Your other three posts can be dealt with together.
First a correction. In quoting Hatcher's 4% I left out a term. In his example, (1250 fps, 1 1/8 oz., fiber wads) it was more like 6%, not 4%. I regret, the error.
Your plan to make the barrel really thick does address my post to AA, in that I take it you can't look straight down into the ports and see the inside of the barrel, and this will direct the gasses back in a way many times more effective than standard ports.
The problem needs some numbers, since what we need is ratios: your claim of 50% or my counter-assertion that that's way, way too high.
I went through the recoil calculation for the powder in a different way in early February's slow powder = more recoil thread but Hatcher's method does a better job of focusing in on the powder effect. It's better for answering this ratio question.
The following analysis is adapted from Hatcher's chapter "The Theory of Recoil," extensions beyond the method are my own as are any errors or misunderstandings they may creep it.
You can account for the momentum of the recoiling gun by adding up the momenta of 1) the shot/wad, 2) the powder, and 3) adding the jet effect of the expansion of the powder at muzzle exit.
1) The momentum of the shot/wad is easy, just the muzzle velocity times the mass.
(OK, here's where we are going to do only the math we need to, and all we need is ratio. To deal with mass accurately, in the above formula, I should include the gravitational constant but I'm not going to because how many would understand it? So please go forward with the understanding that the math "units" won't come out right, but the ratios will. I'm not defending this degree of simplification as a general rule, but here it will work periectly, and clear away some clutter which might otherwise obscure the "meaning" of the result.)
back to 1) With the parenthetical warning in mind, we will call the mass 500 and the speed 1200, leading to a product of 600,000. "Six hundred thousand whats?" you ask, and I say "Just 600,000, that's all we need."
2) The momentum of the powder is more interesting. The mass is easy, and for this example we'll call it 20. But the speed takes some thought. The powder at the muzzle, right at the back of the wad, is going the same speed as the wad, 1200 fps. But the powder (gas, now) still remaining in the shell isn't moving at all. So we'll take the average speed of the powder as half the muzzle velocity, taking into account both very different speeds, zero and full.
So, this term of your momentum will be 20 times 600 = 12,000
3) The jet effect. Experiments have made it possible to estimate that _in a shotgun_ treating the speed of the gas as 1.5 the muzzle velocity (at the outside, also 1.25 is suggested, page 289, for standard shotguns.) We'll use 1.5.
Using the conventions above, we'll multiply 20, the mass of the powder, by 1200, the MV, and then by 1.5 to account for the jet effect. So we get 36,000.
This gives us a sum of 12,000 and 36,000 or 48,000 and this is what we compare to the shot momentum, 600,00. Using these admittedly rough calculations, we can put the effect of the powder at 8% of that of the shot, and so about 7% of the total, which is 648,000
Now imagine we were in a universe where guns worked differently, where the shot went one way and the powder gasses in exactly the opposite. Here the powder effect is subtracted from the shot effect, leaving a sum of 552,000, which is 15% less than our original 648,000. This is the absolute limit of what you can expect from any system, in that it's taken all the powder and turned it back the other way.
If all the powder is turned at 45 degrees, not 90, then you have to at least multiply by 0.7, reducing the max to 10%. Add to that the problems of turning the gas without reducing its speed (unlikely), keeping it's temperature (and so its pressure) up through a passage a third of an inch long, getting a high percentage of the gas to turn at all, and you are down well under 10%.
Shortening the barrel will increase this number, adding shot will lower it.
I can't see it any other way. There's only so much gas can be expected to do. There's not much of it, relative to the mass of the shot, and there's not much pressure in it at the end, relative to rifles, and those are what set its limits.
Neil