The only study Im familiar with used the German 15" gun as the standard.
The particular excerpt for belt penetration:
Using Nathan Okun's article on battleship protective schemes, I quantified their total vulnerability zone range (using the Navy Ballistic Limit as the benchmark for penetration). For instance, Bismarck could put a shell through her own belt from any range under 29,000 yards (the weakest score), whereas she would have to close to within 16,400 yards to punch through Iowa's (which had the best). [Note: for the purposes of this computation, I am rating Iowa's side protection as equivalent to South Dakota's, which is the ship Nathan actually shoots at in his article. Iowa's belt scheme was practically identical to South Dakota's, and both had STS shell plates outboard which serve to de-cap incoming AP projectiles, which is why (stunningly) South Dakota's belt is slightly more effective than Yamato's!] Here are the ratings:
Raw Armor Rating Yamato Iowa Bismarck Richelieu King George V Vittorio Veneto South Dakota
Vulnerability zone ('000's of yards) 17.7 16.4 29 20.8 21.5 17.5 16.4
Remember, in the above table, smaller means better, because the opposing ship has to get closer to you to get through your belt.
Suffice it to say that I am surprised as you that Iowa has the most effective belt armor of the lot; I would have bet on Yamato any day. But Iowa's combination of an inclined belt, and a highly effective STS-steel shell plate outboard of the belt (which has just enough resistance to strip the AP cap off of an incoming shell) tips the score in her favor. Richelieu also had this same design, and very good protection as a result. Bismarck, despite the reputation of her side armor, fares very poorly in this category. From a deck armor perspective, Yamato comes out on top, followed closely again by Richelieu and Iowa. Vittorio Veneto is very vulnerable to high-angle fire, and Bismarck is as well. Yamato thus emerges as the best armored of the lot, followed closely by Iowa and Richelieu. This makes perfect sense to me, as Yamato also had the distinction of carrying the only armor plates which were completely impervious to any battleship weapon ever mounted afloat -- her 660mm turret faceplates. She was, indeed, an awesome beast. It makes the American and French feats of achieving protection within a hair as good, on much smaller displacements (particularly the South Dakota, which has the second smallest displacement of the seven warships detailed here), a very impressive feat as well. On the bottom of the heap, Vittorio Veneto and Bismarck were both penalized for their inability to cope with a long-range gun duel. Bismarck also suffered from the poorest belt armor of the lot.
Now using a heavier shell Im sure the Yamato could have penetrated the Iowas belt from a greater distance but thats not really the point as the Yamato would be able to penetrate its own armor from an even greater distance. With exception to the Yamato the Ohios were the largest battleships and the fastest and the best armored (design and materials vs sheer mass), with smaller guns....
Im not trying to devolve this into a my ships better than yours here!
This is sort of like comparing apples to oranges, maybe potatoes even... The battleships we saw being created just before and during WW2 were subject to the massive amounts of increased technology and general knowledge about them available, meaning we were able to make them better in every way: speed, durability, weapons, armor, AA, etc. The battleships of the far flung future dont have those options tho so yes your absolutly right that its likely the Imperials would have stripped as much mass from the vessel as they could in order to acheive the desired result. Still it would be nice to give an existing ship design a real purpose as opposed to dragging in an entirely different ship and it cant really be argued that by pulling power from the weapons systems they wouldnt be able to acheive similar results. Ok well ya it can I guess but then so can anything, just tell sig the sky is blue
.