## 4 Results and Discussion
### Incline Angle  
The incline angle dominates the relationship between the pitch angle (\(\theta\)) and the fold angle. The pitch angle equals the fold angle with an incline angle of \(90^{\circ}\), while the pitch angle remains constant regardless of the fold angle with the incline angle of \(0^{\circ}\). In this way, the application of an inclined pitch axis slows the pitch movement, compared with a conventional pitch axis. The relationship among three variables is as follows [4]:  
\[\theta=\arctan\frac{\sin\gamma\sin\eta}{\sin^{2}\gamma\cos\eta+\cos^{2}\gamma} \tag{5}\]  
Figure 8: Variables of a wind turbine with \(\gamma~{}=~{}60^{\circ}\): (**a**) swept area (normalized by that of the unfolded blades) and (**b**) \(C_{P}\). The effect of the incline angle on the overall performance of the VAWT was investigated with fold angles from \(-2^{\circ}\) to \(10^{\circ}\). The incline angle was set to \(30^{\circ}\), \(60^{\circ}\), \(90^{\circ}\), \(120^{\circ}\) and \(150^{\circ}\). Variations of the swept area of the wind turbine versus the fold angle for different incline angles are shown in Figure 10. As can be seen, variations of the swept area increased with the incline angles away from \(90^{\circ}\), but were still quite tiny for the range of fold angles observed. The sensitivity of the \(C_{P}\) to the fold angle diminished with the incline angles away from \(90^{\circ}\). A similar effect could be found for the \(C_{Thurst}\) and \(C_{Lateral}\). However, the effect on the \(C_{Vertical}\) was more complicated, which was the comprehensive result of both the variable modulus of aerodynamic forces resulting from the pitch angle and different decompositions of forces resulting from different orientations of the blades. For incline angles from \(90^{\circ}\) to \(60^{\circ}\), vertical forces grew downward for most of the fold angles. Then, for incline angles from \(60^{\circ}\) to \(30^{\circ}\), the vertical forces increased downward for the negative fold angles, but the vertical forces trended upward for the positive fold angles. The opposite changes were observed with \(\gamma~{}>~{}90^{\circ}\). The upward vertical forces could diminish the burden of the gravity of the blades on the supporting structures of the wind turbine. In addition, to clarify the effect of the incline angle, a pitch angle of \(3^{\circ}\) was selected to be constant for various incline angles--\(30^{\circ}\), \(60^{\circ}\), \(90^{\circ}\), \(120^{\circ}\) and \(150^{\circ}\)--leading to corresponding fold angles of \(6^{\circ}\), \(3.5^{\circ}\), \(3^{\circ}\), \(3.5^{\circ}\) and \(6^{\circ}\), respectively. The Average aerodynamic forces of the blade elements along the blade span were evaluated, as shown in Figure 11. It is apparent that incline angles away from \(90^{\circ}\) modified the distribution of aerodynamic forces to asymmetry about the equator. For the \(C_{Ft}\) with \(\gamma~{}<~{}90^{\circ}\), the peak appeared at the upper half of the blade and declined along the blade span downward. The trend was the opposite with \(\gamma~{}>~{}90^{\circ}\). Besides that, the maximum \(C_{Ft}\) with \(\gamma~{}=~{}30^{\circ}\) and \(60^{\circ}\) was 9.1% and 3.0% higher than that at the equator with \(\gamma~{}=~{}90^{\circ}\), respectively. The asymmetry of the \(C_{Ft}\) resulted in additional normal moments on the blade attachment points. Similar phenomena were found for the \(C_{Thurst}\), leading to different tilting moments applied to the main shaft and the tower of the wind turbine. A 2.3% reduction of the tilting moment to the main shaft at \(z/H=-0.5\) with \(\gamma~{}=~{}150^{\circ}\) was estimated, compared with that utilizing \(\gamma~{}=~{}90^{\circ}\). The asymmetry of the \(C_{Lateral}\) caused the same results as the \(C_{Thrust}\) to a minor extent. As for the \(C_{Vertical}\), variations along the blade span could be ignored in view of the values.