## 4 Aerodynamic Design Method Investigation
### Influence of Wing Twist on the Aerodynamic Performance of the Configuration  
Generally, twisting the wing clockwise is an effective way of improving the stall characteristics of the aircraft. Twisting also changes the longitudinal moment characteristics of the aircraft. However, the twist angle of the wing should not be too large. Although it reduces the aerodynamic characteristics of the aircraft, it increases the difficulties of the structure and manufacturing. Therefore, all aspects of the design requirements must be taken into consideration to determine the twist angle of the wing.  
In the initial configuration, the twist angle of the wing is \(0^{\circ}\). As shown in Figure 12, the midpoint of the chord of the wing tip is considered as the twist axis, and the wings of three configurations are twisted by \(-2^{\circ}\), \(-4^{\circ}\), and \(-6^{\circ}\), which are represented by Twist1, Twist2, and Twist3, respectively. The twist angles show a linear distribution along the spanwise of the wing.  
Figure 13 shows the aerodynamic characteristics of the initial and twisted configurations at H = 11 km and Ma = 0.85. The lift coefficients of the twisted configurations decrease with the twist angle of the wing-tip increasing. The pitching moment curve translates upward as the twist angle increases. When \(\alpha<4^{\circ}\), the lift-to-drag ratio of the aircraft decreases. The larger the twist angle of the wing tip, the higher the reduction in the lift-to-drag ratio. The maximum reduction in the lift-to-drag ratio with Twist3 is about 3%, as shown in Figure 14b. When \(\alpha\geq 4^{\circ}\), the lift-to-drag ratio of the aircraft increases slightly. The larger the twist angle of the wing tip, the higher the increase in the lift-to-drag ratio. Furthermore, as the twist angle increases, the cruise angle of attack increases as well.  
Figure 12: Wing twist: (**a**) Wing twist method; (**b**) Twist distribution in spanwise direction.  
Figure 13: Aerodynamic characteristic of the configurations with different twist angles. Ma = 0.85, H = 11 km, \(\alpha=-2^{\circ}\sim 8^{\circ},\Delta\alpha=2^{\circ}\). (**a**) Lift coefficient, lift to drag ratio; (**b**) Pitching moment.  
Although the longitudinal pitching nose-down moment of the aircraft is reduced, for a trapezoidal wing with low aspect ratio, the aerodynamic center of the wing is close to the center of gravity, and the wing tip twist has a little effect on the longitudinal moment of the aircraft. Notably, even the largest twist angle in the Twist3 configuration cannot satisfy the cruise trim requirements.  
Figure 15 depicts the comparison of the pressure distribution of the initial configuration and the three twisted configurations at Y/B = 0.5, 0.75, and 0.92, and \(\alpha\) = 2\({}^{\circ}\), where Y is the y coordinate of the section location and B represents for half of the wingspan. As shown, the twist angle of the wingtip reduces the wing loading along the spanwise direction. The larger the twist angle, the larger the reduction in wing loading.  
As shown in Figure 14, the increment in the nose-up moment is essentially proportional to the twist angle, the factor \(\gamma\) is defined to describe the longitudinal trimming efficiency of twisting as follows:  
\[\gamma=\frac{\Delta C_{m}}{|TwistVal|}, \tag{2}\]  
Figure 14: The increments of C\({}_{m,c}\) and K obtained by twisting the wing at cruise state.(**a**) Pitching moment coefficient; (**b**) Lift-to-drag ratio.  
Figure 15: The positions and pressure coefficient distributions at typical sections of the different twisted configurations. Ma = 0.85, \(\alpha\) = 2\({}^{\circ}\).  
where \(\Delta C_{m}\) is the increment in the nose-up moment and _TwistVal_ is the twist angle. When H = 11 km and Ma = 0.85, the efficiency factor \(\gamma_{\text{tip}}\) is about 0.001.