## 2 Materials and Methods
### [PERSON]/[PERSON] Method
Airspeed and rotational speed of the propeller are described using the advance ratio (\(J\)). A Prandtl-Glauert Mach-number (\(Ma\)) correction in conjunction with a compressible flow aspect ratio (\(A_{R}\)) correction is used (see the last factor in the integral in Equation (7)). Further, for each blade section, three factors are important: the chord (\(c\)); the local lift curve slope (\(C_{la}\)); and a correction due to the unsteady lift lag implemented by utilizing the complex Theodorsen function \(C(k)=F-iG\), which is dependent on the reduced frequency (\(k\)). It is worth noting that according to [PERSON] and [PERSON] (2016), the reduced frequency for each blade section is only dependent on the rotational speed (i.e., \(j\); refer to Equation (9)) and not on the eigenfrequency of the system, which is usually the case in the definition of \(k\). A correction concerning the number of blades (\(N_{b}\)) is provided by [PERSON] and [PERSON] (2016), alongside the correction concerning the lift curve slope referred to above. As already mentioned, steady aerodynamic loading including torque and thrust is neglected within this approach. For more detailed information on blade integrals and corrections, the reader is referred to the original literature ([PERSON], 2016; [PERSON] and [PERSON], 2016). To determine the influence of the propeller derivatives on whirl flutter stability, a sensitivity analysis is conducted for the derivatives according to [PERSON] and [PERSON]. Each of the eight derivative pairs is varied with a scale factor between 60% and 140% of a baseline value while keeping the other seven pairs equal to the baseline value for a reference configuration. For each combination, flutter analyses are performed with varying pivot stiffness to find the required stiffness for neutral stability. These required stiffness values are then converted into uncoupled frequency. The relative difference from the baseline uncoupled frequency (\(\Delta\omega_{stab}\)) serves as the comparison parameter and is defined as  
\[\Delta\omega_{stab}=\frac{\omega_{stab,i}-\omega_{stab,ref}}{\omega_{stab,ref}}, \tag{10}\]  
A positive value indicates a destabilization, since the boundary is shifted to larger frequencies. It is worth noting that the pitch stiffness and yaw stiffness are kept equal during this sensitivity analysis, as this represents the most critical combination for classical whirl flutter (see Figure 1b). The results of the sensitivity study are presented in Figure 2. Stabilizing contributions are seen for \(C_{y\theta}\), \(C_{z\theta}\) and \(C_{mq}\). On the other hand, \(C_{n\theta}\) has a largely destabilizing effect. Negligible influences are observed for \(C_{y\theta}\), \(C_{m\theta}\), \(C_{z\theta}\) and \(C_{n\theta}\). The last two were also often neglected in previous studies due to their comparatively low values ([PERSON] and [PERSON], 2016). Please note that the same relations hold for the symmetrical partners of the mentioned derivatives (both were varied simultaneously during the sensitivity analysis). Figure 2: Sensitivity of whirl flutter with respect to the individual propeller derivatives for varying scale factors.