Ok then back to facts with regards to the possibility of the weapon.
It's possible to fire a .45 from the hand. Its possible to fire a 12 bore from the hand. It's not advisable if you want to hit anything and whilst it will move a lot, it won't break your wrist.
Kick hurts because it's against a relatively immovable object (i.e. you and your shoulder). Because of soft tissue, bones and tendons, your arm is not a solid object. Firing one handed will cause your arm to flex automatically. And thus, your arms move.
I'm informed that your arithmetic with regards to the possible damage to the body are correct - assuming that your arm/hands are an immovable object. The amount of the recoil is almost irrelevant. If you fire a shotgun with it away from your shoulder it doesn't break your wrist, it hurts because it's hitting the immovable object of you.
Then again, a bolt action is not going to be fired one handed as you'll require a second hand to hold it as you reload.
Now back to theory. With regards to newtons law. The projectile does not go from zero to maximum velocity in zero time. There's an acceleration. And this acceleration continues for the whole period that the projectile is in the barrel. The shorter the barrel, the lower the muzzle velocity (surely?) logically under these circumstances the total recoil would be less in a short barrelled gun. Since newtons law is no longer in play once it's out of the barrel. Although since the mass of the weapon is less, it won't cause more damage since it'll just recoil more like some cartoon hand cannon.
I apologise If cages were rattled earlier. Since the only real evidence we have so far is some very rusted relics in the Ypres museum and we have no proof of anything else, pretty much everything in this thread is relatively theoretical.
Also, I would like to point out that whilst the wartime laws stood towards a man's rifle, what are the laws regarding a rifle that had its butt or barrel damaged in combat? A dead man's bent rifle is useless. Why not let a tunneller modify it for self defence?
These are two totally different things, the muzzle velocity would depend on the time during which the acceleration (ab) acted on the ejecta (the bullet and propellant). The recoil of the gun is depends on the Force Fg acting on its mass and the resultant acceleration. Sawing off the barrel or any other part of the gun reduces mg and increases ag (as Fg is a constant), and to all intents and purposes, ag is the 'kick', as it is the acceleration of the weapon towards you.
" Recoil (often called knockback, kickback or simply kick) is the backward momentum of a gun when it is discharged. In technical terms, the recoil caused by the gun exactly balances the forward momentum of the projectile and exhaust gasses (ejecta), according to Newton's third law. In most small arms, the momentum is transferred to the ground through the body of the shooter; while in heavier guns such as mounted machine guns or cannons, the momentum is transferred to the ground through its mount. In order to bring the gun to a halt, a forward counter-recoil force must be applied to the gun over a period of time. Generally, the counter-recoil force is smaller than the recoil force, and is applied over a time period that is longer than the time that the recoil force is being applied (i.e. the time during which the ejecta are still in the barrel of the gun). This imbalance of forces causes the gun to move backward until it is motionless. "
From what I can gather from this, having a shorter barrel may not decrease the force of the recoil, obviously Newton’s 3rd law will still apply " Third law: When two bodies interact by exerting force on each other, these forces (termed the action and the reaction) are equal in magnitude, but opposite in direction. " But, the period of time the force/recoil is applied will be less. Would this shorter time period that the recoil is in effect, make a significant difference when fired from the hand, we should contact " Myth Busters " and ask them to try it !!
Further reading !
The nature of the recoil process is determined by the force of the expanding gases in the barrel upon the gun (recoil force), which is equal and opposite to the force upon the ejecta. It is also determined by the counter-recoil force applied to the gun (e.g. an operators hand or shoulder, or a mount, in the case of a mounted gun).
The recoil force only acts during the time that the ejecta are still in the barrel of the gun.
The counter-recoil force is generally applied over a certain time period and adds forward momentum to the gun equal to the backward momentum supplied by the recoil force, in order to bring the gun to a halt. There are two special cases of counter recoil force: Free-recoil, in which the time duration of the counter-recoil force is very much larger than the duration of the recoil force, and zero-recoil, in which the counter-recoil force matches the recoil force in magnitude and duration. Except for the case of zero-recoil, the counter-recoil force is smaller than the recoil force but lasts for a longer time. Since the recoil force and the counter-recoil force are not matched, the gun will move rearward, slowing down until it comes to rest. In the zero-recoil case, the two forces are matched and the gun will not move when fired. In most cases, a gun is very close to a free-recoil condition, since the recoil process generally lasts much longer than the time needed to move the ejecta down the barrel. An example of near zero-recoil would be a gun securely clamped to a massive or well-anchored table, or supported from behind by a massive wall.
I have been reading through this again, and now agree that the shorter barrel would have more of a " kick " The recoil period is spread over a shorter period of time, with a longer barrel, the recoil has been spread out over a longer period of time, resulting in the "softer" feel.
At the end of the day we can argue the theories of this all we like.
As many have said, there are accounts of cut down rifles happening, and although Robs Newtons Laws seem to suggest its impractical, it's not so impractical that it totally discounts these personal accounts and the findings in the trenches.
P.S Rob what do you consider to be a Large Caliber Weapon? I've never fired the Schwerer Gustav but I've gotten to put a couple of magazines through a Bren.
Also - found these articles which seem to say that .303 sawn offs are possible.... here's an article from the Sydney Morning Herald in 20th November 1947 where a sawn off .303 was used to attack a police officer but apparently failed due to the weapon jamming, and heres an article from the 10th June 1952 where the attackers had more success.
Nowhere in either of those news articles say to what extent the barrels were shortened, therefore can anyone assume that they looked like those that have been discussed in this post, either way the shortening of any barrel increases the recoil dependant on the percentage of charge within the bullet used, a full load .303 will kick like a mule and if not careful will break a wrist, and is very inaccurate, also there is the possibility of a flash back of cordite that is still burning when projected from the muzzle, something which i think might not be welcome in a confined area such as a mine filled with any type of gases produced when digging deep or filled with explosives
Sawn off rifles (and shotguns) are a common criminal weapon in most places except the US where weapons of every kind are pretty freely available legally and otherwise-there is no reason why it could not have been done in WW1 given the scale and circumstances of the Western Front and indeed other areas with static warfare-that it may not have been 'pukka' by regular military standards is all but irrevelant under the conditions and if you can figure out ways of doing practically then the troops would have as well-BCP-you know what a 'jam tin bomb' is?-the improvised grenade you make when you don't have a grenade but need one...
Davejb - true : the article gives us no idea of to what extent the guns were cut down. They could have just had the barrels shortened and kept the stock on or something. Also a fair point about the cordite and flashes near gases and mining equipment.
Lithgow - this is what I was trying to say earlier, that improvisation can and did happen during the first world war. But it seems that unless we have hard facts then some people don't want to know.