## 5 Results and Discussion
### Manoeuvring Tests
#### 5.2.5 Meander Test  
The meander test is similar to the vertical zigzag test, but the only difference is that the angle of the stern plane returns to zero when the desired pitch angle is reached. The main purpose of the meander test is to measure the SFRM's trajectory, motion stability, and ability to remain at a fixed depth. In the simulation, the model sailed straight for 100 s; then, the stern plane was pulled to 20\({}^{\circ}\) immediately, and its position was maintained for 10 s before the stern plane angle was reset to zero. In the meander test, the exact turning time of the stern plane was set to be 1 s.  
Figure 21 illustrates the trajectories in the meander test when the simulated SFRM moved at three different sailing speeds: \(U\) = 0.5, 1, and 1.5 m/s. The SFRM moved farther at high sailing speeds, and a slight vertical pitching motion occurred when the stern plane was reset to zero in the fixed depth test. The depth excursions are 0.051, 0.992, and 2.365 m, corresponding to \(U\) = 0.5, 1, and 1.5 m/s. Moreover, the results of the meander tests indicated that motion stability and depth keeping ability would be unstable for the higher sailing speed by observing the variation of their trajectories.  
Figure 20: 6-DOF velocity components in the vertical zigzag test at different sailing speeds. (**a**) Surge rate: \(u\) [m/s], (**b**) sway rate: \(v\) [m/s], (**c**) heave rate: \(w\) [m/s], (**d**) roll rate: \(p\) [rad/s], (**e**) pitch rate: \(q\) [rad/s], and (**f**) yaw rate: \(r\) [rad/s].  
Figure 22a-c illustrates the time series of the stern plane and pitch angles at different sailing speeds. The simulation results were similar to those of the vertical zigzag test and indicated a high correlation with sailing speed. Figure 22a,b indicates that when \(U=0.5\) and \(1\) m/s, the desired pitch angle could not be reached because of insufficient thrust force. Figure 22c indicates that when \(U=1.5\) m/s, the desired pitch angle was reached. These results were similar to those of the vertical zigzag test, suggesting that changes in pitch angle and ability to remain at a fixed depth have a crucial relationship with sailing speed adjustment. When conducting this test, changes in the vehicle's weight, CG, buoyancy center, and amount of inertia must be considered, and a state of neutral buoyancy must be ensured. Finally, at high speeds, relatively large undulation is likely to be observed in the pitch mode.  
Figure 21: The SFRM’s trajectories in the meander test at different sailing speeds.  
Figure 22: Comparisons of rudder and pitch angles at different sailing speeds. (**a**) \(U=0.5\), (**b**) \(U=1\), and (**c**) \(U=1.5\) m/s.  
Figure 23a-f displays the time series of surge (\(u\)), sway (\(v\)), heave (\(w\)), roll (\(p\)), pitch (\(q\)), and yaw rates (\(r\)) under different sailing speed conditions. Since the meander test is highly similar to the vertical zigzag test, changes of the heave rate in Figure 23c and the pitch rate in Figure 23e were evident. It is obvious in Figure 23b,d,f that the sway, roll, and yaw rates have little variations because the meander test is principally a test of vertical depth-determination ability.  
Figure 23: Time series of 6-DOF velocity components in the meander test. (**a**) Surge rate: \(u\) [m/s], (**b**) sway rate: \(v\) [m/s], (**c**) heave rate: \(w\) [m/s], (**d**) roll rate: \(p\) [rad/s], (**e**) pitch rate: \(q\) [rad/s], and (**f**) yaw rate: \(r\) [rad/s].