CHINA SHIP SCIENTIFIC RESEARCH CENTER
November 1985
Model Experiments on Capsizing of a
Jack-Up Drilling Platform
Cao Zhen-Hai , Chen Xie-Lin
CSSRC Report
English version-85010
(Presented at the Second International Conference on
Stability of Ships and Ocean Vehicles,
Tokyo, Oct.1982)P. 0 . BOX 116, WUXI, JIANGSU
CHINA
SUMMAP.Y
In order to investigate the mechanism
of capsizing of a certain jack-up platform,
which happened to he in
a low freeboard
con-dition in waves under tow,
a model platform
was constructed and tested, with different
amount of flooding of the mud
rump tank.
Experiments were conducted in regular waves
and irregular waves of a certain
realistic
spectrum with and without wind loads.
Characteristic phenomena observed lead
to the conclusion that non-linear
or second
order drifting moments carne into play and
that depending on the amount of
loss of
righting lever due to flooding,
the model
may gradually experience a drift in heel and
trim which would either lead to motions
about an equilibrium inclined condition or
capsizing.
Mechanism of the non-linear drifting
moment is tentatively explained and
quanti-tatively measured. It
was shown that for a
given regular wave condition in
beam or
quartering sea, the non-linear drifting
moment increases with the angle of
heel
which is of importance in
coping with
cap-sizing events of this nature.
g Y! lEO LS
L
length of platform model
Ebreadth of platform model
F. R.
free-board height of platform
model
rolling angle
q,
drift in heel (the mear, angle of
roll)
roll amplitude
pitch amplitude
zheave amplitude
Awave length
hwave height
ciwave slope
MODEL EXPERIMENTS ON CAPSIZING OF A JACK-UP DRILLING PLATFORM
CAO ZHEN-HA! AND CHEN XIE-LIN
China Ship Scientific Research Center
Ch i na
-P1-k
wave nier
characteristic period of wave spectra
Hsignificant wave height
.
natural frequency of roll
encounter frequency of wave
Mfheeling moment by wind
Mr
righting moment of platform model
Heap drifting moment
capsizing moment
insymmetrical excitation moment
ampli-tude caused by wave
m,
asymmetrical excitation moment
ampli-tude caused by shipping water on deck
relative wave height above deck edge
on the side incident to waves
non-linear coefficient of restoring
moment
2,
damping coefficient
X
wave direction
Q
amount of water admitted into the MPT
1. INTRODUCTION
liz
With increasing amount of offshore
engineering carried out around the world,
the importance of stability of drilling
plat-forms in station and under tow could not he
underestimated. To wit, the capsizing of the
Alexander L.Kielland, the Ranger and the
Robai No.2 were three outstanding
cases
occurring in different parts of the world
with heavy losses of lives. The present
report is not meant to he a simulation of
the actual conditions of cansizing of Pchai
No. 2
which has been investigated, hut
rather as a series of extended experiments
on a hypothetical lcw-freeboard jack-up
driLling platform with an aim to investigate
the mechanism of such characteristic
capsiz-ing under a realistic bacgrnund.
The model is mat type jack-up drilling
platform, the outline of which is shown in
Fig.l. A mud pump tank is installed
on the
amount of water is added to investigate the effect of quasi-static stages of flooding of this tank. The principal dimensions of the model are given in Table 1,
Table i in in kg n n rn/s Four kinds cf tests and simulations are carried out:
Towing in regular waves representing beam and quartering seas,
Towing in irregular beam and quar-tering seas,
Bench tests on a plexiglass model of the mud pump tank including forced oscillations of the latter to find out the dynamic moment of moving water acting on the platform under different frequencies,
Simulation on an analogue computer to find out the influence of shipped water on non-linear rolling of the platform in a bears sea.
From analysis of these results., an important view is advanced in the present report which may be quite general to low-freeboard floating platforms or damaged platforms floating under a relatively large angle of heel,i.e. under very unsymmetrical conditions.
2. MODEL EXPERIMENTS
Model experiments were carried out in
CSSPC 69m x 6m x 4m seakeeping basin. The model was towed by a carriage at a speed of
0.25 rn/sec and the tow line was about 12
meters in length. Cyroscopes and accelero-meters were installed in a watertight com-partment of the model to measure its roll, pitch and heave motions. Two capacity wave probes are fixed on port and starboard respectively of the platform deck to measure the relative wave elevations. There are two holes on -the deck, through which water is
admitted into the otherwise intact mud pump tank in precalibrated amounts. 7atertight covers were provided to seal off these holes after each filling of water. Model experi-ments ir the basin were conducted in two
groups:
2.1 Motions and Behaviour of the Model in
Regular Waves
The amount of water admitted into the aft mud pump tank (MPT) were O, 3.87kg and
10.10kg respectively. Righting moment curves corrected for free surface effects corres-ponding to different amount of water in HPT were calculated and shown in Fig.2. Towing
2
experiments were carried out under these conditions in both beam and quartering seas. The wave length ranges from 2.5 meters to 15 meters and the wave height is fixed ìt
approximately 125mm. The measured roll,
pitch and heave response and the mean angle of heel, termed here drift in heel, (and
taken as the mean of the asymmetrical roll angles) are shown in Fig. 3 to Fig.E. F1g.7 shows the mean height of shipped water at the deck edge of the wind ward side of the platform in beam seas. The results obtained from regular wave experiments are as follows:
a) Phipping of water on deck is serious because of the low freeboard of the platform. Pee Fig.8. For shorter waves this shipping of water is even more seriour. Pee Fig.7.
h) Roll amplitude is small, in general, the double amplitude of roll ranges from 5 to 10 in above mentioned ves,
Eut the rolling is rot symmetrical, i.n other words the platform rolls symmetrically about a mean or "drift'
angle of heel which is the asymmetric part of the motion. The magnitude of
this mean angle varies with wave
fre-quency. The largest drift in heel occurs near heave synchronism. The occurrence of this drift n heel is most obviously traced ro the effect of shipping of green water on dec)..
However, there may he other subtle reasons due to unsymmetrical
tres-sures acting on the underwater hull. The drift in heel increases with the
amount of water added in MET. Pee
Fig. 9.
d) The peak value of roll response curve decreases with increasing amount of water added to MET. Put for excitation frequencies larger than the natual frequency of roll, there is little difference in roll
between the three cases of water admission. This shows that water in
the MET acts as a roll-stabilizer in
near resonance frequency, but this effect is not significant when ex-citation frequencies are higher than the synchronism range. This result agreed with bench test of the MET.
(Fee section
L)
2.2 Capsizing Simulation Fxperiment in Irregular Seas
From the above experiments in regular waves, it is demonstrated that with greater
and greater amount of water in MET roll amplitude of the symmetrical nart decreases at roll synchronism tut the asymmetric part of roll increases. That is, with increased amount of water in the MET the drift in
heel s increased. This drift angle is dan-gerous for low-freeboard platforms. We therefore tested with different amount of
Length 1.203 Breadth 1.0 Dispaceinent 320 Height of C.G. above EL 0.25 Mean Freeboard 0.038 Towing Speed 0.25
water in the MPT and set to tow
the model in
irregular waves. The spectrum of
irregular
wave is shown in Fig.lO.
with a
characteris-tic period of Tl.t45sec and significant
wave height H
120mm. When the amount of
water in MFT is increased to llg,
capsiz-ing of the platform model always occurs
even i.f the wind moment were zero, and the
direction of capsizing appears to he
dia-gonaiwise i.e. towards the wind and trimming
aft, see Fig.11. The time history of roll
in
the capsizing process is shown in Fig.12.
This gradual capsizing process is similar to
that of low freeboard ships with shipping
of
green water on deck (ref. 1). Next, a weight
is attached on the leeward side of the deck
to simulate a l.5kg-m wind
heeling moment,
then an amount of 4.5kg of water added to
NPT is sufficient to produce capsizing.
The
direction of capsizing in this case is also
diagonalwise hut is away from the wind i.e.
towards leeward and trimming aft, see
Fig.l3.
The directions of capsizing are also similar
to small low freeboard vessels which
capsize
in windward directicn when it was under a
gentle breeze and in leeward direction when
it was under a strong wind
(ref. 2). The
cause of capsizing diagonaiwise may he traced
to the fact that there is a superstructure
at the bow which is not flooded while
the
flooded mud pump tank is situated oft,
and
that as the heeling angle increases the
trim
by the stern also increases. It is
observed
from the model capsizing experiment that
even if the platform is not
subjected to
any wind
heeling moment and that if initially
the angle of heel were zero, there
will still
develop a drift in heeling angle in the
wind-ward direction presumally caused by
asymme-tric moment due to shipping of water on deck
as a result of the low freeboard
c}ìaroctcri
-stic of the model. Fig.U4(a) and (b) show the
model without wind moment but with an initiai
drift angle in heel towards the wind. The
initial drift angle is derived by the
rela-tive ease of shipping water on the windward
side. In this condition, when a wave crest
arrives at the position shown by Fig.l'4(a),
a drift moment to starboard would be
develop-ed due to water shippdevelop-ed on deck. Again, as
the wave crest moves over to position shown
in Fig.l4(h), a drift moment to starbeard
would still be developed due to the added
buouancy of the port platform which has a
higher freeboard. Thus, with every cycle of
wave passage, the drift in heel increases,
which further aggrevates the situation
caus-ing greater driftcaus-ing moment. The vicious
cycle continues until either an equilibrium
angle of heel is reached, where the righting
moment of the model is sufficient to balance
the drifting moment at the sarre angle but
with the former having a stiffer slope. In
which case the model will roll about the
equilibrium drift angle 4. Fowever, when the
righting moment curve of th
model is below
the drift moment curve, the model capsizes.
?ben there is strong wind blowing in
the direction of wave propagation there will
be wind moment(represented by an offset
3
weight in the experiment), and the model
takes on an initial inclination to
leeward
as shown in Fig.l5(a) and
(h). The sarre
reasoning applies as in the case of
Fip.]4,
except that the direction of
drifting moment
is reversed, and that in
Fig.l5(a), when the
wave crest is over the
windward side there
is an additional impact force and
heeling
moment due to the dynamic pressure
of wave
crest slamming onto the high freeboard side.
gesides, when the wave crest moves over to
the leeward side as shown in Fig.15(b),
although the wave crest is higher than the
deck, there is no shipping of green water
owing to the fact that the wave is
propagat-ing away from the deck side (instead
of
incident to the inclined deck as in Fig
14(h). Conseouentiv, in this half cycle
there
is little apparent drifting moment actnp
to
the port. Again with every cycle
of
'ave
passage, the drift in he1
increases, either
to an equilibrium value, or until
the model
capsizes.
'ith a view to measure this drifting
moment cuantitatively and validate
the above
hypothesis, the following treatment and
analysis of test results were ann]ie.d.
3. ANALYSIS OF TFST RESULTS
As
in the case of measuring slow
drift-ing force of a shir in waves, a soft
sprinc.
is often applied bath to restrain the mode).
and also as a sensor to measure the
driflirig
force. Tn the present experiment a soft
sprirg which both restrains and measures
the
drifting moment in heel is required.
Nov,the 'model-ambient watert' is by itself a
natural soft spring system with a known
restoring moment curve. Therefore, the
right-ing moment curves (5.7 curves) could be
first
ca] culated very accurate) y, by means of
-icomputer, for each case of water
admiscion
in the HFT. The GZ. curves corrected for free
surface could he calculated for any
diaç'onel-wise inclination, i.e. for any combined heel
and trim, hut in the present paper only
(17.curve in the transverse plane
j
considered
and is given in Fig.2. Fince the amount
of
water added to the MPT (ranges
from O-lll<g)
is only a fraction of the model displacement
of 320kg, one could argue that the
addition
of water in the MFT besides altering the
spring characteristic of the "model-ambient
water' system, i.e. flZ curve, has little
influence on changing the attitude of the
model. For instance a change of ¶mm in
averge draft would be obtained correspondng
to 11kg of water admission. lt may
thus he
assumed that as far as wave excitation force
is concerned, the 3 cases of water
admission
correspond aporoxiniately to
one and the
same displacement and attitude of
the model
with respect to the action of wind and
waves. One may then think of
the righting
moments corresponding to mean angles of
roll
response (the drift in heel)
of the model
with 3 different amounts of water in
PT in
a certain regular wave as a measure of the
wave drifting moment developed
for different
beam sea regular wave test Fig.6.(a), if a vertical ordinate is erected at
ùJÇ5
:1.2which corresponds to a wave length of 5,24m and a wave height (double amlitude) cf l25nvn.
One would get intersections of Ol.93, 2.58,
8.2O(ci'4.29) respectively, for amount of water addition QO, 3.87 and 10.10kg
re-spectively. Looking at Fig.2, One finds Mr (which is a measure of the drifting moment) equals 2.37kg-m, 3.25kg-m and 6.29-m re-spectively from the three different "spring" characteristics. Constructing the drifting moment Mcap V.S. drifting angle curve
(heavy solid line) in Fig.16, one gets a curve representing the capsizing moment as a function of drifting angle '. It is worth noting that this curve is a monotonie rising curve, which validates the hypothesis that once an initial heel is started either by
wave or by wind, the nonlinear or second order wave exciting moment builds up as a monotonic rising function of drift angle in heel. The generation of this second order drifting moment is roughly described as the action of shipping water on deck and
non-linear buoyancy effect in the previous section. Work is continuing at present to give a 3-D numerical pressure analysis of the model under test, so as to illustrate further on the nature of 2nd order drifting moment. However, the 2nd order drifting moment curve(Fig.l6) obtained experimentally
reveals an important aspect and peculiar nature of the wave drifting moment in action
in regular waves, a revelation as important as the added resistance experienced by ships moving in regulnr waves. Two conclusions may
be drawn following this analysis.
As far as capsizing in above nentioned regular wave is concerned, the model platform would not capsize for the two cases Q:0 and 3.87kg respectively. It would only roll(with an amplitude, of
5-10) about an angle of heel 1.93 and 2.S8respecti.vely. The drift angle increases rapidly with more addition
of water, and with QlO.lOkg, the Mcap
curve almost coincideswith the righting moment curve Mr of the model and the model would only balance precariously at an angle of heel of 8.25, considering the max. Mr in this case is at 10, the.
model would eventually capsize due to insufficient dynamic stability introduc-ed by rolling. Thus with low freeboard ship or platform, the direct and impor-tant factor of stability is still the maintenance of sufficient righting moment, which may be provided by adjust-ment of many factors including the lowering of center of gravity. For a
platform damaged and inclined by any reason, it is always important to maintain the maximum of residual
stabi-lity, which means all access holes, ventilation ports should be seaworthy and should be easily closed off against flooding of sea water.
In irregmm1i- waves extremely slow oscil-lations may be set up by difference
-4--frequencies and wave grouping ohenomena. However, if the stability of the model
is low, the slow drifting in heel may
just gradually drift the model over and capsizing takes place as a slowly developing process. See Fig.l2. This
diagram is typical of all the capsizing experiments done for the present model-a totmodel-al of 20 cmodel-ases.
. TESTING 0F MUD PUMP TANK MODEL kITH
VARIOUS AMOUNT 0F 'ATER ADMISSION ON A ROLL TABLE
The purpose of this test is to find out the dynamical effect of water in the MPT. It is known that water in MPT may have a threefold effect.
.l Static effect of a deformable added weight with a free surface. This is taken care of in the numerical calculation of GZ or Mr curves as shown in Fig.2.
.2 Symmetrical part of dynamic effect of this moving water behaving like water in a passive anti-rolling tank. This is to be evaluated by the bench test on a roll table constructed for testing of antirolling tanks.
t43
Asymmetrical oart of this water moving i.n the MPT, especially when the neutral point of motion is at an inclined position. This is to he evaluated by a seperats benc}test on the same roll table.
Bench tests were conducted in the hydrodynamnic laboratory of Shanghai Jjao Tung University where a small roll table is employed. The MFT model is made of plexi-glass and to the same scale as the model in tank tests. The amounts of water admitted
into the MFT model were 3.87kg, 10.10kg and 16.35kg respectively. Force gages were placed under the supports of MET, (Eig.17) so that dynamical moments generated by moving water in MPT were measured. Pee Fig.1°. The excitation moments Drovided by driving motor of roll table were measured and further converted accordingly to the wave slopes. So that the effect of the MET on the platform" model expressed as a roll amplitude response is obtained (Eig.l8). It
is to be noted that the amplitude resnonse is high at the natural frequency of roll of the platform model and that the more the amount of water admitted to the MET the more the damping effect of the latter acting as a possive anti-rolling tank. F'owever, at
frequencies higher and lower than the sychrcnism range, the total effect and the difference between any of the 3 cases of water admission is small (Fig.l8). Turning to the amnlitude of dynamical moment measured by the force. gauges under the
supports (Fig.19), it is seen that for cases at arid above the natural frequency of roll, the dynamical moment of tank water is at
least 9Oout of phase and lagging tebind
moment amplitude response is approximately the same as that of the roll amplitude
response. However, the peak moment for those cases with lesser amounts of water admission is hard to measure exactly. For frequencies lower than 0.6, the moment amplitude generated by MPT rises abruptly. This is explained by the fact that the moment amplitude measured at very low frequencies approaches that of the static moment due to tank water behaving as a shifting weight moving in phase with the angle of roll. This effect has already been taken into account in the static effect of tank water outlined in .l, and hence should not be
included in the dynamic effect. In any case, since the effect of wave frequencies
investigated lies on the higher frequency side of synchronism, it may be concluded that the action of water in MPT when the platform is rolling about its up right position is similar to that of an anti-rolling tank, that the total effect is the reduction of roll in synchronous waves, and that this effect is small in higher frequency waves for all 3 quantities of tank water considered. Tests were also
con-ducted for rolling of MPT about an inclined position.(Tablc 2)
Table 2
Amount of water in MPT '4.5kg, 11kg
Preincluded angle about which
MPT is rolled 2 , '4 , 8 , 10 , 12
Rolling frequency 2.Srad/sec., 3.Orad/sec
3. Srad/sec.
Double amplitude of
forced rolling 8
A representative time history of force gauge measurement is presented in Fig.20. Enough is to say that no asymmetric part of dynamical moment is observed for all cases considered. The static moment of' the tank water as a shifted weight at the
prein-dined angle of course has been deducted by
zero setting of the force gauges before the rolling experiment.
5. SIMULATION 0F AN ANALOGUE COMPUTER On the basis of model experiments in regular waves, a simple equation of rolling motion in which the initial heeling angle is
zero, i.e. without consideration of wind moment is set u as follows:
(fl5ifl(cJ.1+) O#(f<7
(5.
1) . oThe first term on the right hand side of eq.
(5.1) represents the wave excitation moment, while the second term considers only the mo-ment produced by shipping of water on deck. As the incident wave crest hit the wind-ward side of flatform, water is shipped on
deck, while for the other half period no water is shipped on deck. It is therefore assumed that moment due to shipping of water varies simusoidally for half a period,
-5-while it is zero for the other half period. The amplitude of excitation moment n,
produced by shipping of water can be cal-culated by the following formula,see Fig.2l.
7 H.'8.2r[cos
8 )SsnJ
(5. 2)
where
relative wave height above dec edge of the wind-ward side, obtained from exoe-iment. P breadth of platforr
1 longitudinal extent of' water shipped on deck measured along the fore and aft axis of the plat-form
y specific gravity of water
F.P. free-board f wind-ward deck edge angle of roll
It has been seen in regular wave
expe-riments that shipping of water on dec1' in
succession would produce a drift in heel. The aim of the analogue simulation is to check on a rough but simple basis, the
ac-tion of shipping water on roll and on drift in heel. Deleting the first term on the
right hand side of equation (5.1),(Fi.22h),
the analogue computation gives an asymmetric roll motion (Fig.22e). Deleting the second
term on the RPS of eq.(5.l) (Fig.22a), the analogue computation would give a syrnmetri-cal roll motion (Fig. 22d) excited ourely by
wave excitation moment. Fig. 22c shows the results produced by two excitation moments together and the total motion produced by such an excitation is shown in Fig.22f, it may be seen that shipping of water not only
produces a drift in heeling angle hut also plays an important role on the amplitude of roll.
Table 3 gives sorne of the input and output results of analogue computation
following the full eq. (5.1) Table 3 w 2.82 3.'12 2p 1.5 1.72 '4.69 4.69 P, 27.1 27 .1
0.057
0.057 m O.20'4 0.356 Computed double 7.73° 6 30 amplitude of roll Experiment double 7.5° 6.1° amplitude of roll Computed drift1.70
2.30
in heel Fxperiment drift l.'4°1 .q6°
in heel 6. CONCLUSIONThe motions of drilling platform in
beam and quartering seas in low free-hoard condition are investigated by systematic experiments in regular and irregular waves, supplemented by bench tests of the Mud Pump Tank with varying amount of water and
analogue simulation on a computer. The following conclusions may be drawn.
6.1 A low free-board drilling plat-form in tow and exposed to beam and quarte ring seas would sooner or later manifest a list toward the wind when the wind moment is neglegibly Email, or a list to leeward if the wind moment is sufficiently strong. In the former case the initial list is caused by periodic shipping of water on deck on the side incident to waves.
6.2 -iith the appearance of an initial list, a vicious cycle is started following each roll. This process is caused by the difference in free-hoard on the wind-ward and leeward side of the deck. Nonlinear drifting moments is generated, of which the most apparent reason is that due to succes-sively intensified unsymmetrical shipping of water, however there might be more subtle second order moments coming into play, for
instance by difference of rr"ssure acting on the underwater hull.. The ure of the non-linear drifting moment Mcap in
speci-fic regular sea as measured by experiment
i a monotonia ircraa sing curve with the
angle of list (drift in heel).
6.3 The intersection of this Mcap (*') curve with that of the righting moment curve
) determines the final angle of repose
of the platform about which the platform will roll.
6. If the Hr ( ) curve is lower than
Mcap ($')by reason of decrease in stability by varying degrees of flooding of MFT, the
platform will capsize. However, since the development of drift in heel takes time,
the capsizing is a slow process. A typical time history is a slow drifting process in heel, on to which is superposed the normal rolling motion.
6.5 A platform with low free-board or a platform inclined to one side
(unsymmetri-cal cross section), would not be lost if its inherent righting moment is sufficiently high. Consequently for future seaworthiness
consideration, utmost attention should he paid to safety measures safeguarding against inflow of water through any of the hatches or ports to the internal spaces of the plat-form. This attention should be paid both in general layout, structural strength design of vent pipes, windows, port covers, water tight doors etc. as well as in the incorpo-ration of automatic closure systems that will close all these ports once a certain critical low free-board or list is exceeded. REFERENCES
1. lKobylinski, L. 'Rational Stability Cri-teria and Probability of Capsizing" Proceedings of the International Con-ference on Stability of Ships and Ocean
-6-Vehicles, 1975
2. Roroday, l.Y. and Pakhmanin, H.N. State of the Art of Ftudies on
Capsiz-ing of an Tntact Ship in Stormy Weather Condition" lL4th ITTC Proceedings, Vol.t4
o
/4,3
m
Fig,1 Principal dimensions of the platform
model
40
/05
o-7-Fig.2. The curves ot tr;tnsverse ri.c'htinr
moment of the platform model
A. Beam ea Tow speed: 0.25m/s. Course relative to wave Z =900 0
Qkg
' Q=3.87kQ1O.1kg
s0
40Fig.3.(a) Roll rcsponne of the platform model
R
B: Quartering seaTow speed
O.25xn/aec
Course relative to wave Q=Okg o Q=3 .87kg Q=1O.lkg s 10Fig. 3.(b) Roll response of the platform model in regular waves
Quartering ea
Tow speed O.25m/sec. Course relatiwe to
wave
X =60°Q=Okg O
Q=3.87kg A Q=10,lkg s
Fig.4. Pitch Amplitude Response of the Platform model in regular waves
-8-o00
A: Beam Sea Tow speed 0.25m/s. Course relativo to wave .=90° Q=Okg oQ3.B7kg
Q10.lkg s
Fig. 5,(a) Heave response of the platform model in regular waves
o
o
Fig. 5.(b) Heave response of the platform model in regular waves
B. Quartering sea Tow speed 0.25mm Course relative to waveZ=6O Q=Okg O Q=3 ' Q=10.lkg. o /
k,
B: Quartcring sea Tow speed 0.25m/s, Course relative to wave
s
Z
=600Q=Okg 0
Q=3.87kg
t
Q=10.lkg s/.0
Fig06.(b) Drift heeling angles of the platform model in regular waves
o
10 s A: Beam sea Tow speed 0.25m/s. Course relative to wave=9«
Q=Okg o Q=3.87kg Q=10.lkg s-9-Fig.6.a(a) Drift heeling angles of the platform in regular waves
Beam sea
Tow speed O.25m/s.
Course rolatie to wavel=90
0kg
o
Fig07. Relative wave height above deck edge on the cide incident to wave in regular sea.
B: Water in 'PT Q=3.67k.g Tow speed Omis0 Course relative to wave, =90
Wave lengthx=m Wave height h=llOmm
Fig.B. Photoes shoving shipping trapping of
water on deck of the platform model in regular waves
lo
-Tino (sec)
Fig.9. Development of Relative Drift; Angles in Heel as Function of Time
A: Water in LPT =0kg Tow speed0om/s.
Course relative to wave =90
Wave length5ui Wave height h=llOmm
Fig.10. The measured irregular wave spectra in seakeeping basin during capsizing experiments of the platform model Tow speed 0.25rn/s.
Courne relative to wave 90
Symboles av lengt.x Wave hig-it
3.73m 128mm 0k A 4.67m 109mm 105mm 3.87kg 3.2rn 1C.lkg
1.1Kg
t
5.97m 119mm 3 ap s i z e .5la
Fig0ll.
Process of capsizing (wind moment NÏ=O, water in K?, Q=llkg) in irregular Beam Sea(}I1/3=l2Omxn, T=1 .4osec).
Fig.12. The time of history of capsizing in irregular waves
Fig013. Process of Capsizing (wind moment Nf=1 .56kgm, water in NPT, Q=4.Skg) in irregular
Fig,14. To illustrate the mechanism oføjn-linear drifting moment when the platform model has initial list forward the waves (wind moment Mf assumed zero),
B:
Pig.15. To illustrate the mechanism of non-linear drifting moment, initial list leeward of the wind and waves (wind moment Mf clockwise) frlw
K-i)
50 20 B: Wave- direction Wave directi III' Tow speed 0.25m/sec
i Course relative wave 90
Wave length 5.24m Wave height 125mm
-
12 -A: A: Fig. 17 Wave direction Wave directionwhen the platform has an assumed acting counter
n
O I9523 5
825 /1 /50'
Fig.160 Diagram illustrating the construction Of the Drifting moment curve Mcap(4") and its relation with
'tra(4')
/0
Wind moment M.f=O
Water in MPT Q=3.&7kgo
Q'10.1kg
Q=16.35kge
/0
Fig.18. Roll amplitude response of IIIT. On Bench test.
Wind moment Mf =0
Water in U-T Q=3.B7kg o Q=10.lkg
Q=1 6.35kg.
Fig.20. A representative time history of force gauge measurement
13
-Fig.21. Damgram to illustrate the
calcula-tion of Drifting moment amplitude Ml
a: Symmetrical wave excitation moment b:, Asymmetrical excitation moment due to
shipping water on deck o: Total excitation moment
Roll motion caused by asymmetrical exci-tation moment
Roll motion caused by asymmetrical excita--tion moment
Roll motion caused by total excitation moment
Fig.22. Input and output time histories of analogue computation
4
I"
f?
aJe[Fig,19. Dynamical moment of MPT during Bench tests.
