Machine learning for predicting the outcome of terminal ballistics events

Machine learning(ML) is well suited for the prediction of high-complexity,high-dimensional problems such as those encountered in terminal ballistics.We evaluate the performance of four popular ML-based regression models,extreme gradient boosting(XGBoost),artificial neural network(ANN),support vector regression(SVR),and Gaussian process regression(GP),on two common terminal ballistics’ problems:(a)predicting the V50ballistic limit of monolithic metallic armour impacted by small and medium calibre projectiles and fragments,and(b) predicting the depth to which a projectile will penetrate a target of semi-infinite thickness.To achieve this we utilise two datasets,each consisting of approximately 1000samples,collated from public release sources.We demonstrate that all four model types provide similarly excellent agreement when interpolating within the training data and diverge when extrapolating outside this range.Although extrapolation is not advisable for ML-based regression models,for applications such as lethality/survivability analysis,such capability is required.To circumvent this,we implement expert knowledge and physics-based models via enforced monotonicity,as a Gaussian prior mean,and through a modified loss function.The physics-informed models demonstrate improved performance over both classical physics-based models and the basic ML regression models,providing an ability to accurately fit experimental data when it is available and then revert to the physics-based model when not.The resulting models demonstrate high levels of predictive accuracy over a very wide range of projectile types,target materials and thicknesses,and impact conditions significantly more diverse than that achievable from any existing analytical approach.Compared with numerical analysis tools such as finite element solvers the ML models run orders of magnitude faster.We provide some general guidelines throughout for the development,application,and reporting of ML models in terminal ballistics problems.

Modelling of internal ballistics of gun systems:A review

A deep understanding of the internal ballistic process and the factors affecting it is of primary importance to efficiently design a gun system and ensure its safe management. One of the main goals of internal ballistics is to estimate the gas pressure into the combustion chamber and the projectile muzzle velocity in order to use the propellant to its higher efficiency while avoiding over-pressure phenomena. Dealing with the internal ballistic problem is a complex undertaking since it requires handling the interaction between different constituents during a transient time lapse with very steep rise of pressure and temperature. Several approaches have been proposed in the literature, based on different assumptions and techniques. Generally, depending on the used mathematical framework, they can be classified into two categories: computational fluid dynamics-based models and lumped-parameter ones. By focusing on gun systems, this paper offers a review of the main contributions in the field by mentioning their advantages and drawbacks. An insight into the limitations of the currently available modelling strategies is provided,as well as some considerations on the choice of one model over another. Lumped-parameter models, for example, are a good candidate for performing parametric analysis and optimisation processes of gun systems, given their minimum requirements of computer resources. Conversely, CFD-based models have a better capacity to address more sophisticated phenomena like pressure waves and turbulent flow effects. The performed review also reveals that too little attention has been given to small calibre guns since the majority of currently available models are conceived for medium and large calibre gun systems.Similarly, aspects like wear phenomena, bore deformations or projectile-barrel interactions still need to be adequately addressed and our suggestion is to dedicate more effort on it.

Simulation of two-dimensional interior ballistics model of solid propellant electrothermal-chem ical launch with discharge rod plasma generator

Instead of the capillary plasma generator(CPG),a discharge rod plasma generator(DRPG)is used in the30 mm electrothermal-chemical(ETC)gun to improve the ignition uniformity of the solid propellant.An axisymmetric two-dimensional interior ballistics model of the solid propellant ETC gun(2D-IB-SPETCG)is presented to describe the process of the ETC launch.Both calculated pressure and projectile muzzle velocity accord well with the experimental results.The feasibility of the 2D-IB-SPETCG model is proved.Depending on the experimental data and initial parameters,detailed distribution of the ballistics parameters can be simulated.With the distribution of pressure and temperature of the gas phase and the propellant,the influence of plasma during the ignition process can be analyzed.Because of the radial flowing plasma,the propellant in the area of the DRPG is ignited within 0.01 ms,while all propellant in the chamber is ignited within 0.09 ms.The radial ignition delay time is much less than the axial delay time.During the ignition process,the radial pressure difference is less than 5 MPa at the place 0.025 m away from the breech.The radial ignition uniformity is proved.The temperature of the gas increases from several thousand K(conventional ignition)to several ten thousand K(plasma ignition).Compare the distribution of the density and temperature of the gas,we know that low density and high temperature gas appears near the exits of the DRPG,while high density and low temperature gas appears at the wall near the breech.The simulation of the 2D-IB-SPETCG model is an effective way to investigate the interior ballistics process of the ETC launch.The 2D-IB-SPETC model can be used for prediction and improvement of experiments.

Approximate ballistics formulas for spherical pellets in free flight

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.

On the Use of Accurate Ignition and Combustion Models in Internal Ballistics Gun Codes

The desire for increased performance from guns is driving the charge designer towards charges that present challenges to numerical modelling.There is a pressing need for accurate,validated ignition and combustion models that can be used to predict the performance of advanced charges and ensure pressure waves are not developed or,if they are,then they can be managed.This paper describes efforts to model complex charge designs using a two-dimensional axi-symmetric multi-phase flow internal ballistics model.

Factors affecting use of ballistics gelatin in laboratory studies of bacterial contamination in projectile wounds

Background: Ballistics gelatin is a common tissue surrogate used in bacterial contamination models for projectile wounds. Although these studies have demonstrated that bacteria are transferred from the surface of the gelatin to the wound track by a projectile, quantifiable results have been inconsistent and not repeatable in successive tests.Methods: In this study, five areas of a typical contamination model in which bacterial recovery or survival are affected were identified for optimization. The first was a contaminated "skin" surrogate, where the novel use of vacuum filtration of a bacterial culture and buffer onto filter paper was employed. The other possibly problematic areas of the bacterial distribution model included the determination of bacterial survival when the contamination model is dried, survival in solid and molten gelatin, and the effect of high-intensity lights used for recording high-speed video.Results: Vacuum filtration of bacteria and buffer resulted in a consistent bacterial distribution and recovery. The use of phosphate buffer M9(pH 7) aided in neutralizing the ballistics gelatin and improving bacterial survival in solid gelatin. Additionally, the use of high-intensity lights to record high-speed video and the use of a 42℃ water bath to melt the gelatin were found to be bactericidal for gram-positive and gram-negative bacteria.Conclusion: Multiple areas of a typical contamination model in which bacterial survival may be impeded were identified, and methods were proposed to improve survival in each area. These methods may be used to optimize the results of bacterial contamination models for medical applications, such as understanding the progression of infection in penetrating wounds and to identify possible sources of contamination for forensic purposes.

Three dimensional simulation of electromagnetic railgun's exterior ballistics

In order to evaluate the electromagnetic railgun＇ s practical combat capability as well as its tactic application prospects, a three dimensional simulation model of electromagnetic railgun＇ s exterior ballistics is presented. On the hypothesis of the Earth＇ s being round and ignoring the influ- ence of rotation, the railgun＇ s atmospheric environment and its motion equations are established by the Simulink Module of Matlab. And the railgun＇ s characteristics of exterior ballistic under different muzzle energy and emission inclinations are discussed. Results show that its incomparable superiori- ty in improving range and lethality to conventional artillery under the same launch condition based on railgun＇ s range and variation of velocities. It is useful for the efficacy evaluation of railgun＇ s combat capability and its practical applications in fields such as ground war, missile interception and so on.

Adaptive optimisation of explosive reactive armour for protection against kinetic energy and shaped charge threats

We evaluate an adaptive optimisation methodology,Bayesian optimisation(BO),for designing a minimum weight explosive reactive armour(ERA)for protection against a surrogate medium calibre kinetic energy(KE)long rod projectile and surrogate shaped charge(SC)warhead.We perform the optimisation using a conventional BO methodology and compare it with a conventional trial-and-error approach from a human expert.A third approach,utilising a novel human-machine teaming framework for BO is also evaluated.Data for the optimisation is generated using numerical simulations that are demonstrated to provide reasonable qualitative agreement with reference experiments.The human-machine teaming methodology is shown to identify the optimum ERA design in the fewest number of evaluations,outperforming both the stand-alone human and stand-alone BO methodologies.From a design space of almost 1800 configurations the human-machine teaming approach identifies the minimum weight ERA design in 10 samples.

Experimental research on the launching system of auxiliary charge with filter cartridge structure

A launching system with a filter cartridge structure was proposed to improve the muzzle velocity of the projectile.The combustion chamber of the launching system is divided into two fixed chambers,one is located in the breech chamber,and the other is arranged in the barrel.The breech chamber charge was ignited first,and the charges in the auxiliary chambers were ignited by the high-temperature,highpressure combustible gas trailing the projectile.In this way,the combustible gas in the auxiliary chambers could compensate for the pressure drop caused by the movement of the projectile.The proposed device features the advantage of launching a projectile with high muzzle velocity without exceeding the maximum pressure in the chamber.In order to obtain some internal ballistic characteristics of the launch system,some critical structure,such as the length of the filter cartridge auxiliary charge,the combustion degree of the propellant in the chamber,and the length of the barrel,are discussed.The experimental results show that with the increased auxiliary charge length,a pressure plateau or even a secondary peak pressure can be formed,which is less than the peak pressure.The projectile velocity increased by 23.57%,14.64%,and 7.65%when the diaphragm thickness was 0 mm,1 mm,and2 mm,respectively.The muzzle velocity of the projectile can be increased by 13.42%by increasing the length of the barrel.Under the same charge condition,with the increase of barrel length,the energy utilization rate of propellant increases by 28.64%.

Multi-Stage Multidisciplinary Design Optimization Method for Enhancing Complete Artillery Internal Ballistic Firing Performance

To enhance the comprehensive performance of artillery internal ballistics—encompassing power,accuracy,and service life—this study proposed a multi-stage multidisciplinary design optimization(MS-MDO)method.First,the comprehensive artillery internal ballistic dynamics(AIBD)model,based on propellant combustion,rotation band engraving,projectile axial motion,and rifling wear models,was established and validated.This model was systematically decomposed into subsystems from a system engineering perspective.The study then detailed the MS-MDO methodology,which included Stage I(MDO stage)employing an improved collaborative optimization method for consistent design variables,and Stage II(Performance Optimization)focusing on the independent optimization of local design variables and performance metrics.The methodology was applied to the AIBD problem.Results demonstrated that the MS-MDO method in Stage I effectively reduced iteration and evaluation counts,thereby accelerating system-level convergence.Meanwhile,Stage II optimization markedly enhanced overall performance.These comprehensive evaluation results affirmed the effectiveness of the MS-MDO method.

A shield of defense:Developing ballistic composite panels with effective electromagnetic interference shielding absorption

The primary goal of this study is to develop cost-effective shield materials that offer effective protection against high-velocity ballistic impact and electromagnetic interference(EMI)shielding capabilities through absorption.Six fiber-reinforced epoxy composite panels,each with a different fabric material and stacking sequence,have been fabricated using a hand-layup vacuum bagging process.Two panels made of Kevlar and glass fibers,referred to as(K-NIJ)and(G-NIJ),have been tested according to the National Institute of Justice ballistic resistance protective materials test NIJ 0108.01 Standard-Level IIIA(9 mm×19 mm FMJ 124 g)test.Three panels,namely,a hybrid of Kevlar and glass(H-S),glass with ceramic particles(C-S),and glass with recycled rubber(R-S)have been impacted by the bullet at the center,while the fourth panel made of glass fiber(G-S)has been impacted at the side.EMI shielding properties have been measured in the X-band frequency range via the reflection-transmission method.Results indicate that four panels(K-NIJ,G-NIJ,H-S,and G-S)are capable of withstanding high-velocity impact by stopping the bullet from penetrating through the panels while maintaining their structural integrity.However,under such conditions,these panels may experience localized delamination with variable severity.The EMI measurements reveal that the highest absorptivity observed is 88% for the KNIJ panel at 10.8 GHz,while all panels maintain an average absorptivity above 65%.All panels act as a lossy medium with a peak absorptivity at different frequencies,with K-NIJ and H-S panels demonstrating the highest absorptivity.In summary,the study results in the development of a novel,costeffective,multifunctional glass fiber epoxy composite that combines ballistic and electromagnetic interference shielding properties.The material has been developed using a simple manufacturing method and exhibits remarkable ballistic protection that outperforms Kevlar in terms of shielding efficiency;no bullet penetration or back face signature is observed,and it also demonstrates high EMI shielding absorption.Overall,the materials developed show great promise for various applications,including the military and defense.

Ballistic limit velocity of small caliber projectiles against SS400 steel plates:Live fire experiments and empirical models

This study presents the ballistic limit velocity of small caliber projectiles against SS400 steel plate derived from live-fire ballistic experiments. Four different small caliber projectiles were tested against SS400 steel plates of 9 mm, 10 mm, and 12 mm thicknesses. The ballistic limit velocity was calculated using two standard methods, MIL-STD-662F and NIJ-STD-0101.06, and additionally using a support vector machine algorithm. The results show a linear relationship between the plate thickness and ballistic limit velocity. Further, the relative penetration performance among five different small caliber projectiles was analyzed using the Penetration Performance Ratio(PPR) introduced in this study, which suggests the potential of PPR to predict the ballistic limit velocity of other untested materials and/or different projectiles.

Dependence of impact regime boundaries on the initial temperatures of projectiles and targets

Towards higher impact velocities,ballistic events are increasingly determined by the material temperatures.Related effects might range from moderate thermal softening to full phase transition.In particular,it is of great interest to quantify the conditions for incipient or full melting of metals during impact interactions,which result in a transition from still strength-affected to hydrodynamic material behavior.In this work,we investigate to which extent the respective melting thresholds are also dependent on the initial,and generally elevated,temperatures of projectiles and targets before impact.This is studied through the application of a model developed recently by the authors to characterize the transition regime between high-velocity and hypervelocity impact,for which the melting thresholds of materials were used as the defining quantities.The obtained results are expected to be of general interest for ballistic application cases where projectiles or targets are preheated.Such conditions might result,for example,from aerodynamic forces acting onto a projectile during atmospheric flight,explosive shapedcharge-jet formation or armor exposure to environmental conditions.The performed analyses also broaden the scientific understanding of the relevance of temperature in penetration events,generally known since the 1960s,but often not considered thoroughly in impact studies.

Ballistic performance of additive manufacturing 316l stainless steel projectiles based on topology optimization method

Material and structure made by additive manufacturing(AM)have received much attention lately due to their flexibility and ability to customize complex structures.This study first implements multiple objective topology optimization simulations based on a projectile perforation model,and a new topologic projectile is obtained.Then two types of 316L stainless steel projectiles(the solid and the topology)are printed in a selective laser melt(SLM)machine to evaluate the penetration performance of the projectiles by the ballistic test.The experiment results show that the dimensionless specific kinetic energy value of topologic projectiles is higher than that of solid projectiles,indicating the better penetration ability of the topologic projectiles.Finally,microscopic studies(scanning electron microscope and X-ray micro-CT)are performed on the remaining projectiles to investigate the failure mechanism of the internal structure of the topologic projectiles.An explicit dynamics simulation was also performed,and the failure locations of the residual topologic projectiles were in good agreement with the experimental results,which can better guide the design of new projectiles combining AM and topology optimization in the future.

Energy dissipation mechanism and ballistic characteristic optimization in foam sandwich panels against spherical projectile impact

This study systematically examines the energy dissipation mechanisms and ballistic characteristics of foam sandwich panels(FSP)under high-velocity impact using the explicit non-linear finite element method.Based on the geometric topology of the FSP system,three FSP configurations with the same areal density are derived,namely multi-layer,gradient core and asymmetric face sheet,and three key structural parameters are identified:core thickness(t_(c)),face sheet thickness(t_(f))and overlap face/core number(n_(o)).The ballistic performance of the FSP system is comprehensively evaluated in terms of the ballistic limit velocity(BLV),deformation modes,energy dissipation mechanism,and specific penetration energy(SPE).The results show that the FSP system exhibits a significant configuration dependence,whose ballistic performance ranking is:asymmetric face sheet>gradient core>multi-layer.The mass distribution of the top and bottom face sheets plays a critical role in the ballistic resistance of the FSP system.Both BLV and SPE increase with tf,while the raising tcor noleads to an increase in BLV but a decrease in SPE.Further,a face-core synchronous enhancement mechanism is discovered by the energy dissipation analysis,based on which the ballistic optimization procedure is also conducted and a design chart is established.This study shed light on the anti-penetration mechanism of the FSP system and might provide a theoretical basis for its engineering application.

Composite armor philosophy(CAP):Holistic design methodology of multi-layered composite protection systems for armored vehicles

A philosophy for the design of novel,lightweight,multi-layered armor,referred to as Composite Armor Philosophy(CAP),which can adapt to the passive protection of light-,medium-,and heavy-armored vehicles,is presented in this study.CAP can serve as a guiding principle to assist designers in comprehending the distinct roles fulfilled by each component.The CAP proposal comprises four functional layers,organized in a suggested hierarchy of materials.Particularly notable is the inclusion of a ceramic-composite principle,representing an advanced and innovative solution in the field of armor design.This paper showcases real-world defense industry applications,offering case studies that demonstrate the effectiveness of this advanced approach.CAP represents a significant milestone in the history of passive protection,marking an evolutionary leap in the field.This philosophical approach provides designers with a powerful toolset with which to enhance the protection capabilities of military vehicles,making them more resilient and better equipped to meet the challenges of modern warfare.

Ballistic design and testing of a composite armour reinforced by CNTs suitable for armoured vehicles

This paper is investigating the use of composite armour reinforced by nanomaterials, for the protection of light armoured(LAV) and medium armoured military vehicles(MAV), and the interaction between the composite materials and high-performance ballistic projectiles. Four armour materials, consisted of front hybrid fibre reinforced polymer cover layer, ceramic strike-face, fibre reinforced polymer intermediate layer and the metal matrix composite reinforced backplate, were manufactured and assembled by adhesive technology. The proposed laminated protection system is suitable for armoured ground vehicles;however, it could be used as armour on ground, air and naval platforms. The design of the protection system, including material selection and thickness, was elaborated depending on the performance requirements of Level 4 + STANAG 4569 military standard(projectile 14.5 mm × 114 mm API B32) and especially on a design philosophy which is analysed with the specifications. The backplate of this new composite is a hybrid material of Metal Matrix Composite(MMC) reinforced with carbon nanotubes(CNTs), manufactured with the use of powder metallurgy technique. The composite backplate material was morphologically, mechanically and chemically analysed. Results show that all plates are presenting high mechanical properties and ballistic characteristics, compared to commonly used armour plates. Real military ballistic tests according to AEP-STANAG 4569 were carried out for the total composite armour systems. After the ballistic tests, AA2024-CNT3 showed the best protection results, compared with the other plates(AA2024-CNT1 and AA2024-CNT2), with the projectile being unable to fully penetrate the composite plate.

On the effect of pitch and yaw angles in oblique impacts of smallcaliber projectiles

A terminal ballistic analysis of the effects of 7.62 mm × 51 AP P80 rounds on inclined high-strength armor steel plates is the focus of the presented study.The findings of an instrumented ballistic testing combined with 3D advanced numerical simulations performed using the IMPETUS Afea? software yielded the conclusions.The experimental verification proved that slight differences in the pitch-andyaw angles of a projectile upon an impact caused different damage types to the projectile’s core.The residual velocities predicted numerically were close to the experimental values and the calculated core deviations were in satisfactory agreement with the experimental results.An extended matrix of the core deviation angles with combinations of pitch-and-yaw upon impact angles was subsequently built on the basis of the numerical study.The presented experimental and numerical investigation examined thoroughly the influence of the initial pitch and yaw angles on the after-perforation projectile’s performance.

An internal ballistic model of electromagnetic railgun based on PFN coupled with multi-physical field and experimental validation

To accelerate the practicality of electromagnetic railguns,it is necessary to use a combination of threedimensional numerical simulation and experiments to study the mechanism of bore damage.In this paper,a three-dimensional numerical model of the augmented railgun with four parallel unconventional rails is introduced to simulate the internal ballistic process and realize the multi-physics field coupling calculation of the rail gun,and a test experiment of a medium-caliber electromagnetic launcher powered by pulse formation network(PFN)is carried out.Various test methods such as spectrometer,fiber grating and high-speed camera are used to test several parameters such as muzzle initial velocity,transient magnetic field strength and stress-strain of rail.Combining the simulation results and experimental data,the damage condition of the contact surface is analyzed.

Protective performance of shear stiffening gel-modified foam against ballistic impact:Experimental and numerical study

As one of the most widely used personal protective equipment(PPE),body armors play an important role in protecting the human body from the high-velocity impact of bullets or projectiles.The body torso and critical organs of the wear may suffer severe behind-armor blunt trauma(BABT)even though the impactor is stopped by the body armor.A type of novel composite material through incorporating shear stiffening gel(STG)into ethylene-vinyl acetate(EVA)foam is developed and used as buffer layers to reduce BABT.In this paper,the protective performance of body armors composed of fabric bulletproof layers and a buffer layer made of foam material is investigated both experimentally and numerically.The effectiveness of STG-modified EVA in damage relief is verified by ballistic tests.In parallel with the experimental study,numerical simulations are conducted by LS-DYNA®to investigate the dynamic response of each component and capture the key mechanical parameters,which are hardly obtained from field tests.To fully describe the material behavior under the transient impact,the selected constitutive models take the failure and strain rate effect into consideration.A good agreement between the experimental observations and numerical results is achieved to prove the validity of the modelling method.The tests and simulations show that the impact-induced deformation on the human body is significantly reduced by using STG-modified EVA as the buffering material.The improvement of protective performance is attributed to better dynamic properties and more outstanding energy absorption capability of the composite foam.