Investigation of Aerodynamic Interference Between Vertically Aligned Quadcopters at Varying Rotor Speeds and Separations

Abstract

With the rapid proliferation of drone applications, multi-UAV formation flights are becoming increasingly prevalent. While most existing studies focus on the aerodynamics of a single drone, aerodynamic interactions within UAV formations—particularly in close-proximity hovering configurations—remain inadequately understood. This study employs computational fluid dynamics simulations to investigate the aerodynamic interactions between two hovering quadcopters at vertical distances of 1 m and 0.5 m, operating under different RPMs. The results indicate that, when the two quadrotors are spaced 1 m apart, increasing RPM enhances the downward airflow from the upper quadcopter, which benefits the lower quadcopter. When the vertical spacing is reduced to 0.5 m, the aerodynamic interaction between the UAVs becomes more pronounced. This configuration can be advantageous if the drones remain perfectly aligned at lower RPMs. However, at higher RPMs, especially above 5000, the intensified vortices disturb the lower UAV, causing destabilization. Additionally, the reduced spacing amplifies the downwash effect, increasing the risk of collisions and loss of control. This work highlights the importance of managing the spacing and RPMs of drone pairs to optimize performance and ensure stability in multiple drone formations.

1. Introduction

Unmanned aerial vehicles (UAVs), commonly known as drones, represent a significant advancement in modern aerial technology. In recent years, they have gained widespread popularity and are increasingly regarded as a valuable alternative to traditional approaches in a range of applications, spanning both civil and military sectors [1,2]. In the military, UAVs are used for surveillance, combat operations, and territory reconnaissance. In contrast, civil applications of UAVs are diverse, including aerial photography and filmmaking, land replanting, building and structure inspection, and cargo delivery services [3,4,5]. The continuous development of UAVs underscores the importance of understanding their aerodynamic qualities to enhance their operating effectiveness, stability, and efficiency [6]. These devices are a modern take on past transportation systems. UAVs are typically categorized into fixed-wing aircraft, helicopters, and multi-rotor copters based on their platform design. Among these, quadcopters, with their compact and maneuverable structure, are particularly well-suited for applications that demand precise control in confined or restricted spaces [7,8]. Their ability to hover, adjust orientation quickly, and navigate tight areas makes them a preferred choice for tasks where versatility and agility are essential. The design and optimization of propellers play a crucial role in enhancing quadcopter performance and efficiency [9,10]. Therefore, the study of their aerodynamic characteristics is very important.

Numerous studies have been conducted to understand the aerodynamic behavior and stability of quadcopter UAVs, particularly during flight in close proximity to the ground and obstacles. Paz et al. used computational fluid dynamics (CFD) to analyze how near-ground effects influence UAV performance, revealing that proximity to surfaces reduces drag while increasing lift and forward pitch moment. These aerodynamic changes become more pronounced at higher translational velocities due to alterations in propeller-induced airflow, which delays interactions with nearby surfaces [11,12]. Additional research has focused on control systems, stabilization strategies, and structural innovations for improved quadcopter performance [13,14]. The aerodynamic optimization of quadcopters has also been explored in terms of propeller interference reduction, force measurement accuracy, and the influence of airflow on propeller geometry and vehicle stability [15,16]. Studies show that changes in rotor RPM directly impact performance. Higher RPM increases lift and reduces drag, leading to improved efficiency [17,18]. Computational approaches employing sliding mesh and multiple reference frame (MRF) techniques have been used to simulate full-quadcopter aerodynamics, confirming that increased RPM enhances lift while reducing drag [19,20].

Additionally, recent research has examined the dynamic modeling of small multi-copter systems [21], and power/RPM-based models commonly assume that thrust and torque scale with the square of rotor speed, an assumption valid primarily for hovering flight [22,23]. In parallel, Six et al. [24] proposed a flight-data-based identification method to estimate thrust, torque, and dynamic parameters of quadrotors, demonstrating reliable parameter estimation without specialized test benches. Similarly, Bianchi et al. [25] developed a robust control framework that incorporates disturbance and uncertainty estimation, ensuring stable quadcopter performance under varying flight conditions. These approaches provide valuable insights for system identification and control.

However, these simplified models fall short in capturing the complex flow dynamics inherent in multi-UAV formation flight. Power-based assumptions often neglect critical aerodynamic phenomena such as rotor-to-rotor interference, wake interaction, and ground effects. In contrast, high-fidelity CFD models employing turbulence models like Reynolds-averaged Navier–Stokes (RANS) and large eddy simulation (LES) provide a more accurate depiction of these interactions [26,27,28]. The use of MRF and sliding mesh methods allows precise evaluation of thrust, lift, and drag distributions in varying flight conditions and RPM levels [29]. These findings highlight a critical gap in the current literature: the need for detailed CFD-based evaluations of aerodynamic interference effects between multiple drones, even under steady-state conditions, where initial flow interaction patterns can be analyzed.

This study investigates the aerodynamic interactions among multiple quadcopters, with a particular focus on how variations in inter-vehicle distance and RPMs affect their aerodynamic performance. Quadcopters generate lift through the rotation of their propellers, and the relationship between rotor speed and aerodynamic output is critical for ensuring stability, maneuverability, and payload capacity. In multi-UAV configurations, changes in these parameters can significantly alter thrust distribution and induce complex aerodynamic interference. By analyzing the resulting thrust forces and aerodynamic moments under different configurations, this research aims to provide deeper insights into the performance and stability characteristics of multi-drone systems.

The work is organized as follows. Section 2 describes the methodology, including the CAD modeling, meshing, and numerical setup. Section 3 presents the validation of the computational model, covering mesh convergence and propeller rotation tests. Section 4 reports the main results of the aerodynamic analysis under different operating conditions. Finally, Section 5 provides a detailed discussion of the findings, followed by concluding remarks and perspectives for future research.

2. Methodology

In this section, the methodology for the simulation-based analysis of multi-quadcopter aerodynamics is outlined, with a focus on the geometry modeling, meshing, and numerical setup. Detailed explanations of the geometry, mesh generation, and numerical method are provided, as they form the foundation for accurate simulations.

2.1. Geometrical Model

In this work, the DJI Phantom 3 UAV was modeled in SolidWorks 2023 as shown in Figure 1 using the import coordinates tool along with loft features on guided curves to accurately capture its design. To analyze performance and safety, the UAVs were arranged in an array formation at different distances along the Z-axis. Two arrangements were analyzed, in Case-I, the UAVs were spaced 1 m apart, while in Case-II, they were 0.5 m apart. The computational fluid domain was designed to be sufficiently large to maintain free-stream conditions at the boundaries for both cases. The UAV diameter (D) was 240 mm. The computational domain was defined relative to this characteristic dimension: the inlet boundary was placed 500 mm upstream of the UAV approximately 2*D, while the outlet boundary was located 2000 mm downstream approximately 8*D to allow for the full development of the wake. The domain diameter was set to 1000 mm approximately 4*D, ensuring sufficient clearance between the UAV and the side boundaries This setup allowed for a more realistic simulation of the UAVs’ aerodynamic performance and interactions. The coordinate system and Z-axis orientation are illustrated in Figure 1.

2.2. Meshing Topology

A high-quality, well-refined mesh is essential for accurately predicting aerodynamic forces on the propellers because it enables precise resolution of the boundary layer and the complex flows at the blade tips and trailing edges. Careful control of mesh density and refinement levels balances computational cost with solution accuracy, particularly in these critical regions. To effectively capture tip vortices and other complex flow phenomena, a finer mesh should be applied at the blade tips and along the leading and trailing edges. At the same time, the overall mesh must balance detail with computational cost, since an excessively fine grid will significantly increase the time and resources required. On the other hand, if the mesh is too coarse, it may overlook important flow details and reduce the accuracy of the analysis. Including the layers adjacent to the blade surfaces supports in precisely resolving the boundary layer, ensuring a gradual increase to prevent mesh distortion and preserve quality. To achieve an optimal mesh, each parameter was calculated separately and then converted into a poly-hexcore structure, as shown in Figure 2A–F. In Figure 2F, it can be clearly observed that the trailing edges of the propeller are captured accurately without any signs of rupture or distortion. The final mesh consisted of 4.2 million poly-hexcore cells.

2.3. Numerical Methodology

This study is divided into two major case studies, with six CFD simulations conducted for each part simultaneously. In Case-I, two drones are positioned at 1 m apart, while in Case-II, the distance is reduced to 0.5 m, as discussed in the geometrical modeling and shown in Figure 2C. In both cases, simulations were performed at six different RPM levels, starting from 3000 RPM, increasing in 1000 RPM increments, and reaching a maximum of 8000 RPM, which is the maximum capacity of the DJI Phantom 3 motor.

The Reynolds-averaged Navier–Stokes (RANS) equations were solved under the assumption of incompressible flow. The governing equations consist of the continuity and momentum equations, expressed in tensor form as:

$$\begin{gathered} {\displaystyle \frac{\partial {\mathrm{u}}_{\mathrm{i}}}{\partial {\mathrm{x}}_{\mathrm{i}}}}=0 \\ \underset{\approx 0}{\underbrace{{\displaystyle \frac{\partial \left(\mathsf{\rho }{\mathrm{u}}_{\mathrm{i}}\right)}{\partial \mathrm{t}}}}}+{\displaystyle \frac{\partial \left(\mathsf{\rho }{\mathrm{u}}_{\mathrm{i}}{\mathrm{u}}_{\mathrm{j}}\right)}{\partial {\mathrm{x}}_{\mathrm{j}}}}=-{\displaystyle \frac{\partial \mathrm{p}}{\partial {\mathrm{x}}_{\mathrm{i}}}}+{\displaystyle \frac{\partial }{\partial {\mathrm{x}}_{\mathrm{j}}}}\left[\mathsf{\mu }\left({\displaystyle \frac{\partial {\mathrm{u}}_{\mathrm{i}}}{\partial {\mathrm{x}}_{\mathrm{j}}}}+{\displaystyle \frac{\partial {\mathrm{u}}_{\mathrm{j}}}{\partial {\mathrm{x}}_{\mathrm{i}}}}\right)\right]-{\displaystyle \frac{\partial }{\partial {\mathrm{x}}_{\mathrm{j}}}}\overline{\left(\mathsf{\rho }{\mathrm{u}}_{\mathrm{i}}^{\prime }{\mathrm{u}}_{\mathrm{j}}^{\prime }\right)} \end{gathered}$$

Here, $u_i$ represents the mean velocity component in the i-th direction, $\rho$ is the mean pressure, and $\overline{\left(\rho u_i^{\prime }{u}_j^{\prime }\right)}$ denotes the Reynolds stress tensor arising from turbulence fluctuations.

The k-ω shear stress transport (SST) turbulence model was employed for its effectiveness in capturing boundary layer behavior and flow separation [29,30]. To close the RANS equations, this two-equation model introduces additional transport equations for the turbulent kinetic energy $\mathrm{k}$ and the specific dissipation rate $\mathsf{\omega }$.

$$\begin{gathered} \mathrm{For} \mathrm{k} \underset{\approx 0}{\underbrace{{\displaystyle \frac{\partial }{\partial \mathrm{t}}}\left(\mathsf{\rho }\mathrm{k}\right)}}+{\displaystyle \frac{\partial }{\partial {\mathrm{x}}_{\mathrm{i}}}}\left(\mathsf{\rho }\mathrm{k}{\mathrm{u}}_{\mathrm{i}}\right)={\displaystyle \frac{\partial }{\partial {\mathrm{x}}_{\mathrm{i}}}}\left[{\mathsf{\Gamma }}_{\mathrm{k}}{\displaystyle \frac{\partial \mathrm{k}}{\partial {\mathrm{x}}_{\mathrm{j}}}}\right]+{\mathrm{G}}_{\mathrm{k}}-{\mathrm{Y}}_{\mathrm{k}}+{\mathrm{S}}_{\mathrm{k}} \\ \mathrm{For} \mathsf{\omega } \underset{\approx 0}{\underbrace{{\displaystyle \frac{\partial }{\partial \mathrm{t}}}\left(\mathsf{\rho }\mathsf{\omega }\right)}}+{\displaystyle \frac{\partial }{\partial {\mathrm{x}}_{\mathrm{i}}}}\left(\mathsf{\rho }\mathsf{\omega }{\mathrm{u}}_{\mathrm{i}}\right)={\displaystyle \frac{\partial }{\partial {\mathrm{x}}_{\mathrm{i}}}}\left[{\mathsf{\Gamma }}_{\mathsf{\omega }}{\displaystyle \frac{\partial \mathsf{\omega }}{\partial {\mathrm{x}}_{\mathrm{j}}}}\right]+{\mathrm{G}}_{\mathsf{\omega }}-{\mathrm{Y}}_{\mathsf{\omega }}+{\mathrm{D}}_{\mathsf{\omega }}+{\mathrm{S}}_{\mathsf{\omega }} \end{gathered}$$

Here, $G_k$ and $G_{\omega }$ denote the generation of turbulence due to mean velocity gradients, $Y_k$ and $Y_{\omega }$ represent the dissipation of turbulence, ${\mathsf{\Gamma }}_k$ and ${\mathsf{\Gamma }}_{\omega }$ are the effective diffusivities of $k$ and $\omega$, $D_{\omega }$ is the cross-diffusion term, and $S_k$ and $S_{\omega }$ are source terms.

The simulations were performed by solving the steady-state formulation of the governing equations, where all time-derivative terms (∂/∂t) are set to zero.

A pressure-based coupled algorithm was employed to ensure solution stability, while a second-order upwind discretization was applied to the momentum, turbulent kinetic energy, and specific dissipation rate equations for improved accuracy. Before defining the boundary conditions, the model was scaled appropriately. A velocity inlet was defined to establish a uniform inflow, and a pressure outlet was applied at the domain exit. However, in practice, the primary flow field around the drone is generated by the rotating propellers, which were modeled using the specified RPM values via a multiple reference frame (MRF).

The multiple reference frame (MRF) approach was applied, and the rotation of the propellers is simulated using the multiple reference frame method. The direction of each propeller rotation is set according to its defined MRF zone. The direction of propeller rotation is illustrated in Figure 3, where two propellers rotate clockwise, while the other two rotate counterclockwise. All numerical simulations were conducted using ANSYS Fluent 2023 R1; all simulations were executed on a workstation equipped with an AMD EPYC 7532 processor (32-core, 128 threads), 128 GB RAM, 1 TB SSD, and 8 TB HDD.

3. Validation

3.1. Mesh Convergence

A mesh independence study was conducted using thrust coefficient ($C_T$) and power coefficient ($C_P$) as key indicators, calculated at different RPMs using the formulas given in Equations (1) and (2).

$${\mathrm{C}}_{\mathrm{T}}={\displaystyle \frac{\mathrm{T}}{\mathsf{\rho }\mathrm{A}{\mathrm{V}}^2}}$$

(1)

$${\mathrm{C}}_{\mathrm{P}}={\displaystyle \frac{\mathrm{P}}{\mathsf{\rho }\mathrm{A}{\mathrm{V}}^3}}$$

(2)

where T is the thrust force, P is the power generated by the propellers, ρ, A, and V represent density, reference area, and reference velocity, respectively.

Multiple simulations were performed at a constant rotational speed of 3000 RPM, with the mesh refined by decreasing the element size from 0.7 mm to 0.1 mm. The primary objective was to identify the optimal mesh size where further refinement would yield negligible changes in the results. The results demonstrated minimal variations in both ${\mathrm{C}}_{\mathrm{T}}$ and ${\mathrm{C}}_{\mathrm{P}}$ across different mesh sizes, indicating that the solution is approaching convergence, as shown in

Table 1. Mesh convergence: evaluation of $C_T$, $C_P$, and mesh quality parameters at 3000 RPM.

Mesh Size (mm)	Max. Skewness	No. of Nodes	No. of Elements	${\mathit{C}}_{\mathit{T}}$	${\mathit{C}}_{\mathit{P}}$
0.7	0.4461	10.4 × 106	3.12 × 106	0.101	0.050
0.6	0.4257	12.3 × 106	3.74 × 106	0.102	0.051
0.5	0.6170	14.2 × 106	4.25 × 106	0.101	0.050
0.4	0.5525	16.1 × 106	4.84 × 106	0.101	0.050
0.3	0.4341	21.6 × 106	6.49 × 106	0.102	0.051
0.2	0.6373	28.9 × 106	8.59 × 106	0.101	0.050
0.1	0.4589	49.5 × 106	14.8 × 106	0.102	0.051

. For ${\mathrm{C}}_{\mathrm{T}}$, the values ranged from 0.10157 for the coarsest mesh (0.7 mm) to 0.10253 for the finest mesh (0.1 mm), with a relative error of 0.94%. Similarly, ${\mathrm{C}}_{\mathrm{P}}$ values varied from 0.05064 to 0.05140 over the same range, with a relative error of 1.48%. These differences are small enough to be considered negligible in practical terms, confirming the stability of the results across the range of mesh sizes.

To quantitatively assess the convergence, the percentage change between successive mesh sizes was calculated. Between the 0.5 mm and 0.4 mm meshes, CT changed by only 0.15%, while CP changed by 0.08%. These values are well below the typical 1% threshold used in CFD studies to define mesh independence. Such small changes validate that the selected mesh size captures the flow behavior accurately without requiring further refinement.

Additionally, the skewness of the elements for the selected mesh size of 0.5 mm is 0.6170, which is within acceptable limits, ensuring that the mesh quality does not compromise the accuracy of the simulation. The computational cost was another critical factor in selecting the final mesh size. The number of nodes and elements increased significantly as the mesh size decreased. For example, the 0.5 mm local mesh has approximately 14.2 million nodes and 4.25 million elements, while the 0.1 mm mesh contains 49.5 million nodes and 14.8 million elements, as given in Table 1. This significant increase in computational resources did not produce a proportional improvement in accuracy, which indicates that the finer meshes are inefficient. By selecting the 0.5 mm mesh, the study achieved an optimal balance between accuracy and efficiency.

In conclusion, the mesh independence study confirmed that the 0.5 mm mesh size is suitable to proceed with further research. It provides accurate results with minimal variations in $C_T$ and $C_P$ while maintaining computational efficiency. The robustness of the selected mesh ensures that the conclusions drawn from the simulations are both reliable and practical for further analysis. The mesh, initially a triangular mesh, was improved by enhancing connectivity and quality before being converted into a poly-hexcore mesh. This conversion resulted in a slight change in the skewness value, but it remained within an acceptable range, below 0.85. In Case-I, the final mesh contained 28.22 million nodes and 8.53 million elements, while in Case-II, it consisted of 27.85 million nodes and 8.43 million elements, as given in

Table 2. Details of mesh characteristics for Case-I and Case-II.

Components	Max. Skewness	No. of Nodes	No. of Elements
Case-I	0.84	28.22 × 106	8.53 × 106
Case-II	0.83	27.85 × 106	8.42 × 106

.

3.2. Propeller Rotation

To validate the chosen methodology for simulating the propeller rotation, multiple simulations were conducted based on the previously published experimental results. These simulations were within the range of steady state analysis performed by [1,4,5]. The performance validation of this work analyzed maximum and averaged lift data and the coefficient of moment through simulations. Regarding the simulations, the geometrical model of the DJI Phantom 3 propeller was evaluated at six different RPMs within the range of the published data. In this case, the aforementioned moving reference frame was applied to each propeller, following the experimental and simulation setups. The experimental results are superimposed on the black and purple curves derived from the experiments by [4], while other results are based on the published data from simulations [1,5] as shown in Figure 4.

This CFD-based simulation lowers the thrust coefficient for RPMs above 3000, but the deviation is less significant. In contrast, the power coefficient calculated using Equation (2) consistently exceeds the experimental values across all RPMs. Despite these differences, this simulation method is reliable for predicting the aerodynamic performance of propellers.

4. Results

4.1. Aerodynamic Interactions and Stability

The simulations, conducted under steady-state conditions with 5000 iterations, provide valuable insights into the lift forces and moment coefficients acting on the UAVs in both Case-I and Case-II scenarios. To establish a baseline for comparison, Figure 5 presents the lift force versus RPM for a single hovering drone, comparing the lift forces generated by two UAVs positioned at 1 m and 0.5 m distances. Analyzing the simulation data, these figures summarize the lift forces across the entire RPM range, from 3000 to 8000, at various rotational speeds and distances, providing a comprehensive assessment of the effects of UAV configuration.

The results reveal a clear relationship between the lift generated and both the spacing between the UAVs and the rotational speed of the propellers. As expected, higher RPMs lead to an increase in lift generation for all cases. However, the presence of a second UAV in close proximity introduces measurable aerodynamic interference, which becomes more pronounced at smaller separations.

When comparing to the single-drone case, it is evident that UAV-1 in the two-drone configuration produces lift forces nearly identical to those of the single hovering drone, indicating that UAV-1 is not influenced by external aerodynamic interaction. In contrast, UAV-2 consistently exhibits lower lift values compared to both UAV-1 and the single drone, due to the wake effect from UAV-1. The lift difference is minor at lower RPMs but becomes more significant as RPM increases. Once the simulation converges, all drones reach steady lift values, demonstrating their capability to generate lift, yet the proximity effect, even at a 1 m distance, continues to impact the performance of the trailing UAV. While higher RPMs result in greater lift overall, aerodynamic interactions between the drones remain, especially in the form of flow disturbances affecting UAV-2.

The coefficient of moment is particularly important in this situation because it reveals the influence of aerodynamic changes on the balance and stability of the drones. In ideal conditions, a positive coefficient of moment indicates that the aerodynamic forces are balanced in such a way that the aircraft experiences a restoring moment, which is favorable for maintaining stability. On the other hand, a negative coefficient of moment suggests that the forces are acting in a destabilizing manner, technically leading to unwanted rotations or loss of control. In Case-I, where the drones are positioned 1 m apart, the interaction between the drones is less pronounced, and the disturbance to the second drone’s aerodynamic stability is moderate. At the higher RPM values, the aerodynamic forces become stronger, but the moment disturbances remain within acceptable limits, with no negative impact, as shown in

Table 3. Coefficient of moment behavior versus RPM for Case-I and Case-II.

RPM	Case-I (At 1 m)		Case-II (At 0.5 m)
	UAV-1	UAV-2	UAV-1	UAV-2
3000	0.001827	0.004895	0.00353	0.00008
4000	0.004078	0.008018	0.00507	0.00143
5000	0.004243	0.011292	0.00582	−0.00050
6000	0.005188	0.016323	0.00412	−0.00312
7000	0.003720	0.021917	0.00544	−0.00387
8000	0.005425	0.028963	0.00804	−0.00790

. This indicates that, at larger distances, the wake effects are somewhat negligible, and the stability of the lower drone can still be maintained.

However, in Case-II, where the two UAVs are positioned at a closer vertical distance of 0.5 m, the aerodynamic interference between them becomes more significant, particularly due to the wake effects from the upper UAV. While the coefficient of moment for the lower UAV remains positive at lower RPMs, it gradually decreases as the RPM increases, showing the growing influence of the wake. For instance, at 3000 RPM, UAV-2 exhibits a coefficient of moment of 0.00008, whereas the upper UAV shows a coefficient of moment of 0.00353. Similarly, at 4000 RPM, the coefficient of moment drops from 0.00507 for the upper UAV to 0.00143 for UAV-2. This indicates that, despite the values being positive, the aerodynamic interaction is not favorable and results in a reduction in the pitching moment. At higher RPMs, UAV-2 even experiences negative coefficient of moment values, suggesting increasing instability due to the intensified downwash and disturbed flow originating from UAV-1, as shown in Table 3. But as the RPM increases beyond 5000, the wake turbulence intensifies, causing a shift in the aerodynamic forces. The coefficient of moment for the lower drone becomes negative, indicating that the vortex is now creating a destabilizing coefficient of moment that leads to undesirable results. These forces can cause the second drone to experience increased pitching or yawing, which could destabilize its flying path and reduce its ability to maintain steady control.

The shift from positive to negative coefficients of moment is a critical observation in this study, as bolded in Table 3. It highlights the importance of maintaining an optimal distance between drones in formation flying. If the drones are too close, the wake turbulence generated by the upper drone can create significant aerodynamic disturbances that negatively impact the stability of the lower drone. This phenomenon becomes particularly harmful at higher RPMs, where the increased thrust and resulting downwash intensify the destabilizing effects. Therefore, the coefficient of moment analysis provides an essential value for understanding and quantifying these interactions, allowing for better design and operational guidelines for multi-drone systems.

These observations highlight the importance of analyzing both the lift generated by the propellers and the coefficient of moment, as these factors reveal how RPMs and proximity impact the drone’s ability to maintain stable and efficient. Such analysis is essential for designing the best multiple UAV formation that minimizes aerodynamic interference and ensures consistent performance across various operational conditions. The swirling flow generated by UAV-1 exerts additional pressure on UAV-2, causing a disturbance in UAV-2 airflow and reducing the thrust it needs to maintain stability. This flow interaction effectively creates an aerodynamic influence zone can be seen in Figure 6, where UAV-2 operates in a region of modified airflow, directly impacting its thrust requirements and efficiency. In terms of velocity, the propellers for both UAVs aim to generate the same air velocity due to the same RPMs to achieve balanced lift and thrust forces as given in

Table 4. Velocities’ magnitudes generated by the thrust for both cases.

RPM	Case-I (m/s)	Case-II (m/s)
3000	37.83	37.83
4000	50.44	50.44
5000	63.05	63.05
6000	75.70	75.70
7000	88.30	88.30
8000	100.89	100.89

.

This proximity effect means that the thrust forces experienced by each propeller are not solely determined by the UAVs’ own rotors but are influenced by their aerodynamic interaction. The flow field generated by UAV-1 alters the local airflow environment around UAV-2, particularly by accelerating the downward flow and modifying the pressure distribution near its propellers. This interaction may reduce the effective pressure differential across UAV-2’s propellers, potentially affecting its thrust generation. While this effect appears to be less detrimental at lower RPMs, it becomes increasingly unfavorable at higher RPMs due to the development of stronger turbulence and unsteady wake interactions.

4.2. Aerodynamic Interactions and Flow Behavior

Understanding the difference between velocity magnitude and airflow interaction is essential for analyzing the aerodynamic behavior of multiple drones, and even small positional adjustments between drones can affect stability and performance, despite maintaining the same RPM settings. In both cases, the air velocity magnitude within the computational domain remains constant due to identical RPM settings, as shown in Table 4.

This similarity in RPM generates comparable airflow velocities from each propeller. However, proximity plays a significant role in altering airflow patterns. In closer formations, such as in Case-II, wake and downwash effects from one drone interfere with the airflow around the other, modifying local flow dynamics while keeping the overall velocity magnitude unchanged. On the other hand, another important component to examine in the aerodynamic effect is the behavior of the fluid streamlines. For instance, the streamlines emitted from the first drone form a smooth, tube-like structure, indicating a stable and controlled airflow around it.

The streamlines provide a visual understanding of how airflow is organized around each drone and reveal important flow interactions that impact velocity. Although the appearance of these lines is influenced by the number of streamlines set in CFD Post, their patterns give insight into the aerodynamic stability of each drone. As shown in Figure 6 and Figure 7, the velocity streamlines exhibit a clear interaction between the two drones, especially in the region below UAV-1 and around UAV-2. As RPM increases, the downward velocity intensifies and the streamlines begin to curve outward more strongly, indicating the presence of swirling flow and wake interaction. This change in the flow field is due to the increasing momentum of the downwash from UAV-1.

The circular flow pattern observed around the second drone in Figure 6 suggests a modification of the surrounding flow field due to the wake of the first drone. It needs to be determined whether this leads to a more stable or uniform pressure distribution. In Figure 7, the streamlines show that, at a closer spacing of 0.5 m, the wake from UAV-1 directly interacts with UAV-2. However, based on the data in Table 3, the moment coefficient of UAV-2 becomes increasingly negative at higher RPMs, indicating a potential reduction in pitch stability. However, at higher RPMs, the intensified turbulence from UAV-1’s swirling flow leads to a negative coefficient of moment for UAV-2, particularly in the pitching moment. This aerodynamic interference becomes more pronounced at higher speeds, undermining the stability gained at lower speeds.

Thus, the fluent streamline behavior is crucial for understanding the impact of positioning and flow interaction on UAV stability and performance. Closer drone spacing amplifies pressure variations, which can affect stability, cause greater structural loading, and potentially create control issues due to uneven pressure fields. At higher RPMs like 5000 to 8000 RPM, the wake formed by the upper drone creates a fluid tube that directly influences the lower drone. This effect is evident in the velocity contours, which highlight complex flow behavior and variations in airflow intensity that impact aerodynamic performance. Following the analysis of streamline behavior, the velocity contours, as illustrated in Figure 6 and Figure 7, further clarify the airflow dynamics between the drones and provide deeper insights into the velocity distribution across different regions. The contours highlight variations in flow velocity around each drone, especially in close proximity configurations, and reveal areas of intensified or reduced airflow that impact aerodynamic performance.

The static pressure distribution is an important factor in analyzing the aerodynamic behavior of two UAVs operating in close proximity. As shown in Figure 8, the left-hand side illustrates Case-I with a spacing of 1 m, while the right-hand side represents Case-II with a spacing of 0.5 m. At the larger spacing, the upper UAV produces a well-defined low-pressure region near its propellers, while the lower UAV is less affected by the disturbed flow from above. This results in a more uniform static pressure distribution across the lower UAVs blades, which in turn supports steadier aerodynamic loading.

When the spacing is reduced to 0.5 m, the effect of the upper UAV wake becomes more pronounced. The static pressure contours around the lower UAV show stronger gradients, with regions of higher pressure concentrated on the forward sections of the blades. This distorted pressure distribution indicates that the lower UAV is subjected to more intense aerodynamic interference, leading to greater imbalance in lift generation and contributing to the onset of negative pitching moments. These differences highlight how spacing directly alters the pressure field, thereby influencing stability and performance.

The influence of propeller rotational speed further intensifies these patterns. At higher RPMs (e.g., 5000–8000 RPM), the downwash from the upper UAV generates stronger low-pressure zones beneath its propellers, which are directly transmitted into the flow field of the lower UAV. This causes amplified pressure variations across the lower rotor disk, making the aerodynamic environment increasingly unstable. Thus, the static pressure distribution plots provide crucial evidence of how both spacing and RPM affect UAV aerodynamic interference, with closer spacing and higher rotational speeds creating more significant destabilizing effects.

In Case-I at a 1 m distance, as shown in Figure 9, the velocity contours show a relatively even distribution, with minimal interference between the two drones. This configuration supports a steady flow field, where each drone’s propellers generate a distinct velocity profile with limited mutual disturbance. The smooth contours around the first drone indicate a well-controlled airflow, contributing to a stable aerodynamic environment with less fluctuation in velocity magnitude.

In contrast, the 0.5 m spacing configuration, displayed in Figure 10, presents notable differences. Here, the velocity contours around the second drone reveal areas of accelerated airflow due to the interaction with the downwash from the first drone. This interaction creates regions of higher velocity, especially near the outer edges, where the streamline pattern strengthens the flow.

The resulting velocity contours in this closer spacing display more complex patterns, with zones of increased velocity surrounding the second drone, which can contribute to higher local static pressures as previously noted. These velocity contour results complement the findings from the streamline analysis, underscoring how reduced spacing between drones amplifies aerodynamic interactions. The intensified airflow near the second drone improves its stability by creating a more uniform high-velocity zone but also demands careful consideration of structural and control factors due to increased aerodynamic forces.

Together, the velocity contours and streamline behavior provide a comprehensive view of the effects of drone positioning on flow stability, pressure distribution, and overall UAV performance. At close proximity, the wake generated by the upper drone substantially alters the velocity field surrounding the lower drone, leading to increased turbulence and reduced flow stability. This intensified aerodynamic interaction becomes more pronounced as the distance decreases.

5. Discussion

This study demonstrates that the aerodynamic performance of UAVs is significantly influenced by both the spacing between drones and their propeller RPMs. Two distinct cases were analyzed. In the first case, where the drones were spaced at 1 m apart, the results showed minimal aerodynamic interference, leading to more stable and predictable flow patterns. In this configuration, the second drone produces less lift force than the first one, due to the wake influence from the leading drone. As the RPM increases, the aerodynamic forces strengthen, and the moment disturbances stay within acceptable limits. However, at higher RPMs, the second UAV experiences a slight decrease in performance. Despite this, the overall trend remains consistent and occurs at higher RPMs.

When comparing the aerodynamic forces between the upper and lower drones in the dual drone configuration, it was observed that the presence of the second drone in close proximity altered the flow dynamics around both UAVs, particularly affecting the lower drone. The first drone wake provides a stabilizing airflow environment for the second drone at lower RPMs by reducing turbulence fluctuations. However, this effect is limited to dynamic stability and does not result in increased lift. In Case-II, with a 0.5 m distance between the drones, the aerodynamic interaction became more pronounced, especially at higher RPMs. The downwash from the upper drone reduced the lift force on the lower drone and also introduced stability issues at higher RPMs, as evidenced by increasingly negative moment coefficients. Although the flow between the drones became more streamlined at closer proximity, the lift on the lower drone remained lower than that of the upper drone due to wake interference. Beyond 5000 RPM, the aerodynamic disturbances shifted from helpful to harmful, disrupting stability and increasing the potential for loss of control. Careful management of distance and RPM is essential to avoid these risks in multi-drone operations.

The study highlights the importance of maintaining a safe distance between drones in multiple UAV configurations, especially at high RPMs, to minimize interference and optimize performance. Further experimental validation of these computational results will be addressed in the future to reinforce these findings and establish practical guidelines for drone spacing in real-world applications.