We present a computational fluid dynamics investigation into the aerodynamic interference characteristics that arise during the wingtip aerial docking of fixed‑wing UAVs. Understanding this interference is critical for the practical application of chained‑wing technology, where multiple fixed‑wing UAVs connect at their wingtips to form a high‑aspect‑ratio combined aircraft, thereby improving overall aerodynamic efficiency and endurance. In this research, we simulate three fundamental docking approaches: longitudinal approach, lateral approach, and vertical approach. We analyze the variations in wing aerodynamic force coefficients and flow field structures under different relative positions and angles of attack. Our results show that reducing the wingtip spacing intensifies wingtip vortex interaction. This interaction produces beneficial lift‑augmentation and drag‑reduction effects, but it also generates interference moments that can compromise flight stability. Among these moments, the rolling moment is the most critical factor influencing docking safety. Furthermore, increasing the angle of attack significantly amplifies both the rolling and yawing moments. Based on the observed variations in aerodynamic parameters and flow field topology, we identify a strong aerodynamic interference zone where the longitudinal, lateral, and vertical separations between the wings are all less than one chord length. A comparison of the three docking methods indicates that lateral docking yields relatively stable changes in both aerodynamic coefficients and flow field structures, making it more favorable for flight attitude control during docking. Additionally, we recommend reducing the angle of attack during the docking phase to mitigate the adverse effects of interference moments. These findings provide practical guidance for the engineering implementation of wingtip‑chained fixed‑wing UAVs.
The concept of joining multiple fixed‑wing UAVs at their wingtips to create a large‑span combined configuration, known as chained‑wing technology, has emerged as a promising solution to extend flight endurance and altitude capability. Instead of relying solely on individual UAV performance, a swarm of fixed‑wing UAVs can assemble mid‑air to function as a single high‑aspect‑ratio aircraft, thereby reducing induced drag and improving lift‑to‑drag ratio. After completing a specific mission segment, the formation can separate again, restoring individual maneuverability. This flexibility makes the chained‑wing approach highly attractive for long‑endurance surveillance, communication relay, and other extended missions. However, the critical phase of wingtip aerial docking introduces complex aerodynamic interactions between adjacent wings. As two fixed‑wing UAVs approach each other, their wingtip vortices begin to interact, alter the local pressure distribution on each wing surface, and generate additional forces and moments that differ significantly from those experienced in isolated flight. A thorough understanding of these interference effects is essential for designing safe docking control laws and for ensuring that the transition from close formation to locked connection occurs without loss of stability.
A number of studies have addressed aerodynamic interference in close formation flight and wingtip coupling. Theoretical models based on lifting‑line theory and vortex‑lattice methods provide rapid estimates of induced velocities and changes in lift and drag. For instance, early analytical work demonstrated that an aft wing flying in the upwash region of a forward wing can experience increased lift and reduced induced drag, a principle exploited by migratory birds. However, these potential‑flow methods lose accuracy when wingtips are extremely close, because viscous effects, vortex core deformation, and mutual distortion of the wake become dominant. Wind‑tunnel experiments with scaled wings have revealed that the pressure distribution on the inboard side of each wing can change drastically when the lateral gap is smaller than one chord. Recent computational studies using Reynolds‑averaged Navier‑Stokes (RANS) solvers have captured the non‑linear evolution of the interacting vortices and the resulting unsteady loads. Nevertheless, most published works focus on steady formation flight with fixed separation, rather than the transient docking maneuver where the relative distances evolve continuously. In addition, many investigations treat one wing as the leader and the other as the follower, neglecting the mutual aerodynamic influence that becomes important when both wings are equally affected. In aerial docking, both fixed‑wing UAVs are actively involved, and their aerodynamic loads change simultaneously. Therefore, we adopt a fully coupled numerical approach that resolves the flow around both wings and accounts for their simultaneous interference.
In this paper, we systematically examine the aerodynamic interference during wingtip docking of two identical rectangular fixed‑wing UAVs. We consider three fundamental docking trajectories: longitudinal approach (the follower moves directly behind the leader along the streamwise direction), lateral approach (the two wings slide sideways toward each other), and vertical approach (one wing rises or descends relative to the other). For each trajectory, we compute the aerodynamic force and moment coefficients on both wings as functions of the separation distance, at several angles of attack. We also visualize the flow field using iso‑surfaces of vorticity and surface pressure contours to explain the underlying physics. Based on the results, we identify the region of strong interference and provide recommendations for the preferred docking method and flight conditions.
We now describe the numerical methodology and model configuration. The geometric model consists of two identical rectangular wings with a chord length of c = 0.24 m, a span of 1.56 m, and an aspect ratio of 6.5. The airfoil section is USA35‑B. This simplified geometry, without fuselage or tail, allows us to isolate the wing‑to‑wing interference effects. The moment reference point is located at the quarter‑chord point of the mid‑span of each wing. We solve the compressible RANS equations using a finite‑volume approach with a second‑order upwind scheme for spatial discretization and a coupled pressure‑velocity algorithm. Turbulence closure is achieved with the k‑ω SST model, which provides good predictions for separated flows and vortex interactions. The computational domain is a rectangular box extending 20 chord lengths in all directions from the two‑wing assembly. The inlet is set as a velocity inlet at a freestream speed of 22 m/s, the outlet as a pressure outlet, and the far‑field boundaries as pressure far‑field. The wing surfaces are modeled as no‑slip walls.
We generate an unstructured mesh with local refinement around the leading edge, trailing edge, and tip regions of each wing. The first cell height normal to the wall is 0.025 mm, yielding y⁺ values around unity, which satisfies the requirement of the k‑ω SST model. A grid independence study is performed at an angle of attack of 0° and a lateral separation of 0.1c. Four grids with cell counts of 4, 7, 10, and 13 million are tested. The lift coefficient converges to within 0.05% when the grid is increased from 10 million to 13 million, demonstrating grid independence. Considering computational cost, we use the 10‑million‑cell grid for all subsequent simulations.
To validate the numerical method, we compare our computed lift coefficients for a two‑wing configuration against experimental data from a previous wind‑tunnel test reported in the literature. That experiment used two USA35‑B wings of slightly different spans (0.26 m and 0.272 m) but identical chord lengths of 0.08 m, at a freestream speed of 20.1 m/s and an angle of attack of 4.5°. The present simulation reproduces the same geometry and flow conditions as closely as possible. The results show excellent agreement: the maximum relative error in the lift coefficient of the follower wing across various lateral separations is only 1.9%. This level of accuracy confirms the reliability of our RANS approach for the present aerodynamic interference problem.
We now present the results for the three docking methods. For clarity, we define the coordinate system as follows: the origin is at the leading edge of the left wingtip of the reference (target) wing; Δx is the positive streamwise distance (positive downstream); Δy is the positive lateral distance (positive to the right, i.e., away from the other wing); Δz is the positive vertical distance (positive upward). All distances are normalized by the chord length c. The aerodynamic coefficients are defined in the standard aircraft body axis frame: lift coefficient CL, drag coefficient CD, side‑force coefficient CY, rolling moment coefficient Cl, pitching moment coefficient Cm, and yawing moment coefficient Cn. The reference area for each wing is its planform area S = b·c, where b = 1.56 m. The moment reference point is at the quarter‑chord of the mid‑span section. All coefficients are non‑dimensionalized using the freestream dynamic pressure.
First, we consider the longitudinal docking. In this scenario, the lateral separation Δy is fixed at 0.05c, the vertical separation Δz is zero, and the longitudinal separation Δx varies from 4c down to 0c. Table 1 lists the percentage changes in CL and CD relative to the isolated wing values for both the forward wing (Wing A) and the aft wing (Wing B) at an angle of attack of 4°. The data show that as Δx decreases from 4c to 1c, the changes are modest (less than 2% in lift and 1% in drag). When Δx drops below 1c, the lift increases sharply, reaching about +6.8% for Wing A and +9.2% for Wing B at Δx = 0.1c. The drag exhibits a non‑monotonic trend: Wing B experiences a significant drag reduction (‑4.5% at Δx = 0.5c) but then increases slightly at the closest distance. This behavior is associated with the strong interaction of the wingtip vortices. At the same time, both wings develop a side force directed inward (toward each other), whose magnitude grows rapidly when Δx < 1c.
| Δx / c | ΔCL Wing A (%) | ΔCL Wing B (%) | ΔCD Wing A (%) | ΔCD Wing B (%) |
|---|---|---|---|---|
| 4.0 | 0.5 | 1.2 | 0.1 | -0.3 |
| 2.0 | 1.1 | 2.4 | 0.3 | -0.8 |
| 1.0 | 1.8 | 3.5 | 0.6 | -1.2 |
| 0.5 | 3.5 | 6.2 | 0.9 | -4.5 |
| 0.2 | 5.7 | 8.5 | -0.2 | -3.1 |
| 0.1 | 6.8 | 9.2 | -1.4 | -2.8 |
The rolling moment coefficients Cl for the two wings in longitudinal docking are plotted as a function of Δx in our simulations. We observe that when Δx > 1c, the rolling moments remain near zero. Once Δx falls below 1c, the magnitude of Cl on both wings increases dramatically, with opposite signs (Wing A rolls inward, Wing B rolls outward). At the smallest separation, the rolling moment coefficient reaches values that are an order of magnitude larger than the yawing and pitching moments, confirming that roll is the dominant stability concern. Increasing the angle of attack from 0° to 8° amplifies the peak rolling moment by roughly a factor of three. The yawing moment also grows but to a lesser extent. The pitching moment decreases gradually as the wings approach each other, but its sensitivity to angle of attack is relatively weak.
Flow visualization reveals that at longitudinal distances greater than 1c, the wingtip vortex from Wing A passes above Wing B’s tip, and the two vortices remain mostly separate. As the gap shrinks below 1c, the aft wing’s tip vortex becomes entrained into the forward wing’s vortex, leading to a complex merged vortex structure that shifts the pressure distribution dramatically. The resulting asymmetry is the source of the large rolling moment.
Next, we examine lateral docking. Here Δx = 0, Δz = 0, and the lateral separation Δy decreases from 4c to 0.05c. Table 2 summarizes the changes in lift and drag at α = 4°. Unlike the longitudinal case, the two wings exhibit nearly identical variations because the flow is symmetric with respect to the mid‑plane between them. The lift coefficient increases as Δy decreases, with a jump of about +7.5% at Δy = 0.1c. The drag coefficient decreases monotonically, reaching a reduction of about -5.0% at the closest proximity. The side force is also inward and symmetric. In terms of moments, the rolling moment on each wing is equal in magnitude but opposite in direction (both wings roll toward each other). The yawing moment also shows the same antisymmetric pattern. The pitching moment decreases slightly. The magnitudes of the rolling and yawing moments grow significantly when Δy < 1c. Again, higher angles of attack exacerbate these moments.
| Δy / c | ΔCL (%) | ΔCD (%) | ΔCY (inward, ×10-3) |
|---|---|---|---|
| 4.0 | 0.2 | 0.0 | 0.1 |
| 2.0 | 0.5 | -0.1 | 0.4 |
| 1.0 | 1.2 | -0.5 | 1.8 |
| 0.5 | 3.6 | -2.1 | 6.2 |
| 0.2 | 6.4 | -4.3 | 15.4 |
| 0.1 | 7.5 | -5.0 | 22.1 |
The vortex interaction in lateral docking is symmetric: the two tip vortices approach each other, they rotate around a common axis, and their cores gradually shift upward. This symmetrical evolution leads to smooth, monotonic changes in aerodynamic coefficients, which is beneficial for control. The flow field remains predominantly two‑dimensional in the sense that the vortex pair does not break symmetry until very close distances (Δy < 0.1c). Even then, the departure is minor compared to the asymmetry observed in longitudinal and vertical docking.
Finally, we present the results for vertical docking. In this case, Δx = 0, Δy = 0.05c, and the vertical separation Δz varies from 4c down to 0 (the two wings are aligned in the same horizontal plane at the final docking state). Table 3 shows the lift and drag changes at α = 4°. Both wings gain lift, but the upper wing gains slightly more. The drag reductions are similar. The side force shows a striking behavior: for Δz > 1c, it is negligible, but when Δz < 1c, the lower wing experiences a side force that reverses direction at certain distances, indicating a strong dependence on the relative vertical offset. The rolling moment on the two wings is again opposite, with magnitudes comparable to the lateral docking case. However, the yawing moment is also significant and non‑monotonic. The flow fields reveal that when one wing is above the other, the upper wing’s tip vortex interferes with the lower wing’s inboard region, creating a cross‑flow that distorts the vortex trajectories. As the vertical gap decreases below 1c, the two vortices merge into a single, highly distorted vortex pair, leading to abrupt changes in pressure distribution and loads.
| Δz / c | ΔCL Upper (%) | ΔCL Lower (%) | ΔCD Upper (%) | ΔCD Lower (%) |
|---|---|---|---|---|
| 4.0 | 0.3 | 0.4 | 0.0 | 0.0 |
| 2.0 | 0.8 | 1.0 | -0.2 | -0.1 |
| 1.0 | 1.5 | 1.8 | -0.6 | -0.5 |
| 0.5 | 3.2 | 3.8 | -1.5 | -1.8 |
| 0.2 | 5.4 | 6.1 | -3.2 | -3.8 |
| 0.0 | 7.0 | 7.5 | -4.1 | -4.6 |
Based on the analysis of all three docking methods, we define the strong aerodynamic interference zone as the region where Δx < 1c, Δy < 1c, and Δz < 1c. When any of these distances is less than one chord, the changes in aerodynamic coefficients become significant (typically >2% in lift and >1% in drag) and the interference moments become substantial enough to require active control compensation. Outside this zone, the interference is weak and monotonically decays with increasing separation. Among the three approaches, lateral docking offers the most predictable and symmetric behavior, making it the preferred choice for actual docking maneuvers. The vortex interaction in lateral docking remains symmetric, the aerodynamic responses are monotonic, and the flow structure is relatively simple. In contrast, longitudinal and vertical docking produce asymmetric vortex interactions that can cause rapid, non‑linear changes in rolling and yawing moments, complicating the flight control task.
We also note that the angle of attack has a strong amplifying effect on the interference moments. For example, at a given small separation, increasing α from 0° to 8° can double or triple the rolling moment coefficient. Therefore, we recommend that the docking maneuver be performed at the smallest practical angle of attack (ideally near zero degrees) to minimize the magnitude of the interference moments and thus reduce the control effort required. However, a very low angle of attack may compromise lift generation and stall margin; a trade‑off is necessary. In practice, a moderate angle of attack (e.g., 2°–4°) may be acceptable, but aggressive high‑angle approaches should be avoided during the final docking phase.
In summary, this study provides a comprehensive numerical investigation of the aerodynamic interference encountered during wingtip aerial docking of fixed‑wing UAVs. Our main conclusions are as follows:
1. As the wingtip spacing decreases, the interaction of wingtip vortices intensifies. This interaction yields beneficial increases in lift and reductions in drag for both wings, but it also generates interference moments—particularly a rolling moment that is an order of magnitude larger than the yawing and pitching moments—posing a major challenge to docking safety.
2. Increasing the angle of attack significantly amplifies the rolling and yawing moments, while the pitching moment is less sensitive to angle‑of‑attack changes.
3. We identify a strong aerodynamic interference zone defined by all three relative distances being less than one chord length. Within this zone, the aerodynamic coefficients and flow structures change rapidly and non‑linearly.
4. Among the three docking methods, lateral docking exhibits the most stable and symmetric aerodynamic variations, making it the most favorable approach for attitude control during the docking process. Longitudinal and vertical docking are more prone to asymmetric flow and abrupt moment changes.
5. For practical implementation of chained‑wing fixed‑wing UAVs, we recommend adopting a lateral docking trajectory and operating at a low angle of attack to mitigate the adverse effects of interference moments. These findings offer valuable guidance for the design of docking control systems and the development of future fixed‑wing UAV swarms capable of in‑flight wingtip connection.
