In modern agriculture, the adoption of unmanned aerial vehicles (UAVs) has revolutionized precision farming, enabling efficient crop monitoring, spraying, and data collection. Among these, multi-rotor agricultural drones, particularly six-rotor configurations, are favored for their stability, payload capacity, and maneuverability. However, a critical challenge in designing such agricultural drones is the force effect coupling arising from aerodynamic interactions between adjacent propellers. This phenomenon significantly impacts lift generation, leading to increased energy consumption and reduced operational efficiency. To address this, we propose a comprehensive analysis method based on Computational Fluid Dynamics (CFD) to evaluate and optimize the force effect coupling in six-rotor agricultural drones. This study focuses on understanding how propeller spacing influences overall performance, including total lift, coupling efficiency, motor force effect, and endurance time, with the aim of providing practical insights for the development and structural layout optimization of agricultural drones.
The importance of agricultural drones cannot be overstated, as they offer solutions for sustainable farming by reducing labor costs and minimizing chemical usage. Specifically, six-rotor agricultural drones are widely used in crop protection due to their reliability and ability to carry substantial payloads, such as pesticides or fertilizers. Yet, the mutual interference of propellers—often referred to as force effect coupling—can degrade performance, making it essential to analyze and mitigate these effects. Previous research has explored various aspects of agricultural drones, including control systems, path planning, and spray systems, but limited attention has been given to the aerodynamic coupling between propellers in multi-rotor setups. Our work fills this gap by employing CFD simulations to investigate the force effect coupling, ultimately guiding the design of more efficient agricultural drones.
We begin by detailing the methodology, which leverages CFD principles to simulate the fluid dynamics around the agricultural drone. CFD involves discretizing the governing equations of fluid flow—such as mass, momentum, and energy conservation—into algebraic equations solvable on computational grids. For this study, we use the SST k-ω turbulence model, which accurately captures the turbulent flows around rotating propellers. The transport equations for this model are given by:
$$ \frac{\partial}{\partial t}(\rho k) + \frac{\partial}{\partial x_i}(\rho k u_i) = \frac{\partial}{\partial x_j}\left(\Gamma_k \frac{\partial k}{\partial x_j}\right) + G_k – Y_k + S_k $$
$$ \frac{\partial}{\partial t}(\rho \omega) + \frac{\partial}{\partial x_i}(\rho \omega u_i) = \frac{\partial}{\partial x_j}\left(\Gamma_\omega \frac{\partial \omega}{\partial x_j}\right) + G_\omega – Y_\omega + D_\omega + S_\omega $$
Here, \( \rho \) represents fluid density, \( k \) is turbulent kinetic energy, \( \omega \) denotes specific dissipation rate, \( u_i \) are velocity components, \( \Gamma_k \) and \( \Gamma_\omega \) are diffusion coefficients, \( G_k \) and \( G_\omega \) represent generation terms, \( Y_k \) and \( Y_\omega \) are dissipation terms, \( D_\omega \) is the cross-diffusion term, and \( S_k \) and \( S_\omega \) are user-defined source terms. These equations form the basis for our simulations, allowing us to predict aerodynamic forces and flow fields around the agricultural drone.
To implement this, we designed a six-rotor agricultural drone model, designated as the HY-810 type, with a payload capacity of 100 kg and propeller dimensions of 60 inches. Using SolidWorks software, we created seven three-dimensional models with varying propeller spacings: 62 mm, 162 mm, 262 mm, 287 mm, 312 mm, 362 mm, and 462 mm. Each model represents a different structural layout, enabling us to study the impact of spacing on force effect coupling. The key parameters for these agricultural drone models are summarized in Table 1, which includes propeller spacing, aircraft axle base, propeller size, body mass, and battery capacity. This tabular representation helps in comparing the design variations systematically.
| Propeller Spacing (mm) | Aircraft Axle Base (mm) | Propeller Size (inches) | Body Mass (kg) | Battery Capacity (W·h) |
|---|---|---|---|---|
| 62 | 3223 | 60 | 166.0 | 488.4 × 24 |
| 162 | 3423 | 60 | 168.0 | 488.4 × 24 |
| 262 | 3623 | 60 | 170.0 | 488.4 × 24 |
| 287 | 3673 | 60 | 170.5 | 488.4 × 24 |
| 312 | 3723 | 60 | 171.0 | 488.4 × 24 |
| 362 | 3823 | 60 | 172.0 | 488.4 × 24 |
| 462 | 4023 | 60 | 174.0 | 488.4 × 24 |
The design of the agricultural drone incorporates six brushless motors (EA160 type) and 24 batteries with a capacity of 488.4 W·h each. For simulation purposes, we simplified the model by integrating the carbon plates and arms into a unified body, which facilitates mesh generation and reduces computational time. The computational domain was divided into inner and outer regions, with the inner domain encompassing the propellers to capture rotational effects. We used Fluent software for the CFD simulations, applying boundary conditions such as inlets, outlets, and walls. The mesh was generated with a global minimum size of 1.5 mm and a maximum size of 300 mm, adhering to the principle of denser grids near the propellers and coarser grids elsewhere. This setup ensures accurate resolution of the flow dynamics around the agricultural drone.
The image above illustrates a typical agricultural drone in operation, highlighting its application in precision agriculture. In our simulations, we focused on monitoring the total lift force generated by the six propellers under different spacing configurations. To establish a baseline, we first simulated a single propeller in isolation, which yielded a maximum lift of approximately 754 N. Thus, the theoretical maximum lift for the six-rotor agricultural drone is 4524 N (6 × 754 N). However, due to force effect coupling, the actual total lift is expected to be lower. The simulation results for the total lift across various propeller spacings are presented in Table 2, along with the calculated force effect coupling efficiency. The coupling efficiency \( \eta \) is defined as the ratio of the actual total lift \( F \) to the theoretical maximum lift \( C \), expressed as:
$$ \eta = \frac{F}{C} \times 100\% $$
This metric quantifies the impact of aerodynamic interference, with higher values indicating better performance. Our findings reveal that the total lift varies significantly with propeller spacing, peaking at 4380.7943 N for a spacing of 262 mm, corresponding to a coupling efficiency of 96.83%. This suggests that optimal spacing minimizes negative interactions, thereby enhancing the agricultural drone’s lift capacity.
| Propeller Spacing (mm) | Total Lift (N) | Force Effect Coupling Efficiency (%) |
|---|---|---|
| 62 | 4163.4736 | 92.33 |
| 162 | 4224.4573 | 96.27 |
| 262 | 4380.7943 | 96.83 |
| 287 | 4295.2998 | 94.94 |
| 312 | 4311.0662 | 95.29 |
| 362 | 4359.6636 | 96.37 |
| 462 | 4370.8863 | 96.62 |
| Theoretical Maximum | 4524.0000 | 100.00 |
To further analyze the performance of the agricultural drone, we examined the motor force effect, which influences power consumption and endurance. The force effect of the brushless motors depends on the throttle percentage, defined as the ratio of the required lift per motor to the maximum lift capacity. Based on the drone’s takeoff mass (sum of body mass and payload mass), we calculated the throttle percentage \( X \) using:
$$ X = \frac{G}{F} \times 100\% $$
where \( G = m g \) is the gravitational force on the takeoff mass, \( m \) is the mass in kg, and \( g = 9.81 \, \text{m/s}^2 \) is gravitational acceleration. The motor force effect values corresponding to different throttle percentages are listed in Table 3, derived from performance data of the EA160 motors. For our agricultural drone models, the force effect ranges from 7.05 to 7.20 g/W, with the highest value of 7.20 g/W observed at a propeller spacing of 262 mm. This indicates that optimal spacing not only improves lift but also enhances motor efficiency, contributing to better overall performance of the agricultural drone.
| Force Effect (g/W) | Throttle Percentage (%) |
|---|---|
| 8.589691203 | 50 |
| 7.352411807 | 60 |
| 6.609071274 | 70 |
| 6.295455547 | 80 |
| 5.722656942 | 90 |
| 5.375402136 | 100 |
Using these force effect values, we computed the endurance time \( t \) for each agricultural drone model, which is a critical parameter for operational efficiency. The endurance time is given by:
$$ t = \frac{P}{E \cdot L} \times 60 $$
where \( P \) is the total battery power per motor (in watts), \( E \) is the motor force effect (in g/W), and \( L \) is the lift required per motor (in N). The results, summarized in Table 4, show that the agricultural drone with a propeller spacing of 262 mm achieves the longest endurance time of 18.75 minutes. This is attributed to the combined benefits of high total lift and optimal motor force effect, reducing energy waste and extending flight duration. In contrast, smaller or larger spacings lead to decreased endurance due to either excessive aerodynamic interference or increased body mass, underscoring the importance of precise layout optimization in agricultural drone design.
| Propeller Spacing (mm) | Endurance Time (minutes) |
|---|---|
| 62 | 17.50 |
| 162 | 18.25 |
| 262 | 18.75 |
| 287 | 18.00 |
| 312 | 18.10 |
| 362 | 17.80 |
| 462 | 18.20 |
Beyond numerical metrics, we analyzed the pressure distribution and flow field patterns around the agricultural drone using CFD post-processing tools. The simulations revealed that at smaller propeller spacings (e.g., 62 mm), strong vortices and pressure imbalances occur between adjacent propellers, leading to significant force effect coupling and reduced lift. As spacing increases, these interactions diminish, but beyond an optimal point, the added body mass from longer arms offsets any gains. For instance, at 262 mm spacing, the flow field exhibits uniform pressure distribution and minimal turbulence, maximizing aerodynamic efficiency. This is visually represented in contour plots of pressure and velocity, which show streamlined airflow and reduced wake interference. Such insights are invaluable for refining the structural layout of agricultural drones, ensuring that propeller arrangements minimize energy losses while maintaining stability.
To validate our simulation results, we conducted flight tests with a physical prototype of the agricultural drone configured with a propeller spacing of 262 mm. The tests included both bench trials and actual field flights, focusing on flight stability, response to control inputs, and endurance measurements. For the bench tests, the agricultural drone was mounted on a debugging frame to monitor its performance under controlled conditions. Subsequently, field flights were carried out with a full payload of 100 kg, using fully charged batteries. Data logged by the flight control system indicated that during hover, the actual throttle input was 65.8%, compared to a theoretical value of 61.6%, resulting in an error of 4.2 percentage points. The actual endurance time was 17.30 minutes, while the simulated value was 18.75 minutes, yielding an error of 5.3%. These discrepancies are within acceptable limits, considering real-world factors like air resistance and battery variability, thus confirming the reliability of our CFD-based analysis for agricultural drone optimization.
The implications of this study extend beyond six-rotor configurations to other multi-rotor agricultural drones. By demonstrating that force effect coupling efficiency is positively correlated with key performance parameters—such as total lift, motor force effect, and endurance time—we provide a framework for designing more efficient agricultural drones. For example, the optimal propeller spacing of 262 mm for our model can serve as a reference for similar-sized agricultural drones, potentially reducing development costs and trial-and-error iterations. Moreover, the CFD methodology employed here can be adapted to analyze other aerodynamic aspects, like downwash effects on spray deposition or the impact of wind conditions on flight stability. As agricultural drones become increasingly integral to precision farming, such optimization efforts will enhance their sustainability and operational scope.
In conclusion, our research presents a detailed force effect coupling analysis for six-rotor agricultural drones using CFD simulations. We found that propeller spacing plays a crucial role in determining aerodynamic performance, with an optimal spacing of 262 mm maximizing total lift (4380.7943 N), force effect coupling efficiency (96.83%), and endurance time (18.75 minutes). The force effect coupling phenomenon exhibits both promoting and inhibiting effects depending on spacing, highlighting the need for careful design considerations. Through flight tests, we validated the simulation results, underscoring the practicality of this approach for agricultural drone development. Future work could explore variable spacing arrangements or integrate machine learning to predict coupling effects under diverse operating conditions. Ultimately, this study contributes to the advancement of agricultural drone technology, paving the way for more efficient and reliable solutions in modern agriculture.
To further elaborate on the CFD principles, we can derive additional equations governing fluid flow around the agricultural drone. For instance, the conservation of mass (continuity equation) and momentum (Navier-Stokes equations) are fundamental to these simulations. In integral form, the continuity equation for an incompressible flow is:
$$ \oint_S \mathbf{v} \cdot d\mathbf{S} = 0 $$
where \( \mathbf{v} \) is the velocity vector and \( S \) is a closed surface. For momentum conservation, the equation can be expressed as:
$$ \rho \left( \frac{\partial \mathbf{v}}{\partial t} + \mathbf{v} \cdot \nabla \mathbf{v} \right) = -\nabla p + \mu \nabla^2 \mathbf{v} + \mathbf{f} $$
Here, \( p \) is pressure, \( \mu \) is dynamic viscosity, and \( \mathbf{f} \) represents body forces. These equations, when solved numerically, allow us to predict forces and moments on the agricultural drone. Additionally, the lift force \( L \) generated by a propeller can be approximated using blade element theory:
$$ L = \frac{1}{2} \rho C_L A v^2 $$
where \( C_L \) is the lift coefficient, \( A \) is the propeller disk area, and \( v \) is the airflow velocity. In multi-rotor setups, interference reduces the effective \( v \), leading to the coupling effects we studied. By optimizing spacing, we maximize \( v \) and thus \( L \), improving the agricultural drone’s efficiency.
We also considered the power consumption of the agricultural drone, which relates to its economic viability. The power \( P_{\text{req}} \) required for hover can be estimated as:
$$ P_{\text{req}} = \frac{T^{3/2}}{\sqrt{2 \rho A}} \cdot \frac{1}{\eta_{\text{prop}}} $$
where \( T \) is thrust, \( \rho \) is air density, \( A \) is total propeller area, and \( \eta_{\text{prop}} \) is propeller efficiency. Our simulations show that at optimal spacing, \( T \) is higher and \( \eta_{\text{prop}} \) improves due to reduced interference, lowering \( P_{\text{req}} \) and extending battery life. This aligns with our endurance calculations, reinforcing the importance of aerodynamic optimization for agricultural drones.
In summary, this comprehensive analysis underscores the value of CFD in designing high-performance agricultural drones. By systematically varying propeller spacing and evaluating key metrics, we have identified optimal configurations that enhance lift, efficiency, and endurance. As the demand for agricultural drones grows in precision farming, such insights will drive innovations, making these tools more accessible and effective for farmers worldwide. The integration of advanced simulation techniques with practical testing ensures that agricultural drone development is both scientifically grounded and operationally relevant, contributing to sustainable agricultural practices.