Impact drag force exerted on a projectile penetrating into a hierarchical granular bed

Context. The impact of a solid object onto a small-body surface can be modeled by the solid impact onto a hierarchically structured granular target. Aims. We develop an impact drag force model for the hierarchically structured granular target based on the experiment. Methods. We performed a set of granular impact experiments in which the mechanical strength and porosity of target grains were systematically varied. Tiny glass beads (5 mu m in diameter) were agglomerated to form porous grains of 2-4 mm in diameter. Then, the grains were sintered to control their strength. A polyethylene sphere (12.7 mm in diameter) was dropped onto a hierarchical granular target consisting of these porous grains. Motion of the penetrating sphere was captured by a high-speed camera and analyzed. Results. We find that the impact drag force produced by the hierarchically structured granular target can be modeled by the sum of inertial drag and depth-proportional drag. The depth-proportional drag in a hierarchical granular impact is much greater than that of the usual granular target consisting of rigid grains. The ratio between the grain strength and the impact dynamic pressure is a key dimensionless parameter for characterizing this extraordinary large depth-proportional drag. Conclusions. Grain fracturing plays an important role in the impact dynamics when the impact dynamic pressure is sufficiently larger than the grain strength. This implies that the effect of grain fracturing should be considered also for the impact on a small body. It may be that the effective strength of the surface grains can be estimated based on kinematic observations of the intrusion or touchdown of a planetary explorator.