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1850's rowhouse renovation- insulating an unvented roof with... XPS?!

I'm rehabbing an 1850's 3 story timber frame rowhouse. The area with the scope of work in question is the 16x16 room that is the third floor, that will eventually be a bedroom. There was previously a lath and plaster ceiling which has since been removed.


The roof is pitched in one direction (shed-type roof) and is currently unvented. Due to the framing and lack of eaves on the low side, I think to vent the roof would be a huge pain. I'm moving forward with the assumption that this will be an unvented roof. Below are some photo's and a sketch of the existing roof assembly. Note we are adding a bathroom in the corner with a shower, so humidity is a factor.





It was suggested by an architect friend of mine to run wood strips run Rigid XPS between the existing rafters, and spray foam/tape the joints. The XPS could sit on a wood 'shelf' so it is not directly touching the underside of shingles. Below is a sketch of the proposed assembly.






With this method though, what's the use of an air space if it does not lead to outside fresh air? Once I drywall the ceiling, this air space will essentially be dead air. At that point I would simply attach the XPS to the underside of the battens, since that does create a small 1/2" gap between the insulation and the shingles. Does this air gap pose a problem if it does not lead to exterior air?


Thoughts on this method? Other suggestions? The easiest method would probably be closed cell spray foam but i'd really like to DIY this to save costs.

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