Assessment of the accuracy of the approximation of the nonlinear parameters of the projectile flight

Abstract

The article evaluates the accuracy of the approximation of the aerodynamic force coefficients (moments) of the projectile and atmospheric parameters, which are significantly nonlinear. The aerodynamic force coefficients (moments) of the 155-mm Assegai M2000 projectile of the South African company Denel Naschem and atmospheric parameters defined by the international standard ISO 2533:1975/Add.1:1985(en) Standard Atmosphere are taken as basis. The estimation of the accuracy of the approximation of the tabular values is presented through the relative error (misalignment) between the given tabular data and the values of the approximated function of the aerodynamic force coefficients (moments). Analytical functions are used as approximating functions, such as the sum of a support function (error function) and a set of basic functions (Gaussian functions), which makes it possible to obtain an approximating function continuously differentiated on the segment of the change in the projectile flight parameter, which can be represented by a single expression. In the Maple software environment, analytical functions (error functions and Gaussian functions) were approximated to the tabulated values of the aerodynamic coefficients of forces (moments) of the 155-mm Assegai M2000 projectile. The obtained values of the single analytical functions of force coefficients (moments) and atmospheric parameters can be used to solve the problems of calculating firing tables, preparing data using ballistic integrating algorithms (ballistic calculators) for firing existing, new artillery systems and those systems being modernized. It is shown that by iterative procedures of approximation of tabular data of aerodynamic force coefficients (moments) and parameters of the atmosphere, it is possible to construct analytical functions in the form of a continuous function of the projectile flight parameter within the entire range of its change, ensuring the given accuracy of its approximation to the tabular data.