A control device for stabilizing a semi-submersible platform with a large list angle in waves

to be read at Workshop on

Floating Structures and Offshore Operations

A Control Device for Stabilizing A Sernisubrnersible Platform

with A Large List Angle in Waves

Mikio Takaki, Yasushi Higo, Masaya Kohno and Ping Xiu

Hiroshima University, JAPAH

Summary

In this paper, the authors develop a new control device for stabilizing a semisubmersible platform with a large list angle in severe sea conditions. This device can freely move the fairlead locations to an

arbitrary points in order to reduce a tilt moment induced by environmental loads to a minimum. And it can be easily applied to an existing every platform without a large remodeling of it.

The model experiments in irregular waves were carried out to assure the estimation accuracy of the numerical simulation program. Both the

static and the dynamic simulation studies were carried out to assure a

validity of the proposed device

It has become clear from the study that this device is very useful for

stabilizing a semisubmersible platform with a large list angle in waves.

Especially it effectively reduces the rolling amplitudes and increases the

air gap between the underdeck and a wave surface.

1. INTRODtJCTIOt

Most of semisubmersible platforms have

been usually being moored to operate in the 'Iorth Sea and other areas for a long time.

The point is completely different from that of the conventional ships. Takarada et al)-'2) have pointed out that the moored

serrtisubmersible platform may get into danger

at the sea conditions where a free floating ship is being safe. In addition, they have

made clear the mechanism of capsizing

phe-nomena of a semisubmersible platform 2) and

have investigated the effects of fairlead location on a stability and sea keeping qualities

of it3.

According to their studies, the horizontal displacements are

restricted by mooring lines, therefore the

mooring force as a reaction force against

wind, current and steady wave force may affect as a heeling moment, which depends on

the fairlead location. Consequently the fairlead location affects not only the

stability but also the motion performances of the platform 2,4)

On the other hand, Takaki et al. have

made clear the following facts 5). _{As a} inclination of a semisubmersible platform

fJ ,

ç

UT

Lcboum vcor

Schhmn

Ârchff

Makewe 2,2628 CD

_Dft

I1. Ùth -EUL 015

-(hereafter we call it "semisub") largely

increases, unstable motions take place. And

the larger the inclination of it becomes,

the larger the rolling amplitudes take place

in the low frequency range of irregular waves. Therefore, a large inclination of

the platform is unfavorable from the

view-point of the safety of the semisub. The phenomena, however, can be disappeared by reducing the list angle.

In this paper, the authors consider it

the best way to change the fairlead location for stabilizing a semisub with a large list angle. So we develop a new control device

which can move freely the fairlead location

to an arbitrary point on a column in order

to reduce a tilt moment induced by

environ-mental loads to a minimum.

The model experiments were carried out

in irregular waves to assure the estimation

accuracy of the numerical simulation program. To assure a validity of the

proposed device, both the static and the

dynamic simulation studies were carried out.

The hydrodynamic coefficients for the simulation studies were obtained by

It has become clear from the study that

this device is very useful for stabilizing a semisub with a large list angle in waves.

Especially it effectively reduces the

rolling amplitudes and increases the air gap between the enderdeck and a wave surface.

2. PROPOSAL OF CONTROL DEVICE

The general arrangement of the developed control device is shown in Fig.l. The fixed pulleys A & B are arranged at both the upper and the lower end of a column, and the

mooring line AP is stretched from the one of

them. In addition, the driving pulley C is arranged at an arbitrary point on the line KP. Let the mooring tensions of the lines

P,

, be Tp, TA, TB respectively.

Let's assume these tensions of three lines

be balanced statically, we get the following equations between the tensions and the

angles Op,c,Oa.

Tp/sin Op = TA/sin 0A = TB/sin 0B

(i)

Fig.l General arrangement of the new mooring system

So we can move the fairlead location C to an arbitrary position between the column AD by

changing the triangle ABC. We can decide the position C by adjusting the tension TB

as a practical usage.

The advantages of this method are as follows:

A tilt moment induced by environmental loads can be reduced by mooring reaction forces, since a fairlead location can be

easily adjusted to an arbitrary position. By adjusting the mooring tensions, the

inclination of the semisub can be easily reduced and can be restored to the righting condition.

The controlling time for adjusting the

inclination due to this method is shorter

than that of adjusting the ballast water. Therefore it is useful for an emergency condition.

This device can be more easily set up

than a pump system of ballast water, and can be easily applied to an existing

every platform without a large remodeling

of it.

By increasing the mooring tensions, this device can generate a larger righting moment rather than that of ballast water which is restricted by the

volume of ballast water and the distance between the lower hulls.

MODEL AND MOORING CONDITION

The model is the 1/50 scale model

consisting of two lower hulls, four columns

and two horizontal braces. The principal dimensions of the model are shown in

Table 1. Fig. 2 shows the right handed coordinate system with the z-axis being

directed vertically upwards. In the same

coordinate system, a tilt moment and a list

angle are defined as shown in Fig. 2. The mooring condition is decided in

accordance with the practical conditioris6'7 as shown in Fig.3. The model is set up in beam sea condition, and the performances of

the model with the initial list angle of lO or 20 degrees are investigated. Under this situation, the righting moment of the

semisub intensely affects the analyses of

its safety performance. Therefore the stability test was carried out, and the

stability curve including the mooring effect

is shown in Fig. 4.

STATIC CONTROL OF INCLINATION OF

SEMI-SUBMERSIBLE PLATFORM WITH INITIAL LIST ANGLE

When a semisub is being inclined by some

damages, a method adjusting the ballast water in the lower hulls is generally used

so far5'8. We have attempted to apply the

proposal device to that condition and to

w

Drift force

,.3 LS. 25%,

Fig. 3 Model setup in beam sea condition

Table i Principal Particulars of model

recover the inclined semisub to the upright condition by changing the fairlead locations and winding up the mooring lines.

Fig.5 shows the fairlead locations on column. Let's define the case which the

fairlead location is set up at the designed point of 0.31 meters upwards from the keel line as Normal Condition. In addition,

let's define the case which the fairlead locations are set up at the upper end PH and the lower end PL of the column as Righting Condition as shown in Fig.5. This Righting Condition can generate the maximum righting moment to restore the inclined platform to the upright condition. It is because the semisub with large list angle of 10 or 20 degrees needs a large righting moment to recover to the upright condition as in

Fig.4. In both Normal and Righting

Condition, as the mooring lines of both sides are being wound up, the values of the

horizontal displacements, the righting moments and the mooring tensions are estimated by the catenary theory, and are shown in Fig. 6 to Fig. 11. In this

calculation, the mooring lines are assumed infinitely long.

Fig. 4 Righting moment curve

Fig. S Fairlead locations in Normal Condition & Righting Condition

Fig. 6 and Fig. 7 show the inclination angles and the righting moment per one of

two couples of the mooring lines

respectively. In Normal Condition, the

inclinations of the semisub slightly reduce

by only 1 degree and 2.5 degrees for the

initial inclination of 10 and 20 degrees

respectively. Whereas in Righting

Condi-tion, the inclinations reduce by larger than 10 degrees for the initial inclination of both 10 and 20 degrees. On the other hand,

in the case of adjusting the ballast water, the inclination recovered by only 3.5 degrees for the same initial inclination of

20 degrees5. It become clear from the

above comparison that this proposed device is useful for controlling the inclination of

a semisub. It is because this device can

generate a larger righting moment due to a change of fairlead locations.

Fig.8 and Fig.9 respectively show the

drift and the sinkage of the platform in both Normal and Righting Condition. In Normal Condition, as the mooring lines are being wound up by 40 centimeters, the

platform comes back to the position of the

upright condition. While in Righting

Condi-h

s. a .5 -22.S -L2.2 -s. a 22.2 22.S AflqI. 3 Length of all L = 1.62 n Breadth of all B = 1.42 n Draught T = 0.41 n Di splacement _A = 0.2095 n3

Length of lower hull LL = 1.62 n Breadth of lower hull EL = 0.32 n Depth of lower hull TL = 0.1472 n Column diameter DC = 0.2672 n Brace diameter DE = 0.0767 n Longitudinal length between columns BL 1.10 n Transverse length between columns = 1.10 n

22 CO 42 -. 00 00

=

1g -O i 0.0 2.1 0.2 0.3 Length (m)

Fig. 6 Heel angles in Wind-up Condition

Fig.

tiori, a large drift takes place, because the fairlead locations firstly are at the upper

and the lower end of column which are

different from the designed positions. In

addition, as the mooring lines are being wound up, the semisub shows a tendency to

come back to the position of upright

condition, but does not completely. It is

because of the difference between the fairlead locations of both sides. The

sinkages due to winding up the mooring lines of 0.40 meters are very small by 0.5 to 0.7 centimeters. Therefore it seems that it

z 00 E o 2.04.0 -0.0 0.1 Length (m) 0.2 0.3 0.4

Fig. 7 Righting moment curves in Wind-up Condition

scarcely affects the air gap between the

under deck and a wave surface.

Fig. 10 shows the horizontal and the

virtical components of the mooring tension

per one line at the fairlead location of inclined side. To wind up the mooring line

strongly affects the horizontal component of

tension but hardly affects the virtical one

so much. The mooring tension of the opposit

side is almost the same as one of the

inclined side except for a slight increase

of the virtical component because of the static balance. (d.l 20 Idog Rt9n Ing oIti.1 AngL. Cond. 10 (d.gi 20 0.q oightng

-n101.1 00gO. 10 dog) 20 (d.q fighiog 0101.1 10 d.g) 20 (d.g) IUq0 Ing

0.0

-0.5

E o e co e -X z i.) -1.0 Fig. Length (ni) g 0 2 2.3 2.4

9 Sinkage in Wind-up Condition 0.2

8

2.1 2.2 2.3

Len9th (m)

Drift In Wind-up Condition 0.4 20.2 E 0.O 12.2 0.0

Length (m)

Fig.1O Horizontal and virtical mooring tensions in Wind-up Condition

5.

DYNAMICAL EFFECT ON PERFORMANCE OF

SEMIStJBMERSIBLE PLATFORM

5.1 Tank test

The tank test was carried out by using

the semisub model mentioned in Chapter 3 to assure the validity of the numerical

simula-tion program at the Experimental Tank of

Hiroshima University (L B D = 100 x 8 X 3.5 meters ). The experimental conditions with the four initial inclinations of ±10

and ±20 degrees were carried out in beam sea

condition. The definition of air gap is a

virtical distance between the under deck of

the model and a wave surface. The

experimental conditions of the model and the air gap (ld) are shown in Table 2.

The irregular waves used in this

experiment are ones having the JONSWAP Spectrum with the significant wave height of H113= 0.18 meters and the mean wave periods of T02 = 1.8 seconds. The mean wave period corresponds to the intermediate value of the wave periods when the maximum inclination

and the minimum air gap take place in regular waves 9.

S( w)=(/2

e1TPf2/'2 o2j

(2) where, f = w/2 , y = 3.3 a = 0.0624/(O.23+0.0336y-O.185(l.9+'yr1J fCa =

0.07 :W Wp

0=

= 2T1/Tp Ca = 0.09 :W Wp Tp

1.408 T02

The motions of the semisub were measured by the position sensor device of Light

Emission Diode Type (LED). After all of the measured data were converted into the digital values around the center of the

gravity of the semisub by the micro

computor, the significant values and the

mean values of the motion amplitudes, air

gaps and mooring tensions are estimated by

spectral analysis.

We have considered the inclined condi-tion to the weather side as the most dangerous condition for the semisub, where

the down flooding took place for many times

in regular waves9. Therefore we will

discuss only the inclined condition to the

weather side in this paper. The

experimen-tal values obtained by the tank test are

denoted by the circle in Fig. 11 to Fig. 13.

5.2 Numerical simulation

The motion equations on a moored floating structure can be generally written by

E [(Mjj+mij)Xj+NijX+Njj(Xj_Uj)Xj_Uj

+C(X1,x2,... X6flFei

(i=l,2,3, 6) (3)

where, X is the displacement of center of

gravity in j-direction, is an added mass or an added mass moment of inertia, Nj is a wave damping coefficient, Nvij is a viscous damping coefficient, Ci is a restoring coefficient including a mooring effect,

is a mean value of wave particle velocity, and Fei is a wave exciting force. The

motion equations of the semisub model are

restricted to the three freedom (i2: sway,

i3

: heave,

i4

roll) in beam sea

condition.

The wave exciting force Fel in Eq. (3) is decomposed into the linear wave force Fwi

and the slow variable force Fdi as follows.

Fei = Fwj +

Fdi

(4)

The difference between the frequencies relating to the forces F1 and Fdj is far part. Therefore, by assuming that there is no hydrodynamic interaction between the

linear force and the slow variable force,

Eq.(3) can be decomposed into two equations

which are related to the

forces Fi and

The radiation forces of the equations relating to the

force F±

are

substituted by the experimental values 11) with the typical wave period of irregular waves, while ones in the equations of

are substituted by the results of the free

oscillation test.

rti.

ng1. 10 (dog) 20 (do)

agree well with the experimental results

except for a part of the air gaps as shown

in these figures. Therefore the numerical simulation program has an accuracy enough

for the estimation. It seems that the discrepancy between the simulation and

experimental ones for the air gap is induced by the wave interaction among the columns.

5.3 Dynamic control to inclination of semisubmerslble platform

In Normal Condition where the fairlead

locations were set up at the designed position of 0.31 meters upwards from the keel line, even if the mooring lines were

wound up, it was hard to generate the large

righting moment as shown in Chapter 4. It was because the moment lever from the center of gravity of the sernisub was small and restricted. So let's define the case

wind-ing up the moorwind-ing line at the speed of

0.005 meters per second as Wind-up

Condi-tion and define the case without winding up

as No Wind-up Condition. In these two

conditions, the numerical simulations are

carried out under the assumption that the

mooring lines areinfinitely long, and are

always touching the sea bottom.

The numerical simulations are shown in Fig.11 to Fig.l4. In No Wind-up Condition,

the time histories are calculated for 180

seconds, and are analyzed in the initial

condition where the fairlead locations are

at both ends of the column. While in

Wind-up Condition, the time histories for 180

seconds, which include the transient

condi-tion for 72 seconds winding up the mooring lines with the speed of 0.005 meters per second, are shown. In addition, the

spectral analyses are carried out on the time histories for 180 to 360 seconds.

Table 3 shows the significant values and the mean values due to the spectral analysis on

Normal Condition, No Wind-up Condition and

Wind-up Condition.

Fig. 11 shows the time histories and the

spectra of swaying motions. The slow drift oscillations become smaller regardless of

the initial inclinations due to winding up

the mooring lines of both sides. The

Initial Radius of Air gap Natural Period (sec)

heel angle KG gyration

Sway Heave Roll

(degrees) (m) R(m) ld(m)

= ±10 0.412 0.605 0.156 20.5 2.82 6.69

= ±20 0.412 0.605 0.052 19.9 2.83 5.39

b

Table 2 Test Conditions

The wave force Fi and the slow variable force Fdi have been evaluated as follows.

The irregular waves having the spectrum due to Eq.(2) can be denoted by

N

(t)=kElk Sin(Wkt+ Ck)

(5)

k =S(Wk)

k

where, Wk is an angular frequency, Ek is an

uniform random number distributing from O to

2 lt , and Wk is a divided width of angular

frequency. The linear wave

force F1

for

irregular waves can be evaluated by using the resoonse function H1( j ) and the phase Cwj of the linear wave force in regular

waves as follows. N

F1(t) E Hwi(wk) _k

k=l

sin[ Wkt+ kwi Wkfl

(6)

The slow variable force _Fdj can be

evaluated by using the response function

Hdi( w ) of the steady forces in accordance with the Pinkster's Method 12) as follows.

NN

Fdj(t)=E

k=ln=lcos[( wk_wfl)t+ Wk- WnJ (7)

The calculations of Eq.(6) and Eq.(7)

are carried out by using the expeimental

values 11) of H(w ), E(w ) and Hdi( w

in this study.

On Eq (3), the restoring force Cj is nonlinear, and the forces and Fdi

fluctuate irregularly . Therefore two kinds of the equations relating to the forces Fwi

and Fdi are separately solved by using the

Runge-Kutta-Gill Method in the time domain, and the time histories are evaluated by adding both solutions.

The results corresponding to Normal

Condition in Fig. 11 to Fig. 14 show the

numerical simulations for 180 seconds on the same condition as one in Section 5.1, and

are compared with the experimental ones. In these figures, the upper and the lower ones show the results corresponding to the

initial inclination of 10 and 20 degrees respectively. The numerical simulations

20 0 0. 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.5 90 10.0 a (rad/sec) 20.0 - 0.0 -20.0 0 18 36 54 72 90 108 126 144 12 10 Tire (sac) 1.0 2.0 3.0 4.0 5.0 6.9 7.0 8.0 9.0 1.9 w (rad/sec) 0EL)0.00 0(11 Scar I c((1,Q3 2(I ib 54 /2 90 lOa 126 144 12 i Tira (sac)

Fig. 11 Comparison of swaying spectra and time histories

sernisub comes back to the initial position of the upright condition. It is because the tension of the weather side becomes larger than that of the lee side. The swaying

amplitudes slightly reduce due to winding up the mooring lines.

The time histories and the spectra of

heaving motions are not shown in this paper. The significant values of heaving motion,

however, become smaller due to winding up

the mooring lines as in Table 3. It is because the arplitudes of the wave exciting force for heave become smaller11' 13) rather than the effect of mooring tensions, as the

inclination of the semisub recovers to the upright.

Fig.l2 shows the time histories and the

spectra of rolling motions. The slow

roll-ing amplitudes become smaller, and the

initial inclinations of 10 and 20 degrees

recover to the mean tilt angles of -0.06 and 7.11 degrees respectively, as the mooring lines are wound up. It has become clear

20.0 e. - 0.0 -20.0 4.0 3.2 2.4 1.6 0.8 20.0 0.0 -20.0 0 18 36 54 801L cE(L.I000 0IG

7

18 36 54 72 90 154 126 144 162 100 Time (sec) 0.0 0 0 1.0 2.0 3.0 4.0 5.0 701L c(lic2o.00 OEil 7.0 0.0 9.0 10.0 w (rad/sec) 72 90 108 126 144 163 100 Time (sec)

Fig. 12 Comparison of rolling spectra and time histories

from the above fact that our proposed

control device is useful for a dynamic

control of the inclinations of a semisub as

well as a static one.

Fig.13 shows the time histories and the

spectra of the air gap. The air gap becomes much larger, and the safety of a semisub is improved much more due to winding up the mooring lines.

Fig.l4 shows the mooring tensions of the weather side and the lee side. The mooring tensions of both sides increase much more due to winding up the mooring lines.

Especially the mooring tensions of the

weather side increases larger than 5 kgf in

the case of the initial inclination of 20

degrees. That value is larger than the

breaking load of the mooring line : 4.9 kgf

(613 ton for the actual line). Therefore this device is restricted from the

view-point of the breaking load of the mooring

line. This problem, however, may be discussed in Section 5.4.

CdItl.. _{sr.rrl SI 7,1717.at -. I.,.}

s.7..L C,.d. 0

-

14.1lV.) 14.1 5t,d-.e

- 16.3 l}

C5.dLtL.... S.,l 517.13 I4t4h! I6,..l Ca..d. O -___ 6.55 ld.S.l 55 Wtsdsp 6.35 lO..qI c.dltl. srtsl stilt

...

cc-..lCs.d. O -..--- ¡7.1 (.1 *5WI..d.ap 14.4

Ccsdltic. 5y..S.1 S1i.lfle.s.

'65 515d.p

- SOi

WtSd'tp 7...t.

- 6.31 Id.q.)

50.0 10.0 ° _2.0 50.0 B 25.0 0.0 25.0 0.0j e 8.0 - 6.0 00 O 3.0 5.0 6.0 7.0 8.0 9.0 10.0 s (rad/sec) 4)413' oEEL)o.ao 061) 4 72 90 108 126 144 162 100 Tice sec) NEEL:20.00 DEI) d gull L

5.4 Automatic control of mooring tension It has become clear in Section 5.3 that

the mooring tension exceeds the breaking load, so that the performance of this device have to be restricted. In addition, if the

anchoring point is located at the same point as the practical design, the mooring tension may increase much more, and the probability exceeding the breaking load of a mooring line may become higher. So we attempt to

apply the automatic control system to the

proposed device in order to reduce the

mooring tension less than the breaking load

of a mooring line.

As the breaking load of the mooring line

TB is 4.9 kgf, the tension TE have to be

always restricted smaller than the breaking

load TB. Therefore we control the winch of as follows.

TE > T let out the mooring lines

(8)

TE < TC wind up the mooring lines

0.40 0.0 10.0 5.0 0.0 t 5.0 On 36 54 72 90 108 126

_Ti0e

144 142 100 5 100 126 144 12 100 Tice )sec) TENO 1. ( )IEED.-20.0 060 1.0 2.0 3.0 4.0 5.0 6.0 7.0 0.0 9.0 14.0 w (rad/nec) 0 36 54 7 9b ibo 16 104 12 10 Time (sec)

Fig. 14 Comparison of tension spectra and time histories

10

where, TC is the tension at which the winch

starts to control.

In addition to that, the mooring configuration is made up the same as one

shown in Fig.3 to adapt the pract1.cal mooring condition. The numerical

simula-tions are carried out under the conditions

that the mooring line is wound up at the

speed of 0.005 meters per second and the

maximum winding up length is 0.325 meters.

Fig. 15 shows the time histories of the mooring line lengths, the rolling

ampli-tudes, the air gaps and the tensions of the weather side for 180 seconds. And the

values defined as Auto-Tension in Table 3

are the significant values and the mean

values obtained by the spectral analysis on

the time histories from 180 to 360 seconds. The mean tilt angle of the semisub with the initial inclination of 10 degrees recovers to the almost upright condition with the list angle of -0.88 degrees, after

the mooring lines of both sides are wound up

4.4. CA). ,m4-.L 00,4. 0 31.0 CC..) ., 8L4e

-S-

34.5 41441..p C..d. 9.7 CC.) 0474434240 S.im) sLq..Lf1,..,t,. 0.74.) 0804. - 0.344 lqf) 0.541 (kqC) ca..att)o.

5r'

Slqo)1).#t. 0.84.4 CO_A.

O -

14.6 CO) 4)74l-Op CO.4.

-

7.0 0.) 18 36 54 72 9ò 1Ô4 16 14 12 Time (seç) 10 0 18 36 54 72 90 1 8 1 6 144 162 140 Tice (ecc)

Fig. 13 Comparison of air gap spectra and time histories

50.0

M000inq I.ino 1.ongth

11

Table 3

Comparison of the significant value

and the mean values

Irdtloi k'851. 10 doq.

-Do.

20 dog.

-ao.o

15 36 54 72 90 100 126 144 162 160

Ti.. (0.0)

Ten,ion-1 oith Onitiol Anglo 10 dog.

8

81

8,8 8

Fig. 15 Comparison of tension spectra

and time histories

by the limited value of

0.325

meters.

In

addition, the mooring tensions never

exceed

the breaking load of 4.9 kgf, and

the

air

gap becomes larger.

On the other

hand,

in

the case of the inclination of

20

degrees,

before the mooring lines of both

sides

are

wound up

by

the

limited

value

of

0.325

meters, the mooring tensions

increase,

so

that the automatic control due to Eq.(8) are

carried out repeatedly.

Therefore the

list

angle of serrtisub does

not

recover

to

the

upright condition, and the mean

tilt

angle

is 12.3 degrees.

Though this inclination is

still large, it is

smaller

than

the

mean

inclination of 15 degrees which Takarada

et

have pointed out that a semisub

might

capsize.

In addition, no zero-air gap takes

place, arid no mooring

tensions

exceed

the

breaking load.

Therefore the

semisub

gets

out of a dangerous condition.

Consequently

it becomes clear from the above

simulations

that the proposed

device

can

control

the

inclination of semisub within

the

breaking

load

of

the

mooring

line

by

using

the

automatic controlling winch together.

6.

CONCLUSIONS

From the viewpoint of the

safety

cf

a

semisub,

we have proposed

the new mooring

system

to

change

easely

the

fairlead

Initial Angle

Condition

(deg) Sway(cro)

Heave

(cro)

Roll

(deg)

Airap

(cm)

Tens-i

(Kgf) Tens-2(Xgf) 5 -Normal Cond. 10 16.1 11.2 6.66 12.0 0.188

0.148

20 17.1 13.4 7.25 11.6 0.248 0.204 Ho Wind up 10 14.2 11.1

6.58

11.9

0.276 0.141 20 16.4 13.7 8.09 12.2 0.528

0.329

Wind-up Cond. lo

14.5

9.3

5.74

9.7

1.480

0.697

20 15.1 10.5 6.56

7.0

3.090 1.920

Auto Tension

10 15.4

9.5

7.01 10.8 3.320 2.870 20

17.7

15.1 9.83

12.5

3.290 2.840 x Normal Cond. 10

-0.07

0.00 9.94 14.6 0.463

0.475

20

-0.04

-0.03

19.70

4.4

0.499

0.520

Ho Wind up 10

10.50

-0.07

7.06

17.4 0.569

0.596

20 10.60

-0.15

17.60

6.4

0.720 0.757

Wind-up Cond. 10

1.53

-0.48

-0.06

24.0

1.598 1.621 20

-1.72

-0.44

7.11 17.0 2.512 2.567 Auto Terosion 10 3.43

-0.57

-0.88

24.7

1.720 1.750 20

6.67

-0.53

12.30

11.6

1.630

1.670

i) 14 16 144 12 Tb. (.00) 180 Tb. (Sod 19 - 36 54 72 90

7.o.ion-L with Onitiwl Angie n wog.

0.0

f6 72 90 18 16 14 162 160

location to an arbitrary point in order to

reduce the tilt moment due to environmental

loads. The main conclusions obtained from

this study may be summarized as follows.

Even the semisub with the initial

inclination of 20 degrees can be stati-cally recovered to the almost upright by this device. Therefore this device is useful for controlling statically the

inclination of a semisub.

The device can reduce the mean tilt

angle and increase the air gap. In

addition, it can reduce the amplitudes of

the slow drift, the slow rolling motion and the heaving amplitudes in irregular

waves. Therefore it can improve the

safety of a semisub in waves.

It is a matter of importance to reduce

the inclination of semisub, before it becomes a large list angle. Because the

mooring tension is restricted within a breaking load.

In case that the mooring tensions exceed the breaking load, the device can control the inclination within the breaking load

of the mooring line together with the

automatic controlling winch.

ACKNOWLEDGEMENT

The authors would like to express their sincere gratitude to Prof. Takezawa of

Yokohama National University, Chairman of

Research Meeting for Offshore Structure and

its members for their helpful discussions.

They also thank the students in the

Laboratory of Dynamics of Ocean Environment for their considerable assistance at the

Department of Naval Architecture and Ocean Engineering in Hiroshima University.

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