# Risk-Based Hybrid Light-Weight Ship Structural Design Accounting for Carbon Footprint
## 5 Risk-Based Design
The annual inflation is assumed as \(i_{nfl}=3\%\), income tax rate \(t_{x}=15\%\) resulting in a capital recovery factor [20] calculated as:  
\[C_{rf}=\frac{r}{1-\left(1+r\right)^{o}} \tag{13}\]  
and the capital cost, \(C_{rft}\), is defined as:  
\[C_{rft}=\frac{r+i_{nfl}+r\;i_{nfl}}{1-\left(r+i_{nfl}+r\;i_{nfl}\right)^{-o} \left(1-t_{x}\right)} \tag{14}\]  
The discounted annual average cost of the investment, \(C_{aaci}\), is defined as [20]:  
Figure 3:0  
The residual cost of the ship, \(C_{residual}\left(t_{j}|\mathbf{X},\;\beta\right)\) is associated with the depth balance plus the interest rate and depreciation accounting for the bank investment, own investment, required net profitability rate, the average annual inflation rate ship operation life, capital recovery and depreciation time, as seen in Figure 3:1  
Additionally, what is defined as the cost of the ship, \(C_{ship}(t_{0}|\mathbf{X},\;\beta)\). The cost of environmental pollution due to ship construction needs to be accounted for as follows:  
Figure 3:2  
where \(W_{CO2}\) is the carbon footprint in tonnes of CO\({}_{2}\) due to the construction of ship hull structures and \(C_{cleaning}\) is the cost of cleaning 1 tonne of CO\({}_{2}\). The air pollution due to ship hull construction [11] and the cost to mitigate the impact for the complete steel and hybrid ship hull structural solution implemented as a sustainable  
Figure 3:3 Ship cost. life cycle solution is estimated for the ship hull structure, built by steel and in for hybrid ship hull structure can be seen in Figure 3:4  
During the progressive ship hull structural collapse, a part of the cargo, \(P_{cargo}\) may be lost, and the associated cost, \(C_{c}\), may be estimated as:  
Figure 3:5  
where \(C_{cargo}\) is the cost of a tonne of cargo and \(P_{cargo}\) is the probability of cargo loss in the case of structural collapse and \(W_{c}\) is the cargo weight (see Figure 6). The accidental fuel and oil need to be cleaned up, leading to the following cost [53]:  
Figure 3:6  
where \(CATS\) is the cost of one tonne of accidentally spilt oil and fuel that needs to be cleaned, \(P_{spill}\) is the probability of spilt and \(P_{sl}\) is the chance of the oil reaching the shoreline (see Figure 7). Estimating the cost of loss of human life is based on the Implied Cost of an Averting Fatality (\(ICAF\)) defined from the average of the \(OCDE\) countries [54]. \(ICAF\) uses the Life Quality Index (\(LQI\)), defined as a function of the \(GDP\) per capita. The cost of loss of human life, \(C_{human}\) considering the probability, \(P_{crew}\) of loss of the crew, \(n_{crew}\) is defined by:  
Figure 3:7  
where \(n_{crew}\) is the number of crew members, \(P_{crew}\) is the probability of loss of human life. In the present study \(C_{human}\) is estimated as 42,496,568 \(\epsilon\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Description** & **Energy** & **Carbon Footprint,** & **Cost of CO2** \\  & **Consumption, MJ** & **Tonnes of CO2** & **Cleaning, \(\epsilon\)** \\ \hline Ship hull structure built of steel & 242,057,415 & 21,774 & 370,158 \\ Hybrid ship hull structure & 192,383,835 & 23,017 & 391,289 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Carbon footprint of ship construction. Figure 6: Cost of loss of cargo. The cost of structural measures accounts for redesigning the ship structure and implementing aluminium honeycomb composite panels instead of steel plates, reducing steel weight, environmental pollution, and cost and increasing cargo capacity. Depending on the design solution, the associated cost of the measure, \(C_{me,i}\), may be defined as (see Figure 8):  
\[C_{me,i}=C_{i}(Design)-C_{steel}(Design) \tag{20}\]  
where \(i=1\) for steel, \(i=2\) for AHS1 and \(i=3\) for AHS2.