## 4 Study Results and Discussion
### Parametric Study  
#### 4.3.1 Effect of Pitching Angle of Aerodynamics  
A parametric study to evaluate the effect of varying pitching angle on the aerodynamics is carried out using UAM. This is because the aerodynamic lift is more sensitive to the pitching angle than the flapping angle. The study is aiming to find an optimal wing motion as a combination of pitching and flapping angles to achieve maximum lift and drag forces for short landing. The range of pitching angles considered in the study are extended to 0\({}^{\circ}\)-45\({}^{\circ}\) and 0\({}^{\circ}\)-60\({}^{\circ}\) in comparison with the experimental case -18\({}^{\circ}\)-44\({}^{\circ}\) used for validation. The lift and drag force results are shown in Figures 15 and 16. Figure 14: Flapping motion and drag forces by UAM, CFD and experiment (drag force obtained in experiments refers to the net horizontal force). The study shows that the average lift force 0.31 N for the pitching angle variation case 0\({}^{\circ}\)\(\sim\)60\({}^{\circ}\) is 19% greater than the case 0\({}^{\circ}\)\(\sim\)45\({}^{\circ}\) (0.25 N), and 52% greater than the experimental case \(-\)18\({}^{\circ}\)\(\sim\)44\({}^{\circ}\) (0.15 N). This is mainly because the negative lift force produced by the up-stroke wing is reduced due to large pitching angle 50\({}^{\circ}\)\(\sim\)60\({}^{\circ}\) during \(\hat{t}\) = 0.4\(\sim\)0.6 as shown in Figure 15. In addition, the maximum lift is increased in down-stroke during \(\hat{t}\) = 0.75-0.95. Regarding the drag results as shown in Figure 16, the average drag force \(-\)0.144 N (negative for thrust) in a flapping cycle for the case 0\({}^{\circ}\)\(\sim\)60\({}^{\circ}\) is 60% greater than the experimental case \(-\)18\({}^{\circ}\)\(\sim\)44\({}^{\circ}\) result of \(-\)0.359 N and 38% greater the case 0\({}^{\circ}\)\(\sim\)45\({}^{\circ}\) result of \(-\)0.234 N. The increased drag or reduced thrust (negative drag value) is preferable for short landing. This is also due to the increased pitching angle during the wing flapping motion. According to the simulation results shown in Figures 15 and 16, it is noted that small positive pitching angle of the wing in down-stroke results in the increase of lift, and a large pitching angle in the up-stroke results in a reduced negative lift and increased drag force. This can be demonstrated by a parametric study of extended range of pitching amplitude from 15\({}^{\circ}\) to 90\({}^{\circ}\). The resultant average lift and drag forces are presented in Table 4 and Figure 17.  
Figure 16: The drag forces of the flapping wing in three cases of pitching angle variation. Figure 15: The lift forces of the flapping wing in three cases of pitching angle variation. As shown in Figure 17, the average lift increases to maximum with the pitching amplitude from 15\({}^{\circ}\) to 75\({}^{\circ}\) before decreases. In the same time, the average thrust (negative drag value) is produced by the wing from 15\({}^{\circ}\) and increases until reaching a maximum for pitching amplitude of 45\({}^{\circ}\). Afterwards, the thrust starts to reduce to zero at about 75\({}^{\circ}\) and then becomes positive (drag) as the pitching amplitude keeps increasing. The average lift and drag forces from the experimental case are also marked in Figure 17 for comparison (the pitching amplitude is 62\({}^{\circ}\) for pitching angle variation -18\({}^{\circ}\)-44\({}^{\circ}\)). From the above case study, it is noted that the maximum average lift force and zero drag force occur for pitching amplitude around 75\({}^{\circ}\). Therefore, the further study is focused on a small range of pitching angles between 45\({}^{\circ}\) and 90\({}^{\circ}\). Figure 18 shows the resulting lift and drag forces in the case of pitching angles varying within 0\({}^{\circ}\)-45\({}^{\circ}\), 0\({}^{\circ}\)-75\({}^{\circ}\), and 0\({}^{\circ}\)-90\({}^{\circ}\) for comparison.