The proliferation of small, low-altitude, slow-speed unmanned aerial vehicles (UAVs), often termed “low, slow, and small” (LSS) drones, presents a significant and growing security challenge. Their affordability, ease of operation, and low observability make them susceptible to misuse, ranging from privacy invasion and smuggling to potential threats to critical infrastructure and aviation safety. Incidents of drones colliding with or disrupting commercial aircraft highlight the urgent need for effective countermeasures. Traditional defense systems, designed for larger, faster threats, are often ill-suited and economically impractical for neutralizing these ubiquitous LSS UAVs. Therefore, developing cost-effective, portable, and safe interception systems is paramount. This article presents a comprehensive study on a non-destructive, net-based anti-UAV capture system, focusing on its underlying launch physics, performance modeling, and multi-objective optimization.
Existing anti-UAV technologies encompass a wide spectrum, including kinetic impact (missiles, projectiles), directed energy (lasers, high-power microwaves), and electronic warfare (jamming, spoofing). While effective in certain scenarios, many have drawbacks such as high cost, collateral damage risk, regulatory restrictions on signal interference, or limited effectiveness in dense urban environments. A compelling alternative is the physical capture using a net, which can safely disable a target drone by entangling its rotors without causing explosive debris or significant electronic interference. The key technological hurdle lies in deploying the net rapidly and accurately over a sufficient range. This research addresses this challenge by employing a specialized launching mechanism and optimizing its performance for field deployment.
The proposed anti-UAV capture device operates on the high-low pressure (HLP) launch principle, a well-established method for achieving relatively high projectile velocities with low acceleration loads, which is ideal for propelling a net payload without damaging it. The system comprises several key components: a high-pressure chamber (HPC) containing the solid propellant, a controllable valve, a low-pressure chamber (LPC), multiple launch tubes, and the folded capture net connected to several projectiles. Upon initiation, the propellant ignites within the sealed HPC, generating high-temperature, high-pressure gas. Once the HPC pressure reaches a predetermined threshold, the valve opens, allowing the gas to flow into the larger-volume LPC. This gas expansion significantly reduces the pressure while increasing the gas volume, creating a forceful but relatively gentle push on the projectiles seated in the launch tubes. The projectiles are expelled simultaneously, pulling the net which unfolds aerodynamically during flight to form a large-area web designed to ensnare the target UAV.
The performance of this anti-UAV launcher is governed by a complex interplay of interior ballistics (the in-barrel motion) and exterior ballistics (the net’s flight). To analyze and optimize this system, a coupled interior-exterior ballistic model is established. The model is based on the following fundamental assumptions to make the problem tractable while retaining critical physics:
- Propellant combustion follows the geometric burning law and the gas is governed by the Nobel-Abel equation of state.
- The burning rate follows an exponential law dependent on pressure.
- Propellant grains burn completely within the HPC and do not flow into the LPC.
- Flow through the valve is treated as isentropic and choked (critical) when the pressure ratio exceeds a critical value.
- Projectile motion in the barrel accounts for resistive forces via a secondary work coefficient ($\phi$).
- Net flight dynamics are simplified by modeling the projectiles (which pull the net corners) as point masses under gravity and aerodynamic drag, assuming a constant angle of attack and neglecting the net’s aerodynamic influence on the trajectory for initial sizing.
- Standard atmospheric conditions with no wind are assumed.
The mathematical model is segmented into three distinct phases.
Phase 1: Valve Closed (Propellant Combustion in Closed HPC)
Before the valve opens, combustion occurs at constant volume in the HPC. The pressure $p_1$ is given by the Nobel-Abel equation:
$$ p_1 = \frac{f m \psi}{V_{01} – \frac{m}{\rho_p}(1-\psi) – \alpha m \psi} $$
where $f$ is the propellant impetus (force), $m$ is the propellant mass, $\psi$ is the fraction of propellant burnt, $V_{01}$ is the initial HPC volume, $\rho_p$ is the propellant density, and $\alpha$ is the co-volume. The form function for progressive burning propellant is:
$$ \psi = \chi z (1 + \lambda z) $$
Here, $\chi$ and $\lambda$ are shape coefficients, and $z$ is the relative burned web thickness. The burning rate equation is:
$$ \frac{dz}{dt} = \frac{u_1 p_1^n}{e_1} $$
where $u_1$ is the burning rate coefficient, $n$ is the pressure exponent, and $e_1$ is the half-web thickness.
Phase 2: Valve Open (Gas Flow and Projectile Motion)
When $p_1$ exceeds the valve opening pressure, gas flows into the LPC. The mass flow rate through the valve of diameter $d_1$ is modeled as:
$$ \frac{d\eta}{dt} = \frac{\pi}{4} d_1^2 \cdot \frac{\varphi_1}{f^{1/2}} \cdot \sqrt{2 p_1 (p_1 – p_2)} $$
where $\eta$ is the fraction of total propellant gas mass that has flowed into the LPC, $\varphi_1$ is the flow discharge coefficient, and $p_2$ is the instantaneous LPC pressure. The HPC pressure now evolves as:
$$ p_1 = \frac{f m (\psi – \eta)}{V_{01} – \frac{m}{\rho_p}(1-\psi) – \alpha m (\psi – \eta)} $$
The LPC pressure, accounting for work done on the $n_1$ projectiles, is:
$$ p_2 = \frac{f m \eta – \frac{n_1}{2}(k-1) \phi m_0 v^2}{V_{02} + n_1 l_1 A} $$
Here, $V_{02}$ is the initial LPC volume, $k$ is the specific heat ratio, $m_0$ is the mass of a single projectile, $v$ is its velocity, $l_1$ is its travel down the launch tube, and $A$ is the tube cross-sectional area. The equations of motion for the projectile in the barrel are:
$$ \frac{dv}{dt} = \frac{p_2 A}{\phi m_0}, \quad \frac{dl_1}{dt} = v $$
Phase 3: Projectile Free Flight (Net Deployment)
After muzzle exit, the projectiles (and the expanding net) are governed by exterior ballistics. The equations of motion in a standard atmosphere, considering only drag and gravity, are:
$$
\begin{aligned}
\frac{dv_x}{dt} &= -c H(y) G(v, c_s) v_x \\
\frac{dv_y}{dt} &= -c H(y) G(v, c_s) v_y – g \\
\frac{dx}{dt} &= v_x, \quad \frac{dy}{dt} = v_y
\end{aligned}
$$
where $v_x$ and $v_y$ are the horizontal and vertical velocity components, $x$ and $y$ are the corresponding coordinates, $c$ is the ballistic coefficient, $H(y)$ is the air density function, $G(v, c_s)$ is the drag function (e.g., G1 or G7), $c_s$ is the speed of sound, and $g$ is gravitational acceleration. For a net to open effectively, the launch tubes are angled outward (e.g., 15° from central axis). The effective launch velocity for determining the net’s centroid trajectory is the component along the central launch angle $\theta_0$.
This coupled system of ordinary differential equations is solved numerically using a fourth-order Runge-Kutta method. A baseline simulation provides key performance metrics. For a representative configuration, the HPC pressure peaks at approximately 89 MPa before the valve opens, after which it transfers energy to the LPC. The LPC pressure pushes four projectiles, each achieving a muzzle velocity of about 17.4 m/s. For a central launch angle of 60°, the projectiles reach an apogee of 8.6 m and a horizontal range of 19 m. Varying the launch angle defines the operational envelope or “capture volume” of the anti-UAV system, which for the baseline extends to roughly 23 m in maximum horizontal range and 11.5 m in altitude.
The performance of this anti-UAV system is sensitive to key design parameters, primarily the propellant mass $m$ and the HPC volume $V_{01}$. To guide design, we define three normalized composite metrics derived from simulation outputs:
- Capture Performance (JP): Normalized muzzle velocity. Higher velocity extends range and reduces time-to-target.
- Portability (JM): Inversely related to the normalized total system mass (and volume). Lighter, more compact systems are preferable for mobile anti-UAV operations.
- Safety (JS): Inversely related to the normalized peak HPC pressure. Lower peak pressures reduce mechanical stress and safety risks.
A perfect system would maximize all three metrics (JP → 1, JM → 1, JS → 1).
Parametric studies reveal intrinsic trade-offs. Increasing propellant mass $m$ boosts muzzle velocity and thus JP. However, it also increases peak pressure (lowering JS) and requires thicker, heavier chamber walls to withstand the pressure, which increases system mass (lowering JM). Conversely, increasing HPC volume $V_{01}$ lowers peak pressure significantly, improving JS and allowing for thinner walls (slightly improving JM), but it can slightly reduce the muzzle velocity (lowering JP) due to a less vigorous pressure rise. These trade-offs necessitate a systematic optimization approach to find the best compromise for an effective anti-UAV device.
We formulate a multi-objective optimization problem. The design variables are the propellant mass ($m$) and the HPC volume ($V_{01}$). The objectives are to maximize the three metrics JP, JS, and JM. The optimization is subject to the following constraints derived from operational requirements:
- The maximum horizontal capture range must be ≥ 15 m.
- The total system mass must be ≤ 20 kg for portability.
- The peak HPC pressure must be ≤ 120 MPa for safety.
- The peak LPC pressure must be ≤ 50 MPa.
To handle these constraints within an optimizer, a penalty function method is employed. An aggregate objective function $F$ is constructed:
$$ F = J_P + M \cdot \sum_i \max(0, g_i(x)) $$
where $g_i(x)$ represents the violation of the i-th constraint (e.g., $g_1(x) = 15 – \text{Range}$), and $M$ is a large positive penalty factor. When all constraints are satisfied, $F = J_P$. Any constraint violation leads to a large penalty, steering the search away from infeasible regions. While JS and JM are also objectives, they are implicitly improved by minimizing peak pressure and system mass, which are part of the constraint and model calculations. The primary direct objective for the optimizer is to maximize the constrained muzzle velocity metric.
The Particle Swarm Optimization (PSO) algorithm, known for its effectiveness in nonlinear, constrained engineering problems, is employed to solve this problem. PSO operates with a population (swarm) of candidate solutions (particles) that move through the design space, guided by their own best experience and the swarm’s best experience. The algorithm efficiently explores the trade-offs between $m$ and $V_{01}$ to find a design that maximizes performance within the defined limits.
The optimization results demonstrate a significant improvement in the overall system design for the anti-UAV launcher. The convergence history of the PSO shows stable attainment of an optimal solution. The optimized design parameters and a comparison with the baseline are summarized below:
| Parameter | Symbol | Baseline | Optimized | Change |
|---|---|---|---|---|
| Propellant Mass | $m$ | 0.520 g | 0.587 g | +12.9% |
| HPC Volume | $V_{01}$ | 10.0 mL | 7.7 mL | -23.0% |
| Peak HPC Pressure | $p_{1,max}$ | 89.0 MPa | 85.0 MPa | -4.5% |
| Peak LPC Pressure | $p_{2,max}$ | 34.7 MPa | 29.5 MPa | -15.0% |
| Muzzle Velocity | $v_0$ | 17.4 m/s | 18.6 m/s | +6.9% |
| System Mass | $m_{sys}$ | 12.0 kg | 9.2 kg | -23.3% |
The optimized pressure-time curves reveal a more controlled interior ballistic process. The HPC pressure rises more gradually to a lower peak, enhancing safety ($J_S$). Simultaneously, the optimized combination of a slightly higher charge mass and a smaller, more efficient HPC volume yields a higher muzzle velocity, directly improving the capture performance ($J_P$). The reduction in required chamber volume and the lower operating pressures allow for a substantial reduction in the structural mass of the launcher, markedly improving portability ($J_M$). The calculated trajectories confirm that the optimized anti-UAV device meets the 15+ m range constraint while offering a larger operational envelope compared to the baseline.
In conclusion, this study presents a validated modeling and optimization framework for a net-based anti-UAV capture system utilizing the high-low pressure launch principle. The developed coupled interior-exterior ballistic model effectively simulates the complete launch and net deployment sequence. Parametric analysis elucidated the critical trade-offs between capture performance, portability, and safety inherent in the design. By applying a Particle Swarm Optimization algorithm with carefully defined objectives and constraints, a significantly improved design was obtained. The optimized launcher configuration simultaneously achieves higher muzzle velocity, lower peak pressures, and reduced system mass compared to an initial baseline, representing a balanced enhancement of its overall effectiveness as a portable, safe, and capable anti-UAV solution. This work provides a solid theoretical foundation and a practical optimization methodology for the continued development and refinement of physical interception systems against LSS drone threats.