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.