Projectile Acceleration Research Articles

Analysis and Decoupling Study of the Coupling Effects on Projectile Acceleration Parameters

Abstract Internal ballistic parameter testing is crucial for evaluating artillery performance and design, with projectile acceleration being a core parameter. During the firing process, projectile acceleration parameters can easily be coupled with the projectile’s modal effects and the transverse effects of triaxial accelerometers, leading to inaccurate measurements. Therefore, this paper innovatively proposes a data decoupling method to improve the accuracy of acceleration measurements. Firstly, the internal ballistic firing mechanism and the transverse effects of triaxial accelerometers are analyzed. Secondly, a simulation analysis of the projectile modal is conducted, combined with the projectile’s motion state within the barrel, to determine the modal orders and frequencies under axial stretching and compression vibration modes. Thirdly, shock tests are performed on triaxial accelerometers using a shock table to establish the relationships between triaxial acceleration signals. Finally, the projectile modal, Empirical Mode Decomposition (EMD), and the transverse effects of triaxial accelerometers are combined to decouple the acceleration signals. A comparison between the decoupled acceleration signals and theoretical data shows that the error is reduced from 8.1% to 3.2%, significantly improving the accuracy of the acceleration signals.

Dynamic analysis of natural supercavitating flow during acceleration and deceleration of an axis-symmetric projectile

Supercavitation is an effective drag reduction technology for high-speed underwater vehicles. However, the evolution of supercavitating flow becomes more complex during acceleration and deceleration compared to steady-state conditions. This paper examines the unsteady supercavitating flow around an axis-symmetric projectile with disk cavitation subjected to various speed transitions. By utilizing the volume of fluid method, the large eddy simulation turbulence model, and the Kunz cavitation model, the study simulates and validates the dynamic behavior of the multiphase flow against experimental and published data. The cavity evolution during acceleration and deceleration is observed in three distinct stages. In the case of acceleration, the stages include initial stabilization, merging of the leading edge and shoulder cavities, and full supercavitation. For deceleration, the stages involve cavity collapse, trailing-edge cavity separation, and shoulder cavity formation. The study also highlights the presence of cavitation hysteresis, especially at higher acceleration and deceleration rates, which influences flow stability and drag reduction. This research provides insights for optimizing the design and control of high-speed underwater vehicles, where stable cavity formation is crucial for minimizing drag. Understanding how acceleration and deceleration influence cavity evolution can guide the refinement of cavitation designs and control strategies, improving vehicle performance during dynamic maneuvers.

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.

A measurement method of in-bore projectile motion acceleration based on bottom pressure correction

Due to factors such as high temperatures, elevated pressures, and severe high-frequency shocks in the bore, there is considerable noise interference in acceleration test signals. This makes it challenging to accurately measure projectile motion acceleration using existing methods. To address this issue, we propose an advanced measurement approach that uses bottom pressure correction. Our model suggests a significant correlation between projectile motion acceleration and thrust. By utilizing the correlations between bottom pressure and motion acceleration in both temporal and frequency domains, we can improve the accuracy of acceleration measurements. Based on these insights, we have developed a novel testing system that synchronously measures bottom pressure and acceleration, using bottom pressure as a corrective mechanism for the measured acceleration signals. Empirical results show that the maximum relative error in peak motion acceleration is only 4.86%, demonstrating the effectiveness of our proposed method.

Dynamic measurement of ballistic impact using an optical fibre sensor

An optical fibre-based sensor is developed for measuring the dynamics of the back face deformation of soft body armor. The measurement system consists of embedding an optical fibre into a thin silicone mat to increase survivability. The silicone sensor mat is placed between the soft body armor and the backing material. The optical fibre experiences times of sticking and slipping. The portions of the impact with the optical fibre stuck are reconstructed into slipping-equivalent strain using exponential extrapolation from adjacent slipping portions. The strain on the optical fibre is related to the projectile acceleration when the optical fibre is slipping. The strain is measured with the optical fibre sensor using a fibre Bragg grating. The system is characterized using a gas gun in combination with high-speed imaging. The system is experimentally demonstrated at the Army Test Center in Aberdeen, MD. Of the 23 shots 17 had an error less than 10%.

Effect of modified method based on recoil motion on interior ballistic performance of ultralight high-low pressure artillery

Light gun is of unique application prospect for its low body mass and projectile initial velocity. In order to solve the problem of calculation error caused by the large free recoil velocity of light artillery in traditional interior ballistic model, a more suitable internal ballistic model for ultralight artillery was proposed through the design and test of a light gun, the accuracy of the algorithm was verified. The model described the effect of the recoil motion of the gun on chamber pressure and projectile acceleration travel, which made the calculation result more accurate when the gun mass was lighter. Compared with the experimental data, the errors of the calculation results using the improved algorithm were 2.90 % and 0.33 % respectively, while that using the traditional algorithm were 20.38 % and 10.02 % respectively. At the same time, the extended calculation was carried out to analyze the impact of the buffer device on the interior ballistic performance. The result showed that the lighter the gun, the greater the improvement brought by the buffer device under the same mass and recoil resistance. When the mass of the projectile and the gun was both 3 kg, the resistance of 70 kN could increase the velocity of projectile by 16.2 %. Furthermore, the internal ballistic elements of the traditional algorithm and the improved algorithm were calculated respectively under the same working conditions. It was found that when the mass of the gun is 8.567 times the mass of the bullet, the error of the two algorithms was less than 1 %, and the error increased gradually with the mass ratio of gun and projectile decreasing.

Strain gauge-based method to determine in-cylinder projectile velocity and gas pressure

Knowledge of internal ballistic pressure and projectile velocity is required to ensure gun safety, reliability, calculation of its range, and evaluation of ammunition. However, existing methods for determining the same are either overly complex, costly or have limitations in their applicability. In this work, the authors address this need by proposing a reliable, simple, cheap, and non-destructive method for determining in-bore pressure, projectile velocity, and acceleration profile using strain measurements. Data from strain gauges were used to detect the projectile’s arrival time at different locations in the barrel and computed projectile velocity and acceleration as a function of projectile position. Finally, acceleration data was used to calculate the pressure behind the projectile. Results were verified using alternative experimental and simulation techniques on two different barrels with different ammunition. It was found that the proposed method works well and thus can be reliably used in similar applications elsewhere.

Simulation of blast propagation and structural effects of accidental hydrogen-air-mixture explosion in a two-stage light-gas gun laboratory for hypervelocity impact experiments

Two-stage light-gas guns allow to accelerate projectiles up to velocities of several kilometers per second to conduct impact experiments. The projectile acceleration is obtained through a mechanism that relies on the expansion of a light gas, such as helium or hydrogen. Hydrogen allows to employ higher projectile velocities and masses than helium, together with lower wear of the launch tube. However, its use requires a thorough assessment of potential risks of explosion. In this work, we present a combined blast and structural numerical analysis to evaluate the effects of hydrogen deflagration as a consequence of accidental leakage scenarios during the operation of a two-stage light-gas gun. As a test case, we study the Large Gun operated at Fraunhofer EMI in Freiburg, Germany. The possible failure of non-structural elements, such as doors and windows, and the subsequent blast propagation into areas adjacent to the room hosting the facility are also accounted for. The simulation procedure presented in this work is scalable to similar and larger facilities for impact research as well as to other contexts involving analogous risks of gas explosions.

An Improved Pulsed Power Supply Circuit for Reluctance Electromagnetic Launcher Based on Bridge-Type Capacitor Circuit

The reluctance electromagnetic launchers mainly use the driving coils to generate high magnetic field to accelerate the ferromagnetic projectiles. Its advantages in accelerating large-mass projectiles have attracted considerable attention. However, during the projectile acceleration of conventional reluctance electromagnetic launchers, residual currents in the drive coils may produce opposing forces that reduce launch speed and efficiency. For this issue, an improved pulsed power supply circuit for reluctance electromagnetic launchers is proposed in this article based on a bridge-type capacitor circuit. The circuit can quickly reduce the residual current of the driving coil and recover the residual current energy. Since the circuit uses the same capacitor to power the drive coil and recover the remaining energy, the remaining energy recovered by the capacitor can be used as the initial energy storage for a new cycle. This can shorten the charging time for new cycles. In this article, the basic principle of the improved pulsed power supply circuit is introduced and analyzed in detail, and a comparative analysis is carried out with the traditional circuit through simulation. The results show that the new circuit has better characteristics in terms of residual energy recovery.

Effect of asymmetric nose shape on the cavity and mechanics of projectile during high-speed water entry

The characteristics of cavity evolution and motion in water entry created by an asymmetrical nose shape projectile at some different dimensionless excision radius are numerically investigated. CFD numerical methods are used to simulate the high-speed water entry process, the cavitation evolution, flow field and force of the projectile are monitored. The numerical results show that when the projectile enters the water with an asymmetrical nose shape, the cavity bends, and with the increase of dimensionless excision radius, the expansion and contraction speed of cavity increase, and the anticlockwise deflection angle of cavity decreases. The pressure of projectile surface shows an obvious asymmetry, and area of low pressure at the edge of the asymmetric surface is found. Meanwhile, there are two peaks of acceleration while water entry, the deflection of the projectile trajectory is caused by the asymmetric nose shape, and with the increase of dimensionless excision radius, the projectile acceleration decreases, the displacement on y direction increases, and the projectile deflection velocity decrease.

An Electromagnetic Circuit Design to Improve a Multi-Stage Coil-Gun’s Energy Conversion Efficiency

We present in this paper a method of improving a coil gun circuit’s energy efficiency and acceleration performance. Particularly, the improvement was performed by designing a solenoid coil and capacitance for projectile velocity enhancement in a multi-stage coil gun, based on simulations and experiments. A projectile decelerates in coil guns when passing through the solenoid coil’s center by being subjugated to a force opposing the launch direction. Thus, we achieved the efficient distribution of the electromagnetic power delivered from the circuit to the projectile by adjusting the capacitance according to the solenoid coil’s shape. This produced a current shape suitable for projectile acceleration, consequently enhancing its performance. Designing the coil using 1.3 mm diameter copper wires, among the coils using copper wires of various diameters, to increase the number of turns and reduce the capacitance improved the energy efficiency while enhancing the acceleration performance. Finally, each stage’s measured and simulated velocities in the coil gun were analyzed and compared. Accordingly, we arrived at an efficient design method for multi-stage coil gun systems.

Sudden Slide Mechanism of a Rock Block in Road Cutting Slope with Soft and Hard Interlayered Bedding Structure Based on Energy Balance Theory

After the road excavation of the hard and soft interlayered bedding slope in the mountainous region's valley area, the bedding slope often results in a catastrophic phenomenon, especially in the project's construction and operation where existed severe safety hazards. A geomechanical two-component model consisting of the slider and the underlying layer is proposed to analyze the rock block instability under the fissure water pressure, the shear deformation, and the compression deformation. The slider's complex stress field is derived by using elastic mechanics. The incremental energy equilibrium Equation is established based on the energy balance theory, and the generalized sliding force relative function of the slider and the generalized shear force relative function of the underlying soft rock are obtained. The deformation energy accumulation, transfer, and energy dissipation characteristics are analyzed. Put a rock slide in the bedding rock cutting slope happened at Jiaojiatan, Pengshui County, Chongqing municipality, China as a case. Results indicate that considering both the compression deformation and the shear deformation of the slider, the kinetic energy, the rapid launch speed of the projectile, the average projectile acceleration, and the failure stroke increase about 15.7 times, 4.0 times, 1.8 times, and 8.9 times respectively than that of only considering the shear deformation, and the dynamic disaster intensity is more severe and worthy of attention. The results that ignored the fissure water pressure and the compressive deformation energy coincide with the existing literature, which verifies the reasonable applied method in this paper. Considering the slider's different displacements and the height-length ratios, when the energy ratio function that represents the ratio of the incremental compression energy to the incremental shear energy concludes that when the range of the height-length ratio is between 0 to 0.95(flat and narrow sliders), the compression energy's contribution to the system's elastic energy should be taken into consideration. The advantage of the energy balance method applied in the stability analysis of the bedding rock slope is that the potential unstable rock block's status can be predicted dynamically according to the variation of the underlying soft rock's deformation and that the elastic impact dynamic parameters can also be obtained compared with other instability analysis approach.

Pressure- and Size-Dependent Aerodynamic Drag Effects on Mach 0.3–2.2 Microspheres for High-Precision Micro-Ballistic Characterization

The acceleration of microparticles to supersonic velocities is required for microscopic ballistic testing, a method for understanding material characteristics under extreme dynamic conditions, and for projectile gene and drug delivery, a needle-free administration technique. However, precise aerodynamic effects upon supersonic microsphere motion at sub-300 Reynolds numbers have not been quantified. We derive drag coefficients for microspheres traveling in air at subsonic, transonic, and supersonic velocities from the measured trajectories of microspheres launched by laser-induced projectile acceleration. Moreover, the observed drag effects on microspheres in atmospheric (760 Torr) and reduced pressure (76 Torr) are compared with existing empirical data and drag coefficient models. We find that the existing models adequately predict the drag coefficient for subsonic microspheres, while rarefaction effects cause a discrepancy between the model and empirical data in the supersonic regime. These results will improve microsphere flight modeling for high-precision microscopic ballistic testing and projectile gene and drug delivery.

Penetration dynamics of steel spheres into a ballistic gelatin: Experiments, nondimensional analysis, and finite element modeling

Ballistic gelatin is widely used as a simulant of soft tissues, and its dynamic responses to high-speed projectile penetration are critical for understanding soft tissue damage, wound ballistics, and protection gear design. Here, we investigate penetration dynamics of spherical steel projectiles with different diameters into a ballistic gelatin at different incident velocities. The projectile diameter ranges from 1 mm to 5 mm, and the incident velocity, from 50 m s−1 to 400 m s−1. Penetration dynamics is captured with high-speed photography. A power-law relation is found between the maximum penetration depth and projectile kinetic energy at high incident velocities, but not at intermediate and low velocities. Nondimensional analysis is applied to the penetration depth; a general relation is established for nondimensional maximum penetration depth as a function of projectile density, projectile diameter and projectile incident velocity for low-, intermediate- and high-speed penetration, and this relation can accurately describe the experiments. The drag force of projectile is analyzed to explain the relation between projectile acceleration and velocity. In addition, a calibrated finite element model reproduces well experimental observations such as the maximum penetration depth and projectile trajectory.

Three-Dimensional Numerical Modeling of Internal Ballistics for Solid Propellant Combinations

The processes that take place within the Internal Ballistics cycle of an artillery round are highly influenced by geometric effects. They are also highly affected by the presence of a combination of energetic materials, such as the propellant, igniter, primer, and the combustible cartridge cases. For a more realistic simulation of these phenomena, a multidimensional and multicomponent numerical model is presented, based on adaptations and improvements of previous models of conservation equations, maintaining a two-phase, Eulerian–Eulerian approximation. A numerical method based on Finite Volumes and conservative flux schemes (Rusanov and AUSM+), with the ability to predict detonation effects, is proposed. As a result, a versatile 3D numerical code was obtained that was tested in the simulation of artillery firing with conventional and modular charges (MACS). Results show the code is able to characterize the heat and mass transfer of the different energetic materials during the combustion of the propellant and the cartridge cases, the gas expansion, and the projectile acceleration.

Characteristics of cavity collapse behind a high-speed projectile entering the water

We investigate cavity collapse regimes behind high-speed projectiles entering the water. Using numerical simulations, we confirmed two different collapse phenomena: deep pinch-off and consecutive collapse. We performed a theoretical analysis to develop the relationship between projectile motion and cavity evolution. We found that projectile acceleration is the most significant factor determining the initial cavity collapse. There is a critical acceleration determining the direction of cavity collapse at the location of deep pinch-off. The pressure field is obviously affected by the collapse. The increase in pressure induced by surface pinch-off accelerates the collapse at the cavity tail. Because of the impact of surface pinch-off, consecutive collapse can be seen if a projectile reaches critical acceleration near a free surface. Otherwise, the cavity will pinch off at a distance from the surface of the water and form a deep pinch-off. Particular attention is paid to the impact of consecutive collapse on the projectile. Numerical calculations show that cavity collapse and a high-speed water jet have an obvious impact on the stability of the projectile. The jet exerts great pressure on the projectile, and the accompanying splash droplets contaminate the cavity wall. Cavity pulsation and the asymmetric geometry of the projectile-cavity system aggravate attitude deflection.

The Adhesive Response of Regolith to Low-Energy Disturbances in Microgravity

Abstract Small, airless bodies are covered by a layer of regolith composed of particles ranging from μm-size dust to cm-size pebbles that evolve under conditions very different than those on Earth. Flight-based microgravity experiments investigating low-velocity collisions of cm-size projectiles into regolith have revealed that certain impact events result in a mass transfer from the target regolith onto the surface of the projectile. The key parameters that produce these events need to be characterized to understand the mechanical behavior of granular media, which is composed of the surfaces of small bodies. We carried out flight and ground-based research campaigns designed to investigate these mass transfer events. The goals of our experimental campaigns were (1) to identify projectile energy thresholds that influence mass transfer outcomes in low-energy collision events between cm-size projectiles and μm-size regolith, (2) to determine whether these mass transfer events required a microgravity environment to be observed, and (3) to determine whether the rebound portion of these collision events could be replicated in a laboratory drop tower environment. We found that (1) mass transfer events occurred for projectile rebound accelerations <7.8 m/s2 and we were unable to identify a corresponding impact velocity threshold, (2) mass transfer events require a microgravity environment, and (3) ourdrop tower experiments were able to produce mass transfer events. However, drop tower experiments do not exactly reproduce the free-particle impacts and rebound of the long-duration microgravity experiments and yielded systematically lower amounts of the overall mass transferred.

Dynamics of Precision Guided Projectile Launch: Solid–Solid Interaction

Precision guided projectiles (PGPs) experience severe shock loads during launch emanating from the propellant gases inside the barrel and the surrounding air. The complex flow environment that exists within the confined space of the barrel and at muzzle exit is greatly influenced by the supersonic speed of the projectile, the compressibility of the air, and the rapid state transition of the projectile from the confined volume of the barrel to the surrounding free-space. In our earlier efforts (X. W. Yin, P. Verberne and S. A. Meguid, Multiphysics modelling of the coupled behaviour of precision-guided projectiles subjected to intense shock loads, Int. J. Mech. Mater. Des. 10 (2014) 439–450; P. Verberne and S. A. Meguid, The coupled behaviour of precision-guided projectiles subject to propellant induced shock loads using multiphysics analysis, in 8th Int. Conf. Mech. Mater. Des. (2019); P. Verberne and S. A. Meguid, Dynamics of precision guided projectile launch: Fluid-structure interaction, Acta Mech. (2020)) examined the fluid–solid interaction problem. In this paper, we expand our earlier effort by examining the underlying mechanisms associated with the solid–solid interaction between the projectile and the barrel walls that severely govern the survivability of the embedded electronic systems (EES). This was achieved by conducting comprehensive finite element (FE) simulations of the dynamics of the entire launch process of a projectile accounting for the intense combustion pressures of the propellant, the large accelerations experienced during the launch and the induced shock waves. Our FE simulations successfully capture the interaction of the projectile with the barrel. Our work reveals that frictional forces due to contact inside the barrel significantly affect the projectile’s acceleration response at muzzle exit. Immediately following muzzle exit, the rapid reduction of the frictional forces inside the barrel results in a rapid increase of the projectile acceleration followed by a rapid reduction due to the free expansion of the propellant gases and air drag, leading to large acceleration fluctuations.

A Comparison of Half and Quarter Space Penetration into Granular Media

Abstract In this study, two experimental techniques are compared for the purpose of visualizing projectile penetration at speeds ranging between 60 and 150 m/s into granular media. The two techniques are half space penetration into a transparent synthetic soil surrogate and quarter space penetration of an opaque natural sand and transparent soil surrogate against an observation window. In both techniques a pneumatic projectile accelerator was employed to launch the projectiles, and high-speed imagery was employed to visualize the penetration events unintrusively. Transparency in transparent targets was achieved by saturating angular fused quartz with a refractive index matched pore fluid made of sucrose. Comparison of both techniques suggests that their results are complimentary. In particular, the terminal depth of penetration is not significantly inhibited by shooting in quarter space. Additionally, both techniques permitted visualizing distinct dilation zones ahead and around penetration. Each technique offers a number of distinct advantages. In particular, half space penetration reduces the possibility of projectile diversion and is much safer, whereas quarter space penetration allows for visualizing penetration into opaque targets at a finer scale than that achieved in half space penetration.

Study of the influence of electrical parameters on launch performance of projectile from the single-stage reluctance coil launcher

To increase the exit velocity of projectile from single-stage reluctance coil launcher, the theoretical analysis is conducted for the projectile acceleration principle. The influence law of the electrical parameters on the projectile velocity is obtained, by the imitation research about the influence rule of the variation of electrical parameters (including capacitor voltage and capacitance) in a single-stage reluctance coil emitter on the transmitting performance, using the two-dimensional transient field solver in the finite element analysis software of Ansoft. At the same time, the single-stage reluctance coil launcher is also set up to conduct relevant tests, and the correctness of simulation analysis is verified. The results show that increasing the voltage and capacitance of the capacitor is beneficial to increase the exit velocity of the projectile, in the condition that the relative position of the projectile and driving coil is constant, The capacitor voltage is less than 1000V, and the capacitor capacitance is less than 1500μF. The simulation and experiment results provide guidance for the related analysis and study of multi-stage reluctance coil launcher.