## 2 UAV Dynamics Model
### Aerodynamic Model Considering the Influence of Distributed Slip Flow
The derivation of the combined velocity \(V_{slip}\) and equivalent angle of attack \(\alpha_{slip}\) in the slip zone is as follows:  
\[\overrightarrow{V_{slip}}=\overrightarrow{V}_{free}+\overrightarrow{V}_{arg} \tag{1}\]  
\[V_{slip}=\sqrt{V_{free}^{2}+V_{avg}^{2}-2V_{free}\cdot V_{avg}\cdot\cos(\pi- \alpha_{free})} \tag{2}\]  
\[\alpha_{slip}=\arcsin\frac{V_{free}\cdot\sin\alpha_{free}}{V_{slip}} \tag{3}\]  
where \(\alpha_{free}\) is the angle of attack of the free flow, namely the angle between the free flow and the x-axis direction of the aircraft. (3) Consider the aerodynamic model of slip flow  
Under the influence of distributed-power propellers, the wings and control surfaces of unmanned aerial vehicles can be divided into the slip flow influence zone and the free flow zone. The influence of slip flow on the aerodynamic force of the aircraft is mainly reflected in the changes in local dynamic pressure and angle of attack on the wings. This paper divides the unmanned aerial vehicle into a free flow zone and eight slip flow zones and analyzes and models the aerodynamic force and aerodynamic torque separately, as shown in Figure 11.  
To simplify modeling, this article assumes that all free flow areas of the entire machine have consistent dynamic pressure and airflow angle. The aerodynamic coefficient within the free flow area can be expressed as follows:  
\[\left\{ \begin{array}{l}C_{D\_free}=C_{D0}+C_{D}^{\alpha}\alpha_{free}+\kappa \cdot\alpha_{free}{}^{2}+\sum\limits_{i=1}^{8}\left(C_{D}^{\delta_{\alpha,i}} \cdot\delta_{\alpha,j}\right)+C_{D}^{\delta_{r}}\cdot\delta_{r}\\ C_{Y\_free}=C_{Y}^{\beta}\beta+\mathrm{m}_{1}\beta^{2}+\mathrm{m}_{2}\beta^{3 }+\sum\limits_{i=1}^{8}\left(C_{Y}^{\delta_{\alpha,i}}\cdot\delta_{\alpha,i} \right)+C_{Y}^{\delta_{r}}\cdot\delta_{r}+C_{Y}^{p}\overline{p}+C_{Y}^{r} \overline{r}\\ C_{L\_free}=C_{L0}+C_{L}^{\alpha}\alpha_{free}+\mathrm{k}_{1}\cdot\alpha_{ free}{}^{2}+\mathrm{k}_{2}\cdot\alpha_{free}{}^{3}+\sum\limits_{i=1}^{8}\left(C_{L}^{ \delta_{\alpha,i}}\cdot\delta_{\alpha,i}\right)+C_{L}^{q}\overline{q}\end{array} \right. \tag{4}\]  
The propeller slip effect of unmanned aerial vehicles is mainly reflected in the changes in local dynamic pressure and airflow angle on the wings. Therefore, in order to simplify modeling and facilitate the construction of dynamic simulation models, it can be considered that the influence of propeller slip on the aerodynamic parameters of unmanned aerial  
Figure 11: MY-UAV wing segmented aerodynamic modeling method considering slip flow. vehicles can be ignored, and only the dynamic pressure and local angle of attack can be changed. The aerodynamic coefficient of the first slip zone can be expressed as follows:  
\[\left\{ \begin{array}{l}C_{D\_slip\_i}=C_{D0}+C_{D}^{\alpha}\alpha_{slip}+\text {k}\cdot\alpha_{slip}{}^{2}+C_{D}^{\delta_{\alpha,j}}\cdot\delta_{\alpha a,j}+ C_{D}^{\delta_{r}}\cdot\delta_{r}\\ C_{Y\_slip\_i}=C_{Y}^{\beta}\beta+m_{1}\beta^{2}+m_{2}\beta^{3}+C_{Y}^{ \delta_{\alpha,j}}\cdot\delta_{\alpha a,j}+C_{Y}^{\delta_{r}}\cdot\delta_{r}+ C_{Y}^{\delta_{r}}\overline{p}+C_{Y}^{\delta_{r}}\overline{p}\\ C_{L\_slip\_i}=C_{L0}+C_{L}^{\alpha}\alpha_{slip}+\text{k}_{1}\cdot\alpha_{ slip}{}^{2}+\text{k}_{2}\cdot\alpha_{slip}{}^{3}+C_{L}^{\delta_{\alpha,j}}\cdot \delta_{\alpha a,j}+C_{L}^{\delta}\overline{q}\end{array} \right. \tag{5}\]  
The three-axis resultant force of the drone is expressed as follows:  
\[F_{A}=F_{free}+F_{slip} \tag{6}\] \[=\left[ \begin{array}{l}\frac{1}{2}C_{D\_free}PV_{free}^{2}S_{ free}+\sum\limits_{i=1}^{8}\left(\frac{1}{2}C_{D\_slip\_i}\rho V_{slip\_i}^{2} \cdot\frac{1}{8}S_{slip}\right)\\ \frac{1}{2}C_{Y\_free}\rho V_{free}^{2}S_{free}+\sum\limits_{i=1}^{8}\left( \frac{1}{2}C_{Y\_slip\_i}\rho V_{slip\_i}^{2}\cdot\frac{1}{8}S_{slip}\right) \\ \frac{1}{2}C_{L\_free}\rho V_{free}^{2}S_{free}+\sum\limits_{i=1}^{8}\left( \frac{1}{2}C_{L\_slip\_i}\rho V_{slip\_i}^{2}\cdot\frac{1}{8}S_{slip}\right) \end{array}