Dynamics of a Projectile Penetrating Sand

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 versustime measurements for the projectile in sand were obtained by means of a photographic‐electronic chronograph developed for the purpose. The striking velocity v 0 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=αv 2 +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=αv 2 ,v 0 >v>v c ;−dv/dt=βv 2 +γ,v c >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.