## 3 Experiment Results and Discussion
### The Effect of Asymmetric Stroke Angles on the Average Lift Generation  
Despite the fact that the motion and efficiency parameters of the FWR under different input conditions have been given in Section 3.3, it is also important to measure the average lift for these cases. The average lift for Case 1 (\(\phi\in[-20,50]\)), Cases 2 (\(\phi\in[-35,35]\)), and Cases 3 (\(\phi\in[-50,20]\)) are then all shown in Figure 11. With the increase of the input voltage, both the total force and lift increase rapidly despite the average inertial force remaining nearly zero. Whatever the input voltage is, the average lifts in Cases 1 (\(\phi\in[-20,50]\)), Cases 2 (\(\phi\in[-35,35]\)), and Cases 3 (\(\phi\in[-50,20]\))) are about 1.25 times those in Cases 2 (\(\phi\in[-35,35]\)) and about 1.5 times those in Cases 3 (\(\phi\in[-35,35]\)). Apart from the cases in Cases 3 (\(\phi\in[-50,20]\)), the average lifts show a nearly linear relationship with the input voltage. In Cases 3 (\(\phi\in[-50,20]\)), the linear relationship only stands when the input voltage is over 4.5 V. From the weight parameters listed in Table 1, it is found that the FWR weighs 0.187 N while the maximum average lift (0.201 N) is achieved in Case 1-8 according to Figure 11. In this case, the lift-to-weight ratio reaches 1.07 and the take-off test is conducted in our previous study [29]. During the take-off test, a 4 g wire was used to connect an external power supply to the FWR model (not taking into account the battery weight). Although the positive average stroke angle can facilitate the lift generation according to the experiment results, the corresponding reason of this phenomenon remains unknown. In our next studies, a certain explanation for the phenomenon is planned to be given by focusing on the real variation curves of the rotary angle (rather than assuming that the rotary speed is a constant value as found in previous studies [23; 24; 25]).  
In order to further confirm that the positive effect of the positive average stroke angle on the FWR's lift observed in the experiment is an inevitable result from the perspective of aerodynamics, the average lifts of the FWR are also calculated based on the CFD method by setting the same motion parameters as those measured by experiment. According to Figure 11, the average lifts from the simulation is larger than those from the experiment and the difference between the simulated average lift and experimental average lift becomes larger with the increase of the input voltage (the flapping frequency is positively correlated with the input voltage as shown in Figure 9). The maximum difference occurs in Case 1-8. In this case, the simulated average lift is larger than the experimental average lift by 49.4%. One of the reasons is that the deformation of the wings is relatively small when a small input voltage (<4 V) is applied while a greater deformation of the wings would be found with the increase of the input voltage. Another reason can be that the rotary speed is not a standard constant, although we make the same assumption as used in previous studies [23; 24; 25].  
Figure 11: Measurement of average force for the FWR.