**Appendix A**

### *Mission Profile in Open Sea*

According to the transit voyage in open sea defined in Section 5.2, the average sea margin over the whole voyage is defined by Equation (A1).

$$\overline{SM} = \frac{SM\_A \cdot P\_{E,A} \cdot t\_A + SM\_B \cdot P\_{E,B} \cdot t\_B + SM\_C \cdot P\_{E,C} \cdot t\_C}{P\_{E,A} \cdot t\_A + P\_{E,B} \cdot t\_B + P\_{E,C} \cdot t\_C} \tag{A1}$$

The average ship speed over the whole voyage is defined by (A2).

$$\overline{V} = \frac{V\_A \cdot t\_A + V\_B \cdot t\_B + V\_C \cdot t\_C}{t\_A + t\_B + t\_C} \tag{A2}$$

The distance of the whole voyage is:

$$V\_A \cdot t\_A + V\_B \cdot t\_B + V\_C \cdot t\_C = 650 \text{ (mmile)}\tag{A3}$$

Voyage I:

The maximum ship speeds in a calm sea state (SM = 5%) and a normal sea state (SM = 15%) in Case I are 13.90 kn and 13.66 kn, respectively. The maximum ship speed in a heavy sea state (SM = 30%) is limited at 12 kn. In order to reach the average ship speed of 13.5 kn over the whole voyage, it is assumed that the ship sails at the maximum speeds at different parts of the voyage defined above. In Voyage I, the average sea margin over the whole voyage is 15%. According to Equations (A1)–(A3), the time the ship sails in different parts of the voyage in Voyage I are: *<sup>t</sup>*I,*A* = 4.27 (h), *<sup>t</sup>*I,*B* = 5.26 (h), *<sup>t</sup>*I,*C* = 38.62 (h).

Voyage II:

The average sea margin of the whole voyage in Voyage II is also 15%. The ship speed over the whole voyage is 12 kn and the corresponding ship effective power over the whole voyage is 1229.59 kW. It is assumed that the time the ship sails in a heavy sea state in Voyage II and Voyage III is the same as that in Voyage I, which is 5.26 h. Then, according to Equations (A1), (A2) and (A3), the time the ship sails in different parts of the voyage are: *<sup>t</sup>*II,*A* = 7.89 (h), *<sup>t</sup>*II,*B* = 5.26 (h), *<sup>t</sup>*II,*C* = 41.02 (h).

Voyage III:

Similar to Voyage II, the time the ship sails in different parts of the voyage in Voyage III, where the average ship speed is 10 kn, are: *<sup>t</sup>*III,*A* = 7.89 (h), *<sup>t</sup>*III,*B* = 5.26 (h), *<sup>t</sup>*III,*C* = 51.85 (h).
