Manny: The only way to understand why putting a bunch of shot down the barrel does NOTHING for patterns, is to understand how air resistence affects each " roundish " pellet both by pushing against the forward " edge " of the pellet, but then also against the sides of the pellets, forcing pellets apart.
Take 3 balloons, all the same size, and round, and in the quiet air of your living room, throw the ballows, together, slowly; then moderately; and then as fast as you can throw an overhand pitched baseball. You will find that as more and more force is applied to move the balloons forward through the air, the quicker they separate, and that if you try to throw them too fast, they actually go less distance. Now, repeat this experience with 3 balloons, all round, but of different diameters, or sizes. You will see that even at modest and slow velocities, the shot spreads quicker than it does when the balloons are the same size. The largest balloon may stay the course, and go the furthest, but both of the smaller ballons will spread out further.
This is what is taking place when shotgun pellets are fired into the air. If you have a widely divergent sizing of pellets, like #4 and #8, the 4s will maintain their pellet energy and bump the smaller #8 shot out of the way, as the #8 shot slows down quicker. But that energy used to bump #8 shot out of the way will also change the path of the #4 pellets, too, and they will spread faster, or lose speed faster than if they were fired with just other #4 pellets.
If you are push this multiple-sized shot load above the sound barrier, ( 1100 fps) the smaller shot will drop below the sound barrier faster than the #4, and fast enough that it will be BUMPING the #4 shot as it does, and causing air currents to hit the #4 pellets from several directions, opening up the #4 shot pattern even more. All the shot will come down through the sound barrier within the first 20 yards, so you are not going to need to shoot at 30 or 40 yards to see these results.
Only by pushing the pellets through the air at very slow speeds can you keep them together for any kind of pattern much beyond 20 feet. If you do that there will not be enough energy in the smaller pellets to do anything to game but wound them, at best.
Bob Brister wrote a monumental work on the Shotgun, " Shotgunning: The Art and the Science ", published in 1976, by Winchester Press. Bob had the use of Winchester Western Ammo facilities at Alton, Illinois to do test patterns, and this clasic work is still as relevant today as it was back then. Winchester did not tell Bob what to do; they listened to what Bob told them with his testing results. It is not likely to be a testing process that will ever be repeated, because of the time and cost. However, it has been the basis for computer simulation programs that are used by other companies in the industry, even now.