## 4 Results for the Stick Model Dynamic Load Computation  
This section presents the results for the three different aircraft configurations considered: the baseline aircraft with a cantilevered wing (CNT), the same aircraft equipped with the SOF controller (SOF), and the aircraft with a modified structure to accommodate the flared FWT (FWT). The results, shown in Figure 4, are presented as dynamic load envelopes at the wing root, which is the area subject to the highest loads.  
Compared with the baseline aircraft, both the active controller and the folding wing tip reduce the dynamic load envelope, with the SOF controller providing a more effective reduction in wing root torsional moments (WRTMs). The load reduction quantification is presented in Table 2.  
Figure 4: Bending and torsional moment envelope at the wing root for the three models.  
Both the SOF controller and FWT reduce the wing root bending moment (WRBM) by 15%, while only the SOF controller significantly reduces the wing root torsional moment (WRTM). Physically, FWT reduces the bending moment associated with the outboard wing section, but its impact on the torsional moment is limited, despite the flare angle, creating bending-torsion coupling. In contrast, the aileron deflection generates a counteracting force at the wing tips, associated with a torque caused by the shift of the aerodynamic pressure center in the chord-wise direction. This mechanism enables the SOF controller to effectively reduce the WRTM as well. The optimization of the baseline aircraft ensures that the model is flutter-free across the flight envelope. For the actively controlled aircraft, stability is guaranteed by constraints imposed during SOF tuning, which require the real part of the closed-loop eigenvalues to remain negative. To assess the aeroelastic stability of FWT, a dedicated flutter analysis was performed, and the results, presented as a V-f and V-g plot, are shown in Figure 5.  
From the comparison of the V-g diagrams for the CNT and FWT configurations, the FWT solution shows a reduction in the damping of the first wing bending mode between 160 m/s and 220 m/s. However, aeroelastic stability is maintained. To assess the impact on the loads, the transfer function (TF) between the gust input and WRBM was analyzed and compared to that of the CNT aircraft, as shown in Figure 6.  
At the frequency corresponding to the first wing bending mode, FWT shows a narrower and higher peak in the transfer function, reflecting the reduced damping observed in the V-g plots. Although FWT's transfer function peak is higher, the dynamic load envelope is still reduced. This is because the input is not a single-tone harmonic but a signal with a broader frequency content. The time response to three gust gradients--namely, the minimum (H = 9 m), the maximum (H = 107 m), and the one tuned to the first wing bending mode (H = 58 m)--is shown in Figure 7, comparing FWT with the CNT configuration. The flight condition is at an altitude of z = 8000 m and a true airspeed of \(V_{TAS}=229\) m/s,  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Configuration** & **WRBM** & **WRTM** \\ \hline SOF & \(-16.1\%\) & \(-13.2\%\) \\ FWT & \(-14.9\%\) & \(-1.4\%\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Dynamic load envelope reduction with respect to the baseline aircraft.  
Figure 5: V-g and V-f plots at z = 8000 m.  
which corresponds to the point of lowest damping, as indicated in the V-g plot in Figure 5. From now on, this flight condition will be used in all future analyses, as it has proven to be the most critical in terms of internal forces.  
For all three gust cases considered, the peak WRBM value is reduced with FWT. However, for the tuned gust, there are persistent oscillations over time, which are associated with the reduced damping. This behavior could pose a concern for the fatigue life of the components and must be carefully considered when designing the wing's fatigue durability.