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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. [Display omitted] • The equivalent aerodynamic forces were formulated from experiments of two pellets flying near to each other. • An Italian made 12-gauge 24 gm. #9½ birdshot with 433 pellets fired from 30-in long cylinder and full choke barrels were simulated. • Two birdshot models with different pellet formations were created to validate the sensitivity of the model. • Average simulated pellet dispersion at 40 yards fired by cylinder has only 0.43% error compared to the experiment. • Birdshot fired by full-choke barrel has 6.0% higher target hit rate compared to cylinder barrel did. [ABSTRACT FROM AUTHOR]

This research used the discrete element method (DEM) with finite element analysis to successfully simulate the interior ballistics performance of a shotgun and the transient dynamics of its barrel and wad, including their stress and deformations. Three projectiles (Italian-made #9½ birdshot with 433 pellets and US #00 buffered and non-buffered buckshots with 9 pellets) fired by two barrels (30″-cylinder and full-choke barrels) were simulated. Each simulation model included four components: barrel, wad, shell case, and pellets. This study first simulated the birdshot and the buffered buckshot fired by the full-choke barrel, until the leading pellet arrived at 1 m away from the muzzle. The simulated average pellet muzzle velocities were compared to the velocities specified by the Sporting Arms and Ammunition Manufactures' Institute. The results showed that there was only a 0. 13% error in the birdshot and a 0. 96% error in the buffered buckshot. Subsequently, other cases were simulated to obtain their interior ballistics performance with pellet dispersions 1 m away from the muzzle. The results showed that the choke effects were very remarkable for the birdshot: the average pellet muzzle velocity increased with pellet dispersion reduction when passing through the choke. However, the choke effects were not as notable for the buckshot: the average pellet muzzle velocity decreased as the pellet dispersion decreased. The simulations also showed that the buffered buckshot could effectively reducing the pellet dispersion compared with the non-buffered buckshot. The research results confirmed the feasibility of using the DEM to predict the interior ballistics of a shotgun. • Introduction of discrete element method in finite element analysis for shotgun interior ballistics. • Three different shotshells—birdshots and buckshots fired by 12-gauge shotguns with cylinder and full-choke barrels—were simulated. • Simulated pellet muzzle velocity showed only 0.13% and 0.96% errors in birdshot and buffered buckshot compared to SAAMI specified. • Birdshot fired by full-choke barrel presented higher muzzle velocity with smaller dispersion than that fired by cylinder barrel. • Buckshots fired by full-choke barrel showed lower muzzle velocity with smaller dispersion than those fired by cylinder barrel. • Buffered buckshot can effectively reduce pellet dispersion compared with non-buffered buckshot. [ABSTRACT FROM AUTHOR]