The damage direction θ accounts for the phenomenon that the longitudinal damage extent will not necessarily be symmetrical around the impact location.

In van de Wiel and van Dorp (2011), it is assumed that θ depends on the impact angle φ and the relative tangential velocity vT as follows: equation(24) θ=0ifφ=0(12(φ90)n)exp(mvT)if0<φ<90(1-12(180-φ90)n)exp(mvT)if90≤φ<1801ifφ=0where vT = −v1cosφ – v2, m = 0.091 and n = 5.62. The penetration depth PD0325901 cost yT is applied to evaluate which longitudinal bulkheads are breached and hence from which tank compartments in the transverse direction oil can spill. Likewise, the longitudinal limits of the collision damage, yL1 and yL2, are applied to evaluate which transverse bulkheads are breached and hence from which tank compartments in the longitudinal direction oil can spill, see Fig. 6. In the utilization of the regression model for damage extent conditional to impact conditions, the statistical quality of the regressions based on the damage cases from

the NRC (2001) report is important. First, it should be noted that the damage extent model is based on damage calculations of relatively large tankers: the smallest SCH727965 considered struck ship is comparable to the larger ships in the considered class of product tankers. This implies that the damage extents based on the presented model are likely to be overestimated. Second, in terms of the actual regression quality, the statistical fit for the predictor variables x1 and x2 in Eq. (14) was established by means of probability plots by van de Wiel 17-DMAG (Alvespimycin) HCl and van Dorp (2011), which is not replicated here. The agreement is good. Predictor variables x3 to x5 follow directly from empirical distributions. The regression quality for the models for yL and yT of Eqs. (18) and (19) is found to be good based on reported R2-values of 70.6% for the

yL-model and 73.6% for the yT-model. The model for the damage direction θ under the parameters m and n in Eq. (24) is validated by comparing the number of times the application of the model produces the same oil outflow as the NRC-data, given the parameters l, yL, yT, φ and vT. The correspondence is very good with a reported 95.6% correct prediction. The BN for product tanker cargo oil outflow conditional to impact scenario is constructed based on the integration of the probabilistic link between impact scenario variables masses m1 and m2, speeds v1 and v2, bow shape parameter η and situational parameters φ and l, with the submodel which links the damage extent, ship particulars and oil outflow.