Yeah, but W=mv[sup]2[/sup]/2, and shot loads (and even slugs) are plenty lighter than the shotgun itself.
Umm, equations aside, isn’t it the simple fact that the shooter is absorbing the expected recoil with their whole body and the shootee is absorbing the unexpected blunt impact with internal organs and rib bones that ain’t that good at absorbing blunt impacts without suffering trauma?
I mean, is anyone doubting that it’s entirely possible to kill someone by hitting them with a baseball bat in the chest? (Traumatic aortic rupture, shattered ribs that sever major arteries or puncture lungs, traumatic injury to other major blood vessels, etc, etc.)
CMC fnord!

Umm, equations aside, isn’t it the simple fact that the shooter is absorbing the expected recoil with their whole body and the shootee is absorbing the unexpected blunt impact with internal organs and rib bones that ain’t that good at absorbing blunt impacts without suffering trauma?
CMC fnord!
Well, with the part of the body which the butt rests against. But I get your point.
Fact is, though, you can fire an ordinary shotgun from your hip (I have!) without taking any damage. But (anecdotal evidence follows!), I once met a guy at a party who had his right hand wrapped in a plaster cast. I asked what had happened to him, and he confessed, somewhat embarrased, that he had had his thumb severely dislocated and/or broken (“nearly ripped off” were his exact words, as far as I can remember) from firing an illegally modified shotgun.
So I think the weight of the weapon relative to the projectile(s) is an important factor.

Well, with the part of the body which the butt rests against. But I get your point.
Fact is, though, you can fire an ordinary shotgun from your hip (I have!) without taking any damage. But (anecdotal evidence follows!), I once met a guy at a party who had his right hand wrapped in a plaster cast. I asked what had happened to him, and he confessed, somewhat embarrased, that he had had his thumb severely dislocated and/or broken (“nearly ripped off” were his exact words, as far as I can remember) from firing an illegally modified shotgun.
So I think the weight of the weapon relative to the projectile(s) is an important factor.
I had a shotgun years ago that was considered very light. The kick was so bad I started using nothing but very light loads in it.

The 1934 National Firearms Act banned a lot of different guns.
National Firearms Act - Wikipedia
Fully automatic guns
Shotguns with barrels under 18"
Short barrel rifles
Silencers
Firearms with a caliber larger than 50 (except shotguns)
Destructive devices (grenades, explosives, poisoned gas)Some of them should be banned. But short barrel shotguns, short barrel rifles and silencers could be legalized.
It’s a semantic distinction (what about gun laws isn’t?), but the weapons in question were severely restricted, not banned. They are somewhat less unobtainable now because unlike 1934 $200 isn’t a lot of money, but the rigmarole it takes to avail yourself of NFA items legally is a huge deterrent for a lot of people.
Of course, that’s for everything but automatic weapons, which are pretty much unobtainable for the average person due to scarcity and the accompanying high prices, but the point is that nothing on that list is banned by federal statute. States are free to make their own laws regarding NFA items, and many have.

Why didn’t the recoil kill the shooter? p=mv
Over what distance is the projectile accelerated in the barrel?
Over what distance is the projectile deceleration on the body armor?
F=ma.

Over what distance is the projectile accelerated in the barrel?
Over what distance is the projectile deceleration on the body armor?
F=ma.
yep. 1 oz projectile, 7 lb gun. pretty simple.
Does sawing off a section of barrel in any way make the pellets spray wider?
I figure, innocent bystanders could catch stray pellets.

Does sawing off a section of barrel in any way make the pellets spray wider?
I figure, innocent bystanders could catch stray pellets.
Shotguns often have a constriction at the end (choke) that tightens the pattern and increases range. Sawing it off removes this.
The spread of a shotgun is pretty minor. I’ve heard tons of BS, including from people who should know better, that you “don’t need to aim.” Actually shooting a shotgun should disabuse this pretty quickly. The widest choke is barely fist sized in spread at indoor distances.
As a general rule of thumb, the damage done by a projectile is roughly proportional to its energy, not to its momentum or force. Some of the energy in your gunpowder (or whatever propellant you’re using) will end up in the gun, and so be imparted to the shooter, but most of it goes into the bullet, and so ends up imparted on the target. The ratio of energies is going to be approximately the ratio of the rigid mass of the gun to the mass of the bullet, which is pretty big.

Does sawing off a section of barrel in any way make the pellets spray wider?
I figure, innocent bystanders could catch stray pellets.
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it depends on if the barrel has a choke or not. most shotguns meant for defense or “tactical” use are cylinder bore, so no choke. the main difference you’d get from shortening the barrel is a big increase in muzzle blast.
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there are a lot of misconceptions about how shotguns work. in the real world the “spread” of pellets is on the order of 0.3-0.5" per yard (again, depending on choke.)
movies have really fucked up people’s ideas about what guns do and don’t do. A shotgun is not a boom-stick you just point in the general direction of thy foe who- being naughty in my sight- shall snuff it. It’s not something you go all Arnold-like and mow down bad guys while shooting 8 rounds from the hip. shooting a 12 gauge from the hip is not easy. these things have brutal recoil and (with the shorter-barreled defensive types) bright and deafening muzzle blast. if you don’t know what you’re doing you’re likely to lose your grip on it when fired.

Does a rifle with a 12" or 16" barrel not have the same effectiveness as a shotgun with the same barrel length? Am genuinely asking, I don’t know why a particular bullet shape/barrel twist would be more effective with a barrel of a given length.
A rifle with a 12 inch barrel is just as illegal as a shotgun with a 12 inch barrel. I think thats the key bit of information you’re missing. Short barreled shotguns and rifles are NFA items. Its about having a short barrel on a a gun with a stock. Its not about the round it fires.
So why is there a concept of “sawed-off shotgun” but not of “sawed-off rifle”? Is there something about rifles that makes shortening of the barrel less desirable (for whatever purpose) than for a shotgun? It sounds like you lose muzzle velocity if you shorten a rifle too much, but that you can still get pretty short without the loss being significant.
Is it just because of the (mistaken) notion that a sawed-off shotgun has a spread so wide that you don’t need to aim?

it depends on if the barrel has a choke or not. most shotguns meant for defense or “tactical” use are cylinder bore, so no choke. the main difference you’d get from shortening the barrel is a big increase in muzzle blast.
there are a lot of misconceptions about how shotguns work. in the real world the “spread” of pellets is on the order of 0.3-0.5" per yard (again, depending on choke.)
movies have really fucked up people’s ideas about what guns do and don’t do. A shotgun is not a boom-stick you just point in the general direction of thy foe who- being naughty in my sight- shall snuff it. It’s not something you go all Arnold-like and mow down bad guys while shooting 8 rounds from the hip. shooting a 12 gauge from the hip is not easy. these things have brutal recoil and (with the shorter-barreled defensive types) bright and deafening muzzle blast. if you don’t know what you’re doing you’re likely to lose your grip on it when fired.
One of the comments
From the article: "We selected this full power, 1325 fps, 2 3/4″ load because we have found that the tactical and reduced recoil loads on the market pattern tighter then non premium buck. . . "
So, they selected a load that is specifically designed to open it’s pattern slower than traditional ammo, and are surprised to find out it opens slower than Grandad (who was using traditional ammo with “old fashioned” wads, not wads with VERY sophisticated modeling involved in their design? Shocking.
Meanwhile, my cylinder bore Mossberg 500, using “non-premium” buckshot (S&B #4 buckshot) and El Cheapo Winchester “party pack” (#7 or #8 birdshot) patterns almost EXACTLY 1" per yard (at least to 11 yards - the maximum distance available in my house, so the max I patterned to). But then, I’m using ammo that is pretty much the same as “Grandad” had available to him. Not far more expensive premium shells.
All shots were from a measured 12 feet from the muzzle to the first wall.
Notice that there is an approximate 3 1/2 inch spread.

So why is there a concept of “sawed-off shotgun” but not of “sawed-off rifle”? Is there something about rifles that makes shortening of the barrel less desirable (for whatever purpose) than for a shotgun? It sounds like you lose muzzle velocity if you shorten a rifle too much, but that you can still get pretty short without the loss being significant.
Is it just because of the (mistaken) notion that a sawed-off shotgun has a spread so wide that you don’t need to aim?
Federal law treats short-barrel rifles and short-barrel shotguns the same. There very much exists the concept of an SBR in federal law, and the penalties for making one without ATF approval are severe.
If you’re asking specifically about the “sawed-off” label, I’m not sure why that gets applied more often to shotguns than rifles, but here’s a guess: Many modern rifles use gas from the firing process to cycle the rifle, so there’s a limit to how much of the barrel could be “sawed-off” before it’s rendered non-functioning. Many shotguns are pump-action and don’t have this limitation, so they could perhaps be “sawed-off” to a shorter length.
Ah, so a standard shotgun can be easily modified to a short-barrel, but such an easy modification won’t work on a rifle due to the action, and so you’d need to more significantly re-design it for a short barrel.

Ah, so a standard shotgun can be easily modified to a short-barrel, but such an easy modification won’t work on a rifle due to the action, and so you’d need to more significantly re-design it for a short barrel.
With a strong dose of “it depends”, yes. It’s not a whole lot more sophisticated than just taking a hacksaw to a Mossberg 500 to end up with something like this: http://cordeliagunexchange.com/product/serbu-super-shorty-mossberg-500-12ga/. For an AR-15, the gas system needs to be adjusted depending on the barrel length.

Ah, so a standard shotgun can be easily modified to a short-barrel, but such an easy modification won’t work on a rifle due to the action, and so you’d need to more significantly re-design it for a short barrel.
Correct. Making a short barreled rifle almost always involves purchasing a new barrel or an entire upper receiver assembly. Shotgun barrels are extremely simple, and almost always smooth bore. They can be (and often are by criminals) simply hack-sawed down to any length desired.
But it isn’t the danger of the round that makes it illegal. It’s the length of the barrel combined with the fact that it has a stock, therefore is shoulder fired. Shoulder fired rifles and shotguns have length restrictions. Even a low-powered .22LR caliber rifle with a 14" barrel is as illegal as a “sawed off” shotgun.

The 1934 National Firearms Act banned a lot of different guns.
National Firearms Act - Wikipedia
Fully automatic guns
Shotguns with barrels under 18"
Short barrel rifles
Silencers
Firearms with a caliber larger than 50 (except shotguns)
Destructive devices (grenades, explosives, poisoned gas)Some of them should be banned. But short barrel shotguns, short barrel rifles and silencers could be legalized.
In the early 1930s the USA was in a moral panic about “gangsters”, courtesy of a few real-life desperados (Bonnie and Clyde, John Dillinger, etc.), and Hollywood’s sensationalizing of same. The items proscribed are exactly the ones most associated with criminals at the time.