This study numerically investigates the aerodynamic interference characteristics during wingtip aerial docking of fixed-wing drones using computational fluid dynamics. We focus on three fundamental docking approaches: longitudinal, lateral, and vertical docking. The analysis details variations in wing aerodynamic parameters, flow field structures, and identifies critical factors influencing docking safety. Our findings provide guidance for the engineering application of chain-wing technology in fixed-wing drone swarms.
1. Introduction
Modern battlefield environments demand enhanced operational capabilities from unmanned aerial systems. Single fixed-wing drones face limitations in endurance, altitude, and payload capacity. To overcome these constraints, fixed-wing drone swarms have emerged as a solution, leveraging collaborative operations to perform complex missions. However, typical swarms suffer from reduced loiter time and lower cruising altitude due to size and maneuverability trade-offs. Chain-wing technology offers a promising paradigm shift by physically connecting multiple fixed-wing drones at their wingtips via docking mechanisms. This creates a large aspect ratio combined aircraft, significantly improving overall aerodynamic efficiency. The ability to separate on demand retains tactical flexibility.
Wingtip aerial docking is a critical phase for realizing chain-wing flight. During this process, the close proximity of multiple fixed-wing drones induces complex aerodynamic interference, primarily driven by wingtip vortex interactions. These interactions alter local aerodynamic load distributions, affecting lift, drag, side force, and inducing significant moments, particularly rolling moments. Understanding and quantifying these interference effects is essential for safe and stable docking control. Prior research often relied on potential flow methods like vortex lattice or lifting line theory, which may lack accuracy when wings are extremely close and viscous effects dominate. Many studies also focused solely on one-way interference from a leader to a follower, neglecting the mutual aerodynamic coupling between adjacent fixed-wing drones. To address these gaps, we employ Reynolds-averaged Navier-Stokes (RANS) simulations with a k-ω SST turbulence model to capture the detailed flow physics of two wings approaching each other.
2. Methodology
2.1 Geometric Model and Computational Setup
We simplify the fixed-wing drone configuration by considering two identical rectangular wings, neglecting the fuselage and empennage to reduce computational cost while focusing on the wingtip interaction. Each wing has a chord length c = 0.24 m, span b = 1.56 m (aspect ratio 6.5), and uses the USA35-B airfoil. A coordinate system is defined with the origin at the leading edge of the left wingtip of the target fixed-wing drone. The relative positions are described by non-dimensional distances: longitudinal (Δx/c), lateral (Δy/c), and vertical (Δz/c). The moment reference point is at the quarter-chord midpoint of each wing.
2.2 Numerical Method and Validation
We solve the RANS equations using a finite volume method with second-order upwind discretization and a coupled pressure-velocity scheme. The k-ω SST turbulence model is selected for its accuracy in capturing flow separation and vortex dynamics. The computational domain extends 20 chord lengths outward from the wings. Boundary conditions include velocity inlet, pressure outlet, pressure far-field, and no-slip walls on wing surfaces. Unstructured meshes are employed with refinement near leading/trailing edges and wingtips. The first cell height normal to the wall is 0.025 mm, yielding y+ ≈ 1.
Grid independence is verified using four mesh densities for a configuration with α = 0° and lateral spacing Δy/c = 0.1. The lift coefficient results are presented in Table 1.
| Grid Number (×104) | Lift Coefficient (CL) |
|---|---|
| 400 | 0.4415 |
| 700 | 0.4462 |
| 1000 | 0.4487 |
| 1300 | 0.4489 |
Based on the grid independence study, a mesh size of approximately 10 million cells is chosen, balancing accuracy and computational efficiency (1.5 hours simulation time).
We validate our numerical method against wind tunnel experimental data from Zhou et al. (2023), who studied fixed-wing drone docking aerodynamics. The test conditions were: free stream velocity 20.1 m/s, angle of attack 4.5°, two wings with USA35-B airfoil (spans 0.26 m and 0.272 m, chord 0.08 m). Figure 5 in the original study showed excellent agreement between our CFD results and the experimental lift coefficient for wing 2 as a function of lateral spacing. The maximum relative error is 1.9%, confirming the reliability of our simulation approach.
3. Results and Discussion
3.1 Longitudinal Docking
In longitudinal docking, the lateral spacing is fixed at Δy/c = 0.05 and vertical spacing Δz/c = 0, while the longitudinal distance Δx/c varies from 4 to 0. We analyze the aerodynamic coefficients for angles of attack α = -2°, 0°, 4°, and 8°.
Table 2 summarizes the key aerodynamic coefficient variations for both the front and rear fixed-wing drone wings at α = 4° as a function of longitudinal spacing. The rear wing experiences significant lift enhancement and drag reduction due to the upwash from the front wing’s wake. As spacing decreases below 1 chord length, lift coefficients increase sharply. Side force shows an inward trend for both wings. Rolling moment emerges as the dominant interference moment, increasing significantly when Δx/c < 1. Yaw moment exhibits non-monotonic behavior for the front wing, while pitching moment decreases steadily. Higher angles of attack amplify rolling and yaw moments considerably but have weaker effect on pitching moment.
| Δx/c | Wing | ΔCL | ΔCD | CY | Cl (×103) | Cn (×103) | Cm (×103) |
|---|---|---|---|---|---|---|---|
| 4.0 | Front | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| Rear | +0.02 | -0.005 | 0.00 | 0.00 | 0.00 | 0.00 | |
| 1.0 | Front | +0.01 | -0.002 | -0.01 | 0.50 | 0.20 | -0.10 |
| Rear | +0.05 | -0.010 | -0.01 | 0.50 | 0.15 | -0.10 | |
| 0.5 | Front | +0.03 | 0.00 | -0.03 | 2.00 | 0.80 | -0.20 |
| Rear | +0.10 | -0.015 | -0.03 | 2.00 | -0.30 | -0.25 | |
| 0.1 | Front | +0.06 | +0.005 | -0.06 | 5.00 | -0.50 | -0.35 |
| Rear | +0.18 | -0.005 | -0.05 | 5.00 | 0.10 | -0.40 |
Note: CL, CD, and CY are lift, drag, and side force coefficients. Cl, Cn, and Cm are rolling, yawing, and pitching moment coefficients.
Flow field analysis reveals that when Δx/c > 1, wingtip vortices from both wings are relatively independent, with slight upward deflection due to mutual induction. As spacing reduces to < 1, the vortices strongly couple. The rear wing’s vortex is squeezed by the front wing’s vortex, becoming irregular. The vortex strength fluctuates, leading to asymmetric pressure distributions on the wing surfaces. Consequently, we define the region where Δx/c < 1 as the strong aerodynamic interference zone for longitudinal docking of fixed-wing drones.
3.2 Lateral Docking
For lateral docking, longitudinal and vertical spacings are zero (Δx/c = 0, Δz/c = 0), while lateral spacing Δy/c varies from 4 to 0.05. Both wings are at the same streamwise position. The results show symmetric aerodynamic behavior between the two fixed-wing drone wings.
Table 3 presents the aerodynamic coefficient changes at α = 4° during lateral docking. As Δy/c decreases, lift increases and drag decreases for both wings, with more pronounced changes below Δy/c = 1. An inward side force develops. Rolling and yaw moments are equal in magnitude but opposite in direction for the two wings, increasing significantly in the close spacing regime. Pitching moment decreases gradually. Higher angles of attack amplify the rolling and yaw moments, similar to longitudinal docking.
| Δy/c | Wing | ΔCL | ΔCD | CY | Cl (×103) | Cn (×103) | Cm (×103) |
|---|---|---|---|---|---|---|---|
| 4.0 | Left | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| Right | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |
| 1.0 | Left | +0.01 | -0.002 | -0.01 | 0.40 | -0.20 | -0.05 |
| Right | +0.01 | -0.002 | +0.01 | -0.40 | +0.20 | -0.05 | |
| 0.5 | Left | +0.04 | -0.008 | -0.04 | 1.50 | -0.80 | -0.15 |
| Right | +0.04 | -0.008 | +0.04 | -1.50 | +0.80 | -0.15 | |
| 0.1 | Left | +0.08 | -0.012 | -0.08 | 4.00 | -2.00 | -0.30 |
| Right | +0.08 | -0.012 | +0.08 | -4.00 | +2.00 | -0.30 |
Flow visualization shows symmetric development of inboard wingtip vortices for the two fixed-wing drone wings. At Δy/c > 1, vortex interaction is weak, and vortices remain regular. As spacing reduces below 1 chord length, the vortices interact strongly, with decreased vortex strength and upward movement of vortex cores. The negative pressure region near the wingtips expands symmetrically. The symmetric and relatively stable aerodynamic changes make lateral docking more favorable for flight attitude control compared to longitudinal or vertical docking. The strong interference zone for lateral docking is defined as Δy/c < 1.
3.3 Vertical Docking
In vertical docking, longitudinal spacing is zero (Δx/c = 0) and lateral spacing is fixed at Δy/c = 0.05, while vertical spacing Δz/c varies from 4 to 0. This configuration involves significant asymmetric flow interactions.
Table 4 summarizes the aerodynamic coefficient changes for the upper and lower fixed-wing drone wings at α = 4°. As vertical spacing decreases, lift increases and drag decreases for both wings, with sharp changes below Δz/c = 1. Side force behavior becomes complex; for the lower wing at high angles of attack, the direction of side force can reverse as spacing reduces. Rolling and yaw moments increase substantially when Δz/c < 1, exhibiting strong asymmetry. Pitching moment decreases monotonically.
| Δz/c | Wing | ΔCL | ΔCD | CY | Cl (×103) | Cn (×103) | Cm (×103) |
|---|---|---|---|---|---|---|---|
| 4.0 | Upper | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| Lower | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |
| 1.0 | Upper | +0.02 | -0.003 | -0.02 | 0.60 | 0.30 | -0.10 |
| Lower | +0.01 | -0.001 | +0.01 | -0.30 | 0.10 | -0.08 | |
| 0.5 | Upper | +0.06 | -0.010 | -0.05 | 4.00 | 1.50 | -0.25 |
| Lower | +0.03 | -0.005 | +0.02 | -2.00 | -0.50 | -0.20 | |
| 0.1 | Upper | +0.12 | -0.015 | -0.10 | 8.00 | 3.00 | -0.40 |
| Lower | +0.05 | -0.008 | +0.04 | -4.00 | -1.00 | -0.30 |
Flow field analysis for vertical docking reveals strong asymmetric vortex coupling. At Δz/c > 1, vortices are regular with weak interaction. When spacing reduces below 1 chord length, the two wingtip vortices strongly interfere. As the wings cross vertically, vortex generation is significantly suppressed, vortex strength decreases, and vortex cores shift upward. Surface pressure distributions become highly asymmetric. This leads to erratic aerodynamic coefficient variations, particularly in side force and yaw moment. The strong interference zone for vertical docking is Δz/c < 1.
3.4 Comparative Analysis and Flight Recommendations
Based on the three docking scenarios, we identify a universal strong aerodynamic interference zone for fixed-wing drone wingtip docking. This zone is defined as the region where any of the longitudinal, lateral, or vertical spacings are less than 1 chord length. Within this zone, aerodynamic parameter changes are severe, and flow field structures are complex, posing challenges for flight control.
Table 5 provides a comparative summary of the three docking modes. The key findings are:
| Feature | Longitudinal Docking | Lateral Docking | Vertical Docking |
|---|---|---|---|
| Symmetricity | Asymmetric | Symmetric | Asymmetric |
| Interference Zone (strong) | Δx/c < 1 | Δy/c < 1 | Δz/c < 1 |
| Rolling Moment Impact | High, asymmetric | High, symmetric | High, asymmetric |
| Yaw Moment Impact | Moderate, complex | Moderate, symmetric | Moderate, complex |
| Pitching Moment | Decreases | Decreases | Decreases |
| Flow Field Complexity | Complex, coupling | Moderate, stable | Complex, strong coupling |
| Control Difficulty | High | Low | High |
| Suitability for Docking | Less favorable | Most favorable | Less favorable |
The most critical finding is that rolling moment is the dominant aerodynamic interference moment, typically an order of magnitude larger than yawing or pitching moments. This moment directly affects the lateral stability and controllability of the fixed-wing drone during docking. Higher angles of attack amplify the rolling and yawing moments significantly, increasing the risk of loss of control. Therefore, minimizing the angle of attack during the docking approach is highly recommended to reduce the adverse effects of interference moments.
Comparing the three modes, lateral docking stands out as the preferred approach. Its symmetric aerodynamic response means that both fixed-wing drones experience identical changes in lift and drag, and the rolling moments on the two wings are equal and opposite, leading to a net cancellation of the overall rolling tendency if the wings are identical and symmetrically positioned. The flow field structure remains more ordered, with predictable vortex evolution. This symmetry and stability greatly simplify the flight attitude control problem for the docking fixed-wing drones. In contrast, longitudinal docking involves asymmetric wake effects, and vertical docking leads to complex, unpredictable vortex coupling and side force reversals, both of which make precise control challenging.
Based on our analysis, we propose the following recommendations for safe and effective wingtip aerial docking of fixed-wing drones:
- Prefer lateral docking approach: Approaching the target fixed-wing drone from the side (varying lateral spacing) offers the most stable aerodynamic environment.
- Minimize angle of attack: Keep the angle of attack as low as possible (e.g., near 0°) throughout the docking phase to reduce interference moments, especially rolling moment.
- Be aware of the strong interference zone: When any spacing (longitudinal, lateral, or vertical) falls below 1 chord length, the aerodynamic changes become rapid and significant, demanding more aggressive control actions.
- Account for mutual interference: Both fixed-wing drones experience the interference, and control systems for both should be designed to handle the coupling.
These insights provide a fundamental understanding of the aerodynamic challenges in fixed-wing drone wingtip docking and can guide the design of docking trajectories and control laws for future chain-wing systems.
4. Conclusions
This study numerically investigated the aerodynamic interference during wingtip aerial docking of fixed-wing drones using CFD. Three fundamental docking approaches (longitudinal, lateral, and vertical) were analyzed across multiple angles of attack. The key conclusions are:
- As the wingtip spacing between two fixed-wing drones decreases, wingtip vortex interaction intensifies. This interaction provides beneficial lift enhancement and drag reduction for both wings. However, it also generates significant aerodynamic interference moments, with the rolling moment being the most critical factor affecting docking safety. An inward side force develops due to asymmetric flow between the wings.
- The magnitude of aerodynamic coefficient changes increases substantially with higher angles of attack. Rolling and yawing moments are particularly sensitive to angle of attack variations, while pitching moment is less affected.
- Based on the aerodynamic parameter variation patterns and flow field topology, the strong aerodynamic interference zone is defined as the region where longitudinal, lateral, or vertical spacing is less than 1 chord length. Within this zone, aerodynamic changes are severe, and flow structures are complex.
- Compared to longitudinal and vertical docking, lateral docking offers relatively stable and symmetric aerodynamic parameter and flow field changes, making it more conducive to flight attitude control. For practical engineering applications, we strongly recommend adopting a lateral docking approach. Additionally, the angle of attack should be minimized during the docking process to reduce the adverse effects of aerodynamic interference moments.
These findings provide essential guidance for the design and control of fixed-wing drone chain-wing systems, contributing to the advancement of intelligent and collaborative unmanned aerial technologies.