This is a semi-auto pistol around the same size but slightly longer than a 6 inch desert eagle. 7 inch barrel.

As I said assume the bullet, chamber and barrel will withstand the pressures and temperatures generated.

The bullet begins at an initial velocity of 0, i need to accelerate it to 900 m/s over a distance of 0.1778 metres. This gives a linear acceleration of 2277840.269966254 metres pre second squared. Thus the bullet took 3.9511111111111111 e-4 seconds to travel that distance.

Using the bullets mass, change in momentum over time = impulse (force). So 0.045359237 kilograms times 900 m/s = 40.8233133 kgm/s divided by 3.9511111111111111 e-4 = 103321.09665338339 newtons. You could also use F=ma, newtons second law. So I'm kinda working it backwards in the sense that I know the velocity I want to achieve which equates to the force of thrust on the bullet which will be required which then equates to a pressure which eventually equates to the mass of the propellant that I will need, so as to figure out the case dimensions and other important stuff. I have just been having trouble finding an equation that relates pressure to an explosive's density, mass, potential chemical energy, detonation velocity etc. Now I am not sure whether the force I calculated is the maximum force after moment of detonation or the overall total additive force down the length of the entire barrel, perhaps you could clarify that.

Unfortunately this constant acceleration is just an estimate since acceleration is not constant because the gases are constantly pushing the bullet with a decreasing amount of thrust force over the time it takes for the bullet to travel the barrel's length due to an increase in the volume the bullet leaves behind it (thus pressure also decreases). How do I account for this? How do I calculate the true acceleration?, the true maximum pressure (chamber pressure) that I am going to require to achieve 900 m/s

**by** taking into account these constant decreases in pressure, thrust etc. Is integration required here? if so how do I begin to approach it.

Also I understand the purpose of deflagration and that is why smokeless powder is used so widely for so long, but do you really mean the most powerful chemical explosive, with a perfect gas ratio and ridiculous maximum pressures can't compensate for the fact it detonates rather than burns, and accelerate a bullet through a 7 inch rifled tube more than gunpowder can, if so then consider me permanently jawdropped!!!!!!!! and i'd best start searching through the chemistry forums to find something better Also, 7 inch barrel, 900 m/s muzzle velocity, far faster than any other semi-auto pistol and I'm still gonna gun for a higher velocity. Surely the bullet doesn't spend enough time in the barrel for deflagration's effect to outweight the fact I am using the highest chemical explosive there is

, cuz I am sure as heck not gonna get a 45 gram bullet to 900 m/s in 7 inches and a handgun with smokeless powder while keeping cartridge size down, it is the whole point of me trying something far more potent.

Sorry If i made my post unclear, I'm still in sixth form.

So do you think you have an equation that relates the parameters of an explosive compound to the pressure it will generate? or perhaps help me calculate the true acceleration/ maximum pressure required/ rate of change of pressure etc. whatever else you think you can help me with.

Thanks for the reply.