## 5 Results
### The Effect of Directions of Waves on the Salvage System
#### 5.2.2 The Effect of Directions of Waves on the Tension of Lifting Cables  
The preceding discussion pertains to examining the motion responses of the three vessels during the salvage operation of a shipweck. Apart from assessing the motion response, it is necessary to evaluate cables' tension responses by calculating the safety factor. In the salvage process, [PERSON] [39] defined the minimum safety factor for lifting cables as 1.67. Figure 15 illustrates the lifting cables' maximum tensions and safety factors under the influence of waves from different directions. Figure 15 illustrates the distribution, with the x-axis depicting various wave directions and the y-axis indicating the number of lifting cables. Cables 1-15 correspond to lifting-barge A, while cables 16-30 represent lifting-barge B. The three stages of the shipweck's ascending process are denoted as P1, P2, and P3. The graph's lowest layer displays the safety factor, which represents the minimum safety factor of the lifting cables during stages P1, P2, and P3 under the influence of waves from the same direction. The maximum  
Figure 15: Maximum tensions and safety factors of lifting cables under the action of waves from different directions. tension of the lifting cables reaches 7.72 \(\times\) 10\({}^{6}\) N, resulting in a safety factor 1.79, which satisfies safety standards. In the P1 stage, lifting the shipwck from the seabed requires overcoming both its weight and the resistance posed by the seabed sediment. Consequently, the cable tension in the P1 stage surpasses those in the P2 and P3 stages. Additionally, examining the tension distribution reveals that because the shipwck's center of gravity favors lifting-barge A, cables 1-15 are under higher tension than cables 16-30. The tension in both cable groups displays a \"middle drooping\" pattern. For a more comprehensive tension analysis, Figure 16 illustrates the maximum cable tension values in all three stages under waves from diverse directions. In Figure 16, different colors distinguish stages P1, P2, and P3, and the maximum tension values during these stages are plotted in the background. The light-red curve represents this mapping. As shown in Figure 16, most curves depicting the maximum tension of cables 1-15 and 16-30 exhibit a \"middle drooping\" pattern. Furthermore, the sagging of the curves slows as the cable numbers approach the middle range (7-9, 22-24). Figure 16: Maximum values of cable tension in P1, P2, P3 stages under the action of waves in different directions: (**a**) 180\({}^{\circ}\); (**b**) 155\({}^{\circ}\); (**c**) 135\({}^{\circ}\); (**d**) 115\({}^{\circ}\); (**e**) 90\({}^{\circ}\). For example, comparing cable No. 15 in the 180\({}^{\circ}\) P1 stage with cable No. 7, the maximum tension of cable No. 15 is 7.04 \(\times\) 10\({}^{6}\), whereas cable No. 7 has a maximum tension of 4.45 \(\times\) 10\({}^{6}\). The maximum tension of cable No. 15 is 1.45 times higher than that of cable No. 7, indicating that cables at the bow and stern ends of the lifting barge have higher tension values and fluctuations than those in the middle. This highlights the need for reinforcement at these cable points. The numerical simulation in this paper encompasses the P1, P2, and P3 stages with waves from five different directions, totaling 15 working conditions. Under nearly all the conditions, the maximum tension values of cables 1-15 and 16-30 exhibit a \"middle drooping\" distribution. However, the maximum tension of lifting cables 1-15 in the P1 stage under waves from the 90\({}^{\circ}\) direction is an exception. As the cable number increases, the tension gradually increases, deviating from the \"middle drooping\" distribution. This phenomenon is attributed to various factors. First, as is evident from Figure 16, as the wave direction decreases from 180\({}^{\circ}\) to 90\({}^{\circ}\), the cable tension significantly decreases. Under waves from the 90\({}^{\circ}\) direction, the cable tension is reduced, which minimizes differences among cable tensions.