Influence of Granular Medium Parameters on Poncelet Drag Coefficient

The Poncelet equation can effectively characterize the resistance of a granular medium to a projectile. However, the determination of the drag coefficient remains challenging. This study aims to explore the potential effects of granular medium parameters on the drag coefficient and to identify key granular medium parameters. Horizontal ballistic tests and quasi-static penetrometer tests were conducted on dry silica sand of four different grain sizes (0.3–0.6 mm, 0.6–2.0 mm, 2.0–4.0 mm and 4.0–8.0 mm). During the ballistic tests, the bulk density of the sand targets was kept consistent, and the entering velocities and the penetration depth of the projectiles were recorded. The bearing strength of the sand targets with different relative densities (30%, 50% and 70%) was measured in the quasi-static tests. Furthermore, two methods were employed to determine the drag coefficients, namely, (1) single-parameter fitting (SF), where the static resistance term was defined as the average bearing strength and the drag coefficients were fitted using the ballistic test data, and (2) two-parameter fitting (TF), where the optimal drag coefficients and bearing strengths were derived from ballistic data. The results showed that the TF method was susceptible to the size effect, differing significantly from the SF method when the projectile diameter was less than 21 times the grain size. The relative density was identified by the SF method as a critical factor affecting the drag coefficient of the granular medium.