Quantitative Study on the Effective Shielding Time Window of UAV Smoke Grenades Based on Geometric Determination and Kinematic Comparison

Abstract

This study aims to quantify the effective duration of concealment provided by a single smoke grenade against an incoming missile, thereby optimizing the deployment strategy for drone smoke decoy grenades. Following a problem decomposition—model construction—precise solution framework, this work employs kinematic modeling and geometric detection. Within a unified coordinate system, it extracts the shielding time window and cumulative shielding duration through time-domain scanning with a fixed time step. To investigate aerodynamic effects, the model performs dynamic comparisons between drag-free flight at constant altitude and flight incorporating quadratic drag. The drag-inclusive model employs fourth-order Runge–Kutta numerical advancement. Results indicate: under no-drag conditions, the masking duration is 1.394 s with a minimum distance of 4.669 m; introducing quadratic drag increases masking duration to 1.809 s while reducing the minimum distance to 2.952 m, validating the positive gain from drag. The model converged through sensitivity analysis, demonstrating robust conclusions.