# Study on the Mechanism of the Variable-Speed Rotor Affecting Rotor Aerodynamic Performance
## 4 Results and Discussion
It can be observed that they have indiscernible aerodynamic characteristics, although with different rotor speeds, that is to say different required powers. The indiscernible aerodynamic characteristics imply that the variable-speed rotor is within a linear aerodynamic region and reduces its required power through a reduction in dynamic pressure. A group of high flight speed cases is implemented. The take-off weights, rotor speed computation points and blade loadings remain the same as in low flight speed cases, and the flight speeds and advance ratios are doubled. The dimensionless parameters and true flight parameters are listed in Table 3.  
Figures 9-11 respectively depict the time history of airfoil AoA, the lift coefficient, \(C_{L}\), and the drag coefficient, \(C_{D}\), with respect to the azimuth, for the three kinds of high flight speed cases. It is found that the prominent drag coefficient appears at the tip of the advancing blade when the rotor speed is high. As the rotor speed decreases, the drag coefficient at the tip of the advancing blade decreases significantly. This implies that during a fast flight, the variable-speed rotor reduces the blade tip compression loss and improves the rotor aerodynamic performance by lowering its rotor speed. That is to say, the dynamic pressure and advancing blade tip compression reductions both contribute to a reduction in the required power for the variable-speed rotor. It is noticed that the three kinds of fast flight cases provided the same advance ratio and blade loading; however, significantly different aerodynamic characteristics were observed. The difference indicates that the variable-speed rotor works within a non-linear aerodynamic region, the non-linearity of which comes from the compression of the advancing blade tip and the dynamic stall of the retreating blade. Figure 10 shows that the region of higher lift coefficient \(C_{L}\) becomes slightly larger as the rotor speed decreases, which means the potential onset of an airfoil dynamic stall. Although the rotor speed is high enough and the blade loading is relatively low, it is not enough to observe the obvious airfoil dynamic stall. \begin{table}
\begin{tabular}{c c c c c} \hline
**Take-Off Weight** & **Advance Ratio** & **Blade Loading** & **Rotor Speed Ratio** & **Flight Speed** \\ \hline
1600 kg & 0.3 & 0.074 & 0.9 & 59 m/s \\
1900 kg & 0.3 & 0.074 & 0.98 & 64 m/s \\
2200 kg & 0.3 & 0.074 & 1.06 & 69 m/s \\ \hline \end{tabular}
\end{table} 
Table 3: Variable-speed rotor in fast flight speed cases. Figure 8: \(\mu=0.15\), drag coefficient, \(C_{D}\), with rotor speed. Figure 9: \(\mu=0.3\), AoA with rotor speed. In hover and slow flight modes, the induced power dominates in the total required rotor power. In Figure 5, the value of the DPL during hover is not sensitive to variation in the rotor speed, which means an increasing \(\eta_{i}\) occurs as rotor speed decreases. From Equation (33), it is known that the induced power is affected by both the value and distribution of the induced inflow and the thrust. If it is assumed that the induced inflow and thrust are uniform, the result given by Equation (33) matches the actuator disc theory. Figure 12 shows the time history of the airfoil coefficient during hover. Considering that, during hover, the value of the airfoil lift coefficients varies as the rotor speed changes, a relative value, \(\Delta C_{L}\), is given by removing the average to allow the effect of distribution on the aerodynamic performance for a variable-speed rotor to be observed. When the rotor speed is low, it is found that the lift coefficients in the advancing blade are high and those in the retreating blade are small, causing a more significant non-uniform distribution than when the rotor speed is high. Therefore, during hover, although a reduced-speed rotor can greatly decrease the dynamic pressure, the rotor required power is not affected.