Identification of nonlinear aerodynamic projectile coefficients based on a modified point mass trajectory model

To increase calculation of projectile flight trajectories effectiveness based on mathematical models which describe the spatial movement of the projectile in the air, a pressing question it is relevant to determine individual aerodynamic projectile coefficients with specified accuracy. The construction of modern mathematical models of projectile flight is based on an approximate approach which is called the small-angle approximation. According to this approach, the aerodynamic coefficients are expanded in a Taylor series in terms of the angle of attack and only the linear terms of the expansion are retained, which allows to significantly simplify the mathematical models of the projectile's flight, but considerably worsens the accuracy of calculating its flight trajectories. The most suitable for determining the aerodynamic coefficients of a projectile is a modified point mass trajectory model, as a mathematical model of projectile flight (STANAG 4355 (Edition 3)). The article presents procedures for converting a modified point mass trajectory model into a system of differential-algebraic equations provided in the real form, which, given the appropriate set of linear and nonlinear aerodynamic coefficients, allows calculating the main parameters of the projectile's flight with less computational resources. Analytical expressions were obtained for identifying the aerodynamic coefficients of the drag force, lift force, Magnus force, decreasing of the projectile's rotational speed, its overturning moment, and the square of the module of the projectile's angle of attack. It is shown that, given a known function of the change in the angular velocity of the projectile's own rotation, the obtained analytical expressions functionally depend exclusively on the parameters obtained from external trajectory measurements (projectile flight coordinates and their derivatives).