## 3 Results and Discussion  
We will start the Results Section by first inspecting some of the time series outputs produced directly by the aeroelastic simulation. Figure 7 shows a short stretch of the time series results obtained for the case of an average wind speed of 9 m/s and a high turbulence intensity. It can be seen that the axial force (rotor thrust) and the in-plane (\"edgewise\") bending moment showed an almost perfectly sinusoidal signal with a period of a little under half a second. By comparison to the power curve, it can be seen that this frequency was consistent with the rotor speed of 130 rpm, expected by design for a wind speed of 9 m/s. The amplitude of the rotor thrust oscillation was only about 5% of the average thrust, which is consistent with the fact that the rotor thrust always created a force in the downward direction, with a minor periodic variation, arising from the fact that the wind speed was higher at the top than at the bottom position. The amplitude of the edgewise oscillations, on the other hand, was almost 100% of the average value. This fact can be qualitatively understood by the observation that at the upper position, the blade sees the highest wind speed (and, consequently, also the highest in-plane force component), at the blade tip where the leverage is the highest, and conversely, the lowest \begin{table}
\begin{tabular}{l l l} \hline \(C_{1a}\) & 1.35 & \\ \(C_{2a}\) & 1.1 & \\ \(C_{3a}\) & 1.2 & \\ \(C_{4a}\) & 1.1 & \\ \hline \(C_{2b}\) & 1.1 & \\ \(C_{3b}\) & 1.0 & \(\frac{\gamma_{Mb}}{C_{ib}}=\gamma_{M0}\prod_{i=2}^{5}C_{ib}=1.9602\) \\ \(C_{5b}\) & 1.2 & \\ \hline \end{tabular}
\end{table} 
Table 4: Calculation of the safety factors. wind speed (and therefore the smallest force) near the root where the leverage is the smallest. At the lower position, on the other hand, the point with the lowest wind speed has the highest leverage whereas the point with the smallest leverage has the highest wind speed. Evidently, this leads to a small in-plane bending moment at the bottom position of the blade and a high bending moment at the top. In any case, no significant difference was observed among the three regulation schemes. Note that the terrain roughness length used in the generation of the stochastic wind field was \(z_{0}=0.01\) m, corresponding to a power law exponent of 0.136. The situation at the out-of-plane or flapwise bending moment, as well as the resulting effective stress, is quite different. Not only were the average values higher for the stall-regulated wind turbine, but also could the presence of strong harmonics be detected, with a much stronger presence of harmonics in the case of stall regulation as compared to both pitch-regulation schemes, which had a nearly identical behavior between them, not unexpectedly, given the very similar regulation characteristics at 9 m/s. After receiving some initial insights from inspecting the time series, it is interesting to study the power spectra. In Figure 8, the primary outputs of the FAST simulation (thrust and bending moments) are shown for all three regulation schemes, again for the case of a 9-m/s wind speed. In the case of the axial force signal, one prominent peak at the primary rotor frequency can be observed, consistent with the almost perfectly sinusoidal signal shown in Figure 7. The situation at the bending moments, however, was quite different, as evidenced by the rich harmonic sequence in both sets of spectra. Whereas the periodicity of the rotor thrust signal can be plausibly interpreted as a result of the different wind speeds at the top and bottom positions of the blade, the periodicity of the bending moments can likely be attributed, at least in part, to the rotational sampling effect described above, which is expected to display a comb of harmonics.