In our research, we focus on the transition corridor of ducted vertical take-off and landing (VTOL) fixed-wing drones. These drones combine the hovering capability of rotorcraft with the endurance and speed of conventional fixed-wing drones. The transition process from vertical flight to forward flight is critical, and the transition corridor defines the feasible region of flight parameters during this phase. We establish a comprehensive model to describe the transition corridor of such a fixed-wing drone, considering both aerodynamic limits and power constraints. Our model provides a method to compute the deflection angle–speed envelope of the powered lift system, which is essential for safe and efficient transition maneuvers.
1. Transition Corridor Model
The transition corridor of a VTOL fixed-wing drone is analogous to the flight envelope of conventional aircraft. We define the corridor using two boundaries: the left boundary (low-speed side) determined by the maximum lift coefficient of the wing, and the right boundary (high-speed side) limited by the available power of the propulsion system. The powered lift system consists of a front lift fan and a rear ducted propulsion unit with deflectable vanes. During transition, the rear ducted unit tilts, and the lift fan adjusts its thrust to balance the drone’s weight and provide forward acceleration.
1.1 Transition Window
The transition window includes the start (hover) condition and the end (safe forward flight) condition. At hover, the drone must maintain a safe altitude with zero forward speed. At the end of transition, the fixed-wing drone must achieve a safe cruising speed above the stall speed. The safe forward speed $V_{safe}$ is typically defined as 1.2 times the stall speed $V_s$:
$$ V_{safe} = 1.2\,V_s $$
where the stall speed is obtained from the equilibrium condition:
$$ G = \frac{1}{2}\rho V_s^2 S\,C_{Lmax} $$
Here $G$ is the weight, $\rho$ the air density, $S$ the wing area, and $C_{Lmax}$ the maximum lift coefficient. The moment balance during hover must also be satisfied:
$$
\begin{cases}
T_f \cos\theta + T_{di}\sin(\alpha_{di}+\theta) + L = G \\
T_f l_f = T_{di}\sin\alpha_{di}\,l_{di}
\end{cases}
$$
where $T_f$ and $T_{di}$ are thrusts of the lift fan and ducted unit, $\theta$ the pitch angle, $\alpha_{di}$ the duct resultant force angle, and $l_f$, $l_{di}$ the moment arms.
1.2 Low-Speed Boundary: Maximum Lift Coefficient Criterion
The left boundary of the transition corridor is established by ensuring the wing does not stall during the tilt transition. The force balance of the fixed-wing drone in transition is:
$$
\begin{cases}
T_f\cos\alpha + T_{di}\sin(\alpha + \alpha_{di}) + L_A = G \\
T_{di}\cos(\alpha + \alpha_{di}) – T_f\sin\alpha = D_A
\end{cases}
$$
where $\alpha$ is the fuselage angle of attack, $L_A$ and $D_A$ are the total lift and drag of the wing (including induced effects from the ducted unit). The lift and drag are expressed as:
$$
\begin{cases}
L_A = q_w A_{fw}C_L + \frac{1}{2}\rho V_{in}^2 C_L A_{mw}\eta_{Lmw} \\
D_A = q_w A_{fw}C_D + \frac{1}{2}\rho V_{in}^2 C_D A_{mw}\eta_{Dmw}
\end{cases}
$$
The wing angle of attack must not exceed the stall angle $\alpha_{lj}$:
$$ \alpha_{lj} = i_w + \alpha $$
where $i_w$ is the wing incidence angle. By solving the balance equations under the condition that the wing operates at the maximum lift coefficient, we obtain the admissible deflection angle $\alpha_{di}$ as a function of forward speed $V$ – this defines the left boundary.
1.3 High-Speed Boundary: Available Power Criterion
The right boundary is determined by the maximum power that can be delivered by the propulsion system (lift fan and ducted unit). The required power $P_r$ for each rotor is composed of induced power $P_i$, profile power $P_{pr}$, parasite power $P_p$, and climb power $P_c$:
$$ P_r = \frac{2}{\eta_p}(P_i + P_{pr} + P_p + P_c) $$
where $\eta_p$ is the transmission efficiency. Using momentum theory and blade element theory, the sum of induced, parasite, and climb power can be written as:
$$ P_{ipc} = T(U_c + K_{ind}v_i) $$
with $U_c$ the climb velocity at the rotor plane and $v_i$ the induced velocity; $K_{ind}$ accounts for non-uniform inflow. The profile power is:
$$ P_{pr} = P_{pr0}(1 + 4.7\mu^2) $$
where $\mu$ is the advance ratio and $P_{pr0} = \sigma\pi R^2\rho V_t^3 C_D/8$ (with $\sigma$ solidity, $V_t$ tip speed). The total required power must be less than the rated power $P_n$:
$$ P_r < P_n $$
By solving the force balance simultaneously with the power limit, we obtain the right boundary of the transition corridor.
1.4 Calculation Procedure
We implement the following iterative scheme:
- Initialize hover conditions using the moment balance equation to obtain $T_f$, $T_{di}$, and $\alpha_{di}$ at $V=0$.
- For a given forward speed $V$, assume an angle of attack $\alpha$ such that the wing lift equals the maximum allowed (left boundary) or assume a duct deflection angle (right boundary).
- Compute aerodynamic coefficients $C_L$, $C_D$ from pre-computed data (e.g., wind tunnel or CFD).
- Solve the force balance equations for $T_f$, $T_{di}$, and $\alpha_{di}$.
- For the right boundary, compute the required power and check if it equals the available power; adjust $\alpha$ iteratively to satisfy the power constraint.
- Repeat for a range of speeds to construct the complete $\alpha_{di}$–$V$ envelope.
The resulting transition corridor is the region enclosed by the left and right boundaries.
2. Case Study: A Representative Ducted VTOL Fixed-wing Drone
We apply our model to a specific ducted VTOL fixed-wing drone configuration. The drone uses a front lift fan and a rear ducted propulsion unit with a fixed vane behind the duct to vector thrust. Key parameters are listed in Table 1.
| Parameter | Symbol | Value | Unit |
|---|---|---|---|
| Duct deflection angle (relative to body) | $i_d$ | 0 – 30 | deg |
| Resultant thrust angle | $\alpha_{di}$ | 0 – 95 | deg |
| Lift fan rated power | $P_f$ | 26 | kW |
| Ducted unit rated power | $P_d$ | 14 | kW |
| Transmission efficiency | $\eta_p$ | 0.95 | – |
| Propeller tip speed | $V_t$ | 180 | m/s |
| Wing area | $S$ | 1.2 | m2 |
| Max lift coefficient | $C_{Lmax}$ | 1.8 | – |
| Stall angle of attack | $\alpha_{lj}$ | 15 | deg |
Using the procedure described in Section 1, we compute the transition corridor for this fixed-wing drone. The left boundary (based on stall margin) is shown in Figure 1 (note: illustration would be inserted here). At hover, the duct resultant angle is about 75°, and the minimum forward speed to achieve fully fixed-wing mode is 43 m/s. The right boundary (based on power limit) indicates that the duct can remain nearly vertical up to a certain speed before power is exhausted; beyond that, the duct must tilt forward to reduce power demand.
2.1 Influence of Pitch Attitude and Duct Tilt Rate
We analyze the effect of different pitch angles during transition. A larger pitch angle allows earlier lift balancing at lower speeds but increases drag and power consumption. A smaller pitch angle requires higher forward speed to generate sufficient wing lift. The transition speed as a function of pitch angle is summarized in Table 2.
| Pitch Angle $\theta$ (deg) | Forward Speed at Duct Fully Forward (m/s) |
|---|---|
| 5 | 48.2 |
| 10 | 43.5 |
| 15 | 39.1 |
| 20 | 35.6 |
The duct tilt rate also influences the ability to maintain equilibrium. Our simulations show that the maximum allowable tilt rate is about 14°/s; beyond that, the lift fan cannot compensate the moment changes. An optimal combination for smooth transition is a pitch angle of 3° with a duct tilt rate of 5°/s and vane rate of 1.5°/s.
2.2 Methods to Expand the Transition Corridor
We investigate two approaches: improving aerodynamic parameters (wing area or maximum lift coefficient) and increasing available power. The left boundary shifts leftward (lower stall speed) when wing area or $C_{Lmax}$ is increased. The right boundary shifts rightward (higher maximum speed) when available power is increased. Table 3 quantifies the corridor width expansion for a 10% change in each parameter.
| Parameter | % Increase | Corridor Width Increase (%) |
|---|---|---|
| Wing area $S$ | 10 | 2.33 |
| Max lift coefficient $C_{Lmax}$ | 10 | 2.33 |
| Available power $P_n$ | 10 | 21.43 |
Clearly, improving power has a much stronger effect on expanding the transition corridor for this fixed-wing drone. A 10% power boost yields a 21.43% wider corridor, whereas aerodynamic improvements yield only about 2.33% expansion. Therefore, in the design of ducted VTOL fixed-wing drones, enhancing propulsion system power is an efficient way to enlarge the safe transition envelope.
3. Conclusions
We have developed a transition corridor model for ducted vertical take-off and landing fixed-wing drones. The model is based on the deflection angle–speed envelope of the powered lift system, bounded by the maximum lift coefficient on the low-speed side and by the available power on the high-speed side. The case study on a representative fixed-wing drone confirms the validity of the approach. The transition corridor is significantly affected by pitch attitude and duct tilt rate. Our analysis shows that increasing available power is far more effective than improving aerodynamic parameters for expanding the corridor: a 10% power increase widens the corridor by 21.43%, while a 10% increase in wing area or $C_{Lmax}$ widens it by only 2.33%. These findings provide guidance for the design and flight control of ducted VTOL fixed-wing drones, ensuring safe and efficient transition flight.