Thank you, that makes perfect sense. My best attempt to calculate how an 175 HP increase impacts the Shiden Kai's speed matches your calculation as well. As far as I can tell you are correct about the continuous military speed of the N1K2-J and I have to compliment your math skills.
But just so others can follow, I've done my best to show my work below:
1. Military speed of Shiden Kai with full-rated Ha-45-21 = Speed of derated Ha-45-21 *(1625 HP/1475 HP)(to the 1/3rd power)
2. Military speed of Shiden Kai with full-rated Ha-45-21 = 610 KPH * (1.11 to the 1/3rd power = 1.03228011)
3. Military speed of Shiden Kai with Full-rated Ha-45-21 = 630 KPH
I rounded off a lot so my numbers are not as precise as yours. Overall, your estimates are the best calculated top speed for the fully rated Shiden Kai available, although I think there are some assumptions made in your WEP calculation that might need some additional research in order to validate. For example, the WEP setting for the Ha-45-21 is 500mm of mercury at 3,000 RPMs. But given that the Homare was already using MW50 injection at military power, then I don't know if it could get another 200 HP because MW50 already added 200 HP according to Japanese records.
But that calculation itself is probably better than anything else out there. However, we could make a better estimate if we knew the Sumitomo-VDM prop efficiency used in the Shiden-Kai. It's also worth noting that their props got better throughout the war. Although US bombing eventually destroyed the Sumitomo Water factories, they did manage to relocate to a basement beneath a department store and continued production.
By the way, I went ahead and
uploaded the Shiden-Kai manual to a free filehosting solution, which anyone can download here. You already have it but in case someone else wants to download it, I hope it helps them.
At nearly 400 pages it will take forever to translate, and the scan quality is bad enough that even AI OCR cannot do an adequate job at translating it automatically. There are a few options available to me but none are good enough to do a comprehensive translation.
This AI seems to be one of the better free options out there.
I have a few questions:
First, are we sure the Shiden Kai in the manual has a derated Ha-45-21? I could not find what engine they are referring to in the engine section. The kanji is almost unreadable.
Second, are we sure that the Homare 21 overboost setting was capable of adding 200 horsepower? It was probably weaker than that given that it used MW50 injection at its military power setting.
Third, if would be helpful if we knew the four-blade VDM propeller efficiency in order to determine how an increase in horsepower would impact top speed. Although this isn't necessary, the fact that their props got better over time means there could have been a speed bump later in the war that's not accounted for.