Though recent translation of a japanese book section suggests these are designs for the last two Kiis
Things may be a little complicated... According to my information, the story was like this:
In 1919.10, Hiraga gave the A-M(N) Designs of "New Capital Ships for the 8-8 Fleet", in order to answer the South Dakota-class battleship, after he just finished Amagi's design. However, ship No.9-No.16 of the 8-8 Fleet had already been ordered in 1918, 4 BBs (No.9-No.12) and 4 BCs (No.13-No.16), although no work of design had begun at that time.
So, the "New Capital Ship Design" was to deal with No.9-No.16, and Hiraga had his A-M designs. And it was known that the A-M Designs were very different from each other, so the Navy set up a conference called the "Main Gun Research Conference" (主砲研究会) in Spring 1920, to discuss the specifications of the New Capital Ships.
iiif.dl.itc.u-tokyo.ac.jp
iiif.dl.itc.u-tokyo.ac.jp
The Conference finally reached an agreement in 1920.9, that was:
1. The ideal main armament of the New Capital Ship should be 10x 46cm/50 guns.
2. However, the Navy didn't have the technique or facilities to build such a gun (the 48cm/47 5 Year Type Gun exploded in a trial shot, a heavy knock to the Navy), so the first task was to upgrade the facilities.
3. Considering the 2nd point, the time for development, ships No.9 and No.10 will remain the same armament, 5xII 41cm/45, as Tosa and Amagi. Since No.11, ships will be armed with 41cm/50 new guns (the answer to 16"/50 Mk2), of 4xIII or 3xIV (like Design B or E, but with new guns). The ultimate objective, 46cm/50 guns, would be armed on ships further.
4. About the defense, the ship could resist 41cm shells.
Hence, the whole plan was like going with the flow, for there was too much uncertainty in the future, except for Hiraga giving Tosa-Mod and Amagi-Mod designs, and the latter finally became the design of Kii and Owari during those several months (These two got their names in 1920.10, before was ordered in 1921.10). Even the design of ship No.11 had not been determined when the Washington Treaty was signed in 1921.12, nor did the so-called "No.13-class".
But, Hiraga indeed specified some of these ships in a year's time, about "The Last 4 Battlecruisers of the 8-8 Fleet" (八々艦隊最後ノ四隻ノ巡洋戦艦ニ就テ) in the document "About the New Ship Type" (
新艦型ニ就テ) (It was weird that the main part of this article was talking about the cruiser Yubari, and Hiraga attached something else at the end.), in 1921.6.11, where he stated:
(No scans, the document is in the book "Collections of Hiraga Yuzuru's Posthumous Manuscripts" (平賀譲遺稿集), but this website has the essentials, just ctrl+f!)
Displacement: 47500-49000t
(Hiraga can tolerate 1 knot down in speed to reach less displacement.)
Armament: 4xII 46cm/45 3rd Year Type, other same as Kii (16xI 14cm/50 3rd Year Type, 4xI 12cm/45 10th Year Type, 8x 61cm Surfaced TT (24x 8th Year Type Torpedoes), 1x Floatplane)
(Hiraga had known the difficulties in developing the 50-cal 46cm guns, so he reduced the requirement to 45-cal.)
(
Navweaps makes a mistake here. The 50-cal gun may be used by Design K, but not for this one.)
Armor:
Belt - Resist 16" shells at a distance of >12000m at best, but not worse than >15000m.
Deck - Resist 16" shells at a distance of <20000m at best, but not worse than <18000m.
Barbette - Same as Belt Armor.
Underwater - Resist torpedoes with 200kg warhead.
Propulsions:
Like Kii. (Probably 4x Steam Turbine (oil-only boilers + coal-oil boilers))
29-30kt (According to displacement)
8000mi @ 14kt
This may be the "Final Version" of the No.13-class battlecruiser, which resembles Design K. It's reasonable to say that the No.13-class battlecruiser was developed from Design K, changing Design K's 50-cal guns to 45-cal ones.
And what about the so-called "The Last 2 Kiis"? Officially, the design of ship No.11-No.16 had never been determined, and Hiraga took No.13-No.16 away, so... Only two of you left, No.11 and No.12, 4xIII or 3xIV? As you wish.
Special thanks to 雾岛铃子's article in Zhihu:
https://zhuanlan.zhihu.com/p/455360724