## 3 Optimization Results
The effect of the combined LE/TE morphing on the \(\text{CL}\)-AoA polars is depicted in Figure 9. The airfoils designed from the PSO and ES algorithms are compared against the initial NACA 64A010 airfoil and the one with the reference deformation, which was used as a starting point for the definition of the control points' intervals (Figure 3). First, stall is delayed, occurring at a higher angle of attack, in comparison to both the original NACA 64A010 and the reference deformation airfoils (17\({}^{\circ}\) for PSO, 14\({}^{\circ}\) for ES, 12\({}^{\circ}\) for reference deformation, 10\({}^{\circ}\) for original NACA 64A010). Second, \(\text{CL}_{\text{max}}\) increases considerably, from 1.1 (original NACA 64A010) to 2.27 and 2.07 for the PSO and the ES airfoils, respectively. A significant increase is also observed with respect to the reference deformation airfoil that presents a \(\text{CL}_{\text{max}}\) of 1.84. In order to distinguish the effect of LE and TE morphing on the overall lift change, additional optimizations are performed applying each one of the two morphings separately. Both PSO and ES algorithm are employed, while the maximum number of generations  
Figure 8: Improvement on the continuity of the optimized PSO airfoil geometry at the connection points between the morphing and the undeformed parts. (**a**) Focus on the connection points of the LE region. (**b**) Focus on the connection points of the TE region. Figure 7: Comparison of the morphing achieved with the aggressive (design 1, four generations) and the conservative (design 2, eight generations) setup using the PSO algorithm. (**a**) LE region and (**b**) TE region. is kept the same with the previous analyses (four generations for PSO and eight generations for ES), to derive results directly comparable with those of the combined LE/TE shape optimization. From the comparison of C\({}_{\rm L}\) polars in Figures 10 and 11, it is observed that:  
* When only LE droop nose is applied, stall is significantly delayed (20\({}^{\circ}\) for PSO-airfoil and at 18\({}^{\circ}\) for ES-airfoil compared to 10\({}^{\circ}\) for the original airfoil), whilst the zero-lift angle of attack remains almost unchanged (similar to the effect of a multi-element slat). As a result, a 60-80% increase (depending on the optimization method used) of the C\({}_{\rm L,max}\) is achieved. * When only TE flap is applied, the effective camber line increase at the TE region results in the shifting of the entire C\({}_{\rm L}\) polar towards lower AoA (similar again to the effect of a multi element flap). In this case, stall occurs at a lower angle of attack (8\({}^{\circ}\) for both airfoils). Furthermore, the slowing down in the rate of the lift increase starts earlier in the morphed airfoil as compared to the baseline undeformed shape. This is an indication of an earlier separation of the flow at the TE region, triggered by the local effect on pressure by the high geometric curvature. The C\({}_{\rm L,max}\) increase in this case is limited to 45%. * When both morphing mechanisms are applied, the two effects are superimposed (though not linearly) and the overall increase in C\({}_{\rm L,max}\) is maximized (88-107%). * Measurements of the lift coefficient polar for an extended and drooped slat configuration on the same NACA 64A010 are also presented in Figures 10 and 11. The Mach number and the flap deployment of the experiment [1] are 0.25 and 14.5\({}^{\circ}\), respectively, very close to the simulated setup. The comparison shows a significant improvement of the C\({}_{\rm L,max}\) when the suggested droop nose morphing is applied, even if the lower Reynolds number of the experiment is considered (3.5 \(\times\) 10\({}^{6}\)). Percentages of C\({}_{\rm L,max}\) increase for the individual LE droop nose and TE flap, as well as for the combined morphing are summarized in Table 5. The C\({}_{\rm L,max}\) increase with respect to the reference deformation airfoil (combined morphing) is 23.5% and 12.3% for the PSO and ES airfoils, respectively.