# The Prediction of the Performance of a Twisted Rudder
## 4 Results and Discussions
### Prediction and Correction of Twist Angles  
The predicted instantaneous axial and transverse velocity distributions on the longitudinal plane passing the nose-tail line of the port flat rudder at \(\delta_{\text{R}}=0^{\circ}\) and 30-knot ship speed are shown in Figure 7. Excluding the region below the rudder, it is seen that the accelerated axial flow occupies about 50-100% region of the span from the root. The flow velocities decreased near the leading edge due to the influence of the wall boundary condition. In the same region, due to the propeller rotation, the distribution of the relatively large transverse velocity is seen to be in the negative y-direction, which means the port rudder will have negative inflow angles along the span direction at \(\delta_{\text{R}}=0^{\circ}\). These results roughly show where the onset flow angles induced by the propeller will be significant. Figure 8a,b show the time-averaged distributions of axial and transverse velocity components, respectively, in front of the rudder at \(\delta_{\text{R}}=0^{\circ}\) on the same plane shown in Figure 7. The profiles of the axial and transverse velocities along an inclined line parallel to the leading edge of the rudder between the propeller and rudder are shown in Figure 8c. The rudder span region where the inflow angle is significant is shown to be clearer. The location of the maximum inflow angle was detected in the region of \(z\)/s = 0.6\(-\)0.8, where the magnitudes of the axial and transverse velocities are larger than their surroundings within the rudder span. The profiles of the velocity components compared with the relative positions of the propeller and rudder seen in Figure 8c show the magnitudes of each inflow velocity component entering the rudder placed behind the wake of the propeller. The humps in the velocity profiles over the rudder region were due to the effects of the accelerated and rotating flow caused in the upper half of the propeller. Figure 6: Measured and numerically predicted rudder forces and moment for the twin flat rudders: (**a**) lift force; (**b**) drag force; (**c**) moment. Figure 7: Instantaneous axial and transverse velocity distributions on the longitudinal plane passing the nose-tail line of the port side flat rudder at \(\delta_{\text{R}}=0^{\circ}\)and 26 knot ship speed: (**a**) axial velocity distribution; (**b**) transverse velocity distribution. Figure 9 shows a transverse plane between the propeller and the rudder aligned with the inclined leading edge of the flat rudder keeping a distance of \(0.26D_{P}\) in which velocity distributions of the axial and transverse components were measured to obtain the inflow angles. Figure 10 shows the numerically predicted flow angle distribution on the measurement plane shown in Figure 9. Due to the propeller rotation, the onset flow angle has opposite  
Figure 8: Time-averaged distributions of axial and transverse velocity components and the profiles of those two velocities in front of the leading edge of the flat rudder: (**a**) axial velocity distribution; (**b**) transverse velocity distribution; (**c**) axial and transverse velocity profiles. Figure 9: Measurement plane location in which inflow angles were predicted using the axial and transverse velocities. signs at the upper and lower propeller planes as seen in Figure 10a. The maximum inflow angles with opposite signs were observed around the radius of \(0.56R_{\rm P}\) in the 7 o'clock and 1 o'clock positions, respectively. The predicted inflow angles along the rudder span direction for the rudder angle range of \(\delta_{\rm R}\) = \(-16^{\circ}\)-\(16^{\circ}\) are shown in Figure 10b. The distribution of the inflow angles along the rudder span direction is in the range of \(0^{\circ}\)-\(11^{\circ}\) for the rudder angle of \(\delta_{\rm R}\) = \(0^{\circ}\). The range of the maximum inflow angle experienced by the rudder at the rudder angle range of \(\delta_{\rm R}\) = \(-16^{\circ}\)-\(16^{\circ}\) corresponds to about \(5^{\circ}\)-\(15^{\circ}\).