This is a fascinating but seemingly unsolvable problem to discuss.
In my mind it is solved. Read "Sporting Shotgun Performance" by Dr. A. Jones.
I have no engineering or higher physics education, but Ive read entirely too many old gun books and shot so many patterns on a plate, that Im a waivering, doubtful, bitter clinger to the idea that maybe, perhaps, there is still enough mystery and art left to shotgun patterns as to occasionally allow a well choked gun to escape the long dead hand of Herr Dr. Gauss.
There is no escape. Gauss works, but Rayleigh is the real hero.
To restate the original posts question to suit the hypothetical:
1. Is is possible to cheat normal Gaussian distribution of shotgun patterns by using a recess (jug choke) before a full (.35-40 thousands) choke to obtain hot centers where the pellets in the center are denser than normal,,,
NO, absolutely not. But it is really Rayleigh.
2. Or do the iron laws of normal (Gaussian) distribution mean that no matter if we lengthen forcing cones, use conical, elliptical, parallel, recessed, or staged or collet chokes, folded crimped hulls with plastic, cushioned, protective wads with nickel plated shot,,,,or not,,,mean that all shotgun patterns remain the same, only at different distances from the muzzle?
Yes.
If the scientists are right, then better patterns are therefore impossible, we can only shoot smaller or larger circles on the plate, at a given distance.
So what is a "better" pattern? There are a few things that have effect on choke effect beyond constriction, but not nearly as much effect as constriction.
Almost, I am persuaded to be a scientist about choke.
Do it. Just do it.
But with quavering faith, I read again my W.W. greener and Bob Brister, shoot a few more patterns on a plate, and the spark of hope still flickers, there might be the one, true choke that produces hot centers, but not too hot, minimal shot balling, patchiness, and fliers, and spreads quickly an inch per yard out to twenty yards and holds that circle out to about forty, leaving a hot center to break targets and kill birds out to sixty yards, perhaps a bit beyond that.
Read Jones. He is the only one to do nearly enough research with statistical analysis to really tell us the truth. Shotgun patterns absolutely must be treated statistically to actually extract data from noise.
I even think I own a few of those artistically choked guns.
Oh, for sure there are magic shotguns. This happens when a shooter comes into a gun that fits him at eight points. Unfortunately, shotguns are quite picky about displaying magic. Just as one mans ale is another's poison, one man's magic shotgun is another's tomato stake. When you are shooting a sudden death at a competition and you opponent is down one, believe with fervent passion that your magic thunder stick has magic chokes reamed and polished by an elderly elf living in a remote forest visited by gunmakers only upon a commission for a magic choke.[/color]
They tend to be 12 gauge guns with about 12-13 thousands constriction.
I'm not going to get into this.
Not quite a light modified, but an improved cylinder, plus.
No, sir, you are on your own.[color:#FF0000]
There might be such a unicorn of a full choked shotgun, if there was a recess choke of a thousandth just before the choke, that makes exceptionally hot cores.
If not, its pretty to think there is.
Truth, but in good humor. ;-}
