From what I understand, high velocity guns tend to use slower burning powder than low velocity guns to avoid overpressure.
For example, a projectile going at about 1000 fps will typically require 3-4% of its weight in powder whereas a projectile going at 2000 fps will require something along the lines of 16-20%. Higher velocity projectiles also tend to have a lower diameter than slower velocity projectiles which means that the barrel bores also do. These two facts mean that if the 2000 fps projectile used powder which burns as fast as the 1000 fps projectile, pressure would go up too quickly inside the barrel of the high velocity weapon. So far, have I got this right?
There are other reasons why higher velocity weapons tend to have longer barrels than low velocity projectiles but I am only interested in the goal of avoiding overpressure.
What I’d like to know is if higher pressures are possible. A lot of small arms seem to top out at around 60 000 psi. Would it be possible to go higher than that? If so, how? Would doubling the thickness of the barrel walls increase pressure resistance by two as well or is it the relationship between wall thickness and pressure resistance non-linear?
Analysis of pressure vessels can be approached in one of two ways. If the wall is thin relative to the diameter of the pressure chamber, then you can safely assume the tensile stress is evenly distributed throughout the thickness of the material. The equations for calculating that stress are simple, and so is the design process. Air compressor tanks, which are typically 1-2 feet in diameter and use steel that’s 1/4" thick, are treated as thin-walled pressure vessels.
When the wall thickness is a large fraction of the diameter of the pressure vessel - as it is in the case of a gun barrel - then you have to use equations for thick-walled pressure vessels. The inner surface is under radial compressive stress, but the outer surface is not. the inner surface is under large tensile stress in the circular direction (called “hoop” stress), but the outer surface is under much smaller hoop stress. At overpressure, failure will manifest first as a crack at the inner surface, where hoop stress is maximum; this crack is a stress concentration that will propagate over time as the gun is fired over and over.
As the ratio of wall thickness to bore diameter increases, the disparity between stresses at the inner and outer surface increases. This means that doubling the wall thickness will not double the pressure capacity. Doubling pressure capacity means increasing the wall thickness by much more than twice.
One way to increase pressure capacity without adding a ton of material is to make the material near the outer surface of the barrel carry its fair share of the load. This can be done by press-fitting an outer sleeve over an inner liner. Under a zero-pressure condition, the outer sleeve now has a tensile preload, and the inner liner now has a compressive preload. Now there will be some relatively intermediate pressure that results in a relatively even stress distribution between the inner liner and the outer sleeve - and at some higher pressure, the inner liner experiences a stress distribution similar to what it would have had by itself at a lower pressure.
I seem to recall that there were some German handguns made many decades ago like this; they were notable for being rather light, despite their caliber. Can any firearms enthusiasts confirm?
Pressure isn’t the real limiting factor, as you suggest, thicker walls will solve that, and this can be carried to the extreme that the guns become to heavy to be useful. With increasing pressure, though, comes increasing temperature. This high temperature gas erodes the barrel. The highest pressure rounds may have a barrel life of only a few hundred rounds before accuracy begins to degrade. Users simply are not willing to tolerate any shorter barrel life. There are some alloys that take heat better, but they tend to be very difficult to machine, and drilling and rifling a barrel is not simple even with cooperative materials.
Making a higher pressure firearm design was a college project I did 25 years ago, it is certainly possible but not particularly cheap or marketable.
The very first thing you need to change is the case. Present chrome-moly barrels are capable of taking more than the ~60,000 psi that is about the standard max, but the brass used in cartridge cases tops out around there. Using steel for 80-100 kpsi or a caseless design for possibly higher is possible, I was reaching for a design that would work at 120k psi. You do need to use higher strength steels at that point, and it would end up expensive but doable. Even then the bore life would not be great, and not something an individual could get ammo for I think.
The muzzle blast & noise was a big concern also at those pressures, I never actually got to the build one and test it stage, but I expect it would be in the ballpark of physically dangerous. I did have a shock absorber system for the recoil, which I felt would probably be painful also (just wag).
The casing can’t contain any serious pressure compared to what the chamber can.
Another thought about cracks. The crack, extending radially from the bore, gives pressurized gas access to its own crack faces. The gas can wedge in there and create greater force than there was before the crack appeared. Of course, the force it creates is also ideally placed to put additional stress on the stress concentrating edge of the crack. So, what might have been a more gradual failure (such as a crack in a beam) can become more explosively catastrophic.c
The case seals the chamber sort of the way an inner-tube seals a tire, though the steel takes most of the pressure. The head of the case needs to seal considerable gaps in many firearms:The cutouts for the extractor and ejector usually. One thing that happens with excessive pressure is that the chamber and case expand on firing. After the pressure decreases, the steel chamber elastically returns to it’s pre-firing dimensions, but the brass case may have been stretched to yield, so it doesn’t return fully. This can lead to extraction problems.
It’s really about larger-scale guns, but there’s a fascinating article on artillery space launch hardware on Greg Geobel’s site here. It detours into a description of the German “Paris gun”, a huge conventional artillery piece designed during the Great War in order to attack Paris from great range.
“The large powder charge melted the lining of the gun slightly every time it was fired. This meant that the shells had to be built in a numbered series, in a sequence of increasing diameters, to be fired in that order until the barrel was replaced and the cycle began again. The barrels were swapped out on a monthly basis.”
Then goes on to tell the mysterious tale of Gerald Bull, who seems like a prototypical mad scientist / James Bond villain, albeit that he doesn’t seem to have had dreams of world conquest. The gist of it - at least in terms of space launchers, rather than small arms - is that there comes a point when rockets are much cheaper and more efficient and generally better.
Wasn’t there a rocket pistol, once? In Vietnam. (Googles) Oh yeah, the Gyrojet. It fired six little rockets but doesn’t seem to have been a great success.