Experimental determination of drag coefficients in low-density polyurethane foam

Abstract

We describe several experiments performed at the LLNL Site 300 firing range and on the LLNL 1/3 scale gun to investigate the deceleration of small projectiles (l {approx} 3-5 [mm]) in low-density foam ({rho} {approx} 0.08-0.32 [g/cm{sup 3}]). The experiments at the firing range researched a passive velocity diagnostic based on Faraday's law of induction, while experiments on the 1/3 scale gun investigated the effects of varying projectile surface area, projectile shape, and foam density on the drag coefficient c{sub d}. Analysis shows that the velocity diagnostic has an uncertainty on the order of 1 percent for projectiles with velocity v {approx} 0.8-1.2 [km/s]. The 1/3 scale gun experiments, dubbed the Krispy Kreme series, included nine shots considering the combinations of 3 projectile surface areas with 3 target densities. The experiments used Tantalum square surface area block projectiles (with an initial velocity v{sub 0} {approx} 1.2 [km/s], a common thickness T = 2.67 [mm], and square side lengths of 3, 4, and 5 [mm]) decelerating in polyurethane foams (with densities {rho}{sub f} of 0.08, 0.16 and 0.32 [g/cm{sup 3}]). Standard fluid models of the Krispy Kreme experiments predict Reynolds numbers Re {approx} 10{sup 5} - 10{sup 6}, Mach numbers Ma {approx} 0.5-2.0, and drag coefficients c{sub d} {approx} 2-3. However, the data indicate that c{sub d} = 1.1-1.2 (c{sub d} = 1.7) for all three block projectiles in the 0.08 and 0.16 [g/cm{sup 3}] targets (0.32 [g/cm{sup 3}] target). First, we conclude that the drag force on projectiles in solid polyurethane foam is less than in fluids with equivalent dimensionless parameters. This result is also supported by an additional Krispy Kreme experiment that used a disk projectile (with diameter d = 4.51 [mm] and thickness T = 2.67 [mm]) penetrating a target with density {rho} = 0.16 [g/cm{sup 3}], i.e., the fluid-like c{sub d} = 1.15 while the measured c{sub d} = 0.63. Second, we conclude that the measured drag coefficient in the lower density foam targets is less than in the larger density foam target. This result is corroborated by firing range experiments with M855 NATO bullets (with diameter 5.56 [mm], mass 4.1 [g], and initial velocity {nu}{sub 0} {approx} 800 [m/s]) fired from an M16 rifle, i.e., c{sub d} = 0.3 (c{sub d} = 0.6) in the 0.16 [g/cm{sup 3}] (0.32 [g/cm{sup 3}]) target. We propose future 1/3 scale gun experiments using a passive velocity diagnostic with increased spatial resolution as well as simple spherical projectiles with 0.5 and 1.0 [cm] diameters.