# The Prediction of the Performance of a Twisted Rudder
## 4 Results and Discussions
### Hydrodynamic Performances of Twisted Rudders
Regarding tip cavitation inception, the rudder tip cavitation inception was also detected at the mid-chord of the tip on each inboard surface of both the starboard and port TR-ini and TR-int rudders equipped with a tip end plate at \(\delta_{\rm R}=0^{\circ}\). On the other hand, such cavitation was observed on the TR-fin rudder above \(\delta_{\rm R}=-6^{\circ}\). This  
Figure 15: Pressure distributions along the chord lines on the twisted rudders: (**a**) z/s = 0.4; (**b**) z/s = 0.6; (**c**) z/s = 0.7; (**d**) z/s = 0.9. It is seen in Figure 17 that the outboard surface cavitation begins to occur on each port twisted rudder at \(\delta_{\text{R}}=-8^{\circ}\). The inboard surface cavitation observed on the starboard twisted rudders at \(\delta_{\text{R}}=-6^{\circ}\) is slightly larger at \(\delta_{\text{R}}=-8^{\circ}\), but it is still the smallest on the TR-fin rudder. At the rudder angle of \(\delta_{\text{R}}=-16^{\circ}\), severe surface cavitation is seen on all the rudder models as shown in Figure 18. For the flat rudder, it is seen that most of the outboard surface of the port rudder is covered with cavitation. Additionally, the inboard surface cavitation on the flat rudder started at \(\delta_{\text{R}}=-14^{\circ}\). To compare roughly the amount of the cavitation occurrence between the port rudders, the border line of the surface cavitation of the port flat rudder was overlaid on the outboard surfaces of the port twisted rudders as a dashed line. For the same purpose, the border line of the inboard surface cavitation of the starboard TR-ini rudder was superposed on the starboard TR-int and TR-fin rudders. The outboard surface cavitation on the port twisted rudders is seen to be largely decreased due to the compensation of the effects of the inflow angles. On the other hand, since a starboard twisted rudder at a negative rudder angle is disadvantageous in compensating the inflow angles, the inboard surface cavitation of the starboard twisted rudder can be increased than that on the flat rudder. For the twisted rudders, it is seen that the starboard surface cavitation on the TR-fin rudder is smaller than those on the other two twisted rudders. Therefore, these results show that the occurrence of surface cavitation in the TR-fin rudders on the starboard and port side is the smallest, showing the validity of the prediction and correction of the inflow angle distribution as described in the previous section. The measured and predicted lift and drag forces and moment for the three twisted rudders at 30 knots and cavitating flow conditions are shown in Figure 19. As discussed for the results of the flat rudder in Section 4.1.3, the current numerical results for the twisted rudders show also a qualitatively good agreement with the experimental data. The minimum drag coefficients of each twisted rudder on the starboard and port side were found to be larger than that of the flat rudder at \(\delta_{\text{R}}=0^{\circ}\) shown in Table 2.0 In Figure 19a,d,g, the minimum positions are seen to be approximately \(\delta_{\text{R}}=\pm 7^{\circ}\), \(\pm 6^{\circ}\) and \(\pm 5^{\circ}\) for the TR-ini, TR-int, and TR-fin rudders, respectively. When considering the total drag of the starboard and port rudders, the total drag coefficients for the twin TR-ini and TR-int rudders were larger than that of the twin flat rudder in the current whole rudder angle range. In the numerical analysis, the total drag coefficient of the twin TR-fin rudders was smaller than that of the twin flat rudder above about \(\delta_{\text{R}}=\pm 6^{\circ}\), although this range was different from the experimental range of \(\delta_{\text{R}}=\pm 4^{\circ}\)\(\sim\)\(\pm 12^{\circ}\). With regard to the effect of the twist angles on rudder lift force, it is seen that each rudder lift force according to the rudder angle on the starboard and port side is almost similar for the TR-fin twisted rudder accounting for a relatively accurate inflow angle distribution as seen in Figure 19b,e,h.