Development of a Methodology for Estimation the Starting Moments of a Set of Light Screens’ Intersection with a Shot Cloud

When studying the process of moving a shot cloud in space, various devices can be used, for example, light screens. For such studies, it is advisable to have a simulation model of the set of optical sensor signals at the intersection of light screens with a shot cloud. Taking into account previous studies, in order to obtain such a model, it is necessary to know the time points of the beginning of the intersection of the shot cloud of light screens (in fact, the moments of the intersection of light screens with the fastest pellet). A technique is proposed that allows for given initial conditions (fraction size, initial velocity, etc.) to determine such moments for a set of light screens installed at specified ranges from the muzzle of the weapon. The essence of the proposed technique is that on the basis of solving a system of differential equations of external ballistics, a set of points is calculated corresponding to the dependence of the time when a fraction reaches a given range on the magnitude of this range. Next, the obtained dependencies are approximated by polynomials of the first, second and third degrees using the least squares method. The estimation of the approximation error by various polynomials for different types of cartridges is performed. An example of using the proposed technique to obtain the time points of the beginning of the intersection with a shot cloud for cartridges loaded with three different types of shot is given. In addition, the estimation of the error of the obtained dependencies in relation to the results of real experiments was performed. It is shown that at ranges up to 24 m, the relative error does not exceed 4 % for all types of cartridges. Based on the results obtained, specific recommendations for the practical use of the developed methodology are proposed. In the future, using the proposed technique, it is possible to create a simulation model of a set of optical sensor signals when a shot cloud crosses a set of light screens located at specified ranges from the muzzle of the weapon.

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