## 3 Results and Discussion
### Example of Calculating the Propelling Torque  
Based on the data obtained from experimental tests and CFD analysis, it was possible to calculate the starting torque of the carousel wind rotor. In accordance to Figure 11, the single blade was affected by aerodynamic drag \(P_{x}\), lift force \(P_{y}\), aerodynamic torque \(M_{xy}\) and by loads associated with the blade \(R_{\eta}\), \(R_{\xi}\) and the torque \(M_{\eta\xi}\) in movable coordinate system \(\eta\), \(\xi\) associated with the blade. The associated forces and torques can be calculated using the following formulas:  
\[R_{\eta}=P_{x}cos\Big{(}\frac{\alpha}{2}\Big{)}-P_{y}sin\Big{(}\frac{\alpha}{ 2}\Big{)} \tag{19}\]  
\[R_{\xi}=P_{x}sin\Big{(}\frac{\alpha}{2}\Big{)}+P_{y}cos\Big{(}\frac{\alpha}{2 }\Big{)} \tag{20}\]  
\[M_{\eta\xi}=M_{xy} \tag{21}\]  
The following assumptions were accepted for calculations: the rotor included three blades; the rotor radius \(R=1.5\) m; the wind angle \(\gamma=\alpha/2\); the peripheral speed \(V_{0}=0\), and the angle \(\beta=0\). In accordance with Figure 4a, the total propelling torque for one blade \(M_{1}(\alpha_{s})\), depending on the angle of the rotor rotation \(\alpha(\alpha\)s) is given by following equation:  
\[M_{1}(\alpha_{s})=\Big{[}-R_{\eta}\cdot cos\Big{(}\frac{\alpha}{2}\Big{)}+R_{ \xi}\cdot sin\Big{(}\frac{\alpha}{2}\Big{)}\Big{]}\cdot R+M_{\eta\xi} \tag{22}\]  
The resultant torque for all rotor blades \(M_{\text{III}}(\alpha_{s})\) related with \(\eta\), \(\xi\) coordinates is the sum of the torques for three rotor blades \(M_{1}(\alpha_{s})\), \(M_{2}(\alpha_{s})\), and \(M_{3}(\alpha_{s})\) as a function of the rotor rotation angle \(\alpha(\alpha\)s). The total torque for all rotor blades can be written as follows:  
\[M_{III}(\alpha_{s})=M_{1}(\alpha_{s})+M_{2}(\alpha_{s})+M_{3}(\alpha_{s}) \tag{23}\]  
The calculations were conducted using data obtained from experiments. The obtained rotor torque values can be used to estimate the maximum rotor peripheral speed, which will no longer increase with the increasing wind speed. The total propelling torque depending on the position of the blade is presented in Figure 21a,b both for the single and dual coherent blades. Since the carousel wind rotor is equipped with self-adjusting system, the blades reach positions A1 for \(0^{\circ}\) and A7 for \(180^{\circ}\) in accordance with Figure 4a.  
The average total torque \(M_{\text{III}}(\alpha_{s})\) for the rotor with three single coherent blades was equal to was 43.7 Nm. In turn for the rotor with three DC blades it reached the value of 41.3 Nm. Comparing these average values, it was concluded that the rotor with single coherent blades generated 5.5% higher total propelling torque. However, it should be noted that despite the higher average total torque for the rotor with SC blades, there were locally larger deviations from the average value of total torque. This means that this rotor operated less smoothly than the rotor with dual coherent blades. The maximum value of total propelling torque was 47.8 Nm for the rotor with SC blades and 44.6 Nm for the rotor with DC blades, which was 6.7% less.  
In addition, for the rotor with SC blades, higher torque values were obtained for the ranges of \(\alpha\)(\(\alpha\)s): 20-80\({}^{\circ}\), 140-200\({}^{\circ}\) and 260-320\({}^{\circ}\), and mainly the lift force was generated. In contrast, for the rotor with DC blades, higher torque values were obtained for the ranges of \(\alpha\)(\(\alpha\)s): 80-100\({}^{\circ}\), 200-220\({}^{\circ}\) and 320-340\({}^{\circ}\), and the drag force was dominated. An analogous analysis can be performed for turbines with various numbers of blades.