## 3 Discussion and Results
### Optimization of Morphing Leading Edge
Figure 14 presents the evaluation of the lift vs. drag polar of the baseline airfoil and of the optimized airfoils for three different flight conditions. Therefore, the increased aerodynamic performance of optimized airfoils in terms of their lift versus drag variation for all three flight conditions can be seen in Figure 14a-d.  
Figure 12: Optimized airfoil and convergence history for drag minimization function; (**a**) the initial (reference) versus the final (optimized or morphed) airfoil shape, (**b**) the convergence trend for the minimum drag optimization function. The pressure coefficients' variations with the chord of optimized airfoils for three flight conditions are shown in Figure 15. It is clear that the major changes in pressures take place near the leading edge at its upper surface, and that the pressure peaks then remain smooth on the rest of the airfoil for all configurations in Figure 15a for an angle of attack of 4\({}^{\circ}\) and in Figure 15b for an angle of attack of 10\({}^{\circ}\). The chord-wise pressure distribution reveals that increased performance was obtained for DNLE configurations. By comparing the chord-wise pressure distributions for different configurations at angles of attack of 10\({}^{\circ}\) for the baseline versus optimized airfoils, it is found that a kink in the suction peak is followed by a constant pressure distribution. The DNLE-optimized configuration at flight condition III undergoes flow separation, and reattaches shortly on the airfoil surface, as seen in Figure 15b. Figure 13: Lift coefficients versus angle of attack at two optimized design configurations; (**a**) Figure 13a show the variations of lift coefficients with the angles of attack at Flight Condition I (**b**) the variations of lift coefficients with the angles of attack at Flight Condition II; (**c**) the variations of lift coefficients with the angles of attack at Flight Condition III; (**d**) the lift coefficient variations for all three flight conditions for Opt. Case I.  
Figure 14: Aerodynamic performance for two optimized design configurations. (**a**) Figure 13a show the drag polar at Flight Condition I; (**b**) drag polar at Flight Condition II; (**c**) drag polar at Flight Condition III; (**d**) drag polar for all three flight conditions for Opt. Case I.  
Figure 15: Pressure coefficients variations with the airfoil chord for Opt. Case I (**a**) at angles of attack of 4\({}^{\circ}\); (**b**) at angles of attack of 10\({}^{\circ}\). Figure 16a illustrates the initial (reference) versus the final (optimized or morphed) airfoil shape, while Figure 16b presents the convergence for aerodynamic endurance optimization while utilizing the PSO algorithm with Pattern Search for the DNLE-optimized airfoil at an angle of attack of 50\({}^{\circ}\). A downward trend followed by constant values is clearly visible for the function, thus indicating the approach to the global optimum. Figure 17 shows that the optimization process led to an increase in endurance maximization characterized by \(\text{C}_{\text{L}}\)\({}^{3/2}\)/\(\text{C}_{\text{D}}\) in the optimized DNLE airfoils for three different flight conditions. The maximum endurance capability given by \(\text{C}_{\text{L}}\)\({}^{3/2}\)/\(\text{C}_{\text{D}}\) for the same lift coefficient of the baseline airfoil to the lift coefficient of the morphing DNLE configuration Opt. Case I was found to be 1.17 and 1.21, respectively. Furthermore, the values of \(\text{C}_{\text{L}}\)\({}^{3/2}\)/\(\text{C}_{\text{D}}\) increased from 117 to 132, thus indicating better endurance performance for the UAS-S45 DNLE airfoil configurations than for its baseline airfoil at three flight conditions. Figure 16: Optimized airfoil and convergence history for endurance maximization function. (**a**) the initial (reference) versus the final (optimized or morphed) airfoil shape; (**b**) the convergence for aerodynamic endurance optimization. Figure 17: Comparison of the endurance for baseline and DNLE airfoils.