Abstract
The estimating of a projectile initial velocity is formulated as a two-point boundary value problem. To solve it, the data of a Doppler Radar or the results of solving the Cauchy problem can be used. The projectile initial velocity v0 estimation process is based on the numerical solution of a system of ordinary differential equations and the bisection method. The iterative calculating process is interrupted when a predetermined accuracy of a projectile initial velocity and a predetermined value of the width of velocity’s search interval is reached. In the article, the block diagram of the algorithm for the projectile initial velocity process is developed. The Mathcad program code for mathematical modeling and a computer simulation of the projectile initial velocity estimation process for a 57mm armor-piercing projectile of ZIS-2 anti-tank gun 1943 model is given.
Highlights
A large number of practical problems of external ballistics of barreled artillery systems require information about a projectile initial velocity (PIV), briefly denoted as v0
- multiple repeated solution of the system of ordinary differential equations (ODEs) of the longitudinal movement of an artillery projectile using a method of numerical integration;
The technique assumes the use of the actual law of air drag, ballistic coefficient (BC), atmospheric parameters and actual angle of departure
Summary
A large number of practical problems of external ballistics of barreled artillery systems require information about a projectile initial velocity (PIV), briefly denoted as v0. If a velocity value at a given time is determined through the ADR measurement or by means of the Cauchy problem solution and if the angle of a projectile departure and the coordinates of the departure point are known, in this case one can formulate a two-point BVP. The result of solving the boundary problem is obtaining the velocity of the projectile on the left border of the interval, the fourth element of the matrix of ICs, v0 (see Figure 1, box 5) is determined. From the point of view of practice, it is of interest to determine the dependence of the error in estimating the PIV PIV as a function of error in determining the boundary condition PIV RB
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