## 3 Results
### Stability  
The differences in aerodynamic stiffness and damping also impact the stability behavior regarding whirl flutter. As Figure 2 already points out, some derivatives have a stabilizing effect, and some, a destabilizing effect. A general over-prediction of the aerodynamic loads (as seen, e.g., in the [PERSON] method), therefore, does not necessarily yield a more stable or unstable system. Slight differences in a derivative with high sensitivity change the results more significantly than differences in others with lower sensitivity. The impact of the aerodynamic methods on stability is explored in this part of the paper. For this, the full frequency-dependent transfer matrices are used and not their linearization. The stability of the system is compared using stability maps as introduced in Figure 1b. For analyzing stability, pole fitting of the coupled system frequency response function is used to obtain the frequency and damping values of the coupled system; see [PERSON] [26]. Finally, a comparison of the different aerodynamic methods is made for different trim conditions and distances between pivot point and propeller hub. Figure 10: Comparison of the linearized derivatives. The dashed horizontal line marks the reference derivatives from the Houbolt/Reed method. Figure 11 shows the full stability maps for the different aerodynamic methods, evaluated with different pylon lengths for operating point \(C_{T}=0,\ V=V_{D}\) from Table 3. Clearly visible is the most critical condition at equal pivot frequency (i.e., stiffness). The stability boundaries with aerodynamics according to the Houbolt/Reed method (black dashed line) are always smaller than the ones from the quasi-steady Houbolt/Reed method (grey dashed line). The mid-fidelity methods, including UPM, DUST-Panel and DUST-UVLM, have similar stability predictions and always lie between the standard and the quasi-steady Houbolt/Reed methods. The boundary with the DUST-LL method is, in contrast to the other mid-fidelity methods, always more conservative (i.e., less stable). It should be emphasized that the analytical Houbolt/Reed method is always less conservative than all mid-fidelity methods. Comparing the boundary obtained with the [PERSON] method with the mid-fidelity codes, it can be seen that [PERSON] often gives more stable predictions, despite having a larger destabilizing term (i.e., \(C_{n\theta}\); compare Figure 2). This is because all terms in the [PERSON] method are over-predicted, including the stabilizing ones, resulting in a cancellation effect. The BEM+Wagner method shows similar results as the Houbolt/Reed methods. Although the same transfer matrices are used for the pylon variations, even the order of the methods in terms of stability predictions changes. This highlights the sensitivity of the stability results with respect to individual derivatives and their relative scaling. In the following, this sensitivity is further explored with respect to the three operating points from Table 3. Uncertainty quantification [36] could give further insights into the sensitivities of the stability predictions but is kept for future work to limit the scope of the paper. Figure 11: Comparison of whirl flutter stability map predictions with different aerodynamic methods and for different pylon lengths. For the long pylon, the quasi-steady Houbolt/Reed results are outside the range at higher frequencies (5.5 Hz for equal stiffness). As already mentioned, for a better comparison of different methods and configurations, the requirement of equal pivot stiffness in pitch and yaw for aeroelastic stability is taken as a measure and normalized with the Houbolt/Reed predictions according to Equation (10). Again, values larger than 0 indicate a more unstable stability prediction than Houbolt/Reed, with smaller values representing a more stable prediction. The comparison is shown in Figure 12 for the three different pylon lengths (columns) and operating points (rows).