## 4 Results
### Helicopter Main Rotor Results
#### 4.2.2 Harmonic Analysis at Low, Medium, and High Flight Speed Cases  
As stated in Section 4.2.1, computational simulations over-predict the mean value of the lead-lag moment at the low speed case. In Table 12, it is shown that this difference is about 17% both for the LL and AL results. However, in the medium and high flight speed, the predicted mean values are within the scatter zone of the measurements of the different blades. The corresponding deflections in Table 13 show a \(\approx\)1% difference. This is consistent in all three flight speeds and is totally in line with the comments made in the previous section. The mean value of the flapwise bending moment is fairly predicted by the two aerodynamic models at 12.3 and 50.5 m/s, whereas an over-estimation of about 1.5 Nm is observed at 69.6 m/s. This difference may seem large (\(\approx\)60%), however it is smaller than the maximum difference of \(\approx\)2.5 Nm between different blades measurements. As far as  
Figure 41: Forward flight at 12.3 m/s, case 983. Torsion angle at \(r/R=0.99\). Figure 40: Forward flight at 12.3 m/s, case 851. Twisting moment at \(r/R=0.332\). the flapwise deflection is concerned, the computational results consistently predict slightly higher mean values at all flight speeds with a maximum difference of \(\approx\)0.4% at 69.9 m/s. Finally, the simulations predict slightly smaller absolute mean values of the twisting moment at all the assessed cases. This difference increases with the flight speed up to 13% at 69.6 m/s. On the other hand, very good agreement is achieved in the tip torsion angle, where a maximum difference of \(\approx\)0.15\({}^{\circ}\) is noted at 50.9 m/s. Both in cases where the predicted values are close to the measured ones and in cases where discrepancies are noted, AL and LL seem to be in good agreement with each other. Fourier analysis is performed on loads. Similar conclusions with respect to the harmonic content are expected to be drawn for deflections. In Figure 42, the amplitude of the \(1/rev\), \(2/rev\), and \(4/rev\) variations are shown for the lead-lag bending moment. These are the highest excited harmonics of the lead lag moment. Both \(1/rev\) and \(2/rev\) amplitudes are fairly predicted by the computational tools, except from a difference in the \(1/rev\) amplitude at 50 m/s (\(\approx\)15% of the mean value) and the \(2/rev\) amplitude at 70 m/s (\(\approx\)6.5% of the mean value for the LL and \(\approx\)5% for the AL). The \(4/rev\) harmonic exhibits much higher amplitudes as compared to predictions. This is attributed to a possible miss-match of the 2 nd lead-lag mode of the wind tunnel model with respect to the design value. The corresponding frequency approaches \(4/rev\) in the test, which explains its high excitation. The 2 nd lead-lag frequency is predicted at 91.58 Hz by the computational structural beam model, well apart from the \(4/rev\) (70 Hz) and close to the design value. This explains the low excitation of the \(4/rev\) in predictions. Better agreement is shown in the phase calculations (Figure 43) where a maximum phase shift is observed in the \(4/rev\) at the high speed case (\(70^{\circ}\) for the LL results and \(110^{\circ}\) for the AL). The flapwise bending moment amplitudes (Figure 44) are generally predicted consistently in the simulations. However, in \(3/rev\) harmonic frequency, a maximum phase shift of \(120^{\circ}\) is seen at the medium flight speed in the LL results and \(110^{\circ}\) at the high flight speed in the AL results (see Figure 45).