How small and fast can a bullet go in atmosphere?

Question

In many sci fi universes that don't have handheld energy weapons, they instead use solid projectiles that either go big (Warhammer 40k) or really small (Mass Effect). The former I have a pretty good understanding off. It is the latter I want to know more about, namely;

How small and fast can someone make a bullet in atmosphere before detrimental effects like friction become an issue?

We can for now ignore how the projectile is launched, though feel free to give it a shot (tee hee).

Lets assume that the atmosphere that we are operating in is Earth like.

A question on how damaging such a projectile would be, and how defend against it, will be asked on another post.

Edit: To clarify on "issue" in the question; a good example would be the critiziem of Mass Effect weaponry, namely that if the sand grain sized projectiles are fast enough to ionize the air, then why is the projectile itself not vaporized? And other issues like why does it not get knocked off course from the air molecules etc.

Answer 1

Assuming a handwavium weapon that can accelerate the projectile as needed, you can have single atomic nuclei moving at close to the speed of light. In fact, such projectiles are fairly common, since extra-solar sources are continually bombarding the Earth with them: https://en.wikipedia.org/wiki/Cosmic_ray

The problem with using them as a weapon is the extreme case of using any small, high-velocity projectile: they're likely to pass through the target without doing much damage. And in the case of really small projectiles, the damage is most likely dying of cancer a few decades later :-)

Answer 2

In addition to what jamesqf said in his answer, another drawback of small projectiles is that they are more effected by drag. Small objects have a higher surface area to volume ratio than large objects of similar shape. Objects with higher surface area to volume ratios lose energy to drag faster than if they had a lower ratio. So your tiny bullets will have relatively short range. This is why real sniper rifles tend to be relatively high-caliber. When a bullet falls below the speed of sound, it loses a great deal of its stability and thus, accuracy. Higher caliber bullets stay supersonic longer than smaller bullets.

If your bullet is molecular or smaller in scale, this distance will be similar to the Mean Free Path. On Earth, the mean free path is about 68nm.

Answer 3

The smaller the projectile, the faster it will lose its speed to atmospheric drag. So to get a usable range you need a higher muzzle velocity. If the projectile's velocity is very high it will heat up and melt/vaporize from the atmospheric drag (or more accurately the compressional heating). There are no solid materials with a melting point higher than a few thousand °C, so that gives you a hard limit that depends on your projectile size, muzzle velocity, and desired range.

You can sidestep that issue by taking individual atoms as your projectiles, as individual atoms cannot melt or vaporize. A few individual atoms won't do much damage, and as jamesfq says the damage they do cause will most likely manifest itself as cancer many years later. But if you have grams or kilograms of atoms at very high velocities they do cause immediate heavy damage (e.g. vaporizing whatever they hit, and causing a small explosion from the cloud of expanding plasma of vaporized material). A few individual high velocity atoms will get scattered by air molecules, but if you have a beam with enough atoms they will push the air molecules away. The speed limit here is where you start to get nuclear reactions when the atoms hit air molecules. If that starts to happen you may get a small explosion at the muzzle of your gun. However if whatever is firing that gun is strong enough to just ignore that, there's no real limit at the velocity you can fire atoms.

The only thing is, firing a beam of atoms is generally classified as an energy weapon. So you'll need to clarify your definition of "projectile" here.