A CAPSIZING
EXPERIMEÑT OF A
SMALL FISHING
BOAT
TA 0
IN BREAKING
WAVES
RVOtTecr
Shiges u ke Ishi d
a, Yoshifu mi Tákais h0tflecJ1fl1N LL
Mekelweg 2.2828 CD f
The Netherland:
Sllß788B13.Fx:...,
This paper deals with tle capsizing of a small fishing
boat in seam seas at zero forward speed. In a basin
four patterns of capsizing could be seen in concentric transietit waves having a couple of crests, some of which were so called Spilling breakers. The
maximum wave heights were comparable to the model breadth. An optical position sensing device was used to measure the shipiotion free from disturbance
by an experithental apparatus. The Contributions of KG, initial heel and initial position of the model relative Lo the wave to the rolling motion and capsizing were also investigated.
As for the mechanism of capsizing it is clarified that the model was heeled over the stabi1iy vanishing angle in a large amplitude rolling motion which was mainly
excited by a non-Impulsive wave exciting force. Thespilling breakers only gave her a small impulsive moment for capsizing, but
they played a significant role in terms of changing the conditions, i.e. heeling angle, angular velocity and so on, to encounter the following
critical waves.
It is interesting to
say. that the breakers worked to prevent capsizing in some cases.
INTRODUCTION
It is well known that one of the major reasons of maritime accidents is capsizing caused by a couple of large successive (breaking) beam waves. In recent research works on capsizing. in beamseas it was
re-ported that capsizing could be caused by an
impul-sive overturning moment due,to a sudden attack of a breaking wave. For example, Dahle and
Kjrland
[1] reported that a research vessel (LOA = 34,7m)
was.forcedto heel over 80 degrees to capsize mainly
by a impulsive force ofa breaker which worked on the higher part of the ship side. On the other hand,
Hirayama and Yamashita [2] conducted an
expeÉi-ment using a model of a fishing boat (LOA 42m)
and concluded that a large impulsive overturning
mo-ment worked on the ship when the breaker pushed up the weather side bottom of the ship. Other than
those papers, for example, Motora et al. [3] and Mor-ral! [4] reported more complicated capsizing patterns. In spite of these efforts the mechanism of
cap-sizing in breaking waves has not been fully
clari-fied. Moreover, the hull 'shapes and ship length in these papers were somewhat different from the ones
of small ships, those are less than or around 10 m
long and frequently reported to have capsized in the record of maritime accidents. Being characteristic to
have a small draft and a large bulwark, those small
ships can have a peculiar capsizing mechanism. lt is of importance and ofemergency Lo 'study the capsiz-ing mechanism of those ships from the viewpoint of sea safety. The purpose of this paper is to study dan-gerous cojiditions for capsizing ofsmall boats and to grasp the mechanism of it.
Ship Research Institute, Mitaka, Tokyo, Japan
ABSTRACT
t t)
-EXPERIMENT
Model Ship
The principal particulars and conditions of the fishing boat model are shown in Table I and 2,
re-spectively. GM iralues were altered by moving dead weights vertically. The characteristic of the stabil-ity curves of ail conditions, see Fig.I, was that GZ value became negative over 39 degrees because of the bulwark top immersion.
The body plan and the arrangement of sensors
are shôwn in Fig.2. Two spot lights on the mast were'
traced by an optical position sensing device, which
was used, not to disturb the ship motion. Accelera-Lion of vertical and lateral directions was measured
at the almost CG position. Two water level gauges, one on the house side and oneon the bulwark side,
and six pressure gauges were fitted on the weather side of the model.,
Experiment
The experiment was carried out in a tank of 50
m long, 8 ni wide and 4.5 rn deep, see Fig.3. The model was set free abeam
to the wave. The ship
motions, i.e. roll, heave and sway, were measured by an optical position sensing device, whose sampling
frequency was 60 liz.. Nine wave gauges, named WGI, WG2,
.., WG9 were arranged with 30 cm
distance along the wave propagation direction. The
initial position of 'the model ship was varied from
WG2 to WG6.
Waves
The signals to the flap type wave, maker were
made with the Ohmatsu'sznethod [5], which can
ünder the assumption that linear theory is valid. In
this experiment wave time histories were intended to have triangle shape at WG5. The duration time
T of the triangles were intended to be 1.5 sec., 2.0
sec. and 2.5 sec,, each wave is called W 1.5, W,2 and
W2.5 hereafter. The amplitude of the flap motions.
was controlled fOr the waves not to break before they
reached WG1n( to break after that position,
be-cause after hre&ing wave shap gets distorted from the intended one by a ju5ti-li near effect. The wave of W2.5, however, didn't have a breaking crest because of the capacity of the wave makér. We used anotherwave for T2 sec. named.
W2S whose height wasslightly smaller than W2, intended to have a similar
time history to W2 hut not to break.
Fig.4 shows the time histories of the four waves.
Sharp crests, for example wave W2 at gauge WG2, mean spilling breakers. Maximum wave heights of
W1.5, W2, W2S and W2.5 were .30 cm, 43 cm, 40
cm and 48.5 cm respectively. Those heights are
com-parable to the breadth of the model ship, that is
commonly said [6] to be the critical wave height for capsizing.CÓNDITION OF CAPSIZING
The result of the experiment, capsized or not capsized, is shown in Table 3. The ship didn't cap-size in the model conditions out of the table. Plu-ral marks at the same column show that repeatabil-ity was confirmed in critical conditions. When the record of the wave gauge on :the bulwark got over the bulwark top, which didn't mean much shipping
water but some impulsive force, each mark has a flag.
From this table we can lead the following
re-marks:
The higher. CG became, in the more various ini-tial positions she capsized.
The difference of 30 cm, Ï.82. m for the real ship, of the initial position had. much influence on cap-sizing.
Without initial heel, capsizing didn't take place
in almost single-crested waves like W2.5 at
W05, but in double-crested ones whose first
crest was breaking capsizing was easily occurred. With initial heel, especially to lee side, the ship was apt to capsize. even with larger GM value.The model only capsized to weather side in the
shortest wave W1.5 and in the heeled condition
to weather side. In both cases the water over
the bulwark top was measured.
Comparing the results in the wave W2 (with breaker) and W2S (without breaker), it is in-teresting to say that the model capsized only in W2S in many conditions when she had initial
heel.
CLASSIFICATION OF CAPSIZING
The processes of capsizing seems to be classi-fied to four patterns by the initiai heel, the existence of a breaker and the direction of capsizing like Table4. We show the ship motion of each pattern
here-after with the record of pressure and lateral acceler-ation. In the föllowing figures symbols , z and y denote roll (positive to lee side), sway (weather side)
and heave (upward) respectively. The contribution of the gravity acceleration is included in the record of lateral acceleration, but that is not of importance
as long as impulsive phenomenon is concerned.
Pattern-A, Capsize to Lee Side without Initial
Heel
Fig.5 shows an example of t.he typical capsizing
pattern in this experiment. The model of the
con-dition C7 capsized to lee side after .she encountered
the wave of W2 at the position of WG2. As shown
in Fig.4(b) the wave W2 at WG2 had two crests and
the first oñe was a spilling breaker. In Fig.5(a) the ship is represented by a straight line and are drawn from the time S to the time E with frequency of 3
Hz. 'l'ue curve means the trajectory of CG. Fig.5(b) also shows the ship motion. with the wave, profiles
from the time S to E. When the rolling motion was drawn on the
- d/di plane the trajectory had a
spiral shape like Fig.5(c).Seeing the capsizing sequence step by step, Being hit by the first breaker the ship swayed to lee side with little heeling angle.
In the trough the ship heeled to weather side. Again she heeled to lee side swaying heavily on the non-breaking second crest.
At last she capsized just after the wave train had passed her.
At the moment or just before capsizing the
wa-ter surface was of almost calm condition and the rolling angle was close to the static stability van-ishing angle, 34 degrees. So, it is clear that
capsiz-ing was not brought about by a large impulsive mo-ment directly but by a larg' amplitude rolling motion
which was excited in the wave train. From Fig.5(c)
also we can see the gradual development of the rolling motion in one and a half cycle.
This kind of capsizing is apparently different from the ones dealt by Dahle and Hirayama which
were mainly caused by a.large impulsive moment. It
looks rather similar to the one of Morall's experi-ment, but we cannot affirm it because there is no detailed description on the capsizing process in his
paper.
The pressure and lateral acceleration is shown
in Fig.6. The impulse of the breaker, evaluated by the lateral acceleration, was about 0.3 kg sec.. The impulsive moment was supposed to be about 0.05
kg. rn
sec. if we asSume that the impulse worked around the water line of the ship. This moment isVsuie
snape as vvz but no breaker, the vessel did not capsize. Sadakane et al. pointed out in their papers -[7J[8} that "the initial condition for
encountering the critical wave plays a significant role for capsizing". In this case, too, the small impulse by the breaker might change the condition to encounter the second wave. Further study on this point will be discussed later.
Pattern-B, Capsize with Initial
Heel to Lee
Side
Fig.7 shows an example of Patter-n-B. The
model of condition CL- capsized
to lee side in the
non-breaking wave W2S. Lookingat the latter half
of the, trajectory of CG and also the trajectory on
the phase plane, -it can be told that the ship motion
before capsizing was similar to the one of Pattern-A.
But these two patterns madea remarkable contrast
because Pattern-B only occurred in the non-breaking waves while- a breaker was a necessary condition for
Pattern-A. In other words the condition to go into
the motion, which leads to capsizing in the end, was different in these two patterns.
The ship motion ¡ri the same-condition as Fig.7 but in the different wave W2, with breaker, is shown
in Fig.8. She did not capsize becaùse of the effect of the breaker. It is interesting that a small breaker
modified the ship motion to prevent capsizing.
Pattern-C, Capsize tO Weather Side Being Hit
by a Breaker
-Fig.9 and 10 show an example of Pattern-C in the breaking wave Wl.5 and the initial position WG3. Iñ this case the vessel had -an initial heeling angle to weather side, but even without initial heel, e.g. wave Wl.5, ship condition C8, initial position
WG2, the pattern of capsizing was almost the same as-shown in Fig.9.
-The ship swayed with little
rolling motionlike Pattern-A after the breaker, but after that she
rapidly heeled to weather side and in the trough the bulwark- - top almost immersed., So she was heeled further by the second wave to weather side, which is the opposite direction to Pattern-A and B, and cap-sized at the second crest. The trajectory in the phase plane is characteristic to indicate a fast development of the rolling motion leading to capsizing in a half cy-cle, while -in the previoustwo patterns it developed gradually.
The acceleration and pressure show two im-pulse, the first one by the breaker and the second one in the trough. The magnitude of the first one was about 1.3 kg. sec., which was about four times larger than Pattern-A. However the impulsive
mo-ment was too small to make her
capsize alone inthis pattern, too. Instead that moment is supposed to have contributed to the fast development of the
rolling motion.
-Pattern-D, Capsize to Weather Side Without
a Breaker
The typical pattern of
weather-side-capsizing12
--
--i --i ano
12. In Fig.l1 a phase plane
is omitted because the
trajectory was similar to theone of Pattern-B.
In this example the
experiment started at
WG5, where the first c-rest of W2S was small. It
is
characteristic that the non-breaking second crest hit
the ship causing an impulse like Fig.12. The impulse was observed to push the vessel and to make it under
a kind of surf-riding condition on the second crest, which seemed to lead to capsizing. In W2, which had a deepertrough at around WG5, no impulse, no
surf-riding -and no capsizing were observed
As shown above and in previous sections, im-pulsesometimes worked at the moment when the rel-ative wave slope was large even if the crest was not
-breaking. This kind of impulsealso have a possibility to have given much effect on the ship motion.
FURTHER STUDY ON THE
MECHANISM OF
CAPSIZING-In this section the mechanism of capsizing willbe studied further using phase planes and a
simula-tion program, focusedon Pattern-A.
Phase P1nes
Ship motion whichcorresponds to Fig.5 ¡s
rep
-resented by two phase planes,
i.e. ydi and id/di,
in Fig.13. The result ¡n thesame experimental con-ditions but in the non--breaking wave W2S, leading to no capsizing, is also shown in Fig.14. The effect
of the breaker will be discussed comparing these two figures.
Every trajectory started from the origin
be-caus the model came across the waves in upright condition. When she capsized, the trajectories went
out of the figures in plus direction. The symbols
A, B, C and D denote the
moments when the ship was on the top of the first crest, in the -bottom of thetrough, y = O on the front slope of the second wave
and on the top of the second crest respectively. Note that this ship was so light that y, heave of her, almost agreed with the displacement of water surface.
In Fig.14(a), without impulse, the trajectory drew a straight line till point B, the trough. So the
rolling motion and the heaving motion, or the water elevation and the rolling motion, wère in phase. We
could see the same kind of straight trajectories iii
regular non-breaking waves [9], in which she didn't capsize in upright conditions. On the other hand in Fig.13(a), it drew an oval because of phase diffèrence
which was caused by the impulse. As a result the condition to encounter thesecond wave, for example
the rolling velocity at point B, was changed from -the one in non-breaking waves.
Looking at the point C
in Fig.l3 the rolling angle was almost zero and the rolling velocity was at the maximum, moreover the wave slope was almost at the maximum, so the rolling motion seems to have been iñ a kind ofresonant condition. As a result the rolling amplitude continued to develop in the secondwave and finally she exceeded the stability
aLive WaVe
F1g.l3 But the rolling velocity had not developed to absorb much energy from that wave excit-'ing moment. So the growth of roll was limited in the
second wave.
Simulation
A simulation was carricd out in order to
con-firm the discussion iñ the previous section. 'nie only unknown variable in the equation of motion was the relative rolling angle to te wave slope _,,,. For
evaluating the contribution from sway z and heave
y the experimental result was used becaus the pur-pose of the simulation was to investigate the efFect of impulsive moment. The change of sway and heave by the impulse was not considered at. this stage. The
eqution of motion was,
I+1Ia+B,,ç6a+ lV.Gi1ff()
+Ay1Ay(Çia)COSÇb
= IM(i)
(1)where denotes the rolling angle like,
(2)
and the coefficients 14,, tiI,, B and W are tue run-ment of inertia, the added morun-ment. of inertia, the
linear damping coefficient and the weight of tire SlflJ)
respectively. The fourth term means the restoring
moment and the experirriental results (see Fig.l) was
used for it. The coefficients for the contribution of sway and heave, from the fifth to eighth terms,
are roughly evaluated using Lewis fornì table and so
on. The lever of moment at the last term lAp() S
the horizontal distance between CG and the center
of buoyancy. IM(I) in the right hand side means
the impulsive moment. The equation was solved by
Runge-Kutta-Gill method with the time step of 1/60 second.
In Fig.15 the calculated rolling motion and the measured one was compared for añ example in W2S,
the non-breaking wave. The wave slope was also
shown. The conformation between (a) and (b) shows the validity of this simplified simulation.
The rolling motion of Pattern-A, presented in
Fig.5 and Fig.13, was calculated and.shown in Fig.l6.
When impulse was not taken into consideration the calculated time history of roll' was far from the
ex-periment like Fig.16(b). When we added an impulse
of IM1 = 0.05kg
in sec. (weather side,eval-uated before) at the moment the breaker hit the
model, the motion became closer to the experiment
till the trough like FigI6(c), but she recovered in
theend. The reason for the recovery is not clear at this stage, but we could recognize a small impulse in Fig.6 when encountering the second wave. With IM2 = 1M1/2, which was temporarily added,.the ship capsized like Fig.16(d) and had a similar time history to the experiment.
ptd.11es cillu sr1nur.roIt' sire ap'1hiii UIt..1l.11I11L VI
Pattern-A can be explained as follows
The impulse caused by the first spilling breaker worked to modulate the ship motioñ. As a result she
encourrterèd the second wave in a kind of resonant condition in which she absorbed much energy froth the wave to develop the rolling motion. In the end, heeling over the stability vanishing angle, she cap-sized when the wave train had almost passed her. Moreover, the small impulse which was measured when running across the second non-breaking wave
might further the development of roil.
As for other patterns the capsizing mechanism
has not been fully studied.
At this stage we can
only mention that the equation of motion (1) can-not give a complete explanation for other patterns. One solution might be including another rohlheave interaction term because a rolling moment due to relative heave in a inclined condition cannot be ne-glected as Tanìiya pointed out [10]. Moreover the
program should be improved to make it possible to simulate heaving and swaying motions in order. to
evaluate the effect of impulse to these motions.
CONCLUDING REMARKS
The shape of the model ship in this experiment
represented the ones of small ships and has charac-teristics such as small draft, big bulwark and neg-ative rightening arm when her bulwark immersed.
The experiment was conducted in four kinds of waves
varying the KG value and the initial position. From
the experimental results and the simulation we could
have following helpful conclusions to the safety of
small ships.
As for critical conditions for capsizing,
In wave trains having a. few crests with
the-heights of the order of the model breadth the vessel frequently capsized. The higher the CG
was, the more frequently she capsized. The
lim-iting value of GM against capsizing was GM/B
= 0.18.
In the wave W2.5, the highest wave but with
small wave slope, capsizing seldom happened.
Without initial heel, capsizing didn't take place in almost single-crested waves but in double-crested ones.
Receiving an impuise from a
breaker was a necessary condition for
capsiz-ing. l'lie capsizing direction was mainly lee side
but rarely weather side in the short steep wave,
WI .5.
For weather-side-capsizing also an impulse by a breaker was a necessary conditioñ regardless of initial heel.
With initial heel, especially to lee side, the ship was apt to capsize even with large GM value.
Comparing the result in wave W2 (with breaker) and .W2S (withoUt breaker), the model capsized
o. i ne cnflerence of JU cm of the encoüntering
po-sition to the wave had much influence on the
occurrence of capsizing.
As for capsizing patterns and mechanism, 7. The process of capsizing were classified to four
patterns by the initiai heel, the existence of a
breaker and the direction of capsizing. They could be divided into two groups. one which was characterized by a rapid growth of roll as
Pattern-C and the other by a gradual growth as
Pattern-A, B and D.
S. In any patterns capsizing was not caused by
a large impulsive overturning moment directly.
The ship capsized because she heeled over the
(static) stability vanishing angle at the last stage of a large rolling motion. The moment which
ex-cited the motion could be explained mainly by a wave slope and partly by a breaker.
9. Capsizing happened in or just after the second
wave. So the encountering condition to it, which
could be changed by the first wave, was a fatal
factor for capsizing.
10: Impulse was measured not only when a breaker hit the ship but also Whefl the relativewave slope
was large in a trough., The impulsive moment
was rather small compared to the rightening
mo-ment of the ship, hùt it played a significant roll
as mentioned above. lt is noticeable that im-pulse actèd to prevent capsizing in sorne cases.
11. Capsizing mechanism of most frequently seen
Pattern-A was investigated using phase planes
and. a simplified simulation program. It was clarified that being hit by the first breaker the ship encountered the second wave in a kind of resonant condition resulting in a large heeling angle over the stability vanishing angle when the wave train had almost passed her.
More-over the small impulse which worked when
run-ning across the second wave might further the
development of the rolling motiön.
The waves used in this experiment should not
be called "freak waves" because the ships in
ser-vice can conceivably encounter the wave train of this
length and this height. So, this kind of capsizing
se-quence is supposed to be rather common in capsizing accidents of small vessels. The authors are planning
to study the capsizing mechanism of other patterns than Pattern-A and the characteristics of "critical
vave trains" through improving the simulation pro-gram.
ACKNOWLEDGEMENTS
This investigation was carried out collaborated
with Japan Craft Inspection Organization. The au-thors would like to thank the organization ttnd the
members of the Research Committee on the
Scakeep 14 Scakeep
-REFERENCES
1. Dahle,E.A. and Kjrland.O. : The Capsizing of
M/S HELLAND HANSEN, J-RINA, (1980)
llirayatra,T and Yamashita,Y. : On the
Cap-sizing Process of a Fishing Vessel in Breaking
Waves, Journalof the Kansai Society of Naval
Architects, Japan, No.196. (1985)
Motora,S., Shinìamoto,S. and Fujlno;M. :
Cap-sizing Experiment on a Totally Enclosed Life
Boat, Second International COnference on bility of Ships and Ocean Vehicles, (1982) Morrail,A. : Capsizing of Small Trawlers, RlN\ Spring Meetings, (1979)
Ohmatsu,S. : Uñe Méthode Simple pour
Générer une Houle Arbitraire dans un Bassi!I
d'Essais, Papers of the Ship Research Institute, No.65, (198i)
& hlirayama,T. and Sadakane.hl.: Capsize of Ships in Breaking Waves and Irregular Waves, Safety and Stability of Ships and 011shore Structures, (1986)
Sadakane,H. On the Rolling of a Ship on a
Billow (2nd Report), (3rd Report), Jàurnal of
the Kansai Society of Naval Atchitects, Japan, No.173(1979), No.180(1981)
Sadakane,H. and Yamamoto,K. : An
Examina-tion on Capsizing CondiExamina-tion of Ships in Beam
Waves, Journal Of the Kansai Society of Naval Architects, Japan, No.194. (1984)
Japan Craft Inspection Organization : Report of the Research on the Seakeeping Capability of Small Vessels, (1989)
Tamiya,S. : A Calculation of linear, Non-symmetric Rolling of Ships, Journal of the Soci-ety of Naval Architectsof Japan, Vol.126, (1969) Ishida,S. and Yasuno,M. r Model Experiment on
Capsizing in Breaking Waves, Abstract Noteof the General Meeting of Ship Research Institute, No.52, (1988)
Ishida,S., Yasuno,M. and Takaishi,Y. : Model Experiment on the Mehanismn ofCapsizing of a Small Ship in Beani Seas, Journal of the Society of Naval Architects of Japan, Vol.167, (1990)
Table 2 Model conditions
9j
IrJV Fig. i GZ curves © Marker Acc. PressureI
Ret. Water o ci + C2 C3 A C4 X C5. CSV Cl
O CS CL. CW WG 2 WG] WG 1. WG S WG 6 .r,.flS.n.
...fln.
n."-.
Optical Position Sensor
k.
r
..-.' :.+.
rn:.
u:::.:g:
..rnn..
n..
u.n
-
in...-'-.n..-.
(a) U.S (b) 2 c) !2S (d) p2.5Fiq.4 Wave time histories
Modal
condition Table 3 Conditions of capsizing
O No Caspsize : Capsize(L Side)
A : Capsize(W.Side) 1A : Water over Bulwark
t, t, o C 7.S°L o 7.W Breoking
.
A Non breckingAI
-B
C C A oCapsize to Lee Side A : Capsize to Wecther Side
Wave Makar
Table 4
Classification of capsizingd-4.Sa
Wave Gage tse - 0.3 42654322 Û Model
.)
f JI50e_o
D
SHIP MODEL Loa Cm) 7.87 1.300 8 Cm) 2.47 0.408 D (In) 1.17 0.193 d (in) 0.27 0.053. W (kg) 2500 11.20 GM Cm) 0.69 0.082-0.055 Tr (sec) 3.41 1.28 - 1.74NO. GM(crn) Tr(sec) IC heel(deg)
Cl 8.19 1.28 0.401 0 C2 7.74 1.31 0.408 0 C3 7.30 1.34 0.413 0 CL. 6.85 1.38 0.417 0 C5 6.40 1.44 0.41 6 0 C6 6.40 1.46 0.434 0 C7 5.96 1.53 0.433 0 CB 5.51 1.74 0.448 0 CL 8.07 1.41 0.400 7.5 1.side CW 8.07 1.41 0.400 7.5 w.se
Wave & Model Condition
WI. 5 W2 W2S W2. 5 78 L
W 5678 L
W 78 I. W TO L W G o g -'4 ...°
o.0000.000:s0000
oo.0000.000:00000
Tr RoWng PerIodFig.3 Experimental apparatus
isec
AP FP
Fig. 2. Layout of sensors and body plan
dt -120 0. 5 -90 o o P6 O5mA4C LAcc 0.5g [
Still Water Level () (n.) 7 (n.) -0.5) 90 1(a . 0 2 4 (a) Trajectory of CG P2 O.SmAq P3 0.5n.Aq[ P4 05n.Aq[ PS 0.5mAq[ (b) Animation -50 0 (C) Phase plane PI 0.5n.Aq[ H j s I -.. (deg) 50 (0 - dO /dt)
Fig.5 Ship motion, Pattern-A
(Wave:W2, Conditjon:C7 POSition:WG2)
1.0 s _n,o.
aIHulIii:iiu.
II I'91uUfl IJH
i I iIIIIlIIIIIIIu,flh,
UULUUJØJ ..LW_L Base Line Fig. 6Pressure and lateral acceleration (Wave:W2, Conditjon:C7 Position:wG2) 16 -dt -120 0. 5 I_j -1.0 -0.5
O5y()
o -c 0I -9o! o o 0. 5 y () dtn.0.333 (...) -1.0 -0.5 E ---.... (a'T
J
2 4 6 t (a) Trajectory of CG (b) Animation (deg/s) 120í)
Y
Fig.7 Ship motion, Pattern-B
(Wave:w2S Condjtjon:CL Position: WG2) O o(e) -0.5 i. . . . L 900 (do1) ..-f'--...'.-,--_..-. -90 h 0 2 6 (a.c) q E
5432)
Wave Gage No.
Fig.8 Ship motion
(Wave:W2, Conditjon:CL POSitjOfl:WG2)
'z-'.. E (deg/s) 3.20 -50 50
(0
-dO/dt)
(c) Phase plane0. 5 (deg/e) o o -90 I L -0.5 0 (m -0.5 (dei) 0 2 4 6 t(..en) (a) Trajectory of CG s (b) Animation 654321
Wave Gage No.
Fig.
i O
Pressure and lateral acceleration (Wave:Wl5, Condition:CW, Position:WG3)0. 5
90
o
Fig. i i Ship motion, Pattern-D
(Wave:w2S, Condition:Cw, Position:wG5)
PI 0.5Aq[ P2 0.5e.Aq[ 63 0.SmAq[
'P
-1.0 -0.5 0 S . E-t---'-'
'---_!
---4. 2 4 6 (i.c) Trajectory of CGIII
um::
T -
hlflhiÑäiI
i!11111
Si. - ....iuuuúiHuiuin
IJ$uIUIJVRlIfllPUIt
:fflÍiIÔIn.4iilafti
I1IIIIHIHI!1IIIJIIJN
lWUhI11Ihii4lipI1IIUHhuIuIIHuIuIuIIuhI
I IIIIflhluIIIIII:
lui :uuunnInhii:
ii-H secFig. ¡ 2 Pressure and lateral acceleration
(Wave:W2S, Condition:CW, Position:WG5) 120 dt o
)h\
rjrt -120 -50 o (deg) 50 Cc) Phase plane ( d /dt)Fig.9 Ship motion, Pattern-C
(Wave:w1.5, Condition:Cw, Position:wG3)
P4 O.5mAg PS 05Aq [
H.°
5ec-po o.s.*q[ jri LL. -- Pb O.SAq [ P2 o.smAq[L,
63 0.SmAq L.Acc. 0.5g 87654 3Wave Gage No.
(b) Animation o -0. 5 -90 o (a)
o
i
C\)A
A -120 -50 0 (deg) (b) Ø - d /dt planeFig.
1 3
Phase planes (Wave:W2, Condition:C7, Position:WG2) -0.5 0 0.5 (a) y - plane O (deg) 50 (b) - dØ/dt planeFig.
1 4
Phase planes(Wave:w2S Condjtjon:C7 POSjtjOfl:WG2) (c) Fig.
1 5
Fig. 1 6 20-0 10--30 f deg) 30 o -10- -20-o (a) Experiment - t (eec, Simulation with impulsive mOment IM1(a) Experiment
2 4 8
t (sec)
(b) Simulation
Time histories of roll and wave slope (Wave±W2S, Condition:C7, Position:wG2)
-10- -20-30 O 2 t (sec) (b) Simulation with no impulsive moment (deg) 30 20-jQ. 30 o t (sec) 4 Simulation with impulsive moment IM1 and IM2 Time histories of roll and wave slope
(Wave:w2, Condi-tjon:C7 Position:WG2)
(d) -50 -0.5 0 , 0.5 (a) y - plane (deg/s) 120 C a, dt vi B- ,) 0 0 (deg) 30 20-r'
