# Performance Improvement in a Wavy Twisted Rudder by Alignment of the Wave Peak
## 3 Results and Discussion
### Rudder Force Results
#### 3.3.1 Model Test Results  
A model test was conducted to evaluate components of rudder performance, such as lift, drag, and torque, based on variations in the rudder angle at a design speed of 24 knots (equivalent model speed: 1.964 m/s). To determine the stall point, a model test was conducted with a large rudder angle. The results from the conventional twisted rudder (TR) [25] are also indicated in the present comparison with the results from the WTR and AWTR. Table 10 lists the measurement range of the rudder angle.  
Figure 11: Wake distribution of the WTR and AWTR: (**a**) WTR; (**b**) AWTR.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Knots**} & \multirow{2}{*}{**Case**} & \multicolumn{3}{c}{**n\({}_{\text{M}}\) (RPS)**} & \multicolumn{3}{c}{**Q\({}_{\text{M}}\) (Nm)**} & \multicolumn{3}{c}{**2\(\pi\)m\({}_{\text{M}}\)Q\({}_{\text{M}}\) (W)**} \\ \cline{3-10}  & & **WTR** & **AWTR** & **Diff. (\%)** & **WTR** & **AWTR** & **Diff. (\%)** & **WTR** & **AWTR** & **Diff. (\%)** \\ \hline
23 & Model test & 10.334 & 10.314 & \(-\)0.19 & 1.048 & 1.047 & \(-\)0.10 & 68.047 & 67.851 & \(-\)0.29 \\  & Model test & 10.882 & 10.875 & \(-\)0.09 & 1.166 & 1.163 & \(-\)0.26 & 79.724 & 79.445 & \(-\)0.35 \\
24 & CFD & 10.866 & 10.831 & \(-\)0.32 & 1.182 & 1.182 & 0.00 & 80.699 & 80.439 & \(-\)0.32 \\  & Diff. (\%) & 0.147 & 0.379 & - & \(-\)1.354 & \(-\)1.607 & - & \(-\)1.235 & \(-\)1.235 & - \\
25 & Model test & 11.480 & 11.453 & \(-\)0.24 & 1.290 & 1.289 & \(-\)0.08 & 93.049 & 92.758 & \(-\)0.31 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Comparison of delivered horsepower at model scale.  
Figure 13 displays the experimental results of the lift based on the rudder angles in the portside and starboard directions. No significant difference existed between the WTR and TR, except for the earliest stall point in the portside turn of the TR, compared to the WTR in a previous study [18]. Although the alignment quantity was not large in the AWTR, the lift of the AWTR and the stall point were greater than those of the other rudders. This discrepancy increased at large angles, which is discussed in the comparison of streamlines at the end of this section. The values of the lift and stall point differed between the starboard and portside in all cases because the portion of the wavy area from the bottom to the center and from the center to the top differed. If this is a problem in an actual scenario, the design should be improved in terms of maneuverability, which could be an area of focus for future study [10].  
Figures 14 and 15 display the drag and torque values, where a greater discrepancy is found between the TR and the other rudders (AWTR and WTR). The AWTR had the lowest torque and drag values. The drag and torque of the twisted rudder increased owing to the top and bottom twisted sections. In particular, there was a significant difference in the stall point in both directions. The drag is an essential parameter in resistance; that is, the energy-saving point and torque are important to the capacity of the steering system, which is closely related to the initial investment. The smooth fairing of the twisting central part of the rudder [10], shown in Figure 8, could reduce the torque and drag to less than those of the conventional twisted rudder.  
Figure 16 displays the lift-to-drag ratios of the two rudders obtained from the model tests on the portside and starboard turns, respectively. The AWTR had a superior lift-to-drag ratio because of the bulb effect of the third wave peak. As shown in Figure 16, the lift-to-drag ratio of the AWTR was greater than that of both the TR and WTR, which means that the presently developed AWTR has superior performance compared to the other rudders, because the lift-to-drag ratio is equivalent to the efficiency.