ORIGINAL: John 3rd
This is the BB Juan devised that is very similar. At 56,000T, this is going to be too big for the quest of NOT expanding the slipways. Figure that we're shooting for about 45,000T to still fit.
At any rate here is what he devised:
Those are still available here, along with artwork (incase you want to use any of it);
tm.asp?m=2179124
John, out of those I would look more at Sagami class (3x3x16.1in), that is a concept based on the design studies done about possible Kongo/Fuso replacements. They are around 42,000tons and 28 knots, more could probably be squeezed out by sacrificing something, and just being laid down a little later with newer, more compact powerplants (think they are '32/33 vintage in AltWNT).
Secondly, there is absolutely no way you are going to get a design with 12x16.1in and a speed of 30 knots with decent protection on anything less than 55-60,000 tons, which means you need those expansions. That means that design above is out if you don't want facility expansions.
Remember that speed is by far the most 'expensive' thing in terms of tonnage at these sizes, and even the difference between 28 and 30 knots can mean several thousand tons of additional weight. Bigger powerplants mean more internal volume, which also means more armour surface, etc. Something of an illustration is comparing Iowa to South Dakota, with the former gaining around 10,000 tons of size with the majority of the coming from direct or indirect impacts to acheive 5 knots of speed.
The only sensible choice given size constraints (around 45-50,000t) for a 'balanced' design at 30 knots is somewhere between 8 to 10 16.1in guns, with protection decreasing with increasing firepower. I tend to favour arrangements with 3 turrets as it cuts down on turret weight somewhat and also plays nice with a larger powerplant by reducing internal volume. An interesting option might be 2x4 with the aft deck used for floatplanes ala Tone, but presents its own engineering challenges due to the quad turrets.
Here's a nice graphic showing some of the proposed layouts during the Yamato design studies - obviously the ship would probably be smaller, but it shows the kind of layouts that were in the minds of the IJN at the time;
http://fc02.deviantart.net/fs71/f/2014/ ... 5hvc0i.png
Here's a list of the design studies with their general characteristics, from Anatomy of the Ship - Battleship Yamato;
http://imageshack.com/a/img540/4725/ZGTq3S.jpg
If you settle on some design criteria I can put together a few design calculations about what it would mean in terms of size, powerplant, cruising ranges, etc.
EDIT: Just saw the Satsuma (Owari class) on the other page, thats probably as good as its going to get to be fair. Gun layout is up for debate as Symon said, but the general characteristics are probably in the right ballpark. That one is using an interesting two forward, 1 center (either amidships or more likely forward but masked ala Nelson), no intermediate 6.1in battery (a good choice imho, but maybe not in line with IJN thinking), and a very heavy secondary DP AA suite based on an upgraded 12cm.
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