# Motion Response of the Submersible Underwater Towed System as Cable Length Changes
## 4 Results and Discussion
### Composite Maneuvering Motion
#### 4.2.1 Accelerated Motion
Due to the influence of these two factors,  
Figure 8: The motion response history of the towed system for different cable deployment speeds during the accelerated 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 9: The motion response history of the towed system for different cable retraction speeds during the accelerated 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. the maximum tension of the towed cable reaches its maximum at this moment. When performing the retraction maneuver, the maximum tension in the towed cable gradually increased as the speed of the cable length change increased. The maximum tension was about 3.6 kN at 0.8 m/s and increased to about 4.2 kN as the speed increased to 1.2 m/s. The tension in the towed cable is caused by a combination of gravity, buoyancy, inertial forces, current resistance, and the forces of retraction and deployment. This tension increases as the speed of the submersible and the rate of change in the length of the towed cable increase. Figure 10b displays the variations in depth of the towed body after different retraction and deployment maneuvers at the conclusion of the towed cable maneuver. In the deployment maneuver, the depth of the towed body increased significantly as the deployment speed increased from 0.8 m/s to 1.2 m/s, with the depth change increasing from about 50 m to about 150 m. During the retraction maneuver, the alteration in speed has a minimal impact on the depth of the towed body, which remains relatively constant at approximately \(-150\) m.  
To ensure the accuracy and suitability of the conclusions, it is important to examine the system's motion response under various structural parameters. The influence of the underwater towed system on motion response in a submersible comes from three sources: the submersible, the towed cable, and the towed body. The submersible's motion serves as the propulsion for the towed system. The towed cable's mass per unit length and diameter jointly control its gravity and buoyancy. In order to account for the various designs of towed bodies that are tailored to distinct mission requirements, it is necessary to consider varying drag coefficients and added mass coefficients, in addition to the effects of gravity and buoyancy on the towed body. As shown in Table 3, the ranges of values of motion and structural parameters for the retraction and deployment maneuvers during the accelerated motion of the towed cable system. The drag coefficient of a towed body in an underwater towed system usually ranges from 0.6 to 1.5 [29], while the added mass coefficient normally falls between 0.5 and 2.0 [30]. Figure 10: The motion response values of the towed system when the rate of change of the length of the towed cable varies during the accelerated motion of the submersible. (**a**) The maximum tension of the towed cable; (**b**) The difference in depth variation of the towed body. Figure 11 displays the motion response values of the towed system for different parameters as the submersible is accelerated and the cable length is changed. The lower the maximum tension in the towed cable and the closer the depth of the towed body is to 0 m, the better the safety and motion stability of the towed system. Figure 11a shows that the maximum tension values during the retraction and deployment of the submarine are 3.71 kN and 3.65 kN, respectively, when the acceleration time is 600 s. These values are considerably lower than the corresponding values for other acceleration times. The reason for this is that as the acceleration time increases, the acceleration of the submersible decreases, resulting in a decrease in both inertial force and current resistance.