Exterior ballistics analysis of shotgun using discrete element method with equivalent aerodynamic forces

This research continues the research of Deng et al. (2022) [1], using Discrete Element Method (DEM) coupled with Finite Element Analysis to solve shotgun exterior ballistics. The simulation examples in this research are using an Italian-made 24 gm #9½ birdshot with 433 pellets fired from 30” long, 12-gauge cylinder and full choke barrels. The simulations of shotgun exterior ballistics of this research included pellet swarm velocity and the pellet dispersion at different distances until 50 yards away from the muzzle. The ballistics simulation of the pellet swarm is completed from interior to exterior consecutively after the shotshell is fired inside the chamber so all ballistics performances can be calculated at one time. Three forces were applied to the pellets for exterior ballistics simulation: the contact force between pellets, the aerodynamic separation force between pellets, and the drag force. Because of the complexity of the aerodynamic forces exerted on pellets, this research used an equivalent aerodynamic force to simulate this complex phenomenon. Two birdshot models with different pellet formations were created; the first one was simulated to calibrate the separation scale factor defined in aerodynamic separation force, and the second one was used for validation and sensitivity of the model. The simulation results show that for #9½ birdshots fired by cylinder barrel, the average Effective Shot Dispersion (ESD) of pellet dispersion of both birdshots inside the 30” diameter of the target circle at 40 yards from the muzzle is 398.53, which is remarkably close to 396.98 of the experiment result. The simulation of the average pellets' target hit rate is 77.14% (inside the 30” diameter of the target circle), which is also remarkably close to the experiment hit rate of 77.57%. The same birdshot fired from a full choke barrel shows that ESD and hit rate rose to 406.34 and 83.14%, respectively. These results demonstrate the effectiveness of using the discrete element method in conjunction with the proposed equivalent aerodynamic force to predict the shotgun's interior and exterior ballistics.