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資料2 詳細計算手法の解説
BLG8/18 ANNEX 4 DRAFT MEPC RESOLUTION
“EXPLANATORY NOTES ON MATTERS RELATED TO THE ACCIDENTAL OIL
OUTFLOW PERFORMANCE FOR MARPOL REGULATION I/21”からの抜粋
10 Paragraph 10.1 of regulation 21
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 Interim Guidelines (2)* referred to in MARPOL regulation I/19.5 and the simplified approach of damaged tank method is described in regulation I/21.
10.1.2 The damaged tank method as applied in MARPOL regulation I/21 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 I/21.10 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 Interim Guidelines (2)* referred to in MARPOL regulation I/19.5 are designated as rigorous calculation procedures in MARPOL regulations I/21.10.1 to I/21.10.3.
10.2 Hypothetical sub-compartment Calculation Procedure:
10.2.1 The probability PS and PB of each cargo tank in regulation 21.8 and 21 .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
Psγ(J,K) = probability of damage by the smallest yjk of sub-compartments of which the probability range between 1-P sf (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 21.8 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 Z lm shall be calculated by the definition of regulation 21.9 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 Interim Guidelines (2)* referred to in MARPOL regulation I/19.5. To simplify the evaluation, the following simple 2-dimensional tank and hull model are assumed.
Ship length = 300 m
Ship breadth = 60 m
Figure 24 - Arrangements for hypothetical sub-compartment calculation example
In the case that no sub-compartment is assumed, the probability Ps is calculated according to the MARPOL regulation I/21.8 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 |
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| y(m) |
PSy |
1-PSy |
| 3 |
0.749 |
0.251 |
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| PS=(1-PSf-PSa)(1-PSy) |
| 0.066766 |
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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 |
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The Psa and 1-PSf values are sorted in ascending order, as shown below:
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:
10.3.2 The results of the calculation together with those by the damage scenario method denoted in the Interim Guidelines (2)* referred to in MARPOL regulation I/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:
*Refers
to reference (2) on page 43.
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