Will attempt to decipher the non-deep thinkin' U. of Mo. version of this PhD thesis "An Experimental and Theoretical Investigation of Shot Cloud Ballistics"
http://discovery.ucl.ac.uk/1382490/1/396689.pdf Here's the background
Experiments by Lowry [16] have shown that for the first metre of flight the shot column of pellets behaves like a single semi-fluid object. The drag force of air resistance and interaction between pellets causes a gradual separation of pellets after the shot cup has fallen away from the load. At some point the pellets have separated sufficiently apart that they are travelling in free air and their only interaction is with air resistance. The shot cloud length is defined as the distance between the first and last pellets in flight and the pattern gives an overview of the pellet distribution across the width of the shot cloud. Generally, at ranges close to the muzzle a more constricted choke will produce a longer shot cloud which patterns tighter.
Shadowgraphs produced by Lowry [16] show the effects of a full choke, where the front pellets in a shot cloud separate away leaving turbulent wakes. He explained that the pellet behind in the wake experience less resistance, due to slip stream effects of the leading pellets, and disperse less rapidly compared to a cylinder choked shot cloud. With the greater dispersion from a cylinder choke the pellets spend a shorter period in a protected atmosphere. Therefore they achieve free flight quicker and become subjected to the full force of air resistance.
Lowry E.D., "A Waterfowl Lethality Model", Western Washington University, M.Sc Thesis, 1981.
p. 45 For spheres in line (180 degrees to flow) with one another the trailing edge sphere can be seen to experiences a very marked decrease in drag until a separation of 3.5 diameters. Unlike the abreast case, the in-line trailing edge sphere will be affected more by the leading edge wake downstream. The leading edge sphere does not seem to be affected too much by the presence of a trailing edge sphere. At close separation the abreast forces are large which could separate the spheres, and when the spheres are inline of one another the reduction in drag means that
the trailing edge sphere would catch the leading edge sphere up and affect its performance.
p. 46 The main interest in this work is to explain how shot clouds develop over time and space by studying the external ballistics of shotguns which use spherical pellets. If the pellets emerged from the muzzle of the gun in a constant order and shape, the interactive forces and downrange performance of the shot cloud could perhaps be modelled by theory.
Unfortunately in shotguns there are many variations, for instance the diameter, shape, and surface roughness of the pellets, which alter the drag coefficient of a sphere. Another major influence on the spread of the pellets in a shot cloud is the choke and shot cup behaviour.
No satisfactory theory yet exists to predict the downrange behavior of shot clouds…p.47 The main conclusion (of Journee’ [1]) was that the pellets in a shot cloud have various trajectories and are subject to random paths. Another experiment carried out by Journee’ showed the effect of random trajectories of pellets by
colour coding different layers of the pellets in the cartridge and using high speed photography and pattern plates. From this it could be seen that the different coloured pellets moved around in the shot cloud with no constant order. Jounee’ did show that in the final pattern the pellets which were at the rear of the cartridge seemed on average more dispersed than those from the middle and front.
Jouree’ Le General, "Tir des Fusils de Chasse", (ed. Gauthier-Villars et Cie.)
p. 48 Lowry’s experiments [2]
Lowry E.D., "Aerodynamic Performance of Lead and Iron Shotshell Loads", Olin Corporation, Winchester Division, Feb. 1970.
p. 50 Some pellets in the shot cloud were observed to have a lower drag than the undamaged leading edge pellets, this is thought to be caused by slip stream (Lee [11]) showed that pellets behind one another experience a reduction in drag) where the leading edge pellets are subject to a greater deceleration than the pellets in the centre of the cloud. As a result the pellets in the middle of the shot cloud caught up with the front pellet, since they experience less air resistance. The work also showed that with an increase in pellet deformation in the shot cloud there was a greater initial spread.
Lee K.C., "Aerodynamic Interaction Between Two Spheres of Reynolds Numbers around 104",
Aeronautical Quarterly, pp. 371-385. Nov. 1978.
p. 51 Oberfell and Thompson’s experiments [38] recognized that the patterns seem to follow a Gaussian distribution.
Oberfell G. and Thompson C., "The Mysteries of Shotgun Patterns",
Oklahoma State University Press, Stillwater, 1960.
