# A Lateral-Directional Control Method for High Aspect Ratio Full-Wing UAV and Flight Tests
## 2 Mathematical Model and Flying Qualities
### Flying Qualities  
The three-view and isometric drawings of the high aspect ratio full-wing configuration UAV in this paper are shown in Figure 4.  
As shown in Figure 4, the UAV has a wingspan of 1.8 m and a chord length of 0.2 m. The wing is composed of three parts: the central wing and two outer wings. The larger dihedral angle of the outer wing reaches six degrees. Two vertical stabilizers are arranged below the central wing, and tires can be installed on the vertical stabilizers as the landing gears. Two motors are mounted on the outer wings, and the distance between them is 0.9 m.  
In order to make a more intuitive comparison, the full-wing UAV in this paper is compared with a conventional configuration UAV with the same wingspan length, chord length, and a similar weight. Their basic parameters are shown in Table 1.  
Table 1 shows that the full-wing drone weighs only 1.053 kg, and the wing load is 2.925 kg/m\({}^{2}\). \(I_{x}\) of the full-wing configuration is smaller than that of the conventional configuration, because the full-wing configuration has no fuselage; thus, it has a more reasonable inertial load distribution. Because of the tail, \(I_{z}\) of the conventional configuration is larger. The static stability derivatives \(C_{l\beta}\) and \(C_{n\beta}\) and the damping derivative \(C_{lp}\) are basically the same for both configurations. However, thanks to the larger vertical stabilizer, the side force derivative \(C_{Y\beta}\) of the full-wing is three-times as large. Meanwhile, because of the tailless design, the yaw damping derivative \(C_{nr}\) of the full-wing is extremely small.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Basic Parameters** & \(M\) & \(I_{x}\) & \(I_{z}\) & \(C_{Y\beta}\) & \(C_{l\beta}\) & \(C_{n\beta}\) & \(C_{lp}\) & \(C_{up}\) & \(C_{lr}\) & \(C_{nr}\) \\ \hline full-wing configuration & 1.053 & 0.160 & 0.164 & \(-0.400\) & \(-0.118\) & 0.020 & \(-0.671\) & \(-0.040\) & 0.113 & \(-0.003\) \\ conventional configuration & 1.090 & 0.111 & 0.208 & \(-0.143\) & \(-0.143\) & 0.016 & \(-0.707\) & \(-0.036\) & 0.102 & \(-0.014\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: The basic parameters of the full-wing and conventional configurations.  
Figure 4: The three-view and isometric drawings of the high aspect ratio full-wing drone.  
Figure 3: Propeller thrust fitting results.  
The lateral-directional modes of both configurations at \(V_{a}=11\) m/s are shown in Table 2.  
Table 2 shows that the roll subsidence mode and dutch roll mode characteristics of the conventional drone are 1.42- and 2.29-times as much as those of the full-wing drone. According to the MIL-F-8785C specification, even if the full-wing configuration does not have a tail, it can still satisfy the Class I flying quality of the lateral-directional mode. The analysis shows that \(C_{Y\beta}\) may play an important role. Recalculate the lateral-directional modes of the full-wing drone in Table 3 after setting \(C_{Y\beta}\) to \(-0.1\), \(-0.2\), \(-0.3\), and \(-0.4\) respectively.  
From Table 3, we can see that \(C_{Y\beta}\) has little effect on the roll subsidence and spiral mode, but it has a very large impact on the real root and damping ratio of the dutch roll mode. Too small a \(C_{Y\beta}\) will lead to the dutch roll mode of the full-wing drone being unstable. Since the vertical stabilizer is the most important component for generating lateral forces, it is important to select properly the size of the vertical stabilizers for the lateral-directional modes of the full-wing configuration.