During my first evening in San Antonio, I sequestered myself in my hotel room to polish up my presentation. Fortunately, there was a Mythbusters marathon on the Discovery Channel at that time, so I was able to keep myself marginally sane by watching the ‘Busters abuse places, things, and themselves for the cause of science.
One of the episodes that played during the marathon contained the “finger in the barrel” myth — the idea that a person can stick a finger in the barrel of a rifle or shotgun as it fires, causing the barrel to split like a banana peel without harm to the finger! The initial investigation of the ‘busters clearly demonstrated that a finger would certainly be lost in the attempt, and that a barrel would not split in the manner suggested. An updated investigation two years later, however, demonstrated that a rifle barrel could be split if sufficiently weakened by use.
In a remarkable case of serendipity, the next evening I was browsing the Proceedings of the Royal Society of Edinburgh and came across an article with the title, “On the bursting of firearms when the muzzle is closed by snow, earth, grease, &c.”! The article, by Professor George Forbes, is a theoretical explanation of the bursting of firearms and was published in the 1878-1879 session of the Royal Society, meaning that Forbes’ investigation was some 130 years before the Mythbusters! The calculation and explanation are short and entertaining, and I thought it would be fun to take a look at them.
The article begins as follows:
It is well known that if an ordinary fowling-piece, charged with shot or ball, have touched the ground or snow, so as to close the muzzle of the gun, or if the muzzle of the gun be in any way artificially closed with grease or other substances, the fowling-piece is certain to burst at the muzzle when it is discharged. This would not be the case if, instead of firing a shot, a piston were driven up the tube by hand. In this case the compressed air would drive out the opposing plug, which offers but a very feeble resistance to the internal pressure. These facts, thoroughly well authenticated, have not, to my knowledge, received a satisfactory explanation, though a clear idea of the conditions of the case is all that is required to explain this, at first sight, anomalous behaviour.
Of course, this article does not mention a “banana peeling” of the barrel, the description of a barrel being “certain to burst at the muzzle” seems pretty close. It’s rather intriguing that Forbes refers to such an occurrence as “well known”; though the Mythbusters had to work very hard to disfigure a barrel, it was apparently quite easy to do with the weapons of Forbes’ time.
The puzzler in this problem is that air forced into the barrel by piston will push out a plug just fine, while an actual gunshot will destroy the barrel before pushing out an identical plug.
The explanation lies in the fact that the charge travels along the bore of the gun, if not with the same velocity as, at least with a velocity comparable to, that of the transmission of pressure through the air, i.e. the velocity of sound. Thus, as the charge advances along the barrel it is continually compressing the air immediately in front of it; but this pressure gets no relaxation by expansion into the front part of the barrel. The compression, of course, generates heat in the air, which increases the velocity of sound through it. But this does not affect the question in its general bearings. It is sufficient to notice that the snow, &c., is driven out with the full velocity of the charge (neglecting the weight of the snow-plug compared with that of the charge). But before the plug can be driven out with this great velocity the pressure behind it must be very great.
The hypothesis, it seems, is that the air pressure grows so quickly that it reaches the point of shattering the barrel before pushing out the plug. Of course, such a hypothesis needs to be backed up by some evidence, and Forbes provides a very simple calculation to justify his claims; we summarize it here (and fix a mistake or two in the math along the way).
It is assumed that the “snow-plug” of mass leaves the gun at velocity comparable to the speed of the bullet. On leaving the gun, it has kinetic energy equal to
This work is produced by the pressure of the gas in the barrel; denoting the cross-section of the bore as and the length of the snow-plug at , and noting that work = force times distance, we have
Solving for , we have
where is the density of the snow-plug. (This number is a factor of 2 different than Forbes’, as he assumed that the speed was created over a distance .)
Forbes assumed a velocity of 1000 feet per second; in terms of meters/second, we have
The density of water at freezing temperature is roughly
Putting these together, we have
A metric ton is 1000 kg; if we convert our number into metric tons per square cm, we have
This is a pretty huge pressure — a half ton per square centimeter. Forbes’ calculation, in English units, results in 7 (English) tons/square inch. My calculation, neglecting his extra factor of 2, would be about 3 (English) tons/square inch.
Forbes summarizes his conclusions with the following:
A pressure which the muzzle of a shot gun is not constructed to withstand, and the theory shows that this great pressure can be produced even by a plug of snow or grease of the shortest length movable inside the barrel with the greatest facility. If the velocity of the ball or wad be less than that of sound the snow-plug is not driven out quite suddenly, and if the velocity be small enough the snow-plug is driven out before the ball or wad reaches the muzzle.
Is his calculation correct? It’s hard to say, as it is a great simplification of a problem with many factors. There does not seem to be anything fundamentally wrong with the basic physics equations he uses, however.
At the very least, Forbes’ paper shows that science-types have long been intrigued by exploding things!
G. Forbes, “On the bursting of firearms when the muzzle is closed by snow, earth, grease, &c.” Proceedings of the Royal Society of Edinburgh 10 (1878-1880), 254-256.
Do try this at home kids! Mathematics is far safer than the improper use of firearms… although not quite so loud.
I’ve always said that part of the reason I went into theory is so that I wouldn’t risk exploding/irradiating parts of my body that I’ve grown quite attached to.
It’s a prudent move . . . although it does tend to limit our opportunities to gain superpowers. I mean, being able to LaTeX at super-speed because you were bitten by a radioactive backslash key is useful, but it ain’t exactly firebending.
Alas, the only superpower I developed during my time as an experimentalist is an incredible frustration with my lab equipment, and an amazing ability to break stuff.
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It is questionable why no historians or gunsmiths were consulted for this episode. Equally depressing is how many self-proclaimed “science types” are ignorant of manufacturing history.
Until the turn of 1900, shotgun barrels were made of laminated iron or damascus. Iron strips were twisted and hammered into ribbons. The ribbons were heated and wrapped around a mandrel. The edges were heat welded together.
Although these barrels were superceded by steel “nitro proof” barrels, they continued in common usage up until right after ww2, when newly manufactured items all of a sudden became inexpensive.
It is not uncommon to go into an old gun shop, and see an old shotgun on display, with a goose-egged, bent, dented, or split barrel.
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The metallurgical comment by munk stump is correct. Using modern shotgun shells in a damascus barrel will usually result in”material failure” of the barrel. In modern rifles and pistols the barrel pressures are routinely at 30,000 – 40,000 psi. When converted to short tons it is 15 – 20 tons per square inch. This is far less than the 7 tons/square inch. Modern shotguns usually see pressures of 8,000 up to 14,000 psi (SAAMI specs), which is 4 – 7 tons/square inch. When testing for burst pressure in current production 12 gauge (Remington 870 specifically) the pressure was increased each round by 5,000 psi. The barrel was able to function correctly with 50,000 psi loads, but failed at 55,000 psi.
All the pressures I referenced above are chamber pressures as that is what is used by the firearms industry for testing. The chamber pressures are going to be far higher than the pressure at the muzzle. From the Journal of the Forensic Science Society empirical tests showed that 8,000 psi at the chamber yielded 500 psi at the muzzle.
Please remember that damascus steel barrels varied greatly in quality along with their ability to withstand pressure. Lower cost (lower grade) shotguns will burst when higher grade shotgun barrels will function well at the same pressures.
If you had an extremely short barrel maybe in perfect conditions it could explode but its a matter of physics you would have to have a plug exerting that same force at exactly the same time…..they welded a plug in and if that didnt blow up…..short of faulty metal or a bad bullet its not possible.They showed how tough gun barrels are when they did the myth about japanese troops cutting machine gun barrels …..if you cant cut a red hot barrel in half it sure as hell isnt gonna explode
Another factor they did not address is using bird shot or buck shot….they used slugs both times
Watching “Support Your Local Sheriff!” on yt and James Garner puts his finger in the barrel of a pistol. I decided once and for all to look up what would really happen. I was very happy to find this article, I loved seeing the physics worked out, but I still feel like I don’t know what would happen. Old Western guns, would they split? Fun read, though, thank you!