Interesting thoughts from the Paris Gun thread: Take your standard 35cm Naval gun, but give it a 20cm shell in a sabot, 1500m/s MV at 530MPa/52,000psi chamber pressures. Instant 100km range from WW1 tech.
We now have extremely low drag shell shapes, like that of the 155mm LRLAP (which also happens to be rocket boosted, but that's a different discussion). LRLAP is 220cm long, 155mm diameter, and weighs 102kg. ELD bullets are usually good for +50% range in small arms, and they get better as they get bigger due to better ballistic coefficients. I'd be surprised if a 155mm ELD shape wouldn't give you +100% range. Now we're talking about 200km or more before we count the rocket booster. LRLAP had a big enough rocket booster to count for at least 50% of the range, so now it's 400+km for a 155mm shell. Still not 1000km, but we're getting there. Admittedly with a stupid expensive shell, but I don't see any way around that.
Build a similar gun for modern day artillery, maybe you can get away with a 20-25cm bore ~55-60 calibers long using a 155mm shell diameter. Composite sabot design more or less copied from the tank guns, though figuring out a driving band interface will be "interesting". Doing that also gives you the option of full bore diameter shells for really dropping the hurt on someone.
You can not extrapolate large caliber artillery from small arm that way.
For small arm, the biggest obstacle of range is air drag, while for large caliber is muzzle velocity.
If a small arm like 7.62mm and a naval gun like 406mm shot in vacuum at 45 degree, e.g on Moon surface, both will have the same range. You can estimate maximum ballistic range in vacuum at best angle (45 degree), by square muzzle velocity then divide by g (9.81m/s2)
For example let say muzzle velocity is 1000m/s, at 45 degree, maxium range in flat surface is 1000x1000/9.81 = ~100,000 m or 100km. But a small arm only has like 5 km range at 45 degree while naval gun like 406mm has 40km range, about ten times larger. The large gun can achieve 50% of maximum ballistic range while small arm only gets 5%. So if a small arm can double the range, it still has nowhere near the percent of large caliber.
The biggest issue here is air drag, and because large shell has much more mass per area to overcome air resistence.
For extreme long range and velocity, like +4km/s and several thousand km in ballistic missile then the curvature of the Earth will be very important because its allow range to increase dramatically than in flat surface.
In short range ballistic, the strategy is to shot at higher angle (50-60 degree) than optimal angle in vacuum (45 degree). This allow the projectile to escapce the dense air faster to reach the low density air in upper atmosphere and retain much more energy to reach further. For shorter range ballistic like smaller artillery, since the shell can not reach upper atmosphere with enough energy, then that method will not apply. At 20km, air density is about 10 percent of sea level, which translate to 10 percent air resistence. You can estimate peak altitude of maximum range in vacuum as 1/4 of range. i.e if it is 100km then it will reach 25km high at 45 degree.
So for 2000m/s like some gun, i.e apfsds, the maximum range in vacuum at 45 degree is 2000x2000/10 = 400km. There is no way you can increase ballistic range above this with lower drag. Even with rocket, you can estimate range as muzzle velocity at the end of burn out plus the range before that. For military rocket like air to air missile or MLRS, the burn out is pretty quick and ballistic range is still similar to the above estimation. E.g for air to air missile you should include velocity and altitude of aircraft at launch for energy of the missile but the ballistic is the same. No thing escape gravity.
At 4km/s in vacuum flat surface gives you 1600 km ~ 1000 miles, but ballistic missile with 4km/s will achieve much more range like 4000km because of altitude and distance travel before burn out. You can estimate a rocket as a gun with really really long barrel and high altitude. And at 4km/s then curvature of Earth will play significanlly.
