Motions, resistance and propulsion of a ship in longitudinal regular waves

TECHNISCHE HOGESCHOOL DELFT

AFDELING DER SCHEEPSBOUW- EN SCHEEPVAARTKUNDE LABORATORIUM VOOR SCHEEPSHYDROMECHANCA

Rapport No. 428

ir. J. M. J. Journée

MOTIONS, RESISTANCE AND PROPULSION

OF A SHIP IN LONGITUDINAL REGULAR WAVES

Deift University of Technology Ship Hydromechanics Laboratory Mekeiweg 2

Deift 2208

s

MOTIONS, RESISTANCE AND PROPULSION OF

A SHIP IN LONGITUDINAL REGULAR WAVES

by ir. J.M.J. Journée,

Ship Hydrornechanics Laboratory,

Deift University of Technology,

The Netherlands.

s uminary

Extensive tests have been carried out to measure motions,

resistance and propulsion in longitudinal regular waves of a model

of a fast cargo ship. The tests have been carried out for full

load condition as well as for light load condition and the

results of these experiments are compared with those of a

theore-tical approach. The first results of this research program have

been published by Gerritsma and Beukelman [ 1] in 1972. For the

Contents

2 Specification of model and experiments i

3 Analysis and presentation of the test results 2

3.1 Heave and pitch motions 2

3.2 Absolute and relative motions forward 3

31,3 Added resistance in regular waves 4

3.4 Propulsion in still water and regular waves 5

4 Conclusions 5 5 Acknowledgements 5 6 References 6 Tables 7 Figures page i Introduction i

1. Introduction

In [ 1J Gerritsma and Beukelman have introduced a new method to

calculate the added resistance of a ship in longitudinal waves. They have assumed that added resistance varies linearly as the squared wave height at a constant wave length and a constant for-ward speed. In their report the added resistance has been

calculated by determining the radiated energy of the damping waves. In neglecting the surge motion heave and pitch motions have been calculated by using the strip theory. Added mass and damping for the ship cross sections have been calculated by using

a close fit procedure to describe accurately the form of the cross sections. To support their theory experiments have been carried out with a towed model of a fast cargo ship in full load condition. In regular longitudinal waves with a varying wave amplitude the frequency characteristics of heave and pitch motions and the

average added resistance due to waves have been measured for dif-ferent speeds. They have shown a satisfactory agreement between

calculated and measured values.

IIn continuation of these tests a measuring program has been set up with the aim of gaining more insight into motion, resistance and propulsion properties in waves of this ship in full load condition as well as in light load condition. Not only heave and pitch motions are observed now, but also the relative motions of the fore-part of the model to the watersurface in order to

determine the dynamical rise of the watersurface near the bow. The measured heave and pitch characteristics and the average added resistance are compared with results of calculations like

those used in { 11 . These calculations have been made with a

computerprogram named TRIAL, of which an earlier version has been

described in E 21 . Added mass and damping for the ship cross

sections have now been calculated by using a Lewis conformal

transformation.

Extensive propulsion tests have been carried out in still water as well as in regular waves with a self-propelled free-running model. These tests are similar to the tests carried out by

Gerritsma, van den Bosch and Beukelman with a model of a combined

passenger and cargo ship [ 3 . They have shown that the mean

in-.

creases of thrust, torgue and revolutions of the propeller, just like added resistance, for a constant speed and wave length vary

as the squared wave amplitude.

2. Specifications of model and experiments

The experiments have been carried out with a model (1:50) of the cargoship m.s. "S.A. van der Stel" of which two loading con-ditions have been considered: full load condition and light load condition. The main particulars of the model in both loading conditions are given in table I and figure 2 shows the bodyplan

of this model.

Four speèds are considered, Fn = 0.15, 0.20, 0.25 and 0.30, while the service speed of the ship corresponds with Fn = 0.26.

The model and wave conditions are shown in table II and table III. Figure 3 shows a schematic diagram of the measuring system. The regular waves have been measured by means of a two-wire con-ductive wave probe at a distance of about 3.50 meter in front of

4kie centre of gravity of the model. Heave and pitch motions have

been measured by two low-friction potentiometers above and at the centre of gravity. Wave amplitude and heave and pitch

character-istics have been obtained by a phase locked loop servo system E 41

At station 20 in full load condition and station 18 in light load condition the vertical absolute and relative motions have been measured too. The absolute motion has been measured by a

low-friction potentiometer and the relative motion by a conductive wave probe consisting of two NACA-profiles fixed on both sides of the model. Both motions have been recorded by an ultra-violet recorder. In full load condition the mean resistance in still water as well as in regular waves has been measured by means of a towing force caused by knowr dead weights. In light load

con-dition this towing force has been generated by a targue motor (see figure 2) and measured by means of a strain gauge dynamometer of which the output has been integrated over a certain time or a

full number of wave periods.

Propulsion tests have been carried out in still water and regular waves, while overload tests in still water have been carried out too. In the propulsion tests the number of revolutions of the

.

propeller has been kept constant by electronical control and therefore the r.p.m. are not affected by cyclic load variations due to wave action. Thrust and torgue have been measured by means of strain gauge dynamometers of which a mean value can be found by integrating the output of the dynamometers. In the overload tests in still water the propeller loading can increase by a

towing force backwards on the model caused by dead weights.

The r.p.m. of the propeller and the modelspeed have been measured with the aid of phototransistors and electronic counters.

3. Analysis arid presentation of the test results

The discussion of the test results has been divided into parts: vertical motions and resistance in regular waves and propulsion in still water and regular waves. The vertical motions are di-vided into heave and pitch motions and relative motions forwards. The theoretical foundations of these phenomena'have been

pre-sented in [ 1] and E 3 II and are not discussed again.

3.1. Heave and pitch motions

For a range of wave length - ship length ratios, as summarized in table III, the measured heave and pitch amplitudes in relation to

the wave amplitudes are given in figures 4, 5, 8 and 9 for both

loading conditions and four Froude numbers. The experiments show the good linearity of the motions, even in cases of extreme ship-ping of water on the fore-deck and emerging of the fore-foot from the water. No significant differences appear in the measured

motion. amplitudes between the selfpropelled model and the towed

model without freedom to surge in the full load condition and with freedom to surge in the ballast condition.

In the same way the measured phase lag between heave and pitch motions and wave motions are presented in figures 6, 7, 10 and 11.

The experiments show that the phase lag is not depending on the wave amplitude. No difference has been measured between a

self-propelled and a towed model.

In figures 12, 13 and 14 the mean non-dimensional heave and pitch amplitudes obtained by least squares method and the mean phase

differences are compared with theoretical values calculated by the program TRIAL mentioned before. The predicted resonance values of

the heave amplitude in figure 12 are too high. For shiplength -wave length ratios above 1.0 there is a fair agreement between

calculation and experiment. Good agreement is shown in figures 13 and 14 for the pitch amplitude as well as for the phase lag of both motions with respect to the wave motion at G.

3.2. Absolute and relative motions forward

At station 20 in full load condition and station 18 in ballast condition, the sinkage of the model due to the speed has been measured in still water. This is shown in figures 16 and 17 and

will be discussed later on.

The bow waves generated by the model running in still water and sinkage of the model cause a statical swell-up, which decreases the geometrical freeboard to an effective freeboard. Figure 15 shows the relative displacements at the stations mentioned before, obtained in two ways. The wave pattern against the hull has been

.

measured from these pictures. On the other hand the relative dis-obtained photografically and the statical swell-up has been

placement has been measured electronically by a conductive wave

probe on a little distance from the hull.

Tasaki gives in j 5,6 1 an empirical formula to e3timate the

statical swell-up at the bow:

T

Lf = 0.753 . -e-- F

2

Le n

in which:

L = Length of the waterline

B = Breadth

Le Entrance length on the waterplane

F = Froude number

For the statical swell-up measured at the top of the bow wave

between station 19 and 20 there is a good agreement between

Tasaki's formula and the measurements.

In order to examine wheather absolute and relative motions in

.

water value the maximum and minimum values of these motions inregular waves are symmetric or asymetric with respect to the still regular waves are measured too. Figure 16 and 17 show these

measurements plotted on a base of wave amplitudes.

The amplitudes of these motions are also calculated from the

measured heave, pitch and wave motions:

V

=z-x .9

xb b

Sxb _Xb xb . 0

in which V is the absolute motion and s is the relative motion.

For the other symbols: see figure 1.

In figures 18 and 19 the derivatives of the measured extreme values in figures 16 and 17 to the wave amplitude, obtained by

the least squares method, are plotted against these calculated non-dimensional amplitudes of the motions. For the absolute motions the plotted values are situated on a 45-degrees line. These motions are symmetric with respect to the still water vàlue

because the mean values are zero. The measuring systems for _heave and pitch motions and absolute motions are independent, so the

figures also underline the reliability of the measuring system.

Figure 20 shows the fair agreement between the calculated and measured amplitudes of the absolute motions. For the relative motions the plotted values in figures 18 and 19 are not situated

on a 45-degrees line. The amplitude of the measured relative

motion is increased by a dynamical swell-up. When the bow immerges the watersurface will rise and when the bow emerges the

watersur-face will fall.

In figure 21 the measured dynamical swell-up is shown in percen-tages of the relative motion calculated from the heave, pitch and

wave motion.

Tasaki [5,6 J carried out forced oscillation tests with a towed

ship model in still water to measure the relative displacement of the watersurface to the bow of the model. From the results of

these experiments he obtained an empirical formula to estimate the

dynamical swell-up at the bow:

LSa Cb - 0.45

\f'

.

--

3 g e

with the restriction for the blockcoefficient:

0.60 < Cb < 0.80

This formula shows a linear relation between dynamical swell-up and the frequency of encounter, which is not proved by these

experiments. The estimated dynamical swell-up can not be

com-pared with the experimeits, because the blockcoefficient of the

model is 0.564.

As shown in figure 21 there is a remarkable difference in dyna-mical swell-up at station 20 and at station 18. This is shown too

in [7 1 for two models of compact frigates.

More investigations will be necessary to estimate a good value for

the dynamical swell-up.

3.3. Added resistance in regular waves

The added resistance in regular waves is determined by sub-tracting the still water resistance from the measured total

re-sistance at the speed concerned.

In [ i J the assumption is discussed that added resistance varies

as the squared wave amplitude. Figures 22 and 23 show the added resistance as a function of the squared wave amplitude. Except in cases of extreme unrealistic motions at resonance conditions in high regular waves a very good linearity is shown here.

Figure 22 shows too that the influence of surge on added

resistance in head waves is negligible. In figure 24 the non-dimensional values of the measured added resistance are compared with calculations, carried out in a way as has been done by

Gerritsma and Beukelman [

i

I

In full load condition there is a very good agreement except in short waves at higher speeds where the diffraction resistance is underestimated. In ballast condition the calculated peak values

are somewhat larger than the measurements.

3.4. Propulsion in still water and re9ular waves

Propulsion tests and overload tests have been carried out in still water with the self-propelled model. The measured r.p.m., thrust

and torgue are shown in figures 25, 26 and 27 on a base of the sum of still wat.r resistance at the speed concerned and overload

force.

Propulsion tests with a free-running model have also been carried out in regular waves at different wave lengths and wave heights. During these tests the r.p.m. have been kept constant by electro-nical control. The measured thrust and torgue of the propeller

are mean values over a large number of wave periods. As shown in figures 25, 26 and 27 there are no significant differences between these measurements and overload tests in still water even in cases

of extreme emerging of the propeller. This means that the pro-pulsive efficiency is the same in both cases. In the near future a separate report on this subject will be published.

As shown before, added resistance varies as the squared wave amplitude. The figures show the linearity between added r.p.m., thrust and torgue and added resistance. So the added r.p.m., added thrust and added torgue vary also as the squared wave amplitude.

4. Conclusions

From the analysis of the experiments and calculations the

follow-ing conclusions may be drawn:

I.. The influence of surge and propulsion on the vertical motions

and added resistance in regular waves may be neglected.

2. At a constant wave length and a constant forward speed it is

shown that:

heave and pitch motions and absolute and relative motions forward vary linearly as the wave amplitude, even in

extreme wave conditions.

phase differences between heave and pitch motions and wave motions are constant for varying wave amplitudes.

C. added resistance varies quadratically with the wave

ampli-tude.

d. added r.p.m., thrust and torgue varies quadratically with

the wave amplitude.

3. The calculated heave and pitch characteristics and added resistance are in good agreement with the measurements, al-though the calculated heave amplitude in the range of

resonance and the peak values of the added resistance in the

ballast condition are somewhat too high.

4. For calculating shipping water and slamming phenomena more attention must be paid to the statical and dynamical swell-up. 5. The propulsive efficiency is not influenced by the wave motion

but only by a decreasing propeller loading.

5 . Acknowledgements

The author wishes to thank prof.ir. J. Gerritsma and Mr. W. Beukelman for the attentìon paid to the following-up of their experiments. The assistance of Mr. R. Onnink and Mr. A.J. van Strien of the Deift Ship Hydromechanics Laboratory and the guests

Mr. R. Kishev and Mr. A. Kovachev of the Bulgarian Ship

Hydro-dynamics Experimental Centre during the experiments is very much

appreciated.

Last but not least the preparation of all the graphs by Mr. P. de

Heer is gratefully acknowledged.

6. References

[ i I J. Gerritsrna and W. Beukelman,

Analysis of the resistance increase in waves of a fast cargo

ship,

Netherlands Ship Research Centre, Report no. 1695, April 1972.

L 2 1 W. Béukelman and E.F. Bijlsma,

Description of a program to calculate the behaviour of a ship

in a sea-way (named TRIAL),

Report no. 83, Deift Ship Hydromechand.cs Laboratory. [ 3 1 J. Gerritsma, J.J. van den Bosch and W. Beukelman,

Propulsion in regular and irregular waves.

International Shipbuilding Progress, Volume 8, no. 82,

June 1961.

[ 4 ] M. Buitenhek and J. Ooms,

A phase locked loop servo system,

Delft Ship Hydromechanics Laboratory. [5 1 R. Taaki,

On shipment of water in head waves, 10th I.T.T.C., London, 1963.

{ 6 II 60th Anntversary Series of the Society of Naval Architects

of Japan, Volume 8, 1963, page 154. [7 ] M.F. van Sluys and Tan Seng Gie,

Behaviour and performance of compact frigates in head seas,

International Shipbuilding Progress, Volume 19, no. 210,

February 1972.

o

Note:

F means: tests are carried out for full load condition. L means: tests are carried out for light load condition. The propulsion tests are carried out with a self propelled

model.

Table I Main particulars of the model

Note:

The scale of the model is 1:50.

Table II Modelconditions 7 full load condition ballast condition Lpp m 3.050 3.050 B m 0.456 0.456 T at even keel m 0.183 0.104 V m3 0.1434 0.0725 cb 0.564 0.503 Lcb/Lpp % -1.10 +0.39 kyy/Lpp % 21.88 26.04 towed model without surge freedom towed model with surge freedom self propelled model motions added resistance F

_[1]

F [ i J F L L F L

8

Table III Wave conditions

Note:

* means: tests are carried out for four Froude numbers: 0.15, 0.20, 0.25 and 0.30. For Fn = 0.15

only wave height w/L = 1/50 has been considered.

l/5Q _1/40

l3Q

z0 A

z zb

X

.-v

ship speed

C wave celerity

wave - = _{aCO5U<Xoc05P - wt) in} X0 y0 Z0

aCO5et)

in xyz ,x=O

heave - _{z = Za C0s(Wet +EZ)}

pitch - e=eacos(wet+Ee)

WeW --VcosI.L

)

I4

i o i 7 20 ießj19 2 16 15 11. 6 13 7 12 8 11 9 10 //////,W t orq u e motor

FIG 2 ARRANGEMENT FOR BODY PLAN AND RESISTANCE TESTS.

10

I

s

ABSOLUTE MOTION. RELATIVE MOTION. PITCH. HEAVE. WAVE. TORQUE. THRUST. SQ REF EREICE. 00- wi.t:

--REFERENCE. O SI.> RESISTANCE .

<)S.I.>

DEMO DEM P.M. L , RES.

q

I RES. RES. SENSORS

Spp: PIEZOELECTRIC PRESSURE TRANSDUCER. Sps: SEMICONDUCTOR PRESSURE TRANSDUCER. Sv : POTENTIOMETER DISPLACEMENT TRANSDUCER.

SS : CONDUCTANCE WAVE HEIGHT TRANSDUCER.

S : TORQUE ST : THRUST 5R : RESISTANCE DYNAMOMETER. REE 1000 Hz DEMO DEM.O P.L.L. PULSER - - - PROPULSION GEARBOX

I:::'-KI:I:-. STRAIN FORCE

TM. (J

FIG.3 SCHEME OF MEASURING SYSTEM

SCOOP

PULSER

COUNTER

s:

i!E

WI. : WAVE INDICATOR.

DEM. : DEMODULATOR.

S.l. : STRÔJNGAGE INDICATOR. REE : REFERENCE SOURCE.

RES. : RESOLVER.

PL.L. : PHASE LOCKED LOOP SYSTEM.

TM. : TORQUE MOTOR. SM. STEPPER MOTOR PM. PROPULSION MOTOR. I : INTEGRATOR A : AMPUFLIER. D.V.M. : DIGITAL VOLTMETER. w L) w z FRt'JTER D VM. COUNTE DEM.O DEM.O I ,' RES. WI.> O

'T

_(cm)

0

(cm)

u EXPERIMENTS WITH TOWED MODEL WITHOUT SURGE MOTION

. EXPERIMENTS WITH SELF PROPELLED MODEL

---=O.6 L L L L L

--=1.6

L L

FIG./. RELATION BETWEEN HEAVE AND WAVE AMPLITUDE (FULL _{LOAD CONDITION)}

5 o 5 J

-:/t/

I

:////

I

FULL LOAD CONDITION

BALLAST CONDITION =.15 Fn=.20 Fn=.25 = .30 5 :_ = 0.6 L L :_ = i .0 L L L =1.6 L -=1.95 L

FIG.5 RELATION BETWEEN HEAVE AND WAVE AMPLITUDE (BALLAST CONDITION)

o 5 5 5

(cm)

..-Ò

EXPERIMENTS WITH TOWED MODEL WITH SURGE MOTION

. EXPERIMENTS WITH SELF PROPELLED MODEL.

Za

Ez (degr) -180 -180 -180 -180 -180 o

.

FULL LOAD CONDITION

=15 Fn=.20 Fn=.25 =.30

-4-4-

À

0.8 L -180

I.

= 0.6 L -180 L L -. =1.46 L L -=1.95 L o 5 M 5 0 5 0 5 (cm)

. EXPERIMENTS WITH TOWED MODEL WITHOUT SURGE MOTION

. EXPERIMENTS WITH SELF PROPELLED MODEL

FIG.6 RELATION BETWEEN PHASE LAG OF HEAVE AND WAVE AND WAVE

180

180

180

180

180

180

180

o 5 0 5 0 5

(cm)

_L

u EXPERIMENTS WITH TOWED MODEL WITH SURGE MOTION . EXPERIMENTS WITH SELF PROPELLED MODEL

BALLAST CONDITION

=.15 Fn=.20 Fn=.25 = .30

u (degr)

5

FIG.7 RELATION BETWEEN PHASE LAG OF HEAVE AND WAVE AND WAVE

AMPLITUDE ( BALLAST CONDITION)

=0.6 L

k

0.8 L L L -. =1.4 L L L

(degr)

FULL LOAD CONDITION

Fn = .15 Fn=.20 Fn=.25 =.30

(cm)

L

. EXPERIMENTS WITH TOWED MODEL WITHOUT SURGE MOTION . EXPERIMENTS WITH SELF PROPELLED MODEL

L L L L

À

1.6 L -=1.95 L

FIG.8 RELATION BETWEEN PITCH AND WAVE AMPLITUDE (FULL LOAD CONDITION)

5

(cm)

L

u EXPERIMENTS WITH TOWED MODEL WITH SURGE MOTION . EXPERIMENTS WITH SELF PROPELLED MODEL.

k.

0.6 L - = 0.8 L L L L -=1.95 L

FIG.9 RELATION BETWEEN PITCH AND WAVE AMPLITUDE (BALLAST CONDITION)

:!!

_iii.!!

O

ru

I

5

4

'

i

r4

BALLAST CONDITION Fn = .15 Fn=.20 Fn=.25 Fn = .30

of

(degr)

FULL LOAD CONDITION Fn=.15 Fn=.20 Fn=.25 Fn=.30

90

270

90

90

I

9°

(degr)

270

90

270

90

270

90

270

.

R..

a.

270

't

o 5 0 5 0 5 0 S (cm) ...

. EXPERIMENTS WITH TOWED MODEL WITHOUT SURGE MOTION

. EXPERIMENTS WITH SELF PROPELLED MODEL

FIG.10 RELATION BETWEEN PHASE LAG OF PITCH AND WAVE AND WAVE

AMPLITUDE ( FULL LOAD CONDITION)

I"

270

Rs

L -f-=1.6 L

(degr)

2

2

2

2

2

2

(cm)

u EXPERIMENTS WITH TOWED MODEL WITH SURGE MOTION . EXPERIMENTS WITH SELF PROPELLED MODEL

FIG.11 _{RELATION BETWEEN PHASE LAG OF PITCH AND WAVE AND WAVE}

AMPLITUDE ( BALLAST CONDITION)

L 0.8 L L L - _1j. L L L

-..

_% 70

w...

_q 70

I

I

.

w--

w 70

%.

_.

-4

i%a

)0 70

..

a.

.

)0 70 i R. 70 )0 _-

..

I

e

'0 5 M 0 5 0 BALLAST CONDITION Fn = .15 Fn=.20 Fn=.25 Fn=.30

Za _Za i .5 1.0 0.5 O 1.5 1.0 _0.5 o o

' 05

1.0 1.510 ' 0.5

.

MEAN EXPERIMENTAL VALUE CALCULATED

FIG.12

MEASURED AND CALCULATED HEAVE AMPLITUDE CHARACTERISTICS

IN REGULAR WAVES.

Fn=.15

Fn=.20

LA

FULL LOAD CONDITION

Fn=.25

.

.

,,,,/..

Fn=.30

1I

.'

.

.

H

.

£

A.

-4--4 Fn=.15 tl_ Fn=.20 BALLAST

1-f-

CONDITION I

.

.

Fn=.25

..

s

.

!

. . .

.

j__ 1.0 1.510 ' 0.5 1.0 1.510 ' 0.5 i .0 1.5 V

ea

_k a Ga

_ka

a

i .5 1.0 _0.5 o 1.5 1.0 _0.5 o o

'

0.5 1.0 1.510 ' 0.5

I

MEAN EXPERIMENTAL VALUE CALCULATED

V L/'

FIG.13

MEASURED AND CALCULATED PITCH AMPLITUDE CHARACTERISTICS IN REGULAR WAVES.

Fn=.15

.

.

;I

Fn=.20 FULL LOAD CONDITION

Fn=.25

.

.

.

1

Fn=.30

'I'

\

.

.

Fn=.15 1l Fn=.20

i

BALLAST CONDITION

...

Fn=.25

,,,//'

_I

-I

-1.0 1.510 ' 0.5 1.0 1.510 ' 0.5 1.0 i .5

o

Ce.

180° _360° (degr) o 180°

_360°

(degr)

vi7

J

Fn=.15 -- -.-...a%%U í_*___.. \Uß Fn=.20

'%

Fn=.25

--Fn=.30 u -U-u. 'u

'\u

u

j

Fn=.15

p--.

Fn=.20

_{-- -u-U-.}

',

u

N

%,_1 I

-

_f

-Fn=.25 -U

!

'

\uI

...,,

'

Fn=.30 .

',

\

\I

r

I

r--- -.-UU-.S

I.

\I

, '%_I

lu

s

J

.j

o 0.5 1.0 1.510 0.5 1.0 1.510 0.5 1.0 1.510 0.5 1.0 1.5 o 0.5 1.0 1.510 0.5 1.0 1.5100.5 1.0 1.510 0.5 1.0 1.5 Ezç

.

u

MEAN EXPERIMENTAL VALUE

--- CALCULATION

FIG.11.

MEASURED AND CALCULATED PHASE CHARACTERISTICS FOR PITCH AND HEAVE IN REGULAR

WAVES.

I

s 5.0

,

j2.5

FULL LOAD CONDITION BALLAST CONDITION

20

;

(cm) o

T

FULL LOAD CONDITION

0.1 0.2 0.3

. RELATIVE WAVE HEIGHT METER. u PHOTOGRAPHIC

FIG.15 RELATIVE DISPLACEMENT OF THE MODEL FOR DIFFERENT

FROUDE NUMBERS. Fn = 0.332 0.281 0.237 0.189 O.142 0.91+ 2.5 (cm) o 16 17 18 19 20 16 17 18 19 20 F.PP FF1?

STATION NUMBER STATION NUMBER

BALLAST CONDITION 5.0 STATION 18 , _{s wi} o o.i 0.2 0.3 Fn =

I,

0.350 0.300 0.250 0.200 0.150 0.100

- Fn

Fn I I I p o 1 2 o 1 2 (m/s) - speed (m/s) speed

(cm)

2

2

2 o

2

. EXPERIMENTS WITH SELF PROPELLED

MODEL.

(cm)

j

FIG.16a RELATION BETWEEN EXTREME VALUES OF

ABSOLUTE

AND RELATIVE MOTIONS AND WAVE AMPLITUDE.

(FULL LOAD CONDITION, STATION 20, Fn=.15)

-FULL LOAD CONDITION

L

:

05:55O5O5

= 0.6 0.8 i .0 i .2 i .6 i .95 o

v,

(cm)

9

2

2

2

2

. EXPERIMENTS WITH SELF PROPELLED MODEL.

(cm)

FIG.16-b RELATION BETWEEN EXTREME VALUES OF ABSOLUTE AND

RELATIVE MOTIONS AND WAVE AMPLITUDE.

(FULL LOAD CONDITION,STATION 20,Fn=.20)

S -FULL I LOAD CONDITION

.

- = 0.6 o .8 i .0 1.2 i .4 1.6 1.95 o v (cm) o

s1

(cm)

2

2

. EXPERIMENTS WITH SELF PROPELLED MODEL.

FIG.16-c RELATION BETWEEN EXTREME VALUES OF ABSOLUTE AND _{RELATIVE MOTIONS AND WAVE AMPLITUDE.}

(FULL LOAD CONDITION, STATION 20, Fn= .25)

- FULL LOAD CONDITION

.

s

I

-- =

0.6 0.8 i .0 i .2 i .4 i .6 i .95

T

o (cm)

2

2 s o (cm)

V_m

(cm

25

-- =

0.6 0.8 i .0

. EXPERIMENTS WITH SELF PROPELLED MODEL.

FIG.16-d RELATION BETWEEN EXTREME VALUES OF ABSOLUTE AND RELATIVE MOTIONS AND WAVE AMPLITUDE.

(FULL LOAD CONDITION,STATION 20,Fn=.30)

1.2

FULL LOAD CONDITION

1.6 O 1.95 5 5 0 5 5 0 5 (cm) 5 5

25

25

25

25

BALLAST CONDITION o 5 0 5 0 5 0 5 0 (cm) ..

u EXPERIMENTS WITH TOWED MODEL WITH SURGE MOTION.

. EXPERIMENTS WITH SELF PROPELLED MODEL.

5 o 5

FIG.17-a RELATION BETWEEN EXTREME VALUES OF ABSOLUTE AND RELATIVE MOTIONS AND WAVE AMPLITUDE.

C BALLAST CONDITION, STATION 18,Fn=.15 )

:_

= 0.6 _{0.8 i .0 1.2} 1 44 _{1.6 i .95}

T

o (cm) o 5 o (cm)

(cm

(cm

BALLAST CONDITION

'FIG.17-b RELATION BETWEEN EXTREME VALUES OF ABSOLUTE AND RELATIVE MOTIONS AND WAVE AMPLITUDE. (BALLAST CONDITION, STATION 18,Fn=.20)

i .6 i .4 i .2 i .0 0.8 = 0.6

I

i .95 5 5 5 5 5 0 5 (cm)

u EXPERIMENTS WITH TOWED MODEL WiTH SURGE MOTION.

i

(cm) (cm 25

0-.---25 25 -25

. EXPERIMENTS WITH TOWED MODEL WITH SURGE . EXPERIMENTS WITH SELF PROPELLED MODEL

FIG.17-c RELATION BETWEEN EXTREME VALUES OF ABSOLUTE

( BALLAST CONDITION, STATION 18, Fn = .25)

BALLAST CONDITION 5 _ß 5 (cm) MOTION AND RELATIVE 5

MOTIONS AND WAVE AMPLITUDE.

e

_Ó

_O

4-

= 0.6 0.8 1.0 1.2 1.4 1.6 1.95

V_m (cm (cm 25

25

25 - 25 BALLAST CONDITION 5 5 0 5 0 5 5 5 5 (cm)

. EXPERIMENTS WITH TOWED MODEL WITH SURGE MOTION

I EXPERIMENTS WITH SELF PROPELLED MODEL

FIG.17-d RELATION BETWEEN EXTREME VALUES OF ABSOLUTE AND _{RELATIVE MOTIONS AND WAVE AMPLITUDE}

( BALLAST CONDITION, STATION 1 8, Fn = .30)

O

I

1.95

4 V_m 2 o

2

4

4 o

2

FULL LOAD CONDITION

-. MEAN EXPERIMENTAL VALUE-.

FIG.18 RELATION BETWEEN MEASURED EXTREME VALUES OF ABSOLUTE

AND RELATIVE MOTION AND THE MOTION AMPLITUDE CALCULATED FROM HEAVE,PITCH AND WAVE.

( FULL LOAD CONDITION, STATION 20)

Fn =.2 5

2

/

Vm

s

-4 2 o BALLAST CONDITION Sa

-.

MEAN EXPERIMENTAL VALUE.

FÌG.19 RELATION BETWEEN MEASURED EXTREME VALUES OF ABSOLUTE

AND RELATIVE MOTION AND THE MOTION AMPLITUDE CALCULATED FROM HEAVE,PITCH AND WAVE.

(BALLAST CONDITION,STATION 18) Fn=.15 Fn=.20 Fn=.25 Fn=.30

/

_Ï

2 L Sm

s

Va Va 3 2 i o 3 2

i

o

MEAN EXPERiMENTAL VALUE

CALCULATED

s TAT ION

18 20 X

FIG.20 MEASURED AND CALCULATED ABSOLUTE MOTION AMPLITUDE CHARACTERISTICS IN REGULAR WAVES.

I

,,,,,,//4fl=.15

,//

I LFn=.20 I L

,11A

I _{FULL LOAD}

I

I//I

I CONDITION ,% I

'

_Fn=.25 I I

'

I 1##b% Fn=.30

,/

/

I

\

'i

,,,'

Ai

,,

I

I

I

I

À

I

/////ÌI

/1/1

L

I

g

.

IIR I

Ir'I

I

1Fn=.2014

BALLAST I I I CONDITION

'l

'1

I/a I

't

I

I

I

Fn=.25 t t t

i!'

"

V

-I

I'

I

I

Fn=.15 I

.-

_II

i.

I

.

-p

I

/

I 1 t

I

I

,

/

/

rt'-5

'

I

'

'

'

I I \

\

'

i.0 O 5 i.0 150 0.5 1.0

1.55

i.0 1.5

1

LSa X loo Sa to, ' 'o %

a

I

50 25 o

FIG.21 MAXIMUM AND MINIMUM VAL.UES

_{OF THE DYNAMICAL SWELL UP.}

FULL LOAD STATION 20

CONDITION _{BALLAST CONDITION} STATION 18

o 0.10 0.20 0.L0I0 0.10 0.20 0.30 0.L0

Fn

.

MAXIMUM VALUE

i

i

i

FULL LOAD CONDITION

r2

Sa

L 0.6 0.8 i.0 1.2 1.4

u a u A V

EXPERIMENTS WITH SURGE MOTION

D

t

O D O V

EXPERIMENTS WITHOUT SURGE MOTION

FIG.22 RELATION BETWEEN ADDED RESISTANCE AND WAVE AMPLITUDE (FULL LOAD CONDITION)

Fn=.30 .01 L 5

;

a

._llI11!:!iV

. '5 o .0 L:

;

u A

.4i'i

L

rr

A _o

.

A ).5 o o io X RAW i ( kg) Fn = .13 Fn=.20 Fn=.25 20 o (cm2) io 20 i .6 i .95

RAW

pg Ç2 B/L

RAW pg 2

B/L

3 2 o 3 2 o o ' 0.5 . EXPERIMENT 1.0 _i.510 ' 0.5 C ALCU LAT E D 1.0 i.510 ' 0.5 V

L/t

i .0 i.510 ' 0.5

FIG U MEASURED AND CALCULATED NONDIMENSIONAL ADDED RESISTANCE IN REGULAR WAVES.

1.0 1.5

Fn=,15 Fn=.20

FULL LOAD CONDITION

Fn=.25 Fn=.30

A

k.

.

.

.

Fn=.i5 I Ir' I

r'

Il

e Fn=.20 \BALLAST CONDITION

I

Fn=.25 s Fn=.30

.\

_s

I

\

s s s

4____}/

4 s _s

30 20 10 20 10 FULL LOAD CONDITION BALLAST CONDITION

s

AW t J Fn =15 Fn t AW =20 I Fn =25 flAW

t

Fn =30 AW . . . RAW

/J

RAW I AW t I Fn=.15 flAW

t

I Fn=.20 Fn =.25 AW

t

I . Fn =.30 AW

t

.

s s . . . . . s s s

..

. s s s . R_4W

--RAW

s s O p, . s

m-R

4W 0

RAW

o

i

210 1 210 i 210 2

o--- EXPERIMENT IN STILL WATER

(overload )

(kg ) R

I

EXPERIMENT IN REGULAR WAVES

FIG.25 MEASUREMENTS OF RESISTANCE AND PROPELLER REVOLUTIONS IN STILL WATER AND IN REGULAR WAVES.

(rps)

o

30

(rps)

s

O

( kg) T (kg) 3 2 i o 3 2

i

o FULL LOAD CONDITION BALLAST CONDITION TAW I L Fn=.15 TAW Fn=.20 I -Fn=.25 -T4 & Fn=.30 T4 L s

.

.

s s s s s s s AW s s s

.

s s s s s s s RAW

-. R

_AW RAW TA! Fn=.15 AW Fn=.20 I Fn=.25 TAW I-Fn =.30 4

.

s s b s s s

55

_s.

s s s s s s s s s s s S s s s s s AW RAW s

--R

AW RAW 2 Iü o

i

210 1 210

o--- EXPERIMENT IN STILL WATER (overload) (kg) - R

I

EXPERIMENT IN REGULAR WAVES

FLG.26 MEASUREMENTS OF RESISTANCE AND THRUST IN STILL WATER AND IN REGULAR WAVES.

.

O

.

.

Q Q 0.075 0.050 0.025 (kgm) o 0.075 0.050

f

0.025 (kgm) o FULL LOAD CONDITI ON BALLAST CONDITION ' Fn=.15 I Fn=.20 I -Fn=.25 -Fn=.30 0AVV

.

0AW s Aw

t

. . .' . °AW s

.

s s .

.

. .

.

-

RAw

RAW

"-RAW

I Fn=.15 I Fn=.20 Fn=.25 I Fn=.30

,

°AW °AW I . 0AW _0AW s . s s

.

s s s s

.

s RAWs s s s s ______ s s RAW RAW o i 210 1 210 i 210 i 2

o---. EXPERIMENT IN STILL WATER (overload )

( kg) R

EXPERIMENT IN REGULAR WAVES

o-1 _FIG.27