Anti-rolling structure for box-type floating body

Details Anti-rolling structure for box-type floating body Anti-rolling structure for box-type floating body

2001-09-26

2002-12-03

Avila, Stephen (Department: 3617)

Ships

Ballasting

C114S122000

Reexamination Certificate

active

06487982

ABSTRACT:

BACKGROUND OF THE INVENTION
The present invention relates to an anti-rolling structure for a box-type floating body such as a hull of a work-ship or -vessel or a hull for FPSO (Floating Production, Storage and Off-Loading).
In recent years, various new types of active anti-rolling systems for reducing roll motion of a hull in waves have been studied and some of them are already in practical use. Active anti-rolling systems are evidently superior to passive ones in terms of their roll reducing effect.
However, various active anti-rolling systems for reducing roll motion of hulls are generally complicated in structure, large-sized and heavy-weighted and require a large installation space. For reasons of economy and space, such systems are usually difficult to adopt for hulls.
Then, studies have been consequently made on passive anti-rolling systems which reduce roll motion by devising specifications and forms of hulls. A result of such studies was published in the bulletin of the Kansai Society of Naval Architects, extra volume with issue number 232 (September 1999). “Several studies on reducing roll motion in waves” (pp 63-70) is a paper of studies published in this bulletin. According to the paper, roll motion of box-type floating bodies can be reduced by adjusting height of the center of gravity. The content of the paper is now referred to below.
FIG. 1
shows an example of a box-type floating body
1
seen from the rear. The floating body
1
has a breadth B and a draft d. A center G of gravity of the floating body
1
is located near an origin O at which a waterline lies, or for example, a little above the origin O.
When the box-type floating body
1
as described above is subjected to beam seas, rolling motion
2
is generated which acts to rotate the floating body
1
around the center G of gravity.
The paper studies on reduction of roll motion of the box-type floating body
1
having a large ratio of the breadth B to the draft d (a large breadth/draft ratio) and argues that the roll motion can be reduced by shifting the position of the center G of gravity of the floating body
1
.
Theoretical foundation of the study is an equation of motion with one degree of freedom for roll motion (rolling) having a synchronous influence on sway motion (swaying). Here the sway motion means a motion in which the box-type floating body
1
horizontally moves to right and left; and the roll motion, a motion in which the floating body
1
rotationally moves around the center G of gravity. An equation of motion with one degree of freedom, which is expressed in a more simple form, is useful in estimating a possibility of the reduction of roll motion.
An equation of motion with one degree of freedom for roll motion in which simultaneousness of the sway and rolling motions is considered is given as follows from an equation of synchronized motion of rolling and swaying:
[
D
4
-
D
24
2
D
2
]
⁢
X
4
ζ
A
=
H
4
-
D
24
D
2
⁢
H
2
(
1
)
where X
4
is an amplitude of the roll motion; H
j
(j=2, 4), the Kochin function; D
j
and D
24
, coefficients that depend on hydrodynamic force; and j=2 and 4, the sway motion and the roll motion, respectively.
The right-hand side of Equation (1) is the wave exciting moment of roll motion in a broad sense, which includes influence from the sway motion. A relationship is formed as the equation below between the wave exciting moment of roll motion and effective wave slope coefficient &ggr;.
γ
·
GM
=
-
i
⁢
 
⁢
H
4
-
(
D
24
/
D
2
)
⁢
H
2
K
⁢
 
⁢
∇
/
(
B
/
2
)
(
2
)
Next, define an added mass coefficient k
2
of sway motion, hydrodynamic force lever l
2
and wave exciting moment lever l
w
, giving
k
2
=
m
22
/
ρ
⁢
 
∇
l
2
=
-
m
24
/
m
22
l
w
/
(
B
/
2
)
=
-
H
4
/
H
2
}
(
3
)
where l
2
and l
w
are distances measured from the center G of gravity of the box-type floating body
1
to the points where respective forces act and are defined as positive toward upwards.
With l
20
and l
wo
as moment levers being defined about the origin O, giving
l
(
K
)=
k
2
l
20
−(1
+k
2
)
l
wo
  (4)
When
&ggr;
s
=(
i/K
∇){
H
2
/(1
+k
2
)}  (5)
holds, Equation (2) can be rewritten as
&ggr;·
GM=&ggr;s{OG
−1(
K
)}  (6),
where OG is distance from the origin O lying at the waterline to the center G of gravity and is defined as positive when the center G of gravity is located below the origin O; GM is height of the metacenter M (the distance from the center G of gravity to the metacenter M).
&ggr;s corresponds to an approximate value of the amplitude of single sway motion, and a moment lever l(K) is a value independent of the location of the center of gravity. Both &ggr;s and l(K) depend on the shape and motion frequency of the box-type floating body
1
.
&ggr;s, a component of an effective wave slope coefficient, and the moment lever l(K) were calculated on the box-type floating body
1
. The floating body l on which the calculations are made has six different values of B/d: 2.5, 5, 7.5, 10, 12.5 and 20. The two-dimensional velocity potential continuation method is used for calculation in which three-dimensional influence on a hydrodynamic force is not considered.
Calculated values of &ggr;s are shown in FIG.
2
. The abscissa in
FIG. 2
represents a non-dimensional frequency K(B/2) where K=&ohgr;
2
/g, &ohgr;=2&pgr;/T, and &ohgr; and T are a frequency and wave period, respectively.
As shown in
FIG. 2
, &ggr;s flatly decreases as the frequency increases. &ggr;s changes a little with a change in the breadth/draft ratio of the box-type floating body
1
; in shallow-draft box-type floating bodies having a B/d ratio of 5 or more, the values of &ggr;s may be regarded as similar.
FIG. 3
shows the relationship between the ratio of the moment lever l(K) to a half-breadth B/2, or l(K)/(B/2) (the ordinate), and the non-dimensional frequency K(B/2) (the abscissa) with B/d as a parameter. l(K)/(B/2) varies slightly against the frequency, but varies considerably with the breadth/draft ratio. The greater the B/d, the greater the absolute value of l(K)/(B/2). With B/d=5, l(K)/(B/d) is nearly zero, showing substantially no change against the frequency. The value of 1(K) is obtainable from
FIG. 3
if both the breadth/draft ratio B/d and the wave frequency of a sea area where the floating structure is installed are given.
There are three fundamental ideas to reduce the motion of a box-type floating body in waves: increase in damping force, prolongation of the natural period of the motion and reduction in the wave exciting force. In the equation (1) of synchronized motion, reducing the wave exciting force means to make smaller the value of the right-hand side, which can be achieved by making &ggr;·GM smaller as can be seen from Equation (2). Since &ggr;·GM can be expressed as Equation (6), &ggr;·GM=0 either when &ggr;s=0 at a certain frequency or when OG=l(K). In this paper reduction in roll motion is realized with this idea.
First, H
2
(K)=0 is needed in order to have &ggr;s=0, which is theoretically achievable by selecting the shape of a floating body which has no sway waves. However, realistic shapes may not be obtainable for box-type floating bodies having larger breadth/draft ratios.
On the other hand, OG=l(K) may be achieved depending on the height OG of the center of gravity. Although it has been conventionally said that obtaining OG=l (K) is difficult for sea areas with relatively long wave lengths, such a case applies to ships with a general shape; and it is obtainable in box-type floating bodies having large breadth/draft ratios.
Realizing OG=l(K) through adjustment of the OG value may be achieved by, for example, making OG larger by installing a base on the box-type floating body to mount a heavy object on it. However, when OG is made larger, the value of GM becomes smaller, which may make the floating body unstable depending on its shape.

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