Minimizing roof profile
I am designing a home in Zone 6 (Park City, UT) with a 6-to-12 roof slope, spanning 24′ (each span at 12′ horizontal from the wall to the peak), with an interior cathedral ceiling. To meet R49 requirements and a 40 psf snow load, I am currently using 2x8s as rafters (to be filled) with 5″ (R25) of polyiso outboard of the sheathing. The entire composition–dry wall, rafters, sheathing, rigid foam, sheathing, and metal roof–has a profile of approximately 14-to-15″ thick. (I am also struggling with not overfilling the inboard rafter bays to maintain the 51-to-49 exterior to interior R-values.) Interesting (at least to me) is that 2×6 rafters filled with rock wool looks to give the right R nominal and percentage values, but they are structurally inadequate.
Is there a better approach to cost-effectively “thin down” the (cathedral) roof profile from 14-15 inches to somewhere in the 12″ range while maintaining the R values?
Thanks for all the incredibly useful content on your site!
Todd
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Replies
I'd read below and consider building "better than code/recommendations".
https://buildingscience.com/documents/insights/bsi-046-dam-ice-dam
Todd,
When you say "thin down", what is the aim? What does the extra depth affect that you are trying to avoid? Knowing that will help us suggest solutions.
You can reduce the spans of your rafters by integrating braced purlins at the mid-span. You'll need to support the bracing with a wall or header beam. I'd recommend an engineer for this. This might allow you to size down your rafters to 2x6s.
It is worth noting that your whole assembly does not have to be R-49. There are alternative code minimums if you are willing to do a little math for your whole-assembly calculations.
In the IRC, they provide alternative equivalent U factors for the whole assembly (Table N1102.1.2). For Zone 6, that equivalent is 0.026, or ~R38.5. Your insulation between the rafters is ~R23, which you have to average with the thermal conductivity of your rafters (depends on spacing). Throw in the insulation values of sheathing and drywall, and that will likely reduce the amount of foam you need outside the assembly to ~3" of polyiso. I'm note sure that meets the minimum requirements to control condensation, though even if it does nominally polyiso has reduced cold weather performance, so I'd be careful.
Edit: If your goal is to gain ceiling height, you could put between 6" and 7" of exterior foam and leave the rafters completely exposed.
What Aedi said- go for code compliance on a U-factor basis. It'll probably take more than 3" of polyiso, but it won't be more than 4" (R24 labeled, no worse than R20 derated for climate and stackup), with 5" -5.5" of open cell foam (R19-R21) sprayed onto the underside of the roof deck, or a low density R25 fiberglass batt (which performs at R24 when compressed into a 7.25" deep rafter bay), or finally, a rock-wool R23 or high density R21 fiberglass batt dense enough to not need an interior side air barrier to hit it's performance marks.
That saves about an inch anyway. It would be over R44 (insulation only) at center cavity, and clear the U-factor hurdle with ease.
Dropping that to 3" of exterior polyiso is probably not going to make it, since it requires dropping back to R15-R17 on the interior side as well for dew point control, and even stacking up the air films and sheathing layers would probably come in under R38.5 even at center cavity, let alone the framing fraction.
To hit the ~12" range, 2" of exterior polyiso (R12), and 2" of closed cell foam (R12-R14) on the under side of the roof deck would leave 5.25" into which an R23 rock wool batt can be stuffed, performing at R22 for a center-cavity R of R46-R48, if only ~R20 on the framing fraction (2" polyiso + 7.25" of wood). That's still higher performance than R49 between fully thermally bridged rafters, no exterior foam. At 2" the closed cell foam is in the middle of the Class-II vapor retardency range, which is still adequate drying capacity for the roof deck, but sufficiently low to protect it from wintertime moisture drives.
How about raised heel scissor trusses, a vented roof, cellulose insulation and skipping all that foam?
All, thanks for your thoughtful replies; it was a lot to absorb. I obviously need to get smart on the U factor calculations.
Dana, would your inclination (using your first insulation thought above) be to use unfaced fiberglass that would fill the entire 2x8" rafter depth (~R24) vice using 5.5 inches of Comfortbatt (R23) and having 2 inches of airspace? Would this air gap between the rock wool and drywall (or T&G cedar) be of any particular concern from a moisture, air, or vapor concern? Is there a preferred way to address the 2" air gap?