## 3 Experiment Results and Discussion
### Experimental and CFD Simulation Comparison  
From the measuring results in Figure 9a, it can be found that Case 1-6, Cases 2-5, and Cases 3-5 share a similar flapping frequency (around 8.2 Hz). Then, the three cases are emphasized as the typical cases, and the total force (T), the inertial force (I), and the aerodynamic lift forces (L) in the three cases are shown in Figure 10. The force-time curves of the three cases start at the beginning of the upstroke when the maximum negative inertial force is found. An about 90\({}^{\circ}\) phase difference between the inertial force (I) and lift force (L)  
Figure 9: (**a**) Flapping frequency; (**b**) rotary speed; (**c**) lift-to-power ratio; and (**d**) peak values in the inertial forces’ curves of the flapping-wing rotor under different voltage. is observed since the minimum vertical acceleration occurs at the mid-downstroke while the aerodynamic lift nearly reaches the maximum value at this moment. From Figure 10a, for Case 1-6, the peak values of the total force (T), inertial force (I), and lift force (L) are around 39 g, 18.6 g, and 34.5 g, respectively, wherein the average inertial force throughout the whole flapping period is very close to zero as it should be, theoretically. Although significant negative total force occurs during the upstroke, the negative lift is nearly zero. This means the instantaneous negative total force results from the negative inertial force and the rotary motion has already eliminated the negative lift during the whole flapping period. At the same time, it is noted that the stroke angle goes to 15\({}^{\circ}\) at the mid-downstroke (as marked by point A) instead of 0\({}^{\circ}\) (as marked by point B) in Figure 10a. At the mid-downstroke, the wings' flapping velocity reaches its peak which leads to the largest normal forces perpendicular to the wings' surface. However, the lift is the vertical component of the normal forces at this moment. It is not until the time marked as point B that the lift equals to the normal forces and the flapping velocity is smaller than the peak it can reach. Thus, the maximum lift occurs between point A and point B when  
Figure 10: Total force, inertial force, and lift force of the FWR. the flapping velocity is close to the peak it can reach and the stroke angle is close to 0\({}^{\circ}\) so that the lift is close to the normal forces. As for Case 2-5, the peak values of the total force (T), inertial force (I), and lift force (L) are around 0.32 N, 0.193 N, and 0.239 N, respectively. A similar variation trend is found for the force curves in Case 1-6 and Case 2-5. Although a different average stroke angle is found in Case 1-6 and Case 2-5, they share a similar peak inertial force due to the similar flapping frequency. Meanwhile, the ratio between the peak of the lift force and inertial force is 1.2 in Case 2-5, which is smaller than that in Case 1-6 (1.73). The average lift in Case 1-6 (0.16 N) is found to be higher than that in Case 2-5 (0.119 N) by 35%. When it comes to Case 3-5, it is found that there exists an apparent negative instantaneous lift force during the upstroke (about \(-0.1\) N), accounting for about 42% of the peak positive lift force (about 0.24 N) during the downstroke. Thus, the average force of the FWR decreases to an even lower value (0.07 N). Moreover, in both Figure 9(a)-c, similar peaks of the inertial forces are found in Case 1-6, Case 2-5, and Case 3-5. According to Figure 10, the variation trend of the inertial forces' curves from the ADAMS simulation is close to those from the experiment despite there being some small bumps during the end of the upstroke and the end of the downstroke. Since the stroke angle nearly follows a sinusoidal function, at the end of the upstroke and the end of the downstroke, the magnitude of the stroke acceleration reaches the peak and the changing rate of the stroke acceleration is relatively small.