Terminal Ballistics Research Articles

A graph network-based learnable simulator for spatial-temporal prediction of rigid projectile penetration

Predicting plate penetration by rigid projectiles (PPRP) is crucial in terminal ballistics, with broad applications in civil and military engineering. Empirical and analytical methods face challenges in predicting field variables like displacement and stress in target plates. Although numerical methods offer high accuracy, they suffer from low computational efficiency. Herein, we introduce an efficient data-driven machine learning (ML) method based on graph neural networks (GNNs), named PGN, specifically tailored to address the PPRP problem. Unlike traditional ML methods that establish direct input-output mappings, PGN predicts comprehensive spatial-temporal information pertaining to the projectile-target interaction process. A thorough analysis of PGN's performance in terms of accuracy, computational efficiency and generalization ability was performed. Compared to validated results of numerical simulations, PGN maintained high precision with RMSE for displacement, stress, and strain predictions below 0.5 %, 9.5 %, and 2.1 %, respectively. It also achieved R2 values exceeding 0.92 for the time history of projectile velocity and acceleration, while requiring only 9.8 % of the computation time compared to LS-DYNA. In generalization tests, PGN exhibited remarkable adaptability in tackling challenging scenarios that extend far beyond the training data distribution, with overall RMSE between 11 % and 13 %. Furthermore, we find that the maximum information propagation capacity of a simulated physical system must meet or exceed the information propagation need of the real-world physical phenomenon it aims to replicate. Consequently, an approach was proposed to determine the critical connectivity radius of the massage passing method directly from the wave speed in the target medium, which greatly improved the accuracy and efficiency of PGN.

Terminal ballistics performance of 9 × 19mm cartridges in 10% ballistic gelatin: FBI Protocol based analysis of Brazilian-made law enforcement ammunition.

Understanding that a projectile entering the human body can cause damage or destruction to live tissues through a variety of wounding mechanisms - permanent cavity, temporary cavity, and fragmentation - is crucial for researching terminal ballistics and understand the patterns of gunshot wound configuration. The present work tested four different types of ammunition in caliber 9 × 19mm (Full Metal Jacketed, Gold Hex, Copper Bullet Tactical and Bonded), using ballistic gelatin at 10% as soft tissue surrogate. The tests were based on the Federal Bureau of Investigation Protocol and included shots through bare gelatin, heavy clothing, plywood, steel sheets and auto glass. As a comparison parameter, the American-made Federal™ HST, used by several law enforcement agencies in the USA, was also tested in the same conditions. The Full Metal Jacketed cartridge had a uniform performance throughout the experiment, showing high penetration levels and no expansion, as expected. Gold Hex demonstrated a strong tendency to fragment with low levels of penetration and weight retention. Copper Bullet Tactical did not achieve the 12" minimum penetration in the soft barrier phases but expanded aggressively. Finally, Bonded only failed to achieve the 12" mark of penetration in phase 5 (auto glass), the hardest barrier in the whole Protocol. Tested for comparison purposes, Federal HST showed aggressive expansion in the initial phases (over 100%), after surpassing the 12" threshold. The study concluded that heavier projectiles (CBC Bonded and Federal HST) performed better than lighter and faster bullets in terms of terminal ballistics.

Experimental Tests on External and Terminal Ballistics of Different Types of Projectiles Fired From .38 SPL Caliber Cartridges and Study of Permanent Cavitation in Anatomical Modeling With 10% Ballistic Gelatin.

The present study investigated the main morphological differences between the permanent cavities formed by 4 different types of projectiles fired from .38 SPL caliber cartridges in blocks of 10% ballistic gelatin with standardized formulation (Federal Bureau of Investigation Protocol), all fired from the same distance and from the same firearm, associated with its performances in external and terminal ballistics. The velocity or the mass presented by a firearm projectile will not always be solely responsible for the final configuration of the permanent cavity, in which the projectile design, for example, is an equally important element. Each type of projectile tested in the present work generated a different kind of permanent cavity, but they also varied in velocity (m/s) and energy (J). The use of 10% ballistic gelatin in scientific research that seeks to investigate the external and terminal ballistics of projectiles can contribute to the practice of professionals working either in forensic pathology or applied ballistics scenarios, as they can experimentally simulate the events that can occur in the tissues of victims inflicted by gunshot wounds, which also allows important applications in the medical, commercial, civil, and military sectors that deal with products and technologies related to the human body.

Theoretical study on the sabot separation process of a sub-caliber projectile fired from rifled guns

Sub-caliber projectiles have been widely used in modern warfare due to their ability to enhance accuracy and ballistic performance. For such projectiles, however, an effective separation of the penetrator from the sabot upon exiting the barrel is extremely important for achieving the desired accuracy and terminal ballistics. In this paper, we present a theoretical model for studying the aspects of the penetrator-sabot separation process for a sub-caliber projectile fired from 7.62mm pistols. The method used in this paper is a combination of analytical and numerical approaches. Firstly, an equation system was analytically established to describe the motion of the sabot and the penetrator in absolute coordinates. Then, the Computational fluid dynamics simulation approach was applied to determine the aerodynamic forces acting on the sabot and the penetrator. Finally, the equation system was solved using Newton’s method to calculate the position of the sabot and the penetrator during the separation process. Based on the proposed model, the effect of some parameters on the separation process was investigated. The investigation results have shown that the initial friction force between the sabot and the penetrator significantly influences the separation process. The findings in this study provide valuable contributions to the design and optimization of sub-caliber projectile-weapon systems.

Penetration mechanics of rigid projectiles impacting metallic and concrete targets—A summary of our work

The physical mechanisms operating during the penetration and perforation of metallic and concrete targets by rigid projectiles are reviewed in this paper. The review covers our approach to these phenomena, as detailed in several papers that were published during the last decade. This approach is based on experimental data and their numerical simulations, through which we constructed analytical expressions for the penetration depths and the ballistic limit velocities of the corresponding projectile/target pairs. This review article will benefit researchers in the terminal ballistics community because it presents a full picture of our approach to the subject, and it also outlines the development in our thinking over the years.

Analysis of Terminal Ballistics on Medical Forensics: Criteria and Challenges in the Forensic Area in Brazil

Analysis of Terminal Ballistics on Medical Forensics: Criteria and Challenges in the Forensic Area in Brazil

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 V50 ballistic 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 1000 samples, 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.

Terminal Ballistics of Stone-Tipped Atlatl Darts and Arrows: Results From Exploratory Naturalistic Experiments

Abstract This study describes an effective protocol for naturalistic archaeological weapons experiments that improves cross-validation with controlled experiments and allows testing of multiple hypotheses. Stone-tipped atlatl darts and arrows were launched by skilled users against fresh carcasses, with high-speed cameras and radar guns capturing details of ballistic performance, impacts to bone and stone armatures, and other variables. The results pertaining to terminal ballistics in soft tissues are presented, with implications for what made ancient hunting projectiles effective and can be observed archaeologically. Fine-grained knappable stones seem to produce sharper armatures that can dramatically improve penetration, and presumably, lethality. Two commonly used metrics by archaeologists for estimating armature efficacy, tip cross-sectional area (TCSA), and perimeter (TCSP), are not among the significant variables for capturing penetration depth in soft tissues. However, armatures with larger TCSAs tend to be fitted to larger shafts that carry more energy and penetrate more deeply, providing one method for predicting wounding potential. The variability within weapon systems means that isolating efficacy to individual variables, such as tip cross-sectional size of stone armatures, can lead to erroneous interpretations.

Ballistic Model of Two-Stage Light Gas Gun

A physical model and specificity of a two-stage light gas gun propulsion system are presented in this paper. For the considered system, a mathematical model of phenomena inside a combustion chamber, a light gas filled chamber, and a barrel was worked out. A numerical solution of the proposed model for the considered propulsion system gives pressures of powder gases, pressure of light gas, and motion parameters of a piston and a projectile. On the basis of the results of the accomplished calculations, influence of system structural parameters on the maximum pressure inside a compression chamber and a muzzle velocity of a projectile has been analysed. The final results of this work were used for development of the first in Poland a laboratory station with two-stage light gas gun intended for experimental investigation in the field of terminal ballistics of objects moving at hypersonic velocities.

ВПЛИВ ТЕМПЕРАТУРИ ІМІТАТОРА ЦІЛІ З БАЛІСТИЧНОГО ПЛАСТИЛІНУ НА РЕЗУЛЬТАТИ ДІЇ ЕЛЕМЕНТА, ЩО ВРАЖАЄ

Due to the complexity of modeling terminal ballistics processes and the necessity to apply numerous assumptions, the investigation of the impact of the projectile's energy characteristics on the target is best conducted using experimental methods. Ballistic plasticine, especially the "Beschussmasse" brand, is widely used for simulating processes associated with firearm injuries. A challenge with any target simulator is the temperature dependence of its mechanical properties. Decreased temperatures lead to increased strength and reduced plasticity of materials and vice versa. It has been established that the volume and shape of the cavity depend not only on the target simulator's temperature but also on the kinetic energy of the impacting element. The research has yielded empirical relationships between the volume of the final cavity in the ballistic plasticine target simulator and the temperature of the target simulator and the kinetic energy of the impacting element. These relationships allow for the assessment of the impact of the striking element on the target simulator, specifically on the volume of the final cavity within the temperature range of the plasticine target simulator from 5°C to 25°C. Results obtained at any given temperature of the target simulator can be adjusted to the volume of the final cavity at normal temperature. This eliminates the need to strictly adhere to the normal temperature of the target simulator, significantly simplifying the process of related experimental research. To reduce the relative error in measuring the volume of the final cavity, it is advisable to prefer higher temperatures of the target simulator (within the investigated range). The direction of further research involves establishing the relationship between the effects of the impacting element with identical characteristics on a biological target and a target simulator, followed by correlating the damages of the target simulator to the biological target.

Gunshots through laminated glass: expelled compounded fragments as a function of bullet type

In the frame of an experimental setting, the formation of round-shaped compounded glass fragments on the exit site after gunshots through a windshield was examined. For that purpose, a 9 × 19 mm pistol (HK P30) and two different cartridges containing (a) a full metal jacketed round-nosed projectile and (b) a deformation projectile were used. On the basis of 52 gunshots, the morphology, impact angles and terminal ballistics of occurring compounded glass fragments were examined. The results showed that the compounded glass fragments’ morphology allowed for the differentiation of two used projectiles. Fragments were able to cause round-shaped defects in a single cotton layer (T-shirt) with subsequent penetration of up to 2.4 cm into ballistic gelatin (10%, 4 °C). As a function of the projectile type, the compounded glass fragments showed different reproducible impact angles that differed notably from the known conical pattern of expelled glass fragments after bullet penetration. These findings might help to explain the atypical morphology of gunshot wounds with laminated glass as an intermediate target and prevent possible misinterpretations when reconstructing the sequence of events.

Predictions on multi-class terminal ballistics datasets using conditional Generative Adversarial Networks

Ballistic impacts are a primary risk in both civil and military defence applications, where successfully predicting the dynamic response of a material or structure to impact crucial to the design of safe and fit-for-purpose protective structures. This study proposes a conditional Generative Adversarial Network (cGAN) architecture that can learn directly from available ballistic data and can be conditioned on additional information, such as class labels, to govern its output. A single Multi-Layer Perceptron (MLP) cGAN architecture is trained on a multi-class ballistic training set consisting of 10 classes labelled 0−9 where each class refers to a ballistic curve with a different ballistic limit velocity, vbl. A total of 5 models are trained on datasets consisting of 5, 10, 15, 20 and 25 samples within each class. For integer class labels 0−9, all cGAN models successfully predict the vbl with a maximum error of 4.12%. Additionally, for non-integer class labels between 0−9 the vbl predictions are similar despite not explicitly appearing in the training set. Moreover, each cGAN model is challenged to generate new samples for class labels that exist beyond the scope of the training set for class labels between 9−20. Four of the models predict the vbl with an error of less than 1.5% in all cases. This study showcases how a cGAN model can learn directly from a multi-class ballistic dataset and generate additional samples representative of that data for classes that do not appear explicitly in the training set.

Данные об истории замедления тела в реологической среде как основа для верификации расчетных задач

Relying on data on the history of body deceleration during high-speed penetration into the target, the paper reviews the Proceedings of the 23rd – 31st International Symposiums on Ballistics, as well as the findings in the field of terminal ballistics, i.e. the study of body acting on a target, and the history of striker deceleration in the target material. The paper observes a half-century path of development of the technology as a new scientific direction, started in the department of High-Precision Airborne Devices at Bauman Moscow State Technical University. Strikers in measuring technology are equipped with shock accelerometers and original electrical recorder communication systems. Theoretical and experimental studies revealed a new law of medium penetration resistance. The law allows the use of engineering methods to solve problems, e.g. spatial problems of penetration. The data on the history of the measuring striker deceleration recorded in the experiments provided additional opportunities for verifying the models and the results of virtual simulation of the processes of spatial penetration. The paper introduces the studies carried out by the authors in a wide range of different initial conditions of impact and designs of strikers and targets. New technical solutions in measuring technology developed recently are also presented.

Surrogate drag model of non-spherical fragments based on artificial neural networks

The hazard evaluation of the fragments produced from an explosion requires an accurate prediction of the motion of fragments subjected to gravity and aerodynamic forces. The drag coefficient (Cd) is among the most crucial components of various aerodynamic models. Limited experiments cannot reproduce the Cd (Mach) curves of all shapes of fragments. In this study, we develop a surrogate model of the average drag coefficient, C¯d, for the randomly tumbling non-spherical fragment using artificial neutral networks. To train and validate the surrogate model, a comprehensive dataset was developed through mesoscale simulations of Cd for a wide variety of fragment shapes combined with icosahedron average method. The surrogate model shows that the dependence of C¯d on different Mach numbers varies with fragment shape. The fully validated surrogate model of C¯d allows us to derive the statistics of C¯d for a host of fragments from a specific explosion, subsequently gaining insight into the terminal ballistics of the fragments.

External and Terminal Ballistics of Early Bronze Age Lithic Arrowheads: Experimental Verification

ABSTRACT Lithic archery projectiles during the short timespan at the end of the Eneolithic period and the beginning of the Bronze Age in Europe have alternately been deemed hunting implements, weapons, or symbolic artefacts. More than 400 projectiles of this period have been analysed in 3D metrics. All but a few are triangular barbed projectiles. Despite differences in size and weight, four types of arrowheads have been identified using 3D shape alone. Experiments to clarify their ballistic behaviour, based on weight, Tip Cross-Sectional Area (TCSA), differences in the shaping of their tips, the height of the cross-section, and cross-sectional asymmetry in distribution of mass were carried out. The 3D data on the projectiles, their wound cavities, and their measured initial and impact velocities were used to verify functional differences and the potential wounding impact.

Projectile Explosion Position Parameters Data Fusion Calculation and Measurement Method Based on Distributed Multi-Acoustic Sensor Arrays

In conventional weapon test field, the parameter of projectile explosion position is an important index to measure the control ability and damage efficiency of fuze. Due to the random deviation of gun firing and the difference of detection performance of fuze itself, the projectile explosion position is uncertain and relatively scattered in terminal ballistic, which is easy to miss the projectile explosion information. In order to obtain the parameters of projectile explosion position in large area of in terminal ballistic, this paper constructs a projectile explosion position testing system with distributed multiple acoustic sensor basic arrays, establishes the calculation model of projectile explosion position by a basic array, researches a multi-source data fusion algorithm based on the measurement data of multiple array acoustic basic arrays and gets real projectile explosion coordinates. To improve the measurement accuracy, we use the wavelet transform filtering method to filter the output signal of the acoustic sensors, and propose the time extraction algorithm of the projectile explosion acoustic signal with the wavelet modulus maximum. Through experiment and analysis, we collect the sound signal of the actual projectile explosion and verify the rationality and correctness of the proposed calculation model and algorithm.

ОБҐРУНТУВАННЯ НЕОБХІДНОСТІ ВДОСКОНАЛЕННЯ НАУКОВО-МЕТОДИЧНОГО АПАРАТУ ФОРМУВАННЯ ВИМОГ ДО ЕНЕРГЕТИЧНИХ ХАРАКТЕРИСТИК ПОРАЖАЮЧОГО ЕЛЕМЕНТА КІНЕТИЧНОЇ ЗБРОЇ НЕСМЕРТЕЛЬНОЇ ДІЇ

The scientific-methodical apparatus for predicting damage to biological objects of non-lethal kinetic weapons is considered, which mainly takes into account only the energy characteristics of the damaging elements, namely, kinetic and specific energy. An analysis of the nominal ballistic characteristics of samples of non-lethal kinetic weapons, which are in service with law enforcement agencies and military formations of Ukraine, was carried out, based on the determination of only the specific energy of the striking elements. The energy characteristics of bullets or striking elements for various samples of non-lethal kinetic weapons vary within fairly wide limits. In particular, such an important indicator as the specific energy varies from 0.34 to 1.33 J/mm2, that is, even the same type of weapon, intended for use at certain distances to the target, in the case of using different cartridges, has a significantly different specific energy (the difference reaches 30%). An analysis of known developments in the field of terminal ballistics is given, which indicates the need to take into account the speed of meeting the target under the conditions of conservation of constant kinetic energy. So, with the same mass, a bullet with a higher speed will have more energy. Such a ball has the ability to give a different part of its energy to the affected tissues. The main feature of cartridges with a traumatic effect, which distinguishes them from ordinary cartridges for firearms, is the mechanical characteristics of the striking elements. The striking elements require a high "stopping" effect, i.e. quick and complete incapacitation of the opponent when hitting any part of the body - this is a short range of "fire contact". For this, striking elements must quickly and maximally transfer their kinetic energy to the target upon hitting it. Therefore, most bullets for police and civilian weapons are blunt-end ("impact") - with a rounded or flat area on the main part. So important are the shape and strength (stiffness) of the striking elements and the shape of the main part that directly interacts with the target. The need to improve the scientific and methodological apparatus for predicting damage to biological objects when using non-lethal kinetic weapons by taking into account an expanded list of factors (speed, strength, rigidity and shape of the striking element) in order to increase the adequacy of the obtained models is substantiated.

Woundary ballistics of biological tissue’s plastic deformation on the model of ballistic plastiline using hollow point and shape-stable bullets

Introduction. Modern military conflicts make many challenges for military surgeons associated with the use of new types of weapons – hollow point bullets. The solution to this problem, firstly, depends on studying the characteristics of the terminal ballistics of such ammunition and comparing the data obtained with the characteristics of traditional weapon.
 The aim of the work is to conduct experimental modeling of the wound canal and residual wound cavity, which is formed due to plastic deformation from hollow point and non-hollow point bullets.
 Materials and methods. The studies were carried out on 40 blocks of ballistic plasticine, in each of which one shot was fired from an AKS-74 assault rifle and a ZBROYAR Z-10 carbine. Depending on the type of ammunition, the blocks of ballistic plasticine were divided into 4 groups: Group 1 – 10 blocks into which shots were made with 5.45 mm non-hollow point military cartridges with "PS" bullets with a steel core "7N6"; Group 2 (10 blocks) – 5.45x39 mm cartridges with "V-Max" hollow point bullets; Group 3 (10 blocks) – with cartridges 7.62x39 mm; Group 4 (10 blocks) – cartridges 7.62x39 mm with hollow point bullets of the "SP" type.
 Results and discussion. Only for a 5.45 mm military cartridge with "PS" bullets, both inlet and outlet bullet holes were detected in all 10 observations. When using non-hollow point bullets, the outer area of ​​the bullet inlet correlates with the caliber of the projectile (1.6 times larger when using 7.62 mm bullets). For hollow point bullets, the caliber of the projectile does not significantly affect the area of ​​the inlet (P < 0.05). The expansive properties of the bullet significantly increase the area of ​​the bullet hole by 14.87-31.2 times compared to non-hollow point ammunition. Increasing the caliber of the non-hollow point bullet leads to a significant increase in the area of ​​the sagittal section of the residual wound cavity in 1.59-2.03 times; whereas the expansive properties of the bullet do not significantly affect either the perimeter or the area of ​​the sagittal section of the residual wound cavity. For non-hollow point bullets, the volume of the residual wound cavity is more correlated with the caliber of the bullet (increases by 3.36 times); whereas for an hollow point bullet, its caliber has a smaller effect on the volume of the residual cavity (increases by 1.37 times). The expansive properties of the bullet affect the volume of the residual wound cavity in two ways: for 5.45 mm bullets the residual wound cavity increases 1.49 times, for 7.62 mm bullets it decreases 1.65 times. The use of hollow point bullets of 7.62 mm leads to greater collateral damage (zone of secondary necrosis, molecular shock) due to the scattering of the kinetic energy of the bullet to the elastic deformation of near-woundary tissues compared to non-hollow point analogues. The use of 5.45 mm expansive bullets leads to the formation of a larger volume of irreversible damage due to plastic deformation compared to non-hollow point analogues.
 Conclusions. The resulting model of plastic deformation of soft tissues, depending on the type of modern small arms, showed the dependence of the spatial configuration of the inlet bullet hole, residual wound cavity and deformation and fragmentation of the bullet on the caliber of the cartridge and its expansive properties.

Data transmission bit error rate modeling and analysis of multi‐screen measurement system based on optical communication link

AbstractTo reduce the bit error rate of data transmission in the field of the long‐distance ballistic trajectory of weapon range, this article utilizes a MIMO‐OFDM atmospheric laser link communication model to transfer the obtained data using the four‐screen measurement system in the terminal ballistic. First, the atmospheric attenuation channel model caused by haze and fog in the atmospheric link communication is analyzed. Then the atmospheric attenuation factors of haze day are introduced and the received optical power of the system is calculated. Lastly, the atmospheric laser link communication model in different weather environment is established. The calculation functions of signal‐to‐noise ratio and bit error rate in the long‐distance link communication are derived. Through the calculation and analysis, the attenuation of laser's power caused by fog and haze with different visibilities is obtained. The results show that the lower is the visibility under fog or haze days, the faster is the attenuation of the laser's power and the higher is the bit error rate of the communication link. The atmospheric attenuation can be reduced by increasing the laser's power. The results verify the feasibility of the MIMO‐OFDM atmospheric laser link communication model. The proposed model has a certain guiding significance for the further study of reliable data transmission in the ultra‐long‐range ballistic.

NUMERICAL ANALYSIS OF KINETIC ENERGY PROJECTILE SABOT STRUCTURE INFLUENCING THE ARMOUR PENETRATION DEPTH. PART II – ANALYSIS OF PROJECTILE DEVELOPING OPTIONS

Numerical calculations were used to investigate influence of sabot structures of kinetic energy projectiles into the armour penetration depth. Areas of sabot structure for possible optimization and the influence of various sabot materials on the projectile combat efficiency were indicated. The analysis was performed using the finite element method in the Solidworks Simulation environment. It allowed examination of dynamic loads the sabot is subjected to at the time of the shot. Impact of various sabot materials and projectile geometry modifications on the strength of penetrator - sabot connection was investigated. Distributions of dynamical loads for penetrator-sabot connections were simulated and visualised. Calculations on terminal ballistics were performed for some options of the structure. It allowed identification of development trends for this type of ammunition.