# Multidisciplinary Aerodynamic Design of a Rotor
## 3 Validation  
An ultra-light helicopter is used as the baseline for the GOE method in this study. The helicopter parameters are listed in Table 1.  
Since there is a lack of wake data, the 2 MRTS wake experiment [19; 20] is adopted to validate the prescribed wake method (PWM) used in this study. The following conditions are implemented in the validation: thrust coefficient \(C_{T}=0.0064\), advance ratio \(\mu=0.15\), and rotor shaft \(\alpha_{s}=-3^{0}\). The induced velocity is computed on a plane one-chord above TPP, the same as the experiment setting. Time-average induced velocity is shown in Figure 3. Comparing with experimental data (EXP) [19] and free vortex method (FVM) [21], it is well understood that the prescribed wake method (PWM) is able to capture the non-uniform distribution of induced velocity, especially in the blade tip region. Slight deviations can be seen in the root region, which may be due to ignoring the root cut-out effect in this study, where root vortices may exist [20]. The strongest downwash presents near the tip for a rotating blade; hence, non-uniform distribution and rotor performance estimation are a major responsibility in induced velocity.  
Figure 4 shows the trim results of the ultra-light helicopter, comparing with UMARC and CAMRAD II results from [PERSON] et al. [22]. With the increase in flight speed, the longitudinal flap coefficient \(\beta_{c}\) increases, providing propulsive force through the tilted TPP. The lateral trim results at present have the same trends as UMARC and CAMRAD II. With an increase in flight speed, a steady deviation of about 1 degree between present simulation and CAMRAD II always exists, the same as in the UMARC result. This may be caused by the inflow model, as [PERSON], [PERSON] and [PERSON] [22] have mentioned. With a high advance ratio, the lateral flap coefficient \(\beta_{s}\) rises more slowly than UMARC, and may benefit from the prescribed wake method. As for rotor power loss, minimal consumption is  
\begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Vehicle Parameters**} \\ \hline Gross weight & 414 kg \\ CG position & 19 mm in front of hub center; \\  & 1285 mm beneath the hub \\ Parasite drag area ratio & 0.0315 \\ \hline \multicolumn{2}{c}{**Rotor Parameters**} \\ \hline Blade number & 2 \\ Rotor type & Teetering; rectangular blade \\ Nominal speed & 525 rpm \\ Rotor diameter & 7010 mm \\ Chord length & 170 mm \\ Twist angle & \(-8\) deg \\ Pre-cone angle & 3 deg \\ Shaft tilt & 3 deg \\ Solidity & 0.0309 \\ Lock number & 5.01 \\ Airfoil & Boeing VR-7 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Main parameters of an ultra-light helicopter.  
Figure 3: Induced velocity on TPP for the wake measurement experiment. PWM expresses the present prescribed wake method; FVM expresses the free-vortex method referred to Bhagwat [21]; EXP is the experimental data [19].  
achieved with the medium advance ratio, due to a reduction of induced power \(P_{i}\) and an increase of profile power \(P_{o}\) as flight speed rises. With flight speed increases, \(P_{i}\) is lower than in hover, which is because there is more mass flux contributed by freestream in forward flight, a bit of induced inflow can produce adequate thrust for the entire helicopter. Therefore, it can be seen that \(P_{o}\) is larger than \(P_{i}\) in forward flight, and becomes the bottleneck in performance improvement. Figure 5 depicts the time history of \(P_{i}\) and \(P_{o}\) of a blade. In hover, the time histories of both power losses are steady, because of the symmetric aerodynamic environment; whereas in forward flight, \(P_{i}\) reduces from 0-degree azimuth to 180-degree azimuth, and becomes negative when the induced flow is upwash. The larger \(P_{o}\) is consumed near the blade tip, especially in the advancing blade when dynamic pressure is highest. Therefore, a tapered or tip swept blade could be implemented to reduce rotor profile power loss in this study.