# Study of Airfoil Deflections for Unsteady Aerodynamics Optimization in Pitching Airfoils +
## 2 Materials and Methods
### Deflection Parameters
The variation of lift-to-drag ratio with angle of attack, C\({}_{\text{l}}\)/ C\({}_{\text{d}}\) vs. \(\alpha\), showed that the TE deflection increases the performance of the airfoil over a range of angles of attack below 6 degrees, whereas the LE deflections increase the performance of the airfoil at a higher range of angles of attack, closer to \(\alpha\) = 10 degrees. This is important, as it provides a performance increase over two drastically different areas of the range of angle of attack. Figure 1: LE and TE deflections of VR-12 airfoil from 1 to 12 degrees. After reviewing these data, two initial shapes were chosen to be produced and tested experimentally. These two shapes were a 4-degree deflection in the trailing edge and a 6-degree deflection in the leading edge. Although there were some deflections that showed an increase in performance over these two airfoils, they also showed a decrease in the usable range of angle of attack, whereas the 4-degree TE and 6-degree LE offered beneficial performance over the baseline Boeing VR-12 while also being able to offer that increase in performance over a wider range of angles of attack [15]. In comparing the two selected deflections by themselves (6\({}^{\circ}\) LE and 4\({}^{\circ}\) TE) with the baseline Boeing VR-12 airfoil, the variation of \(C_{\text{I}}\) vs. \(C_{\text{d}}\) indicates that drag is at its minimum in the region corresponding to \(C_{\text{I}}\) values of 0 and 0.8. From the variation of \(C_{\text{I}}\) with the angle of attack, shown in Figure 2a, this \(C_{\text{I}}\) range corresponds to the angles of attack ranging from \(-4\) to 7 degrees. Figure 2c shows the benefits of the LE and TE deflection airfoils over the baseline in the \(C_{\text{I}}\)/\(C_{\text{d}}\) vs. \(\alpha\) plot. It can be seen that at both low and high angles of attack, the LE and TE airfoils are providing an increase in \(C_{\text{I}}\)/\(C_{\text{d}}\) compared to the baseline airfoil. Following the same trend in Figure 2a,b for \(C_{\text{I}}\) vs. \(\alpha\) and \(C_{\text{d}}\) vs. \(\alpha\), respectively, it is clear that the TE deflection shows higher lift and lower drag at lower angles of attack, around \(\alpha=0\), and the LE deflection shows higher lift and lower drag at higher angles of attack,around \(\alpha\) = 10. For both of the deflections, values of the maximum lift coefficient, C\({}_{\text{max}}\), are increased, and for the airfoil with the LE deflection, the stall is delayed compared to the baseline airfoil. Evaluations of various combinations of leading and trailing edge shape changes with deflections at 25% chord for the leading edge and 85% chord at the trailing edge were then performed. These airfoils were evaluated under the same flow conditions as the previous airfoils in order to select a fourth airfoil that has both LE and TE deflections that improve the aerodynamic characteristics. Figure 2a-d include the comparisons of computed aerodynamic coefficients of modified VR-12 airfoils with combined LE and TE deflections against the baseline VR-12 airfoil, VR-12 with 6-degree LE deflection only and VR-12 with 4-degree TE deflection only. From the comparisons shown in Figure 2, it can be seen that the combination of a leading and trailing edge deflection can provide benefits in areas that just the LE or just the TE cannot, for instance, in Figure 2c, C\({}_{\text{I}}\)/C\({}_{\text{d}}\) vs. \(\alpha\), it can be seen that the combination of both an LE and TE deflection is beneficial in the range of angles of attack where C\({}_{\text{I}}\)/C\({}_{\text{d}}\) is lower with only the LE and only the TE deflection. Figure 2d, showing C\({}_{\text{I}}\) vs. C\({}_{\text{d}}\), indicates that combinations of LE and TE deflections with higher angles show an increase in drag at lower lift coefficients, which correspond to operational angles of attack of the airfoils.