Hi Keith,
It would also be interesting to find, or develop, a model that includes heat transfer to the barrel. This could potentially explain the temperature sensitivity of powders, and if so, would say that all powders are susceptible, and that the only way to avoid the problem is to keep the barrel at the same temperature. I wouldn't be surprised if someone has already analyzed this.
Cheers,
Keith
I don't know the extent of previous study in the subject. I'd be surprised if there hadn't been a lot of military effort put into the problem for artillery use. Unfortunately the young gunnery colonel I used to know, died a few years ago
, so I can't pick either his brains or those of his contacts.
What follows is guess work, plus I've got a rotten cold at present, so apologies in advance if my thinking is even more off than it usually is.
I'll try to limit my thinking to straight nitro cellulose powder, I've read some suggestions that double base powders may burn the NG content off first, though I'm not deep enough into the subject yet to know if more recent papers still follow that thinking.
The picture I'm starting to build up (and please chip in if I'm getting this completely wrong) is of the reaction front, however thick that might be, progressing by conduction into the powder grains. I’m assuming that there is no melting or boiling at the surface of the grain while it burns. As the pressure of the gas surrounding the powder grain goes up, so does the gas' temperature (though how applicable the ideal gas equations are, I'm not sure), there is also going to be radiant heating from the surrounding grains.
I think those two processes will reduce the amount of heat lost from the reaction front to the surrounding gas, and in effect increase the temperature gradient into the powder grain, speeding the reaction, hence why smokeless burns faster when confined, and why, with overloads, pressures climb disproportionately quickly, as there is a feedback loop operating: the higher pressure goes, the faster the powder burns.
I don’t know whether or not there is a limiting factor, with increasing pressure slowing the escape of gasses from the reaction front and acting to slow the reaction.
I haven't got my head around what is going to happen in the barrel yet. I'm thinking of the burning powder grains in a sort of gas fluidised suspension chasing the bullet up the bore* as they fill the available space, but what scale effects take place, I don't know. On the one hand, you have expansion ratio as a variable, but I think you will also have some sort of "squish" effect analagous to i c engine combustion chambers, where heat loss to the barrel slows or perhaps even quenches burning.
Certainly with rock blasting, there is a limit to column diameter (drill hole diameter for putting the explosive into) for each different explosive, and if you go below that diameter, the detonation front (which travels at the speed of sound in that material, rather than the speed of heat conduction!) loses so much energy to its surroundings that the detonation dies out and you get a partial mis fire. The unfired explosive is left in the hole.
It may be that even minor changes in barrel temperature are enough for a transition to occur between quenched or almost quenched powder in the barrel, and it burning normally, thus giving a sudden jump in pressure.
Like explosives, this will probably be (if I have the process identified it will almost certainly be) scale dependant, a larger cartridge and bore but with otherwise identical expansion ratio, will have a much smaller proportion of cold barrel wall to soak up heat from the burning powder column (it is a square : cube relationship). Thinking about IC engines, I’ve seen old experimental single cylinders in a museum. They were made to explore the upper limit of cylinder size for spark ignition engines for aero engines. As the cylinder gets larger, there is proportionately less wall area to soak up the heat as the mixture is compressed, so they reach a point where the compression ratio has to be decreased to prevent the mixture pre igniting, and also detonating with the spark. I think the theoretical limit for a practical spark ignition engine is about 5K HP, hence ships and trains use diesels, or gas turbines, which just go on getting more efficeint as they get bigger.
Assuming that there is a scale effect operating, we might see some calibres more susceptible than others. Has anyone seen a cut off point, say 6mm and smaller giving trouble with high pressures on hot days but all of the .30 calibres OK? (presumably it will only be the long range guys who’d see this, where a variety of calibres get used).
Just adding in double base powders again for a moment. I don't know at what temperature NG becomes unstable within a powder, and how that changes with pressure. It may be beginning to decompose ahead of firing in a hot chamber, a sort of not quite cook off, so that the reaction front is able to be both deeper and faster. I don't know.
I think I am starting to understand why duplex loads are such a dangerous no no. Even a small amount of a fast burning powder will raise the early pressure and temperature in the case, thus greatly accelerating the burning of the main charge of slower powder, and possibly getting into the runaway feedback loop of dramatically rising pressure.
In the ideal Otto cycle for a heat engine, it is assumed that the working fluid is fully heated instantly when the piston is at top dead centre (before the bullet starts to move). (this is described as constant volume combustion, but this is an ideal which can never be achieved in reality) this means that all of the heat (heat equals pressure equals energy) is there to be expanded through the full piston / bullet travel. any heating / pressure rise after the piston / bullet starts to move, represents heat / pressure that wasn't there to be used from the start.
my current guess for the reason people used duplex loads in the past (eg Elmer Keith and his pals), is that the guys thought they were getting extra performance, when all they were actually getting was the same performance that they would have got by using an overload of a faster powder.
When Diesel began developing his engine, his idea was to compress the air as much as possible, then, knowing that he was already at the strength limit of the engine, the idea was to burn fuel gradually, to maintain that high pressure despite the piston moving away. In the "Diesel" cycle (modern Diesel engines work on the Otto cycle), any drop in that constant pressure before the end of burning represents potentially useable power wasted.
The two most obvious limits in applying any of this to guns are the max pressure, and the limit of acceleration that the bullet will put up with before the jacket and core join shears.
The theoretical ideal graph wit bullet travel along the horizontal axis and pressure increasing up the vertical would show pressure rising to the max before the bullet starts to move (all of the energy to cause that pressure rise would then get to expand (= work) for the full length of the barrel).
Pressure would then continue at that max level after the bullet begins to move, to give the additional energy required for the muzzel velocity you want, and all burning would be completed before that pressure began to drop. After that, the hot gas would expand for the remainder of the bullet's travel in the bore.
Now, how to achieve
K
*Could this be why cases with steep shoulder angles are popularly supposed to give less throat erosion than those with shallow angles? is part of erosion the impact of powder grains hitting the throat, rather than making their first impact with the case neck? or is that particular claim for steep shoulders an old wives tale? Or worse, me thinking I’ve remembered something that was never actually said?
