## 4 Discussion  
As it was shown previously that once a consistent period of time elapses, ships with any loading condition are going to roll according to waves' frequencies, in this section, it is discussed whether a similar behaviour is produced when an idle ship with a certain loading condition is under the influence of different sea state conditions. For that purpose, a loading condition of Td = 12 s, considered representative enough of most merchant fleets in normal ballast or loading conditions, is selected. Without considering a Tw = 12 s, which corresponds to a synchronism phenomenon and whose results would not be representative, the condition for waves far away from Tw with the same values in excess and deficit, i.e., Tw = 6 s, 10 s, 14 s, and 18 s, were studied. Figure 14 shows the roll angles of the mentioned studied case while keeping the roll damping coefficient (0.015) and the maximum initial rolling angle (8.0\({}^{\circ}\)). From Figure 10, it can be seen that no coupling of frequencies is produced between different sea state conditions. However, it is worth noting that once the first 200 s elapses, the ship is going to roll with a constant roll angle amplitude and period. Furthermore, it is relevant to note that higher rolling angles are reached with Tw = 14 s than, for instance, with Tw = 18 s, this last case being a worst sea state condition. This result can be related to being in the vicinity of the synchronism phenomenon, which can be studied in more detail in future research works. Concerning the obtained results of the rolling angles registered to opposites sides, when Td < Tw or Td > Tw, at zero-speed conditions and under the influence of beam waves, it can be concluded that they do not have relevance when a single ship is studied. However, this conclusion can be relevant in ship-to-ship operations (lightering or bunkering, for example), where the loading condition of both ships is changed permanently. The fact that coupling occurs, but that each ship reaches this coupling by rolling to the opposite side of the other ship, can produce damage to the fenders or structures. Regarding sailing in dynamic conditions, with the ship at a non-zero speed and receiving waves from any direction (\(\alpha\)), if a Te is considered, for instance, at double the ship's speed with respect to the wave velocity (Vs/Vw = 2) and an \(\alpha\) angle of 0.20 rad, the new Te will be one-third of the Tw. In consequence, the coupling time changes to smooth sea conditions. Therefore, by changing the ship's speed (Vs) and heading (\(\alpha\)) with the same ship's loading condition (Td), it is possible to reduce the rolling angle and its consequences such as the coupling time and the maximum angle. Furthermore, according to Equation (41), by changing the ship heading angle or speed, the time to reach the maximum rolling angle will shorten (one-third of the time). For instance, for an encounter period of one-third of the waves' period, the dynamic coupling time will change in this same proportion, and it is reduced by one-third. At the same time, the maximum rolling angle is reduced as well. With the aim of providing a practical guide for shipmasters, Figure 15 intends to show and relate in a 3D map the three main variables at play during navigation, i.e., the two navigational parameters to be controlled by ship operators (ship speed and heading angle, \(\alpha\)), and Te, a result of the relationship between wave's characteristics and the navigational parameters. For this reason, in the first two cases, a \(\text{Tw}=18\) s (a) and \(\text{Tw}=21\) s (b) are depicted, i.e., very rough sea state conditions. As it can be observed, the maximum Te is registered at the maximum ship speed and with the maximum \(\alpha\) angles, i.e., following the seas. This tendency is also observed with \(\text{Tw}=14\) s (c), registering a very high relative peak at the maximum ship speed and \(\alpha\) angle.