An investigation into pellet dispersion ballistics.

Existing works on pellet dispersion ballistics are confined to some data-based models derived from statistical analysis of observed patterns on targets but the underlying process causing the dispersion lacks due attention. The present article delves into the relatively unexplored areas of dispersion phenomena, and attempts to develop a theoretical model for general application. The radial velocity distribution of pellets has been worked out by probing into the physical process of dispersion based on transfer of momentum from undispersed shot mass to dispersed pellets. The ratio 2u/v0 (u = root mean square (r.m.s.) radial velocity and v0 = muzzle velocity of the pellets) is found to be fairly constant for a fixed gun-ammunition combination and has been suitably designated as 'Dispersion Index' (DI) characterising its dispersion capability. The present model adequately accounts for pellet distribution on targets and it appears that 'Effective Shot Dispersion' (ESD) as introduced by Mattoo and Nabar [ESD = [(4/N0)sigma Ri2]1/2, where N(0) is the total number of pellets and Ri is the radial distance of the i-th pellet from centre of pattern], gives a faithful numerical measure of overall dispersion at a given distance. A relationship between ESD and firing distance, incorporating the effects of air resistance and gravity has been worked out, which reveals that DI controls the dispersion at a given distance. For small distances (less than 20 m) the relation reduces to a linear one, as already observed empirically and looks like ESD = E0+DI x firing distance, E0 being a parameter dependent on gun and ammunition. The present model, unlike earlier ones, is versatile enough to explain the natures of the dependence of dispersion on firing distance as well as on gun-ammunition parameters, which are essential for a faithful reconstruction of a crime scene. The model has been tested with such experimental data as are available and reasonable agreement is observed.