Influence height of projectile detonation to formation of fragmentation field

Modeling of fragmentation field is essential to solving the problem of increasing the effectiveness action of the projectile at the target. In the dynamic conditions of the experiment setting is difficult, since detonation point depends on many random factors. The article presents the methods of mathematical modeling separation of fragments and fragmentation field construction, depending on the height of projectile detonation on the trajectory. A mathematical model separation of fragments is described by a system of differential equations for given mass characteristics, initial velocities and directions of movement. The initial velocity of the fragments obtained on the law of energy conservation, taking into account the speed of the projectile at the detonation point. Construction of the fragmentation field based on multiple simulations of projectile fragmentation on the trajectory. On the basis of fragmentation density field defined boundaries of the affected area, depending on the critical values of specific fragments of energy per unit area.
The paper describes an example construction of the fragmentation field, depending on the height of the detonation. Height of detonation point varied from 1 to 30 meters. The main mass of fragments of the projectile is distributed near the detonation point and is concentrated in a region having an arcuate view that due to the high rate of separation of fragments and form a cylindrical shell. It is shown that with increasing height of undermining the total energy of the fragments is reduced and the square of the affected area behaves non-monotonically and reaches its maximum value at detonation the projectile at an altitude of 19 meters for the given set of conditions. The analysis of the convergence of the algorithm for constructing the affected areas showed that the total energy and the square of affected area is stabilized with an increase of the number of repeat tests.
The results obtained may provide a basis for the placement of the targets at firing range, determine the time of detonation of the projectile and placement of instrumentation that will improve the quality of experimental determination of the projectile fragmentation and reduce the preparation and conduct of field tests costs.