Projectile Trajectory Research Articles

Localization of a Bullet in a Firearm Injury Victim Using X-ray Imaging During Autopsy: A Case Report

Firearm injuries can result in varying degrees of trauma, depending on factors such as the type of firearm, range, and wound location. This case report presents the role of X-ray imaging in detecting a projectile causing fatal penetrating abdominal trauma in a 45-year-old male. The patient was found with a gunshot wound in his abdomen, and despite medical interventions, he succumbed to his injuries. X-ray imaging revealed a hyper-dense area resembling a bullet lodged in the abdominal cavity. Autopsy confirmed a close-range gunshot with significant internal damage to the peritoneum, mesentery, liver, and the bullet lodged near the L1 vertebra. This case underscores the value of radiological imaging in identifying projectile trajectory and injury severity, particularly in resource-limited settings. X-rays assist in distinguishing between penetrating and perforating wounds, aiding both forensic investigation and legal procedures. The integration of imaging in forensic autopsies improves the accuracy of injury assessment, especially in cases involving gunshot wounds.

Study the variation of the pitching frequency of sounding rockets

Sounding rockets typically feature an axially symmetric design and are launched vertically to facilitate research and high-altitude atmospheric data collection. Manufacturing errors can cause axial asymmetry, leading to undesirable rocket trajectory dispersion. Sounding rockets are often designed to spin around their axis to mitigate these effects. However, axial spinning motion can resonate with short-period oscillations, creating large normal loads that may damage the rocket’s structures. This paper focuses on analyzing the variations in the pitching frequency, which may help predict the roll resonance phenomenon. In this study, the authors constructed a six-degree-of-freedom dynamic model for a sounding rocket, considering all aerodynamic problems and the variation of inertial characteristics. To determine the pitching frequency, an impulse is applied to the rocket to generate short-period oscillation. The Fourier transform is then used to analyze and obtain the frequency of the rocket while oscillating in space. The results demonstrate agreement with the theoretical model, thereby substantiating the validity of the current method. The findings of this research provide valuable recommendations for the design and manufacturing process of sounding rockets, which may help mitigate the adverse effects of motion resonance during flight.

An improved particle filtering projectile trajectory estimation algorithm fusing velocity information

This study proposes an improved particle-filtering projectile trajectory estimation method that fuses velocity information to address the susceptibility to interference and large fluctuations in position and velocity measurements of a single-antenna-two-dimensional trajectory correction fuze. By considering the Doppler effect in satellite velocity measurements and the residuals between the model-derived velocity and velocity derived from the translational Doppler frequency shift, a sliding time window was established to generate velocity weight coefficients that dynamically adjust the weight of the velocity in filtering. By modifying the likelihood function, a particle-filtering algorithm was designed to achieve a fusion estimation of the projectile trajectory. Tests indicate that this method provides more accurate estimates of the position and velocity of the projectile compared to other existing methods, which can reduce the impact of velocity fluctuations to a certain extent. In addition, the computational burden is not increased and can directly replace existing mature algorithms in engineering.

Analysis of ballistic trajectories and its association with clinical outcomes in civilian penetrating brain injury.

Civilian penetrating brain injuries (PBI) caused by firearms are a medical emergency with high rates of morbidity and mortality. The aim of this study was to evaluate the association between trajectory vectors in CT brain angiography and clinical outcomes in patients with civilian gunshots. This is a retrospective analytical cross-sectional study that includes patients over 15 years of age with PBI due to firearms, admitted from January 2019 to December 2021 at a University Hospital in Cali, Colombia. A brain CT with angio-CT was performed the first day of admission. An XYZ coordinate system centered on the Turk's saddle was developed. Trajectories of projectiles were plotted and compared to a patient 0 in a 3D-Slicer software. A bivariate analysis of the clinical and geometric characteristics of the trajectory was performed. Primary outcomes include mortality and disability at 6 months. Twenty-eight patients with a mean age of 27.39 ± 11.66 years were included. The vectors of non-survivors show a trend, crossing at a specific area. This area was designated as a "potential lethal zone" and inside this area, injuries around 25.3mm from the circle of Willis, were associated with greater mortality (p < 0.005). In our study PBI avoiding the ventricular system, brain stem, dorsum sellae and the circle of Willis were associated with more survivability. A "potential lethal zone" was detected and associated with poor outcome after civilian PBI due to firearms. A better evaluation of the performance of this "potential lethal zone" in larger studies will be required.

A modified bond-based peridynamic approach for rigid projectile perforation on concrete slabs

Peridynamic (PD) has a unique advantage in describing the crack growth and fragmentation of brittle materials. Concerning the dynamic behaviors and failure patterns of concrete slabs under projectile perforations, a modified bond-based PD approach maintaining both the easy implementation and computational stability characteristics was firstly developed from the following three aspects, (i) a rate-dependent PD constitutive model was proposed for describing the dynamic behaviors of concrete; (ii) a progressive damage criterion considering the tension-compression anisotropy, softening behavior, and strain rate effect of concrete was incorporated to more accurately reproduce the damage and failure of concrete; (iii) an improved micro-modulus function related to bond length was introduced to reveal the internal length effect of bond force. Then, numerical simulations of projectile perforation on concrete slabs by utilizing the developed modified bond-based PD approach, as well as the corresponding sensitivity analyses of discretization parameters including horizon size and particle spacing were performed. Based on the recommended horizon size and particle spacing, the predicted residual velocity of projectile and failure patterns of concrete slabs exhibited an excellent agreement with the test data. Furthermore, by comparisons of the traditional bond-based PD and classical finite element methods, the superiority of developed approach in describing the perforation damage of concrete targets against projectile impact was demonstrated. Finally, the modified bond-based PD approach was employed to blind simulate the projectile normal and oblique perforating multi-layered spaced concrete target plates. It was found that the modified PD model reasonably predicted the terminal ballistic trajectory, deflection angle, and residual velocity of projectile, as well as the failure patterns of target plates. The present work provides a new way to predict the terminal ballistic effect of projectile and dynamic behaviors of concrete slabs.

Supersonic Waves Generated by the 18 November 2023 Starship Flight and Explosions: Unexpected Northward Propagation and a Man‐Made Non‐chemical Depletion

AbstractOn 18 November 2023, SpaceX launched the Starship, the tallest and the most powerful rocket ever built. The Super Heavy engine separated from the Starship spacecraft and exploded at 90 km of altitude, while the main core Starship continued to rise up to 149 km and exploded after ∼8 min of flight. In this work, we used data from ground‐based GNSS receivers and we analyzed total electron content (TEC) response to the Starship flight and the two explosions. For the first time, we observed large‐distance northward propagation of intensive 2,000 km V‐shaped ionospheric disturbances from the rocket trajectory. The observed perturbations, most likely, represent shock waves propagating with the cone angle of ∼14° on the North and ∼7° on the South against the flight track that corresponds to the Mach angle of the shock waves in the lower atmosphere. The Starship explosion also produced a non‐chemical depletion in the ionospheric TEC.

Design of 2-DOF Thrust vector control system for Rockets and Missiles

This paper outlines the development and implementation of a Thrust Vector Control (TVC) system tailored specifically for solid propellant rocket engines, aimed at enhancing the portability of hybrid and liquid propellant rocket systems. The proposed system ensures trajectory stability and rapid response to flight emergencies by effectively addressing external perturbations like wind. Key components are Gyroscopic (GYRO) sensors, good micro-controller, and Servo motors, collectively referred to as Thrust vectoring components, which dynamically adjust thrust direction opposite to the rocket's trajectory to maintain stability. Drawing from an extensive literature review analyzing existing TVC system designs, with a focus on thrust characteristics and engine combustion timings, the design integrates considerations of geometric properties, kinematics, forces, energy requirements, safety, cost, and control methods, aligning with both mechanical and avionic design principles. The anticipated outcome is an advancement in rocket propulsion technology, characterized by improved angular speed control, trajectory linearity, and rapid response capabilities.

Study of the payload extraction trajectory heavy class carrier rocket

Relevance. As the weight and complexity of the payload that needs to be launched into orbit increases, the relevance of rational trajectory selection to ensure maximum efficiency and minimum costs for delivering the payload to a given orbit increases. Rational choice of the trajectory of a heavy-class launch vehicle has a number of important practical applications. Firstly, it allows you to increase the payload capacity of the launch vehicle and reduce the cost of delivering payload to the target orbit. This is especially important in the context of the development of the space industry, when more and more companies and organizations are showing interest in launching their own satellites and other spacecraft in conditions of fierce economic competition. Choosing a rational trajectory for launching a payload into orbit will significantly reduce the cost of launches and make them available to a wider range of potential customers. Secondly, the choice of launch vehicle trajectory parameters is important for ensuring safety and minimizing risks during spacecraft launches. Thanks to the rational choice of trajectory, it is possible to reduce adverse impacts on the environment and eliminate the possibility of emergency situations associated with loss of control over the flight of the launch vehicle. Rational selection of launch vehicle trajectory parameters is a complex task that requires comprehensive research and consideration of various factors, such as aerodynamic parameters of the atmosphere, mass and characteristics of the payload (spacecraft), engine operating parameters, characteristics of the target orbit, features of the launch of the launch vehicle and many other factors. A more thorough and systematic study of the influence of these parameters will significantly improve the efficiency and reliability of launching spacecraft into orbit. Thus, the choice of rational parameters for the launch vehicle trajectory is a relevant and important topic for scientific research. Increasing the rocket's payload capacity, reducing the cost of delivering a spacecraft to a given orbit, and ensuring launch safety are tasks that depend on the chosen shape and parameters of the rocket's trajectory. Such research has important practical significance and can become the basis for the development of new technologies and methods in the space industry. The purpose of the study is to study and select rational parameters for the trajectory of a heavy-class launch vehicle when launching a payload. The main task is to determine the flight path parameters that will allow achieving maximum efficiency and accuracy in delivering the payload to a given orbit. To achieve the goal of the study, an analysis of various factors influencing the launch parameters of the spacecraft is required, such as the structural and aerodynamic characteristics of the rocket, the influence of aerodynamic factors and the Earth’s gravitational field on the flight path. Taking these factors into account, numerical calculations were carried out on the basis of a system of differential equations of motion using a computer program created in the MAPLE software package. Based on calculations, modeling of the shape and parameters of the launch vehicle flight path was carried out. Research results. During the study, the rational parameters of the trajectory of a heavy-class launch vehicle were selected. Calculations were carried out using numerical modeling of the parameters of payload launch trajectories, and an analysis of the resulting trajectories was carried out. Minimizing the rocket's flight time was identified as the main criterion for the rational choice of trajectory, which allows increasing launch efficiency and saving energy resources. An increase in payload mass and minimization of fuel consumption were adopted as additional criteria. Conclusion. The procedure for choosing rational parameters for the trajectory of a heavy-class launch vehicle proposed in this work will improve the delivery accuracy and reliability of spacecraft launches at the stage of ballistic analysis when designing rockets. The results of the study have practical significance for the development of future heavy-duty launch vehicle missions and improving the efficiency of space launches.

Wartime penetrating skull base trauma with unpredictable internal fragment ricochet and migration: illustrative case.

Transnasal transsphenoidal penetrating craniocerebral injury is very rare even in wartime. Cases with good outcomes are even less common. A 20-year-old male sustained multiple fragment wounds to his head and face from a landmine explosion. One metal fragment entered his right nostril, traversed the nasal septum and anterior sphenoid sinus, and ricocheted superiorly off the clivus. The fragment then traveled almost to the surface of the left parietal lobe. Subsequently, under its own weight, it migrated back down its original track. The patient suffered cerebrospinal fluid rhinorrhea, pneumocephalus, and right-sided hemiparesis. Digital subtraction angiography was followed by microscopic transnasal skull base reconstruction supplemented by external lumbar drainage. Follow-up brain computed tomogrpahy showed further metallic fragment migration through the ventricular system. The fragment was removed through a transcortical approach. The patient's neurological examination and brain magnetic resonance imaging results demonstrated good recovery. The absence of external signs of deep injuries does not exclude the presence of a penetrating craniocerebral injury. Metal fragments may undergo ricochet and internal migration in both the brain parenchyma and the ventricular system. Timely diagnosis including three-dimensional reconstruction of a projectile's trajectory may facilitate appropriate surgical planning in complex cases. Intraventricular fragment migration may necessitate microsurgical removal. https://thejns.org/doi/10.3171/CASE24128.

Understanding post-impact biomechanics of ballistic cranial injury by smoothed particle hydrodynamics numerical modelling

AbstractVirtual crime scene investigation using numerical models has the potential to assist in the forensic investigation of firearm-related fatalities, where ethical concerns and expensive resources limit the scope of physical experiments to comprehend the post-impact biomechanics comprehensively. The human cranial numerical model developed in this study incorporates three main components (skin, skull, and brain) with dynamic biomaterial properties. The virtual model provides valuable insights into the post-impact biomechanics of cranial ballistic injuries, particularly in high-speed events beyond conventional investigative capabilities, including the velocity of ejected blood backspatter, cavitation collapsing, and pressure waves. The validation of the numerical model, both quantitatively and qualitatively, demonstrates its ability to replicate similar bone fractures, entrance wound shapes, and backward skin ballooning observed in physical experiments of the human cranial geometry. The model also yields similar temporary cavity sizes, wound sizes, and blood backspatter time against the physical cranial model, aiding in bloodstain pattern analysis. Additionally, the numerical model enables exploration of ballistic factors that vary in each crime scene environment and influence cranial injuries, such as projectile type, velocity, impact location, and impact angle. These established injury patterns contribute to crime scene reconstruction by providing essential information on projectile trajectory, discharge distance, and firearm type, assisting in the resolution of court cases. In conclusion, the developed human cranial geometry in this study offers a reliable tool for investigating firearm-related cranial injuries, serving as a statistical reference in forensic science. Virtual crime scene investigations using these models have the potential to enhance the accuracy and efficiency of forensic analyses.

Energy absorption and impact response of ballistic resistance laminate

Abstract High-speed impact performance has significantly expanded over the past few decades. The target response based on the impact conditions has been more difficult to visualise and evaluate. In this article, Ansys model analysis has been used to measure, visualise, and predict the projectile and target responses of Kevlar® (K) and Ramie® textile-reinforced unsaturated polyester resin (UP) matrix. The laminate thickness threshold was detected experimentally based on the highest stress intensity factor and energy release rates. Furthermore, tensile strength and bending of the laminate were found. The impact conditions have a significant impact on the target response; thus, an explicit dynamic analysis was used to visualise the impact response based on the number of target fixed supports (FSs). Two FS (2 FS) target absorbs 11% more energy than four FS (4 FS) target. Additionally, the target size has a major effect on the projectile and laminate responses, and a successful arrest of the projectile was detected in both cases. The smallest targets with 2 FS have the highest and wider response, where a successful change in the projectile trajectory was obtained.

Dual-mode Antenna Tracking System for Rocket Launch Applications

Rocket launches are complex events that require tracking antennas to maintain a communication link. This study introduces a hybrid tracking strategy that combines manual and program modes by utilizing a predetermined trajectory of the rocket. Automatic switching between tracking modes ensures ongoing monitoring, even during unexpected trajectory changes with the monopulse approach. The dual parabolic antenna arrangement enables this switching. The system estimates the monopulse ratio from the signal strength of each antenna, allowing automatic program tracking to shift to manual mode when reception concerns arise. Performance evaluations included manual, programmable, and dual-mode tests. The system responded to human input and automatically aligned the antenna with slight elevation errors during the initial phase. Adjusting the initial elevation reduced the error. The mode transition was examined by measuring the antenna radiation patterns and monopulse ratio. The system’s performance was evaluated in rocket launches, with the rocket trajectory input into the graphical user interface. The antenna exhibited an azimuthal movement of up to 10 °, and the ratio fluctuation values remained within the antenna’s field of view. After 8.8 seconds, the mode switched from program to manual, indicating that the functioning of the system’s functioning was stable.

Trajectory planning and control strategy optimization design of double electric cylinder erecting device

The transition of the rocket from a horizontal to an erect state before its launch on the offshore platform is a crucial stage. Compared with erecting the rocket on the ground, higher servo control and synchronization accuracy are required for erecting it on the offshore platform. Most rocket erecting devices on offshore platforms rely on hydraulic drive systems, posing challenges due to their lower servo control accuracy and difficulties in achieving high-precision synchronization. The erecting process, trajectory planning, control system, and control strategies of rockets driven by a double electric cylinder erecting device are studied, aiming at the requirement of erecting rocket devices on offshore platforms. This paper commences by establishing the kinematic model of erecting the rocket with a double electric cylinder erecting device. It delves into the process and trajectory of the erection rocket with a double electric cylinder erecting device. Subsequently, the focus shifts toward designing the control system, while inclination and angular velocity sensors monitor the erection process. Finally, designing and demonstrating control strategies for a double electric cylinder erecting device, three different control strategies, master control, master-slave control, and cross-coupling control, are analyzed, and the cross-coupling control strategy is selected as the control strategy of the double electric cylinder offshore platform rocket erecting device.

Investigations on the Johnson-Cook Constitutive and Damage-Fracture Model Parameters of a Q345C Steel

Due to the rapid development of high-speed trains, the service safety of vehicle body materials and structures has become a focal point in transport and impact engineering. Numerical simulations on the collision resistance of vehicle materials and structures are crucial for the safety assessment and optimal structural design of high-speed trains but have not been fully investigated due to the lack of damage model parameters. This study focuses on the Johnson-Cook (J-C) constitutive and damage-fracture models of a typical vehicle material, Q345C steel. A series of mechanical tests are conducted on the Q345C steel, including the quasi-static and dynamic compression/tension tests, quasi-static tension tests at different temperatures, and fracture tests along different stress paths, using the material test system and the split Hopkinson pressure/tension bar. Then, the parameters of the Johnson-Cook constitutive and damage-fracture models are calibrated based on the experimental results. In terms of the damage parameters related to stress paths, a new method of combining experiments and simulations is proposed to obtain the real, local fracture strains of the Q345C steel samples. This method allows the measurements of equivalent plastic strain and stress triaxiality histories under nonlinear stress paths, which are hardly accessible from individual experiments, and facilitates the accurate calibration of stress-path-related damage parameters. In addition, a high-speed plate penetration test is used to validate the J-C parameters, which can be directly implemented in the commercial finite element software Abaqus. The projectile trajectories from the simulation and experiment agree well with each other, demonstrating the reliability of the model parameters for impact scenarios and the efficiency of the experimental procedures utilized for calibration.

Trajectory prediction of rigid projectile for oblique penetration into multi-layer aluminum targets

Multi-layer targets and nonideal initial conditions significantly increase the complexity of penetration trajectory prediction. To address this issue, a general multi-layer target trajectory model was developed based on expanding spherical cavity in layered finite targets, comprising the wake separation and finite free-surface effects. The trajectory prediction model adopted the developed geometric description of the ogive- and conical-nosed projectiles, combined with the proposed transfer functions and plane motion equation. Experiments of the two types projectiles penetration into layered 2A12 aluminum targets were conducted, and the actual projectile trajectories in targets were obtained through the section scan method. The predicted trajectories aligned well with the experimental data within the application range. The layering effect considerably influences the projectile trajectories impacting at higher velocities and oblique angles. More layers reduce the resistance of the targets, increasing the penetration but reducing the angle deflection of the trajectory performance. Compared with the ogive projectile, the conical projectile exhibited a deeper penetration and improved anti-deflection capabilities. This preliminary study on penetration trajectory characteristics of multi-layer targets provides experimental and theoretical support for correcting penetration trajectories.

Reproducibility of real-time time-dependent density functional theory calculations of electronic stopping power in warm dense matter

Reproducibility of real-time time-dependent density functional theory calculations of electronic stopping power in warm dense matter

Experimental study on vertical water entry of the projectile with canard-wing

Flow control techniques play an important role during water entry. In this paper, the idea of water entry of the projectile with single canard-wing is proposed and applied to the water entry problem. The cavity evolution and motion characteristics of projectile with canard-wing were investigated through experiments, and the cavity length, trajectory, and attitude changes of projectile with canard-wing during water entry were quantified. The results show that, different from the water entry process of projectile without wing, the projectile with canard-wing has the typical characteristics of forming the attached cavity on the wing. Due to the influence of canard-wing, the trajectory deflection is always toward the side without the wing, and the initial moment of trajectory deflection is advanced with the increase in the impact velocity. The length of the fore-end cavity and the attached cavity on the wing increases as the impact velocity increases and the pinch-off depth of the fore-end cavity also increases. Moreover, the deviation of the trajectory and the attitude angle of the projectile with canard-wing increases as the impact velocity increases during water entry. The results can provide important support for the passive flow control during the water entry of the projectile and the development of the trans-media aircraft.

Comparison of Two Aerodynamic Models for Projectile Trajectory Simulation

The accuracy of aerodynamically controlled guided projectile simulations is largely determined by the aerodynamic model employed in flight simulations which impacts vehicle interaction with the surrounding air. In this work, the performance of projectile path following with two distinct aerodynamic models is examined for their possible influence on trajectory following accuracy. The study incorporates the path following guidance algorithm, which enables the object to navigate along a predefined path. The simulation mathematical model is developed in the MATLAB/Simulink environment. In addition, by integrating the path-following algorithm with the two aerodynamic models, the dynamic behaviour of the aerodynamically controlled projectile can be compared. This allows for a more comprehensive analysis of the trajectory and the effects of each model on the desired flight path. Further research can explore the differences between the two models in greater detail and quantify their impact on unmanned projectile trajectory predictions, in addition to further exploring the specific characteristics and limitations of each model. This will involve analysing their assumptions, computational methods, and inputs to identify potential sources of error or uncertainty in the simulations. Moreover, these results have important implications for the design of aerodynamically controlled projectiles as well as a deeper understanding of aerodynamic mathematical modelling in flight simulation.

A 56-Year-Old Man with an Unusual Projectile Trajectory of Gunshot Wound at Head and Neck Region: A Rare Case Report

Background: Gunshot injuries to the neck are linked to a substantial risk of high mortality and morbidity due to the presence of critical vascular and vital structures. However, there are rare instances where a bullet trajectory through the neck region avoids damaging these vital structures. In this context, we report a specific case involving a 56-year-old male who presented to the emergency department with a gunshot wound to the right maxilla through the left anterior neck region.&#x0D; Case presentation: During the examination, a hematoma was observed in the left neck without an apparent entrance wound. The occurrence of a bullet injury to the neck without affecting any vital structures is exceptionally uncommon. Effectively managing patients with high-velocity penetrating injuries to the head and neck entails prioritizing tasks such as securing the airway, controlling hemorrhage, and promptly addressing any residual traumatic deformities for optimal outcomes. The presented case involves a gunshot injury to the head and neck, and a comprehensive review of the literature is provided.&#x0D; Conclusion: Gunshot injuries to the head and neck are complex and serious, demanding swift and thorough medical attention. The case emphasizes the significance of post-surgery monitoring for potential complications, contributing valuable insights to the ongoing discourse on managing such injuries.

Mathematical Model of Impact Projectile Flight Dynamics as an Element of its Digital Twin

This paper gives the analysis of the structure and characteristics of the mathematical model of the impact projectile’s flight dynamics. The model is designed for being used as an element of the projectile’s digital twin. The model is based on differential motion equations of a gyro-stabilized solid with an axisymmetric mass distribution. Different types of angle variables were chosen for describing aerodynamics and formulating equations of motion. Non-linear (considering the nutation angle) dependences for aerodynamic coefficients are proposed. They are created by applying proven scientific concepts and research methods in aerodynamics of axisymmetric body and by comparing with known numerical and experimental results obtained in exterior ballistics of gyro-stabilized aviation and artillery projectiles. Special aspects of initial conditions for angles and angular velocity were also studied. Since the impact projectile is considered as an axially symmetric body, its self-rotation angle is not of practical inte rest. Using algebraic manipulations, the differential equation for this angle was eliminated from the set of equations. This has made it possible to significantly reduce stiff of the remaining system of differential equations. The Dormand-Prince method is recommended as a method of numerical integration. The method of the eight-order (with seventh-order uncertainty estimate) allows getting the high accurate solution of the differential equations set under relatively small computing costs. The model allows computing the projectile trajectory under various initial conditions, including the flight with high nutation angles up to 87°—89°. As a result, there is a possibility to determine the nature of the interaction between impact projectiles and typical targets (ricochet, surface effect, after-penetration effect) within a wide range of approach angles to the target’s surface (skin) unattainable during the full-scale tests. The possibility of solving similar problems allows to recommend the designed model as an element of the impact projectile’s digital twin intended for testing its exterior ballistics on the digital (virtual) test range. All testing calculations and final modeling were made by using the "GNU Octave" computational software package.