# Motion Response of the Submersible Underwater Towed System as Cable Length Changes
## 4 Results and Discussion
### Composite Maneuvering Motion
#### 4.2.1 Accelerated Motion
However, the depth of the towed body for the deployment at an acceleration time of 600 s has the largest change of 127 m. From Figure 11b, it is evident that when the buoyancy of the towed body is equivalent to the force of gravity, the maximum tension is minimized, and the depth variation approaches zero meters. When the ratio of buoyancy to gravity of the towed body is 1.0, the maximum tension in the deployment state is 3.67 kN, and the change in depth is 38 m. In the retraction state, the maximum tension is 3.89 kN, and the change in depth is \(-100\) m. It is worth noting that when the ratio of 2.0 is when the deployment of the depth change value is 0, is this an indication of more time to meet the depth change value of 0 m requirements? The answer is no because when the ratio is 2.0 when the towed body is floating in the water, it does not meet the requirements of the towed body submerged in the water. Figure 11c demonstrates that when the drag coefficient of the towed body decreases, the maximum tension also decreases, and the depth variation value deviates further from 0 m. At a resistance coefficient of 0.6, the maximum tension experienced during deployment is 3.71 kN, while the greatest tension during retraction is 3.01 kN. On the other hand, when the resistance coefficient is 1.5, the depth change during deployment is 90 m, and the maximum tension during retraction is \(-161\) m. According to Figure 11d, the added mass coefficient of the towed body solely impacts the maximum tension during the deployment maneuver. The maximum tension decreases as the added mass coefficient decreases. When the added mass coefficient is 0.5, the maximum tension is 3.90 kN. According to Figure 11e, when the buoyancy force per unit length of the towed cable is equal to gravity, the maximum tension of the cable is at its minimum, and the depth change is closer to 0. The maximum tension at the time of retraction is 4.01 kN, and the value of the depth change is \(-117\) m. The maximum tension at the time of deployment is 3.94 kN, and the value of the depth change is 81 m. This occurs when the buoyancy force per unit length of the towed cable is in equilibrium with the force of gravity, resulting in the cancellation of these two forces. As a result, the pull at the first end of the towed cable is reduced. \begin{table}
\begin{tabular}{c c} \hline
**Motion and Structural Parameters** & **Ranges of Values** \\ \hline Acceleration time/s & 300, 400, 500, 600 \\ Buoyancy-to-gravity ratio of towed body & 0.5, 1.0, 1.2, 1.5, 2.0 \\ Drag coefficient in \(x,y,z\) directions of towed body & 0.6, 1.0, 1.3, 1.5 \\ Added mass coefficient in \(x,y,z\) directions of towed body & 0.5, 1.0, 1.5, 2.0 \\ Buoyancy-to-gravity ratio of towed cable & 1.0, 1.3, 1.5, 2.0 \\ \hline \end{tabular}
\end{table} 
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. into two phases: transient and long-periodic steady states. This study aims to analyze the motion response of the towed system during the steady-state period under the towed cable maneuver. The towed cable maneuver is carried out only after the towed system enters steady-state operation, so the towed cable maneuver is chosen to be carried out 3000 s after the start of the simulation. As shown in Figure 12, the variation of towed cable shape during the retraction and deployment maneuver during the rotational motion is plotted. Figure 12a shows the variation of the towed cable shape at a retraction speed of 1.0 m/s. Figure 12a shows the variation of the towed cable shape at the deployment speed of 1.0 m/s. Figures 13 and 14 demonstrate the submersible engaging in cable deployment and retraction actions while executing circular rotational movement. The figures depict variations in towed body motion depth and towed cable tension at varying deployment and retraction speeds.