Our team undertook the engineering development of a rope-hook recovery device tailored for small fixed-wing UAVs. The primary objective was to enhance the energy absorption capacity beyond existing benchmarks, specifically targeting a recovery energy exceeding 28.9 kJ. This paper details the systematic design process, dynamic modeling, component analysis, and experimental validation of the device.
System-Level Design and Composition
The recovery process for a fixed-wing UAV using a rope-hook system is divided into three distinct phases. Initially, the UAV, guided by differential GPS, precisely strikes the recovery rope with its wing. The rope slides along the wing surface until it is captured by a wingtip hook, which triggers the engine shutdown. Subsequently, due to inertia, the UAV continues forward, tensioning the rope. This phase transitions the UAV’s motion from pure translation towards a rotational movement around the rope. Finally, when the rope reaches its elastic limit, the remaining kinetic energy is absorbed through the elastic deformation of the device’s mechanical structure. The system’s core components include a telescopic arm assembly for Y-direction extension, a rotary table assembly for pitch movement, a slewing assembly for complete rotation, and a crossbar assembly driven by a hydraulic motor. The hydraulic system, powered by a power take-off (PTO) from a vehicle transmission, utilizes proportional valves for precise control of various actuators, including the main luffing cylinder, folding arm cylinders, and telescopic cylinder.
Dynamic Modeling of the Recovery Rope
A critical design element was the recovery rope itself. To simplify the system and enhance reliability, we opted for a direct energy absorption mechanism using a rope with specific elastic properties, bypassing more complex solutions like accumulators or motor-driven systems. To rapidly characterize the system’s dynamics, we derived the equations of motion using the Lagrange method, establishing a spring-damper equivalent model, as shown in the schematic below.
In this model, the recovery rope is represented as a spring-damper system with stiffness \(k\) and damping coefficient \(c\). The mechanical structure’s flexibility is captured by lateral stiffness values \(k_3\) and \(k_2\) for the upper and lower crossbars, with equivalent masses \(m_3\) and \(m_2\). The UAV’s effective mass is \(m_1\). The rope lengths from the impact point to the upper and lower attachment points are \(R_{10}\) and \(R_{20}\), respectively. With a total span of approximately 17 meters for the extended crossbars, we assumed \(R_{10} = 8.5\) meters.
For a fixed-wing UAV with a mass of 70 kg and a recovery speed of 30 m/s, representing a kinetic energy of 31.5 kJ, we solved the system equations using the MATLAB platform with a central difference method. The response characteristics for acceleration and velocity over time were obtained, as summarized in the response curve analysis. From this simulation, we determined the maximum rope tension at the moment of peak deceleration to be approximately 5300 N. This value served as the primary mechanical input for the rope’s design.
Recovery Rope Development and Materials
The recovery rope’s tension is a function of its length, material composition, and elastic modulus. For our design, we chose a composite rope structure consisting of a static nylon (polyurethane) rope with 3.6% elongation and a core elastic rope made of TPU wrapped in polypropylene fibers. The static rope provides the main structural framework, while the elastic rope performs the primary energy buffering function. The assembly includes an arresting rope section with a buckle, which is the primary point of impact with the UAV’s wingtip hook. This two-segment design enhances both the energy absorption capacity and the maintainability of the rope assembly, allowing for easy inspection and replacement of the most stressed parts.
To validate the material selection, we conducted static tensile tests. The maximum theoretical tension from our model was 5300 N. Applying a safety factor of 1.5 to 2 for dynamic loading, we required a rope with a minimum static breaking strength around 10600 N. Our tests on a 10 mm diameter rubber-elastic rope (synthetic rubber with fiber reinforcement) showed a maximum static failure load of 16200 N, providing a comfortable margin of safety. The following table summarizes the key parameters of the recovery rope assembly.
| Component | Material | Elongation | Primary Function | Static Failure Load (N) |
|---|---|---|---|---|
| Static Rope (Main Frame) | Nylon (Polyurethane) | 3.6% | Structural framework | > 16200 |
| Elastic Rope (Buffer) | TPU wrapped in Polypropylene | High elasticity | Energy absorption via stretching | > 16200 |
| Arresting Rope (Buckle) | Static + Elastic rope segments | Composite | Direct UAV wingtip hook contact | > 16200 |
Structural Analysis of the Recovery Device
After the recovery rope has absorbed a portion of the UAV’s kinetic energy, the remainder is dissipated through the elastic deformation of the mechanical frame. We performed a finite element analysis (FEA) on the entire recovery device to verify its structural integrity under worst-case loading conditions. The constraints and loads were defined based on a peak recovery overload of 10g and the force decomposition from the rope tension, which included the effects of a 7-level wind load for a conservative assessment.
The FEA results identified several high-stress concentration zones. The primary results for the most critical components are summarized in the table below. The main structural material selected was Q690E steel, with a yield strength \(\sigma_s = 690\) MPa and a tensile strength \(\sigma_b = 770\) MPa. The allowable stress was calculated using the following formula:
$$[\sigma] = \frac{0.5\sigma_s + 0.3\sigma_b}{n}$$
Where \(n = 1.34\) is the safety factor accounting for wind loads. This yielded a basic allowable stress \([\sigma] = 458.58\) MPa. For localized stress concentrations, a contact stress criterion of \(1.4[\sigma]\) or \(1.5\sigma_s\) was employed, ensuring the design remained within safe limits. For instance, components like the slewing table and basic crossbar arm showed stresses up to 904.47 MPa, but after accounting for model simplifications and localized contact stresses, the global stress levels were deemed acceptable.
| Assembly | Component Name | Max Stress (MPa) | Location of Max Stress |
|---|---|---|---|
| Telescopic Arm | 1st Arm | 626.38 | Main cable bracket |
| 2nd Arm | 691.64 | Arm head | |
| 3rd Arm | 685.00 | Slider connection joint | |
| 4th Arm | 853.38 | Slider contact surface (stress concentration) | |
| Slewing Table | Slewing Table Body | 913.89 | Local arc transition (stress concentration) |
| 1st Link | 450.85 | Busher edge | |
| 2nd Link | 476.52 | Hinge point edge | |
| 3rd Link | 218.82 | Hinge point edge | |
| Crossbar | End Segment | 714.56 | End of reinforcing plate |
| Basic Segment | 904.47 | Connection bushing (stress concentration) | |
| Folding Arm | End Segment | 573.44 | Edge diagonal |
| Basic Segment | 458.00 | Cylinder hinge point |
Overturning Load Calculation
The recovery device, when fully deployed, reaches a height of 17 meters (or 20 meters when mounted on a vehicle chassis). A critical aspect of the vehicle integration was calculating the overturning moment to design a proper mounting base. The total overturning load \(M\) is composed of three main parts: the self-weight of the structure \(M_1\), the load from the UAV’s impact \(M_q\), and the wind load \(M_F\). The calculation is as follows:
$$M = M_1 + M_q + M_F$$
$$M = m_1 g L_1 + (F_2 L_2 + F_3 L_3) + \frac{C_p q A L_3}{2}$$
Where \(m_1\) is the equivalent mass of the device’s center of gravity, \(L_1\) is the horizontal distance from the center of gravity to the base center. \(F_2\) and \(F_3\) are the Y and X components of the force at the upper crossbar tip (4000 N and 2800 N, respectively, derived from the 5300 N rope tension). \(L_2\) and \(L_3\) are the corresponding moment arms. \(C_p\) is the wind pressure correction factor, \(q\) is the standard wind load value, and \(A\) is the windward area of the device. The calculation yielded a total overturning moment of 137.3 kN·m and an axial force of 32000 N, providing the essential data for the slewing assembly and anti-overturning design.
Operational Sequence
The operation of the vehicle-mounted recovery device follows a standardized four-step procedure. First, the transport lock is released, and the slewing assembly rotates the device to the required azimuth. Second, the telescopic arm is raised, the recovery rope is attached, and the lower crossbar is deployed by the hydraulic motor-driven mechanism. Third, the folding arms are extended to deploy the upper crossbar. Finally, the telescopic arm is extended to its full height. The entire sequence is controlled via a multi-way valve from a control panel.
Experimental Validation and Test Results
We conducted a series of tests to validate the performance of the recovery system, following a risk-mitigation principle of increasing energy levels. Initial qualification tests were performed using a HY30 fixed-wing UAV with a mass of 25 kg and a recovery speed of 25 m/s. These tests confirmed the basic functionality and measured a maximum rope tension of approximately 500 N, corresponding to a 2g overload.
The final verification tests were conducted with a heavier military-trade fixed-wing UAV with a takeoff weight of 87 kg. These tests were performed to validate the device’s maximum capability. An NI cRIO data acquisition system with an ICP force sensor (12800 Hz sampling rate) and an onboard fiber-optic inertial navigation system were used to collect data. The results from six successful recovery tests are presented in the table below.
| Recovery Mass (kg) | Ground Speed (m/s) | Synthetic Overload (g) | Recovery Energy (kJ, measured) |
|---|---|---|---|
| 65.85 | 23.00 | 4.4 | 17.4 |
| 62.22 | 23.50 | 4.6 | 17.2 |
| 63.40 | 25.25 | 5.4 | 20.2 |
| 68.75 | 28.25 | 6.9 | 27.4 |
| 66.55 | 29.25 | 7.1 | 28.5 |
| 72.00 | 30.00 | 7.5 | 32.4 |
The test data demonstrates that the device achieved a maximum measured recovery energy of 32.4 kJ. This surpasses the theoretical 28.9 kJ benchmark for certain comparable systems like the RQ21. The maximum synthetic overload recorded during these tests was 7.5g, which is well within the structural limits of the target fixed-wing UAV, which is designed for a 20g launch overload. Based on this data, the device is theoretically capable of recovering a fixed-wing UAV with a mass of 82.65 kg and a recovery speed of 28 m/s, fully satisfying the requirements for both normal and emergency recovery scenarios for the intended UAV system.
Conclusion
Our engineering development of the rope-hook recovery device for small fixed-wing UAVs successfully demonstrated a combined energy absorption strategy using a “recovery rope + elastic deformation” mechanism. The key conclusions from this work are as follows:
The Lagrange-based dynamic modeling, solved via MATLAB, provided accurate static and dynamic force inputs for the recovery rope design. The composite rope design, consisting of a static frame and an elastic core, offers a robust and maintainable solution.
Finite element analysis identified critical stress concentrations in the telescopic arm, slewing table, and crossbar, guiding the selection of high-strength Q690E steel and validating the structural design against a 10g overload criterion. The overturning load calculation provides a critical reference for vehicle integration.
Experimental validation confirmed the device’s ability to achieve a maximum recovery energy of 32.4 kJ, a 12% improvement over comparable systems, while maintaining a maximum overload of only 7.5g, thereby ensuring the safe recovery of the fixed-wing UAV. This device successfully resolved the precision recovery challenge for a specific long-endurance small fixed-wing UAV system.