International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 4
Number 4
December 2010
473
1 INTRODUCTION
Even highly organized fleets struggle with accidents
and technical breakdowns which cannot be com-
pletely eliminated. The breakdowns can be classified
based on their causes. The basic causes of the break-
downs are: warfare, defects of materials and defects
within the production process, constructional de-
fects, technological defects in the process of renova-
tion, material’s wear and tear, not meeting the re-
quirements in operating and servicing an equipment,
not taking security measures while storing danger-
ous cargoes, e.g. explosive materials, petroleum
products and other chemical components of serious
fire hazard.
A partial or total loss in functionality of mecha-
nisms and installations can occur both during war-
fare and during daily operating a ship.
Failures caused by navigational mistakes or
wrong maneuverability represent a group of ship ac-
cidents and breakdowns which can lead to dangerous
lost of floating of a ship due to flooding its com-
partments.
The statistical data prepared by the Polish Navy
Commission of Warship Accidents and Breakdowns
reveal 156 warship accidents and breakdowns be-
tween 1985 and 2004 year. The data mentioned are
presented in Figure 1. (Korczewski & Wróbel,
2005).
Figure 1. The overall structure of accidents and breakdowns
between 1985- 2004
In a situation of a breakdown crew activities de-
ciding about ability of a warship to fight should be
directed to take a proper actions during the process
of damage control and to protect stability, sinkability
and maneuverability of the ship.
Exercises within the confines of the process of
damage control, apart from construction solutions,
increase the safety of both a ship and crew. Training
is carried out in well prepared training centres. The
centers are equipped with ship models designed for
simulating failure states which most frequently oc-
cur while operating a ship. The same models were
also used in the experiments reported in the paper.
One of the goals of the experiments mentioned was
to determine the following parameters: t
f
and GM.
The information about t
f
and stability parameters
is very important for a commanding officer. It ena-
The Influence of the Flooding Damaged
Compartment on the Metacentric Height Ship
Type 888
W. Mironiuk
Polish Naval Academy, Gdynia, Poland
ABSTRACT: Research on damage stability and unsinkability is a valuable source of knowledge of behaving
a ship while flooding its compartments. In the paper, a short description of accidents and damages of Polish
warships taking place in 1985-2004 is presented. The time when compartments are flooded (t
f
) and stability
parameters are one of the key elements which have influence on a rescue action. The knowledge of the time
mentioned and a metacentric height (GM) are very important for a commanding officer making decisions
while fighting for unsinkability and survival of the ship. To provide the information about the time t
f
a new
method was designed. The method was tested experimentally and results of the tests are presented in the pa-
per. In the experiments, the flooding process of compartments in a ship of the type 888 was simulated. The re-
sults of the experiments can be a base to define general rules to make proper decisions during the process of
damage control.
The a
n-
nual mean of
accidents and
1985
1991
1999
474
bles him to make a proper decision during the pro-
cess of damage control. The officer, based on the in-
formation should determine the point in time, when
further fighting for unsinkability is senseless and
when all effort should be directed to save the crew
and documents (Miller, 1994).
2 CALCULATING THE TIME OF FLOODING
SHIP’S COMPARTMENT
When calculating t
f
, first, the velocity of water run-
ning through the damaged hull has to be determined.
The water flowing through a hole can be compared
to liquid flowing from a tank of a surface A. The
water velocity can be obtained from the following
formula (Troskolanski 1961):
2
0
z
w
A
A
1
hg2
v
−
⋅⋅
=
(1)
where
0
A
=cross section of a hole; A = horizontal
cross section of a tank; g = acceleration due to
gravity, and
z
h
= height of a liquid inside the tank.
Because the surface of a hole is much smaller
than a sea surface, the water velocity can be ob-
tained according to Torricelli’s formula (Troskolan-
ski 1961):
hg2v
w
⋅⋅=
(2)
where
h
= depth of a hole.
For the real liquid the formula (2) can be present-
ed as follows (Troskolanski 1961):
hg2v
w
⋅⋅⋅=
ϕ
(3)
where
98,097,0 ÷=
ϕ
- the velocity coefficient de-
pendant on the kind of liquid.
The equation (3) is applied when the water sur-
face inside a hull is below a lower edge of a hole, i.e.
for a constant pressure of the water. When the water
pressure is changeable (the water surface inside a
hull is above an edge of a hole and still grows up)
the velocity of the water flowing to the compartment
can be obtained according to the formula (Tros-
kolanski 1961):
( )
0w
hhg2v −⋅⋅⋅=
ϕ
(4)
where
0
h
= height of liquid inside a tank above an
edge of a hole.
The hole in the body can have a different shape
and dimension dependant on the reason of damage.
The shape of the hole influences a quantity Q of the
water flowing to the compartment. The quantity Q
depends on ν, which in turn is a product of coeffi-
cient
ϕ
and narrowing coefficient
64,061,0 ÷=
χ
(Troskolanski 1961). Therefore, the quantity of wa-
ter Q flooded to the interior compartment can be ob-
tained from the formula (Troskolanski 1961):
hg2AQ
0
⋅⋅⋅⋅=
ν
(5)
When the pressure of the water is changeable the
quantity of water Q inside the compartment is calcu-
lated from the formula (Troskolanski 1961):
( )
00
hhg2AQ −⋅⋅⋅⋅=
ν
(6)
a) b)
Figure 2. Compartment being flooded:
a) with constant water pressure,
b) with variable water pressure.
The time t
f
is as follows (Troskolanski 1961):
Q
V
t
f
=
(7)
where V= the volume of the water inside a com-
partment.
3 CALCULATING THE VOLUME OF
DAMAGED COMPARTMENTS
The calculation of t
f
was conducted for a damaged
engine room and auxiliary power plant of the ship
type 888. To enable the calculations above simulat-
ing computer program was built. The program made
it possible to fix basic and necessary parameters to
make a correct evaluation of the state of a ship. In
turn, the information about the parameters men-
tioned above makes it possible to take proper deci-
sions during the process of the damage control.
3.1 Computing the volume of damaged
compartments
The volume of a damaged compartment is necessary
to calculate the time t
f
. The lines plan of the ship’s
hull is used to compute the theoretical volume
t
v
.
Moreover, the plan was also used to make extracted
sections on ribs number 25, 30, 35, 40, 45, 50 of the
damaged compartment. The sections are shown in
Figure 3 (Tarnowski 2008, Kowalke 2006).
475
a)
b)
Figure 3. Sections of compartments:
a) auxiliary power plant,
b) engine room.
The area of the sections was calculated to esti-
mate the accurate volume of the damaged compart-
ment. Integral curves of sectional areas, obtained in
this way, are presented in graphic form as a multi-
nomial degree 7 in Figure 4.
a)
b)
Figure 4. Integral curve sectional areas:
a) auxiliary power plan;
b) engine room.
Using section areas and a distance between them,
the theoretical compartment volume
t
v
can be calcu-
lated, by the formula (Deret 2003, Dudziak 2006):
( )
∑
⋅+
=
+
2
1 wii
t
lFF
v
(8)
where
w
l
= the distance between sectional areas, and
1
,
+ii
FF
= section areas.
3.2 The permeabilities calculation
The volume of the empty compartment was calculat-
ed by means of the computer program. The real
quantity of the water, flooding the compartment, is
less than the theoretical volume of the compartment
due to the volume of all mechanisms and devices in-
side the compartment. Usually, to calculate a real
quantity of the water, the permeability of flooding
compartment μ is used. The values of permeabilities
for two compartments are calculated by the formula
(Deret 2003):
t
v
v
=
µ
(9)
where
t
v
= theoretical compartment volume;
v
- real
quantity of the water inside the compartment.
The numerical value of the permeabilities de-
pends on both, a kind and destination of damaged
compartment. The permeability of the compartment
μ , which is announced in the SOLAS Convention, is
usually used to calculate the real volume of the
compartment. In preliminary research, permeabili-
ties of both, the auxiliary power plant and the engine
room were estimated. Their value depends on the
height of the water inside the compartment. The
graph of the permeabilities is shown in Figure 5
(Tarnowski 2008, Kowalke 2006).
a)
Permeability µ
v
0
1
2
3
4
5
6
7
0 1 2 3 4 5 6 7
y [m]
rib 25 rib 35
Height of the compartment z [m]
0
1
2
3
4
5
6
7
0 5 10 15 20 25 30 35
2
Sections F[m ]
rib 25 rib 35
z [m]
0
1
2
3
4
5
6
7
0
10
20
30
40
Sections
F [m
2
]
Height of the compartment
[]
rib 35
rib 40
ribs 45 i 50
476
Figure 5. Graph of the permeability μ
v
:
a) auxiliary power plant,
b) engine room.
The average value of the permeability for chosen
compartments, obtained as a result of experiments, is
comparable with the value of the SOLAS Conven-
tion and equals 0,85.
3.3 The model of simulation for damaged
compartment
The simulation model of the auxiliary power plant and
the engine room
, equipped with all main mechanisms
and devices, was made in the next part of the re-
search. The view of the compartments being flooded
is shown in Figure 6 (Tarnowski 2008, Kowalke
2006).
a)
b)
Figure 6. Compartments being flooded:
a) auxiliary power plant,
b) engine room.
4 THE ANALYSIS OF THE INFLUENCE OF
DAMAGE PARAMETERS ON THE TIME t
f
FOR THE COMPARTMENTS SHIP TYPE 888
The experimental research on t
f
for the auxiliary pow-
er plant
and the engine room ship type 888 was car-
ried out for different parameters of damages. In the
research, the place and the dimension of damage
were taken into consideration.
In the first stage of the research, t
f
for the auxiliary
power plant
was fixed. The calculations of t
f
were
made for the following example conditions: ship’s
draught T=4m, the dimension of damages R=0,1 m
and R=0,2 m (R denotes radius). The holes were
placed from 0,1m to 3,0 m below the surface of the
sea. The results of the research are shown in Figure
6.
Figure 6. t
f
for auxiliary power plant
In the next step, t
f
for the engine room was calcu-
lated. The results of the research are shown in Figure
7.
Figure 7. t
f
for engine room
Figure 7 presents that t
f
for the compartment with
dimension of damage R=0,4m, placed 3 m below the
surface of the sea, equals 3,4 minutes. This time is
too short to seal the damage. Consequently, further
activities of crew should be directed to protect
spreading the water covering interior of the ship and
0
1
2
3
4
5
6
7
0.7 0.75 0.8 0.85 0.9 0.95 1
The permeability μv
Height of the compartment z [m]
0
0,5
1
1,5
2
2,5
0,00 0,50 1,00 1,50 2,00 2,50 3,00 3,50
De pth of the hole h [m]
R=0,1 m R=0,2 m
The flooding time t[h]
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5
Depth of the hole h [m]
Floding time t [min]
R=0,02 m R=0,06 m R=0,15 m R=0,4 m
477
to strengthen the construction of the watertight bulk-
head.
5 THE METACENTRIC HEIGHT
CALCULATION
The next part of the research was devoted to esti-
mate a metacentric height while flooding a damaged
compartment. To calculate this parameter the added
mass method was used. The result of calculations is
shown in Figure 10.
Figure10. Metacentric height
GM- initial metacentric height (before demage);
GuMu- metacentric height while flooding engine room;
GupMu- metacentric height while flooding engine room with
free surface.
To calculate the metacentric height the free sur-
face effect was taken into consideration. Figure 10
implies that in the early stage of flooding the com-
partment, the metacentric height GupMu, is less than
GM. In the later stages, GupMu increases and im-
proves stability of a ship. This situation takes place
due to adding a mass in the lower part of the ship.
6 CONCLUSIONS
The method of determining the permeability presented in
the paper enables us to make calculating the time t
f
more
accurate.
The time t
f
depends on both the dimension and
the place of a damage.
The knowledge of the time t
f
and metacentric
height allows a commanding officer to make deci-
sions while fighting for unsinkability and for the
survival of the ship.
The modified method can be used to calculate the
time t
f
for ship type 888 with different types of hull
damages. The method can be adopted for different
type of warships.
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wa
0
0,5
1
1,5
2
2,5
0 0,5
1 1,5 2 2,5 3 3,5 4
The level of the water inside the compartment z
w
[m]
GuMu GupMu
GM
GuMu, GupMu, GM [m]
