Our laser-guided Copperhead and GPS-guided Excalibur howitzer rounds already undergo thousands of Gs of acceleration upon firing. Due to possible interference from cloud cover, the Copperhead's fins pop out at low terminal trajectory to do final guidance to the target. The Excalibur pops its fins at the top of the arc, giving it a much wider range of correction to the target, but less accuracy due to GPS (10m vs. pinpoint for the Copperhead). All the initial firing has to do for both is get the round close enough to the target so that it is within the ability of the terminal correction.
It would also have to have some hard core processors to remain on target considering its own velocity.
The Copperhead is over 20 years old. The Excalibur has been used successfully in combat.
Glorious at 29,465 yards took 90 seconds to get there. It averaged 880 f.p.s., which means it lost over 65% of its initial energy.
Count four times the speed with a much smaller shell, probably a small fraction of the frontal cross-section and thus much less wind resistance. It's hard to calculate what arc they'd fire it in since I have no idea of the terminal velocity of the shell.
Ballistic coefficient is a function of mass over diameter. Bigger bullets are more efficient. For example, the 69 grain Sierra MatchKing bullet for the 5.56mm has a BC around .305. The 200 grain .338 bullet BC is around .750. I’m told they are tremendous fun in the .338 Lapua. The 16” round is actually very efficient.
The Copperhead has a muzzle velocity around 1700 f.p.s. from a barrel about 20 feet long. I exaggerated when I said the rail gun might fight on the Nimitz, which is just over 1,000 feet long. In order to make it possible to aim the thing and install it on a ship, the barrel would be more like 50 feet long. You can see the difference. The Copperhead accelerates at around 4,500g. The rail gun, if we use a 50 foot launch platform, accelerates to 10,000 f.p.s. in .005 seconds. This is 62,000g.
Also, the Copperhead cost $40,000 in 1998. It has a 30 pound warhead. I expect that a special ship would have to be designed to deploy the rail gun. It would be a nuke, so power is not an issue. But it would have a crew and maintenance, so the cost would must include capital outlay and service. Meanwhile, we already have planes that can deliver weapons with similar destructive power and we have guys who get off on flying them and taking pictures of Achmed as he gets smoked. I rather enjoy those videos.
I just don’t see the need for this thing.