## 3 Results and Discussion  
The resultant forces acting on the blade at wind speed \(W=5\) m/s and peripheral speed \(V_{0}=1.35\) m/s were determined based on Equations (6) and (7) according to a simplified analytical model. The calculations also required Equations (2) and (5), which include the forces \(F_{x}\) and \(F_{y}\) acting on the blade at the analyzed wind speed and circumferential speed. Since we had the experimental values of \(P_{x}\) and \(P_{y}\) forces for a dual-coherent blade of the same size, but the experiment was carried out at a wind speed of 12.5 m/s [30], it was necessary to calculate the aerodynamic coefficients \(C_{x}\) and \(C_{y}\) for the considered blade geometry. Based on aerodynamic coefficients, it was possible to determine the forces on the blades for any wind speed. For this purpose, it was necessary to determine the aerodynamic coefficients related to the drag of the blade in planetary motion. These were the values of the coefficients \(C_{xD}\) and \(C_{yD}\), which are the values of \(C_{x}\) and \(C_{y}\) in reverse order. In turn, the reference area was defined as \(A_{refD}=A_{ref}(\alpha)\), where \(\alpha=180^{\circ}\div 0^{\circ}\). The obtained coefficients and the corresponding reference areas are summarized in Table 7.  
Figure 10: Torque coefficient depending on domain width \(W\). Figure 11 presents the results of the drag and lift forces obtained for analytical and CFD-based approaches. Points (A), (B), and (C) indicate significant discrepancies. Point (A) in Figure 8a refers to the rotor rotation angle of 70\({}^{\circ}\). For that angular position of the rotor, the CFD-based drag force of blade 1 is locally almost twice the drag force obtained based on the analytical approach. In the analytical approach, the resultant force acting on the blade arises from the load component consistent with the wind direction and the component tangential to the rotor diameter. In contrast, in the CFD approach, due to the rotational motion of the rotor and the blade, the airflow is directed between the lobes of the dual-coherent blade, as shown in Figure 12a. As a result, the pressure distribution is affected, as shown in Figure 12b. Figure 13 shows velocity pathlines around blade 1. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \multicolumn{6}{c}{**Wind Tunnel Results**} & \multicolumn{6}{c}{**Results Arranged to Calculate Air Drag**} \\ \hline \(P_{x}\)* [N] & \(P_{y}\)* [N] & \(C_{x}\) & \(C_{y}\) & \(A_{\textit{ref}}\) & Angle & \(A_{\textit{ref}D}\) & \(P_{\textit{xD}}\) & \(P_{\textit{yD}}\) &  
It can be noticed that behind the first lobe of blade 1, a vortex is formed, which causes a negative pressure. Consequently, the total load on the first lobe increases. On the other hand, due to the flow separation on the first lobe, a stream of air that accelerates is directed at the second lobe. As a result, the second lobe is additionally pressurized. In the analytical approach, where the reference surface has a crucial effect on the load value, the second lobe is considered to be in the aerodynamic shadow. This results in a lower load on the blade in the analytical approach. Point (B) in Figure 8a refers to the rotor rotation angle of 200\({}^{\circ}\) shown in Figure 14a. For this angular rotor position, blade 1 has a large reference area, so the maximum load in the wind direction is obtained. However, the CFD-based maximum of \(F_{x}\) is higher than the maximum value obtained using an analytical approach. This is caused by the negative pressure, visible in Figure 14b, that is not considered in the analytical approach. The negative pressure behind the second lobe of blade 1, which increases the total \(F_{x}\) load, is caused by the rotation of the rotor and blade domains. Rotations generate the vortices shown in Figure 15 and the corresponding pressure drop. Figure 12: Results of CFD simulation for \(\alpha=70^{\circ}\): (**a**) velocity distribution; (**b**) pressure distrribution. Figure 13: Velocity pathlines around blade 1 for \(\alpha=70^{\circ}\).