Velocity

blackdieselThink of a baseball vs a badminton.


+1....Excellent analogy. The pressure spike from a firearm is much more than the 3 to 4000 psi our pellets use. If you could get the pellet to go 3000 it would probably be fairly acccurate if the twist rate of the barrel was designed for those speeds. The problem is when the pellet is traveling too close to the speed of sound. watch a video on youtube of a jet approaching the speed of sound. The jet will start to get turbulance as it approaches the sound wave. As it breaks through......its almost like a bomb going off shaking the whole aircraft. Once past that speed.....smooth as silk. The pellet slows down so fast that even if you shot it at like 1400 fps......as the pellet slows to like 1150 it crosses that pressure wave again destabilizing the pellet. Best to stay around 20% below the speed of sound with our airguns.
 
If you look at the drag profile of a pellet vs the speed in Mach you'll see that the drag vastly increases when approaching Mach 1. When Mach 1 is passed the drag becomes pretty linear again. The fast changing drag combined with crossing the sound barrier destabilizes the pellet which leads to inaccuracy.



(the picture above is a G1 drag profile, not exactly the pellet drag but the shape is similar)

As stated above, if you shoot a pellet above the speed of sound which such speed that it stays there for at least the first 100 meters it'll probably be stable (if twist rate, weight etc, are properly tuned)
 
Have you ever watched a video on long range shooting with a centerfire rifle? They'll be hitting near MOA targets out thousands of yards, then all of a sudden they can't hit anything and the bullets are dusting all around the target. That is because the bullet has slowed from its 3000fps muzzle velocity to somewhere around 1100fps at range and has encountered the sound barrier turbulence.
 
An easy way to think about what happens is a boat on plain with the wave front running behind the boat, as the boat slows the wave catches up and slews the boat.
I think that there are multiple hurdles that stop airguns from shooting at higher speeds
1. (Most likely the biggest ) BreadNButter If airguns started being able to shoot at speeds comparable to powder burners more state and fed restrictions would soon follow. Manufacturers don't want that to happen (neither does most air gunners)
2. Compression issues. This part is over my head but you are moving air from one chamber through a valve into another chamber where expansion and escape happens, It does not matter what material is involved gas liquid or solid a sudden expansion will result in heat. And any valves or orifice that the gas passes through would erode and wear out.