Abstract
Herein, a twin-boom, inverted V-tailed unmanned aerial vehicle (UAV) featuring a foldable bi-wing configuration is proposed for logistics and transportation applications. We employed the Navier–Stokes solver to numerically simulate steady, incompressible flow conditions. By examining the effects of key design parameters on aerodynamic characteristics and bypass flow fields in a two-dimensional state, we were able to suggest a more optimized foldable wing design. Building on the two-dimensional analysis, we performed aerodynamic assessments of the three-dimensional aircraft geometry. Our results indicated that appropriate wing and gap parameters can significantly enhance lift characteristics, maintaining high lift even during large-angle flights. Specifically, when compared to a mono-wing, the lift coefficient of the bi-wing increased by 27.1% at a 14° angle of attack, demonstrating the effectiveness of our wing-and-gap design. Optimal aerodynamic performance was achieved when the gap distance equalled the chord length in both flow and vertical directions. Further, the right combination of airfoil configuration, wing axes angle, and wingspan can improve flow field aerodynamic characteristics, while also enhancing the wing’s stall capacity. The lift coefficient reached its maximum value at an angle of attack of 15°, which has the potential to reduce takeoff and landing distances, thereby enhancing the UAV’s overall safety.
1. Introduction
Given the advancements in general aviation technology and improvements in logistics efficiency, there has been a consistent rise in demand for faster and larger load-carrying capabilities in the logistics and transportation sectors [1]. While land and air cargo transport have gained traction, the cost and efficiency of transporting goods in mountainous, plateau, and island regions remain a challenge. Unmanned aerial vehicles (UAVs) have emerged as a promising solution, offering quicker transport times and reduced labour costs [2–6]. Reports by Szalanczi-Orban and Vaczi show that the global drone market is on an upward trajectory, demonstrating ever-increasing growth and economic potential [7]. According to Kapustina et al., the global drone market is expected to grow from $20 billion to $45 billion by 2025, cementing drones as a burgeoning application area in logistics [8]. Given their technology-intensive nature, drones are poised to have a significant positive impact on the market. Research by Merkert et al. indicates that, all things being equal, people generally prefer traditional postal delivery, but drones could gain substantial market share if they offer quicker and more cost-effective options [9].
In comparison to motorized transport, traditional UAVs often require fixed runways for takeoff and landing. This presents challenges in constructing long enough runways in areas such as mountains or hills. Tilt-rotor aircraft, while innovative, tend to underperform fixed-wing UAVs in aspects like equipment weight, aerodynamic efficiency, and energy consumption. The payload limitations of these UAVs also reduce their efficiency per transport. In contrast, fixed-wing aircraft, known for their superior aerodynamic performance, are generally used for heavy cargo transport. To be viable for logistics, these UAVs must possess sufficient takeoff lift and short takeoff and landing (STOL) capabilities, all while minimizing aerodynamic losses during cruising. This has become a key research direction in the field of logistics-focused UAVs.
High-lift devices (HLDs) are frequently commonly by aircraft designers to enhance lift coefficients. These devices are categorized into two main types: leading-edge high-lift devices (LEHLDs) and trailing-edge high-lift devices (TEHLDs or flaps). LEHLDs improve the wing’s stall angle of attack and maximum lift coefficient without causing significant deviations in the wing’s lift curve. Often, they are used in tandem with TEHLDs, which also serve to increase the maximum lift coefficient. Together, LEHLDs and TEHLDs alter the airfoil’s camber and delay flow separation [10] (pp. 35-113).
However, implementing LEHLDs and TEHLDs in UAVs with short chord lengths presents challenges. The aerodynamic forces exerted by these flaps are borne by structural reinforcement points on the wings, requiring thicker skin to handle the increased torque. An imperfect structural design can compromise wing strength, while the thicker skin can reduce payload weight—a significant drawback for logistics-focused aircraft with high load requirements. The use of two-section or multisection wings can effectively improve lift coefficients without sacrificing wing strength.
In terms of biplane design schemes, Zhang and Ye have studied the aerodynamic characteristics of aircraft with row-type biplane layouts [11]. The research analysed the impact of regular airfoil thickness and hindwing deflection angle on double-tandem wing aerodynamic traits across various angles of attack. Their findings reveal that the tandem wing configuration could delay or even prevent trailing-edge separation, thereby significantly enhancing aerodynamic efficiency. This suggests that such configurations are particularly promising for UAVs. Zhan et al. further investigated biplane configurations aimed at improving the aerodynamic attributes of fixed-wing microair vehicles (MAVs) through low-speed wind tunnel experiments [12]. The study compared the aerodynamic characteristics of various planforms, monoplanes, and biplanes while examining the effects of different gaps, stagger positions, and planform configurations. Based on experimental results, the interaction mechanisms of the flow field were analysed. The study concluded that biplane configurations can indeed improve the aerodynamic characteristics of monoplane fixed-wing MAVs, and that the relative positioning of the biplanes plays a significant role in influencing these aerodynamic attributes.
Several scholars have designed the flap angles in multielement airfoils. Lv et al. [13] used the Reynolds-averaged Navier–Stokes equation to study how various wing and flap angles affect aerodynamic characteristics, specifically employing a DLR-F11 wing for the study. The research identified the optimal flap deflection angle for both takeoff and landing, offering valuable insights for fine-tuning flap control procedures. Similarly, Li et al. [14] focused on a two-section wing, exploring the influence of trailing-edge flap profiles based on specific trainer design requirements. The study investigated how slot size and overlap affect flap lift and surface pressure coefficients. Kong et al. proposed a new trailing-edge lift device based on a large aircraft’s basic airfoil to scrutinize the aerodynamic effects brought about by flap bending and spoiler deflection [15]. The study found that downward spoiler deflection enhanced slot airflow, subsequently improving aerodynamic performance. Remarkably, even a slight spoiler deflection could result in significant aerodynamic gains in the linear stage with a small angle of attack.
This paper proposes a twin-boom, inverted V-tailed UAV equipped with a foldable wings configuration [16–18]. The wings of this UAV are designed to adapt to different mission stages; they spread out to provide sufficient lift during takeoff and landing and fold in during cruising to reduce aerodynamic drag. A suitable folding mechanism allows the UAV to transition between these configurations without compromising structural wing strength or flight safety. However, each wing configuration has a unique influence on the flow field. To optimize lift and ensure an effective flow field distribution, it is imperative to examine various wing configurations. To end this, this study employed computational fluid dynamics (CFD) for numerical analysis based on this concept.
Figure 1 depicts the research roadmap for this study. The preconceptual design stage involved defining the mission requirements and generating an initial aircraft size and configuration. Guided by pertinent parameters and requirements, the biplane design process was initiated. This design stage is comprised of two-dimensional airfoil design and analysis, as well as three-dimensional bi-wing design and analysis. CFD simulations are employed to compute and assess both the two-dimensional and three-dimensional models. Subsequently, the design parameters for the bi-wing are finalized. The CFD results are then leveraged to evaluate the aerodynamic characteristics and overall stability of the UAV.
The remainder of this paper is structured as follows. Section 2 introduces methodologies employed for the conceptual and preliminary design stages of the UAV. These methodologies encompass weight estimation and aerodynamic design, both aligned with the initial mission requirements. The numerical computational model, including mesh convergence analysis and method validation, is also elaborated. Section 3 delves into the numerical examination of the aerodynamic characteristics based on four key parameters and provides a detailed aerodynamic analysis focusing on the three-dimensional wingspan, aircraft flight performance and static flight stability. The paper concludes with Section 4, summarizing the key findings.
2. Materials and Methods
2.1. Mission Specifications
Mountainous regions and islands are the primary focus for the logistics UAVs in this study, given the unique challenges and mission requirements of these terrains. Constructing long, flat runways in such areas is impractical due to rugged mountainous terrain and the fragmented nature of island groups, which often lack comprehensive road networks. Moreover, these remote locations are often far removed from logistics distribution centres and mainland facilities. Traditional transportation methods such as human portage and trucking are inefficient and inconvenient, while rotorcrafts are ill-suited for carrying large quantities of cargo in areas with variable airflows. In this study, we focussed on using UAVs for the last five-kilometre delivery, aiming to augment mountainous and island-based logistics systems.
To align with these unique geographical constraints, this study conducted a thorough analysis of the flight phases of a logistics UAV to determine the aerodynamic design requirements and objectives.
Two locations in China were selected to represent typical geographical features: Xinyang City in Henan Province, known for its mountainous hills, and Zhoushan City in Zhejiang Province, characterized by its island archipelagos. In Xinyang, the production of Maojian tea is concentrated in mountainous areas, making it difficult for large container vehicles to navigate the region. As a result, tea is usually transported manually, which is both inefficient and poses safety risks. Using rotorcrafts to airlift tea would require significant energy to counteract gravity, making it less efficient for multiple deliveries. Therefore, we considered using logistics UAVs to bridge this gap. By constructing a short runway on a mountain, UAVs can take off and land efficiently, allowing for a larger cargo capacity and higher aerodynamic efficiency, ultimately reducing the total energy consumption of flights. Employing UAVs for quick, short-distance transport between the tea-picking locations on the mountain and the tea-processing centres at lower elevations could streamline the tea industry and significantly reduce labour costs.
For the case study, the UAV was chosen to operate within the airspace of Xinyang. Accordingly, a 40 km round-trip design range was determined to be optimal for covering the major tea-producing areas within Xinyang, such as Shihe, Pingqiao, and Luoshan (as shown in Figure 2). This ensures that the primary tea-producing locations fall within the operational scope of the UAV.
The Zhoushan aquatic product base is a rich source of fresh marine produce that needs to be swiftly transported to various processing points [19]. Given the densely forested and fragmented nature of the Zhoushan Islands, along with scattered fishing locations, traditional ground transportation is infeasible. Rotorcrafts also face limitations in carrying large quantities of heavy aquatic products. Logistics UAVs, however, are well-suited for quickly moving large volumes of aquatic produce between multiple islands, thus ensuring product freshness. Considering the unique mission requirements for operations in mountainous, hilly, and island terrains, the logistics UAVs must possess essential capabilities such as short takeoff and landing distances, large payload capacities, and excellent cruising aerodynamics. Additionally, these geographical features often present strong convective environments, necessitating a thorough evaluation of UAV stability.
For the case study focusing on the Zhoushan Islands, the UAV is configured for a 40 km operational range, covering major aquatic bases and major fisheries such as Shengshan, Daji, Huangze, Daiqu, Zhougxian, and Jintang (as depicted in Figure 3).
To adapt to different mission requirements, the UAV’s aerodynamic configuration can be altered accordingly. Figure 4 illustrates typical flight profiles. During takeoff and landing, the UAV’s wings are fully extended to maximize the lift coefficient, facilitating short-distance takeoff and landing. In the cruising phase, the UAV’s wings are folded to minimize drag by reducing the aircraft’s windward and wetted areas. This enhances the lift-to-drag ratio, extends the flight range, and improved payload capacity.
2.2. Weight Estimation
For initial sizing calculations, Raymer’s methodology was employed. The maximum takeoff weight was then estimated using the following equation: where represents the aircraft weight and the subscripts and correspond to the payload and empty weight, respectively. Equipment such as aircraft power plants and batteries are included in the empty weight category. The UAV’s total takeoff weight can be expressed using Equation (2): where denotes the UAV’s empty weight coefficient.
The relative empty-to-weight ratio of the total weight engineering empirical formula is .
Here, represents the constant for variable sweep value. Given that this UAV has a fixed sweepback configuration, , , and , leading to the UAV’s empty-to-weight ratio.
Experience statistics on the logarithm of both the takeoff empty weight and the total weight adheres to a linear relationship.
Based on data for similar UAV configurations (shown in Table 1), according to Equation (4), the UAV’s total takeoff weight , its empty weight , and the empty-to-weight ratio is .
2.3. Aerodynamic Sizing
Airfoils with a relative thickness of 17% were selected for the GA(W)-1 merge condition. During climb, , the airfoil’s maximum lift coefficient reaches 1.6, and its lift-to-drag ratio (L/D) is 65, based on wind tunnel tests at and [26]. The wings are designed with two configurations, GA(W)-1, NACA0030, and NACA4412, and their specifications are provided in Table 2. Figure 5 shows the nondimensional coordinates of these three airfoils.
(a) GA(W)-1
(b) NACA0030
(c) NACA4412
Traditional methods for estimating long-wing lift coefficients are based on simplifying wing geometry. By averaging the maximum lift coefficients of the wing root and tip, treating the wing as having a constant airfoil section, and applying a three-dimensional correction, the maximum lift coefficient is obtained using the following equation: where is the maximum lift coefficient of the wing.
To calculate the wing area corresponding to the estimated stall speed of 13 m/s, the simplified maximum lift factor is used. The drag coefficient is then determined by assuming that the minimum drag coefficient equals the zero-lift drag coefficient, as expressed in the following equations: where , , , , and correspond to the drag coefficient, zero-lift drag coefficient, total wetted area of the aircraft, wing reference area, and equivalent skin friction drag coefficient, respectively. As referenced in Table 3, .
This UAV is designed as a transport aircraft with a focus on excellent stall performance. Consequently, it features a straight wing with no sweep angle. Using the straight-wing Oswald efficiency factor, where is the Oswald efficiency factor, and is the aspect ratio.
Table 4 summarizes the preliminary estimates for the UAV’s geometric dimensions and related parameters.
2.4. Logistics UAV Geometry and Key Design Parameters
Figure 6 illustrates the aircraft’s geometry, which incorporates a single straight wing, no dihedral or twist angle, and a twin-boom inverted V-tail configuration [16–18]. Key design parameters are outlined in Table 5, including a sizable takeoff weight of 82 kg and a cruising speed of 108 km/h.
The estimated weights for the primary aerodynamic surfaces and system components are provided in Table 6. The UAV is powered by a GA160 KV67 motor, paired with a 28-inch propeller and an EP-120A-HV electronic speed controller. The total weight of this power unit is approximately 3.44 kg. Energy is supplied by two 12S 27000 mAh batteries from DUPU, weighing 9.4 kg, enabling a cruising flight time of up to 0.8 h at 60% engine power. The aircraft’s fuselage, internal frames, and stringers are constructed from aluminium alloy and composite materials. The cargo compartment features a double-layered aluminium cargo skid and a fixed support to accommodate a variety of cargo sizes and weights. Given that the wings and V-tail are responsible for carrying the aircraft’s full weight and cargo, they must meet stringent strength and modulus specifications while preserving their original geometric design to achieve the intended aerodynamic performance. The skin and key internal structures, such as the main wing ribs and main spar, are made of aluminium alloy and other materials. Carbon fibre and glass fibre composites are used for the tail boom and other critical connecting components to enhance both economy and repairability. Additionally, the aircraft is equipped with a remote flight control and communication system for defining the mission envelope and for real-time flight monitoring and control.
In traditional lift, large cargo, transport, and general aviation aircraft often utilize leading-edge slats and trailing-edge flaps during takeoff and landing stages to enhance the lift coefficient. However, the wings of small to medium-sized feeder general aviation UAVs are usually thin with short chord lengths. For larger logistics UAVs, having openings at the front and rear edges compromises wing strength. Additionally, the short chord length makes it challenging to design slat-wing flaps large enough to generate adequate lift. To address these issues, this work introduces a UAV featuring a foldable biplane configuration. The wings spread out during takeoff and landing to maximize lift [6] and fold into a single, integral wing during cruise to minimize drag. The primary focus of this investigation is on how the unfolded wing configuration impacts lift characteristics during takeoff and landing.
Building on existing research on bi-wing configurations [11–13, 30–32], the definitions of the bi-wing elements are illustrated in Figure 7.
In this paper, the terms upper and lower wings are used to describe the two wings of the aircraft. The chord length of the upper wing is denoted by C1 while C2 represents the chord length of the lower wing. Both C1 and C2 were set at 200 mm based on the results of the conceptual design. S signifies the distance between the leading edges of the upper and lower wings in the direction of incoming airflow, while G indicates the vertical distance between these leading-edge points. θ represents the angle between the axes of the upper and lower wings.
2.5. Foldable Wing Design Schemes
The UAV is engineered with foldable wings; during the cruising phase, the wings integrate into a single-wing form, and during landing and takeoff, they expand into a biplane configuration, facilitated by a specialized folding mechanism. Figure 8 presents models illustrating both wing configurations.
(a) Wings folded during cruise phase
(b) Wings unfolded during takeoff and landing phases
2.6. Numerical Method and Verification
The design calculations set the flow velocity at 30 m/s, with a side slip angle of zero, yielding a project-specific Reynolds number approximately equal to based on the mean aerodynamic chord (MAC). Computational fluid dynamics simulations were conducted using ANSYS FLUENT with the SST turbulence model. The boundary conditions consisted of a far-field velocity inlet and far-field pressure outlet. A second-order upwind discretization scheme was employed to solve the governing equations, and an anisotropic prismatic layer mesh was generated near the object surface. The first layer grid thickness was approximately 10-5 the average aerodynamic chord length, with corresponding dimensionless mesh parameters [33, 34].
Given that the primary focus is on wing parameters, only the wing was modelled and simulated in this initial study to save computational resources. The complete three-dimensional aerodynamic analysis will follow, based on the derived wing parameters. Two types of meshes were created: a two-dimensional airfoil mesh and a three-dimensional aircraft mesh [35]. During meshing, the effects of far-field boundary conditions were thoroughly considered, and a symmetrical three-dimensional flow field was generated relative to the aircraft’s longitudinal profile. To optimize computational time, only half of the geometry was simulated, implementing a symmetry plane along the -plane.
The far-field radius for velocity in the two-dimensional quadrilateral mesh was set to be 10 times the model wall’s chord length, and the pressure outlet was 20 times the chord length [36–40]. The SIMPLEC algorithm was employed for pressure-velocity coupling. Three levels of mesh density were evaluated, generated by a systematic refinement of the reference structured block grid [41]. Aerodynamics coefficients at zero angle of attack were calculated and are presented in Table 7.
Table 6 reveals that the relative errors for the lift and drag coefficients are less than 0.44% and 2.94%, respectively, when the mesh count is between 11.29 million and 22.58 million. Considering both computational accuracy and resource efficiency, the second mesh configuration, with 11.29 million elements, was selected for subsequent two-dimensional calculations and airfoil meshing, as illustrated in Figure 9.
The upstream velocity inlet boundary radius for the three-dimensional tetrahedral mesh was set at 10 times the feature length, while the pressure outlet boundary was 20 times the feature length from the model wall. The pressure and velocity coupling employed the coupled algorithm. The three-dimensional UAV mesh is depicted in Figure 10.
2.7. Numerical Method Validation
The UAV features a high-aspect-ratio, twin-boom inverted V-tail, similar to Bravo-Mosquera’s UAV [42]. The computational tool’s accuracy was validated by comparing simulation data with wind tunnel experiment results. Key dimensions for Bravo-Mosquera’s UAV configuration include a wingspan , total length , and . The incoming flow velocity, determined through CFD simulation, was fixed at 29 m/s, resulting in a Reynolds number . Experiments were performed in the LAE-1 closed-circuit wind tunnel at the Aircraft Laboratory of São Carlos Engineering School-University of São Paulo, Brazil (EESC-USP). The LAE-1 wind tunnel was originally designed for automotive tests but is now a multimission facility primarily used for aerospace tests. The tunnel is equipped with an eight-blade fan, driven by a 110 Hp electric motor with seven straighteners located downstream the fan, capable of achieving a maximum speed of 50 m/s with a turbulence level of 0.25% credit due to two 54% porosity screens located before the contraction cone. Instrumentation is composed of a six-component overhead balance, scanivalves and digital pressure scans, and three-channel hot wire anemometer plus 3D traverse gear [43, 44]. The working section has dimensions of 1.29 m in height, 1.67 m in width, and a usable length of 3 m. Atmospheric conditions at the wind tunnel location were recorded as , , °C, and . The aerodynamic balance measures two key forces on the model: lift and drag, with an uncertainty of ±0.01 N. A computational tool in the “Lab View” (National Instrument) program was used, setting to take 5000 samples with a frequency sample of 500 samples per second. The dynamic pressure was measured using a micromanometer with an uncertainty of ±0.1 Pa. Measurement uncertainties of ±0.001 m for chord and wing span, respectively. The experimental uncertainty for each aerodynamic coefficient was thus calculated. and [45]. The reference URCUNINA-UAV scale model was manufactured by Cliever CL2 Pro Plus 3D printer, using polylactic acid (PLA). Figure 11 shows the model of reference UAV at the wind tunnel test section and its setup [42, 44]. Figure 12 compares the CFD calculations at varying angles of attack with wind tunnel data.
The CFD calculations align well with the wind tunnel experimental data across the studied range of angles of attack [42]. Specifically, the maximum error between the calculated and experimental values before reaching a 13-degree angle of attack is just 2.81%, with an average error of 1.17%. Given these minimal discrepancies and considering the inherent limitations of turbulence models and CFD algorithms when dealing with large angles of attack, both the numerical and experimental methods employed in this study can be deemed highly reliable for future calculations and analysis.
3. Results and Discussion
3.1. Two-Dimensional Aerodynamic Design and Analysis
Compared to its three-dimensional counterpart, a two-dimensional mesh significantly reduces calculation time while still obtaining the influence of the main parameters on aerodynamic characteristics and flow field. Therefore, we initially focus on analysing the flow field around the two-dimensional airfoil [46, 47].
We explored the influence of different variables on the flow field of the wing by changing four key variables: the flow direction distance S, vertical spacing G, angle of the wing axes θ, and the wing airfoil type [48–51]. The foundational airfoil considered for this paper is NACA0030 [52–54].
3.1.1. Effects of Flow Direction Distance
Figure 13 compares the pressure contours, stream traces, and vorticity contours at , 1C, and 1.25C. The coefficient of pressure distributions diagram in Figure 14 reveals that when is less than 1C, the bi-wing gap becomes too narrow. This constriction squeezes the trailing edge of the upper wing, blocking and weakening the high-pressure area and thus causing negative lift. Conversely, when is greater than 1C, the gap between the wings is too large, diminishing the acceleration of the airflow and the influence of the low-pressure area. This nonuniformity in the high-pressure area adversely affects the upper airfoil, causing airflow separation at the trailing edge. As a result, an value of 1C was deemed optimal for the incoming flow direction.
(a)
(b)
(c)
(a)
(b)
(c)
3.1.2. Effects of Vertical Spacing
Figure 15 compares the pressure contours, pathlines, and vorticity contours at , 0.25C, and 0.375C states. Figure 16 shows the comparison of pressure coefficient distributions between different values. When the vertical spacing is less than 0.25C, the gap between the wings is too narrow, obstructing airflow and compromising the low-pressure area of the lower wing. This leads to a flow-blocking bubble and produces a large vortex at the upper wing’s trailing edge. Conversely, when the spacing exceeds 0.25C, the gap becomes excessively wide, diminishing the airflow’s acceleration in the interwing space and disrupting the low-pressure area of the upper wing. This affects the trailing edge, moves the centre of the low-pressure area forward, exacerbates airflow separation, and weakens the lower wing’s lift. Hence, a vertical spacing , i.e., 50 mm is considered more reasonable.
(a)
(b)
(c)
(a)
(b)
(c)
3.1.3. Effects of Different Airfoil Combinations
To maximize lift, airfoils with good aerodynamic performance need to be selected. In this context, the GA(W)-1, NACA4412, and NACA0030 airfoils were evaluated. Figure 17 illustrates the pressure contours, pathlines, and vorticity contours of the upper wing GA(W)-1/lower wing NACA0030, as well as upper wing NACA4412/lower wing GA(W)-1 airfoil combinations. Figure 18 shows the comparison of pressure coefficient distributions between the two airfoil combinations.
(a) GA(W)-1/NACA0030
(b) NACA4412/GA(W)-1
(a) GA(W)-1/NACA0030
(b) NACA4412/GA(W)-1
Analysing the pressure contour and pressure coefficient diagrams (Figure 17) reveals that the upper wing generates more lift than the lower wing. The primary role of the lower wing is to affect the surrounding flow field, change the pressure distribution, and thereby increase the total lift. Our calculations indicate that the lift contribution ratio between the upper and lower wings is approximately 7 : 3. As a result, an airfoil with better lift performance should be selected for the upper wing, while the lower wing should feature an airfoil with considerable thickness and a smoother surface. This configuration minimizes lift loss while generating beneficial flow field interference. Accordingly, the upper wing employs the NACA4412 airfoil, and the lower wing employs the GA(W)-1 airfoil.
3.1.4. Effects of Angle θ between Wing Axes
Kong’s numerical analysis focused on the aerodynamic properties related to aircraft flap bending and spoilers on the lower wing, while Zhang investigated the aerodynamic characteristics of multisegment wings. Both concluded that a deflection angle of 25–30 degrees on the lower wing of the flap or multisegment wing ensures sufficient lift and a more reasonable flow field distribution [53, 54]. Based on these findings, three models with different angles—0°, 10°, and 25°—were developed. Figures 19 and 20 depict the calculated pressure contours, pathlines, vorticity contours, and pressure coefficient distributions for these models.
(a) °
(b) °
(c) °
(a) °
(b) °
(c) °
The angle between the two wings’ axes critically influences the pressure distribution at the gap opening. At a smaller angle, the gap narrows, severely disrupting the low-pressure distribution of the upper wing surface on the lower wing and preventing an effective pressure differential. Conversely, increasing the angle to 25° yields a more uniform and continuous low-pressure area distribution on both wings, significantly improving the pressure distribution.
Figure 21 depicts the lift characteristic curves for both bi-wing and mono-wing models.
The mono-wing model exhibits pronounced stalling beyond AOA of 14°, while the bi-wing model avoids stalling across all AOAs [55]. Notably, the bi-wing model’s lift coefficient surpasses that of the mono-wing model when the AOA is below 10°, providing enhanced lift during the initial takeoff stage and enabling quicker ascents [55–58].
3.2. Three-Dimensional Aerodynamic Design and Analysis
Based on prior research into two-dimensional bi-wings, the following design parameters were established: , , °, NACA4412 airfoil for the upper wing, GA(W)-1 airfoil for the lower wing, and a wingspan of 2 m.
3.2.1. Effects of Different Combinations of Wingspans
Since the two wings together constitute a complete wing system, various bi-wing configurations with different wingspan combinations were analysed. Five typical wingspan configurations were selected for analysis.
Building on a bi-wing span of , the model is designed to maintain a constant projection area on the horizontal, which are , , , , and . These five groups of bi-wing models were consistently designed in terms of their two-dimensional sections, meshing protocols, computational environments, and conditions. Figure 22 displays the velocity vortex distribution for these wingspan combinations, and Figure 23 depicts the evolution of the lift coefficient across the five sets.
(a) Front view
(b) Side view
(c) Top view
(a) Evolution of lift coefficient of wings among five groups of wingspan combinations
(b) Evolution of lift coefficient of the upper wing among five groups of wingspan combinations
(c) Evolution of lift coefficient of the lower wing among five groups of wingspan combinations
Figure 22 reveals that as the upper wingspan expands, the wingtip vortices on both wings diminish, along with the vortex interference at the lower wingtip. The lower wing surface in the combination with a shorter upper wingspan showed early vortex separation, as illustrated in the top view of Figure 22(c). A smaller upper wingspan led to increased vortex separation at the lower wingtip. When the upper wingspan surpassed that of the lower wing, the airflow separation between the two wings was suppressed.
Table 8 and Figure 24 list the lift coefficients for various span combinations.
The lift coefficients peaked for an upper wingspan of 1.1 m and a lower wingspan of 0.9 m. As the gap between the wings narrowed, the lift coefficient of the upper wing declined. Specifically, when the upper wingspan was 1.2 m and the lower wingspan was 0.8 m, the narrow gap could not compensate for the lift loss due to leading-edge separation, resulting in a pronounced stall on the upper wing. Figure 24 indicates that the lift ratio between the upper and lower wings consistently hovered around 6 : 4 across the five wingspan sets, explaining the biplane’s stall when the upper wingspan exceeded 1.1 m.
Changes in the lower wing’s lift coefficient were relatively subdued, making the overall bi-wing lift substantially influenced by the upper wing. Therefore, priority should be given to the lift characteristics of the upper wing. Given the trends in total bi-wing lift and upper wing lift, the optimal wingspan combination was identified as 1.1 m for the upper wing and 0.9 m for the lower wing.
Figures 25–27 showcase the aerodynamic performance for this wingspan combination.
The upper wing, although influenced by the gap, did not experience stalling. The lift coefficient of the lower wing started to decline past an angle of attack of 5°; however, the decrease was minimal, and the total lift coefficient reached its apex at an angle of attack of 10°.
3.2.2. Analysis of Aerodynamic Characteristics of UAV
Figures 28–30 present the aerodynamic coefficient curves for both the entire UAV and its bi-wing configuration. During the flight, an expansive continuous low-pressure zone forms between the wing gaps, offsetting lift loss at the upper wing’s leading edge and significantly improving its lift coefficient. Due to the 25° angle of attack between the lower wing and incoming airflow when the wings are deployed, the lower wing experiences a higher angle of attack during the fight, thereby exacerbating airflow separation and limiting any lift coefficient increase. However, the bi-wing configuration still yields a higher lift coefficient compared to a two-dimensional airfoil. Throughout the range of flight angles of attack, the UAV maintains a high lift coefficient and only starts to stall at an angle of attack of 12°. This meets the UAV’s lift requirements for both takeoff and landing at high angles of attack.
3.2.3. Analysis of Static Stability of Whole UAV
Each component of the UAV contributes to its overall stability, either by influencing its centre of gravity and moment of inertia or by generating aerodynamic forces. The tail, in particular, plays a crucial role in the aircraft’s overall stability. A conceptual analysis was conducted to validate the tail design, focusing on longitudinal static stability. The contributions to longitudinal stability from each component were calculated to maintain a constant moment-coefficient derivative. The moment coefficient at the centre of gravity for each component is charted against the angle of attack in Figure 31. Consequently, the trim angle () for the UAV is established at 10°.
Figure 32 shows the UAV’s lateral and directional stability at a 10° angle of attack, displaying the variation curves for both rolling and yaw moment coefficients with respect to yaw angle β. The variations curve of the yaw moment coefficient as a function of the yaw angle β is illustrated in Figure 33, while the static stability derivatives for both lateral and directional stability of the UAV are detailed in Table 9.
Figure 32 reveals that the total UAV’s roll moment curve has a positive slope, indicating lateral instability. Figure 33 shows that the yaw moment curve of the total UAV has a positive slope, signifying directional stability.
A deeper examination of each UAV component’s effects on lateral and directional stability was conducted, with the results illustrated in Figures 34 and 35. These figures demonstrate that the tail is a significant contributor to the UAV’s lateral and directional static stability [59–61].
4. Conclusions
Our study focused on the conceptual design and aerodynamic analysis of a twin-boom, inverted V-tailed UAV with a foldable wing configuration, specifically tailored for the challenging terrains of mountains and islands. We began by reviewing the current state of logistics UAV technology, market demand forecasts, and existing limitations in this field. Given that many mountainous and island regions grapple with inefficient transportation and limited capacity, our research was further motivated to create a UAV capable of meeting varying flight performance requirements across different mission stages. Initially, we conducted an in-depth analysis of the UAV’s mission requirements, which led to a comprehensive aircraft design. This paper consolidates insights and findings from various researchers in the realm of biplane design, proposing a targeted design scheme for our study. Subsequently, we employed reliable CFD methods to scrutinize both two-dimensional and three-dimensional design configurations of the biplane, thereby deriving optimal design parameters. A tailored static stability analysis was also conducted in the context of the UAV’s operational environment.
In summary, our aerodynamic analysis elucidated the impact of four critical wing parameters on the wing’s flow field. At an incoming flow direction distance of 1 C, both the high and low pressures on the upper wing surface were too negligible to induce interference, while the high pressure at the lower wing surface near the gap was too dominant to effectively collaborate with the upper wing’s low pressure. For vertical spacing , a value of 0.25 C was found to be optimal. Anything less inhibited airflow acceleration at the gap, whereas a larger value negated the beneficial effects of the gap altogether. An axial wing angle of 25° proved ideal for promoting a large-scale, low-pressure area on the upper wing surface, thereby enhancing the aerodynamic performance of the wing as a whole.
Once the wings are deployed, the aircraft experiences a significant boost in its lift coefficient, meeting the high lift demands necessary for both takeoff and landing. The gap between the wings accelerates the airflow, lowering the pressure behind the gap and directing the airflow on the upper wing surface downward. This not only mitigates separation on the upper wing but virtually eliminates it on the lower wing’s upper surface. The result is a uniform pressure distribution across both wings, thereby increasing lift.
Moreover, the interwing gap’s acceleration and deflection effects enhance the wing’s separation characteristics at high angles of attack. This localized separation only affects the upper wing root and leading edge, allowing the aircraft to maintain sufficient lift. Such attributes improve stall characteristics, ensuring safe takeoffs and landings even on short runways and at high angles of attack.
As for future research avenues, key areas warrant further investigation: Given the evolving complexity of transportation scenarios, drones of various sizes and load capacities should be considered. This calls for a comprehensive analysis of cargo bay loading designs as well as UAV load capacities. Logistics UAVs are subject to rigorous structural strength requirements, necessitating meticulous design and analysis of the aircraft’s overall structure. An integrated approach to cargo compartment, load capacity, and structural design can help establish a balanced centre of gravity, thereby enhancing flight stability. Employing multidisciplinary design optimization (MDO) could pave the way for the development of new computational methods, ultimately leading to optimal design solutions.
Data Availability
The data used to support the findings of this study are included within the article.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
Funding support is provided by the Science and Technology Project of Henan Province (grant numbers 232102220029, 212102210334, and 202102210267) and the Henan Key Laboratory of General Aviation Technology (grant number ZHKF-230201).