Projectile Dynamics Research Articles

Compound cavity formation and splash crown suppression by water entry through proximally adjacent polystyrene beads

We move forward the important topic of water entry by documenting splash dynamics arising from the impact of hydrophilic spheres with buoyant millimetric microplastics, mimicked in our study by polystyrene beads. Collision with small, buoyant beads is yet another means to manipulate splash dynamics. In this experimental study, we investigate the fluid–structure interactions between beads and hydrophilic spheres for Froude numbers in the range of 20−100. Generally, hydrophilic spheres entering a liquid bath below the critical velocity of 8 m/s produce minimal fluid displacement and no cavity formation. The presence of proximally adjacent beads atop the fluid with respect to impacting spheres promote flow separation and compound cavities for sufficiently large Froude numbers, while suppressing the growth of splash crowns. Compound cavities consist of a shallow, quasi-static first cavity that seals near the water line, and a second, deeper cavity produced in the wake of descending spheres. A vertically protruding Worthington jet follows cavity collapse. The resulting splash metrics differ from those of hydrophobic spheres with respect to the properties of impacted beads. We find impactors traversing a deep liquid pool layered with beads experience drag reduction when compared to entry into a clean pool due to the drag-reducing benefits of flow separation while not offering a high inertial penalty. Our study unravels the physics behind the widely encountered interaction of solid projectiles impacting passively floating particles, and our results translate to the entry dynamics of water-diving creatures and projectiles into water bodies polluted by floating millimetric microplastics.

High-speed perforation of IN718 plates by spherical TC4 Ti alloy projectiles: Experiments and modeling

Data and knowledge on ballistic performance of Inconel-718 (IN718) alloy is critical for evaluating the resistance of turbine blades against foreign object impacts in aeronautical and astronautical industries. Ballistic perforation experiments (impact velocity 480 ms−1 to 1340 ms−1) with TC4 spherical projectiles (5-mm-diameter) are conducted on IN718 target plates (2-mm-thick) in this work, along with high-speed photography. The IN718 plates show multiple deformation and failure modes (bulging, dishing, petaling and plugging). The ballistic limit velocity for the investigated projectile/target combination is 823 ms−1. Postmortem material characterizations (optical photography, scanned electron microscopy and energy dispersive spectrometry) are conducted on recovered projectiles and bullet hole inner walls, and the observations indicate adiabatic shearing, surface melting and abrasion of projectile material. A finite element model based on the Johnson–Cook constitutive model and failure criterion is established, and reproduces the ballistic experiments. Dimensionless analyses are conducted on the dimensions of postmortem projectiles and bullet holes, and the projectile residual velocity/mass. On the basis of experimental observations and theoretical analysis of the projectile dynamics, the whole perforation process is divided into three stages (the entering, cratering and plugging stages). A multi-stage analytical model on perforation is then developed considering the effects of cavity expansion, projectile deformation and abrasion, and can well predict the projectile dynamics during entering and cratering stages.

CFD-DEM analysis of oblique water entry under a polar environment

Research on the water entry behavior of detectors passing through crushed ice zones in polar environments is essential for the exploration of polar oil resources. This study integrates computational fluid dynamics (CFD) and the discrete element method (DEM) with laboratory experiments to analyze projectiles' oblique water entry behavior through crushed ice zones. The investigation reveals that the unique polar environment, characterized by crushed ice accumulation, significantly influences the projectile's water entry behavior. Key parameters, such as water entry angle and the height of ice accumulation, are examined for their impact on the water entry process, flow field evolution, and projectile dynamics. The study identifies a complex multi-body coupling mechanism among the projectile, crushed ice particles, and fluid during oblique water entry. Crushed ice alters the cavity evolution and deflection patterns of projectiles, affecting the flow field dynamics. Variations in water entry angles modify the interaction patterns among the projectile, liquid level, and crushed ice, influencing cavity formation and fluid-ice coupling. Increasing crushed ice height enhances the coupling effects, leading to a greater degree of projectile deflection. These findings provide insights into optimizing detector design and launch strategies, contributing to more efficient oil exploration in polar environments.

The effect of particle shape on the dynamics of spherical projectile impacting into granular media

The effect of particle shape on the dynamics of spherical projectile impacting into granular media

Predicting projectile residual velocities using an advanced artificial neural network model

In this research, we delve into the fascinating dynamics of projectiles and their interactions with materials, with a keen focus on residual velocity — the speed a projectile retains after striking a target. This parameter is pivotal, especially when considering the design of protective barriers in various environments. Traditional methods of gauging residual velocity have been cumbersome, resource-intensive, and occasionally inconsistent. To address these challenges, we introduce an innovative approach using an Artificial Neural Network (ANN) model through MATLAB R2021a. This computerized tool, trained on a rich dataset from prior research, can predict residual velocities by considering multiple factors, including the initial speed of the projectile, its material and shape, and the thickness of the target. This paper meticulously details the development, training, and validation of the ANN model, highlighting its superior accuracy when compared to traditional methods like the Recht-Ipson model. The developed ANN model demonstrated remarkable performance compared to the Recht-Ipson model. During training, it exhibited a Mean Absolute Percentage Error (MAPE) of 0.0259 and a Root Mean Squared Error (RMSE) of 1.5993. For validation, MAPE was 0.0295, and RMSE was 2.2056. In contrast, the Recht-Ipson model displayed higher errors, with MAPE and RMSE values of 0.2349 and 14.1791, respectively. Furthermore, we discuss the potential of the ANN model in predicting not just residual velocities but also absorbed energy, showcasing its versatility. The practical implications of our findings are vast. From designing safer infrastructures in urban settings to enhancing armour systems in military applications, the ANN model's predictions can be a cornerstone for innovation.

Impact Dynamics Simulation for Magnetorheological Fluid Saturated Fabric Barriers

Abstract Experimental research has investigated the non-Newtonian fluid augmentation of fabric barrier materials, aimed at adding impact energy dissipation mechanisms and thereby improving ballistic performance. Published experimental results on the effectiveness of these augmentations are mixed, and numerical models supporting complimentary modeling research are lacking, primarily due to the multiple geometric and material nonlinearities present in the system. The combination of Hamiltonian mechanics with hybrid particle-element kinematics offers a very general modeling approach to impact simulation for these systems, one which includes interstitial fluid–structure interactions, the yarn level dynamics of projectile impacts, and yarn fracture without the introduction of slidelines and without mass or energy discard. Three-dimensional (3D) impact simulations show good agreement with published experiments for magnetorheological (MR) fluid-saturated Kevlar, including fabric tested under bulk field excitation of the target region and magnetomechanically edge-clamped fabric sliding in an excited air gap. The Hamiltonian method employed to develop the system-level model allows for computationally efficient partitioning of the modeled physics while maintaining a thermodynamically consistent formulation.

Linear Parameter-Varying Polytopic Modeling and Control Design for Guided Projectiles

In this paper, a linear parameter varying (LPV) modeling and control design approach is applied to a new class of guided projectiles, aiming to exploit the advantages of the LPV framework in terms of guaranteed stability and performance. The investigated concept consists of a planar symmetric 155 mm fin-stabilized projectile equipped with a reduced amount of control actuators and characterized by a predominantly unstable behavior across the analyzed flight envelope. A dedicated modeling procedure allows reformulating the nonlinear projectile dynamics as a LPV polytopic system, employed for the controller design. The procedure intends to reduce the computational complexity and the conservativeness affecting the overall controller synthesis. A trajectory-tracking simulation scenario is performed in a realistic simulator environment to assess the performance of the resulting LPV polytopic autopilot across the entire flight envelope.

Experimental Study and Numerical Calculation of Projectile Dynamic Engraving Process

The high temperature and pressure gas in the combustion chamber pushes the projectile towards the muzzle during the firing of the gun. The projectile belt is squeezed and deformed by the forcing cone. In order to study the dynamic engraving characteristics of the projectile, a short-barrel gun launcher was designed for experimental research. The projectile dynamics and projectile base pressure curves during the engraving process were obtained. Based on the experimental loading conditions, the J-C elastic-plastic model was used to numerically simulate the dynamic engraving process of the copper elastic belt. The deformation process of the elastic belt and the change characteristics of the resistance after the elastic were studied and the intrusion displacement obtained by the numerical calculation was compared with the experimental results and the results are consistent.

Dynamic Simulation and Research of Land-Based Missile Tilt Launch Platform

In order to study the influence of the structural factors of the launch device on the missile tilt projectile dynamics, a dynamic model of the missile tilt launch platform was established based on the finite element method. The effects of shock absorber stiffness, angle between shock absorber and horizontal plane and tilt of the launch device were studied on the missile and launch platform’s ejection response characteristics. The research results show that the greater the rigidity of the shock absorber, the smaller the angle between the shock absorber and the horizontal plane, and the smaller the vibration amplitude of the initial disturbance of the missile and the launch cylinder; when the tilt angle of the launch device is within 6 °, the angle change has a smaller impact on the speed of the missile outlet, and there is a sufficient safety distance between the missile and the launch canister during the launch process. The larger the vibration amplitude of the initial disturbance and the launch tube. The research results can provide a theoretical reference for the design and optimization of the tilted launch platform.

Analysis of the cavity evolution law of the projectile passing through the underwater ice-hole

It is essential for the launch of polar ocean detectors to study the water entry behavior of projectiles passing through underwater ice-holes. In this paper, numerical simulation combined with overlapping grid technology and a volume-of-fluid (VOF) model is used to study the cavity dynamics of projectiles passing through underwater ice-holes, and the variations of velocity circulation and the movement stability of the projectile are also studied. The results show that the cavity experiences the process of first shrinking and then expanding when the projectile passes through the underwater ice-hole, and unique “cavity splash crown” and “combined cavity” are generated. The presence of the hole affects the velocity circulation and vector around the projectile. The parameters of the holes have a strong influence on the cavity dynamics. When a projectile passes through a large-sized underwater ice-hole, the cavity size inside the hole (hnr) increases, the cavity size at the upper border of the hole (hur) decreases, and the cavity length (hcr) after pinch-off increases; additionally, the amplitude of force and velocity fluctuations decreases, and the projectile's movement stability increases. The ability of the cavity at the top border of the hole to expand and contract is reduced when the hole is farther away from the free liquid surface, the area of the cavity that wraps the projectile after pinch-off is also reduced, and the trajectory of the projectile shows obvious deflection during this process.

Ab initio electronic stationary states for nuclear projectiles in solids

The process by which a nuclear projectile is decelerated by the electrons of the condensed matter it traverses is currently being studied by following the explicit dynamics of projectile and electrons from first principles in a simulation box with a sample of the host matter in periodic boundary conditions. The approach has been quite successful for diverse systems even in the strong-coupling regime of maximal dissipation. This technique is here revisited for periodic solids in light of the Floquet theory of stopping, a time-periodic scattering framework characterizing the stationary dynamical solutions for a constant velocity projectile in an infinite solid. The effect of proton projectiles in diamond is studied under that light, using time-dependent density-functional theory in real time. The Floquet quasienergy-conserving stationary scattering regime, characterized by time-periodic properties such as particle density and the time derivative of energy, is obtained for a converged system size of 1000 atoms. The validity of the customary calculation of electronic stopping power from the average slope of the density-functional total energy is discussed. Quasienergy conservation, as well as the implied fundamental approximations, are critically reviewed.

Coupled extreme learning machine and particle swarm optimization variant for projectile aerodynamic identification

Accurate aerodynamic parameters are the basis for the research of uncontrolled projectile drop point dispersion and precise strike. The traditional methods for aerodynamic parameters rely strongly on the projectile dynamics system. To weaken the influence of kinetic effects, an extreme learning machine (ELM) optimized by particle swarm optimization (PSO) is applied. However, the iterative optimization process of PSO makes the algorithm more complicated and impairs the real-time performance of ELM. To accelerate the convergence of PSO, a new hybrid optimization strategy is proposed. The hybrid optimization strategy combines the advantages of the chaos optimization strategy, the adaptive update strategy, and the mutation strategy. The chaos optimization strategy optimizes the distribution of the initial swarm to improve the optimization efficiency of PSO. The adaptive update strategy tunes the velocity inertia weight based on the value of the evolutionary factor to match the current searching state of the particles. The mutation strategy mutates the particles to break out of the local convergence. Numerical experiments show that the introduction of the hybrid optimization strategy enables ELM to exhibit excellent robustness, real-time performance, and accuracy in noisy environments. The hybrid algorithm has excellent prospects for application and extension for the parameter identification of dynamic systems in complex environments.

Influence of Inter-Particle Friction and Damping on the Dynamics of Spherical Projectile Impacting Onto a Soil Bed

This study investigates the dynamics of a spherical projectile impact onto a granular bed via numerical simulations by discrete element method (DEM). The granular bed is modeled as an assembly of polydisperse spherical particles and the projectile is represented by a rigid sphere. The DEM model is used to investigate the cratering process, including the dynamics of the projectile and energy transformation and dissipation. The cratering process is illustrated by tracking the motion of the projectile and granular particles in the bed. The numerical results show that the dynamics of the projectile follows the generalized Poncelet law that the final penetration depth is a power-law function of the falling height. The numerical results can match well the experimental data reported in the literature, demonstrating the reliability of the DEM model in analyzing the impact of a spherical projectile on a granular bed. Further analyses illustrate that the impact process consists of three main stages, namely the impact, penetration and collapse, as characterized by the evolution of projective velocity, strong force chains and crater shape. The initial kinetic and potential energy of the projectile is dissipated mainly by inter-particle friction which governs the projectile dynamics. The stopping time of projectile decreases as the initial impact velocity increases. The final penetration depth scales as one-third the power of total falling height and is inversely proportional to the macroscopic granular friction coefficient.

Quasi-LPV Modeling of Guided Projectile Pitch Dynamics through State Transformation Technique

In this paper, we develop a reliable Linear Parameter-Varying (LPV) model of the pitch channel dynamics of a fin-stabilized projectile. Among the available LPV design approaches, the State Transformation is analyzed, being particularly suitable for a class of systems defined as output nonlinear, and compatible with the projectile dynamics formulation. The State Transformation provides a quasi-LPV representation, which corresponds to an exact transformation of the original nonlinear model, preserving relevant couplings that are usually lost through the classical approximation methods. Some important considerations regarding the limitations of this approach are also discussed and verified in the missile dynamics. The accuracy of the obtained quasi-LPV model is assessed by means of open-loop simulations, comparing the performance to the original nonlinear model at selected flight conditions.

External dynamics of OF-462Z he projectiles

Theoretical studies of the determination of the components of the air resistance forces to the projectile's propulsion are quite complex and do not always give the desired accuracy of calculations. Therefore, the main methods for their determination are experimental studies. The most common method is to conduct special firing at landfills. This allows us to estimate the integral value of the air resistance forces and to determine the value of certain parameters of the dynamics of projectile movement. Based on the results of the firing range and theoretical studies, tables of firing on ground targets by artillery shells were constructed. In the case of firing under conditions other than normal, corrections must be made. Formulas for determining their values, are obtained, preferably, by decomposing the corresponding dependences into a numerical series taking into account its first terms. If the values of the parameters change slightly, then the values of the amendments give little discrepancy with the practice of their application. However, otherwise, the differences become significant.In this article a mathematical model for determining the functional dependence of the magnitude of the frontal air resistance force of the projectile on its velocity, mass and caliber, temperature and density of air, atmospheric pressure, speed of sound in air is investigated and proposed by the authors. Functional dependence has the same form of recording when a projectile moves with supersonic or subsonic speeds, but the values of their coefficients are different. To determine their values, the inverse dynamics problem is solved, that is, knowing the results of experimental studies for this type of projectile by the method of iteration, their values are selected.Based on the proposed mathematical model kinematic parameters of the movement of HE projectiles OF-462Z 122 mm caliber were determined and the values of the corrections if the air temperature is different from the standard were obtained.Therefore, the proposed mathematical model of determining the functional dependence of the magnitude of the frontal air resistance force of the projectile’s movement allows us to investigate the influence of deterministic and non-deterministic factors on the kinematic parameters of the motion of the projectile that is to determine the magnitude of corrections and to create the appropriate software.

The viscoelastic-like response of a repulsive granular medium during projectile impact and penetration

We study experimentally the penetration of a projectile into a two-dimensional granular bed composed of magnetic repelling grains. The projectile can experience either repulsive, attractive or neutral interaction with the particles generating different dynamics: i) the repulsive intruder compresses the granular bed without contact and experiences rebounds before stopping; ii) the attractive intruder is first accelerated when it approaches the bed, then, some magnets attach to its surface increasing its effective diameter and the drag force acting on the intruder until it reaches the repose; and iii) the neutral projectile penetrates deeper into the granular bed than in the two previous cases because there is no magnetic interaction with the particles. In addition, we developed molecular dynamics simulations able to reproduce the experimental results and used to determine the effect of the magnetic strength and the role of friction between the particles and the container walls. The results show that the medium behaves similar to a viscoelastic micellar fluid on impact, and the projectile dynamics can be modelled by a spring-dashpot model. Our findings can be useful in the design of new magnetic granular dampers.

Water-entry behavior of projectiles under the protection of polyurethane buffer head

The water entry behaviors of projectiles with cylindrical buffer head were studied experimentally and theoretically, focusing on projectile dynamics and impact reduction. Based on the elastic, perfectly plastic, strain rate dependent, compacting model, the equation of motion was developed for the projectiles to describe their motion before compaction of the buffer. The validity of the equation was proven both experimentally and numerically. The peak deceleration of the projectiles was investigated by numerical simulations in LS-DYNA using Lagrange–Euler coupling, and an empirical formula was proposed to accurately describe the impact reduction based on the experimental and numerical results. When the impact velocity and buffer dimension were held constant, an optimum buffer density existed for the reduction of impact by the buffer head. At a constant buffer density, the impact was larger when the initial velocity increased or when the buffer had a larger cross section compared with its length. Good agreements were observed between the analytical and experimental results.

Water entry behaviours of hemisphere-head projectiles with high velocity

The water-entry behaviours of projectiles with hemisphere-head were studied experimentally and theoretically, focusing on projectile dynamics and drag coefficient. Based on equivalent cone theory proposed by Baldwin, the equation of drag coefficient was developed to describe the resistance of hemispherical head projectiles from the time when the projectile contacts the water to the time the hemispherical head is submerged. A set of experimental apparatus was set up to record the water-entry process by high-speed photography, the variation of resistance during water-entry was obtained experimentally. Compared the acceleration calculated by conventional method, new method and experimental results, the new method is more consistent with the experimental value.

Study on the chaotic dynamics in yaw–pitch–roll coupling of asymmetric rolling projectiles with nonlinear aerodynamics

To predict the coning motion forms of a rolling projectile with configurational asymmetries, the nonlinear characteristics for the system are investigated in this paper. The nonlinear dynamic model of rolling projectiles in coning motion is built by considering the nonlinear aerodynamics and roll orientation-dependent aerodynamics. The configurational asymmetry is modeled as a periodically parametric excitation in order to study its effect on the periodic response stability of the rolling projectile. Numerical continuation method is resorted to determine the parametric zone for the steady motions, and the possible stable rotational speeds are discussed. The numerical simulations, Lyapunov exponent spectrum analysis and Poincaré sections are performed to confirm the existence of chaotic coning motion. The results shown in this study not only contribute to an in-depth understanding for the nonlinear dynamics of rolling projectiles but also provide an important reference for the further study of the control design for the yaw–pitch–roll coupling of asymmetric rolling projectiles with nonlinear aerodynamics.

Study on flight dynamics of flexible projectiles based on closed-loop feedback control

Since projectiles with large slenderness ratio are prone to elastic deformation, the effect of structural deformation is necessary to be taken into consideration for dynamic modeling. In order to obtain the precise aerodynamic performance and flight dynamic characteristics of flexible projectiles, a new numerical flight simulation system is developed based on computational fluid dynamics and generalized dynamic-mesh technique. Furthermore, flight dynamic stability of a typical flexible projectile is carried out in detail by introducing PID controller. By means of installing the sensors at various locations, the effect of different mode shapes on the characteristics of the closed-loop flight dynamic system is researched. Numerical results indicate that, when the disturbance due to elastic vibration is added into the mixed signals gained from the angular velocity/acceleration sensors, the feedback response of the closed-loop system becomes adversely divergent. In contrast, the stability of the closed-loop system is not sensitive to the elastic disturbance added to the centroid velocity and acceleration. Moreover, the stability of closed-loop system is much less affected by the unsteady aerodynamic loading due to elastic vibration than the interference of the elastic vibration on the dynamic signals detected by the sensors. The phenomenon can be explained by the requirement on the stability of the long and short period modes of flight dynamics, which can provide some guidance for the layout of the sensor and the design of control system of the projectiles with large slenderness ratio.