Insulating vaulted ceiling

I need to decide whether to use 2x10 or 2x12 rafters in an 8' x 10' mudroom/foyer, which will be vaulted. I am in zone 4, which requires an R-38. I'd like to go with 2x10s, but not if it is going to cause complications. Is there a combination of foam board and batts that will get me to R-38 in a 2x10 cavity? An R30C compressed with a 2" R-10 foam board gets me close (R-37). How about 2 layers of rigid foam (R-20) and an R-19? Seems like that would work. Foam board is expensive though, but it's not a very large space. Looks like R-38C is pricey as well ($400+ per bundle). Maybe I should just go with 2x12's.

Is there supposed to be some separation between the insulation and roof sheathing? Or is that only for batts? There will not be any soffit vents because the top of the roof adjoins a vertical wall ("lean-to" design).

What about rock wool insulation?

 

Decided to go with 2x12's and R-38 batts. The batts are sold in smaller quantities in the store than what was advertised online.

 

Question, how are you figuring you will get R-38 out of those batts? I don't know what your ceiling looks like but you can't fill cavities completely full, you need a ventilation gap above with an air path from soffit to ridge or other high venting.

But, let's back up. I haven't researched zone 4 but in my zone 6 I'm allowed to install less than what code specifies for a limited area when insulating a vaulted ceiling. Interested?

Bud

 

Why does it need to be a vaulted ceiling?
Harder to heat, cool and vent.
With a flat ceiling you could have an R-50.

 

This is a small mudroom/foyer addition with a "lean-to" roof, and there is no ventilation with this type of roof. We're only talking 80 sq ft. Reason I am vaulting it is because the far wall is under 8' due to other reasons I won't go in to. I'm leaning towards using a 2" foam board (R-10) combined with an R-38 batt, which, compressed to 9-1/4", will give me an R-32 for a total of R-42. Code is minimum R-30 for areas under 500 sq ft. The plan is to glue the foam board to the roof sheathing then fill the cavities with the batts. No good?

It will have metal roofing as well, which will reflect some energy.

 

Still would like to hear from some about the proper way to execute an unvented ceiling. I read a pretty informative article on the subject, and one of the options was to install rigid foam with batts like I am proposing. It sounds like a vapor barrier should not be used in this type of installation because moisture is supposed to dry to the interior. In fact code says a vapor barrier is not required in Zone 4A and 4B ceilings (402.5 exception 2).

Basically the two options I am considering are:

1) Use only R-30 batts, which will leave a 1-3/4" air gap between insulation a roof sheathing and yield an R-30.
2) Use 3" foam panels (R-15) tight against the roof sheathing with R-30 batts compressed to 8-1/4" with a total R value of approximately 41. I would leave about a 1/4" gap between the foam boards and rafters and fill them with spray foam for an air tight seal.

 

Did a little more research and found that the 2012 IRC makes it pretty clear. I will need to use 3" of foam board (R-15 for zone 4A) for my air-impermeable layer laid flat against the underside of the roof sheathing and sealed along the perimeter, and an R-30 fiberglass batt for my air permeable layer with no vapor barrier. IRC section R806.5 "Unvented attic and unvented enclosed rafter assemblies."