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A computational study of a projectile (either 2024 aluminum or TiAl6V4 titanium alloy) impacting a plate (either titanium alloy or aluminum) is presented in this paper. Projectile velocity (ranging from 250 m/s to 1500 m/s) with varying impact angles are considered. The presence of ricochet (if any) is identified over the ranges of the projectile velocity and impact angle considered. For the cases where ricochet is identified, the ricochet angle and velocity are predicted as functions of the incident angle and the incident velocity. The numerical results are compared with an analytical solution of the ricochet problem. The analytical solutions are from a model developed to predict the ballistic ricochet of a projectile (projectile) penetrator. The dynamics and the deformation of an aluminum (or a titanium alloy) projectile impacting on a finite thickness titanium alloy (or aluminum) plate are simulated. The current work is interesting in that it looks in the field of ballistics of different material combinations than are traditionally studied. The present simulations based on detailed material models for the aluminum and the titanium alloy and the impact physics modelling features in the LS-DYNA code provide interesting details regarding the projectile/plate deformations and post-impact projectile shape and geometry. The present results indicate that for no cases (for specified incoming velocities and impact angles considered) can an aluminum projectile penetrate a titanium alloy plate. The ricochet ‘mode predictions ‘obtained from the present simulations agree well with the ricochet ‘mode predictions’ given in an analytical model.

Levitating nanoparticles trapped in optical potentials at low pressure open the experimental investigation of nonlinear ballistic phenomena. With engineered non-linear potentials and fast optical detection, the observation of autonomous transient mechanical effects, such as instantaneous speed and acceleration stimulated purely by initial position uncertainty, are now achievable. By using parameters of current low pressure experiments, we simulate and analyse such uncertainty-induced particle ballistics in a cubic optical potential demonstrating their evolution, faster than their standard deviations, justifying the feasibility of the experimental verification. We predict, the maxima of instantaneous speed and acceleration distributions shift alongside the potential force, while the maximum of position distribution moves opposite to it. We report that cryogenic cooling is not necessary in order to observe the transient effects, while a low uncertainty in initial particle speed is required, via cooling or post-selection, to not mask the effects. These results stimulate the discussion for both attractive stochastic thermodynamics, and extension of recently explored quantum regime.

During their operation, solid rocket boosters experience axial stresses caused among other things also by fluid mechanical loads from the internal flow. The accurate prediction of the flowfield is ...

A vast majority of widely accepted granular segregation mechanisms are attributed to dynamic phenomena such as percolation, kinetic sieving, convection-induced segregation, condensation, inertia and granular temperature gradients. We distinguish the ballistics of the particles from such dynamic and material properties and show that the former is a dominant mechanism in the segregation of particles sedimented in a container. We first perform granular sedimentation experiments with glass beads in water that exhibit size-segregation of bidisperse grains. We then show through simulations using a simple, first-order model that the ballistics of the particles alone is sufficient to qualitatively predict this segregation.

The article is devoted to the study of the optimal control of propellant consumption during vertical lifting of rocket in homogeneous atmosphere using regularized solution of integral equation of the first kind. The problem of lifting of a rocket into desired height along optimal trajectory in the view of minimal consumption of propellant leads to solving the set of differential and integral equations. Problem of optimal control of propellant consumption during lifting of rocket in homogeneous atmosphere is solved using regularized solution of integral equation of the first kind which is solution of corresponding Euler equation on discrete time net. Influence of the regularization parameter and some additional parameters on precision of discreted problem is investigated. Considered algorithm is summed up easily to the case of non-homogeneous atmosphere by introducing dependence of the ballistic coefficient on altitude of flight and to problem of putting spacecraft into determined orbit and suborbital flights by setting desired altitude and velocity and modifying of motion equations.

Analysis of crime scenes involving single-fire-gun projectiles requires the determination of the direction of arrival of a projectile at the target and other factors to reconstruct events. The movement of a projectile can be analyzed by applying Euler’s equations to a solid symmetrical rigid body. The present work starts from a Newtonian reformulation of these equations to show that, in the presence of a gravitational field, the system can be expressed with a complex variable nonlinear equation, where the inclusion of small nutation variables allows us to find possible solutions. As a particular case, we analyzed the movement of a 9-mm projectile fired from distances greater than 1 m to demonstrate that the direction of arrival of the projectile at the target cannot be traced by a stick placed in the target hole, as is usually performed in crime investigations. A series of shots were fired from distances varying between 1 m and 7 m. Impact data were recorded on Riemann planes of projection for the description of nutation and precession motions, allowing the observation of the motion dynamics of the projectile. We show that the direction of arrival at the target can be determined approximately from the analysis of the nutation and precession curves through Riemann planes of projection. The results presented in this work will allow more accurate judgements to be made in judicial investigations.

In this paper the bombardment of the Constantinople Theodosian Walls by the great cannon of Orban is numerically reproduced deploying Struc­tural Mechanics. Overall gun dimensions were assessed based on historical reports, whereby, the gun­powder charge p was estimated at 177 kg, and the gun was placed at 500 m from the Inner Walls. Gun ballistics and effect on target have been evaluated analytically. The analysis has verified Orban’s gun muzzle velocity, cannonball trajectory and its effect on Constantinople Walls by successfully calculating the length of the breach in the wall, referred in historical reports, as well as the cannon ball penetration into soil. The evaluated sound pressure level inside Constantinople, produced by the bombard, con­firmed the tremendous psychological effect of the cannon’s blast on the City’s population. A numerical effort was made to assess the combined effect of powder chamber internal pressure with associate temperature produced by powder ignition.

In shooting crimes, ballistics tests are often recommended in order to reproduce the wound characteristics of the involved persons. For this purpose, several “simulants” can be used. However, despite the efforts in the research of “surrogates” in the field of forensic ballistic, the development of synthetic models needs still to be improved through a validation process based on specific real caseworks. This study has been triggered by the findings observed during the autopsy performed on two victims killed in the same shooting incident, with similar wounding characteristics; namely two retained head shots with ricochet against the interior wall of the skull; both projectiles have been recovered during the autopsies after migration in the brain parenchyma. The thickness of the different tissues and structures along the bullets trajectories as well as the incident angles between the bullets paths and the skull walls have been measured and reproduced during the assemblage of the synthetic head models. Two different types of models (“open shape” and “spherical”) have been assembled using leather, polyurethane and gelatine to simulate respectively skin, bone and soft tissues. Six shots have been performed in total. The results of the models have been compared to the findings of post-mortem computed tomography (PMCT) and the autopsy findings.Out of the six shots, two perforated the models and four were retained. When the projectile was retained, the use of both models allowed reproducing the wounds characteristics observed on both victims in terms of penetration and ricochet behaviour. However, the projectiles recovered from the models showed less deformation than the bullets collected during the autopsies. The “open shape” model allowed a better controlling on the shooting parameters than the “spherical” model. Finally, the difference in bullet deformation could be caused by the choice of the bone simulant, which might under-represent either the strength or the density of the human bone. In our opinion, it would be worth to develop a new, more representative material for ballistic which simulates the human bone.

The study of the process of firing a firearm, taking into account the degree of wear of the barrel, requires an assessment of the losses of powder gases due to their breakthrough between the barrel walls and the projectile. Currently, the known methods for solving the equations of internal ballistics do not provide for obtaining results wich take into account the loss of part of the powder gases. As a result, there was a need to overcome the contradiction between the needs of applied ballistics and the capabilities of the existing scientific and methodological apparatus for solving the equations of internal ballistics. The principles of construction of the difference scheme for the numerical solution of the equations of internal ballistics on the condition of the influence of typical defects of the barrel channels and ammunition are stated. Recurrent expressions for step-by-step calculation of ballistic elements of the shot are given, initial conditions for the first and second periods of the shot are defined. The practical testing of the difference scheme by the numerical solution of the equations of internal ballistics for characteristic combinations of initial data is carried out and its adequacy is confirmed. The expediency of creating a database of ballistic shot elements for typical defects of the barrel channels and powder charges is substantiated. As a result of researches, the difference scheme for the numerical solution of the equations of internal ballistics wich provide the possibility of taking into account the influence of typical defects of the barrel channels and ammunition on ballistic elements of the shot is obtained. This opens the way to improving the operational control of the technical condition of weapons and ammunition by advancing its reliability and efficiency. Based on the numerical solution of the equations of internal ballistics, it is possible to simulate the influence of the deviation of the geometrical parameters of the barrel channel and the degradation of the powder charge on the course of the shot process. This explains the importance and usefulness of the work for applied ballistics

Sabot asymmetric discard after the projectile being launched from the muzzle at various angles of attack and 4Ma is investigated. This is implemented by the coupling computational fluid dynamics (CFD) and six degrees-of-freedom exterior ballistic code through the unstructured dynamic mesh and user defined function. The flow field characteristics during sabot discard process and the trajectory parameters of all three sabots have been obtained. In addition, the aerodynamic coefficients of the projectile are also obtained. The numerical results show that the asymmetric discard of sabot is more obvious along with the increasing angle of attack. Moreover, the aerodynamic forces of projectile have a larger change and the pressure distribution of its surface is more asymmetric and complex. This means the aerodynamic interference at a non-zero angle of attack contributes more significantly to shooting dispersion and flight stability than that at zero angle of attack and the influence increases as the angle of attack increases.

A dynamical moving pressure structural numerical calculation model using the internal ballistics calculation pressure-time results was constituted and the vicinity of the internal ballistics and quasi-internal ballistics structural model was checked. The Von Mises stresses obtained by the dynamical structural numerical model calculations and the Von Mises stresses calculated from the shot test strain measurements were compared. The difference for the worse case was 20% and for the best case was 0.1%. Furthermore, the model gave better agreement for the higher charge masses. The numerical structural quasi-internal ballistics computation model created was verified for the top charge mass which represents the highest stress condition and used in a gun barrel design. Keywords: Gun tube design, Thick wall cylinder, Residual stress, Internal ballistics, Service pressure, Wall thickness, Numerical modeling of internal ballistics

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.

Minimizing the aerodynamic drag has been a major concern in the field of ballistics in order to increase the performance of projectiles and missiles. The reason behind the increase in aerodynamic drag acting over the projectile is due to the flow separation occurring at the rear end of the body leading to the formation of wake. Hence, the main objective in our current study is to develop an efficient method to minimize the aerodynamic drag. In our study, we explore how the lift and drag coefficients behave for various geometrical modifications carried out on the standard projectile. The Standard M549 155 mm projectile was chosen for our study. The optimum M549 155 mm projectile is modified and analysed in ANSYS Fluent for multiple Mach numbers. The boattail after body is being replaced by shape optimizations such as multistep after body and splitter plates which are expected to minimize the vortices generated at the rear end of the projectile. Non-spinning cases of multistep after body and splitter plates are included in the current paper.

A predictive numerical approach, based on Reynolds-averaged Navier–Stokes simulations including the effects of turbulence, chemistry, fluid/surface interaction, and radiation, has been developed fo...

In this research paper, empirical relation between burn rate and pressure index of spherical gun propellant was carried out in the closed bomb. This is double base propellant and used in power cartridge to destroy the suspicious unattended objects. The novelty in this research is that, the author proposed a novel empirical relation among force constant, burning rate coefficient, pressure index and peak pressure. Ballistics properties like burning rate of propellant is depend upon on its shape and size (configuration), chemical composition, temperature, loading density and pressure. The major outcome of this research study has direct relevance for the performance prediction of propellant in the form of powder related to dynamic firings. The peak pressure of the propellant is 235.04 MPa, the rise time 1.95 ms, burn rate coefficient 0.073, pressure index 1.29, flame temperature 2680 0K and force constant 953.2 J/g were obtained during experiment. The burning rate for the spherical gun propellant is experimentally expressed as 1.29

The fabrication error and assembly error of warhead and fuse will cause the dynamic unbalance of howitzer projectile, which will bring a negative impact on the safety and reliability of fuse. In order to obtain the motion of a certain 155 mm howitzer projectile on the exterior ballistics, the six-dimensional rigid body motion equations of the projectile were studied. The aerodynamic parameters which needed for the six-dimensional rigid body motion equations of the projectile’s exterior ballistics need to be obtained by simulation. Firstly, the credibility of the simulation method is verified in this paper. Then the aerodynamic parameters of the projectile are obtained by numerical simulation of the projectile flow field. When solving the six-dimensional rigid body motion equations of projectile exterior ballistics, the dynamic unbalance of projectile is considered. The calculation results are very important for the safety and reliability of fuze on the projectile under the condition of dynamic unbalance.

In this study, we examined the aerodynamic loading on a small caliber rifle (spin stabilized) projectile moving in a muzzle flow field using an element method to analyze the loading and the effect of the angle of attack (for small angles from 0 to 3 deg) on the different components. The temporal pressure distribution on the projectile, which forms the basis of the element method, was computed using a computational fluid dynamics (CFD) analysis combined with a classical interior ballistics model. Then, a high-speed optical experiment was conducted to verify the results of the CFD method and ensure the accuracy of the calculations. The results were as follows: (a) similar to a large caliber projectile, the total axial force, which consisted primarily of the axial forces on the base and boattail, was found to have an inverse exponential relationship with time; (b) the overall lift was a combination of the lift of the base, boattail, cylinder, and nose; and (c) the interaction between the pitch moment of the base and that of the boattail was found to be the primary contributing factor to the total pitch moment. Based on these results, we recommend that the characteristics of the base and boattail be considered when specifying the geometric configuration of a projectile.

Most glasses are often exposed to impact loading during their service life, which may lead to the failure of the structure. While in situ experimental studies on impact-induced damage are challenging due to the short timescales involved, continuum-based computational studies are complicated by the discontinuity in the displacement field arising from the propagation of cracks. Here, using peridynamics simulations, we investigate the role of the mechanical properties and geometry in determining the overall damage on a glass plate subjected to ballistic impact. In particular, we analyze the role of bullet velocity, bullet material, and elastic modulus, fracture energy, and radius of the plate. Interestingly, we observe a power-law dependence between the total damage and the fracture energy of the glass plate. Through an auto-regressive analysis of the evolution of cracks, we demonstrate that the self-affine growth of cracks leads to this power-law dependence. Overall, the present study illustrates how peridynamics simulations can offer new insights into the fracture mechanics of glasses subjected to ballistic impacts. This improved understanding can pave way to the design and development of glasses with improved impact-resistance for applications ranging from wind-shields and smart-phone screens to ballistics.

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.

In this paper the bombardment of the Constantinople Theodosian Walls by the great cannon of Orban is numerically reproduced with the aid of Structural Mechanics. Overall gun dimensions were assessed based on historical reports, whereby, the gunpowder charge p was estimated at 177 kg, and the gun was placed at a distance of 500 m from the Inner Walls. Gun ballistics and effect on target have been evaluated analytically. The analysis has verified Orban’s gun muzzle velocity, cannonball trajectory and its effect on Constantinople Walls by successfully calculating the length of the breach in the wall, referred to in historical reports, as well as the cannon ball penetration into soil. Finally, a numerical effort was made to assess the sound pressure level inside Constantinople during bombardment confirming the tremendous psychological effect of the cannon’s blast on the City’s population.

In practice of forensic medicine and forensic ballistics there are quite often the cases of different types ofgunshot wounds infliction by atypical damaging elements which were used in illegal independent loading of cartridges to the rifle weapon. The purpose of the researches being performed - studying on a concrete example from criminalistics practice of damaging properties of 7.62 mm rifle bullets of type FMJBT (Full Metal Jacketed Boat Tail) which were used for loading by self-made way cartridges of 7.62 * 39 caliber. Originally, during natural tests in the conditions of a ballistic track the ballistic characteristics of the shot bullets and the value of their ballistic coefficient were established. At the following stage of researches the losses of kinetic energy of rifle bullets on punching blocks of ballistic plasticine with the thickness of 100-140 mm were determined. As a result of tests the character of formation of the damage channel in the thickness of biological tissues simulator is established at the stable and unstable movement of the bullets in the visco elastic medium. Besides, during the researches the values of the parameters necessary for calculations ofpenetration depth of the bullets into a fabric of biological object depending on their speed at the moment of hit in the target, were determined. In particular it was established that at unstable movement of an investigated bullet in thickness of the simulator the value of boundary speed amounts 138.1 m/s, and the value of the medium drag factor - 1.782. Using estimated values offlight speed of the bullets in the trajectory the values of depth wound channels in biological tissues were calculated and the conclusion was drawn on the guaranteed causing of penetrating wounds in all established distances of shooting. Thus, use of the methodfor estimation of damaging properties of investigated bullets, the criterion of which is the length of the wound channel and its boundary value was obviously demonstrated.

Recent microscale ballistic experiments have revealed that multilayer graphene membranes exhibit exceptionally high ballistic limit velocity and specific penetration energy. A key feature contributing to the exceptional performance of these systems is the cone wave that develops at impact, which propagates radially at a very high speed for ultra-light and stiff graphene membranes, distributing the kinetic energy of the projectile away from the impact zone. Current theories on ballistic impact consider infinitely wide membranes, and atomistic simulations involve very small projectiles and specimen dimensions, and thus cannot ascertain whether microscale ballistics observations are scalable and size-independent. Here, we discover a particular size effect due to the reflection of cone wave that has not been previously observed or considered. We present molecular dynamics simulations showing that there exists a critical membrane size below which the cone wave reflections from the boundaries induce perforation; a phenomenon that is particularly relevant for microballistic testing of graphene membranes. We present an analytical relationship, verified by simulation data, which predicts the critical membrane size simply as a function of the projectile size, membrane thickness and the ratio of the projectile and membrane densities. Our findings provide timely guidance for future microscale experiments and atomistic simulations for accurate characterization of the impact performance of 2D nanomaterials.

This research conducts 300 small-scale ammunition experiments using moderate bullet speeds and a variety of bullet configurations in order to understand the relationship between penetration behavior and bullet shape. To maximize the survivability of soldiers and reduce their vulnerability and ballistics wounds, it is very important to understand the penetration physics of bullets. Inside human bodies, tumbling and traveling trajectories are important factors to consider when analyzing human injuries due to ballistics. Therefore, many kinds of bullets and armor have been proposed to minimize or maximize human damage. In this study, to support the development of bullets, 10 bullets with different head angle shapes and different diameters were manufactured and fired at speeds less than 200 m/s towards transparent gelatin blocks, and the damage mechanisms, i.e., temporary cavities and permanent cavities, were studied by taking penetration images using a high speed camera. It was found that the tumbling and rotations of bullets are influenced by kinetic energies and the shapes of bullets, and several empirical relationships are derived. The results suggest that the shapes and the diameters are crucial factors for ballistics wounds.

This paper presents a selection of deliverables of a research project intended to develop a technology demonstrator for an active protection system smart counterprojectile. Numerical simulations were completed to analyse the effects of geometry and weight of the counterprojectile warhead on the counterprojectile flight (motion) parameters. This paper investigates four variants of the counterprojectile warhead shape and three variants of the counterprojectile warhead weight. Given the investigated geometric and weight variants, the PRODAS software environment was used to develop geometric models of the counterprojectile warhead, followed by the determination of the model aerodynamic characteristics. The final deliverable of this work are the results of the numerical simulation of the counterprojectile motion along the initial flight path length. Given the required activation of the active protection system in direct proximity of the protected object, the analyses of counterprojectile motion parameters were restricted to a distance of ten-odd metres from the counterprojectile launching system.

The study concerns a man-weapon interaction during a gunshot. The recoil force measurements obtained for the Kalashnikov automatic rifle are presented and analyzed. The influence of shooter’s mass, height and position is described. The breech pressure and projectile velocity data are presented as well. In addition, a finite element (FE) model of the shooter-rifle system is developed in order to qualitatively assess the quantities which could not be determined experimentally, i.e. the stress, strain and displacement fields which are generated in the human body due to the rifle recoil. Several conclusions are drawn that allow for better understanding of the recoil phenomenon and can be useful from the weapon designer’s point of view.

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.

Large pyroclasts—often called ballistic projectiles—cause many casualties and serious damage on people and infrastructures. One useful measure of avoiding such disasters is to numerically simulate the ballistic trajectories and forecast where large pyroclasts deposit. Numerical models are based on the transport dynamics of these particles. Therefore, in order to accurately forecast the spatial distribution of these particles, large pyroclasts from the 2015 Aso Strombolian eruptions were observed with a video camera. In order to extrapolate the mechanism of particle transport, we have analyzed the frame-by-frame images and obtained particle trajectories. Using the trajectory data, we investigated the features of Strombolian activity such as ejection velocity, explosion energy, and particle release depth. As gas flow around airborne particles can be one of the strongest controlling factors of particle transport, the gas flow velocities were estimated by comparing the simulated and observed trajectories. The range of the ejection velocity of the observed eruptions was 5.1–35.5 m/s, while the gas flow velocity, which is larger than the ejection velocity, reached a maximum of 90 m/s, with mean values of 25–52 m/s for each bursting event. The particle release depth, where pyroclasts start to move separately from the chunk of magmatic fragments, was estimated to be 11–13 m using linear extrapolation of the trajectories. Although these parabolic trajectories provide us with an illusion of particles unaffected by the gas flow, the parameter values show that the particles are transported by the gas flow, which is possibly released from inside the conduit.

For the numerical description of high velocity impact, Smooth-Particle-Hydrodynamics (SPH) has gained more and more interest. The standard Lagrangian Finite-Element (FE) approach has difficulties in describing large deformations and fracture. However, a simulation based on SPH only is very expensive due to the small size of the particles. A well adopted solution to this is to couple both methods, using SPH only where it is necessary, and capturing the outer boundary conditions with a bias FE-mesh correctly - without considerable extra computational cost. We apply such a hybrid approach in LS-DYNA® for the characterization of threats in terminal ballistics. Different meshing approaches for the projectile and target were implemented to guarantee an optimal initial condition. The particle size and the required size of the SPH-region were studied to exclude discretization effects. Exemplarily, a projectile surrogate with simplified geometry is investigated for a fixed impact velocity and two different angles of obliquity. A qualitative comparison between experiments, observed with X-ray cinematography, reveals a good potential of this approach towards predicting fracture and ricochet during high velocity impact events.

The high-velocity launch of a projectile is subjected to a number of disturbances which exert an influence on the flight trajectory. In the case of sub-caliber projectiles, sabot separation is one of the critical aspects. In this work, we focus on the projectiles and the launch package of an electric railgun launch, i.e. on the behavior of the launch-package, when transitioning from the gun barrel to free-flight. This work further addresses the use of a hydrocode for creating numerical models which are capable of predicting the motion and deflection of the sabot parts during their separation from the projectile after exiting the muzzle. An earlier study showed that the air flow around the projectile and the sabot can be modeled with sufficiently high accuracy by means of a simulation code that uses an Eulerian description of the gas flow. Within a time interval of several milliseconds, just the duration that a projectile needs to enter quasi-stationary flight, viscous effects of the air or gas flow have relatively little influence on the sabot discard process. If the Eulerian gas flow is coupled with the Lagrangian structural parts, the mechanical response of the latter to the gas pressure can be complex in terms of deformation and damage, and in that way, can affect the gas flow. In this study, the hydrocode model is applied to a medium caliber launch package concept for accelerating long rod projectiles. The computed results agree well with the corresponding experimental values obtained from a launch package model test in the shock tunnel at Mach 4.5. This demonstrates that the presented hydrocode model can be used for launch package design optimizations with high confidence.

Droplets merging on hydrophobic nanocones jump off, and the takeoff speed is found to be maximum at microscale, below and above which viscosity and inertia, respectively, cap this speed. Microdroplets successively experience strong lift off, slow flight, and smooth landing, which impedes bouncing.

The “super-gun„ class of weaponry has been around for a long time. However, its unusual physics is largely ignored to this day in mainstream physics. We study an example of such a “super gun„, the “Paris gun„. We first look into the historic accounts of the firing distance of such a gun and try to reconcile it with our physical understanding of ballistics. We do this by looking into the drag component in the equations of motion for ballistic movement, which is usually neglected. The drag component of the equations of motion is the main reason for symmetry breaking in ballistics. We study ballistics for several air density profiles and discuss the results. We then proceed to look into the effects of muzzle velocity as well as mass and ground temperature on the optimal firing angle and firing range. We find that, even in the simplest case of fixed air density, the effects of including drag are far reaching. We also determine that in the “sensible„ range of projectile mass, the muzzle velocity is the most important factor in determining the maximal firing range. We have found that even the simplest of complications that include air density, shifts the optimal angle from the schoolbook’s 45-degree angle, ground temperature plays a major role. While the optimal angle changes by a mere two degrees in response to a huge change in ground temperature, the maximal distance is largely affected. Muzzle velocity is perhaps the most influential variable when working within a sensible projectile mass range. In the current essay, this principle is described and examples are provided where students can apply them. For each problem, we provide both the force consideration solution approach and the energy consideration solution approach.

The stress response of an artillery barrel when fired is principally due to loading from gas pressure and contact force with the projectile. This paper reports a research project in which a dynamic model of a barrel and a projectile was established in order to investigate the stress response of an artillery barrel. Calculations of propellant gas pressure, in part determined by the position of the moving projectile, were carried out using user-defined subroutines developed in the abaqus/explicit software. Numerical simulations of the dynamic loading process of the barrel were carried out to examine the radial effects of gas pressures. Using this methodology, the evolution of barrel stress distributions was simulated, providing a visualized representation of the barrel's dynamic response. The calculated dynamic stress due to projectile contact alone can reach a peak value of 181 MPa, reflecting the significant effect of contact force on the barrel's dynamic response. Following this, the effect of propellant combustion on the dynamic response was explored, and the results obtained showed that higher initial temperatures produced more pronounced dynamic responses. Moreover, significant differences in stress distributions computed for the barrel revealed deficiencies in the static strength theory for evaluating the operating conditions, due in part to the omission of contact force and other dynamic effects. This paper proposes an alternative investigative approach for evaluating the dynamic stress response of barrels during the initial phases of the ballistics process, and provides information that should lead to updates and improvements of barrel strength theory, ultimately leading to better predictions of firing reliability and operator safety.

In a majority of works devoted to the research of the exterior ballistics of the bullet movement and missiles the rate of the missile’s form and the reference function of the frontal air is used. However, the obtained on this ground theoretical results not always qualitatively and quantitively coincided with experimental. In the work of authors an alternate approach to the study of the dynamics of the bullets and missiles movement is considered. It is widely thought that the scalar force of the frontal air resistance of the bullet movement depends on the following characteristics: its aerodynamics rate; the greatest cross-section area plane surface vertical to the velocity attitude; its movement rate; air density and the speed of sound in the air. Although it has different values of certain coefficients in cases when the bullet is moved with supersonic and subsonic velocities. Using the law of dynamics – the system of differential equation is obtained, which describe the bullet movement in the air. To determine the certain coefficients of the frontal air resistance value function we should solve the inverse problem of the particle dynamics, taking into consideration the results of the experimental investigations. Solution of the differential equation system is obtained by a numerical method and the coefficients’ value is defined by trial and error method. As an example, the bullet movement from the machine guns such as PK, PKB, PKS and PKT. The functional dependency of the bullet movement frontal air resistance value has been obtained from its velocity and the respective diagram has been created. The received theoretical values of the bullet’s velocity on certain distances were different from the results of experimental measurements within limits of less than one percent. Knowledge of the law of the value change of the frontal air resistance on the bullet movement from its velocity, air density, and speed of sound in the air allows defining the influence of change of these values on the traveltime parameters of the bullet movement. At the same time we can investigate the influence of the change of the muzzle velocity of the bullet, angle of elevation, velocity and direction of the wind on the exterior ballistics of the bullet movement. As an illustration the influence of the angle of position on the traveltime characteristics has been investigated., В работе авторами проводится исследование динамики движения пули в воздухе отдельно на ее сверхзвуковой и дозвуковой скоростях. При этом аналитические зависимости силы лобового сопротивления воздуха имеют разный вид. На основе второго закона динамики решена обратная задача, что в дальнейшем, учитывая результаты экспериментальных исследований, дает возможность определить функциональную зависимость силы лобового сопротивления воздуха от скорости пули. Зная эту зависимость, можно решать задачи по определению кинематических параметров движения пули., У роботі авторами проводиться дослідження динаміки руху кулі в повітрі окремо на її надзвуковій та дозвуковій швидкостях, тому аналітичні залежності сили лобового опору повітря мають різний вигляд. На основі 2-го закону динаміки розв’язується обернена задача, що в подальшому, знаючи результати експериментальних досліджень, дозволить визначити функціональну залежність сили лобового опору повітря від швидкості кулі. Знаючи цю залежність, можна розв’язувати задачі про визначення кінематичних параметрів руху кулі.

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.

An unsteady quasi-one-dimensional flow solver for simulating internal ballistics and axial acoustic fluctuations in solid rocket motors is presented in this paper. Higher-order numerical solutions of quasi-one-dimensional governing equations are prone to numerical oscillations due to the nonconservative form of the governing equations and the nonsmooth axial variations of the cross-sectional area. Adding artificial dissipation to a central scheme is found to be inadequate for suppression of such oscillations, and so a simple low dissipation shock-capturing scheme (named SLAU2) is used instead. The inherent numerical dissipation of this scheme is helpful in the proper capturing of steep-fronted acoustic waves (that develop at the onset of triggered instabilities) without undesirable numerical damping of the acoustic waves. Using the new solver, a procedure for computing characteristic frequencies, corresponding mode shapes, and damping rates is proposed and validated for a motor with a cylindrical grain ge...

The dynamic pressure on a rocket body caused by atmospheric drag must be kept small to prevent the missile from breaking up during its trajectory in the earth's lower atmosphere. Gravity turn guidance minimises this dynamic pressure load on the body structure by aligning the rocket's thrust in the direction opposite to the drag force, along the direction of the missile's inertial velocity relative to the inertial velocity of the earth's atmosphere. In this study, the authors first show why the trajectories of ballistic missiles under gravity turn guidance are accurately approximated by motion that is closely confined to an earth-centred, earth-fixed plane. They then introduce a new cylindrical coordinate trajectory profile model that exploits this inherent near planar motion. It is shown that this model interpolates the numerically integrated solution to the rocket equations of motion down to centimetres of position accuracy and tenths of centimetres per second in velocity error.

We study the transient indirect effect of a rifle bullet on bone in the gelatin-bone composite target experimentally and computationally. The process of a 56 type 7.62-mm rifle bullet penetrating the composite target has been simulated using numerical method. The experiment provided the criteria for verifying the correctness of the numerical model. We have obtained tomographic data of bone by CT scans, and also defined the bone as different layers by the gray scale to simulate its heterogeneity. The computed results are in good agreement with the experimental data. Effects of the impact velocity and bone location on damage caused to the composite target have also been studied. The numerical results imply the follows: When the velocity of bullet increases, the stress on bone also increases with the earlier pressure peak; When the bone is located in a certain distance from the trajectory, it will not be fractured, although it is affected by the stress wave.