Easy question, if you approach it correctly.
Find the plural of Kansas. Then precede that with “Ar.”
Yeah, my thought, too. I’d probably shorten it a little more: “The Arkansas class engines were …”. That’s somewhat improper in that it’s not clear that you mean the engines of the Arkansas class ships rather than the engines themselves having a class, but it’s not likely to be misunderstood in context of an article discussing Arkansas class monitors. “The Arkansas class had **** engines” works, too.
Sorry, I wrote quite carelessly. The rule is (possibly with some exceptions according to the style guide) that the singular possessive is formed using ‘s : Jones’s friend, Camus’s writings, Arkansas’s history. I agree that in the plural you should write the Joneses’ friend (stipulating that Joneses is the correct plural) because it ends in -s. So Arkansas’ (according to my first suggestion) and Arkansases’ would be consistent with that. The question is, what to do with a plural word ending in silent s. (Enfants terribles? I need to think of some better examples.) You are probably right that it is still just an apostrophe, but now I need to hunt down multiple style guides to be sure…
Whoo Pig!!
Quite apart from the ship example of the OP, the word “Arkansas” can also refer to a type of novaculite, or a whetstone made from it, so in a conversation about geology, mineralogy, or blade sharpening, it might make sense to refer to different specimens or varieties in the plural.
Technically Kansas is plural; it’s the plural of the Kansa people who occupied part of what is now Kansas.
Fun fact, one of the Kansas was Herbert Hoover’s Vice President, Charles Curtis. (He was also from Kansas.)
Of course we’re talking about the state so that’s a bit of a tangent. 
The state, by the way, was named for the Kansas River, which was named for the Kansa people (also called the Kaw Nation).
It’s “technically” plural in the same way that “panini” is “technically” plural—which is to say, in a way that’s completely irrelevant for this thread’s English-language question.
This is the one situation where English has, like Slovene, two forms of nominative plural. It goes: one Arkansas, two Arakain, three (or more,) Arrkanzid.
However the genetive plural is the same for any number more than one of Arrkanzid; it’s ‘Arkainy’.
OK, for instance A Comprehensive Grammar of the English Language distinguishes nouns with a regular plural, in which case the genitive is always written with a final apostrophe: “boys’”, from irregular plurals whose genitive is formed with ‘s. It doesn’t seem to involve the pronunciation of the ending except in the singular case, where Jones’ vs Jones’s is discussed.
This begs the question, is Arkansas supposed to be a regular, or an irregular plural? (Or is there an omission from their chart? “Analyses” is mentioned as an example of an irregular plural, but what does it become in the genitive? They don’t say, at least not clearly. Anyone else want to double-check the text?) A regular plural “Arkansases” (cf. Joneses) seems to be ruled out because the noun does not end in a sibilant, but, of course, it might be an irregular plural! But it seems the plural of a singular “Arkansas” should be “Arkansas” (with a /z/) on the model of “corps” and “chassis”, which would make the genitive plural a regular Arkansas’ , corps’ as far as I interpret the rules in that chapter (and it would be “enfants terribles’s” !?! and also would have been “Arkansas’s” in the plural too if Arkansas-with-a-silent-s were plural) That’s the one book, anyway.
Kansas is pronounced with an /s/, so its plural is Kansases and genitive plural is Kansases’.
As I said above about Arkansas, Kansas may be plural in derivation but it is treated as a singular noun in English. Kansas is a US state, not Kansas are a US state.
Thank you all. Sorry for my typo. I seem to be making more and more of them in the last few years.
This from the woman who murdered piglet!
This. The wiki article on them seems badly written as this is the standard way of referring to a particular class of ships.
*Carni!!-don’t make me come to the big Rock to find you.
*nickname
any way it was like 22 piglets…none were pink or wore clothes
BTW…the lil’wrekker says in her *infinite wisdom: More than one Arkansas is an Arkans-ass
(*She’s a young whippersnapper with almost 3 years at University under her belt)
I thought that was the Crow people (haw).
That’s a rookie mistake to make!
That is how I would pronounce it and spell it. If you google “two Arkansases” you can find a few uses of the Arkansas plural on the web and in print that way. (“Two Arkansases” as in the context of, say, a rural and urban Arkansas divide. Come to think of it, my state, Illinois, would have a rather awkward plural, as well: Illinoises. “A Tale of Two Illinoises.” I would pronounce that as “Ill-in-oyz” not “Ill-in-oyz-es.”)
That said, there is precedent in the English language to pluralize words with a terminal silent-S by leaving the word as-is. Take the plurals of “chassis,” “rendezvous,” and “patois,” for instance. All, so far as I can find, have identical singular and plural spellings (though one dictionary notes “rendezvouses” as a “rare” plural, listing “rendezvous” as the preferred plural). Even “faux pas” is made “faux pas” in the plural. (In all these cases, though, the pronunciation does change, with the “s” being sounded in the plural.) I actually cannot find a case in which a word with a silent-s at the end is made plural by adding “es.” That said, there’s not a wealth of examples in English.
So there is some merit to the idea of pluralizing “Arkansas” by leaving it alone. My instinct would be just to append the standard plural marker (“es” in this case) absent guidance from a dictionary declaring “Arkansas” to be the plural, but if we were to extrapolate a rule based on other terminal silent-s words, leaving it alone would be defensible.
Since the spelling of words like “Illinois” and “Arkansas” comes from French orthography, maybe, like in French, the final silent “s” should sometimes be allowed to be un-silent.
So, I propose that in the plurals “Arkansases” and “Illinoises” that the Ses are all pronounced. I’ve been sitting here saying them to myself and getting used to it.
This is the correct answer to this and almost all “this structure seems incredibly awkward to express clearly and grammatically” questions. Re-write it so that it is can be clear and grammatical.
This is also why brand names usually do not officially have a plural. You’re not supposed to say “Rolls-Royces,” you’re supposed to say “Rolls-Royce automobiles.” Cite.