## 2 Materials and Methods
### Aerodynamic Methods
The mid-fidelity methods used in this paper rely on different types of blade discretization, ranging from a full 3D surface grid using 3D doublets and source panels over 2D vortex lattice formulations to 1D lifting line theory with radial discretization into airfoil sections [32]. The wake models in UPM and DUST, on the other hand, are very similar, using free-wake methods with panel wake [29; 30; 31] or discrete vortex particle wake [32; 33]. Free-wake methods allow for the capturing of the induced velocities of the wake affecting the wake itself and the propeller. Due to this complete description of the wake, no tip loss model is required. The low-fidelity methods are based on a strip theory approach for blade aerodynamics, using airfoil polars for the primary relationship between angle of attack and lift. To capture the unsteady effect of the near wake, a time-domain formulation for the lift lag effect according to Wagner's function (see [34] for details) is applied in some methods. The induced velocities of the whole wake due to thrust and torque on the propeller are either neglected or described quasi-steadily using the blade element momentum (BEM) method [35]. Due to the non-axial inflow condition during propeller disc pitch motion, a special formulation of the BEM, the Weighted BEM from [16], is used to cover the azimuthal variation in the induced velocities. Still, in the BEM, no interaction of the radial sections is considered, so a tip loss model using Prandtl-Glauert's tip (and hub) loss factor is used in the BEM method [35]. A more detailed discussion of the influence of the different BEM-formulations on the results are presented in Appendix C. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Method** & **Blade Lift Method** & **Wake Method** & **Tip Loss** & **Comp. Time** \\ \hline DUST-Panel & 3D doublet and source panels & Free vortex & Included in free wake & Hours \\
[32; 33] & on blade surface & Particle wake & & \\ \hline DUST-UVLM & 2D vortex lattice on & Free vortex & Included in free wake & Hours \\
[32; 33] & camber surface & particle wake & & \\ \hline DUST-LL & 1D lifting line & Free vortex & Included in free wake & Minutes–Hours \\
[32; 33] & using airfoil polars & particle wake & & \\ \hline  & Strip theory & & & \\  & using airfoil polars & Weighted blade & & \\  & + [PERSON]’s function & element momentum & Prandtl–Glauert & Minutes \\  & for unsteady lift & theory [16; 35] & & \\ \hline  & Strip theory & & & \\  & using airfoil polars & No induced & & \\ [PERSON] & + [PERSON]’s function & velocity model & No tip loss model & Seconds \\  & for unsteady lift & lag [34] & & \\ \hline Quasi-steady & Strip theory & No induced & & \\  & using airfoil polars & velocity model & No tip loss model & Seconds \\ \hline  & Linearized strip theory & & & \\  & (C\({}_{La}\) only) + & No induced & & \\  & [PERSON]’s function & velocity model & & \\  & for unsteady lift lag & & & \\ \hline  & & & & \\ \hline  & & & & \\ \end{tabular}
\end{table} 
Table 1: _Cont._The method by [PERSON] and [PERSON] was described earlier. The relevant features for the comparison in Table 1 are the linearized form of the strip theory (only taking perturbational lift contributions from \(C_{la}\) into account), the optional correction for lift lag using [PERSON]'s function (see Equation (7)), the lack of a model for the induced velocities and the finite blade span (or tip loss) correction using the blade aspect ratio (\(A_{R}\)).