TL;DR: In this paper, a 1-inch-diameter steel sphere was dropped from a wide range of heights into non-cohesive glass beads, and the interaction between the sphere and the medium can be decomposed into the sum of velocity-dependent inertial drag plus depth-dependent friction.
Abstract: Experiments on the low-speed impact of solid objects into granular media have been used both to mimic geophysical events1,2,3,4,5 and to probe the unusual nature of the granular state of matter6,7,8,9,10. Observations have been interpreted in terms of conflicting stopping forces: product of powers of projectile depth and speed6; linear in speed7; constant, proportional to the initial impact speed8; and proportional to depth9,10. This is reminiscent of high-speed ballistics impact in the nineteenth and twentieth centuries, when a plethora of empirical rules were proposed11,12. To make progress, we developed a means to measure projectile dynamics with 100 nm and 20 μs precision. For a 1-inch-diameter steel sphere dropped from a wide range of heights into non-cohesive glass beads, we reproduce previous observations6,7,8,9,10 either as reasonable approximations or as limiting behaviours. Furthermore, we demonstrate that the interaction between the projectile and the medium can be decomposed into the sum of velocity-dependent inertial drag plus depth-dependent friction. Thus, we achieve a unified description of low-speed impact phenomena and show that the complex response of granular materials to impact, although fundamentally different from that of liquids and solids, can be simply understood.
TL;DR: In this paper, an analytical model for the ballistic impact response of fibrous materials of interest in body armor applications is presented, focusing on an un-tensioned 2D membrane impacted transversely by a blunt-nosed projectile, a problem that has remained unsolved for a half a century.
TL;DR: Ballistics: Theory and Design of Guns and Ammunition, Third Edition as mentioned in this paper encourages superior design and innovative applications in the field of ballistics and examines the analytical and computational tools for predicting a weapon's behavior in terms of pressure, stress, and velocity, demonstrating their applications in ammunition and weapons design.
Abstract: With new chapters, homework problems, case studies, figures, and examples, Ballistics: Theory and Design of Guns and Ammunition, Third Edition encourages superior design and innovative applications in the field of ballistics. It examines the analytical and computational tools for predicting a weapon’s behavior in terms of pressure, stress, and velocity, demonstrating their applications in ammunition and weapons design. New coverage in the Third Edition includes gas-powered guns, and naval ordinance. With its thorough coverage of interior, exterior and terminal ballistics, this new edition continues to be the standard resource for those studying the technology of guns and ammunition.
TL;DR: In this article, a low cost and highly accurate sniper detection and localization system uses observations of the shock wave from supersonic bullets to estimate the bullet trajectory, Mach number, and caliber.
Abstract: A low cost and highly accurate sniper detection and localization system uses observations of the shock wave from supersonic bullets to estimate the bullet trajectory, Mach number, and caliber. If available, muzzle blast observations from an unsilenced firearm is used to estimate the exact sniper location along the trajectory. The system may be fixed or portable and may be wearable on a user's body. The system utilizes a distributed array of acoustic sensors to detect the projectile's shock wave and the muzzle blast from a firearm. The detection of the shock wave and muzzle blast is used to measure the wave arrival times of each waveform type at the sensors. This time of arrival (TOA) information for the shock wave and blast wave are used to determine the projectile's trajectory and a line of bearing to the origin of the projectile. A very accurate model of the bullet ballistics and acoustic radiation is used which includes bullet deceleration. This allows the use of very flexible acoustic sensor types and placements, since the system can model the bullet's flight, and hence the acoustic observations, over a wide area very accurately. System sensor configurations can be as simple as two small three element tetrahedral microphone arrays on either side of the area to be protected or six omnidirectional microphones spread over the area to be monitored. Sensors may also be monitored to a helmet as used with the wearable system. Sensor nodes provide information to a command node via wireless network telemetry or hardwired cables for the command node comprising a computer to effect processing and display.
TL;DR: In this article, the ballistic response of laminated composite panels has been investigated through direct impacts of two non-deforming projectiles (7.5mm diameter hardened steel 120° cylindrical-conical, and 9mm hemispherical nosed) selected to enhance different failure mechanisms including penetration and delamination.