO

PIT CH

/

---0.5 0 1.5 2 H E A VE t /1

/7

-

. R OLL IO-5

/

O

-.

0 05 .0 .5 2.0

WAVE LENGTH / MODEL LNGTH , X / L

0.5 1,0 5 2D

Fig. 2-3. Amplitudes of pitch, heave and roll as a function of wave length for each course angle to waves, F=O.1O

NJ z ., 0.5 o u. z l'O N 0.5

Io 0.5 HEAVE o fANs F

.5

'1 ¡ u-z o 5 o

Fn = 015

PITCH 0.5 1.5 05 .0 15 20 X/L R OLL

- -.

.I.

-00 _{0,5 0} 1$

WAVE LENGTH / MODEL LENGTH

2.0

2,0 1/ L Fig. 2-4. Amplitudes of pitch, heave and roll as a function of

z o I-4 o IL z 0.5

t

o .5 4 '- ¡.0 N 0.5 o N' 5 4 00 H E AVE 0,5 0 0.5 R OLL ¡.0 k / L .7 I

'.

_.. ..

ji

.0 5 2,0 ?\/ L 0,5 .0 5 2.0

WAVE LENiGTI-4 / MODEL LENGTH, X/L

Fig. 2-5. Amplitudes of pitch, heave and roll as a function of wave length for each course angle to waves, F.=O.2O

o

.0 0.5 o N 2 Ñ H o

-

o û-z (D o

Fn = 0.25

ROLL

/

.\

Fig. 2-6. Amplitudes of pitch, heave and roll as a function of wave length for each course angle to waves, F7=O.25

17

o 0.5 1.0 1.5 2.0

NIL

0 05 1,0 5 2.0

WAVE LENGTH / MODEL LENGTH X/L

Fig. 3-1. Increase of mean thrust, torque and shaft revolution in waves as a function of wave length for each course angle to waves, F=O.O5 Fn

0.05

I 9O 450

-w

z

'-'J L,J > (J_) 3.0- 2.0-1.0 THRUST

-r r woIwz

)I

o

I TORQUE ¡ I

E

-I 0 ¿5 '.0

l5

20

NI L

Fig. 3-2. Increase of mean thrust, torque and shaft revolution in waves as a function of wave length for each course angle to waves, F=O.1O 19 Fn=

C=I80°

_{350_} 900 450

0°

-*

uj > w o Li w > 3.0--- 2.0-

LO-0

z.---THRUST H

-f = I

--

=

---

=

.->-

-- 0.5-T

O

-TORQUE

-

--

LOo

-PROPELLER REVOLUTION J I f

-O O5 l'O '5 2O

7/

L

Fig. 3-3. Increase of mean thrust, torque and shaft revolution in waves as a function of wave length for each course angle to waves, F=0.15

En = 0.

r

₈₀₀ 900_ 45 0°

-135° LU z LU o c o- 3.0- 2.0- LO-O I THRUST

_.._

= =

-

1H

>i-

--- 0.5-I I I TORQUE

-i

rt0

O

-PROPELLER REVOLUTION

-(.

O O'5 IO I5 2O

Fig. 3-4. Increase of mean thrust, torque and shaft revolution in waves as a function of wave length for each course angle to waves, F=O.2O 21 Fn

0.20

3.0- THRUST X 1800 I35° = 900 450 = 00 2.0-O.) e H Wz > 1.0-

-'

)<

--

:----

i__

w o o

__

J TORQUE 0.5- u-w Efl(1

-..

._-/

L

w o

/

/ .

----I' / >

/

(r) D 20 I I

- O-

l.0-o -

.

-PROPELLER REVOLUTION O 0!5 I0 l.5

7'/ L

Fig. 3-5. Increase of mean thrust, torque and shaft revolution in waves as a function of wave length for each course angle to waves, F=O.25 Fn

0.25

I THRUST =IB00 = 135° 3.0-

-- 2.0-TORQUE 0.5-

-Jr

..

...

o

-(f)

/

-J

7

-

1.0-o

_{PROPELLER REVOLUTION}

/

O 016 l0 .5 20

2'/ L

Fig. 4-1. Fluctuations of thrust and torque in waves as a func-tion of wave length for each course angle to waves, F=O.O5

23 Fn = 0.05

x,i8o_

30 THRUST = 450 = 00 2.0 ¡.0 >

o- -

-z o TORQUE I-D I- 0.2 (-) D -J 0.1

/

7'/ L

Fig. 4-2. Fluctuations of thrust and torque in waves as a func-tion of wave length for each course angle to waves, F=O.1O

Fn=OHO

-/

D C-) D -j 3.0- 2.0- LO-THRUST I 0.3- 0,2-001 TORQUE

-0 01.5 I0 '5 2\/ L

Fig. 4-3. _{Fluctuations of thrust and torque in waves as a} func-tion of wave length for each course angle to waves, F5=O.15

Fn = 0. 5 3.0- ¡ THRUST 2.0-

-

LO

-TORQUE o

0.3-o

0.2-0. --

-

--

-

---

.___ o

/

-f I O 0.5 1.0 .5 2.0 7\/ L

26

Fig. 4-4. Fluctuations of thrust and torque in waves as a func-tion of wave length for each course angle to waves, F=O.2O

fl 0.20

-o 0.3- 0.2- OH--O THRUST

0.3-Kf I TORQUE I I

-7/ L

Fn = 0.25 (J-) w > z (n

z

o H cf D H t-) D J 1i

if

3.0 2.0 1.0 o 03 0.2 01 6 THRUST TORQUE 0 0:5 '0 .5 2.0

?/ L

WAVE LENGTH / SHIP LENGTH

Fig. 4-5. Fluctuations of thrust and torque in wavesas a func-tion of wave length for each course angle towaves, F,=O.25

Fig. 5. Comparison with the results obtained at three othertanks for pitch-ing amplitudes in head sease, FA=0, 0.10 and 0.20

Fig. 6. Comparison with the results obtained at three other tanks for heav-ing amplitudes in head seas, F=0, 0.10 and 0.20

I

= 8O

I I

I i

Fn0.20

0.4 - _{:_..} EXPERIMENTS AT SHIP RESEARCH INST.

/ /

O A D .. OSAKA UNIVERSITY

0.2 - '.

/

_r

fI

MESURO MODEL

BASIN-GERRITSMA O I I J 0.5 0 1.5 2.0 N IL I I I I I J .2 - = V r Fn

I.0

/

---/

-D -I -

______10

:

D -. NI 2 r t

//

/ I

- _O .

-EXPEKIvENTS 5T SHIP RESEARCN INC'

O

¡f

0.2 - O A C

s

-OSAKA UNIVERSITY MESURO MODEL BASIN

o A r

I I I I I

0.5 LO .5 2.0

Fig. 7. Comparison with the results obtained at three other tanks for increase of mean thrust in head seas, F,=0.10 and 0.20

Fig. 8. Comparison with the results obtained at three other tanks for increase of mean torque in head seas, FA=O.lO and 0.20

29 I I I I 2.0 - = I ° _{EXPERIMENTS AT} -w (n , 1.5-

/ \

SHIP RESEARCH INST

OSAKA UNIVERSITY w o z S MEGURO MODEL 54515 IO-I-. (n

I

z 0.5-Ui O IO 0---- _o 8 I I I I 0.5 1.0 .5 2.0 NIL I I I EXPERIMENTS AT I

SHIP RESEARCH INST.

0.5 - - I 8 0 0 A _{OSAKA UNIVERSITY}

S _{MESURO MODEL BASIN}

LU z o

z

0.3-° . Fn0.20 o

-o _0I0 I I I 0.5 1.0 1,5 2.0

7\/L

\ \, \o 254- ., 0 202 X I 5 0 \ -f ). I900') p.-.₅ 1.4 IO 8 2.0 2.2

Fig. 9-1. Amplitudes of pitching for eacn wave length asa func. tion of circular frequency of encounter, for head seas

9 IO Il -2 21,1.0.3e '5 .559 =0.76 o 0,90 0 .1.20 :1.50 * .1.00

Fig. 9-2. Amplitudes of pitching for each wave length as a func. tion of circular frequency of encounter, for bow seas

1.0 06 s X 06 0.6 0 02 o X -90

Fig. 9-3. Amplitudes of pitching for each wave length as a func-tion of model speed, for beam seas

X45

02

2 3 5 6 7

a., (SEC)

04 06 0.8 1.0 I2 IO

Fig. 9-4. Amplitudes of pitching for each wave length as a func-tion of circular frequency of encounter, for quartering seas

3 s .4 0.8 0, 04 0.2 08 2 02

Fig. 9-5. Amplitudes of pitching for each wave length as a func-tion of circular frequency of encounter, for following seas

Fig. 10-1. Amplitudes of heaving for each wave length as a func. tion of circular frequency of encounter, for head sease

6 7 e

Ce (SEC)

lb

O

Fig. 10-2. Amplitudes of heaving for each wave length as a func-tion of circular frequency of encounter, for bow seas

I.8

I.e

Xo

.4

.20 .25

Fig. 10-3. Amplitudes of heaving for each wave length as a func-tion of model speed, for beam seas

33 .05 02 04 0,6 0.8 0 ve (m,$) FO 5

s

0,6

X 45

Fig. 10-4. Amplitudes of heaving for each wave length as a func. tion of circular frequency of encounter, for quartering seas

2 3 8 5 3

u, SEC)

06 IO 12

Fig. 10-5. Amplitudes of heaving for each wave length as a

X 9 o ', _T 4 5 5 7 (Je sEc-) iN. 6 20 Fig. 11-1.

Amplitudes of rolling for each

Fig. 11-2a.

Amplitudes of rolling for each

wave length as a function of circular

wave length as a function of circular

frequency of encounter, for bow seas

"4 43 0 X, 9o 0 02 04 06 00 .0 1.2 4 5J in/S F, 45 X4s 04 Fig. 11-2b.

Amplitudes of rolling for each

Fig. 11-3.

Amplitudes of rolling for each

wave length as a function of model

wave length as a function of circular

speed, for beam beam seas

Fig. 12-1. Amplitudes of yawing for each wave length as a func-tion of circular frequency of encounter, for bow seas

Fig. 12-2. Amplitudes of yawing for each wave length as a func-tion of circular frequency of encounter, for quartering seas

%= 1352 C) 1¼/L.0,36 V -0.56 O _'0.75 o 0.98 .20 '1.50 1.90 J b ie X I 80' G X.#L.O.S0 ï '0.58 V .0.76 0 .090 0 '1.20 '1.50 '190 -, ) 8 04 2 02 (0) (000) Io 37 I.e .2 0.9 I-0.4 ₆ Ii 4

Li!

0/

/. /

JI/

X

0.8 1 06 s ₀₄ 02 o a Fig. 13-1. Increase of mean thrust for each wave len3th as

2.0 1,2 08 0,4

,

0.8 -j 04 -00 X. 90 2.

j

-

Y

-- Y --' --

-

____ . -02 x-45' .2 06 0,8 1.0 0 I 2 4 5 8 V Im's I

Fig. 13-3. Increase of mean thrust for each wave length as a function of model speed, for beam seas

Fig. 13-4. Increase of mean thrust for each wave length as a function of circular frequency of encounter, for quartering seas

00 I 2 3 7 IO

(û8 (0G)

Fig. 13-2. Increase of mean thrust for each wave length as a function of circular frequency of encounter, for bow seas

o 03 -J 0 0.2 o. 0J o or W, ISEC)

Fig. 13-5. Increase of mean thrust for each wave length as a

function of circular frequency of encounter, for following seas

/

/

7O\

/

/

I.

/

0 6 7 8 a SOCI

Fig. 14-1. Increase of mean torque for each wave length as a fuction of circular frequency of encounter, for head seas

X 135

2 4 0 6 7

a.

Fig. 11-2. Increase of mean torque for each wave length as a

function of circular frequency of encounter, for bow seas

39 05 - X-iSo 0.4 Y .0.58 '0.75 'to _.004 O 03 o-02

/

/

40

Fig. 14-3. Increase of mean torque for each wave length as a function of model speed, for beam seas

0,4 02-'D Oo O C ..

.--/

-02 4 e (I)'. ISEC)

Fig. 14-4. Increase of mean torque for each wave length as a function of circular frequency of encounter, for quartering seas

0.4 0.3

-01

4 0

(D'. (0ECI

Fig. 14-5. Increase of mean torque for each wave length as a

function of circular frequency of encounter, for following seas

1.2 I I

0.0 03 IC

0.4

20

2 3 4 5 6 7 6 9 lO

Fig. 15-1. _{Increase of shaft revolution for each wave length as a} function of circular frequency of encounter, for head seas

X 35

2 3

(SEC)

Fig. 15-2. Increase of shaft revolution for each wave length as a

function of circular frequency of encounter, for bow seas

24 2 -J 1.6-> 0 .2-C 08 0. X 8O - î-III

/'Í

A

/

/

-V

Y

/

O Y A X/L0,58 0.08 0.98 .20 1.60

42 .2 -J 0.8 0.4 o o -0.4 0.8 _{4 5} 6 W SC)

Fig. 15-4. Increase of shaft revolution for each wave length as a function of circular frequency of encounter, for quartering seas

LJ ISEC)

Fig. 15-3. Increase of shaft revolution for each wave length as a function of model speed, for beam seas

X 45'

W, Sr1

Fig. 15-5. Increase of shaft revolution for each wave length as a function of circular freguency of encounter, for following seas

u

.0

o

0.05

IN STILL WATER {WTIO'Ç)

02 IO 2 4 IM

MODEL SPEED

010 015 020 025 Fn

Fig. 16 _{Thrust, torque and revolution of the shaft in still water}

3 4 7 8 We s00I 20/L.058 Y 058 .098 o =J 20 ¿S

Fig. 17-1. _{Fluctuations of thrust for each wave length as a}

func-tion of circular frequency of encounter, for head seas

't35

r i s

5 6 7

(Lie 5E0)

IO

Fig. 17-2. Fluctuations of thrust far each wave length as a func-tion of circular frequency of encounter, for bow seas

1.5

Fig. 17-3. Fluctuations of thrust for each wave length as a func-tion of model speed, for beam seas

X 45

i L

O 4 5

We (

Fig. 17-4. Fluctuations of thrust for each wave length as a

.30 .25 a 0. a .05 LS OS 0 5 6 7 (Lie SE C

Fig. 17-5. Fluctuations of thrust for each wave length as a func.

tion of circular frequency of encounter, for following seas

- XSçj,

I I

6 B

(Lie SEO

Fig. 18-1. Fluctuations of torque for each wave length as a func.

tion of circular frequency of encounter, for head seas X I35

(

_/

/

(18 OEC)

Fig. 18-2. Fluctuations of torque for each wave length as a func-tion of circular frequency of encounter, for bow seas

a Q. 'N o -J 'tE a

'to

'N o .15 .10 05 S

Fig. 183. Fluctuations of torque for each wave length as a func. tion of model speed, for beam seas

05 X 90' -

-

.----Vo ,s.'si X o' IS

Fig. 18-4. Fluctuations of torque for each wave length as a func-tion of circular frequency of encounter, for quartering seas

4 5 6 7

(35 SE 0)

A A

(Je i SEC)

Fig. 18-5. Fluctuations of torque for each wave length as a func-tion of circular frequency of encounter, for following seas

IT o6 _os X 45' .15 -J a S-'N o

47

Fig. 19. Dimensionless

angu-lar velocity and speed re-duction ratio of turning

Fig. 20. Advance, transfer

and tactical diameter

= 0.70 Lpp 4.00 m 0.8 AR/LXT 1/61.83 Full load -02 Sm PORT -40 -30 -20 - IO

-j'

/

(02

IO 20 0.4 _{OIMENSIONLESS} VELOCITY 30 40 STARB. ANGULAR REDUCTION

P

::

SPEED C =0.70 Lpp =400m AR/LXT= 1/61.83 a Full load Sm PORT -40 -30 -20 -IO hh_

I

ir

IO 20 4 -c----Sm 30 40 STARB ADVANCE TRANSFER TACTICAL OIAMETER -'---IO

--(-L