In my world, there is no access to modern or traditional gunpowder. I was wondering if a dedicated technician with a modern shop (cnc machines, and a surplus of parts and raw material, etc) would be able to develop a bullet the fires from compressed air that is in the same cartridge as the projectile. Issues I am not sure of are: How big would the cartridge have to be to push a 30 caliber bullet at lethal trajectory? and how thick would the air chamber have to be to hold that pressure?
Combining the projectile directly with the air chamber and a single use valve is possible, (and exact sizing would depend on materials and valve design) but it is vastly inferior to a bulk storage tank design that is separate from your projectiles:
- Bulk tank storage means that you need 1-2 valves to fire potentially dozens of rounds at lethal velocities in place of at least one valve per shot.
- Reduced valve count translates into reduced maintenance (and potentially increased safety)
- Handling the independent projectiles does not introduce risks of damage or leaking charges.
- Bulk storage allows option for consistent regulation and reduces the risk of shot-to-shot variance due to differences in cartridge pressures.
Consider the Girandoni air rifle - each cylinder allowed approximately 30 rounds to be fired, and the soldier was typically issued two spares. The accompanying (ball) ammunition occupies a very small and highly flexible volume - This translates into ease of carrying and handling.
Contrast this to the (non-lethal) options seen in paintball and the obscure 'goblin' shells that held one paintball and an air charge to fire it: These proved unreliable, inconsistent, and took up far more space than a CO2 cartridge beside the paintballs that could be fired with one. And the small 12 gram CO2 cartridges weigh more and take up more space than what could be achieved with a larger bulk tank.
For handling and ergonomics, a mixed Tank+Magazine design may be what you're really after - A single bulk tank with capacity to hold a charge for multiple rounds, and a magazine of ammunition that the tank can reliably fire.
(Answer can be improved with exact numbers by myself, or another member, if needed/someone gets around to crunching the numbers - Material options and exact bullet size/weight would need to be established for accurate figures.)
The Brocock Air Cartridge System seems to fit your description. The cartridges are loaded with an airgun pellet and primed from a pump or diving tank. They are designed to resemble and function as close to real firearm cartridges as possible, rather than being designed for the kind of power you describe.
I've actually designed (though not built) a cartridge that works like this. By my calculation, and by comparison to conventional precompressed air guns, I think a cartridge the size of a .30-06 round holding pressure similar to that used in PCP air guns should be able to propel a lightweight .30 caliber bullet (say, 100 grain or lighter) at close to the speed of sound, or a heavier bullet at somewhat slower velocity.
This is adequate for hunting small game (squirrels, rabbits, etc.), or marginally adequate for self defense against unarmored assailants -- ballistically, it would be similar power to a .32 ACP handgun cartridge, possibly as good as a .32 H&R Magnum (the former fires an 88 grain bullet at slightly subsonic speed; the latter fires a 100 grain bullet at supersonic muzzle velocity). It would be "single shot" in a handgun, but in a rifle sized arm could be loaded from as magazine, as was done starting in the 1890s with powder weapons.
This could be scaled up some -- a larger air capacity cartridge will give more velocity and/or propel a heavier bullet -- but there's a limit to how big it's practical to make your cartridges. If you need something like a .50 BMG cartridge to hold enough air to propel a 180 grain .35 bullet at Mach 1.5 (i.e. enough power to reliably kill deer at moderate range), the ammunition bulk is likely to limit how many rounds you can carry.