assuming the warship is being fired from a naval gun of truly massive proportions based on the AGS Mark 5, firing a saboted warship based on the LRLAP ( since they were made for the Zumwalt class and cost a million a round, making them the obvious best choice.)
And why not, let’s also make the warship a Zumwaltz class, for flavor synergy.
The LRLAP weighd 225lbs and had an effective range of 150km, so thats ~ 100kg at 150km, and it would travel at 825 mps, let’s say ours needs to go 800, were in no rush.
Projectile Mass: A Zumwalt weighs, rounded down, 15,000 long tons, which is 15,240,704 kg Let’s say 15,000,000 kilograms. They emptied it, unloaded the ammunition, decommissioned the AGS, so it weighs a little less. Zumwalts are 610 feet long, let’s make that 1000 total to account for an aerodynamic sabot and charge, so 300m. The bore length was 378" and the shell 88", so that gives us a ratio of 4.29:1
Our barrel is 1287m long, let’s just say 1200m.
Saboted Zumwalt: 15,000,000Kg
Barrel length of gun: 1200m
Distance: We’re gonna park this gun on Gotland, middle of lake NATO. Well need some space, and that’s right in the middle. It’s 1,168.31 km as the crow flies, so we’ll round up to 1200 km.
So, our 1.2Km long nuclear cannon would send our saboted 15,000,000 ton Zumwalt 1200km @ 800 mps, requiring 1200 Kilotons of energy, rounded up. The boat would be in flight for about 25 minutes.
My math is quite accurate, please do not double check it.