10 Regulation 23.10.1
10.1 Introduction
10.1.1 The mean oil outflow parameter (OM)
may be calculated either damage scenario method or damaged tank method.
The damage scenario method is denoted in the Revised Interim Guidelines
referred to in the revised MARPOL Annex I regulation 19.5 and the
simplified approach of damaged tank method is described in regulation 23.
10.1.2 The damaged tank method as applied in the
revised MARPOL Annex I regulation
23 is much simpler, and gives the same calculation results
as those by the damage scenario method for the ships having rectangular
hull form and tanks. For the actual ships having hull curvature and
sloped shape tanks, however, the calculation results by the simplified
method are higher than the correct values.
10.1.3 Considering the above gap by the simplified
damaged tank method, regulation
23.10 states that more rigorous calculations may be appropriate.
The damaged tank method through application of hypothetical sub-compartments,
as well as the damage scenario method denoted in the Revised Interim
Guidelines referred to in the revised MARPOL Annex I regulation 19.5 are designated
as rigorous calculation procedures in the revised MARPOL Annex I regulations 23.10.1 to 23.10.3.
10.2 Hypothetical sub-compartment Calculation Procedure:
10.2.1 The probability PS and PB of
each cargo tank in regulation 23.8
and 23.9 can be calculated through application of hypothetical
sub-compartments using the following equations:
where:
|
nsx
|
= |
total
number of longitudinal sub-compartments |
|
nsz
|
= |
total
number of vertical sub-compartments |
|
j
|
= |
1
~ nsx, represents each longitudinal sub-compartment
|
|
k
|
= |
1
~ nsz, represents each vertical sub-compartment
|
|
Psx(J)
|
= |
probability
of damage for longitudinal sub-compartment, in small order of 1-Psf (j) and Psa(j), j = 1~nsx
|
|
Psz(k)
|
= |
probability
of damage for vertical sub-compartment, in small order of 1-Psu(k) and
Psl (k), k = 1~nsz
|
|
J |
= |
1~2nsx
|
|
K |
= |
1~2nsz
|
|
PsΥ(J,K)
|
= |
probability of damage by the smallest yjk of sub-compartments
of which the probability range between 1-Psf (j)
and Psa (j) or between 1-Psu(k) and
Psl (k) includes the range between Psx(J+1) and
Psx(J) or between Psz(K+1) and Psz(K)
|
|
|
= |
Psf (j), Psa (j)
, Psu(k), Psl (k) and yjk shall
be calculated by the definition of regulation
23.8 for sub-compartments
|
where:
|
nBX
|
= |
total
number of longitudinal sub-compartments |
|
nBy
|
= |
total
number of transverse sub-compartments |
|
l
|
= |
1~nBx,
represents each longitudinal sub-compartment |
|
m
|
= |
1~nBy,
represents each transverse sub-compartment |
|
PBx (L)
|
= |
probability
of damage for longitudinal sub-compartment, in small order of 1-PBf
(l) and PBa (l), l = 1~nBx
|
|
PBy (M)
|
= |
probability
of damage for transverse sub-compartment, in small order of 1-PBp
(m) and PBs(m), m= 1~nBy
|
|
L |
= |
1~2nBx
|
|
M |
= |
1~2nBy
|
|
PBz(L,M)
|
= |
probability
of damage by the smallest zlm of sub-compartments of which
the probability range between 1-PBf (l) and PBa (l) or
between 1-PBp (m) and PBs (m) includes the
range between PBx (L+1) and PBx (L) or between
PBy (M+1) and PBy (M)
|
|
|
= |
PBf (l), PBa (l), PBs (m),
PBp (m) and zlm shall be calculated by the definition
of regulation 23.9 for sub-compartments
|
10.3 Example of the hypothetical sub-compartment
calculation
10.3.1 Sample calculations by the above procedure
are carried out for the side damage and the probabilities Ps are compared
with those by the damage scenario method denoted in the Revised Interim
Guidelines referred to in the revised MARPOL Annex I regulation 19.5. To simplify the
evaluation, the following simple 2-dimensional tank and hull model
are assumed.
Arrangements for hypothetical sub-compartment calculation example
In the case that no sub-compartment is assumed, the probability
Ps is calculated according to the revised MARPOL Annex I regulation 23.8 as follows:
| Xa (m)
|
Xf (m)
|
Xa/L
|
Xf/L
|
Psa
|
Psf
|
1-Psf
|
1-Psf-Psa
|
| 60
|
120
|
0.20
|
0.40
|
0.167
|
0.567
|
0.433
|
0.266
|
|
|
|
|
|
|
|
|
|
|
y (m)
|
Psy
|
1- Psy
|
|
Ps=(1-Psf-Psa)( 1- Psy)
|
|
| 3
|
0.749
|
0.251
|
|
0.066766
|
|
Calculations by the formula
in paragraph 10.2 are carried out for several numbers of sub-compartments.
For example, the probability Ps assuming four (4) sub-compartments
is shown below:
|
j.
|
Xa (m)
|
Xf (m)
|
Xa/L
|
Xf/L
|
Psa
|
Psf
|
1-Psf
|
| 1
|
60
|
75
|
0.20
|
0.25
|
0.167
|
0.717
|
0.283
|
| 2
|
75
|
90
|
0.25
|
0.30
|
0.217
|
0.667
|
0.333
|
| 3
|
90
|
105
|
0.30
|
0.35
|
0.267
|
0.617
|
0.383
|
| 4
|
105
|
120
|
0.35
|
0.40
|
0.317
|
0.567
|
0.433
|
The Psa and
1-Psf values are sorted in ascending order, as shown below:
|
|
Psa
|
|
1-Psf
|
|
|
|
| J.
|
Values sorted ascending
|
|
Psx (J)
|
|
| 1
|
0,167
|
|
|
→
|
0,167
|
Psx (J+1)
|
| 2
|
0,217
|
|
|
→
|
0,217
|
0,217
|
| 3
|
0,267
|
|
|
→
|
0,267
|
0,267
|
| 4
|
|
|
0,283
|
→
|
0,283
|
0,283
|
| 5
|
0,317
|
|
|
→
|
0,317
|
0,317
|
| 6
|
|
|
0,333
|
→
|
0,333
|
0,333
|
| 7
|
|
|
0,383
|
→
|
0,383
|
0,383
|
| 8
|
|
|
0,433
|
→
|
0,433
|
In the table below, each
hypothetical sub-compartment or group of hypothetical sub-compartments
(j) is associated with the minimum distance (y) to the outer shell.
Each probability of breaching a hypothetical sub-compartment or exact
group of hypothetical sub-compartments (j) is then evaluated by multiplying
the longitudinal and transverse probabilities:
| J
|
Psx (J)
|
Psx (J+1)
|
Psx (J+1) -
Psx (J)
|
j
|
y(m)
|
Psy (J)
|
1- Psy (J)
|
(Psx (J+1)
- Psx (J))
x (1- Psy (J))
|
| 1
|
0.167
|
0.217
|
0.050
|
1
|
3
|
0.749
|
0.251
|
0.012550
|
| 2
|
0.217
|
0.267
|
0.050
|
1,2
|
3
|
0.749
|
0.251
|
0.012550
|
| 3
|
0.267
|
0.283
|
0.016
|
1,2,3
|
3
|
0.749
|
0.251
|
0.004016
|
| 4
|
0.283
|
0.317
|
0.034
|
2,3
|
6
|
0.888
|
0.112
|
0.003808
|
| 5
|
0.317
|
0.333
|
0.016
|
2,3,4
|
6
|
0.888
|
0.112
|
0.001792
|
| 6
|
0.333
|
0.383
|
0.050
|
3,4
|
9
|
0.916
|
0.084
|
0.004200
|
| 7
|
0.383
|
0.433
|
0.050
|
4
|
12
|
0.944
|
0.056
|
0.002800
|
|
|
|
|
|
|
|
|
|
0.041716
|
10.3.2 The results of the calculation together
with those by the damage scenario method denoted in the Revised Interim
Guidelines referred to in the revised MARPOL Annex I regulation 19.5 are shown in the
following graph. It is demonstrated that the calculation procedure
through application of hypothetical sub-compartments gives the damage
probability gradually approaching to the correct value as the number
of sub-compartments is increased:
| Calculation method
|
Definition of N
|
Symbol
|
Other calculation
conditions
|
| Damaged tank method through
application of hypothetical sub-compartments
|
The number of longitudinal
sub-compartments
|
|
-
|
| Damage scenario method
denoted in the Revised Interim Guidelines referred to in regulation 19.5
|
The number of steps
for longitudinal location
|
▪
|
Longitudinal extent at 3
steps
Transverse extent at 6 steps
|
| ▴
|
Longitudinal extent at 6
steps
Transverse extent at 6 steps
|
| •
|
Longitudinal extent at 6
steps
Transverse extent at 12 steps
|
|
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