How much did she run at full speed before the engines started breaking down? The wear showed at Falklands, but had it been seen earlier? And how much has Leipzig run ITTL?
Also, while Izumo is also somewhat worn down, has she previously done any full speed? That's what really hammers reciprocating engines.
I assume she hit it during the R-J war, not sure how many battles she was in but I imagine she was run fairly hard at least a few times.
Izumo pushed it quite hard during the Russo-Japanese war, but as noted, there almost certainly was an overhaul that essentially rebuilt her engines. That said, the extended hard usage she saw, and Izumo was used quite hard, coupled with the pre and post war high tempo patrols, certainly would have had a permanent effect on her. I'm not an expert here, but triple expansion engines in older shups seemed to drop a knot or two in performance regardless of refits. Little things dont help either, fouling for instance should affect her larger hull form, although her crew should be able to sustain a longer run of stoker heart attacks from back breaking work.
Izumo also has had quite a long voyage herself.
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On the BC coast, in the 1890s to 1940s and later, the passenger liners on the Triangle Run between Vancouver, Victoria, and Seattle would run at full speed almost all the time on reciprocating engines. It was how the steamship lines retained market share, by being fast. These ships also received a lot of scheduled maintenance, but I am not convinced that triple expansion engines are necessarily hand grenades.
HMCS Rainbow, OTL and ITTL is an exception. She was truly worn out already.
YYJ, before writing more about CA's, I want to compliment you in a "serious" way. Despite my quiet guess that you and I have different thoughts politically, you've written this in a way that isn't aggressively political. In a time where that seems rare, I do appreciate it. You've kept it moral, but haven't demonized, and I do appreciate it.
(Not that we probably disagree THAT much politically; I mean I'm a Mormon, and while that may mean that my social views are generally old fashioned, the biggest things probably see us agree).
Anyway, hope that wasnt too sappy or anything. I doubt I'm alone on this though.
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NOW, on the CAs, CLs and engines.
The engines from the time, while certainly not the engineering spectaculars of the 21st century, were pretty reliable. The idea that Leipzig escaping (in the short term) is unlikely is absurd. It was designed with newer, better engines and, like most CLs, was designed with escaping from CAs in mind.
Remember, CAs were about protecting commerce, providing flagships to foreign stations and even standing in the battle line. They really weren't going to chase down lighter cruisers ten years their junior. Izumo finding them at all, let alone tracking Leipzig thru the night, is quite unlikely. Being clear, the larger size of Izumos power plant and the older state of it probably makes it more likely for some portion of it to fail first.
Izumo being here does exactly what CAs were made for, that is that she either protects the entire BC coast with her presence OR she istantly chases Leipzig and prevents her from ever being a threat. CAs aren't sprinters but do work darned well. As noted above, Izumo may well be able to continue a chase for a long time. There aren't many places for Leipzig to go, and there's a decent chance of neutrals quietly giving intel to Canada. It isn't like Leipzig can just run anywhere as the Pacific is REALLY big and Leipzig doesn't have a coalier.
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Regarding the outcome of an engagement between them, that's been well covered. Several engagements lay out the pattern: both sides take hits, the light ship gradually losing functionality and the CA shrugging it off with generally light damage. The range closes and the CL is murdered. A torpedo attack may land a hit, though I'd not bet on it, but even then it will almost certainly be at the cost of the CL.
(Ok, there is always the chance of an ammo detonation or something, but I do not bet on 4" shells doing that to the Izumo. Crazier things have happened though.)
While Leipzig is made with a ram, and would be pretty effective against similar or smaller sized ships, a 3000 ton ship ramming a full size CA should raise some red flags in our heads. Size does matter...