## 5 Numerical Analysis
### Prestressing Force  
When laying the flexible skin, it is necessary to provide an appropriate amount of prestress to maintain the wing shape. As displayed in Figure 26, the spanwise prestress \(P_{\rm s}\) and chord prestress \(P_{\rm c}\) can be provided by using the tensioning device. These two types of prestress will affect both the initial state and the loaded state of the membrane shape. The numerical analysis method is used to research the influence of prestress on simulation results of the S-A model. Figure 26: Spanwise and chordal prestress of membrane skin. Figure 24: Streamline of 50% span wing section (\(p\) = 6.4 m/s, \(\alpha\) = 4\({}^{\circ}\)): (a) Rigid-skin wing; (b) Polymide-skin wing. Compared with the skin deformation when normal prestress is applied (Figures 27a and 28b), when the spanwise prestress is increased to three times, the deformation of the membrane decreases (Figures 27c and 28c), while the overall trend of deformation remains unchanged. This is because the spanwise prestress only affects the skin tension and does not affect the section shape, so it only reduces the deformation amplitude but does not affect the trend. When the chordal prestress is increased by three times, the deformation behavior of the membrane changes obviously (Figures 27b and 28b). First, the prestress makes the convex membrane on the upper surface concave, and the pneumatic suction cannot resist the concave trend, resulting in negative deformation. The concavity in the front area of the lower surface increases because the prestress itself will provide the concavity of the convex surface, and the aerodynamic force intensifies this trend. Prestress makes the rear area convex, and the pneumatic pressure cannot resist the convex trend, resulting in negative local deformation. Generally, chord prestress has a greater impact on the shape of the wing section, which will cause the airfoil to deviate from the rigid shape. As displayed in Figure 29a,b, there is little difference in the lift and drag coefficients caused by skin deformation before and after increasing spanwise prestress because spanwise prestress hardly changes the shape of wing section. However, because the increase of spanwise prestress weakens the skin deformation, the change of airfoil curvature is no longer obvious, so the change rate of pitch moment coefficient decreases accordingly, as observed in Figure 29c. With the increase of chordal prestress, the lift and drag coefficient of the wing are obviously lost in the range of \(-4^{\circ}\)\(\sim\)10\({}^{\circ}\) angle of attack, and the pitch moment decreases obviously. This is because the larger chord prestress makes the airfoil curve irregularly deformed, the camber and thickness of the airfoil are reduced, and the wing has deviated from the initial shape. This state will cause large deviation between the real aerodynamic characteristics and the numerical simulation results of the aircraft, which should be avoided as much as possible. Figure 28: Lower surface deformation under different prestress: (a) \(P_{\rm s}=0.017\) MPa, \(P_{\rm c}=0.017\) MPa; (b) \(P_{\rm s}=0.017\) MPa, \(P_{\rm c}=0.051\) MPa; (c) \(P_{\rm s}=0.051\) MPa, \(P_{\rm c}=0.017\) MPa. The above research provides a scientific basis for the laying of membrane skin of long-endurance low-speed UAV. Firstly, the spanwise prestress can be increased as much as possible if the structure permits, so that the aerodynamic characteristics are closer to the numerical results based on the assumption of rigid body. Secondly, the chordal prestress can be properly applied on the upper surface according to the wing load, which is helpful to eliminate the deformation caused by aerodynamic force. However, if the prestress is too large, it will also lead to the concave of convex surface and the damage of the section shape. Finally, the chordal prestress should not be applied to the lower surface.