inspired by the railgun thread, I have a question about conventional guns. What is the rate of change of acceleration experienced by a bullet traveling down a gun barrel? Pick any gun, the bigger the better. After the gunpowder turns to gas, the bullet begins to accelerate (actually I suspect the acceleration begins before all the powder burns). Is there a maximum initial acceleration that reduces as the volume behind the bullet increases? Perhaps that is one advantage of a railgun? A very large and constant acceleration can be applied over the entire length of the “barrel”. Since the projectile obviously has to be strong enough to withstand the maximum acceleration, maintaining this maximum acceleration would be an advantage.
Yer pretty much right: there are microscopically-timed factors that require integrals I’m not what you’d call “qualified” to integrate.
From the exact moment of the firing pin being struck:
- The primer is struck and needs to burn
- The powder burn is initiated, and needs to burn fully
- The bullet needs to seperate from the cartridge casing and begin it’s travel down the barrel.
For the most part, the major part of acceleration is where the main powder burns. The biggest part of the OP is at which point the bullet separates from the cartridge–because at that point is where acceleration of the bullet (however negligible) would constitute his answer.
With the primer burning, the powder burning. . . etc, it’s all too instantaneous, and I don’t think any study has been done to actually draw the line.
Tripler
For me: acceleration doesn’t matter–it’s the muzzle velocity and ‘slug size’.
Numerous studies are done of the velocity of the bullet in the barrel and the pressure profile. Such investigations are ongoing. The object is to burn the powder at an optimum rate so as to maintain barrel pressure and thus acceleration throughout the travel within the barrel. There is is whole field of study called interior ballistics devoted to the subject.
By God, I stand corrected! 
Tripler
There’s a line drawn. . . hell, there’s a study!
Interior ballistics indeed! The most interesting of the three (Interior, exterior and terminal ballistics.) One of the factors involved is that the weight of the powder involved must be factored in. If X mass of the projectile is there, there is Y mass of powder charge. While the powder burns and its volume expands, it’s mass does not change, and it must propel itself down the barrel as well. So the more powder you put behind the bullet, the more powder you need. Several different approaches have be made to this over the years. Winchester Ball Powders are excellent for an initial burst, and are the best choice for many applications, mostly short barreled applications. Best pistol powder around. As the balls ignite they have a lot of surface area so they burn very fast, and as the spheres get smaller the burn rate goes down. A big blast. DuPont took the approach of cylindrical power with a hollow tube. The outside of the tube has a huge surface area to burn, The inside very little. As the outside burns, it’s area becomes less and the burn rate decreases, but as the inside of the tube burns it becomes larger area wise and burns faster, offsetting the reduction in the outside tube burnin, Nice even pressure curve. But only in longer barrels. To really send a big projectile into next week, either magnetic acceleration and let momentum ride, compressed helium (still experimental) or just plain old boring rocket power. Loose mass along the way.
Thanks!
So, the powder really does burn, as in a spreading flame?
There’s a definition of “explosion” that tests whether ignition proceeds by pressure wave, as opposed to temperature. An explosion by this definition can be much more powerful because the timing is limited only by sonic velocity in the perhaps solid explosion, and perhaps at high pressure too. Shorter time for the same energy means more power.
I guess gunpowder is only a thermally spreading flame? Is the oxidizer already finely mixed with the reducer?
I’ve heard of powder charges detonating in handguns and rifles, usually involving small charges of fast-burning powder in large cartridge cases. It’s a very bad thing.
Gunpowder “explodes” via deflagration; that is, burning on the surface of the grains. This provides a fairly gradual (in relative terms) increasing and decreasing pressure distribution so that the work is done over a distributed period and the pressure never exceeds levels that would cause normal gun chamber materials to fail. Some smokeless gunpowders are “double base” or “triple base”–including nitroglycerine and nitroguanidine along with the nitrocellulose base or normal smokeless powder–which increases the energy available, but you then have to be careful not to overload or underload them lest you set up a pressure wave that actually causes the shock-sensitive trinitrides to detonate rather than burn, which, as mks57 indicates, is a very bad thing, especially when it happens in a chamber that is next to your head.
Stranger
Traditional black powder is a mechanical mixture of the ingredients, charcoal, sulphur and potassium nitrate.
It is more than an intimate mixture of fine powders - the ingredients are mashed together, in a pestle and mortar, or by ball milling or other milling. It can then be milled or wet-compressed into a hard mass and broken and sieved to make grains of a uniform size.
As you guessed, black powder deflagrates, the flame propagating over the grain surfaces and burning inwards. Grain size therefore has a large influence on burn rate, the larger the grains, the smaller the burn rate. In Neal Stephenson’s Baroque Cycle, bag charges for naval cannon are saboutaged by grinding the grains into a fine powder, causing the cannon to burst.
Modern smokeless powders tend to consist of carbohydrates or hydrocarbons that have been nitrated, i.e. -NO[sub]2[/sub] groups are chemically attached to make nitrated molecules. This group provides the necessary oxygen, even more readily than an intimately mixed oxidiser would.
Interestingly, the smokiness of black powder is largely due to the sulphur constituent, which is necessary for spark sensitivity. With a sufficiently energetic means of ignition, it’s possible to use sulphur-free black powder. http://www.musketeer.ch/blackpowder/recipe.html
As posted by Stranger on a Train
This rings true of the advice I had read in many handloading manuals published by bullet makers, powder makers and handloading equipment makers. I have been out of the game for twenty years. All took great pains to stress an underload is as dangerous as an overload due to danger of detonation. Such an underload was known as a “Squib”. It was usually used by target shooters who wanted to be able to practice in a confined area and have minimal backstop. I believe it was Speer ( a bullet manufacturer) who marketed a reusable plastic .38 casing that threw a reusable plastic bullet powered by primer only and could be stopped by a blanket hung from a floor joist in the basement at a range of twenty feet. I used them many times and they were great. I did have to open the cellar doors though or it would stink up the house. The noise was minimal.