## 3 Numerical Validation
### Flying Wing with Coupled Flight Dynamics and Aeroelasticity
#### 3.2.2 Effects of Structural Model and Mass Distribution on Trim  
Figures 8 and 9 show, respectively, the trimmed configurations, AOAs and flap deflection angles obtained with different structural models and different payload distributions. It can be seen that, for the concentrated payload located at the central pod, results from rigid, linear and nonlinear structural models are quite different. The rigid model keeps its initial shape, while the AOA increases and the flap deflection decreases linearly with the payload.  
Figure 6: Trim results of the flying wing with varying payload mass.  
Figure 7: Trimmed configurations of different models with heavy payload.  
The difference in trimmed AOAs between linear and rigid structural models is brought by the aeroelastic deformation, especially the torsional deformations. Under the aerodynamic loads, the wings bend upward and twist positively, i.e., nose-up. With the positive torsion, a lower AOA is sufficient to provide the required lift, thus the linear model shows a lower AOA compared to the rigid one. On the other hand, as a follower force, the local lift is always perpendicular to the airfoil, with the directions changing continuously with the deformed configurations of the wing, so that it no longer acts in the vertical direction. Large bending deflections and the associated loss of vertical lift lead to the requirement of a higher AOA. This is the main reason the AOAs from the nonlinear model are higher than those from the rigid one when the payload exceeds 160 kg.  
Figure 8: Trim AOA the flying wing with different models.  
Figure 9: Flap deflection of the flying wing with different models.  
Furthermore, it can also be seen in Figure 7 that the bending deflection at wingtip of the nonlinear structural model is about 53% larger than that of the linear one, which indicates higher loss of lift, and results in a higher AOA, as illustrated in Figure 8.  
The flap is mainly used to balance the pitch moment. Since there are no deformations, the flap deflection of rigid model decreases linearly with the payload as a result of the increasing pitch-down moment brought by the increasing AOA. The nonlinear structural model has larger deformations than the linear one, resulting in a larger back-shift of the aerodynamic center and larger pitch-down moment, and the flap deflections are much lower than those given by the linear structural model, as shown in Figure 9.  
In Figure 7, we can see that, if the payload is concentrated on the central pod, the flexible aircraft will perform a highly deformed \"U\" shape configuration, leading to the dramatic changes in its trim and further in flight dynamic performances. If we now spread the payload equally to the three pods, there will be an almost evenly distributed mass that is balanced by the lift, and the deformations will be nearly negligible even with the heaviest payload. The variations of trim AOA and flap deflection angle of a highly flexible aircraft will behave almost as a rigid one, despite the slight differences that are mainly brought by the torsional deformations, as shown in Figures 8 and 9.  
Given the trim parameters and the deformed configurations, the aerodynamic characteristics, static and dynamic stabilities of the aircraft at each trimmed condition can be assessed accordingly, which are the topics of static aeroelasticity, and related studies were done in the previous works of the authors [35; 36]. In addition, the comparison in Figure 6 shows excellent agreement with results from [PERSON] [17] and [PERSON] [13], indicating the static aeroelastic characteristics of the flying wing calculated here are sufficiently accurate.