Side wind and tank speed influence on lateral displacement of the projectile

This article indicates the scope of the formula for determining the magnitude of the lateral displacement of the projectile under the action of crosswind, which is used in the compilation of firing tables. This formula is valid under the following conditions: the force of frontal air resistance to the motion of the projectile is proportional to the its velocity squared; wind speed components are much smaller than the horizontal component of projectile velocity; the projectile velocity projections on the Oy and Oz axes are much smaller than the projections on the Ox axis; the dimensionless coefficient of resistance and the magnitude of the crosswind are constant values. However, in reality, the force of frontal air resistance to the motion of the projectile is only sometimes proportional to the its velocity squared; the projectile velocity projections on the Oz axis may be are much smaller than the projections on the Ox axis and may even be greater than it; the coefficient of resistance is depends on the value of the Makh number, so it can be considered constant only when shooting at short distances. The authors propose a mathematical model for determining the magnitude of the lateral displacement of the projectile under the action of crosswinds. It is believed that the force of the crosswind on the projectile depends on the following factors: air density; the maximum area of the longitudinal section of the projectile; the difference between the value of the lateral component of the wind speed and the speed of the lateral displacement of the projectile, which is raised to a certain power. The magnitude of the values of the lateral displacement of the projectile under the action of the crosswind when shooting at short distances, determined based on the proposed mathematical model, slightly differ from the values of the lateral displacement specified in the firing tables. However, with increasing firing distance, the difference between these values is constantly increasing and the value of the lateral displacement of the projectile determined theoretically is much larger than indicated in the firing tables. In addition, in this research the influence of the tank velocity on the value of the projectile lateral displacement taking into account the action of the crosswind is studied.

Impact and Ricochet of a High Speed Projectile from a Plate

A computational study of a projectile (either 2024 aluminum or TiAl6V4 titanium alloy) impacting a plate (either titanium alloy or aluminum) is presented in this paper. Projectile velocity (ranging from 250 m/s to 1500 m/s) with varying impact angles are considered. The presence of ricochet (if any) is identified over the ranges of the projectile velocity and impact angle considered. For the cases where ricochet is identified, the ricochet angle and velocity are predicted as functions of the incident angle and the incident velocity. The numerical results are compared with an analytical solution of the ricochet problem. The analytical solutions are from a model developed to predict the ballistic ricochet of a projectile (projectile) penetrator. The dynamics and the deformation of an aluminum (or a titanium alloy) projectile impacting on a finite thickness titanium alloy (or aluminum) plate are simulated. The current work is interesting in that it looks in the field of ballistics of different material combinations than are traditionally studied. The present simulations based on detailed material models for the aluminum and the titanium alloy and the impact physics modelling features in the LS-DYNA code provide interesting details regarding the projectile/plate deformations and post-impact projectile shape and geometry. The present results indicate that for no cases (for specified incoming velocities and impact angles considered) can an aluminum projectile penetrate a titanium alloy plate. The ricochet ‘mode predictions ‘obtained from the present simulations agree well with the ricochet ‘mode predictions’ given in an analytical model.

Comparative Analysis of the Trajectories of Projectiles Fired from Polish Small Arms Systems: MSBS-5.56 and BERYL

This paper presents the results of the theoretical external ballistic calculations for projectiles fired from barrels which correspond to the barrels used in two Polish small arms systems: MSBS- 5.56 system (MSBS GROT standard rifle and MSBS GROT carbine) and BERYL system (BERYL standard rifle and MINI BERYL carbine). The results obtained allowed the analyse of the effects of barrel length and the associated initial projectile velocity on the nature of projectile trajectory, particularly the over height and projectile range obtained along the trajectories. The analysis of the results facilitated an assessment of the scope of proposed changes in the settings of the firearm sights, resulting from the use of barrels of different lengths and the consequential changes in projectile trajectory.

External ballistics howitzer projectile

In this scientific work, the team of authors presents a mathematical model for studying the dynamics of the motion of a projectile in the air, fired from cannon. One of the main problems of external ballistics is to determine the magnitude of the force of the air resistance to the movement of the projectile. Usually in studies, a discrete relationship between the magnitude of the force of resistance and projectile velocity has been established. However, to improve the accuracy of firing, it is necessary to determine the functional dependence of air resistance on projectile velocity, deterministic and non-deterministic factors. The authors, when processing the results of landfill studies, which are presented in the tables of firing, found that the magnitude of the force of air resistance to the movement of the projectile depends not only on its speed but also on acceleration Based on this, the functional dependence of the force of air resistance is described separately during the movement of the projectile with the following velocities: supersonic (stage I); subsonic - with negative acceleration (stage II); subsonic with positive acceleration (stage III). To determine the coefficients of functional dependences, it is proposed to use inverse dynamics problems. Boundary conditions were considered - the full horizontal range of the projectile, depending on the specific angle of impact, obtained from the results of landfill research and given in the firing tables. Under the condition of a certain functional dependence of the force of counter-air resistance, taking into account the weight of the projectile and the Carioles’ force, as a result of this work is obtained the system of differential equations, which describes the motion of the projectile in air. The initial conditions for the first stage were taken the initial velocity of the projectile and zero (original) coordinates; for the second stage - the value of the kinematic parameters of the projectile at a time when its speed became equal to the speed of sound in the air; for the third stage - the value of the kinematic parameters of the projectile at the time when its velocity began to increase. By solving the system of differential equations, using the appropriate software, can be determined the impact of projectile charge and air temperatures, atmospheric pressure, changes in projectile mass and its initial velocity on the kinematic parameters of projectile motion. In addition, it allows you to automate the process of determining the aiming angle (it is better to ask the gunners the correctness of this concept) depending on the firing range, taking into account the above factors. Also, in the work on the basis of the method proposed by the authors, the is carried out comparison of the kinematic parameters of the projectile with the results given in the firing tables. They indicate minor differences when shooting at short distances, but when shooting at long distances - these differences increase, as the results in the tables of shootings are quite approximate.

Preliminary Comparative Investigations on Ballistic Properties of Intermediate Cartridges

The preliminary results of comparative investigations on intermediate cartridges were presented in this paper. The research focused mainly on the adopted assumptions and verification of research methods. Pressure ballistic test barrels, manufactured according to NATO EPVAT standards, were used for tests. The pressure courses of propellant gases in the barrel and the projectile velocity at four points of the bullet trajectory were measured. The pressure impulses, R100 parameter at 50 m and average bullet drag coefficient were calculated for each type of cartridge. The results allowed for a preliminary ballistic comparison of the most popular types of intermediate cartridges.

Numerical Simulation and Design of a High-Temperature, High-Pressure Fluid Transport Pipe

When designing a hand caliber with a high-temperature, high-pressure internal fluid transport pipe, reliability, safe use, and performance must be considered. Reliability refers to the stress caused by thermo-mechanical load; safe use refers to the low-temperature burns that might occur upon contact, and high-temperature burns caused by gas leakage occurring in the cylinder gap; and performance refers to projectile velocity. In this study, numerical simulation methods for heat transfer, structure analysis, and gas leakage are proposed so that solutions can be designed to account for the above three criteria. Furthermore, a hand-caliber design guide is presented. For heat transfer and structural analysis, mesh size, the transient convective heat transfer coefficient, and boundary conditions are described. Regarding gas leakage, methods reflecting projectile motion and determination of the molecular weight of the propellant are described. As a result, a designed hand caliber will have a high reliability, because the thermo-mechanical stress is lower than the yield stress. There will be little risk of low-temperature burns, but there will be a high temperature-burn risk, owing to gas leakage in the cylinder gap. The larger the cylinder-gap size, the greater the gas leakage and the smaller projectile velocity. The presented numerical simulation method can be applied to evaluate various aspects of other structures that require high-temperature, high-pressure fluid-transport pipes.