# Performance Improvement in a Wavy Twisted Rudder by Alignment of the Wave Peak
## 3 Results and Discussion
### Rudder Force Results
#### 3.3.2 Comparison of Numerical and Experimental Rudder Force Results  
Figure 17 displays the lift obtained from the numerical analyses and model tests. On both the portside and starboard turns, the lift distributions for the AWTR were greater than those for the WTR in both the model test and the numerical analyses.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Rudder** & **Starboard Turn** & **Portside Turn** & **Model Ship** \\  & **Angle Range** & **Angle Range** & **Speed (m/s)** \\ \hline Twisted rudder & 5–40\({}^{\circ}\), every 5\({}^{\circ}\) & 5–40\({}^{\circ}\), every 5\({}^{\circ}\) & \\ Wavy twisted rudder (WTR) & 5–40\({}^{\circ}\), every 5\({}^{\circ}\) & 5–40\({}^{\circ}\), every 5\({}^{\circ}\) & \\ Aligned wavy twisted & 5–45\({}^{\circ}\), every 5\({}^{\circ}\) & 5–40\({}^{\circ}\), every 5\({}^{\circ}\) & \\ rudder (AWTR) & & & \\ \hline \hline \end{tabular}
\end{table}
Table 10: Measurement range of the rudder angle.  
Figure 12: Rudder-induced forces and the definition of rudder direction.  
Figure 14: Experimental results for drag: (**a**) starboard turn; (**b**) portside turn.  
Figure 13: Experimental results for lift: (**a**) starboard turn; (**b**) portside turn.  
Figure 15: Experimental results for torque: (**a**) starboard turn; (**b**) portside turn.  
The stall point of the AWTR was approximately \(5^{\circ}\) greater than that of the WTR in both directions, and the CFD numerical result of the stall point was approximately \(5^{\circ}\) greater than the experimental result in both directions. Although quantitative discrepancies exist between the experimental and numerical results, the results are qualitatively consistent.  
Figures 18 and 19 display a comparison of the drag and torque of the AWTR and WTR obtained from the numerical analyses and the model tests based on the rudder angles. At a low rudder angle, the difference in drag and torque between the WTR and AWTR was insignificant, whereas the drag and torque of the AWTR were somewhat less than those of the WTR owing to the increase in the rudder angle in both directions.  
The lift-to-drag ratios of the two rudders (AWTR and WTR) are displayed in Figure 20. The results demonstrate a similar trend. There could be a difference between the model test and the CFD computation because there was a laminar region in the model, whereas the turbulent model was applied to the entire region in CFD. Although there was a difference in the quantitative value between the experiment and CFD, the comparison of performance between the WTR and AWTR was qualitatively consistent in the experiment and in the CFD.  
Figure 16: Experimental results of lift-to-drag ratio: (**a**) starboard turn; (**b**) portside turn.  
Figure 17: Comparison of numerical and experimental results for lift: (**a**) starboard turn; (**b**) portside turn.  
Figure 19: Comparison of numerical and experimental results for torque: (**a**) starboard turn; (**b**) portside turn.  
Figure 20: Comparison of numerical and experimental results for lift to drag ratio: (**a**) starboard turn; (**b**) portside turn.  
With a wavy configuration of the rudder, a streamwise vortex was generated using the pressure and speed differences at the location of the vortex. Energy was continuously supplied such that the flow could overcome the frictional force on the surface. The numerical results demonstrate an acceptable overall agreement with the experimental results, qualitatively. In the case of a special rudder-like flap rudder, the section of the rudder is larger than that of a merchant ship, whereas the present aligned twisted rudder has virtually the same rudder section as a merchant ship, which leads to high efficiency. Another important merit is the high lift due to the delay of the stall compared with a conventional rudder, as shown in Figure 16. In addition, there are no complicated moving parts as in a flap rudder, implying easy installation, maintenance, and handling; accordingly, cavitation performance is another advantage of an aligned twisted rudder.