The paper analyzes the application area of the formula for determining the lateral projectile displacement under the action of crosswind, which is used nowadays in the compilation of range-tables. It is established that this formula is true: if the drag force to the projectile movement is proportional to the square of its velocity; wind velocity components are much less than the horizontal component of projectile velocity; the projectile velocity projections on the Oy and Oz axes are much less than the projections on the Ox axis; the dimensionless factor of resistance and the crosswind value are constant values. However, the power of resistance of the projectile movement only sometimes is proportional to its squared velocity; the projectile velocity component about the axis Oz is not always much less than its component about the axis Ox, and may even be larger than it; the factor of resistance is not a constant value, but depends on the value of the Mach number, so it can be constant only at short-range firing. The authors propose mathematical model for determining the lateral projectile displacement under the action of crosswind. It is considered that the efficiency of the crosswind on the projectile depends on: air density; projectile maximum area of longitudinal section raised to centain power; the difference between the value of the cross component of wind and the velocity of the projectile lateral displacement to some extent. The values of the projectile lateral displacement under the crosswind action at short-range firing differ slightly from the values of the lateral displacement specified in the range-tables. The values are obtained by applying the proposed mathematical model. However, with extending the shooting range, the difference between these values is constantly increasing and reaches the values of the same order with the values of the lateral displacement determined by the theoretical method or specified in the range-table. Analyzing the velocity of the projectile lateral displacement under the crosswind action, it was obtained that its theoretical value constantly grows along with the increase duration of the projectile flight endurance. However, the velocity of the projectile lateral displacement obtained using table values initially increases, but with increase of shooting range it begins to decrease, which does not comply with the laws of dynamics. Therefore, the table values of the projectile lateral displacement under the crosswind action do not quite accurately indicate its value.

/pdf/vpliv-bichnogo-vitru-na-dinamiku-rukhu-snariada-32k3sd5m1a.pdf

Вплив бічного вітру на динаміку руху снаряда

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.

/pdf/zovnishnia-dinamika-oskolkovo-fugasnogo-snariada-of-462zh-412i287h7i.pdf

Зовнішня динаміка осколково-фугасного снаряда ОФ-462Ж

In the paper, the effect of cartridge charge and air temperatures on the kinematic parameters of movement of  the bullet released in the air is investigated. It is established that an increase in the temperature of the charge of a cartridge or air contributes to a significant increase in the range of flying bullets, a slight increase in its speed and time of flight. Preferably, the air and charge temperatures are not the same; therefore, the effect of the change in the temperature of only the air or only the charge on the dynamics of the bullet was studied.  It has been  established that  the value of the temperature of the charge of the cartridge, exceeding the air temperature, affects the kinematic parameters of the bullet  movement during shooting at a distance of up to 600 meters; when shooting at a distance of 700-900 meters, the effects of charge and air temperatures on the movement of the bullet are almost identical; when shooting at a distance of more than 900 meters, the prevailing influence on the kinematics of the movement of the bullet becomes the temperature of the air.  If the temperature of the cartridge and air charge is the same or higher than 15° C, then the theoretical range of the flying bullet is greater than that given in the shooting tables. The difference between them increases with increasing distance, which is shooting. So, at a temperature of 35° C it reaches up to 10%. With a decrease in the temperature of charge and air than 15° C, the coordinate of the zero point of the trajectory of the motion of the bullet determined by the theoretical method will be less than the given in the shooting tables and the absolute value of the difference between them increases. Analyzing the values of the wind deflection of the bullet under the influence of the crosswind when the temperature of the air changed, we can state that the increase/decrease of the air temperature significantly increases/decreases the range of the flying ball, but the values of its wind deflection slightly differ from the values indicated in air temperature 15° C. The difference between the theoretical values of the wind deflection of the bullet and the given in the shooting tables is experimentally significant, if the firing is at a distance greater than 900 meters. However, the theoretical investigations allow to state that the values of wind deflection of the bullet, given in the shooting tables, for distances larger than 900 meters are questionable.

/pdf/influence-of-cartridge-charge-and-air-temperatures-on-the-5c48gz040x.pdf

Influence of cartridge charge and air temperatures on the kinematic parameters of movement of the bullet released from the SVD

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Зовнішня динаміка осколково-фугасного снаряда ОФ-462Ж

Influence of cartridge charge and air temperatures on the kinematic parameters of movement of the bullet released from the SVD