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The ballistics equations for spherical pellets in free flight are simplified through appropriate scaling of the pellet velocity and pellet distance. Two different drag coefficient curves are averaged to yield a single curve applicable to shot pellets and round balls. The resulting S-shaped drag coefficient curve is approximated by three straight-line segments. The scaled ballistics equations are then solved exactly and simple formulas are found for the velocity and flight time with respect to trajectory distance. The formulas are applicable to spherical shot pellets and round balls of any composition under any atmospheric conditions. The formulas are amenable to quick and easy computation and may also serve as an aid in understanding and comparing black-box ballistics calculators. For shotshell ballistics, an important assumption in the present investigation is that the pellets are moving as single, free spheres and not as a dense cloud or in a shot column, in particular, the pellets are not interacting during flight. Therefore, the formulas are most appropriate for single round balls, for large shot sizes, and for pellets of small shot size fired from open chokes. The formulas are clear and accessible, and can be implemented by military or law enforcement personnel as well as hunters and shooters. This work differs from previous investigations in that accurate ballistics formulas are derived for spherical projectiles of shotguns and muzzleloaders using realistic drag coefficients.

An experimental study and hydrocode simulation was conducted to investigate the correlation between hardness of steel and the ballistic performance of steel-encapsulated SiC armour modules against long rod impact. The armour module design composed of a SiC tile in confinement within 10 mm backing and 5 mm cover plates, which were made of AISI 4340 steel with varying hardnesses between HRC 30 to 50. The armour modules were subjected to normal impact by conical tungsten alloy long rods of 8.3 mm diameter and 115 mm length, at a nominal striking velocity of 1.25 km/s. A witness block of AISI 4340 steel was placed behind the armour module to capture the residual projectile. Failure analysis of the armour modules and the measurement of residual penetration in the witness blocks were applied to characterize ballistic performance of the ceramic armour modules. The different modes of failure of the backing plate and its influence on ballistic performance of the module were verified through visual inspection of test modules and analysis of high speed videos. Hydrocode simulation of the experiments using LS-DYNA was carried out to model the penetration and failure processes that occurred in the armour modules. The Johnson Cook model was applied in simulation of the steel confinement, accounting for the influence of hardness on JC model parameters. Results showed that increasing hardness of the backing enhanced the performance of the module while cover plate hardness had no influence within the range of hardnesses tested. This study paves the way for future studies to further understand the influence of steel hardness on the ballistics performance of steel-encapsulated silicon carbide (SiC) armour modules.

In support for the development of a new small-arm ballistic computer based on the NATO Armaments Ballistic Kernel (NABK) for the Canadian snipers, DRDC Valcartier Research Centre was asked to carry out high-fidelity 6 degree-of-freedom (6-DOF) trajectory simulations for a set of relevant vignettes for the snipers, and to compare the direct fire 6-DOF simulation results with those obtained with the 4-DOF NATO Armaments Ballistic Kernel (NABK) adapted to simulate small-arm ammunition trajectories. To conduct this study, DRDC Valcartier Research Centre used BALCO v1.0b. This paper presents (1) the process and the methodology employed to carry out the sniper direct fire solution study, (2) the modeling and the simulation of the sniper projectile, the approach used in calculating the firing solutions, and the results of direct fire simulations for the sniper vignettes, and (3) an analysis of firing solutions obtained with the BALCO engine versus those of NABK. The work presented in this paper serves to validate the use of NABK for the new sniper ballistic computer.

An optimization method is introduced to design the aerodynamic parameters of a dual-spin two-dimensional guided projectile with the canards for trajectory correction. The nose guidance component contains two pairs of canards which can provide lift and despin with the projectile for stability. The optimal design algorithm is developed to decide the profiles both of the steering and spinning canards, and their deflection angles are also simulated to meet the needs of trajectory correction capabilities. Finally, the aerodynamic efficiency of the specific canards is discussed according to the CFD simulations. Results that obtained here can be further applied to the exterior ballistics design.

One of the primary design considerations of earth-orbiting spacecraft is the mitigation of the damage that might occur from an on-orbit MMOD impact. Traditional damage-resistant design consists of a ‘bumper’ that is placed a small distance away from a spacecraft component or from the wall of the element in which it is housed. The performance of such a multi-wall structural element is typically characterized by its ballistic limit equation (BLE), which defines the threshold particle size that results in a failure of the spacecraft element. BLEs are also key components of any micro-meteoroid/orbital debris (MMOD) risk assessment calculations. However, these assessments often call for BLEs to predict impact response for projectiles made of materials not used in the development of those BLEs. The question naturally arises regarding how close are the predictions of such BLEs when used in impact scenarios involving projectiles made of materials not necessarily considered in their development. In an effort to address this issue, a study was performed with the objective of assessing the validity of the NNO BLE for non-aluminum particles. Particle materials considered included steel, copper, and Al 2 O 3 (i.e. particles that are made of materials that are more dense than aluminum). Comparisons are made between actual test results involving these non-aluminum projectiles and the predictions of the NNO BLE. In nearly all cases, the NNO BLE was found not to work very well in the predicting failure / no failure response of these non-aluminum projectiles. A new NNO-type BLE is then developed that can be used to more reliably predict the response of dual-wall systems under the hypervelocity impact of such “heavier” non-aluminum projectiles.

Ballistics is the study of a projectiles motion and can be broken down into four stages: internal, intermediate, external and terminal ballistics. The study of the effects a projectile has on a living tissue is referred to as wound ballistics and falls within terminal ballistics. To understand the effects a projectile has on living tissues the mechanisms of wounding need to be understood. These include the permanent and temporary cavities, energy, yawing, tumbling and fragmenting. Much ballistics research has been conducted including using cadavers, animal models and simulants such as ballistics ordnance gelatine. Further research is being conducted into developing anatomical, 3D, experimental and computational models. However, these models need to accurately represent the human body and its heterogeneous nature which involves understanding the biomechanical properties of the different tissues and organs. Further research is needed to accurately represent the human tissues with simulants and is slowly being conducted.

The paper deals with a possibility of the local repairing of damaged composite armours. The proposed repairs can be performed directly in the field, allowing thus to recover the full ballistic protection in a short time. Several solutions (temporary or permanent) were designed and tested both experimentally and using numerical simulations. Overlapping of the damaged area with patch from armour steel after filling the hole with ceramic balls showed to be optimal as a temporary repair. The calculation clearly showed that the depth of penetration of the projectile is reduced in all cases of designed permanent repairs in comparison to original armour configuration. The experiments confirmed supposed enhancing of ballistic resistance, but only some repair techniques met the requirements of multi-hit testing. However, the reason of failure after multi-hit could be clearly explained with the help of used numerical simulations.

The fundamental components of any meteoroid/orbital debris (MOD) risk assessment calculation are environment models, damage response predictor equations, and failure criteria. In the case of a spacecraft operating in low earth orbit, the response predictor equation typically takes the form of a ballistic limit equation (BLE) that defines the threshold particle sizes that cause failure of a spacecraft wall or component. Spacecraft risk assessments often call for BLEs for spacecraft components that do not exist. In such cases, it is a common procedure to use an existing BLE after first equivalencing the actual materials and/or wall thicknesses to the materials that were used in the development of the existing BLE. The question naturally arises regarding how close are the predictions of such an ‘adapted BLE’ to the response characteristics of the actual materials/wall configurations under high speed projectile impacts. This paper presents the results of a study that compared the predictions of a commonly used BLE when adapted to the Soyuz OM wall configuration against those of a new BLE that was developed specifically for that Soyuz wall configuration. It was found that the critical projectile diameters predicted by the new Soyuz OM wall BLE can exceed those predicted by the adapted use of the existing BLE by as much as 50% of the existing BLE values. Thus, using the adapted version of the existing BLE in this particular case would contribute to a more conservative value of assessed risk. If the same trends were to hold true for other spacecraft wall configurations, then it is also possible that using existing BLEs, even after they have been adjusted for differences in materials, etc., may result in predictions of smaller critical diameters (i.e., increased assessed risk) than would using BLEs purposely developed for actual spacecraft configurations of interest.

The mechanisms of progressive penetration for two ultrahigh molecular weight polyethylene (UHMWPE) reinforced laminates have been investigated. One used an UHMWPE fiber reinforcement while the other utilized molecularly aligned tape. Both materials had similar out of plane compressive strengths, but the fiber system had a 40% higher in plane tensile strength than the tape. Laminated, 6 mm thick plates with a [0°/90°] ply architecture were impacted by a 12.7 mm diameter sphere under conditions that either allowed out of plane plate deflection or eliminated this deflection by rear support of the target. The depth of penetration and the ballistic limit in the rear-supported tests were identical for the two materials, and proceeded by progressive ply failure. However, tests in the edge clamped condition resulted in a substantially higher penetration resistance, especially for the higher tensile strength fiber-reinforced material. Edge clamped testing of a bilayer target, where the front third was composed of the tape material and the remainder comprised fiber reinforced laminate, had the same ballistic limit as a target composed of only the higher ply tensile strength fiber reinforced material. Penetration in both test support conditions was discovered to occur by tensile ply rupture under the projectile, consistent with a recently proposed mechanism for converting out of plane compression to in plane ply tension. Lateral displacement of plies was also observed near the sides of impact craters in both materials, indicating the existence of a second mechanism impeding penetration of the spherical shaped projectile.

Based on its intrinsic mass and velocity, a bullet has an upper limit of wounding potential. Actual wound severity is a function of the bullet construction and trajectory, as well as the properties of the tissues traversed. Interpreting physicians must evaluate the bullet trajectory and describe patterns of injury resulting from the effect of energy transfer from the projectile into living tissue. A basic understanding of firearms, projectiles, and wound ballistics can help the interpreting physicians in conceptualizing these injuries and interpreting these cases.

Monolithic, porous, thermal protection systems were used heavily on the Apollo command module, and they are currently being used on the next generation of US manned spacecraft, Orion. These systems insulate reentry critical components of a spacecraft against the intense thermal environments of atmospheric reentry. Additionally, these materials may be highly exposed to space environment hazards like solid particle impacts. This paper discusses impact studies up to 10 km/s on nominally 0.56 g/cm 3 Avcoat ablator with phenolic flexible hexcore. An impact model that describes projectile dispersion in a monolithic material is described that provides excellent agreement with observations over a broad range of impact velocities, obliquities and projectile materials.

The number of head wounds due to firearms remains low in France because these cases are primarily linked to suicide (or attempted suicide) and, to a lesser extent, to attacks or hunting accidents [1]. Characterized by the impact of a projectile, which in most cases is made of metal, at high levels of kinetic energy, such acts generally result in severe trans-cerebral lesions with significant levels of morbidity/mortality [2]. Seldom are cases reported in the literature that give a detailed study of intracranial foreign bodies made of bone in such situations [3]. Here we report on the case of two suicides resulting from a transcranial gunshot wounds caused by weapons and ammunition issued by the French police force. Each case helped distinguish a characteristic bone fragment, in the form of a "patch", equivalent in size to the caliber of the bullet.

Whipple shields were first proposed as a means of protecting spacecraft from the impact of micrometeoroids in 1947 [1] and are currently in use as micrometeoroid and orbital debris shields on modern spacecraft. In the intervening years, the function of the thin bumper used to shatter or melt threatening particles has been augmented and enhanced by the use of various types and configurations of intermediate layers of various materials. All shield designs serve to minimize the threat of a spall failure or perforation of the main wall of the spacecraft as a result of the impact of the fragments. With increasing use of Whipple shields, various ballistic limit equations (BLEs) for guiding the design and estimating the performance of shield systems have been developed. Perhaps the best known and most used are the "new" modified Cour-Palais (Christiansen) equations [2]. These equations address the three phases of impact: (1) ballistic ( 7 km/s), where the projectile melts or vaporizes at impact. The performance of Whipple shields and the adequacy of the BLEs have been examined for the first two phases using the results of impact tests obtained from two-stage, light-gas gun test firings. Shield performance and the adequacy of the BLEs has not been evaluated in the melt/vaporization phase until now because of the limitations of launchers used to accelerate projectiles with controlled properties to velocities above 7.5 km/s. A three-stage, light-gas gun, developed at the University of Dayton Research Institute (UDRI) [3], is capable of launching small, aluminum spheres to velocities above 9 km/s. This launcher was used to evaluate the ballistic performance of two Whipple shield systems, various thermal protection system materials, and other spacecraft-related materials to the impact of 1.6-mm- to 2.6-mm-diameter, 2017-T4 aluminum spheres at impact velocities ranging from 8.91 km/s to 9.28 km/s. Test results, details of the shield systems, and nominal ballistic limits for the two Whipple shields are shown in Figures 1 and 2.

The impact of three different projectiles (0.357 Magnum, 9-mm FMJ and 0.30 cal FSP) onto Kevlar® was modeled using a commercial finite-element program. The focus of the research was on simulating full-scale body armor targets, which were modeled at the yarn level, by reducing to a minimum the number of solid elements per yarn. A thorough validation of the impact physics was performed at the yarn level, single-layer level, and a full body armor system. A verification was performed by checking the numerical model against analytical predictions for yarn impact. For one-layer and multiple-layer targets validation consisted on matching experimental data of pyramid formation recorded by an ultra-high-speed camera. The full-scale targets were also instrumented with nickel–chromium wires that stretch with the yarn during the penetration event. The wires provided a second validation data set since the numerical model can reproduce the signal recorded by the wires. The third and final validation of the model is provided by a comparison of the ballistic limit predicted by the model and data obtained in tests. This is a check of the failure model used in the numerical simulations. This paper shows that the main features of the impact physics are well reproduced by the finite-element model. Prediction of ballistic limits for the 9-mm FMJ and FSP projectiles were within the scatter of the tests, while for the 0.357 projectile the difference was only 15%.

Three-dimensional FE model is presented for perforation under normal and oblique impact of sharp nosed projectiles on single and layered ductile targets. Numerical simulations have been carried out to study the behavior of Weldox 460 E steel and 1100-H12 aluminum targets impacted by conical and ogive nosed steel projectiles respectively. Weldox 460 E steel targets of 12 mm thickness in single and double layered combination (2 × 6 mm) and 1100-H12 aluminum targets of 1 mm thickness in single and double layered combination (2 × 0.5 mm) impacted at 0°, 15° and 30° obliquity were considered for simulations. The results of monolithic and layered targets were compared for each angle of impact. Monolithic targets were found to have higher ballistic resistance than that of the layered in-contact targets of equivalent thickness. Failure of both the targets occurred through ductile hole enlargement. However, ogive nosed projectile failed 1 mm thick aluminum target through petal formation and conical nosed projectile failed 12 mm thick steel target through a circular or elliptical hole enclosed by a bulge at rear surface. The explicit algorithm of ABAQUS finite element code was used to carry out the numerical simulations. Various parameters which play critical role in numerical simulation such as element size and its aspect ratio have been studied.

An experimental study was made of the pressures generated by a single hydrodynamic ram event. A generic box type fuel tank simulator was fabricated to study the phenomenon and was capable of containing 3785.4 l of liquid thereby isolating the phases of the event from tank wall reflections, and enable separation of the effects of each phase. Tungsten, steel, and aluminum spherical projectiles were fired into the tank and the result was measured using high-speed pressure transducers, which were located throughout the tank, and compared to the pressure waves and events recorded inside the tank simulator with a high-speed video. It was determined that a high-pressure initial wave is generated at impact and is followed by the more gradual drag pressure around the projectile. The angular distribution of the initial wave and the variation with distance were investigated along with the effect of projectile mass on the drag pressure. This region of pressure decreases in the projectile wake, forming a trailing cavity that remains at a low pressure until the cavity begins to collapse. This results in the largest recorded pressure inside the simulator.

The known fiber and polymeric-matrix material properties, unit-cell microstructural characteristics and unit-cell level finite-element analyses are used to construct a new ballistic material model for 0°/90° cross-plied oriented polyethylene fiber-based armor-grade composite laminates. The model is constructed in such a way that it can be readily integrated into commercial finite-element programs like ANSYS/Autodyn [ANSYS/Autodyn version 11.0, User Documentation, Century Dynamics Inc., a subsidiary of ANSYS Inc., 2007] and ABAQUS/Explicit [ABAQUS version 6.7, User Documentation, Dessault Systems, 2007] as a user material subroutine. To validate the model, a series of transient non-linear dynamics simulations of the transverse impact of armor-grade composite laminates with two types of bullets/projectiles is carried out. The results obtained are next compared with their experimental counterparts. This comparison revealed that a relatively good agreement is obtained between the experimental and the computational analysis relative to: (a) the success of the armor panels of different areal densities in defeating the bullets at different initial bullet velocities; (b) post-mortem spatial distribution of damage within the panels; (c) the temporal evolution of a bulge at the back-face of the armor; and (d) the existence of three distinct armor-penetration stages (i.e. an initial filament shearing/cutting dominated stage, an intermediate stage characterized by pronounced filament/matrix de-bonding/decohesion and the final stage associated with the extensive bulging of the armor panel).

Laminated ballistic composite panels are an important part of hard-plate protective body armour and may be subjected to a wide variety of impact conditions depending on the projectile, impact velocity and armour construction, to name a few. The ballistic response of laminated composite panels has been investigated through direct impacts of two non-deforming projectiles (7.5 mm diameter hardened steel 120° cylindrical–conical, and 9 mm hemispherical nosed) selected to enhance different failure mechanisms including penetration and delamination. Experimental and numerical studies were carried out to determine the ballistic response of laminated Kevlar® 29 and 129 composite panels, commonly used in protective body armour. These panels were impacted at velocities between 130 and 250 m/s, which were below the penetration limit of the panels. A numerical parametric study was initially undertaken to determine those material properties which reduce back face signature (BFS; maximum dynamic displacement), one of the important performance indicators for assessing personal protection. Experimental material characterization then allowed mechanical property data to be determined for numerical simulations, which showed good agreement with the experimental data, particularly for the conical projectile impacts on both types of Kevlar® panels. Numerical simulations of the impact tests accurately predicted the BFS and dynamic response for the conical projectile impacts, while the BFS for the hemispherical projectiles was slightly low. This can be attributed to the dominant delamination failure mechanisms, which may not be completely captured by the numerical model. Importantly, the numerical analysis accurately predicted the initial velocity of the panel back face for the hemispherical projectiles and the time to reach maximum BFS for the conical projectiles.

When a shotgun or rifle is fired, the shooter experiences an impact to the upper body known as recoil. This force felt by the shooter is a consequence of the momentum transfer from the accelerating ballistic charge to the firearm, which is ultimately transferred to the shooter as he/she restrains the firearm's induced motion. The accelerating ballistic charge responsible for the recoil has two components. The first is the acceleration of the projectile itself. The recoil associated with this action is known as primary recoil. The second component is associated with the acceleration of the gases created by the combustion of the gunpowder propellant. For competitors in the shooting sports, gun recoil can affect performance and create discomfort. An objective method of measuring felt recoil forces would be useful to evaluate methods of recoil reduction. An experimental test apparatus was developed to measure recoil forces of sporting rifles and shotguns. No modifications to the firearms themselves were necessary to make the measurements. Through both inertial and dissipative restraint mechanisms, the apparatus reproduced gun movement that was representative of that experienced by a particular shooter. This should result in measured recoil forces similar to those experienced by the shooter. The apparatus measures the horizontal shoulder force and the vertical force component exerted at the stock comb. The recoil event was found to be quite short, having duration on the order of 10 ms. Peak recoil forces for common shotgun target loads were in the range of 1.6-2.2 kN (360-494 lbf). The apparatus was found sensitive enough to measure recoil force differences among different factory loaded ammunition, and differences in recoil force imparted by different firearms shooting the same ammunition. The apparatus should prove useful for quantifying differences in felt recoil as affected by ammunition type, gunstock geometry, barrel porting, recoil reduction devices, and gun weight, among other factors.

The present paper constructs a rigid–plastic model to assess the effect of a soft nose on the perforation of metallic plates struck by a stubby projectile. A low-density nose-cabin-column, i.e., an assembly of seeker and guidance/control unit, is installed in the front of a real missile. It usually acts as an energy absorber and buffer in the perforation of metallic plates and notably affects the terminal results of projectile. The problem is equivalent to a blunt rigid projectile with a soft nose perforating a circular metallic plate. Effects of transverse shear, bending and membrane deformations on the perforation process are included in a rigid–plastic analysis. Especially the effect of an ahead structural response, induced by the soft nose impacting the target plate, is considered in the model. Analytical formulae for the ballistic performance are obtained for a range of plate thicknesses, which agree well with available experimental results.

We analyze, with the computer code LS-DYNA, three-dimensional (3D) transient deformations of a 10-layer woven Kevlar armor held in a square steel frame and impacted at normal incidence by a 9 mm FMJ (full metal jacket), 124 grain projectile. The composite armor is discretized into weft and warp yarns to simulate its woven structure. The yarn is modeled as a 3D continuum. We consider failure of the yarn, and friction between adjoining layers and between the armor and the frame bars. For the armor perfectly bonded to the rigid frame bars, the computed residual speed and the residual kinetic energy of the projectile are found to increase with a decrease in the frame size implying thereby that the armor fixed in a smaller frame will have lower V50 than that of the same armor clamped in a larger frame. (The V50 of an armor equals the speed of a standard projectile that upon normal impact has 50% probability of just perforating the armor). For the armor allowed to slide between the frame bars, we have studied the effect of the pressure applied to the bars of the two- and the four-bar frames on the speed and the kinetic energy of the residual projectile. For both the two- and the four-bar frames, the speed of the residual projectile is found to increase with an increase in the applied pressure. Computed results also show that the armor fixed in the two-bar frame exhibits higher impact resistance than that held in the four-bar frame. The V50 is found to be ∼270 m/s when the woven armor is held in a four-bar frame with a clamping pressure of 200 MPa. The V50 decreases with an increase in the pressure applied to either the two-bar or the four-bar frames.

This paper presents the results of a series of experimental tests, aimed at investigating the impact and dynamic response of a volcanic shelter. Similar shelters are to be installed in the Stromboli island (Aeolian archipelago, Sicily, Italy), to protect human lives from the pyroclastic eruptions of the volcano. Basically, the Shelter consists of two homologous reinforced concrete shells, interconnected by rubber-based special devices, which absorb and dissipate most of the impact energy. The Shelter has been specifically designed to resist, without damage, an impact with a 150 kg mass rock, knocking the surface of the external shell at 62.5 m/s speed. The experimental tests were carried out on a 1:2-scale model, using a testing apparatus purposely realised to simulate impact conditions comparable with those considered in the design. Impact energy and mass ratio between projectile and reinforced concrete shell were assumed as main experimental parameters and varied during the tests. A finite element model of the Shelter was also implemented and direct-integration time-history analyses were performed, to validate the experimental results. Reference to the Hertz's law was made to simulate the impact between the two bodies. The experimental tests proved the ability of the Shelter to resist impacts without damage. Acceptable agreement between numerical predictions and experimental results was found.

The aim of this work is to develop a methodology for the evaluation of the ballistic requirements of a helicopter component. The situation studied in the work refers to the possibility of a damaged helicopter performing an emergency manoeuvre and a 30-min return flight after the impact of a 7.62 NATO projectile on a shaft of the tail rotor transmission. The paper describes the finite element methodology adopted to simulate the impact of the projectile on the shaft, and outlines the hypotheses on which this methodology is based. The numerical simulation of the propagation of the crack originating from the damage caused by the impact is also described. It is thus possible to determine the time required to reach failure of the shaft. The effect of the residual stresses on the residual life of the shaft is studied in detail.

A new computational approach is developed to predict the impact behaviour of fabric panels based on the detailed response of the smallest repeating unit (unit cell) in the fabric. The unit cell is constructed and calibrated using measured geometrical (weave architecture, crimp, voids, etc.) and mechanical properties of the fabric. A pre-processor is developed to create a 3D finite element mesh of the unit cell using the measured fabric cross-sectional micro-images. To render an efficient method for simulation of multi-layer packs, these unit cells are replaced with orthotropic shell elements that have similar macroscopic (smeared) mechanical properties as the unit cell. The aim is to capture the essence of the response of a unit cell in a single representative shell element, which would replace the more complicated and numerically costly 3D solid model of the yarns in a crossover. The 3D finite element analysis of the unit cell is used to provide a baseline mechanical response for calibrating the constitutive model in the equivalent shell representation. This shell element takes advantage of a simple physics-based analytical relationship to predict the behaviour of the fabric's warp and weft yarns under general applied displacements in these directions. The analytical model is implemented in the commercial explicit finite element code, LS-DYNA, as a user material routine (UMAT) for shell elements. Layers of fabric constructed from these specialized elements are stacked together to create fabric targets that are then analysed under projectile impact. This approach provides an efficient numerical model for the dynamic analysis of multi-layer fabric structures while taking into account several geometrical and material attributes of the yarns and the fabric.

This paper presents the results of scale size experiments using a tungsten-alloy long-rod projectile fired against 97.5% Al2O3 ceramic targets at 1.8 and 2.6 km/s. Two targets were used, one having lateral steel confinement; the other without. The projectile overmatched the target, and residual projectile length and velocity were recorded using ballistic-syncro photography. Flash radiography was used during penetration of the unconfined target to obtain the penetration velocity. Manganin pressure gauges were also used to obtain additional data on the response of the ceramic target during penetration. Results from the eight experiments indicate that the confinement reduced the residual energy of the projectile at both impact velocities. Expressed in terms of the projectile impact energy, 55–56% was lost in the unconfined target at 2.6 km/s compared with 60% for the confined design. The same trend was found at 1.8 km/s with 68% and 72–73% for the unconfined and confined, respectively. Predictions using the QinetiQ GRIM2D hydrocode and a simplified form of the Johnson–Holmquist ceramic material model agreed well with the experiments for three out of the four test configurations. The predicted projectile erosion and retardation against the confined target at 1.8 km/s was excessively high. Analytical predictions using the Tate modified Bernoulli equation also gave reasonably accurate predictions for three of the tests, but values for the Tate target ‘strength’ extracted from experiments using a different target configuration were not accurate for the target design used in this paper. r 2006 Elsevier Ltd. All rights reserved.

Ballistic limit curves (BLCs) for dual- or multi-wall spacecraft wall systems impacted by spherical projectiles exist for a variety of impact conditions. However, meteoroids and orbital debris particles can take any shape, and non-spherical projectiles can be more damaging than equal mass spherical projectiles under the same impact conditions. In a recent study, a series of BLCs for a typical dual-wall configuration impacted by a variety of non-spherical projectiles were developed and presented in terms of equivalent spherical projectile diameter as a function of impact velocity. In order to be more consistent with debris environment predictions and to be useful for spacecraft design, such BLCs need to be drawn in units that are consistent with environment flux models used in that design process. In this paper, we have recast the equivalent spherical projectile diameter BLCs and now present them using radar cross-section (RCS) diameter as the characteristic length parameter. The recast BLCs are seen to be more tightly grouped and are not as spread out as they were when plotted using equivalent spherical projectile diameter. Thus, the effect of projectile shape on penetrating ability is shown to be somewhat reduced when considering characteristic length as the size parameter as opposed to an equivalent mass diameter.

The ability to destroy the key assets of an enemy is an important goal of an attacking force and requires an agile and adaptable military capability effective against a number of very different threats. In ballistics, this contributes to an interest in moving to higher projectile velocities to benefit from the potential to increase the range of a projectile. It also generates an interest in the study of the benefits of increased kinetic energy that can be delivered to a target. The paper describes the work to produce a projectile design solution under certain constraints but with an impact velocity of about 2 km s −1 , good in-bore and in-flight stability and acceptable retardation at the target. The paper shows that a projectile with these characteristics was achieved with a projectile mass of 8.1 kg. The second phase of the research programme was concerned with building a hollow aluminium carrier shell. The paper describes the research to assess the integrity and stability of the projectile under gun launch conditions, to demonstrate acceptable dispersion and impact yaw at the target and to demonstrate a minimum impact velocity of 2.1 km s −1 .

This paper develops an analytical model for the ballistic impact response of fibrous materials of interest in body armor applications. It focuses on an un-tensioned 2D membrane impacted transversely by a blunt-nosed projectile, a problem that has remained unsolved for a half a century. Membrane properties are assumed characteristic of the best current body armor materials (Kevlar®, Spectra®, Zylon®, S2 glass), which have very high stiffness and strength per unit weight, and low strain-to-failure. Successful comparisons will be made with extensive experimental data on such material systems as reported by Cunniff [Decoupled response of textile body armor. Proc. 18th Int. Symp. of Ballistics, San Antonio, Texas, 1999a, pp. 814–821; Vs–Vr relationships in textile system impact. Proc. 18th Int. Symp. of Ballistics, San Antonio, Texas, 1999b; Dimensional parameters for optimization of textile-based body armor systems, Proc. 18th Int. Symp. of Ballistics, San Antonio, Texas, 1999c, pp. 1303–1310]. Our mathematical formulation draws on the seminal work of Rakhmatulin and Dem’yanov [Strength Under High Transient Loads, 1961, pp. 94–152]. Under constant projectile velocity we first develop self-similar solution forms for the tensile ‘implosion’ wave and the curved cone wave that develops in its wake. Through matching boundary conditions at the cone wave front, we obtain an accurate approximate solution for the membrane response including cone wave speed and strain distribution. We then consider projectile deceleration due to membrane reactive forces, and obtain results on cone velocity, displacement and strain concentration versus time. Other results obtained are the membrane ballistic limit, or V50 velocity, and the residual velocity when penetrated above this limit. We then derive an exact functional representation of a V50 ‘master curve’ found empirically by Cunniff [ibid] to reduce data for a wide variety of fabric systems impacted by blunt cylindrical projectiles. This curve is given in terms two dimensionless parameters based only on fiber mechanical properties and the ratio of the fabric areal density to the projectile mass divided by its area of fabric contact. Our functional representation has no fitting parameters beyond one reflecting uncertainty in the effective diameter of the impact zone relative to the projectile diameter, and even then the values are consistent across several experimental systems. The extremely successful comparison of our analytical model to experimental results in the literature raises fundamental questions about many long-held views on fabric system impact behavior and parameters thought to be important.

The Walker–Anderson and Ravid–Bodner analytical models for penetration of projectiles in metallic plates are well known in the ballistics community. The Walker–Anderson model uses the centerline momentum balance in the projectile and target to calculate the penetration history into a semi-infinite medium, while the Ravid–Bodner model uses the upper bound theorem of plasticity theory modified to include dynamic effects. The Ravid–Bodner model also includes a rich selection of failure modes suitable for finite-thick metallic targets. In this paper a blended model is presented: momentum balance is used to calculate the semi-infinite portion penetration (before the back of the target plate begins to flow), and the Ravid–Bodner failure modes are used to determine projectile perforation. In addition, the model has been extended to handle multiple plate impact. Numerical simulations show that after target failure the projectile still continues to erode for some microseconds. This time has been estimated and incorporated into the model. Examples are presented for long-rod projectiles against thick and spaced-plate targets backed by a witness pack that is separated from the main target element(s) by an air gap. Agreement with results from numerical simulations is quite good.

An anisotropic cohesive model of fracture is applied to the numerical simulation of Coker and Rosakis experiments (2001). In these experiments, a unidirectional graphite–epoxy composites plate was impacted with a projectile, resulting in an intersonic shear-dominated crack growth. The simulations account for explicit crack nucleation––through a selfadaptive remeshing procedure––crack closure and frictional sliding. The parameters used in the cohesive model are obtained from quasi-static fracture experiments, and successfully predict the dynamic fracture behavior. In keeping with the experiments, the calculations indicate that there is a preferred intersonic speed for locally steady-state growth of dynamic shear cracks, provided that sufficient energy is supplied to the crack tip. The calculations also show that the crack tip can attain speeds in the vicinity of the longitudinal wave speed in the direction of the fibers, if impacted at higher speeds. In addition, a double-shock which emanates from a finite size contact region behind the crack tip is observed in the simulations. The predicted double-shock structure of the near-tip fields is in close agreement with the experimental observations. The calculations additionally predict the presence of a string of surface hot spots which arise following the passage of the crack tip. The observed and computed hot spot structures agree both in geometry as well as in the magnitude of the temperature elevation. The analysis thus suggests intermittent friction as the origin of the experimentally observed hot spots. 2002 Elsevier Science Ltd. All rights reserved.

The deviation of bullets passing through window pane glass of a thickness of 6 mm was investigated for varying angles of incidence. Projectiles of calibre 0.22 and 0.38 (wadcutter) were used. The 0.22 bullets break into multiple pieces, resulting in a large distribution of exit angles. An increasing deviation of 0.38 wadcutter projectiles was seen for increasing angles of incidence. For incident angles larger than 35°, an unexpected ricochet was noticed. This phenomenon is of importance when examining crime scenes. A number of parameters which have to be taken into account for further experiments is suggested.

Summary Investigations are conducted at ISL on new hypervelocity launchers to fulfill requirements in different fields of ballistics such as launching dynamics, aeroballistics, terminal ballistics, aerothermodynamics, and supersonic combustion studies. One objective considered is to determine the operational conditions to accelerate a 90mm-caliber projectile with a mass of ~1.5kg to a velocity of 3km/s while keeping the acceleration level below 40,000g. This moderate level of acceleration is required to investigate at high velocities models that are fragile because of their design and/or their onboard opto-electronical equipments. A means to fulfill these velocity and acceleration requirements is ram-accelerator technology. This paper presents research conducted at ISL with smooth-bore ram-accelerators in the thermally choked propulsion mode. Therefore, two accelerators in calibers 30 and 90mm respectively, operated within the launch room of the aeroballistic range facility are described. Experimental results are presented describing the two-fold strategy followed to achieve the maximum performance, i.e., optimization of the projectile configuration and optimization of the combustible gas mixtures. To date a maximum velocity of about 1985m/s has been achieved with the 90mm accelerator (projectile mass = 1.34kg, ram-section length 16.2m, injection velocity in the ram-section 1330m/s) and 2380m/s with the 30mm accelerator (projectile mass 68.6g, ram-section length 9m, injection velocity in the ram-section = 1380m/s). Potential applications of ram-accelerators for ballistic studies are discussed and performances compared to those of conventional launchers that are currently used at ISL for ballistic studies. Finally, very first preliminary experiments are presented describing the acceleration of high l/d rods using a ram-accelerator.

The wounding potential and mechanisms of tissue damage of firearms are reviewed. Internal ballistics is the study of projectile flight within a firearm while external ballistics describes projectile flight through air to the target. Terminal ballistics characterizes the final effects of the bullet after it has impacted its target. Upon impact, three tissue phenomena are noted: sonic wave formation, temporary cavitation, and permanent cavitation. Subsequent tissue damage is dependent on the characteristics of the firearm that fired the projectile (e.g. rifle versus handgun), the nature of the projectile itself (e.g. fully jacketed versus expanding bullet), and the attributes of the target tissue (e.g. tissue elasticity).

The dual objective of developing the present ballistic model is to predict an accurate force-time history in a monolithic thick plate due to penetration by a projectile, and to analytically describe the physical phenomena that occur during a penetration experiment in conjunction with measuring the physical parameters. The analytical model developed considers the evaluation, and prediction of the following quantities: (a) shape and size of the cavity, (b) residual strength of the target, (c) depth of penetration in the target, (d) residual length of the projectile, (e) pressure distribution along the cavity wall and (f) force-time history for the penetration event.

Launch behaviour of push and traction driven saboted penetrators are examined for three experimental 60-mm sabot/rod systems. Finite element simulations of the launch packages were performed to determine structural integrity and survivability during the launch phases of projectiles in the 1.9–2.4 km/s velocity range. Results from ballistics experiments from a 60-mm experimental gun are examined. Performance and limitations of the three systems are reviewed.

Herein, we study the technique of improving the gun performance by installing a diaphragm in the pump tube of the gun. A CFD study is carried out for the 0.28 in. gun in the Hypervelocity Free Flight Radiation (HFF RAD) range at the NASA Ames Research Center. The normal, full-length pump tube is studied as well as two pump tubes of reduced length (approximately 75% and approximately 33% of the normal length). Significant improvements in performance are calculated to be gained for the reduced length pump tubes upon the addition of the diaphragm. These improvements are identified as reductions in maximum pressures in the pump tube and at the projectile base of approximately 20%, while maintaining the projectile muzzle velocity or as increases in muzzle velocity of approximately 0.5 km/sec while not increasing the maximum pressures in the gun. Also, it is found that both guns with reduced pump tube length (with diaphragms) could maintain the performance of gun with the full length pump tube without diaphragms, whereas the guns with reduced pump tube lengths without diaphragms could not. A five-shot experimental investigation of the pump tube diaphragm technique is carried out for the gun with a pump tube length of 75% normal. The CFD predictions of increased muzzle velocity are borne out by the experimental data. Modest, but useful muzzle velocity increases (2.5 - 6%) are obtained upon the installation of a diaphragm, compared to a benchmark shot without a diaphragm.

Summary We conducted depth of penetration experiments with ogive-nose projectiles concrete targets with unconfined compressive strengths of nominally 14 MPa (2 ksi), 35 MPa (5 ksi), and 97 MPa (14 ksi). From our data and the data presented by Canfield and Clator [ J. A. Canfield and I. G. Clator , Development of a scaling law and techniques to investigate penetration in concrete. NWL Report No. 2057, U.S. Naval Weapons Laboratory, Dahlgren, VA (1966) ] [1], we developed an empirical equation for penetration depth of ogive-nose projectiles penetrating concrete targets at normal impact. Our penetration equation contains a single, dimensionless empirical constant that depends only on the unconfined compressive strength of the target. We determine the empirical constant from penetration depth versus striking velocity data with six sets of penetration data for striking velocities between 250 and 800 m/s. Predictions are in good agreement with all six data sets.

The experimental discovery of the super-deep penetration of microparticles into strong materials by hypervelocity impact documented the reality of earlier predictions of fracture mechanics concerning the anomalously low drag of a body moving like a wedge in a brittle medium. In the present paper, some wedge-embedded penetration regimen models, taking into account arbitrary friction and plastic deformations near contact areas, shaving effects, and a complex or even fractal geometry of a cracking front, are advanced. The equation for drag is derived using the author's invariant Γ-integral equivalent to the energy conservation law. The thrust of a motor necessary to propel a projectile or vehicle in hard rock is evaluated. It is shown that the thrust of the NASA space shuttle's rocket booster suffices to provide the penetration of a small projectile or vehicle in strong granite for the distance of a mile during a short span of time. Super-deep penetration of microparticles is examined using results from fracture quantum mechanics. The hypothesis is advanced that the super-deep penetration of microparticles represents the self-propagation of a specific internal solitary wave forming a cavity with a projectile moving inside the cavity without drag. This solitary wave is named the rayleighon, because it propagates with the Rayleigh speed. It is suggested that this paper would provide a possible stimulus for conversion of some Department of Defense rocket motor industries towards civil exploration of the Earth, which is studied much less than the cosmos.

Summary The effect of projectile nose shape on penetration is examined numerically using the nonlinear, large deformation wavecode CTH. In particular, the impact of a tungsten alloy, long rod projectile into a 4340 steel target is investigated for three different nose shapes: blunt, hemispherical, and conical. The pressures are sufficiently high that erosion of the projectile begins immediately upon impact. The decays of the shocks are examined, as are the resulting material flow fields. Later-time effects are also explored, such as how the nose shape affects penetration, and how long each case takes to arrive at a quasi-steady-state flow configuration in which the tungsten-steel interface is completely determined by eroding plastic flow.

An electromagnetic (EM) railgun launcher facility has been developed to routinely conduct hypervelocity impact tests. Two types of completely reusable EM launchers have launched sabot/impactor packages between 2 and 43 grams to velocities between 1.5 and 8.5 km/s. The highly reliable railguns have conducted over 250 projectile launchings and have established a projectile/launcer data base covering interior as well as exterior ballistic considerations. A conventional type instrumented ballistics range is compatible with the EM launcher and can be used to conduct anti-armor and lethality experiments at hypervelocities.

The present investigation is concerned with the generation of controlled tumbling of a blunt-nosed hard-steel projectile and, to some extent, the effect of this tumbling on targets struck subsequently. The mechanism for producing this motion from an initial state of translation in the direction of the projectile axis consisted of the impingement of the bullet on the edge of deflector plates of aluminum, steel or plastic of various thicknesses with various degrees of overlap. These initially plane rectangular plates were rigidly held on three sides and struck at the center of the fourth, or free, edge. This first portion of the study consists of the continuum-mechanical analysis of the impact of the projectile on the plate and the subsequent motion of the projectile. A mode shape analysis is employed to ascertain the deplection of the plate with the impact area modeled as a hexagon. The projection is considered as rigid and its motion as planar prior and subsequent to the impact with the deflector plate, which is modeled as a rigid-perfectly plastic material. The numerical predictions of the theoretical development, the experimental set-up and the data derived from the tests, as well as a comparison between the analytical and measured values, are presented in a companion paper [Ruiz and Goldsmith, Int. J. Impact Engng Vol. 7 , in press (1988)].

The Lawrence Livermore National Laboratory 100-kV electric gun has been used to launch flat-plate projectiles for use in studies of spall and hypervelocity impact penetration of thin plates. Impactors were 0.3-mm thick Kapton with dimensions and velocities ranging from 100 mm 2 at 4 km/s to 10 mm 2 at 18 km/s. A Fabry-Perot laser velocimeter, an electronic streak camera, and a flash x ray were used as diagnostics of the flyer-plate impact on the selected specimen. Experiments generally included the recovery of the remnant specimen and fragments for detailed examination, permitting a study of incipient spall, onset of melting, and fraction fragmented. Experiments to be described include spall measurements on simple and composite target walls at normal and oblique incidence and “reverse ballistics” impacts of the thin-plate impactor on a stationary penetrator (e.g., Kapton impactors at 15 km/s incident on rods of steel, aluminum, and lead) for calibration of hypervelocity impact codes.

An experimental program has been undertaken to study the phenomenon of both normal and oblique impact of cylindro-conical and cylindrical projectiles on metallic plates, a domain where almost no test data are available. Hard-steel strikers of 12.7 mm nominal diameter and either 60° conical or blunt tips and blunt soft aluminum cylinders of the same diameter were fired at 2024-0 aluminum targets with thickness from 1.78 to 25.4 mm and at both mild steel and medium carbon steel with thickness up to 19.05 mm. Inital velocities ranged from about 20 to 1025 m s−1, achieved with the aid of a pneumatic cannon at low speeds and a powder gun in the upper velocity range. Initial target obliquity was varied from normal to 50°. The primary results obtained involved the measurement of the velocity drop and change in projectile orientation as the result of passage through the target. The target damage, consisting of dishing, petals, plugs and bands separated from the crater, was examined and metallurgical determinations were executed for a selected set of runs. The information obtained should provide a good basis for understanding the mechanisms involved in this type of impact and perforation. It will also serve as a reliable source of data for comparison with the predictions from analytical models of the process which do not currently exist, but will most certainly be developed in the future.

Simulation of ballistic impact generally falls into one of two categories: analytical models which assume certain dominant physical phenomena and numerical simulations, where the general continuum conservation equations are integrated in time at all points in a spatial mesh to obtain the spatial time history of stresses, strains, velocities, etc., in the projectile and target. Analytical formulations model the mechanical processes over the full field of influence which leads to approximate conservation equations for the entire region in an impact event. These for mulations have met with considerable success so long as the assumptions inherent in the model are applicable. Numerical simulations (hydrocodes) compute the wave (shock) interactions important at early times. Mechanical effects, e.g. plugging, erosion, etc., require realistic constitutive modeling which includes failure criteria and failure propagation. This paper gives a broad overview of both analytical and hydrocode modeling and examines the technical issues, uncertainties and potential diffuculties for advancement in predictive capability.

INSTANTANEOUS photography by means of an -electric spark provides the investigator of highspeed phenomena with a most valuable source of data. Such photographs are of the shadow variety, the bullet shadow being projected upon a photographic plate by a spark of great intensity and short duration. If the bullet is moving with a speed equal to or greater than that of sound, it propagates from both its nose and base a compressional wave. Light from the photographing spark in passing through the denser atmosphere of the compressional wave is refracted as by a lens, so that the wave front is also projected upon the photographic plate with the bullet. The method lends itself readily to the investigation of a projectile's stability at various points along its trajectory and to many allied problems of exterior ballistics. Instructive photographs of the recoil and shell ejection of automatic rifles, pistols, and machine guns may also be obtained in this manner.

The calculus of perturbations, as commonly used in exterior ballistics, is modified for application to rocket missiles, that is, to projectiles which experience thrust and lift forces. In this form, the calculus can be used as in conventional ballistics, to investigate the effect of disturbing factors upon a trajectory. In addition to this, it is of considerable value in establishing analytically certain principles of guidance and control. Two examples are given of this: the theory of range control of the German V-2 missile, and a theoretical system of free flight guidance by radio.