## 4 Results Analysis
### Power Output  
The power output along the radial direction is presented in Figure 14; its value is equal to the sum of the power output of a stream tube in the upwind part and the corresponding downwind part, which can be written as Equation (11). Adding the power outputs of the stream tubes in all of the radial and heights positions, and subsequently dividing the power of the free wind, the total power coefficient is obtained through Equation (12):  
\[P_{i}=P_{up,i}+P_{dw,i} \tag{11}\]  
\[C_{P,t}=\sum_{-H}^{H}\sum_{i=-R}^{R}\frac{Pi}{\frac{1}{2}S\rho V_{\rm w}^{3}} \tag{12}\]  
where \(C_{P}\) denotes the power coefficient; the subscript \(i\) is the radial position of the stream tube; \(up\) and \(dw\) represent the upwind and downwind region, respectively; \(t\) means total; and \(S\) is the swept area. As shown in Figure 14, the power output of the FP-blade shows the peak value in the radial position of \(r=0\); toward the two sides, the power is gradually reduced, and reaches zero or even a negative power in the \(-R\) or \(R\) positions. The whole curve of the FP-blade is a downward parabolic line. In comparison, the new VP-approach extends the position generated at the peak power from one point in the FP-VAWT to a wide radial zone. Therefore, the final distribution of the power output is similar to a trapezoid when the TSR = 4.5 and 5. For a TSR = 5.5, although a drop of the torque occurs downstream, as shown in Figure 13, the VP-blade still experiences an increase in the power output in most radial positions, because of a larger torque increase in the upwind region. The results presented in Figure 14 also show a small drop in the position of \(r=0\), but a larger increase occurs in other positions. Thus, the total power output will be absolutely increased.  
Figure 14: _Cont._A comparison of the power coefficient of the two types of VAWTs when the TSR = 4 to 5.5 is shown in Figure 15, which reveals the obvious promotion of the power coefficient at a TSR = 4.5, 5, and 5.5. The increase is 16% at a TSR = 4.5, and becomes larger as the TSR increases. Finally, an 18.9% increase of the peak power efficiency of the VP-VAWT is achieved when the TSR = 5. The new curve has a wider TSR zone with a high power coefficient, and the drop in the power coefficient starts when the TSR = 5.5, but at a low rate. The results in Figure 15 clearly indicate that the new approach is highly suitable for improving the peak efficiency of the VAWT at the optimum or larger TSR.  
Figure 14: Power output of a blade as a function of position in VP-VAWTs and FP-VAWTs. (**a**) TSR = 4; (**b**) TSR = 4.5; (**c**) TSR = 5; (**d**) TSR = 5.5.  
Figure 15: Power coefficient curves of VP-VAWTs and FP-VAWTs.  
Since the parasitic drag of the radial arm was not considered in the investigation, the prediction value may be higher than the real one in Figure 15. While the structure of the arm can be well-designed, such as using an airfoil profile and being installed at a zero AoA relative to the free wind, several methods such as this can greatly reduce their parasitic drag. Therefore, the new pitching approach does effectively promote the overall performance of the turbine, even after considering the parasitic drag of the arm.