## 5 Results
### The Effect of Cables among Three Ships on the Salvage System
#### 5.3.1 The Effect of Cables among Three Ships on Ships' Motion Responses  
Figure 18 illustrates the shipw neck in the P1 stage, with the wave direction set at the classical 180\({}^{\circ}\). Four connecting cables are positioned on the water's surface, sharing the same connection points as the lifting barges but differing in slack lengths. The inclined lifting cable is installed underwater, and the connection points between it and the lifting barges are the same as those in the previous four schemes. There are five schemes in total. To assess these schemes, the increase in the MA of the 6 DOFs serves as an evaluative metric. This assessment visually showcases the motion response of the salvage system after the addition of cables among the ships, with the pre-cable addition working condition serving as the reference. Figure 19 presents the increases in all the DOFs. Figure 18: Schematic diagram of salvaging a shipw in deep water: (**a**) Schemes 1–4 and (**b**) Scheme 5. In Figure 19, the changes in the motion responses of lifting-barge A, lifting-barge B, and shipw C are depicted in light red, light yellow, and light blue, respectively. The black dotted line represents a 0% increase. Adding the inclined lifting cable results in negative changes for the 6 DOFs, with greater reductions observed compared to the four schemes involving connecting cables between the two lifting barges. Regarding the roll motion, the lifting-barge B and shipw C changes are predominantly negative and are particularly pronounced after including the inclined lifting cable. Except for the case of adding 1d connecting cable between the lifting barges, the changes for lifting-barge A in the other four cases are positive. The introduction of connecting cables among the three ships primarily aims to mitigate the significant translational movement of the vessels, resembling a \"pendulum effect\", in the transverse and longitudinal directions during the salvage of shipw in deep water. This constraint is achieved by alternating the tension and slackness of the cables. Although the three ships are constrained, there may be an increase in the turning angle in specific directions. However, such cases are infrequent. In most instances, the growth rate of the 6 DOFs is negative. Concerning the pitch response, apart from a positive increase of 3-10% observed when the inclined lifting cable is added, the changes in the other four solutions range from approximately \(-\)30% to \(-\)5%. Consequently, adding cables among the three boats effectively restrains the pitch motion. Similar conclusions can be drawn for the surge and sway responses, which exhibit negative changes for the three ships--notably, lifting-barge A shows the most significant decrease, ranging from approximately \(-\)30% to \(-\)20%. However, the yaw response is distinct, with negative changes observed only when the inclined lifting cable is added, while the changes in the other four schemes are all positive. This reaffirms the particularity of the salvage system. Similar conclusions can be made for the sway and heave responses. A quantitative evaluation is warranted, given the distinct characteristics of each 6 DOF among the five schemes. Figure 20 illustrates the individual DOF scores for the five schemes, while Figure 21 presents the total score of the 6 DOFs for the five schemes. Figure 19: Increases in the maximum absolute motion amplitudes of 6 DOFs after adding connecting cables among the three ships. The evaluation of the three ships is based on the MA and RMS. Six new samples (\(MA_{a}\), \(MA_{b}\), \(Ma_{c}\), \(RMS_{a}\), \(RMS_{b}\), and \(RMS_{c}\)) are ranked in ascending order based on their magnitudes, with higher rankings indicating higher scores. The score of a single DOF is the sum of these six parameters. With a total of five schemes, each sample is assigned a rank from 1 to 5, resulting in ranking scores ranging from 5 to 1. Considering that the highest score among the five schemes is 5 points and the lowest is 1 point, the middle 3 points serve as the threshold.