# Motion Response of the Submersible Underwater Towed System as Cable Length Changes
## 4 Results and Discussion
### Composite Maneuvering Motion
#### 4.2.1 Accelerated Motion
During the deployment maneuver, the towed body depth change progresses through three distinct phases: linear variation from the start to the end of the maneuver, followed by a reverse linear variation, and finally a transition phase where the depth gradually stabilizes to a long-periodic variation. Shock effects impact the towed cable at the start and finish of the deployment movement. The tension in the towed cable varies significantly, increasing as the line is deployed at a higher rate. The depth of the towed body varies rapidly with the retraction maneuver when the retraction maneuver is performed. At the end of the retraction maneuver, the towed body depth gradually returns to a steady state with long periodic variations. During the retraction maneuver, the towed cable has a shock effect at the start and end of the process. The tension in the towed cable experiences considerable fluctuations at the start and end of the retraction process, with the magnitude of the shift being proportional to the speed of retraction. Comparing the towed body depth change during retraction and deployment reveals that the towed body depth requires more time to stabilize during deployment. Figure 12: Changes in cable shape of the towed cable at a retraction and deployment speed of 1.0 m/s during rotational motion of the submersible. (**a**) Cable shape change of towed cable during retraction; (**b**) Cable shape change of towed cable during deployment. Figure 15 displays the variations in motion response induced by the submersible while executing circular rotating motion and cable retraction and deploying processes. Figure 15a shows the maximum tension of the towed cable during circular rotational motion at different retraction and deployment maneuvering speeds. The maximum tension values for both retraction and deployment were 1.66 kN and 2.39 kN at a rate of variation of 1.2 m/s in cable length. While the maximum tension is reached when the rate of change of cable length is at its peak, the rise in maximum tension does not directly correspond to the increase in the rate of change of cable length. This is due to the fact that the variation of the towed cable tension during the submersible circular rotational motion shows an obvious long periodicity and the time of the maximum tension appearing at different rates of cable length change is not consistent. The maximum tension can be greatly diminished if the alteration in cable length concludes at the minimum point of the tension fluctuation cycle. Figure 15b shows the change in towed cable depth at the completion of a maneuver when retracting and deploying are carried out during the steady condition of circular rotating motion. A higher rate of cable length change during retraction results in a lesser depth change. At a cable retraction speed of 0.8 m/s, the depth change of the towed body is  
Figure 14: The motion response history of the towed system for different cable retraction speeds during the circular rotational motion of the submersible. (**a**) The trend of tension in the towed cable over time; (**b**) The trend of the depth of the towed body over time. Figure 13: The motion response history of the towed system for different cable deployment speeds during the circular rotational motion of the submersible. (**a**) The trend of tension in the towed cable over time; (**b**) The trend of the depth of the towed body over time. \(-148\) m. A higher rate of change in cable length during deployment results in a larger difference in depth. When the cable is deployed at a speed of 1.2 m/s, the depth of the towed body varies by 147 m.  
To examine the impact of various maneuvering and structural parameters on the motion response during circular rotation, the range of parameters used is essentially identical to that specified in Table 3. The \"acceleration time/s\" is replaced by \"rotational speed/kN\", and the value ranges are 2 kN, 4 kN, 6 kN, and 8 kN.