Dynamics of a Projectile Penetrating Sand

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Abstract
The experiment reported in this paper was designed to obtain data on the dynamics of a nonrotating, conical-nosed projectile penetrating randomly-packed sand. Position versus time measurements for the projectile in sand were obtained by means of a photographic-electronic chronograph developed for the purpose. The striking velocity v0 of all rounds was about 700 m/sec. The negative acceleration of a 5-in. long, 0.50-caliber, 80-gram projectile was found to be roughly expressible by the equation −dv/dt=αv2+βv+γ where the coefficients α, β, and γ are positive constants. This general relation includes as special cases the conventional penetration formulas of Robins-Euler, Poncelet, and Résal. A new theory of penetration is proposed based on the equations: −dv/dt=αv2,v0>v>vc;−dv/dt=βv2+γ,vc>v>0 where the coefficients α, β, γ are positive constants and α<β. An abrupt transition in the drag force that occurs at the critical velocity vc of about 100 m/sec is believed due to transition from inelastic to quasi-elastic impact.