Moreover, the mentioned models are more

oriented towards ship design and also have limitations leading to particular uncertainties and biases. In the model by Ehlers and Tabri (2012), e.g. the bow shape of the striking vessel is simplified to only the bulbous bow, leading to uncertainty and bias in regards to the actual damage extents. In the model by Hogström (2012), the bow geometry is accounted for but the collision damage is calculated assuming a fixed vessel body, which leads to uncertainties related to the redistribution of kinetic energy into deformation energy, particularly for impacts in the bow or stern area (Ehlers and Tabri, 2012). The model by Chen and Brown (2002), which lays at the basis of the model

by van de Wiel and van Dorp (2011), is a simpler model in terms of collision energy SGI-1776 chemical structure and structural damage but accounts both for bow shape and external dynamics. The polynomial regression model by van de Wiel and van Dorp (2011) uses a set of predictor variables to link the impact scenario variables to the longitudinal and transversal damage extents. These predictor variables are representative of the impact scenario. An impact scenario can be described through the vessel masses m1 and m2, the vessel speeds v1 and v2, the impact angle φ, the relative damage location l and the striking ship’s bow half-entrance angle η, see Fig. 6. An additional variable is used EPZ015666 price as a scaling factor between the results of the small and the large tankers given in the set of damage cases ( NRC, 2001). This variable is set as the vessel length L or the vessel width B depending on whether longitudinal or transversal damage extents are calculated. As predictor variables, dimensionless variables xi are applied as follows: equation(14) x1=1-exp-ek,pβpαpx2=1-exp-ek,tβtαtx3=Beta(l∗+12|1.25,1.45)-Beta(-l∗+12|1.25,1.45)x4=CDF(η)x5=CDF(L)orCDF(B)where ek,p and ek,t are respectively the perpendicular and tangential collision L-NAME HCl kinetic energy, l* the relative impact location

with reference to midship and αp, βp, αt and βt parameters of a Weibull distribution for the predictor variables involving respectively the perpendicular and tangential kinetic energy. These are given in Table 4, along with the values for the empirical CDF of the bow half entrance angle η and the empirical CDF(L) and CDF(B).We write: equation(15) l∗=l-12 equation(16) ek,p=12(m1+m2)(v1sin(φ))2 equation(17) ek,t=12(m1+m2)(v2+v1cos(φ))2Using these predictor variables, a polynomial regression model is made for respectively the expected damage length yL and penetration depth yT: equation(18) yL=exp(hL(x|β^l)) equation(19) yT=exp(hT(x|β^t))with: equation(20) hL(x|β^l)=∑i=15β^0l+∑j=15β^i,jlxji equation(21) hT(x|β^t)=∑i=15β^0t+∑j=15β^i,jtxjiThe regression coefficients for the expressions hL and hT are given in Table 5.