## 3 Results and Discussions
### Uniform Twist Control with Single-Harmonic Inputs  
A parametric sweep of the amplitude and phase angle for the uniform single-harmonic active twist control is performed. Up to 5/rev harmonic inputs were applied. For the 0/rev active twist control, the amplitude of twist rate is varied from \(-1.5^{\circ}\)/m to \(1.5^{\circ}\)/m in the steps of \(0.1^{\circ}\)/m. For the 1-5/rev active twist control, the amplitude is varied from \(0.1^{\circ}\)/m to \(1.5^{\circ}\)/m in steps of \(0.1^{\circ}\)/m, and the phase angle is varied from \(0^{\circ}\) to \(345^{\circ}\) in the steps of \(15^{\circ}\). The pitch angles of the blade elements for the uniform single-harmonic active twist control are defined, as follows:  
\[\theta(r_{B},\psi)=\theta_{0}+\theta_{1c}\cos\psi+\theta_{1s}\sin\psi+r\theta_ {i}\cos(i\psi+\phi_{i}) \tag{6}\]  
where \(\theta_{i}\) is the amplitude of the \(i\)/rev active twist control and \(\phi_{i}\) is the phase angle. In Figure 9 and Table 3, the percentage of rotor power reduction relative to the baseline rotor is shown. For the four selected flight conditions, the 0-3/rev uniform twist control obtains distinct effects. The 0/rev control shows performance gains for larger weight coefficient conditions (2.27% and 3.03% rotor power reduction for condition C and D respectively, \(C_{W}=0.0083\)), while the 1/rev control show benefits for smaller weight coefficient conditions (1.76% and 2.08% rotor power reduction for condition A and B, \(C_{W}=0.0065\)). The 2/rev control shows the most remarkable gains for high-speed flight conditions (4.01% and 5.07% rotor power reductions for condition B and D, respectively, \(\mu=0.35\)). The power reductions using 3/rev control for high-speed flight conditions (1.09% and 0.94% rotor power reductions for condition B and D, respectively, \(\mu=0.35\)) are higher than those that are obtained for cruise flight conditions. Figure 9: Rotor power reduction using uniform twist control with single-harmonic inputs. Figure 10 shows the results of the parametric sweep of amplitude. In a certain range, the rotor power reduction increases when the amplitude of twist rate increases. However, the larger amplitude results in the penalty of power reduction. The optimal amplitudes and phase angles diverge for different harmonic inputs. An analysis of parametric sweep and optimization results reveals similar regularities in the optimal segment control for the four selected conditions. Condition B is used as an example in the subsequent detailed analysis of rotor loads to facilitate the comparative analysis. Figure 11 shows the rotor aerodynamic load distribution of the baseline rotor for condition B, which can explain the limitation of rotor performance. The loads of the rotor disc are shown in terms of the blade sectional lift, drag, induced drag, profile drag, shaft moment, and angle of attack. In the baseline case, due to the difference in dynamic pressure between the advancing side and the retreating side, negative pre-twist, and trim control, there is a large area of negative lift on the advancing side. The lift of the rotor is mainly carried by the front and rear regions of the rotor disc. High induced drag loads appear in the rear region of the rotor disc, while high profile drag loads appear in the tip region on the advancing side. The poor load distribution and drag divergence in the transonic region \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Condition**} & \multicolumn{5}{c}{**Power Reduction**} \\  & **0/rev** & **1/rev** & **2/rev** & **3/rev** & **4/rev** & **5/rev** \\ \hline A & 0.02\% & 1.76\% & 1.40\% & 0.28\% & 0.13\% & 0.0\% \\ B & 0.08\% & 2.08\% & 4.01\% & 1.09\% & 0.51\% & 0.0\% \\ C & 2.27\% & 0.40\% & 1.69\% & 0.19\% & 0.10\% & 0.0\% \\ D & 3.03\% & 0.45\% & 5.07\% & 0.94\% & 0.34\% & 0.0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Rotor power reduction using uniform twist control with single-harmonic inputs. Figure 10: Rotor power reduction of uniform twist control with the 0/rev and single-harmonic inputs.