## 5 Results
### The Effect of Directions of Waves on the Salvage System
#### 5.2.3 Summaries  
In this section, a comprehensive study examined the motion responses of two lifting barges and a shipwck and the tension responses of lifting cables under the influence of waves from different directions to evaluate safety. (1) By analyzing the MA of the three ships' 6 DOFs under waves from different directions, this paper draws the following conclusions: As the wave direction increases from 90\({}^{\circ}\) to 180\({}^{\circ}\), the roll and heave responses show decreasing amplitudes. In contrast, the pitch and surge responses exhibit significant increases. Generally, except for the heave response, the response amplitude is more pronounced in the P3 stage. Under various wave directions, the MA of lifting-barge A's 6 DOFs is greater than that of lifting-barge B's 6 DOFs. This disparity is particularly noticeable in the heave and roll responses. The reason for this phenomenon is that, on the one hand, the transverse center of gravity of the sunken ship is biased toward lifting-barge A; on the other hand, it shields against waves. (2) In the investigation of the motion responses of the three ships, this section formulated evaluation criteria based on three parameters: MA, RMS, and CV. These criteria quantitatively assess the safety of the three ships during the salvage operation. The results indicate that two operating windows are relatively safe. Specifically, the suitable operating windows for the salvage operation are the adjacent areas of waves in the 0\({}^{\circ}\) and 180\({}^{\circ}\) directions, as well as in wave intervals of (115\({}^{\circ}\), 155\({}^{\circ}\)) and (205\({}^{\circ}\), 245\({}^{\circ}\)). These operating windows help to reduce operational challenges and enhance the safety of the salvage system. (3) This section examined the maximum tension, safety factor, and relative increase rate of lifting cables at different positions to study the tension responses of the cables. The results revealed that curves depicting the maximum tensions of cables 1 -15 and 16-30 exhibited a \"middle drooping\" shape distribution under almost all the working conditions. The sagging of the curves becomes slower as the cable numbers approach the middle range (7-9, 22-24). The tension values of the lifting cables in the P1 stage are higher than those of the lifting cables in the other two stages. The tension response was the most severe under wave action in the 180\({}^{\circ}\) direction. Under the influence of waves in the 90\({}^{\circ}\) direction, the tension of the lifting cables showed the smallest response and the best safety performance. (4) General conclusions can be derived by combining the above findings and conducting a comprehensive study of the motion responses of the three ships and the tension responses of the lifting cables. Waves in the 90\({}^{\circ}\) and 180\({}^{\circ}\) directions exhibit distinct characteristics. This uniqueness is particularly evident in the roll and pitch responses depicted in Figure 12. Regarding the tension response of the lifting cables, the response is the smallest when waves act in the 90\({}^{\circ}\) direction, while it is the most severe under the wave action in the 180\({}^{\circ}\) direction. Additionally, only the heave response amplitude decreases in the P3 phase, while the amplitudes of the other 5 DOFs increase. Hence, we can tentatively conclude that the heave response determines the total value of the lifting-cables' tension, and the roll and pitch responses determine the discrete degree of tension distribution in the lifting cables. (5) To enhance the safety of the three ships in salvage operations, the adjacent areas of waves at 0\({}^{\circ}\) and 180\({}^{\circ}\) can be selected as operating windows. Similarly, the wave intervalsof (115\({}^{\circ}\), 155\({}^{\circ}\)) and (205\({}^{\circ}\), 245\({}^{\circ}\)) are viable options. It is worth noting that the former offers narrower operating windows, whereas the latter provides broader operating windows.