Shipbucket

Here the Ark Royal class aircraft carrier HHIMS Terrible.

I really do not know if this is any good as I have almost no experience with aircraft carriers.

You'll need to heighten the airdeck a lot, since the hanger is usually fitted on top of the hull, with the airdeck on top of it.
Ditch either the 4,7in or the 4,5in guns. There is no reason to keep both.
I suggest using light AA guns from the parts sheets too.

The name is good ... really good.

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Nobody expects the Imperial Inquisition!

Well, lets see this aircarft carrier... Ok, I admit it, APDAF, You're making overall progress but...
Question one: will it float? - Yes, it will (most likely).
Question two: is it a workable design - No (at least not yet).
You've got no space for hangar, I don't see workable funnels (though I can guess where do You think they are), island is weird, to say the least, equipment (antennas etc.) the same and You've got no stuff like lifeboats etc., and merging into one group airplane that looks to be ca. 1920 with airplane that looks to be ca. 1935 is weird, to say the least - btw. with that monoplane move the main landing gear forward, roughly to front edge of the wing.

Say that to the ones that designed the Fairey Swordfish!

I have done the maths and I do have space for a hanger as if you look at the draught I have plenty of room for the engines, bunker and the other gubbins.

I have amble room for the crew as well.

And how many crew this thing have ? We can assume that ad least 100 pilots/rear gunners from air wing ...

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Nobody expects the Imperial Inquisition!

Excluding flight crew about 700-800.

APDAF, the hull would have to be a bloody cube for there to be proper space.
If I'm to take one of my own examples, the Nymark class, which is calculated to carry a bit less than thirty planes, and that has met no complains:

As you can see, this ship HAS a hangar mounted on top of the hull.
Your ship is admittedly slightly longer, and presumably wider, but there is no way it will fit both the space and service parts of the ship, along with an engine of acceptable power.

... and fuel, food, water, ammo, ect.

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Nobody expects the Imperial Inquisition!