## 3 UAV Transition Corridor
### Ducted Lift-Increasing System's Deflection Angle-Speed Envelope Based on Stall Angle of Attack  
The transition corridor in the low-speed section starts from the hovering state until the ducted lift-increasing system deflects to the fixed-wing flight mode. At this time, the angle of attack is the stall angle of attack. When hovering, the aerodynamic force of the ducted lift-increasing system and the aerodynamic force of the front lift fan balance the gravity of the UAV. Under normal circumstances, the attitude angle of the UAV is zero. At this time, the lift fan pull and ducted lift-increasing system's aerodynamic force are vertically upward. Due to the existence of the small wing, the deflection angle of the rising duct is generally less than 90 degrees. The aerodynamic deflection angle of the ducted lift-increasing system is related to the deflection angle of the duct and the deflection angle of the small wing, which can be expressed as  
\[i_{di}=f(i_{d},i_{iw}) \tag{12}\]  
where \(i_{di}\) is the resultant deflection angle of the ducted lift-increasing system, \(i_{d}\) is the deflection angle of the duct relative to the airframe, and \(i_{iw}\) is the deflection angle of the ducted lift-increasing system relative to the small wing.  
Figure 5 shows the force diagram of the UAV during the transition flight. In this diagram, \(\alpha\) is the fuselage angle of attack, and \(L\) and \(D\) are the wing aerodynamic lift and drag respectively, which include the aerodynamic force of the main wing's free flow and the main wing-induced aerodynamic force. According to the force of the UAV, the balance relationship can be analyzed as follows:  
\[\left.\begin{array}{c}T_{f}cos\alpha+T_{di}sin(\alpha+i_{di})+L_{A}=G\\ T_{di}cos(\alpha+i_{di})-T_{f}sin\alpha=D_{A}\end{array}\right\} \tag{13}\]  
where lift \(L_{A}\) and drag \(D_{A}\) can be expressed as  
\[\left.\begin{array}{c}L_{A}=L+L_{muv}=q_{w}A_{fw}C_{L}+\frac{1}{2}\rho V_{in }^{2}\cdot C_{L}\cdot A_{mv}\cdot\eta_{Lmuv}\\ D_{A}=D+D_{muv}=q_{w}A_{fw}C_{D}+\frac{1}{2}\rho V_{in}^{2}\cdot C_{D}\cdot A _{muv}\cdot\eta_{Dmuv}\end{array}\right. \tag{14}\]  
where subscript \"\(A\)\" represents all aerodynamic forces, including free-flow aerodynamic forces and induced aerodynamic forces on the main wing caused by duct inlet airflow. \(L_{muv}\) and \(D_{muv}\) in the formula are the induced lift and induced drag of the duct on the main wing, and the subscript \"\(muv\)\" represents the main wing-induced force.  
During the transition of a vertical take-off and landing fixed-wing UAV, the gravity of the UAV is mainly balanced by the lift fan and the ducted lift-increasing system to transition to aerodynamic balance. Early transition flight speed is low, and the wing provides a lift limitation to the critical stall angle of attack. When calculating the envelope of the transition low-speed section, the maximum angle of attack is taken as the critical angle of attack, and the maximum angle of attack in the low-speed section of the transition flight envelope satisfies the following relationship:  
\[\alpha_{ij}=i_{w}+\alpha \tag{15}\]  
where \(\alpha_{ij}\) is the critical angle of attack of the wing and \(i_{w}\) is the wing installation angle.