If the attic is included in the conditioned space of the house (and not vented), the attic space can't be claimed as insulation even if it did contribute something, which I don't think it does. (The free movement of air in a space transfers heat by convection and transfer by radiation occurs across the space without heating the air.)

What kind of insulation would give you an R value of 5.27 per inch of thickness (R29/5.5")?

Closed-cell foam would give you an R of 37 to 40 and using 2x8 rafters would give you an R of 49. It seems to me that 2x6 rafters would only work for a very small house.

What you've told us doesn't seem to add up.

I was quoted an r value of 4 per inch of foam. The builder said that to achieve an r of 49 I'd have to go to 2x12 rafters. He has not encapsulated many attics so maybe what he's quoting is not correct.

There are foams that go up to R-7 per inch (closed cell). If you are going for open cell, then r-4 maybe about right.

Quote your location. R49 seems like a cold climate so does your a/c duct location matter that much?

No you can't count the attic space as anything but you can insulate the floor of the attic and get some if the attic is not liveable space.

A 2x6 is 5 1/2" deep. 5 1/2" X R4/inch = R22 not R29 which is a 32% overstatement of R value. Even R4 is a bit of an exaggeration for the R value of open-cell foam so the truth is probably closer to R20 so R29 would be a 450% overstatement. You need to be more accurate with the numbers.

It would take 2x8 rafters (7 1/4" deep) to give you R29 with R4 foam. In reality that would be closer to R26.

If you want R49 you will need to use closed-cell foam in 2x8 rafters or use fiberglass or open-cell foam with 13 1/4" deep rafters or insulate the rafters and the floor of the attic to achieve the same total of insulation as one of the above configurations.

You might also need to reconsider the R49 goal. To get that result from the DOE site I suspect you would have to have a very inefficient HVAC system. R38 might be a more realistic goal.

sounds to me that it is open cell.
what comprises a good install for me
is that the foam be of a uniform thickness
with no bellys or voids. I've seen installs
were you could see the plywood sheathing on the
roof in spots. it takes experience to do a good
install, and for attic to actually be encapsulated.
in testing unvented attics it is not uncommon to find
that there is still ambient air entering the attic.
don't be anyone's test run at encapsulating the attic.
hire some one with experience.

that said...although the rafters are 2x6 foam should be installed where the faces of the rafters are not visible.
you should see foam and no wood on roofline install.
the foam can be thicker than the rafter,
with 2" more than 2x width by installing foam thicker. then thermal bridging of rafters is also beneficial.

I personally am glad that you are exploring open cell.
This is all that I recommend, given that it will allow
moisture to pass through and not trap it as closed cell
does in our climate.I agree that R-38 is what is used in our area, and that there are many many ways to achieve this.
btw,,,what is the approx size of the house and roof pitch?
these would be factors for me in deciding what type of
insulation to choose.

Oh and incorperating ADA (air tight drywall approach)
on top of the bibs system will give you tight structure,
just make sure that the sole plates are sealed at the slab.

best of luck,

Perhaps the house roof design didn't consider the loss of heat issue. I would compromise on the R goal

Building in Dallas. House is 2 story & about 5600sf. Roof pitch is 8/12. Roof material is concrete tile.

Thanks

The DOE recommends between R30 and R60 for attics in most of Texas with the exception of very northern Texas where it recommends R38-R60. Was R49 pulled by just picking something in the middle? It seems like it might be overkill.

And 2x6 sounds really small for a roof system on that large house. I'm from NY so we have snowloads to worry about and we mostly use trusses so I might have a poor frame of reference on that.

DOE reference here

It is also possible to add spray foam or rigid foam insulation to the exterior portion of the roof.

Here is a link that might be useful: SPF in Unvented Attics