APPENDIX D: TRAJECTORY MODELLING

On the basis that sporting shotgun is used at relatively short range (i.e. less than 100m) and that the mean velocity of the pellets is high, it is assumed that the pellet trajectories are unaffected by gravity. Errors due to this assumption are rendered insignificant by the relatively large disperse patterns of pellets from shotguns.

This assumed straight-line trajectory is calculated using the drag coefficient curve for a spherical projectile due to Braun (see References). Points taken from this drag curve include:

The program includes a drag factor to allow for variable surface finish or deformation of the pellets. The default value of the drag factor is 1.00. To properly determine the value of the drag factor requires knowledge of pellet velocity at two ranges. The drag factor value can be expected to lie in the range 0.90 to 1.15. The effect of drag on the computed down-range velocities can be observed in the 'Table' display of the program.

The program extrapolates velocity back to the muzzle in accordance with the drag coefficient and drag factor, then computes downrange trajectory from the muzzle. Actual muzzle velocity is affected by muzzle blast and the mutual interference of pellets and wads. The program does not allow for the distribution of pellet velocities within the shot cloud from one firing, but the effect of pellet velocity on overall effectiveness can be examined by use of fictitious pellets velocities. If measured velocities are used, the method of measurement should be noted: optical chronographs commonly give the velocity of only the fastest pellets in the shot cloud, whereas ballistic pendulum and induction coil types are preferable in that they give an indication of the mean velocity.

The integration of the trajectory is achieved by a one-dimensional Runge-Kutta routine with a fixed time step of 0.005 seconds.