APPENDIX C: SHOTGUN CHOKE AND HIT PROBABILITY

The relative displacement of each simulated aimpoint from the target gives a 'miss distance' which enables the pellet areal probability density at the target to be found by reference to the pattern density of pellets due to the muzzle choke, calculated as a standard deviation sChoke at that range.

The choke of the shotgun is defined here using the traditional measures as follows

The shot cloud is taken to have a Gaussian distribution of pellets. This is fitted to the percentage, %pattern, of pellets falling within a 30 inch diameter circle at 40 yards:

Whereas a linear increase in pattern size with range is generally assumed, a disproportionate growth in pattern (i.e. 'trumpeting') has been reputed. More recently Giblin and Compton (see references) have noted that pattern standard deviation varies in proportion to the pellet time of flight, so this program uses the ratio of pellet flight times, t, to scale pattern size to range R:

and the probability of hit against each presented region of quarry susceptibility is

where the effective area AEff allows for the size D of pellets passing close to each quarry region, area A, approximated as circular, so

and n being the number of pellets in the cartridge given by

where r is the pellet material density, D is their diameter, and M is total shot mass.