## 3 Discussion and Results
### Optimization of Morphing Leading Edge  
The Droop Nose Leading Edge (DNLE) optimization was performed to satisfy the objective functions defined in Equation (1) for drag minimization and in Equation (5) for endurance maximization. The optimization processes were carried out for two cases of DNLE control point deflections, defined as \"Opt. Case I\" and \"Opt. Case II\". In \"Opt. Case I\", a morphing DNLE is a smooth single structural layout with a morphing leading edge starting location fixed at 22% of the chord. The trailing-edge is not allowed to move, while the leading edge points are only allowed to move in the vertical direction to effectively adapt the chord-length variation of the baseline airfoil. In \"Opt. Case II\", the morphing DNLE is free to change its shape anywhere from 0 to 22% of the chord. The starting point and the end point of the leading edge are used to represent the morphing DNLE shape. The parameterization of the DNLE shape was obtained by using the Bezier-PARSEC (BP) method, in which the leading edge radius of the airfoil and 5 Bezier control points were used to maintain the slope continuity within the airfoil shape. The XFoil software was used to efficiently investigate the aerodynamics of the optimized morphing geometries. The aerodynamic performance of the DNLE was evaluated to determine its best airfoil design shape for each flight condition. The computations were performed for the three flight conditions listed in Table 5. The results were obtained in terms of aerodynamic lift and drag coefficients variations with angle of attack and pressure distributions versus the airfoil chord locations for the optimized airfoil geometries. Figure 11: Contour plots of turbulent intensity comparison for baseline airfoil at the airspeed of 34 m/s. (**a**) the turbulent intensity at a low angle of attack of 4\({}^{\circ}\); (**b**) the turbulent intensity at a low angle of attack of 10\({}^{\circ}\)  
Figure 12a illustrates the initial (reference) versus the final (optimized or morphed) airfoil shape, while Figure 12b shows the convergence trend for the minimum drag optimization function for an optimized airfoil shape with DNLE at an angle of attack of 50. The algorithms PSO with Pattern Search converge to the optimal solution after 90 iterations. The x-axis indicates the number of function evaluations, and the y-axis shows the value of the fitness. The fitness value is the objective function value of each particle of the algorithm, expressing the performance of any airfoil shapes. These results for the droop nose leading edge (DNLE) optimization are shown in Figures 13 and 14, and the UAS-S45 baseline airfoil aerodynamic coefficients were compared to those of the optimized airfoils. Figure 13a-d show the variations of lift coefficients with the angles of attack. The lift coefficient variations for all three flight conditions for Opt. Case I and Opt. Case II and the baseline airfoil in Figure 13a-c show that higher lift coefficients were obtained for Opt. Cases I and II than those of the baseline airfoil. Figure 13d shows that the DNLE designs for Opt. Case I at three different flight conditions. It is found that Opt. Case I DNLE design is the best at Flight Condition III. These optimal shapes revealed that maximum increment of the lift coefficient with respect to the baseline airfoil of up to almost 21% was found for Opt. Case I design seen in Figure 13c. In addition, an increase of 9.6% was obtained for the maximum lift coefficient, associated with a stall angle delay of 3\({}^{\circ}\) as seen in Figure 13c. Therefore, it was found that both Opt. Case I and Opt. Case II results are better than the baseline airfoil results. These better results can be explained by the pressure distribution change around the airfoil. The DNLE design does not cause an adverse pressure gradient as the flap configuration, but instead, it decreases the maximum speed at the airfoil leading edge, which is similar to the findings [80].