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Old October 30, 2012, 04:47 PM   #12
Unclenick
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Join Date: March 4, 2005
Location: Ohio
Posts: 10,221
This is actually quite a complicated subject. Powders include deterrents and stabilizers. As a result, not only are the generated gas species different for different powders, the total potential energy content varies substantially. QuickLOAD's database has the black powder substitutes as the lowest energy powders, at about 3050 J/g. The lowest energy rifle powder, no doubt owing to massive quantities of deterrent, is Accurate 8700 at 3460 J/g. At the other extreme are Alliant Power Pistol and Bullseye, at 5150 J/g and 5158 J/g, respectively. So the ratio is as much as 1.7:1. Obviously, a higher energy powder with the same burn rate as a lower energy one can produce higher average temperature and therefore a higher pressure with less total gas (you would need less of the higher energy powder to get the same velocity). The average for all the QL database powders is about 3950 J/g. Further, due to ash and particle suspension and heat transfer to the bullet and bore and kinetic energy translation into the bullet’s kinetic energy, and the constantly changing temperature, this stuff won’t behave exactly like an ideal gas.

Since QuickLOAD has the complicating factors taken into account, I can use its output to make an estimate of gas volume. At 3910 J/g, IMR 4198 is reasonably close to average in energy content. If I put a 21 grain charge of it behind a 53 grain SMK bullet in a .223 Remington with a 24" barrel with the bullet seated 1 caliber into a case that has 28.8 grains fired water overflow capacity (lower than usual, but the program default), the program tells me the volume under the bullet is 1.725 cm³. The expansion ratio of that barrel length is then 9.28 relative to that bullet base position and case capacity, so the volume behind the bullet at the moment the bullet reaches the muzzle in this case is 16 cm³. The muzzle pressure at that moment will be 6075 psi, while the breech pressure will be 7520 psi (there's a pressure gradient), for an average of 6798 psi. Divided by one atmosphere (14.7 psi), you get an expansion of 462 times after the gas exits the muzzle.

462 times 16 cm³ = 7.4 liters. However, that's at whatever temperature the gas has at the muzzle. If the peak temperature is 5,000°F (5,460°R) at the peak pressure of 49,500 psi, at which point the expansion ratio has progressed only to about 1.2, volume behind the bullet is at that moment 2.07 cm³ and about 52% of the powder has burned. Almost 100% of the powder is burned by the time the bullet gets to the muzzle, so then, based on volume alone, you would expect muzzle temperature taken as a proportion of gas and pressure to be about 5,460°R×2.07 cm³/16 cm³/0.52 or about 1358°R, which is 899°F. If your ambient temperature is 75°F or 535°R, then you’d expect 7.4 liters of gas at 899°F to decrease in volume by 535°R/1358°R or a factor of 0.39, becoming 2.9 liters when it finally got all the way down to air pressure and temperature.

Anyway, that’s for 21 grains of a fairly average energy single-base powder burned in a 24” barrel. It comes out at 7.4 liters and drops rapidly toward 2.9 liters at standard temperature and pressure. So your estimate wasn't far off if you pick the right temperatures. Double that charge as in, say, a .308 Winchester and you’ll be at roughly double those volumes as long as the powder choice burns fast enough to burn completely in the barrel. Real volumes will obviously be affected by that percent of burn which, in most instances, won’t be that high. But for a worst case it’s best to pretend it will.
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