# A Study of Wind Shear Influences on the Aerodynamic Performances of a UAV Airfoil
## 3 Results and Discussion
### Effect on Velocity Distribution  
Wind shear affects aerodynamic performance by changing the air direction flow across the airfoil. As a result, velocity distribution at the leading edge of the airfoil is changed. As seen in Figure 6a, \(L\) is the distance to the leading edge of the airfoil. When the wind velocity gradient is positive, velocity near the chord axis at \(L=\) c (c is the chord length of the airfoil) is smaller than that of the Gradient-free wind case. It is found that the surface pressure is reduced as wind velocity decreases, resulting in a lift reduction. Shear velocity  
Figure 4: Schematic diagram of logarithmically distributed shear wind. near the airfoil surface and friction drag is also reduced as the wind velocity gradient near the chord axis decreases. The velocity profile before the airfoil was under different gradients is illustrated in Figure 6b. As the airflow passes the airfoil, the rearranged velocity distributions are depicted in Figure 7. It is shown that the velocity magnitude near the chord axis decreases from 125 m/s to 118 m/s as the velocity gradient increase from 0 to 3.05. On the other hand, air velocity behind the lower airfoil surface remains almost the same in the four cases. It can be estimated that lift has decreased as the velocity gradient increased from 0 to 3.05. Influences of negative velocity gradient are also discussed in the current research as shown in Figure 8. Wind velocity decreases with height for the negative velocity gradient case. Contrary to the positive gradient case, more large wind velocity appears near the chord axis at \(L=\) c, as shown in Figure 8a. The velocity contour around the airfoil is illustrated in Figure 8b. In order to quantitively measure the variation of the flow field, both velocity profile and pressure distribution along the airfoil upper surface are extracted as shown in Figure 9a,b. It is shown that air around the airfoil has been accelerated above the  
Figure 6: Velocity distribution near the chord axis in Linear distributed shear wind (\(L=\) c, \(\alpha=7^{\circ}\)): (**a**) At a positive gradient and no gradient state; (**b**) At a different positive gradient state. Figure 7: Velocity magnitude contour near the airfoil surface (\(\alpha=7^{\circ}\)). airfoil up surface due to the negative effect while the one below the lower surface remains almost the same. On the other hand, a negative gradient has decreased pressure along the upper surface but increased the one along the lower surface. This negative effect is impressively found at the airfoil leading edge resulting in an enhanced pressure suction phenomenon. Thus, the lift is estimated to be enhanced. Furthermore, surface shear stress increases against the velocity gradient which usually implies a larger frictional drag. As shown in Figure 10, the Logarithmic distribution of shear wind, velocities at \(L=c\) ahead of the leading edge is found to be smaller than the one of the linear distributed shear wind field with \(dV_{W}/dh=3.05\). Because the velocity gradient \(dV_{W}/dh\) ahead of the leading edge is larger than 3.05 for the logarithmic distribution shear wind case, it results in smaller airfoil leading edge velocities and velocity gradients compared with those of linear distributions shear wind which is \(dV_{W}/dh=3.05\). The logarithmically distributed effect results in dramatically slowed down air above the upper surface which in turn leads to a decrease in lift. Similarly, the logarithmic distribution leads to a decrease in the velocity gradient near the chord axis, which in turn reduces the shear stress and frictional drag. Figure 8: Velocity distribution of linear distributed shear wind field: (**a**) Velocity distribution near chord axis (\(L=c\), \(\alpha=7^{\circ}\)); (**b**) Velocity magnitude contour near the airfoil surface (\(\alpha=7^{\circ}\)). Figure 9: Velocity profile and pressure distribution around airfoil surface (\(\alpha=7^{\circ}\)): (**a**) Velocity profile of upper surface (x/c = 0.5); (**b**) Pressure distribution.