# The Prediction of the Performance of a Twisted Rudder
## 4 Results and Discussions
### Summary of Twisted Rudder Performances  
One of the important design criteria in the current work in the development of a twisted rudder in this study was an improvement in the cavitation performance compared with that of the reference flat rudder at the reference rudder angle of \(\delta_{\rm R}=15^{\circ}\). At the same reference rudder angle, the maintenance of rudder lift performance which affects the ship's maneuverability, and the reduction of rudder moment applied to the rudder axis were the next important criteria. With respect to the ship's self-propulsion performance, the final thing was to reduce the drag increase of a twin twisted rudder at \(\delta_{\rm R}=0^{\circ}\) up to an appropriate level. Figure 20 shows the hydrodynamic performances of the final designed twisted rudder, TR-fin, related to the cavitation occurrence, forces, and moment. In the numerical analysis, the amount of cavitation was obtained through integration of the cavitation volume, and in  
Figure 19: Measured and numerically predicted rudder forces and moment for the twisted rudders on the starboard and port side: (**a**) drag force for TR-ini; (**b**) lift force for TR-ini; (**c**) moment for TR-ini; (**d**) drag force for TR-int; (**e**) lift force for TR-int; (**f**) moment for TR-int; (**g**) drag force for TR-fin; (**h**) lift force for TR-fin; (**i**) moment for TR-fin. the experiment, it was calculated through image analysis taken from the side and top views of rudder cavitation. The experimental image analysis was done only for the flat and TR-fin rudders. In general, the numerical results were somewhat underestimated compared to the experimental results in each item, but it is seen that the former reflects the experimental trend very well. First, as shown in Figure 20a, the total cavitation amount on the twin TR-fin rudder at \(\delta_{\text{R}}=-15^{\circ}\) was reduced by about 43% and 34.4% in the experiment and numerical prediction, respectively. This is a significant reduction and shows the importance of the accurate prediction of the inflow angles. The computed total cavitation reductions for the twin TR-ini and TR-int rudders were 2.8% and 8.2%, respectively. These values are relatively small, and the reasons can be found in the discussions of Figures 16-18. The predicted total lift forces for each twin twisted rudder at \(\delta_{\text{R}}=-15^{\circ}\) are seen in Figure 20b with that of the twin flat rudder. As discussed in Figure 19, the total lift coefficients for each twin twisted rudder were slightly larger than that of the twin flat rudder by about 6-11% in the measurements and by about 3-11% in the numerical simulations. The measured and predicted total life coefficients were 1.0887 and 0.9429 for the twin TR-fin rudder, respectively, while those values for the twin flat rudder were 1.0319 and 0.9150, respectively. Finally, the twin TR-fin rudder gained about 5.5% and 3% increase in the total lift coefficient in the experiment and numerical simulation, respectively. This implies that the use of twisted rudders will be more effective without a loss of the ship's maneuverability. The maximum moment coefficients for all the twisted rudders are smaller than that of the flat rudder as seen in Figure 20c. The change in the rudder moment according to twist angle distribution was not critical. However, the maximum moment coefficient was the smallest for the TR-fin rudder. As shown in Figure 20c, the decrease in the rudder moment for the TR-fin rudder was 37% and 66.5% in the experiment and numerical simulation, respectively. The total drag forces for all the twin twisted rudders at the rudder angle of \(\delta_{\text{R}}=0^{\circ}\) are relatively larger than that of the twin flat rudder as seen in Figure 20d. It is seen that  
Figure 20: Qualitative comparisons of cavitation occurrence, rudder forces, and moment for the twin flat and twisted rudders: (**a**) cavitation amount; (**b**) total lift force; (**c**) maximum moment; (**d**) total drag force.