Granular Matter

, Volume 12, Issue 4, pp 337–344

Effects of density ratio and diameter ratio on critical incident angles of projectiles impacting granular media


DOI: 10.1007/s10035-010-0186-7

Cite this article as:
Nishida, M., Okumura, M. & Tanaka, K. Granular Matter (2010) 12: 337. doi:10.1007/s10035-010-0186-7


The dynamic behavior of projectiles upon impact with granular media was recorded using two high-speed video cameras for capturing different angles. We used steel, brass, tungsten carbide spheres, and alumina ceramic spheres with diameters in the range of 6–20 mm as the projectiles and polystyrene beads (6 mm in diameter) and glass beads (1.7 mm in diameter) as the granular media. Upon impact, the projectiles penetrated the media, rebounded from the media, or were deflected such that their resulting motion was in a horizontal direction. Post-impact motion of the projectiles depended on the impact angles of the projectiles, the density ratio (bulk density/projectile density), and the diameter ratio (granular diameter/projectile diameter) and not on the impact velocity. The post-impact motion of the projectiles did not follow a clear trend in terms of the transient angle; instead, we observed the existence of a transient region. On the basis of the area of the transient regions, an empirical equation was derived for determining the critical angle of projectiles (the angle at which they can penetrate the granular media) as a function of the density ratio and the diameter ratio.


Critical incident anglesOblique impactProjectile motionPenetrationReboundRicochet off

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Nagoya Institute of TechnologyNagoyaJapan