The model in this paper looks inappropriate for normal cartridges, since the reaction wave starts on the wrong end of the porous solid, and the solid is assumed to have zero velocity until the wave passes through it. A more accurate model would have the solid particles accelerating along with the reaction gases. I don't know where to point you for a better model, but please let me know what you find. Have you tried CompendexWeb?
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
It is not a barrel chilling the expanding gasses it is the slower ignition of the powder if its cold.
Tim,
If that were the case, then powder temperature, but not barrel temperature, should affect maximum chamber pressure, right? There are some well-documented experiments here (www.shootingsoftware.com/ftp/Pressure Factors.pdf) that show that both ammo and barrel temperature affect maximum chamber pressure.
A simple calculation (from the current tuner thread) shows that the thermal capacity of an 80 oz stainless steel barrel is 1135 joules per degree Kelvin, while the energy that we get out of the gunpowder (for a 30BR) is about 2200 ft lb or 2983 joules. So the barrel, by soaking up enough heat to raise its temperature one degree Kelvin quenches over 1/3 as much energy as we get out of the charge.
How about this for a hypothesis: powder temperature, neck tension, seating depth, etc., determine peak pressure during the first couple of inches of bullet travel, but barrel temperature (and maybe several other things) determines energy (proportional to the area under the pressure vs. time curve)?
Cheers,
Keith
Tim,
If that were the case, then powder temperature, but not barrel temperature, should affect maximum chamber pressure, right? There are some well-documented experiments here (www.shootingsoftware.com/ftp/Pressure Factors.pdf) that show that both ammo and barrel temperature affect maximum chamber pressure.
Cheers,
Keith
If your read all the way to the end the author got to where I was going while I was reading the article. The barrel temperature effect is in its effect on primer temperature not on the cooling of the combustion gases. Heat transfer from the barrel to the cartridge case and primer is much faster that to the powder or the thermocoulple in the middle of the case.
Tim
Heat transfer from powder gasses to the barrel is not very dependant on the barrel temperature. That heat transfer is taking place whether the barrel is cold or hot because the barrel is always much colder than the combustion temperature. It is slightly greater when the barrel is cold because of the slightly greater delta T but I don't believe that the difference is significant (meaning make a meaning full difference and even then it is not large perfromance driver but is detectable) until you are getting barrel temperture in the sub freezing or sub zero range. I also think you have an error in you heat transfer analysis, I think you used the bullet KE instead of total energy. Either need to use the energy of liberation of the chemical reaction (burning powder) or the sum of all energy created during the shot, bullet KE plus bullet temp rise, gas KE plus gas temperature rise, and barrel temperature rise due to bullet friction. This leads to the additional error in your the barrel rise temperature analysis how much of the barrel temperature rise is due to the friction of the bullet passing thru the bore at high velocity and how much is due to heat transfer from the gas. You are underestimating the energy available for heat transfer to the barrel and overestimating the heat transfer contribution of the combustion gasses.
Tim
Tim,
In a second round of experiments, Bramwell found that primer temperature had no effect on chamber pressure or muzzle velocity (www.snipershide.com/UserFiles/.../powder_primer_temp_experiment_2.pdf). However, cartridge and barrel temperature were both important, with barrel temperature being more important than cartridge temperature. Here is what he says:
"The fundamental reason that ammunition temperature has an effect on pressure and velocity is that heat energy absorbed by the cartridge components is energy lost to propulsion. Warm cartridges absorb less heat than cold cartridges.
Similarly, cold receivers and barrels absorb more propulsion energy than warm ones. Since the thermal mass of a barrel and receiver is much larger than that of a cartridge, this effect is much stronger than the effect of cartridge temperature."
Keith
Tim,
My calculation of 1135 joules per degree K is just the result of multiplying the mass of the barrel times its specific heat. It is just a property of the steel, and doesn't depend on kinetic energy or friction.
A surprisingly small change in heat transfer could possibly explain significant changes in muzzle velocity. A 1% change in muzzle velocity is large (30 fps change from 3000 fps nominal). A 1% change in heat transfer could result from a 22 K barrel temperature change (2500 K flame temperature, 300 K nominal barrel temperature). That's about a 40 F change. I'm not ready to rule out the effect of barrel temperature just yet.
Cheers,
Keith
PS. For those who are keeping track, I underestimated flame temperature over in the tuner thread. Sorry.
Tim,
Cheers,
Keith
PS. For those who are keeping track, I underestimated flame temperature over in the tuner thread. Sorry.
Keith
The link for exp. #2 did not work for me but I would be glad if primer temperature did not effect velocity. I did not intend to inticate that barrel temperature or "Gun Temperature" did not effect velocity, my point was that the effects were small and if I was to build a model for internal ballistics for small arms that the other factors I mentioned would be where I would put most of my effort.
Tim