## how to predict performance of a propellant in relation to another propellant

John paul III - 27-6-2020 at 05:27

I am trying to figure out how much more anfo would one need in a cartridge to obtain the same effect as x grams of nitrocellulose. Pressure is certainly a factor so P=nRT/V; that means that i need to calculate the number of moles of gas after combustion per gram (easy) and temperature. I have the Relative Effectiveness factor data from wikipedia on both substances - Its just energy per mass. So:

1.Is the average combustion temperature proportional to energy/kg or is there a different way to calculate T?

2. Is comparing the pressure from the gas law a reasonable approximation of the relative performance of two substances as propellants? (im intentionally not taking into considering the grain geometry)

Also before anyone says ANFO is a high explosive and will burst the barrel - no it doesn't, i've tested it

[Edited on 27-6-2020 by John paul III]

Microtek - 27-6-2020 at 11:05

If you wanted to use the ideal gas law, you would need the number of moles of gas in the barrel. This is not so simple, since explosive decomposition products can vary quite a lot depending on the manner of decomposition (low or high order detonation, deflagration) and also on pressure. You would need to make so many assumptions that I would suggest that you do a series of experiments instead.
John paul III - 27-6-2020 at 14:22

Im only concerned with low order deflagration and im certain I know what the combustion products will be.
One issue i can think of is that gas with higher number of moles will lose less temperature per given pressure drop:

for 20 moles of gas
P-x=20*R*(T1-x/20*R)
because x=20*R*dT, so dT=x/20*R
for 10 moles of gas
P-x=10*R*(T-(x/10*R)
Because x = 10*R*dT, so dT=x/20*R

I think i can figure this out if i can confirm energy per mass is proportional to temperature or is it strictly energy per particle? :
Would one 100 particles weighing 10g have the same temperature as 1000 particles weighing 1g if they all travel at the same velocity?

+i don't own a chronograph so i cannot really test the power

[Edited on 27-6-2020 by John paul III]

[Edited on 27-6-2020 by John paul III]

Twospoons - 28-6-2020 at 14:18

Have you considered trying something like Propep? Its used to estimate rocket propellant performance. Not quite the same situation, of course, but might provide some comparative insight at least.
Dornier 335A - 3-7-2020 at 14:33

1. Every gas molecule has the same kinetic energy at a given temperature. But gases store energy in rotation and vibrations as well, so the total energy is proportional to the total number atoms and the temperature. This approximation is fairly accurate at high temperatures. E ~ N*T

2. No, constant volume combustion pressure is not a good measure for the performance of a propellant. Since you want to ignore grain geometry you could look at two different measures that set absolute limits to the performance of your propellant. One is energy content, assuming all energy goes to accelerating the bullet and the gas itself (since it has to keep up with the bullet)
vmax = sqrt(2*E/(mgas + mbullet))

The other is the speed of sound, since the gas cannot propel a bullet faster than 2/(γ-1) times the speed of sound in the gas. A more reasonable real world estimate I'd say is 0.6*speed of sound.

You can calculate the ideal speed of sound with c = sqrt(γ*R*T/M) where M is the average molar mass in the gas, and γ is the adiabatic index. γ is also related to the ways energy is stored in the gas so you can probably get a decent estimate using this formula I just came up with:
γ = 1 + 2/(3*N/n) where N is the number of atoms in your gas and n is the number of molecules.