## 5 Results and Discussion
### Trim Polygon  
Similar to the arrangement of a submarine, the SFRM ought to have several types of ballast tanks. The main ballast tanks are designed for diving and surfacing, whereas the trimming tanks are used for adjusting the submarine's attitude on the surface or underwater. Due to the limitation of the compartment space in the scale model, the trimming tanks were replaced by the attitude adjusting system without water compensation. Specifically, the design of the attitude adjusting system is a slider mechanism device installed in the midsection for adjusting the trim angle. Figure 9 presents the time series of the mass changes in the forward and aft ballast tanks, respectively. Both the inflow and outflow rates were given as 20 cm\({}^{3}\)/s during the periods of 20 to 50 s and 70 to 100 s. Figure 10 exhibits the time series of the corresponding pitch angles in the forward and aft ballast tanks, respectively. Apparently, the maximum pitch angle of the SFRM reached \(-8^{\circ}\) when the forward ballast tank was full. There were some oscillations accompanied by the variation of the pitch angle. For the aft ballast tank, by using the same mass-variation history of the forward ballast tank, the maximum pitch angle of the SFRM reached \(5^{\circ}\) with slight oscillations. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Test** & **Purpose** & **Measured Parameters** \\ \hline \multirow{3}{*}{Trim Polygon} & Determine all the possible changes & \\  & in SFRM’s mass and & Mass and trimming moment \\  & longitudinal CG & \\ \hline \multirow{3}{*}{Turning Circle} & Determine steady turning & Advance, transfer, \\  & performance & and tactical diameter \\ \hline \multirow{3}{*}{Horizontal Zigzag} & Demonstrate course-varying & Yaw overshoot, width of path \\  & performance in the horizontal plane & overshoot, time at which each \\  & & change of the rudder plane angle is \\  & performance in the horizontal plane & initiated, and time to the maximum \\  & & width excursion \\ \hline \multirow{3}{*}{Spiral} & Determine control authority and & Steady yaw rate for \\  & straight-line stability & each rudder angle \\ \hline \multirow{3}{*}{Vertical Zigzag} & \multirow{3}{*}{Demonstrate depth-varying} & Pitch overshoot, width of depth \\  & & overshoot, time at which each \\ \cline{1-1}  & & change of the stern plane angle is \\ \cline{1-1}  & performance in the vertical plane & initiated, and time to the maximum \\ \cline{1-1}  & & depth excursion \\ \hline \multirow{3}{*}{Meander} & Determine motion stability and & \multirow{3}{*}{Path of the SFRM} \\ \cline{1-1}  & depth keeping performance & \\ \end{tabular}
\end{table} 
Table 4: Standard manoeuvring tests for the SFRM. Figure 11 shows a typical trim polygon (equilibrium polygon), which is useful to assess the arrangement of the SFRM. Definitely, it is crucial to determine whether the ballast tanks and the attitude adjusting system are available to estimate the variation of SFRM's mass and the longitudinal CG. According to the procedure [35], the effects of the ballast tanks and the attitude adjusting system can be plotted as a function of mass and trimming moment as follows:  
In the initial stage, the location with zero mass and zero trimming moment indicated all empty tanks and a zero pitch angle. Move forward the weight of the slider mechanism device. In this stage, there is no mass variation, but there is an increase of trimming moment due to the movement of the longitudinal CG. The forward ballast tank is filled completely. There are increases in mass and trimming moment due to moving forward of the longitudinal CG. The aft ballast tank is filled completely. This is continued until the previous procedure has been completed. There is an increase in mass but a slight decrease in trimming moment due to moving backward of the longitudinal CG. Move the weight of the slider mechanism device to the initial location. There is no change in mass, but there is a slight difference in trimming moment compared with the line in step 1.