# Motion Response of the Submersible Underwater Towed System as Cable Length Changes
## 4 Results and Discussion
### Composite Maneuvering Motion  
#### 4.2.1 Accelerated Motion  
To investigate the impact of various towed cable speeds on motion response during accelerated motion, the towed cable's initial length is 1000 m, the submersible operates  
Figure 4: The course of the motion response of a towed system in circular rotational motion. (**a**) The trend of tension in the towed cable over time; (**b**) The trend of the depth of the towed body over time. Figure 5: Changes in cable shape of the towed cable during acceleration motion of the submersible. Figure 6: Changes in cable shape of the towed cable during circular rotational motion of the submersible. 500 m below the horizontal plane, and the cable speeds are 0.8, 0.9, 1.0, 1.1, and 1.2 m/s. The speed of the retraction and deployment cables is taken from the Zhang literature [20], and this speed satisfies practical engineering applications. The lengths of submersibles under different speeds of towed cable have been adjusted to 500 m, with time and speed range changes matching those in Section 4.1. This study presents the course diagram of motion response during acceleration and the change diagram of motion response during variable speed change cable length. The plot in Figure 7 illustrates the change in shape of the towed cable during the retraction and deployment maneuver while undergoing acceleration. Figure 7a shows the variation of the towed cable shape at a retraction speed of 1.0 m/s. Figure 7b shows the variation of the towed cable shape at the deployment speed of 1.0 m/s. Figures 8 and 9 illustrate the submersible executing cable retraction and deployment actions while in accelerated motion. The course curves of the depth of towed body motion and towed cable tension for different retraction and deployment speeds. As the deployment maneuver increases the length of the towed cable, the depth of the towed body decreases. The faster the deployment speed, the smaller the towed body depth. The depth of the towed body gradually stabilized at \(-336\) m at different deployment speeds at the end of the cable deployment maneuver. The towed cable experiences a large shock impact at the end of the deployment maneuver, leading to a rapid increase in tension. After executing the retraction maneuver, the depth of the towed body increased linearly and eventually stabilized at \(-432\) m. At the moment of the end of the retraction maneuver, the towed cable is significantly affected by the shock effect, and the towed cable tension is then drastically reduced. Figure 7: Changes in cable shape of the towed cable at a retraction and deployment speed of 1.0 m/s during acceleration of the submersible. (**a**) Cable shape change of towed cable during retraction; (**b**) Cable shape change of towed cable during deployment. Figure 10 illustrates the motion response values of the towed system while the submersible undergoes accelerated motion and the rate of change of the cable length of the towed cable is altered. Figure 10a shows the maximum tension on the towed cable at different retraction and deployment maneuvering speeds. When the deployment maneuver is performed, with the increase in the towed cable length change speed from 0.8 m/s to 1.2 m/s, the maximum tension of the towed cable first increases and then slightly decreases, and the maximum tension value appears at 1.0 m/s. There are two primary factors contributing to this phenomenon. Firstly, the submersible generates additional inertial force when performing acceleration maneuvers. Secondly, the length of the towed cable continuously increases during the deployment process, and the tension of the cable increases as the rate of change in cable length increases. Upon completion of the deployment maneuver, the towed cable will abruptly cease its release, resulting in a swift and significant alteration in towed cable tension. When the rate of change of the length of the towed cable is 1.0 m/s, the acceleration maneuvering motion of the submersible terminates at the same time as the deployment maneuver of the towed cable.