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The arcticle gives a spatial gas-dynamic formulation of the backpressure problem, which describes the change in pressure in front of an accelerating projectile when it moves along the bore. This takes into account the geometry of the front of the projectile and its influence on the formation of the shock wave. An unsteady spatial flow of the displaced medium ahead of the projectile body without and taking into account the forces of viscosity is considered. The paper considers the solution to the problem of throwing a body using the energy of gunpowder combustion. The internal ballistics problem, which determines the dynamics of the projectile movement, is solved in terms of averaged parameters. A two-step Runge-Kutta scheme with a second order of accuracy is used to numerically integrate a system of ordinary differential equations in time. The control volume method is used for the numerical solution of the system of gas-dynamic equations. The gas parameters at the boundaries of the control volumes are determined using a self-similar solution to the problem of the decay of an arbitrary discontinuity. A comparison is presented of taking into account the backpressure as the pressure behind the detached shock wave, obtained from the analytical solution of the problem of the supersonic motion of a flat piston in a pipe at a constant velocity, and the pressure acting on the projectile, determined from the solution of nonstationary one-dimensional and spatial (axisymmetric) equations of gas dynamics. It was found that taking into account the viscosity practically does not affect the results of calculating the backpressure, while taking into account the shape of the front part of the projectile leads to a significant difference in the pressure fields behind the front of the shock wave compared to the solution in the framework of the one-dimensional formulation of the problem, where the shape of the front part of the projectile cannot be taken into account. It is concluded that this can significantly affect the results of modeling the ballistics of a shot at high throwing speeds.

This paper is concerned with mathematical model for numerical simulation of meteoroid dynamics. The simulations of bolide ballistics are carried out via hard sphere approximation. System of differential equations for movement and heat transfer is solved in Lagrange variables via Runge-Kutta methods. The drag force of atmospheric air is computed via Henderson formula, valid for wide ranges of Reynolds and Mach numbers. The parameters of surrounding gas are obtained from standard atmosphere model. The impact pressure is computed taking into account entropy jump through bow head shockwave and consequent isentropic deceleration of the flow in the vicinity of streamlined sphere. Meteoroid fragmentation is modeled as sequential division of parent body into two parts using random weighting coefficient for parent mass. The condition for fragmentation event occur when the hemisphere-averaged value of impact pressure exceeds the threshold of relative body strength, which nonlinearly depends on ration of initial meteoroid mass to current mass of considered fragment. To compute trajectory divergence for newly-formed splinters we introduce the repulsive force, dependent on impact pressure, cross sectional areas of mutually repulsing bodies and distances between them. The set of mathematical models is implemented as the program complex. Preliminary computational results show that fragmentation altitude, terminal velocities and maximum splinter masses are in good agreement with corresponding observations and measurements.

A twin Lumonics K922M pulsed TEA CO2 laser system (∼50 ns FWHM spike, with selectable 1.5 or 2.5 μs tail—depending upon laser gas mixture) was employed to experimentally measure the axial impulse behavior of a family of lightcraft engine geometries, using a lightweight ballistic pendulum. Axial impulse performance in both airbreathing and solid ablative rocket (SAR) modes was examined as a function of: a) laser pulse energy (∼12 to 40 Joules); b) pulse duration (∼50 ns spike with 1.5 or 2.5 μs tail); and, c) engine geometry. The four engines under investigation were the Lightcraft Types ♯150, ♯200 and ♯250, and a 11 cm parabolic bell. Lightcraft ♯200 axial CM performance reached 250 N/MW, which is sharply higher than the 120 N/MW previously reported for the engine using long pulse (e.g., 10‐18 μs) CO2 electric discharge lasers.

The ‘piston effect’, namely the time response of a fluid to an instantaneous change in the temperature of its boundaries, is studied for a rarefied gas confined in a slab. The problem is solved for the entire range of Knudsen numbers in the case where the prescribed temperature jumps at the walls are small. Analytic solutions are obtained in both collisionless and continuum limits and compared with low‐variance direct Monte Carlo simulations (LVDSMC) of the Boltzmann equation. The collisionless analysis captures well the early‐time dynamics of the system (at times t of the order of the mean collision time τcoll), where the gas motion is essentially ballistic, and the continuum‐limit analysis agrees with LVDSMC predictions at times t≥50τcoll, where the system behaviour is dominated by molecular collisions. Between these two limits, the dynamics of the system is governed by the solution of the complete linearized Boltzmann equation. The results supply insight into the mechanism of continuum breakdown in hea...

Digital Speckle Radiography (DSR) is a technique allowing full field displacement maps in a plan within an opaque material to be determined. The displacements are determined by tracking the motions of small sub‐sections of a deforming speckle pattern, produced by seeding an internal layer of lead and taking flash x‐ray images. An improved DSR algorithm is discussed which can improve the often poor contrast in DSR images, such that the mean and variance of the speckle pattern is uniform. This considerably improves the correlation success relative to other similar algorithms for DSR experiments. A series of experiments involving the penetration of granular media by long‐rod projectiles, and the improved correlation achieved using this new algorithm, are discussed.

A high‐speed digital camera was used to observe the deflection‐time history of a Kevlar® fabric to bullet impact. It was observed, as others have, that the deflecting fabric has the shape of a pyramid. The average apex angle of the pyramid was calculated from the digital images and was found to be constant with time for the first 50 to 70 microseconds. Using this information, a simple momentum transfer model is shown to capture the velocity‐time history of fabric deflection until ply failure. As expected, once ply failure occurs, the model overpredicts deceleration of the bullet.

Operation of a two‐stage implosion‐driven hypervelocity launcher in which the launch tube is imploded behind the projectile is examined. In particular, techniques to generate a high phase velocity of implosion are explored, and the technique of using a variable thickness flyer plate with a constant thickness layer of explosive is selected for further investigation. An analytic model, based on the Gurney analysis for flyer plate acceleration, is developed to determine the thickness profile necessary to deliver the desired phase velocity. Finite element simulations and experimental implementation of this approach results in the correct increase in phase velocity along the launch tube, however, the velocity profile does not generate the desired constant acceleration profile.

The effects of blast‐fragmentation warheads need to be carefully characterized in a variety of applications like passive and active vehicle protection or hard target defeat and TBM defense. With these applications in mind, we have developed a collection of tools called FI‐BLAST (Fast Interface for Blast‐Fragment Load Analysis of Structures). In the present paper we describe the essential part of these tools, namely the close range blast‐fragment model. The meaning of “close range” is here defined as the standoff to a charge at which blast effects can inflict serious damage on massive structures. In order to quantify our model’s range of validity, examples of measured and calculated momentum of bare and confined charges are given in the present paper. Short (L/D = 0.5) and long (L/D = 5) cylindrical charges are included as well as spherical charges. The presented examples demonstrate that the model gives reasonable results in the intended domains of application.

With the development of plasticity theory in the 1940s and 1950s, the modeling of penetration has become increasingly analytical and accurate. Currently, analytic penetration models are able to accurately predict depths of penetration for simple penetration geometries where the target and projectile are metals. The most accurate models use sophisticated plasticity analysis to obtain target resistances, but they usually end up expressible as relatively simple explicit differential equations. The most promising development in recent years is the centerline momentum balance, and this technique will be reviewed with some discussion of the meaning of terms by way of first principle physics. A recent model that successfully predicts ballistic limits of fabrics will also be discussed. In addition to addressing what is known, the most pressing questions that need to be answered and what is currently known on those problems will be discussed. Questions include: the transition from eroding to rigid penetration; the...

Conductance behavior of quantum double-point contacts is presented for symmetrical and asymmetrical models. The numerical results show peak and dip structures in conductance steps. The origin of these structures is clarified for these systems.

We present a numerical method as applied to flows generated by ignition and combustion of reactive solid particles. Strong shock waves are characteristic features of these flows and must be correctly resolved. For configurations that are typical of Interior Ballistics we adopt a two‐phase, two‐dimensional, axially‐symmetry and unsteady mathematical model. Numerical results for test problems are presented.