## 4 Study Results and Discussion
### UAM Validation  
Given the flapping wing motion as shown in Figure 9 obtained from the test data and Equations (20) and (21), the aerodynamic lift and drag forces are calculated using the UAM and CFD, and shown in Figures 13 and 14 respectively. Aerodynamic lift and drag forces obtained in experiments refer to the net vertical and horizontal forces, respectively. As shown in Figure 13, it is noted that the aerodynamic lift forces by the three methods are of the same characteristics. In particular the UAM results agree with the experimental results very well considering the small difference of the idealized flapping motion from the measured one. The CFD results show more time delay comparing with the test data. In terms of average lift in a flapping cycle, the force 0.150 N calculated by UAM is very close to the CFD result of 0.152 N but greater than the measured force 0.123 N. Refer to the motion of the flapping wing, it can be found that when the wing is at the midpoint of the down-stroke \(\hat{t}=0\) and \(\hat{t}=1\), all the lifting forces reach the peak value (UAM: 2.00 N, CFD: 1.96 N, and experiment: 2.02 N) with difference less than 3%. At this moment, the speed of flapping wing motion is at its maximum and the pitching angle is \(-10^{\circ}\), which should result in a thrust force (see Figure 14).  
Figure 12: The aerodynamic lift (**a**) and drag (or thrust), (**b**) extracted from the experimental data.  
Figure 13: Flapping motion and lift forces by UAM, CFD and experiment (lift force obtained in experiments refers to the net vertical force; down-stroke: \(\hat{t}=0\)–0.25; up-stroke: \(\hat{t}=0.25\)–0.75; down-stroke: \(\hat{t}=0.75\)–1).  
It is observed from Figure 13 that the large difference between the forces occurs in the up-stroke during \(\hat{t}=0.3\) and \(\hat{t}=0.7\). When the wing is moving close to the midpoint in upstroke at \(\hat{t}=0.4\)-0.5, the lift forces reach the minimum value, and the timing for UAM and experiment is about 0.1T earlier than the CFD result. The values from UAM (-1.33 N) and CFD (-1.42 N) are of 13.1% and 6.3% difference from the experiment result (-1.53 N) respectively. At the end of the down-stroke (\(\hat{t}=0.25\)) when the flapping speed is nearly zero with pitching angle 18\({}^{\circ}\), the lift from CFD shows a small positive value due to the wing rotation from negative to positive pitching angle, and soon reduces to zero during up-stroke motion at \(\hat{t}=0.32\). While the lift forces from UAM and experiment reach zero earlier at \(\hat{t}=0.2\)-0.22. The same situation occurs at the end of up-stroke (\(\hat{t}=0.75\)) where the UAM and experimental results become zero, but the CFD result is still a negative value.  
As shown in Figure 14, the two peak values of drag force in a flapping cycle occurring at \(\hat{t}=0.19\) and \(\hat{t}=0.75\) for the UAM are very close to the CFD and experimental results. The difference of average drag force in a flapping cycle by UAM (-0.37 N) and the CFD (-0.42 N) from the experimental result (-0.43 N) is 14% and 2.3%, respectively.  
The results show that the UAM and CFD methods can capture the aerodynamic characteristics measured in the experiment including the force variation and peak values. In particular, the difference of maximum force values in down-stroke is less than 3%. The difference of the average force in a-flapping cycle calculated by the UAM and CFD is only 1.3%. However, the difference of the results from the measured force obtained in the experiment is 18%. Although this is caused by a number of reasons, including the approximate wing motion measured at limited points and inertia force, the main reason is likely to be the ignorance of the skin flexibility of the wing in the UAM and CFD model. Nevertheless, the UAM provides a method of high efficiency and adequate accuracy to calculate the aerodynamic forces of the flapping wing model.