What insulation do I need?

[MarkSSL]

I want to insulate the roof on our circa 1890’s cottage. It’s solid stone wall construction. The roof has been rebuilt using slate, breathable felt and new treated timber. The rafter depth is 75mm. I want to vault it. So 2m up, 2m horizontal and 2m back down. The flat part is easy with 300mm of insulation, however, I don’t know what I need use on the angled parts in between the rafters. I’m thinking some sort of breathable wool then to clad it with pallet wood for a nice effect. I’ve seen sheeps wool insulation and earth wool for sale. I understand with breathable material that it can be installed against the felt whereas rigid boards require a 50mm air space.
Any ideas please?

 

[John D v2.0]

With breathable membrane you don't need an air gap as the moisture can pass through the membrane. Unless you have an extreme case.
However unless it's counter battened above, which I doubt, the membrane needs to drape slightly between the rafters, 10mm or so, to let the water run straight off.

This means with fibre insulation you need to make sure it's clear and won't push up against the membrane.

 

[^woody^]

The requirement for an air gap will depend on the manufacturer's recommendation and more specifically on the permeability of the membrane.

As the OP wants to clad the ceiling with pallets, then thought needs to be given to either stopping moist air getting in to the roof structure, and if it does, letting it get out. Choices of materials and detailing will matter. If no moisture is to be alllowed in to the roof structure, then there wont be any need to allow for any needing to get out.

BTW [flammable] timber on a ceiling is never a good idea. And insurers wont like it one bit.