## 3 Results and Discussion
### Modified Airfoil  
Figure 14a shows the \(C_{L}\) versus the angle of attack for the stock NACA 0012 and the modified airfoil with the three flap angles of \(10^{\circ}\), \(15^{\circ}\), and \(20^{\circ}\). As the modified airfoil is not symmetrical, there is now also lift at \(\alpha=0\). The modified airfoils show increased \(C_{L}\) compared to the NACA 0012. The NACA 0012 slope begins to decrease at higher \(\alpha\), and as such, the change in lift coefficient between it and the modified airfoils is larger at \(14^{\circ}\) than \(0^{\circ}\). These results match the trends found in the literature [20]. The flap increases the \(C_{L}\) and the slope gradient remains (mostly) the same. Comparing the different flap angles, a larger angle further increases the \(C_{L}\). Figure 14b shows the drag coefficients of the same setups mentioned above. Furthermore, NACA 0012 \(C_{D}\) data from [PERSON] [15] are also included. First, we compared the simulated NACA 0012 results to the experimental data. The overall trends match: \(C_{D}\) increases with increasing alpha and the slope increases at higher angles. The simulation does significantly overestimate the amount of drag compared to the experimental results. This is due to the flow model assuming the boundary layer is turbulent over the entire length of the airfoil, when in fact, the flow is partially laminar. The laminar flow results in a lower \(C_{D}\), and consequently the \(C_{D}\) is overestimated by the flow model [36]. By creating a more fully turbulent boundary layer across the airfoil surface in experiments, for example, by roughening the surface, the results between simulation and experimental would be closer. For example, the simulated results show better agreement with the experimental results from [PERSON] and [PERSON] when the surface is more roughened [3]. Next, we compared the NACA 0012 to the modified airfoil. The introduction of the flap results in an increase in \(c_{D}\). Compared to the literature, while the high lift device is different, a similar result is observed [20]. In Figure 14b, the NACA 0012 has a higher \(C_{D}\) at higher angles of attack than the modified airfoils, this is due to the difference reference angles. If the relative wind was used as \(\alpha=0\), the \(C_{D}\) of the modified airfoil would be higher for all angles. Additionally, a larger flap angle increases the \(C_{D}\). These results confirm the hypothesis that the modified airfoil would have an increased \(C_{L}\) and \(C_{D}\) compared to the NACA 0012. These results show how a movable flap can be used to adapt to situations where either the lift or drag coefficient might be more important. The performance can be further improved by adding additional high lift devices, for example, a slat or multiple slotted flaps. The change in performance resulting from the addition of slotted flaps and slats is caused by multiple effects: the slat effect, the circulation effect, the dumping effect, off-the-surface pressure recovery, and the fresh boundary layer effect. A full explanation of all these effects is beyond the scope of this work and can be found in [40]. Figure 15 displays the \(C_{L}/C_{D}\) ratios. There is a large difference between the NACA 0012 simulation and the Ladson data due to the \(C_{D}\). The profile is similar for all setups, showing a parabolic profile. The reason for this profile shape is that the \(C_{D}\) increases exponentially, whereas \(C_{L}\) increases linearly. The flap significantly improves the  
Figure 13: Lift coefficients of physics-controlled automated meshes and the user-controlled mesh compared to experimental data from Ladson. ratio compared to the stock NACA 0012 for all angles of attack; additionally, the \(C_{L}/C_{D}\) ratio is further improved with larger flap angles. Overall, the modified airfoil shows significant improvements in \(C_{L}\) and \(C_{L}/C_{D}\), and a substantial increase in \(C_{D}\). These results show how a movable flap can be used to adapt to the different stages of flight.