The rapid advancement of microelectronics, computational power, and battery technology has led to significant improvements in the size, weight, maneuverability, and agility of unmanned aerial vehicles (UAVs). Among the various configurations, the quadrotor drone, characterized by its four rotors in a cross-arrangement, stands out for its mechanical simplicity and straightforward control logic. By independently adjusting the rotational speed of its four motors, such a drone can achieve complex flight maneuvers and stable hovering. This has made quadrotor drones, exemplified by models like the DJI F450, ubiquitous in applications ranging from aerial photography and cinematography to agricultural monitoring, news gathering, and search-and-rescue operations. However, the proliferation of operations in low-altitude and ultra-low-altitude airspace has concurrently increased the risk of in-flight failures, operator errors, and subsequent ground impact. Such crash events pose threats not only to the drone’s structural integrity but also to personnel safety, public order, and ground-based assets. Therefore, a thorough investigation into the crash dynamics and damage characteristics of quadrotor drones is crucial for enhancing operational safety, guiding crash-resistant structural design, and informing the development of relevant safety standards and regulations. While considerable research focuses on the flight control systems of quadrotor drones, analysis of their impact dynamics remains relatively limited.
Finite Element (FE) explicit dynamics analysis has become a cornerstone engineering methodology for investigating transient events such as impacts, blasts, and crashes, finding extensive validation in high-stakes fields like aerospace and automotive crashworthiness. This method can accurately replicate the complex mechanical responses during a short-duration impact by employing precise material constitutive models, appropriate boundary conditions, and a finely discretized mesh. This study employs the Explicit Dynamics module within ANSYS Workbench to perform a numerical simulation of the crash sequence of a DJI F450 quadrotor drone. The objective is to model the structural response during a ground impact resulting from a failure-induced fall under varying operational parameters. The results provide critical insights for assessing the structural safety envelope of this class of drones and defining key limiting parameters for safe operation.
The core solver for explicit dynamics within Workbench utilizes a central difference method for the time integration of the equations of motion. The fundamental dynamic equilibrium equation for a discretized system is given by:
$$
[M]\{\ddot{x}\} + [C]\{\dot{x}\} + [K]\{x\} = \{F(t)\} – \{H\}
$$
where $[M]$ is the global mass matrix, $[C]$ is the damping matrix, $[K]$ is the stiffness matrix, $\{x\}$ is the nodal displacement vector, $\{\dot{x}\}$ is the velocity vector, $\{\ddot{x}\}$ is the acceleration vector, $\{F(t)\}$ is the applied external load vector, and $\{H\}$ represents the hourglass control forces used to suppress zero-energy deformation modes.
In explicit time integration, the acceleration and velocity are approximated using central difference formulas. The velocity and acceleration at time $t$ are calculated from the displacements at surrounding time steps:
$$
\{\dot{x}(t)\} = \frac{1}{2\Delta t} \left( \{x(t+\Delta t)\} – \{x(t-\Delta t)\} \right)
$$
$$
\{\ddot{x}(t)\} = \frac{1}{\Delta t^2} \left( \{x(t+\Delta t)\} – 2\{x(t)\} + \{x(t-\Delta t)\} \right)
$$
Substituting these into the equation of motion allows for solving the displacement at the next time step $t+\Delta t$ directly from known quantities at the current and previous steps:
$$
\{x(t+\Delta t)\} = [M]^{-1} \Delta t^2 \left( \{F(t)\} – \{H\} – [C]\{\dot{x}(t)\} – [K]\{x(t)\} \right) + 2\{x(t)\} – \{x(t-\Delta t)\}
$$
This formulation is conditionally stable, requiring a time step $\Delta t$ smaller than the critical Courant–Friedrichs–Lewy (CFL) condition, which is based on the smallest element size and the material’s wave speed. This method is highly efficient for simulating short-duration, high-speed events like the crash impact of a quadrotor drone, as it avoids the need for solving large systems of coupled equations at each step, unlike implicit methods.
The DJI F450 frame represents a widely adopted platform in the hobbyist, educational, and professional prototyping sectors. Its structure is archetypal of many commercial quadrotor drones. The primary load-bearing structure consists of a central plate, typically made from a lightweight composite, from which four arms radiate in a cruciform pattern. A brushless motor is mounted at the end of each arm, driving a propeller. The adjacent propellers rotate in opposite directions to cancel out reactive torque, while diagonally opposite propellers rotate in the same direction. An undercarriage or landing gear is attached to the central plate or arms to absorb landing loads. The flight controller, battery, and other avionics are mounted on the central plate. For the purpose of this crash simulation, a simplified yet representative 3D model of the F450 quadrotor drone was created.
The finite element model was developed within ANSYS Workbench Explicit Dynamics. A hierarchical modeling strategy was employed to balance accuracy and computational efficiency. The central plate, arms, landing gear, and the rigid ground were all modeled using SOLID164 hexahedral elements, suitable for explicit dynamic analysis. A mapped meshing technique was applied with a global element size of 2.0 mm, following a mesh sensitivity study that confirmed result convergence at this resolution. Critical connection points, such as where the arms meet the central plate and where the landing gear attaches, were modeled using shared nodes to simulate rigid connections, a reasonable assumption for a bonded or tightly bolted frame. Non-structural but mass-critical components, including the motors, electronic speed controllers (ESCs), flight controller, and battery, were not geometrically modeled in detail. Instead, their mass contributions were accounted for by defining non-structural mass points (MASS166 elements) at their respective centers of gravity, connected to the structural mesh via rigid body constraints. This approach accurately captures the inertial effects during impact without unnecessarily complicating the model geometry and contact definitions. The total mass of the model was parametrically adjustable within the typical flight weight range of the F450 platform, from 0.8 kg to 1.6 kg.
Accurate material properties are essential for credible simulation results. The central plate was assigned properties representative of a T700-12K carbon fiber composite, known for its high strength-to-weight ratio. The arms and landing gear were modeled using the properties of ABS (Acrylonitrile Butadiene Styrene) engineering plastic, a common material for drone frames due to its toughness and manufacturability. The ground was modeled as a rigid concrete surface. The key material properties used in the simulation are summarized in Table 1.
| Component | Material | Young’s Modulus (MPa) | Poisson’s Ratio | Density (g/cm³) | Failure Stress (MPa) |
|---|---|---|---|---|---|
| Central Plate | T700-12K Carbon Fiber | 2.10 x 10⁵ | 0.307 | 1.76 | 3400 |
| Arms & Landing Gear | ABS Plastic | 2410 | 0.3897 | 1.07 | 90 |
| Ground | Concrete | 6.84 x 10⁴ | 0.2000 | 2.50 | N/A (Rigid) |
The crash scenario simulated is a vertical free-fall due to a sudden mid-air failure, resulting in the quadrotor drone impacting a flat, rigid ground. The initial condition for the impact was defined by an initial downward velocity, calculated from the theoretical free-fall velocity just before impact, neglecting air resistance. This velocity $v$ is a function of the drop height $h$:
$$
v = \sqrt{2 g h}
$$
where $g$ is the acceleration due to gravity (9.81 m/s²). The drone model was initially positioned slightly above (0.1 mm) the ground surface, and this calculated velocity was applied as an initial condition to the entire drone model. The ground was assigned a fixed support boundary condition. A general “Automatic Surface-to-Surface” contact was defined between the drone and the ground, with a friction coefficient of 0.3. The simulation time was set to 1 millisecond (0.001 s), sufficient to capture the primary impact event and the initial stress wave propagation. A parameterized study was conducted by varying two key operational parameters: the drop height $h$ (from 1 m to 8 m) and the total drone mass $m$ (0.8 kg, 1.2 kg, 1.6 kg).
To ensure the validity of the simulation setup, a two-pronged verification was performed. First, a theoretical check confirmed that the kinetic energy at impact in the simulation aligned with the potential energy from the drop height, with relative errors in impact velocity below 0.5%. Second, a mesh sensitivity analysis for a baseline case (1.2 kg, 5 m) demonstrated that the maximum stress in the critical landing gear region varied by less than 2.3% when the mesh size was reduced from 2.5 mm to 2.0 mm and further to 1.5 mm, indicating that the chosen 2.0 mm mesh provided results independent of further refinement.
The primary metric for structural safety assessment is the von Mises equivalent stress, which is used to predict yielding in ductile materials like ABS plastic. For brittle materials like the carbon fiber composite (in this context), maximum principal stress is often more critical, but von Mises stress provides a consistent comparison. Allowable stresses $[\sigma]$ were determined from material failure strengths using appropriate safety factors ($n$):
For the brittle carbon fiber central plate: $[\sigma]_{plate} = \frac{\sigma_{ultimate}}{n_{brittle}} = \frac{3400 \text{ MPa}}{5} = 680 \text{ MPa}$.
For the ductile ABS arms and landing gear: $[\sigma]_{abs} = \frac{\sigma_{yield}}{n_{ductile}} = \frac{90 \text{ MPa}}{1.5} = 60 \text{ MPa}$.
The simulation results for the maximum equivalent stress observed in the main drone structure (primarily the central plate) and specifically in the landing gear are compiled in Table 2. The landing gear was consistently identified as the most critically stressed component, acting as the first point of contact and primary energy absorber during the vertical impact.
| Height (m) | Mass (kg) | Max Drone Stress (MPa) | Max Landing Gear Stress (MPa) | Structural Status |
|---|---|---|---|---|
| 1 | 0.8 | 39.25 | 23.71 | Safe |
| 1.2 | 40.75 | 24.79 | Safe | |
| 1.6 | 43.66 | 25.79 | Safe | |
| 2 | 0.8 | 67.08 | 35.02 | Safe |
| 1.2 | 69.14 | 37.19 | Safe | |
| 1.6 | 71.28 | 39.23 | Safe | |
| 3 | 0.8 | 94.23 | 43.31 | Safe |
| 1.2 | 96.34 | 46.59 | Safe | |
| 1.6 | 99.57 | 49.59 | Safe | |
| 4 | 0.8 | 117.68 | 50.96 | Safe |
| 1.2 | 119.95 | 54.18 | Safe | |
| 1.6 | 123.89 | 56.23 | Safe | |
| 5 | 0.8 | 138.23 | 58.43 | Safe |
| 1.2 | 140.12 | 60.53 | Marginal (0.9% over) | |
| 1.6 | 144.37 | 62.71 | Marginal (4.5% over) | |
| 6 | 0.8 | 155.30 | 61.31 | Marginal (2.2% over) |
| 1.2 | 157.34 | 66.40 | Damage Likely | |
| 1.6 | 161.44 | 69.57 | Damage Likely | |
| 7 | 0.8 | 170.28 | 69.71 | Damage Likely |
| 1.2 | 173.06 | 71.90 | Damage Likely | |
| 1.6 | 178.53 | 76.96 | Damage Likely |
The data reveals a clear, monotonic relationship: the induced stress in the quadrotor drone structure increases with both drop height and total mass. This is expected, as the impact kinetic energy $E_k$ is proportional to both parameters:
$$
E_k = \frac{1}{2} m v^2 = m g h
$$
The central plate stresses, while increasing, remained well below the allowable 680 MPa in all simulated scenarios, indicating the primary structure is robust against such vertical impacts. The critical component is unequivocally the landing gear made of ABS plastic. For a quadrotor drone weighing 1.2 kg, the landing gear stress reaches the allowable limit of 60 MPa at approximately a 5-meter drop height (60.53 MPa, 0.9% over). At 6 meters, the stress rises to 66.40 MPa (10.7% over), a level consistent with experimental failure thresholds reported for ABS components under impact, suggesting a high probability of plastic deformation or fracture.
The analysis defines a safety envelope for the quadrotor drone under the modeled failure condition. For the DJI F450-type structure with ABS landing gear, to ensure a high probability of avoiding structural damage in the event of a vertical crash:
- The operational flight height should be limited to **5 meters or less** when flying near the ground or over areas where a crash could cause damage.
- The total take-off weight should not exceed **1.6 kg**. At this maximum weight and a 5m height, the landing gear stress is 62.71 MPa, which is 4.5% over the nominal allowable limit but may be tolerated within a small safety margin for a ductile material. For more conservative operation, a lower weight limit is advisable.
This study demonstrates the effective application of explicit dynamics finite element analysis to assess the crashworthiness of a quadrotor drone. The methodology efficiently identifies the weakest structural link (the landing gear) and quantifies the influence of key operational parameters (mass and altitude) on impact severity. The defined safety thresholds of a 5-meter maximum safe drop height and a 1.6 kg maximum safe weight provide practical, data-driven guidelines for the structural design and operational planning of similar quadrotor drone platforms. Future work could extend this analysis to include oblique impacts, different ground materials (e.g., soil, asphalt), and the implementation of failure criteria to model actual fracture, providing an even more comprehensive safety assessment framework for quadrotor drone development and deployment.