Geometry-controlled Onset of Inertial Drag in Granular Impact

Abstract: The impact of solid intruders into granular media is commonly described by a combination of quasi-static resistance and an inertial drag force proportional to the square of the impact speed. While intruder geometry is known to influence force magnitudes, its role in controlling the onset of inertial drag has remained largely unexplored. Here we present systematic impact experiments using conical intruders spanning a wide range of apex angles. By measuring the peak acceleration during impact, we show that the emergence of a well-defined inertial response depends sensitively on cone geometry. Blunt cones exhibit quadratic scaling with impact speed over the full range of velocities studied, whereas sharper cones display a delayed transition to inertial behavior at higher speeds. We define a geometry-dependent crossover speed marking the onset of the inertial regime and find that it scales approximately linearly with the cone angle through $\tanφ$. Once the inertial regime is established, the peak force collapses when rescaled by $\tanφ$, indicating that cone geometry controls the effective momentum transfer to the grains. These results demonstrate that intruder geometry governs not only the magnitude of inertial drag, but also the impact speed at which it becomes dominant.