I have a client who has built a home that is ready for insulation. That said - it is what it is and I am not looking for what should have been done - there will be no reconstruction. We are the insulator. 

House is in Hot Dry climate in Climate Zone 3. Here are the average/mean temps http://www.weather.com/weather/wxclimatology/monthly/85601

The home has a standing seam metal roof over tar paper underlayment and plywood sheathing. No insulating sheathing was applied on this outer assembly - so no control of the condensing surface.

The space we have to insulate is 2x8 cavity with plywood sheathing on one side and tongue and groove wood planking at the bottom chord of 2x8. They planned to ventilate the ceiling assembly - they have a ridge vent and soffit vents(that could be plugged if we decide on unvented assembly. They want me to either downgrade the insulation to allow for the vent space or look into the "eggcrate" spacers or something of the type. Doesn't leave much room for insulation. She is not too keen on spray foam due to "chemicals" but I can try that route.

The question is - How would you do it considering the roof is installed and there is no control of condensing surface and we only have 7.25"?

Thanks for  your input 

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Sorry guys, I was talking about Spray Foam, not rigid foam. We offer open/closed cell in addition to our blown/batt options.

@Tedd - Thanks for the advice. We are not quoting against anyone and I always consider these situations part of my continuing education as I love engaging with this forum full of highly experience fellow building scientists. It is how I expand my knowledge. I am also never the cheapest bid and usually win with information and backing everything with building science. ALSO - the roof is Silver Galvanized - pic attached

@Glen - I am in Southern Arizona. Our county recently adopted 2012 code so we are R-38 roof.

@Sean - As mentioned above we are a closed cell SPF installer and I am leaning towards that. There is just no way they are going to properly vent the "Octagon" room with all the framing triangles meeting at the peak.

Considering the mean monthly temp never gets below 50 deg, our only consideration is the effects of night sky radiation. It seems this surface would not get below dew point for long enough to effect the long-term durability of the structure even with night sky radiation. The question is, how much closed cell without breaking the budget. Lets remember their alternative is stuffing an R30 batt in the cavity. The closed cell we spray has a vapor permeance of 0.80 Perms at 1” and 0.23 Perms at 3.5”, so considered a vapor retarder - so how much moisture is getting to the condensing surface even if it was at a low enough temp to cause condensation considerable enough to cause a durability problem?

Attachments:

If memory serves me correctly you need 2" per codes to qualify which should put you over the R5 or R10 also called out for in the code books - the only exception is tile roofing in a few areas but it doesn't sound like you qualify

One item to recall is that wood in the desert areas gets very dry, so any chance of sucking up moisture it takes leading to dry-rot, etc... & with temps that can plummet by 30 degrees quite easily during a monsoon or even more during the overnight periods (especially in the rural desert areas as compared to metro areas), don't rule out dew points being reached

As for an air / vapor barrier inside - I think the thought that comes to mind is a big he11 no, think about which way heat flows & what  will happen to any water that gets in that cavity - the reason you don't see issues is they don't install them. The only thing I would consider installing is a net for blown in cellulose & would probably recommend that instead of batts

As for fire concerns - if the wood is thick enough it qualifies as a thermal / fire break, same with certain insulation materials

I don't know if this would change your response, but I mentioned an inside Vapor Permeable Air Barrier

Out of curiosity if we were to install R30 in the cavity - what about installing a vapor permeable air barrier sealed at seams and edges at the bottom chord before installing tongue and groove? I know it is sacrilege, but I actually see vented and unvented enclosed cavities with R19-R30 here all the time in retrofit applications and never even heard of a moisture issue. Seems if an air barrier was installed, the risk would be even smaller. This was also what they asked about originally, so I would just be giving them a quote based on their design. I just wasn't sure what to use as an air barrier - I could suggest drywall but would seem to be too pricey. Maybe Tyvek or other building wrap? Only thing I can think of that is vapor permeable/air tight.

I would not.  I would go with suggestions that bring the space to normal building practices as you would expect to see. I would go with drywall. Drywall is also a fire barrier besides being an air barrier and none of your suggestions are. Drywall in my view is not expensive and what should be installed

Tongue and groove is considered a 15 minute thermal barrier

These people want tongue in groove, and do not want to install it over drywall.  (More details that would be helpful to know up front for good critical path design process.)

Tongue in groove is almost guaranteed to leak air.  Plastic is guaranteed to leak somewhere, AND puts a very low perm non absorptive condensing surface where I don't think you want one.  (water stained tongue in groove looks crappy imo)

Everything about this screams 3.5 inch closed cell to the roof deck.  Make that roof one component performing all tasks.  Too many potential risks and headaches with the other approaches.  

What is the magic of that extra 0.5" vs 2 or 3 in?

Surface temp.  

The thicker the foam, the less likely you'll have condensing surface temps on the inside. 

2 passes should net 3.5 nominal lift.  

Might as well do two full passes.

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