Yes, Don, the sound barrel does not take a vacation for any ball diameter, or gauge.
Seriously, this is a matter of aerodynamics, and laws of physics, which are mostly beyond my education and training. I have the luxury of having a twin brother who is Mechanical Engineer, who I consult on all these scientific questions. Bob Brister wrote a wonderful book, Shotgunning, The Art and Science, published by Winchester Press in 1976. He convinced me that you " Can't fool Mother Nature".
If you can find some round balloons, you can better understand what is happening to shot in the air: Use just 3 of them, all the same size. Take one of them and throw it as hard as you can, doing this in your living room so we don't have to deal with any winds. Mark the floor or carpet to indicate where it lands. Now, from the same starting point, throw a balloon as soft, or slowly as you can. Mark its landing point. Now increase the velocity of your throw until the balloon goes the furthest. You will find that there is a " Less than maximum " throwing speed that allows the round balloon to travel the furthest distance. By comparison, the hardest throw competes with the softest throw for the shortest distance.
Now, do the same experiment using three balloons at once. Grab the three by their knots, and this time, the objective is to find a speed that keeps the three balloons the closest together while going the furthest. Air not only pushes on the Nose of a round ball, but on its sides, two, causing it to spread apart from the pellets around it. You will find that the speed you can throw the three balloons that keeps them together when they land on your floor or rug is slightly less than the most optimum speed for the single balloon.
These same observations can be made shooting shot, as the principles of aerodynamics are the same on all round objects traveling through air. It does not matter as to the size or weight of the object: air drags all of them pretty much the same. Using balloons in your living room is just an easier way to see all this, in the relatively short space available in your home.
Now, The SOUND BARRIER: Actually, my brother says there is a " Transonic Zone" from about 1100fps, to 1250 fps. where changes in the drag factors as a ball or pellet nears or passes through the sound barrier change. There are cones of air being pushed aside by the nose of the pellet, and a second one following behind the pellet, due to a vacuum that is created by the ball exceeding the speed of sound. Its the creation or elimination of that vacuum, as the ball or pellet approaches or comes back down through the transonic zone, that batters and buffets the pellet in the air, and sends it off line-of-travel. Put two or more balls, or pellets together, and you have gravity, and the affect of air traveling between the pellets and pushing them away from each other to accellerate the drag factors( friction of the air on the pellet causes more rapid slowing, but not evenly because a pellet may be directly behind one in front, or have several pellets around it limiting the air that hits it, causing the pellet to go faster than the ones in front and therefore bumping into those pellets in front of it, before losing speed, and veering off from the line of travel). Think of shot trying to separate the way you would think of a high speed auto accident involving several hundred cars.
We see this very occasionally in Stock car races, with cars going everywhere but straight ahead on the course. Some cars make it through the mess, and continue on.
That is about what happens to shot pellets in the air. In addition, the two cones merge as one as the pellet comes down below the sound barrier, and there is " fluttering " along the surfaces of the pellet as this process happens. Any imperfection or flat on a pellet will cause this action to send the pellet out of the pattern, slowing that pellet very quickly.
Because the .410 has such a small bore diameter, there are relatively MORE pellets rubbing against the bore than with a similar weight charge from a larger gauge barrel. That makes it doubly important for patterns to NOT kick the load so hard on firing that it rubs lead off all those pellets. ( Plastic shot cups have done more to round out the patterns of the .410 than any other gauge. The patterns are still pretty much the same size, regardless of choke, but they are more round). Using FFg or even Fg powder in a .410 so that you get much slower chamber pressure, and less of a " kick " to the shot charge is about the only way to improve pattern density. The other, of course, is to reduce the velocity, by usin the lighter loads. Since this is a 20-25 yard gun MAX., reducing the velocity is not going to reduce pellet energy AT THIS SHORT RANGE much at all. You can substitute single pellet energy by putting more pellets on the game, and do this by improving pattern density. Some kind of paper shot cup can also be used, to protect the shot, and I am a recent convert to lubing the barrel after seating the shot charge and OS cards, to allow the shot or shot cup to slide down the barrel, rather than have the pellets rubbing lead off in streaks down the barrel as they exit.
Oh, I don't think the 3 inch .410 shells do anything for the shooter past the first shot, and then its a maybe, only, in modern breechloaders. I believe the higher velocity these longer shells are loaded to cause more plastic deposits to be rubbed off against the barrel, and that plastic makes subsequent shot patterns more and more ragged by dragging on the next shotcup fired down the barrel.
I hope this helps explain. If you will read V.M. Starr's article on loads for the shotgun in Bob Spenser's Site, Black Powder Notebook, he comes to the same conclusion more than 50 years ago, and he also recommends light loads for the .410.
