This site is a true classic of the internet, with a lot of interesting info if you dig around. I see others claim that the site is wrong, and that the Yamato should score better. I don't buy this, but would love to see a breakdown on how the site is wrong.
During the late 1930s/early 1940s, the Soviet Union attempted to build the Sovetsky Soyuz class battleships. It did not go well. The Soviets had never built any ships larger than a light cruiser or armed with 16 inch guns. (Though navweaps does mention that 16 inch armed battleships were planned prior to the Russian Revolution). Also, Soviet steel manufacturers proved unable to manufacture armor in the required thickness. This, along with other flaws, meant that of 16 planned battleships, only four were laid down by 1941, and all of those were scrapped after the war (none came close to completion).
In retrospect, it would have been better if the steel, time, and other resources on the battleships had gone to other uses. However, could the Soviets have developed a reasonably competent battleship or heavy cruiser design in that time period? If so, what might it have looked like?
So I got goaded into writing posts about the North Carolina class.
For additional reading about warship design:
http://navweaps.com/index_tech/tech-035.htm (I moved this up to the front because it's good and I'm angling for a general thing here).
The weird and wonderful world of North Carolina sketches
So the US found itself in the mid 1930s with a need for a new battleship with a treaty in place limiting it to 35k tons displacement and 14 inch guns. The first and most important thing about this design process is that they were in the middle of figuring out what a modern navy was and how it should work. They'd traditionally prioritized protection at the expense of speed and slightly less so firepower, giving them a battle line of slow football shaped things that could take a pounding and dish one out.
Problem was those damnable carrier things. The first US carrier, the Langley, was a slow collier conversion, but the next two were conversions of the battlecruisers Lexington and Saratoga, (which were a lot like the mad, flammable fever dreams of Jackie Fisher in terms of protection, so it was probably a good thing in the end). The reason for this was the negotiations for the treaty. Unlike in RtW there was a lot of quid pro quo. The US had just finished the Colorado, Maryland and West Virginia, and the Japanese had just finished the Nagato and Mutsu. The British had the Courageous, Glorious, and Furious, which were in severe danger of starting to make sense. So the UK got to build the Nelsons so they could have nice modern battleships armed with and against 16" guns, and the US and Japan could get some carriers.
So the US built the Lexingtons, which promptly showed the supremacy of the big fast carrier. Not only could they get places really quick to do important carrier things, they could also operate planes in larger numbers much more easily and in much worse weather. So the treaty carrier force was decided on being hulls as big as they could make them and 30+ knots. Suddenly that 21 knot battleship speed looks like a massive operational and strategic liability if they want to not have their carriers run in fright at sight of a battleship (This is still the time of the Lexington class carrying a heavy 8" armament to fight off cruisers, air power just couldn't be expected to head off heavy surface attack and conceding the sea wasn't necessarily a winner).
The sum of all this was that they knew they were going to be making a major departure to what had gone before but they really weren't sure what that would be. To this end they tried a lot of ideas to see what they could get. These ideas are A, A1, B, B1, C, C1, D, E, F, G, H, I, J, J1, K, L, 1, 3, 4, I, II, II-A, III, IV, IV-A, IV-B, IX-C, IX-D, IX-E, X-A, X-B, XI-A, XI-B, IV-C, V, VI-A, VI-B, VII, VIII, IX-A, IX-B, XII, XIII, XIII-A, XIII-B, XIV, XV, XV-A, XV-B, XV-C, XV-E, XVI, XVI-A, XVI-B, XVI-C, XVI-D (Word says that list has 55 commas so that's 56 sets of specs considered).
For obvious reasons I'm going to talk more about the fun designs.
Scheme A had 3 triple 14" turrets forward and 30 knots speed with a thin 11.5" belt. A1 added to the belt with 13.5" and the same 9x14".
B and C tried for more protection and a more conventional layout. BuOrd introduced a super-heavy 14" shell that made their targets for immune zone unattainable, (that's where A1 comes from).
The CNO asked for ideas for a minimum displacement ship emphasizing defensive features. They didn't get dignified with an actual name on that list (Preliminary design called the worst, with 8x12" and 23 knots a deathtrap).
D and E were armed with the shiny new 16" rifle to see what a ship armed with and armored against it would look like. However after a thorough search of their couch cushions, they couldn't turn up the 5,000 tons to make them fit the treaty limits.
F makes me cry. 8 guns in two rear mounted quads. Wait, rear? They needed to free up the front for the three aircraft catapults. FDR apparently liked this demented battleship version of what the Tone class did better.
G and H were slow 23 knot designs. They were nice, reasonable, balanced battleships and the spiritual successors of the standards. They also didn't fit the fleet's needs.
So that left them looking at a 30 knot ship or a slower, better armed ship. Yes, this is the USN that previously considered a battleship to be a football made of armor.
J tried to go with four turrets. It turns out that getting an idea and hammering the belt armor down to 8" to make it work is frowned upon.
K made the belt narrower over A1 to make it thicker, but was considered too tight to the treaty limit.
L is where we get to the good stuff and bring back the noble quadruple turret, which would have been 12 guns forward and crazy fun to play in WoWS.
After that we get the thirty five (that we know of) sketch designs elaborating on those ideas. I through V show the development of the brilliant feature of fitting the ship for but not with 100 rounds more than the 100 per gun to save weight by careful manipulation of paper. I and II moved a turret aft to see if they could save weight there.
Anyway, this is dragging on, I'll just post this and add a part 2 so we can get further adventures of people trying desperately trying to fit 40k+ tons of battleship that people can't even decide on the shape of into 35k tons.