Mission-Oriented Propulsion System Configuration and Whole Aircraft Redundancy Safety Performance for Distributed Electric Propulsion UAVs

Abstract

Distributed electric propulsion has emerged as a prominent research area in aerospace engineering. The capabilities of shorter takeoff distance and efficient cruise flight are the important advantages of a distributed propulsion UAV over a traditional fixed-wing UAV, and the composition of multiple motors can significantly improve the safety of the aircraft. This paper proposed an overall design method for the power system of the distributed propulsion UAV with the mission requirements as inputs, using the Actuator Disk Theory and Vortex Lattice Method to analyze the aerodynamic performance corresponding to different propeller numbers and layouts, and combining with the BP neural network to obtain the optimal propeller position. Meanwhile, the Linear Quadratic Regulator method was employed to analyze different configurations of UAVs, and the effects of the number of propellers and thrust redundancy on their safety were explored. The parametric study revealed that as the number of propellers increased, the optimal horizontal distance between the propeller and the leading edge of the wing gradually decreased (closer to the wing), and the vertical distance also gradually decreased (lower to the wing). The safety study revealed that when the number of propellers reached eight or more, the UAV could maintain stable flight with a probability exceeding 70% even when two or three propulsion components fail. The computational method and safety analysis for different propeller combinations studied in this paper feature high efficiency and low computational consumption, which can provide an effective reference for the overall design phase of distributed propulsion aircraft.

1. Introduction

In recent years, air transportation, as an efficient mode, has contributed significantly to global economic growth [1]. Traditional large manned aircraft handle long-distance bulk cargo transport, while vertical takeoff and landing (VTOL) aircraft perform low-altitude emergency and rapid transport [2]. However, amid the growing diversification and personalization of demands, traditional aircraft face challenges in handling tasks, such as e-commerce transportation, while VTOL aircraft are deficient in cruising efficiency and loading capacity. Consequently, neither type is well-suited for medium-distance, medium-load missions [2].

Extensive analysis shows that distributed propulsion (DP) technology has great potential to replace traditional propulsion in this field [3]. DP technology collectively provides thrust to the aircraft’s powertrain by distributing power to multiple electric motor/engine-driven small thrusters [4]. This technology has the following advantages: (1) short-runway takeoff/landing reduces infrastructure dependence; (2) propulsion-aerodynamic coupling boosts lift-to-drag ratio and lift, increasing transport efficiency by 15–30% compared to traditional layouts; (3) redundant power units enhance safety, ensuring stable flight during engine failures for unmanned operation; (4) superior cruise aerodynamic efficiency compared to VTOL aircraft increases payload capacity by 2–3 times. At the same time, unmanned transport further improves efficiency, cutting human-induced time waste, risks, and costs, and fitting modern intelligent transport needs [5].

The personalized demand for air transportation has also further strengthened the mission adaptability requirements of the UAV. During the design process of DP systems, a key focus is on aerodynamic parameters, takeoff distance, landing distance and cruise performance, which are critical indicators in aircraft design. Corresponding to the distinct mission requirements of different flight platforms, the customized design of UAV power systems becomes essential to fully utilize DP technology.

For distributed propulsion UAVs, the propulsion components generally operate at full load during the takeoff and landing phases to provide the UAV with the maximum pulling force or negative thrust. Compared with traditional propeller designs, distributed propulsion technology necessitates a novel high-lift propeller configuration to meet UAV power demands during takeoff and landing. Patterson et al. [6] effectively reduced propeller power and thrust losses by optimizing blade angle and chord length and improving axial-induced velocity distribution behind the propeller disk, tailored to high-lift propeller operating characteristics in DP aircraft. Whitmore et al. [7] proposed a nonlinear numerical solution based on blade element momentum theory, verifying its accuracy and efficiency via performance parameters across pitch angles and advance ratios compared to wind tunnel data. Sinnige et al. [8] studied wingtip propellers’ impact on wing aerodynamics via wind tunnel tests and high-precision CFD. The results show that the wingtip propellers notably reduce wing drag, weaken wingtip vortex strength, and boost cruise aerodynamic advantages.

Wang et al. [9] enhanced the augmentation effect of propeller slipstream on wing lift by means of optimizing the aerodynamic load distribution on the propeller disk, which effectively strengthened the mean turbulence intensity compared to conventional propellers. Firnhaber et al. [10] studied propeller–wing interaction in a DP aircraft’s high-lift configuration (high flaps deflection, high angle of attack) via RANS simulations and analyzed design parameter sensitivity at high angle of attack. Comunian et al. [11] developed a numerical framework combining Vortex Lattice Method (VLM) and blade element momentum theory, optimizing DP layout via genetic algorithm. It showed higher lift coefficient, improved propulsion efficiency, and overall aerodynamic performance. Wang et al. [12] provided a detailed analysis of the propeller-wing integration flow characteristics at low Reynolds number and optimized the distributed propeller layout position. The optimized design of the propeller–wing combination has a maximum lift-to-drag ratio of 72.81.

DP aircraft face unique challenges due to their special configurations, requiring extensive computation and analysis of large datasets. High-fidelity CFD simulations and wind tunnel testing, while accurate, demand significant computational resources and financial investment. Therefore, medium-fidelity methods with efficient analysis capabilities are the preferred approach for the overall design phase of such aircraft. Thus, during the overall design phase of such aircraft, the utilization of medium-fidelity analysis methods with higher computational efficiency can significantly reduce the computational time associated with the iterative process. Sheridan et al. [13] presented the process of using the VLM to calculate aircraft aerodynamic performance and compared its results with OVERFLOW solver outputs to assess its feasibility in overall design. De Vries et al. [14] used a mid-fidelity numerical method to evaluate DP systems’ effects on lift, drag, and propulsive efficiency, validating accuracy with experimental data.

Qiao et al. [15] investigated wingtip propellers via high-fidelity CFD, finding that their wing interaction reduces induced drag and enhances lift, with lower rotational speeds yielding higher efficiency. Ma et al. [16] simulated wingtip propellers’ aerodynamic influence, showing that their slipstream shifts the trailing vortex core outward, improves lift distribution, and optimized configurations increase range by 6%. Gao et al. [17] used a meshless reconstructed vortex particle method to study multi-propeller-wing interference in distributed electric propulsion, revealing that co-rotating configurations achieve 34.33% lift augmentation and that slipstream vortex effects significantly impact aerodynamics. Guo et al. [18] optimized distributed hybrid electric propulsion energy management via nonlinear model predictive control, integrating slipstream effects to achieve 34% higher lift and 6.12% lower energy consumption, validating DP’s efficiency and endurance advantages.

In the overall design phase, aircraft safety redundancy analysis is critical, as distributed layouts make propulsion components more failure-prone than conventional ones [19]. Three main fault diagnosis techniques exist: physical model-based, expert experience-based, and machine learning-based. Miao et al. [20] proposed an adaptive nonlinear PI observer for physical model-based diagnosis, improving accuracy via real-time parameter adjustment and validating it on the L-1011 UAV. Guo et al. [21] developed a priority-coefficient fault tree expert system, balancing component importance and diagnostic time to resolve conflicts, which greatly improves the accuracy and significantly reduces the diagnostic time for landing gear fault diagnosis in aircraft. Zhang et al. [22] used principal component analysis and Bayesian optimization for Support Vector Machines in machine learning-based diagnosis, achieving 98.7% accuracy in classifying manipulator surface faults and strong generalization across rudder faults (cross-validation > 95%).

Fault-tolerant control comprises active and passive methods. With advancing aircraft design, actuators and sensors have grown more complex, increasing potential fault types. Active fault-tolerant controllers, the mainstream approach, detect and identify faults, then reconstruct commands [22]. Baskaya et al. [23] analyzed the dynamics and control structure of a small UAV with multiple power components, established a framework containing flight control and distribution modules, and designed a Support Vector Machines-based method to classify and diagnose system faults for safer and more stable flight of small UAVs. Morani et al. [24] proposed a Robust Servo LQR (RS-LQR) strategy. Compared to classical LQR, it introduced a new state-cost weighting matrix and used a yaw moment equilibrium factor to balance thrust contributions.

The main contributions of this paper are as follows:

• Establish a complete overall design method for propeller layout based on design indexes, highlighting DP UAV’s short takeoff/landing performance and cruise capability with smaller wings.
• Explore the effects of propeller numbers on aerodynamic performance and compare wingtip propeller installation impacts on flight performance.
• Automatically generate large-scale propeller geometry data via a BP neural network to match thrust requirements, maximizing distributed UAV configuration potential.
• Taking the whole UAV as the research object instead of the isolated wing–propeller model, in order to maximize the closeness to the design process of the actual UAV, and to provide a reference for engineering needs.
• Calculate the safety redundancy of different DP UAV configurations using the LQR method.

The paper structure is as follows: Section 2 presents the design specifications and geometric configuration of the DP UAV, along with the computational methodologies employed in this study and their validation. Section 3 shows the calculation results of propeller performance parameters, the takeoff distance of the aircraft, aerodynamic performance parameters of the entire aircraft, and determines the optimal propeller layout position. Section 4 analyzes the safety redundancy and stability performance under propulsion system failure conditions. Finally, conclusions are drawn in Section 5.

2. Methodology and Model

According to DP technology’s characteristics and indexes, the overall design route of “power component analysis—propeller matching—optimal layout optimization—safety analysis” is established, which is shown in Figure 1. The workflow includes (1) calculating duration, payload, weight, and aerodynamic effects via UAV energy balance and lift-weight equilibrium; (2) analyzing propulsion performance for different propeller parameters; (3) comparing flight performance across propeller quantities/layouts to find optimal aircraft configurations; (4) conducting thrust redundancy safety analysis.

2.1. Analysis of Overall Aircraft Design Metrics

Using the Tecnam P2006T as a baseline, this study replaces its conventional side-mounted engines with multiple tractor propellers to create a DP UAV for layout optimization research. The UAV’s basic parameters are listed in

Table 1. Indicators of the overall design of the UAV.

Design Indicators	Values
Takeoff weight	3000 kg
Takeoff ground roll distance	200 m
Wingspan	19.8 m
Height	3.58 m
Length	9.7 m
Aspect ratio	13.6
Cruise speed	250 km/h
Cruise altitude	6000 m
Maximum cruise speed	500 km/h

.

The DP UAVs are categorized into two classes based on wingtip configurations: the first with winglets and 3–8 propellers per wing; the second with larger wingtip propellers and 4–9 propellers per wing. Both configurations are shown in Figure 2.

2.1.1. Requirement Analysis of the Whole Machine Design Index

The 500–5000 kg range is a common load range for airborne unmanned transport aircraft. In the process of specific UAV design tasks, the fuel weight $W_{\mathrm{fuel}}$, aircraft structure weight $W_{\mathrm{empty}}$, and total aircraft weight $W_{\mathrm{tol}}$ can be calculated based on the mission load, using Roskam’s aircraft design equations and flight radius. Meanwhile, $W_{\mathrm{PL}}$ stands for payload weight.

$$W_{\mathrm{tol}}=W_{\mathrm{empty}}+W_{\mathrm{fuel}}+W_{\mathrm{PL}}$$

(1)

Aircraft takeoff and landing performance, determining airport compatibility and operational agility, is a key design focus. An analysis of DP aircraft such as “Partizan”, “X-57”, and “EcoPulse”, considering their engine conditions, indicates that takeoff roll typically ranges from 50 to 250 m, accounting for site altitude, engine parameters, and special airports designed for limited-distance maneuvers with safety margins.

For fixed-wing UAVs propelled by conventionally configured propellers, their maximum flight speed is typically limited to Mach 0.6 or below. One of the primary objectives is to avoid flow separation in the propeller tip region and the consequent risk of propeller stall, where the flow separation originates from the propeller. With the increase in flight speed, the vector resultant velocity of the propeller tip’s rotational linear velocity and the freestream velocity tends to approach or reach the speed of sound. Meanwhile, if the mismatch between the freestream velocity and rotational speed causes the local angle of attack of the propeller blades to exceed the critical value, flow separation on the blades will also be induced. This directly disrupts the aerodynamic load distribution of the propeller, ultimately leading to propeller stall, characterized by a sudden drop in thrust and increased vibration.

Therefore, design considerations such as speed limitations and rotational speed optimization are required to mitigate the stall risk. Furthermore, the cruise speed of conventional UAVs is usually matched to the peak lift-to-drag ratio, while the maximum cruise speed needs to be comprehensively determined by considering the regional radius and time requirements for mission response.

After setting initial design parameters, the mission attributes are fine-tuned with varying performance, index, and safety redundancy demands. The UAV in this study, designed for a 1-ton payload, has a maximum takeoff weight of 3 tons and a maximum takeoff roll of 150 m.

2.1.2. Takeoff Distance Analysis

The takeoff process includes two phases: the ground roll phase and the climb phase. The moment when the aircraft’s rear wheels leave the ground marks their transition. The takeoff is considered complete when the aircraft reaches a safe altitude of 35 feet. The ground roll stage is further divided into two parts: accelerating and lifting the front wheel.

The takeoff distance calculation needs to take into account the aircraft’s aerodynamic performance, power system, and local environmental conditions. The takeoff weight and wing geometry determine the critical angle of approach and stall margin, which are the criteria for calculating the corresponding speed when the aircraft reaches the lift–weight balance. Among the environmental factors, wind speed has a significant impact on the takeoff roll distance by altering the ground speed. Upwind condition improves the efficiency of effective lift generation. Additionally, the wing configuration parameters play a crucial role. And the takeoff roll distance is calculated as follows, where $Vx$ is the liftoff speed of aircraft:

$$S={\displaystyle {\int }_0^{V_x}\frac{V}{a}}dV$$

(2)

The acceleration is reasonably calculated from the forces applied to the airplane, which can be given as a general expression for the forces applied:

$$a={\displaystyle \frac{g}{G}}\left[T\cos \left(\alpha +{\phi }_T\right)-\mu G-\left(C_D-\mu C_L\right){\displaystyle \frac{\rho V^{2}S}{2}}\right]$$

(3)

Bringing the above equation into the distance formula yields a generalized equation for takeoff ground roll distance and time:

$$S={\displaystyle {\int }_0^{V_x}\frac{GV}{g\left[T\cos \left(\alpha +{\phi }_T\right)-\mu G-\left(C_D-\mu C_L\right)\frac{\rho V^{2}S}{2}\right]}}dV$$

(4)

$$t={\displaystyle {\int }_0^{V_x}\frac{G}{g\left[T\cos \left(\alpha +{\phi }_T\right)-\mu G-\left(C_D-\mu C_L\right)\frac{\rho V^{2}S}{2}\right]}}dV$$

(5)

It should be noted that in the phase of lifting the front wheel of the aircraft, the force will change with the variation in the thrust direction, which will also have some influence on the takeoff roll distance. And it is necessary to take into account the angular velocity and angular acceleration of the aircraft in order to calculate the distance of the process of lifting the front wheel. In the subsequent calculations, the takeoff ground roll distance calculation model, including the process of lifting the front wheel, will be used, and at the same time, the aerodynamic–dynamic matching design should be used to ensure the maximization of the energy utilization efficiency in the takeoff stage.

2.1.3. Cruise and High-Speed Flight Analysis

During the cruise stage, the objective is to optimize energy efficiency. Accordingly, the cruise speed must satisfy two primary constraints: the lift-to-weight equilibrium and the thrust-to-drag balance. Additionally, it should lie within the airfoil’s optimal lift-to-drag ratio range to ensure aerodynamic efficiency.

Airfoil selection must also meet the high lift coefficient requirements associated with short takeoff and landing (STOL) operations. For instance, the reference aircraft in this study is designed to meet a takeoff distance requirement of 150 m, necessitating a maximum lift coefficient in the range of 2.5 to 3.5. This requirement is dependent on the propulsion system’s thrust output. Therefore, during wing design, it is imperative to ensure that the required lift coefficient is achieved under full flap deployment.

Based on the takeoff performance and propulsion characteristics, the cruise speed is set to 250 km/h, while the maximum cruise speed is defined as 500 km/h. The aerodynamic characteristics of the airfoil directly influence the flight envelope. For example, the NACA 64-series laminar flow airfoil exhibits a maximum lift-to-drag ratio of approximately 25 at a Reynolds number of 6 × 10⁶, corresponding to a lift coefficient of 0.8. The speed associated with this peak ratio is regarded as the theoretical optimal cruise speed.

2.1.4. Flight Condition Analysis

In the practical UAV design process, propeller parameters must be carefully matched to varying flight conditions to minimize energy consumption while satisfying all design performance requirements. Therefore, a detailed analysis of the aircraft’s flight conditions is required prior to propeller configuration design and performance calculation. The flight conditions considered in this analysis are listed in

Table 2. UAV flight condition analysis.

Flight Stages	Flying Height	Flight Speed	Reynolds Number (×106)	Air Density	Temperature
Takeoff ground roll stage	0 m	0–40 m/s	0–2.27	1.23 kg/m3	288 K
Cruise stage	6000 m	70 m/s	1.71	0.47 kg/m3	249 K
High speed stage	4000 m	140 m/s	5.73	0.82 kg/m3	262 K
Landing ground roll stage	0 m	40–0 m/s	0–2	1.23 kg/m3	288 K
Climbing and descending stage	2000–0 m	70–40 m/s	3.39–2.27	1.01–1.23 kg/m3	275–288 K

. The mean aerodynamic chord of the UAV is 0.83 m, which is used to calculate the Reynolds number for aerodynamic performance evaluation.

2.2. Research and Analysis of UAV Propulsion Components

This section presents a propeller thrust design framework based on takeoff ground roll distance and liftoff speed. For a known takeoff weight and allowable ground roll (150 ± 10 m), total required thrust is numerically determined, using UAV lift/drag coefficients as variables to match output. The goal is lift–weight equilibrium at liftoff speed to ensure safe transition near stall speed. According to a study conducted by [25], when the flight Mach number is maintained within the range of [0.25, 0.5], the propulsive efficiency of the engine can remain at a stably high value. The investigation in this section will adhere to this Mach number range to ensure efficient power output of the aircraft.

2.2.1. Analysis of Propeller Design to Meet Design Requirements

In the estimation of takeoff distance, propeller thrust and aircraft lift coefficient are the primary influencing factors. To accurately model the takeoff process, this study employs a time-marching numerical method based on the average velocity formula. Within each interval, flight state variables—such as velocity, acceleration, lift, and drag—are updated iteratively to progressively approximate the actual takeoff trajectory. This approach enables a quantitative assessment of takeoff performance under specific conditions and provides a theoretical foundation for STOL design.

Figure 3 shows that with thrust 9000–12,000 N and lift coefficient 2.0–3.5, the UAV meets the target takeoff distance, takeoff ground roll distance and liftoff speed variations. Additionally, propeller performance—including thrust and efficiency—varies with inflow velocity, advance ratio, and flight Reynolds number. As these parameters change during flight, both propulsive efficiency and thrust decrease accordingly. For short takeoff, focus is placed on two strategies: maximizing thrust (10,000 N as baseline, within wing structural limits); optimizing propulsion integration via propeller slipstream effects.

2.2.2. Thrust Design for Different Numbers of Propellers

To meet thrust requirements, isolated propeller output is analyzed via engine power, rotational speed, and C_T–C_P, with wingtip propellers (for cruise) designed to produce more thrust than inboard ones; this study focuses on wing-mounted configurations labeled NP3–NP8 (winglets) and TP4–TP9 (wingtip propellers).

$$F_{total}=n\times F_{propeller}$$

(6)

To meet the STOL performance requirements of the UAV, the total thrust $F_{total}$ requirement is determined to be 10,000 N through calculations.

Table 3. Propeller thrust distribution.

Label	Propeller Thrust	Label	Propeller Thrust	Wingtip Propeller Thrust
NP3	1667 N	TP4	1000 N	2000 N
NP4	1250 N	TP5	775 N	1900 N
NP5	1000 N	TP6	640 N	1800 N
NP6	833 N	TP7	550 N	1700 N
NP7	714 N	TP8	486 N	1600 N
NP8	625 N	TP9	438 N	1500 N

presents the minimum thrust requirement for each individual propeller $F_{propeller}$ under different propeller quantity configurations, which is derived by dividing the total thrust by the number of propellers. It should be noted that as the number of propellers increases, the diameter of each individual propeller must be reduced while the rotational speed must be correspondingly increased to meet the thrust requirement. Detailed parameters such as specific diameters and rotational speeds of propellers under different configurations are provided in Appendix A,

Table A5. Power system output for different UAV configurations.

Configuration	Propeller Size	Speed	Total Power	Propeller Thrust Output	Wingtip Propeller Thrust Output	CL of α = 14°
NP3CO	1.41 m	3200 rpm	156 kW	1667 N	/	2.5
NP4CO	1.21 m	3800 rpm	158 kW	1250 N	/	1.9
NP5CO	1.14 m	3800 rpm	149 kW	1000 N	/	1.8
NP6CO	1.01 m	4400 rpm	153 kW	833 N	/	1.86
NP7CO	0.91 m	5000 rpm	157 kW	714 N	/	1.94
NP8CO	0.88 m	5000 rpm	151 kW	625 N	/	2.09
NP3CT	1.41 m	3200 rpm	156 kW	1667 N	/	2.6
NP4CT	1.21 m	3800 rpm	158 kW	1250 N	/	1.85
NP5CT	1.14 m	3800 rpm	149 kW	1000 N	/	1.78
NP6CT	1.01 m	4400 rpm	153 kW	833 N	/	1.82
NP7CT	0.91 m	5000 rpm	157 kW	714 N	/	1.89
NP8CT	0.88 m	5000 rpm	151 kW	625 N	/	2.08
TP4CO	1.14/1.48 m	3800/3200 rpm	221 kW	1000 N	2000 N	1.65
TP5CO	0.93/1.46 m	5000/3200 rpm	222 kW	775 N	1900 N	1.3
TP6CO	0.89/1.44 m	5000/3200 rpm	212 kW	640 N	1800 N	1.88
TP7CO	0.78/1.42 m	6000/3200 rpm	212 kW	550 N	1700 N	1.8
TP8CO	0.76/1.40 m	6000/3200 rpm	204 kW	486 N	1600 N	1.9
TP9CO	0.74/1.37 m	6000/3200 rpm	196 kW	438 N	1500 N	1.88
TP4CT	1.14/1.48 m	3800/3200 rpm	221 kW	1000 N	2000 N	1.7
TP5CT	0.93/1.46 m	5000/3200 rpm	222 kW	775 N	1900 N	1.35
TP6CT	0.89/1.44 m	5000/3200 rpm	212 kW	640 N	1800 N	1.87
TP7CT	0.78/1.42 m	6000/3200 rpm	212 kW	550 N	1700 N	1.82
TP8CT	0.76/1.40 m	6000/3200 rpm	204 kW	486 N	1600 N	1.88
TP9CT	0.74/1.37 m	6000/3200 rpm	196 kW	438 N	1500 N	1.91

.

The thrust values in Table 3 are minimum design values to meet STOL requirements. In practical engineering applications, a safety factor must be incorporated for verification. Particularly in high-altitude environments with low air density or under high wind speed conditions, a safety factor is necessary to compensate for the attenuation of aerodynamic performance, ensuring flight safety and performance redundancy.

2.2.3. Calculation and Analysis of Isolated Propeller Design Parameters

This subsection conducts parametric analysis to determine propeller geometric and performance parameters. Key parameters include rotational speed, diameter, and thrust/power coefficients, with initial estimates via empirical correlations refined by blade element momentum theory to design aerodynamically and thrust-satisfying shapes.

As shown in the equation below, propeller thrust $T$ is determined by the thrust coefficient $C_T$, air density $\rho$, propeller diameter $D$, and rotational speed $n$. Based on the analysis of typical UAV propellers, $C_T$ generally ranges from 0.10 to 0.15, while C_P ranges from 0.02 to 0.10. Both coefficients tend to decrease with increasing advance ratio and inflow velocity, assuming constant propeller speed and diameter. For computational efficiency, these variations are treated as linear trends in the subsequent analysis.

$$T=C_T\times \rho \times D^4\times n^2$$

(7)

Based on the previous calculations, preliminary propeller designs were extracted for different thrust levels. The geometric parameters of the propellers corresponding to each vehicle configuration were obtained and are shown in the Appendix A. The low-Reynolds-number-suited RAF 3 airfoil was selected for DP applications, with chord/twist distributions predesigned for 10 spanwise elements, which are shown in Figure 4, optimized for maximum performance under specified conditions. The performance parameters of the propeller are calculated based on BEMT.

Based on the overall thrust requirements, propeller quantity, and aerodynamic constraints, a preliminary scheme for propeller geometric parameters was established in accordance with the BEMT. Targeting the flight speed range and Reynolds number variation interval of the UAV, the RAF 3 airfoil was selected as the blade element airfoil for the propeller. Figure 4 presents the distribution results of chord lengths and twist angles for 10 spanwise blade elements. This design enables the UAV to achieve high propulsive efficiency during takeoff stage, with the initial geometric parameters of the propeller exhibiting the following characteristics: the chord length increases rapidly in the root region before stabilizing to bear concentrated loads, and gradually decreases in the tip region to reduce induced drag; the twist angle decreases progressively from approximately 70° at the root to around 25° at the tip, compensating for circumferential velocity differences to ensure uniform angles of attack across all blade elements; the angle of attack of each blade element is maintained within the efficient range of 3–5° to avoid flow separation. Building upon this preliminary propeller design, the propeller geometry was optimized incrementally, enabling it to maintain relatively efficient output under cruise, high-speed, and other operating conditions while retaining high propulsive efficiency during takeoff stage.

The BEMT integrates blade element theory and momentum theory to precisely compute the aerodynamic performance of propellers, analyzing variations in local blade element lift, drag, and induction factors, and by replacing the assumptions of “uniform disk loading” and “non-rotating flow” with “radial discretization” and “rotational flow inclusion”. Owing to space constraints, this paper presents only the most representative core equations of the BEMT framework, encompassing key components such as velocity synthesis, elemental load calculations, and momentum balance equations to support and elucidate subsequent performance analyses and computations. Figure 5 illustrates the definitions of various parameters for the propeller cross-section.

Within this framework, $W$ denotes the resultant velocity of the propeller’s rotation (Equation (8)), the inflow angle $\varphi$ is derived from the velocity components (Equation (9)), and the corresponding thrust and torque at each blade station are subsequently computed using blade element theory (Equations (10) and (11)). Herein, $V_a$ and $v_a$ denote axial freestream velocity and axial induced velocity; $V_t$ and $v_t$ represent tangential freestream velocity and tangential induced velocity, while $b$ and $dr$ correspond to local blade chord and length of the radial blade element.

$$W=\sqrt{{(V_a+v_a)}^2+{(V_t-v_t)}^2}$$

(8)

$$\tan \varphi ={\displaystyle \frac{V_a+v_a}{V_t-v_t}}$$

(9)

$$d{T}_{BEM}={\displaystyle \frac{1}{2}}\rho W^{2}b(C_L\cos \varphi -C_D\sin \varphi )dr$$

(10)

$$d{Q}_{BEM}={\displaystyle \frac{1}{2}}\rho W^{2}b(C_L\sin \varphi +C_D\cos \varphi )dr$$

(11)

Incorporating the contribution of radial velocity to thrust and relevant correction terms, the relationships between thrust, torque, and velocity are derived through solution (Equations (12)–(14)). Herein, $V_0$ denotes the far-field freestream velocity, $dA$ represents the area of the annular ring, while ${\overrightarrow{v}}_{\mathrm{i}}$ and $\overrightarrow{v}$ correspond to the mean induced velocity at the disk and the total velocity increment through the disk, respectively.

$$dF=\rho dA(V_0+{\overrightarrow{v}}_{\mathrm{i}})\overrightarrow{v}$$

(12)

$$\overrightarrow{v}=2{\overrightarrow{v}}_{\mathrm{i}}$$

(13)

$$\left[\begin{array}{c}dT\\ dQ\end{array}\right]=2\rho dA\left[\begin{array}{c}{v}_a(V_{a0}+v_a)+v_t(V_{t0}+v_t)\\ v_t(V_{a0}+v_a)+{\displaystyle \frac{v_t^2}{v_a}}(V_{t0}+v_t)\end{array}\right]$$

(14)

By coupling the equations of blade element theory and momentum theory, the numerical solution of the induced velocity is obtained (Equations (15) and (16)). The variables in blade element theory and momentum theory follow the relationship $V_{a0}=V_a$. Herein, $F_1$ denotes the tip loss factor and $N_B$ represents the number of blades.

$$4\pi rdr\rho F_1{v}_a(V_{a0}+F_1{v}_a)=N_B{\displaystyle \frac{1}{2}}\rho W^{2}b(C_L\cos \varphi -C_D\sin \varphi )dr$$

(15)

$$4\pi rdr\rho F_1{v}_t(V_{a0}+F_1{v}_a)=N_B{\displaystyle \frac{1}{2}}\rho W^{2}b(C_L\sin \varphi +C_D\cos \varphi )dr$$

(16)

Based on the thrust and torque distributions derived from the BEMT, and in conjunction with the geometric parameters of the propeller, key performance parameters such as the thrust coefficient and power coefficient are further computed. These parameters provide a basis for calculating the aerodynamic efficiency of the aircraft under different operating conditions in the subsequent sections.

2.3. Computational Methods Research

This paper utilizes the Vortex Lattice Method and the Actuator Disk Theory (ADT) to calculate the overall aerodynamic performance of the UAV. Both are widely used analytical methods in the preliminary design phase of aircraft, characterized by high efficiency, low computational resource consumption, grid-based implementation, and a certain level of accuracy.

2.3.1. Vortex Lattice Method and the Actuator Disk Method

The VLM discretizes the lifting surface into a network of horseshoe vortices, which approximates the solution to the steady linearized potential flow equations under small disturbance theory. This method transforms aerodynamic problems into a numerically solvable system of discrete vortex elements, exhibiting significant computational efficiency and adaptability to various geometric configurations.

The induced velocity at each control point, generated by the horseshoe vortices, is computed via the Biot–Savart law:

$$w={\displaystyle \frac{\Gamma }{4\pi }}{\displaystyle {\int }_c\frac{dl\times r}{{\left|r\right|}^3}}$$

(17)

By bringing in the Neumann boundary condition equation,

$$\nabla ({\varphi }_{\mathrm{VLM}}+{\varphi }_{\infty })\cdot n_{VLM}=0$$

(18)

where $\nabla$ is the Hamiltonian operator and $n_{VLM}$ is the horseshoe vortex normal vector, we obtain

$$A_{\mathrm{VLM}}\mathbf{·}{G}_{\mathrm{VLM}}=RHS$$

(19)

where $RHS$ is a column vector containing information about the free stream velocity and angle of attack:

$$rh{s}_i=-{\mathit{Q}}_{\infty }\cdot {\mathit{n}}_i$$

(20)

Upon determining the vortex ring strengths, aerodynamic loads are computed via the Kutta–Joukowski theorem.

The ADT is a simplified aerodynamic modeling technique for simulating the interaction between propellers and the flow field. Based on momentum theory, it employs an idealized thin disk to replace rotating blades for thrust simulation, while neglecting blade geometry and rotational details. In the ADT, the lift and drag coefficients at each location on the disk are determined by the relative velocity of the blade airfoil along the disk radius, and the pressure increase at each location is related to the propeller thrust per unit disk area as given in Equation (21):

$$\Delta p={\displaystyle \frac{N_{\mathrm{B}}dT}{2\pi rdr}}$$

(21)

The total thrust output by the propeller disk is obtained by integrating the thrust along the disk radius. The increase in tangential induced velocity at each location on the disk is derived from Equation (23). The variable meanings in this equation are consistent with those in BEMT, all representing information such as the velocity and angular velocity at each position of the propeller blades.

$$dT={\displaystyle \frac{1}{2}}\rho W^{2}b(c_1\cos {\varphi }_1-c_d\sin {\varphi }_1)dr$$

(22)

$$\Delta v_t=sign({\omega }_i,1){\displaystyle \frac{NdT}{4\pi r{V}_1}}{W}^{2}b(C_L\sin \varphi +C_D\cos \varphi )$$

(23)

In CFD simulations, the ADT simulates axial induced velocity by imposing a steady pressure jump across its surface and approximates rotational effects via circumferentially averaged swirl components, thereby transferring the blade angular momentum to the flow field.

This paper employs a MATLAB (v2024)-based interface coupled with the open-source tools OpenVSP (3.35.3) and VSPAERO to calculate the UAV’s aerodynamic coefficients. Parametric modeling techniques facilitate efficient generation of UAV configurations with diverse propeller arrangements using MATLAB. OpenVSP uses VLM for lifting surface discretization, while ADT simplifies propellers to disks for slipstream-induced velocity and overall aerodynamic parameter derivation.

The VSPAERO module within OpenVSP is utilized to simulate the evolution of slipstream characteristics as freestream flows interact with propellers. This enables analysis of mutual interference effects between slipstream streamlines of different propellers, thereby facilitating effective evaluation of aerodynamic interaction characteristics among multiple propellers in distributed propulsion systems.

Figure 6 shows the 8° angle-of-attack computational mesh and streamline patterns, verifying convergence and analyzing propeller–wing aerodynamic coupling, particularly propeller placement effects on surface pressure distributions.

2.3.2. Statement of Validity

In the research on propeller–wing aerodynamic interference, the VLM-ADT method has undergone systematic validation through numerical and experimental comparisons in numerous studies, with its applicability and reliability supported by sufficient evidence. To validate the accuracy of the VLM and the computational software OpenVSP introduced in the preceding subsection, experimental data from the reference were employed to verify the results of the VLM-ADT method concerning the propeller–wing interaction effect [8]. The selected physical model and simulation conditions were matched with those of the experiment.

Sinnige et al. [8] presented experimental values of thrust coefficient, power coefficient, propeller efficiency, and system aerodynamic parameters under different advance ratios achieved by varying propeller rotational speed. The figure provides validation of the simulated and experimental results for the system lift coefficient under both propeller-off and propeller-clockwise-rotation conditions. The results indicate that the simulation results are in good agreement with the experimental data, with only a slight deviation observed at large angles of attack, which is shown in Figure 7.

This deviation may arise from the insufficient capability of OpenVSP in simulating flow separation. However, this angle-of-attack regime is not the focus of the present study, and the error in the remaining intervals is less than 6%, which meets the accuracy requirements for the overall design phase.

The aforementioned validation efforts were centered on the coupling mechanism between isolated propellers and wings, as well as the accuracy in solving wing aerodynamic parameters. For distributed propulsion UAVs, propellers can not only fulfill the power output function but can also enhance the overall aircraft flight performance by acting on the wing via the slipstream effect; thus, the accurate calculation of wing aerodynamic parameters under slipstream influence constitutes a critical link in the computational process. In this study, the propeller–wing layout relationships and operating parameter ranges exhibit high similarity to the validation scenarios reported by Sinnige, with both falling within the valid application range of the method. Therefore, this method can be extended to the calculation of aerodynamic performance for distributed propulsion UAVs with different propeller combinations, providing a reliable foundation for subsequent propeller layout optimization and the solution of key performance parameters such as takeoff distance.

To validate the reliability of propeller calculation results, this paper compares the thrust and efficiency results obtained via the BEMT and OpenVSP methods for the optimized TP3 propeller with those from CFD calculations. For the CFD computations, a multiple reference frame (MRF) grid model is employed, establishing a rotating inner domain containing the propeller and a stationary outer domain. The computational domain structure is illustrated in Figure 8, where R denotes the propeller radius. The SST k-ω turbulence model with low-Reynolds-number correction is adopted, with boundary conditions set as velocity inlet and pressure outlet. Comparisons are performed using results under the aircraft’s takeoff conditions.

Under the same operating conditions, the thrust and efficiency calculated by the BEMT and OpenVSP methods are in good agreement with the RANS simulation results from Fluent, as shown in Figure 9, with the error range generally within 5.7%. This provides a reliable basis for subsequent aerodynamic data calculation of the entire aircraft.

In studies on propeller–wing aerodynamic interference, the VLM-ADT method has been validated through numerical and experimental comparisons in multiple studies, wherein Jiang et al. [26] employed the actuator disk model approach to investigate a four-engine propeller aircraft, validating the method’s effectiveness by comparing computational results with full-blade models and actuator disk models. Additionally, Cheng [27], based on the VLM-ADT method, compared results from OpenVSP simulations and wind tunnel tests for the PROWIN standard model, as well as computational results of full-blade and actuator disk configurations for the X-57 high-lift propeller, with errors within acceptable ranges, thereby validating the method’s reliability.

2.4. UAV Safety Redundancy Study

This study presents an LQR-based control strategy for maintaining flight stability in DP UAVs during single/multiple propulsion unit failures. The LQR method achieves optimal control by minimizing a quadratic cost function of state deviations and control inputs, which is widely adopted in flight control systems due to its computational efficiency and implementation simplicity. This research focuses on dynamically adjusting thrust distribution among remaining propulsion units via LQR to compensate for thrust–drag and yaw moment imbalances, while lift–gravity equilibrium and transient changes in other moments are excluded from the scope. Additionally, the system is assumed to instantaneously detect faults, and propeller dynamic delays and adjacent slipstream interactions are neglected.

First, the simplified model of the aircraft in the yaw direction is introduced. The state-space equation of the system is shown in Equation (24). The state variables $x$ are the sideslip angle, yaw angle, and yaw rate, respectively. The control input $u$ represents the thrust command of propellers (speed control of the propeller). The total thrust and yaw moment can be changed by adjusting $Fi$, where $Fi\in \left[\begin{array}{cc}{F}_{\min }& F_{\min }\end{array}\right]$. This is mainly determined by the specific changes in motor performance, which will be discussed in detail in Section 4.

$$x=\left[\begin{array}{c}\beta \\ \psi \\ r\end{array}\right]$$

(24)

$$u=\left[\begin{array}{c}{\omega }_1\\ {\omega }_2\\ ⋮\\ {\omega }_N\end{array}\right]$$

(25)

The following equation is the propeller thrust output formula, where the thrust is determined by propeller performance parameters and rotational speed.

$$F_i=k_F(V_i){\omega }_i^2$$

(26)

$$\stackrel{.}{x}=Ax+Bu$$

(27)

The system matrix $A$ is obtained by linearizing the lateral–directional dynamic equations, with its elements calculated from aerodynamic derivatives and UAV physical parameters, reflecting the natural coupling relationships among state variables. Among these, the yaw rate $r$, as a key state variable, characterizes the angular velocity of the aircraft rotating about the vertical axis, and its coupling relationships with the sideslip angle $\beta$ and thrust input are established through linearization. When a propulsion system failure occurs, asymmetric thrust will disrupt the original moment balance, leading to a non-zero drift of $r$ and thereby inducing yaw motion. The evolution of this variable is dominated by the aerodynamic derivatives $N_{\beta }$ and $N_r$, which reflect the sideslip restoring moment and angular rate damping effect, respectively. The input matrix $B$ is determined by the propeller thrust model $F_i$ and the moment arm $di$, mapping the rotational speed input ${\omega }_i$ to the change in yaw moment. Each column corresponds to the control efficiency of a propeller, and the column corresponding to the failed unit should be set to zero in the event of a failure.

$$\left\{\begin{array}{l}m(\dot{v}+u_{0}r)=Y_{\beta }\beta +Y_{r}r+Y_{{\delta }_r}{\delta }_r\hfill \\ I_{zz}\dot{r}=N_{\beta }\beta +N_{r}r+N_{{\delta }_r}{\delta }_r+{\tau }_{\psi ,\mathrm{thrust}}\hfill \end{array}\right.$$

(28)

$$\dot{\beta }={\displaystyle \frac{Y_{\beta }}{m{u}_0}}\beta +\left({\displaystyle \frac{Y_r}{m{u}_0}}-1\right)r$$

(29)

$$\dot{r}={\displaystyle \frac{N_{\beta }}{I_{zz}}}\beta +{\displaystyle \frac{N_r}{I_{zz}}}r$$

(30)

Based on the solution to the above equation, we convert the coupling relationships among the sideslip angle, yaw angle, and their rates of change into a matrix form, thereby constructing the system matrix $A$. Meanwhile, by analyzing the contribution of propeller thrust to the yaw moment and combining the quadratic relationship between thrust and rotational speed, as well as its linearization processing, the specific expression of the input matrix $B$ is derived.

$$A=\left[\begin{array}{ccc}-{\displaystyle \frac{Y_{\beta }}{mV}}& 0& {\displaystyle \frac{Y_r}{mV}}-1\\ 0& 0& 1\\ {\displaystyle \frac{N_{\beta }}{I_{zz}}}& 0& {\displaystyle \frac{N_r}{I_{zz}}}\end{array}\right]$$

(31)

$$B=\left[\begin{array}{ccc}0& \dots & 0\\ 0& \dots & 0\\ {\displaystyle \frac{\partial {\tau }_{\psi }}{\partial {\omega }_1}}& \dots & {\displaystyle \frac{\partial {\tau }_{\psi }}{\partial {\omega }_N}}\end{array}\right]$$

(32)

In the design of the weight matrix, for the thrust allocation constraints of a 3-ton fixed-wing UAV with a cruising speed of about 120 km/h, the determination of the $R$ matrix coefficient of 1.56 × 10⁻⁶ s²/rad²; comprehensively considers the physical limitations of the propulsion system. According to the maximum thrust of 1500 N corresponding to the maximum propeller rotational speed of 700 rad/s, the input weight is normalized to the reciprocal of the square of the rotational speed using Bryson’s rule. Meanwhile, to prevent attitude oscillations caused by local lift changes exceeding 10% due to sudden thrust changes, the ratio of the yaw angle weight (25, corresponding to a maximum allowable error of 0.3 rad) to the sideslip angle weight (10) in the $Q$ matrix has been verified through CFD aerodynamic coupling analysis. This ensures that both the recovery time < 5 s and power consumption < 20% increase requirements can be simultaneously met within the thrust range of 1000–1500 N.

$$Q=\left[\begin{array}{ccc}{q}_{\beta }& 0& 0\\ 0& q_{\psi }& 0\\ 0& 0& q_r\end{array}\right]$$

(33)

$$R=r_0{I}_N$$

(34)

The objective function of LQR is as follows:

$$J={\displaystyle {\int }_0^{\infty }\left(x^{\mathrm{T}}Qx+u^{\mathrm{T}}Ru\right)}dt$$

(35)

Optimal control applies the minimum principle to obtain the optimal control action $u=-Kx$ under the condition that the objective Equation (35) is minimized. In this context, the state feedback gain matrix is given by $K=R^{-1}{B}^{\mathrm{T}}P$. $P$ represents the positive semi-definite solution to the Riccati Equation $A^{\mathrm{T}}P+PA-PB{R}^{-1}{B}^{\mathrm{T}}P+Q=0$. Given the substantial computational load involved in solving the Riccati Equation, the linear quadratic optimal toolbox in MATLAB is employed herein to obtain the solution.

3. Results

This section numerically investigates aerodynamic characteristics of DP UAVs, emphasizing safety redundancy analysis. It evaluates flow field and aerodynamic performance across configurations (with/without wingtip propellers, varying rotation directions) to facilitate comparative studies. These configurations, categorized in Figure 10, use standardized nomenclature:

• Wingtip propellers: ‘T’ (with) and ‘N’ (without).
• Quantity: ‘P’ + numeral (e.g., ‘P3’ for three).
• Rotation: ‘CO’ (co-rotating), ‘CT’ (counter-rotating).
• Positioning: ‘X’ (chordwise) and ‘Z’ (spanwise) coordinates relative to wing leading edge.

Existing literature suggests that densely clustered propeller arrangements demonstrate negligible aerodynamic performance advantages compared to uniformly distributed configurations, while introducing significant motor integration challenges and structural constraints. Consequently, this investigation exclusively considers uniformly spaced propeller distributions to maintain focus on fundamental aerodynamic interactions.

3.1. UAV Aerodynamic Performance Parameter Results

3.1.1. Propeller Aerodynamic Performance Data

This section presents a numerical simulation of aerodynamic coefficients for the DP UAV using an integrated VLM and ADT approach. The actuator disk parameters are derived from computational analysis of propeller model characteristics conducted in the preceding section. The simulation results enable a comprehensive evaluation of key performance metrics, including takeoff distance, cruise speed, and maximum flight velocity, with takeoff performance as the primary evaluation criterion, given its significance for STOL capability.

The propeller design process integrates BEMT with optimal circulation distribution principles. Taking the initial BEMT-derived configuration (Figure 4) as the baseline, optimization adheres to the principle of “prioritizing takeoff performance (10% allowable degradation margin) with equal weights for cruise and high-speed conditions”. The two-bladed propeller geometry finally optimized is illustrated in Figure 11, which balances performance across takeoff/landing, cruise, and high-speed flight regimes.

Based on the propeller geometry, aerodynamic parameters under different conditions are calculated using OpenVSP’s propeller analysis module. Taking the NP5CO configuration as an example, performance parameters for different advance ratios (in Appendix A) serve as inputs for UAV takeoff distance calculation, with analysis on aerodynamic performance of propellers with different blade numbers (same diameter) at varying incoming velocities.

At J = 0.14, the thrust coefficient increases from 0.18 to 0.40 (112% thrust enhancement) as blades rise from 2 to 5, but with higher power consumption. Multi-blade propellers excel at low J (J < 0.2) in thrust, while fewer blades are more efficient at high J (J > 0.4).

Engineers prefer multi-blade for high-thrust phases (takeoff/climb) and fewer blades for efficient cruise. Thus, wingtip propellers use three blades and wing-mounted ones use four blades, ensuring takeoff/landing thrust and cruise efficiency.

After determining geometry and blade count, power and thrust coefficients across conditions are inputs for subsequent calculations. At 20 m/s freestream, propeller thrust/power and UAV lift coefficient at α = 14° (stall angle) are evaluated (UAV lifts off before this angle; propeller installation angle 0°). The computational results are summarized in Appendix A. Figure 12 shows the lift coefficient and lift-to-drag ratio of different UAV configurations for angles of attack from 5° to 14°.

3.1.2. Calculation Results of Propeller Performance Parameters and Takeoff Ground Roll Distance of the UAV

The aerodynamic performance characteristics of a propeller are closely related to the advance ratio. The aggravation of flow separation on the propeller blade surface is mainly attributed to the mismatch between freestream velocity and rotational speed, rather than a mere excess of rotational speed increment over flight velocity.

It should be noted that when the freestream Mach number approaches or reaches the critical value, the supersonic flow and shock wave effects in the propeller tip region will be significantly enhanced.

Under such circumstances, the effectiveness of solutions such as pure rotational speed adjustment in suppressing separation will be obviously limited, and meanwhile, there will be a large discrepancy between the actual flight performance of the UAV and the numerical simulation results. Following preliminary diameter analysis, the aerodynamic parameters corresponding to various advance ratios are determined through unsteady propeller modeling.

During takeoff distance calculations, the variation in propeller thrust between low-speed and high-speed regimes necessitates the development of a thrust–velocity mathematical model. This physics-based approach enables accurate integration of acceleration and distance computations throughout the ground roll phase. The iterative calculation methodology, illustrated in Figure 13, utilizes propeller performance parameters, operational conditions, and initial values as inputs to compute incremental taxiing distances. The analysis yields the total takeoff distance for DP UAV, encompassing both the ground roll phase and rotation-to-liftoff transition. The specific results are shown in

Table 4. Takeoff taxi distance for different UAV configurations.

Configuration	Takeoff Ground Roll Distance	LiftOff Distance	Total Distance	Configuration	Takeoff Ground Roll Distance	LiftOff Distance	Total Distance
NP3CO	119 m	38 m	157 m	TP4CO	124 m	39 m	163 m
NP4CO	112 m	37 m	149 m	TP5CO	115 m	38 m	153 m
NP5CO	111 m	37 m	148 m	TP6CO	114 m	37 m	151 m
NP6CO	116 m	34 m	150 m	TP7CO	108 m	33 m	141 m
NP7CO	105 m	34 m	139 m	TP8CO	103 m	33 m	136 m
NP8CO	101 m	33 m	134 m	TP9CO	100 m	31 m	131 m
NP3CT	116 m	40 m	156 m	TP4CT	119 m	41 m	160 m
NP4CT	110 m	37 m	147 m	TP5CT	116 m	38 m	154 m
NP5CT	108 m	37 m	145 m	TP6CT	112 m	38 m	150 m
NP6CT	106 m	34 m	140 m	TP7CT	107 m	35 m	142 m
NP7CT	109 m	34 m	143 m	TP8CT	106 m	34 m	140 m
NP8CT	102 m	32 m	134 m	TP9CT	102 m	32 m	134 m

.

3.1.3. Aerodynamic Performance of UAV in Cruise and High-Speed Stage

Following the completion of propeller modeling, the aerodynamic characteristics of the prototype UAV are evaluated for both cruise and high-speed flight conditions. The analysis procedure consists of three primary stages: First, the propeller’s aerodynamic performance is computed under specified operational conditions, including atmospheric parameters and Reynolds number effects, to determine thrust output during cruise and high-speed stage. Subsequently, an integrated VLM-ADT is employed to calculate the complete UAV’s aerodynamic characteristics. This enables assessment of power requirements during cruise, with subsequent adjustment of key parameters such as cruise altitude or wing installation angle based on the wing’s lift-to-drag ratio characteristics. Finally, the UAV’s maximum speed is determined through analysis of the airframe’s drag characteristics at full power system loading.

3.2. Optimization Calculations

This paper introduces a BP neural network to predict UAV aerodynamic performance. In this study, aerodynamic data, including key parameters such as lift coefficient, drag coefficient, and lift-to-drag ratio under various propeller layouts, are first obtained through numerical simulation. The network uses propeller position coordinates as inputs and aerodynamic coefficients as outputs, with hidden layers/neurons determined via cross-validation for fitting and generalization balance.

For the sample UAV under investigation, the propulsion components are equally spaced, with the propeller’s chordwise position varying from 0.1 m to 0.7 m relative to the wing leading edge and its vertical position ranging from +0.5 m (above wing axis) to −0.7 m, using an interval step size of 0.05 m to compute the theoretical dynamic performance at different configurations. The BP neural network enables aerodynamic performance prediction at a finer resolution than the original 0.05 m interval. While the initial 0.05 m step size generates 325 data points, the neural network predicts performance at a refined 0.01 m interval, producing 7381 data points. Under cruise conditions, the wing lift coefficient distribution obtained through this method is shown in Figure 14.

The optimal propeller positions obtained from the optimization of each aforementioned configuration were aggregated and comparatively analyzed, with specific results presented in Figure 15. In this figure, different curves correspond to different UAV configurations, where X denotes the horizontal distance between the optimized propeller disk center and the wing leading edge point, and Y represents the vertical distance between the optimized propeller disk center and the wing leading edge point.

The results indicate that the optimal chordwise position gradually decreases with increasing propeller count, demonstrating that propellers should be installed progressively closer to the wing leading edge. Simultaneously, the optimal vertical position decreases, indicating that the propeller installation location should move downward along the wing, while winglet configurations maintain a higher elevation compared to wingtip propeller installations. These conclusions are consistent with the findings reported in Ref. [10] regarding the aerodynamic interaction between isolated propellers and DP systems with wing configurations.

4. Security Redundancy Analysis Results

The stability maintenance capability of a distributed electric propulsion UAV in various propulsion component failure scenarios (1–4 failed units) was investigated through MATLAB/OpenVSP simulations, examining different propeller configurations and thrust redundancy levels (30%, 50%, and 100%). Figure 16 shows the stability trends versus propulsion component count.

This study introduces a stabilization rate metric, defined as the ratio of recoverable failure cases (where stability is maintained through thrust redistribution within specified redundancy limits) to total possible failure combinations. For example, a six-propeller configuration with 30% thrust redundancy achieves a stabilization rate of 2/6, successfully recovering stability in two out of six single-component failure scenarios.

The results demonstrate that UAV stability during propulsion failures is positively correlated with both system thrust redundancy and propeller count while being negatively correlated with the number of simultaneous failures, which is consistent with established system safety principles.

Specific operational thresholds are identified as follows: At 30% redundancy, ≥12 propellers maintain stability under single failures, ≥14 for multiple failures; at 50%, ≥8 and ≥12, respectively; at 100%, any configuration withstands single failures, ≥10 needed for multiple scenarios.

This subsection presents propulsion system control response following a single component failure, analyzed via an eight-propeller UAV (50% thrust redundancy). Upon failure detection (t = 5 s), the LQR algorithm adjusts the remaining units to restore thrust–drag equilibrium and yaw moment balance. Figure 17 shows thrust variations and corresponding UAV mechanical property changes.

Post-failure (t = 5 s, unit #5), dynamic adjustment has three phases: initial rapid response (0 to 0.8 s) with symmetric unit #6 increasing thrust, establishing compensation within 800 ms; coordinated adjustment with outermost units optimizing thrust distribution and yaw compensation; steady convergence stabilizing at 1000 ± 5 N total thrust with torque stability, validating the algorithm. Figure 18 details component responses, with color-coded strips showing operational unit thrust variations relative to the failed component.

5. Conclusions

This study presents a comprehensive investigation into DP system design for UAV, addressing key challenges including multiple configuration options, complex layout methodologies, and coupled geometric parameters of propulsion components. By employing an integrated approach combining the VLM and ADT, we achieve significant improvements in computational efficiency while maintaining rigorous aerodynamic analysis accuracy, enabling thorough evaluation of multiple UAV configurations during overall design stages.

The research develops a novel propeller design methodology specifically tailored for mission-optimized DP UAVs, with particular emphasis on mass variation relative to takeoff ground roll distance. Performance validation through “BEMT” and OpenVSP software establishes a robust closed-loop analysis framework that effectively verifies compliance with design specifications. Our analysis reveals important trends in optimal propeller positioning: as the number of propellers increases, the optimal chordwise installation position moves closer to the wing leading edge while the vertical position shifts downward. Comparative studies further demonstrate that winglet-equipped configurations exhibit characteristically different placement, being positioned farther aft and higher vertically compared to wingtip-mounted propeller arrangements.

Critical redundancy requirements are quantitatively established through systematic analysis. For 30% thrust redundancy, configurations require at least 12 components to maintain stability during single failures and 14 components for multiple failures. These thresholds reduce to 8 and 12 components, respectively, at 50% redundancy, while 100% redundant systems can withstand single failures with any position of components and multiple failures with 10 or more components. These findings provide essential guidelines for DP system design and configuration optimization.

The method developed in this paper provides an efficient analytical framework for the overall design of DP UAV, which can significantly reduce computational time, improve design efficiency, and serve as a reference for the design of DP UAV.