Experimental Tests of the Proportionality of Aerodynamic Drag to Air Density for Supersonic Projectiles

Pure theory recognizes the dependence of supersonic drag coefficients on both Mach number and Reynolds number, which includes an implicit dependence of drag coefficient on air density. However, many modern approaches to computing trajectories for artillery and small arms treat drag coefficients as a function of Mach number and assume no dependence on Reynolds number. If drag force is strictly proportional to air density for supersonic projectiles (as suggested by applied theory), the drag coefficient should be independent of air density over a range of Mach numbers. Experimental data to directly support this are not widely available for supersonic projectiles. The experiment determined drag on a 2.59 g projectile from M1.2 to M2.9 using optical chronographs to measure initial and final velocities over a separation of 91.44 m. The free flight determination of drag coefficients was performed at two significantly different atmospheric densities (0.93 kg/m3 and 1.15 kg/m3 ). This experiment supported direct proportionality of aerodynamic drag to air density from M1.2 to M2.9 within the experimental error of 1%-2%.