Table of R for insulated stud wall
Because the issue of thermal losses by direct conduction through studs (thermal bridging) comes up frequently, I thought it would be useful to have a table showing effective R for the combination of insulation and studs. I built a spreadsheet with a line for different R/inch of whatever insulation is in the stud bays, what the center of insulation is, and what the effective R including stud losses comes to for 16 and 24″ oc stud spacing. It ignores losses through top and bottom plates, and the numbers don’t include R for drywall or exterior sheating and siding. R= 1/inch is assumed for the wood. It’s interesting to note that the percent reduction for stud losses is more dramatic for high-R insulation material than for low-R material. For example, a foam that provides R 6/inch in a 2×6 stud wall, 16″ oc, gives R 33 for just the insulation layer, but the effect of the stud losses reduces the whole wall R to just 22.5, a loss of a third the R.
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Yes, that loss at the higher R-values is bigger than I thought it would be. One question I have is what type of wood they assumed for the studs. There is a difference in density between say Douglas fir and yellow pine or hemlock, and I wonder if that would change the heat losses through the studs.
I've seen all sorts of numbers on R/inch of various wood materials. Generally, it seems to range from only 0.7 for hardwoods to as high as 1.4 for softwoods. One source just gave 1.25 for "softwood/plywood." Clearly, thermal conductivity is highly species and moisture dependent, and it will vary from one stud to the next in the pile.
In the posted table, R=1/inch was used, as I noted earlier. If I do the calc for R6/inch insulation between studs 16" oc, this time using R 1.25/inch for the wood, I get 24.3, vs. 22.5 from the table for R=1/inch. I doubt anyone would propose use of balsa wood for studs, but that would reduce thermal bridging even more. I'll look again for R for various framing materials. I had something good once, but search engines tend to find too much to sift through.
For anyone who wants to know what is behind the calculations, start with the basic heat transmission equation: Q = U * Area * dT, where Q (English units, only in the US and a few remaining oddball places) is heat loss, BTU/hr; U is heat transfer coefficient (related to thermal conductivity), BTU/(sq.ft - hr - degree F); and dT is the temperature difference, degrees F. For convenience in calculating insulation values, R is defined as the reciprocal of U. Thus Q=Area*dT/R. If heat loss is known, the effective R is Area*dT/Q. Effective R for a wall assembly is then total area/total heat loss per degree. For a foot-high piece of wall, the heat loss per degree of temperature difference through a stud and the adjacent insulated area would be, for 16" oc stud spacing:
Qs= (1.5/12)/Rs where the Qs and Rs refer to the stud, and the 12 converts to feet.
Qi= (14.5/12)/Ri where the Qi and Ri refer to the insulation.
For effective R of the wall (ignoring drywall, sheathing, siding):
R(eff.) = (16/12)/(Qs + Qi)
The calculation can be cast into a single equation for spreadsheet calcs, canceling out the divisions by 12, using SS for stud spacing and SD for stud depth (3.5 for a 2x4, 5.5 for a 2x6), and redefining Rs and Ri to be R/inch:
R(eff.) = SS/[ {1.5/(Rs*SD)} + {(SS-1.5)/(Ri*SD)} ]
Any uniform material covering the wall assembly uniformly, such as the mentioned drywall, sheathing, and siding, are handled by just adding the R values of those layers to the effective R of the stud/insulation part.
Also ignored are the heat losses through top and bottom plates, rim, etc., and they all add to total heat loss. Effective R value for a wall is useful for evaluating different construction and materials, but what is really important is the whole-house heat loss. That is what programs like RESCheck do; it adds up heat losses for all components of the exterior building envelope and presents a total U*A, which can be used with minimum outside temperature to get peak heat loss for sizing the heating system and with heating degree days for the location to estimate annual heating bills.
and they all add to total heat loss
I'm guessing infiltration is also not factored in as all that does is add a level of complexity the modeling probably does not need.
That, and you start introducing "fit" to the insulating material and having to reweight the R/inch--all to no great good . . .
Does make me wish we could find a generally-reliable way to model the top plate ceiling joist interaction area (so I could have a "stick" to better beat detail compliance into lackadasical soffit builders <g>).Occupational hazard of my occupation not being around (sorry Bubba)
True, convective heat loss isn't in there; the calcs are strictly for conductive heat loss for that theoretical wall made of stud and insulation side by side. Once other things are to be figured in then things get quite complicated, like lateral conduction in walls having framing that does not go all the way through (there is no "elimination" of thermal bridging for studs sticking part way through the insulation, only reduction, but that reduction can be to the point of negligible contribution to total heat loss). Nor is "goodness of fit" counted. Maybe it should be called badness of fit, because anything less than perfect fit just contributes to heat loss.
Frenchy, by "preaching to the choir" I guess I was really referring to the issue of poor performance of FG batts in cold weather. Maybe you should show the Minnesota folks the ORNL report on how poorly it does. Then they could call a 2x6 wall with a FG batt "code compliant" but only for the parts of the state where it doesn't get below, say, 40 F in winter. They've at least called for HRVs in new construction to provide fresh air. So why do they still allow FG batts to be called "R19?"
Maybe you should show the Minnesota folks
LoL!
Just think of all of those attics "floored" in layers of loose-fitting batts with all that balmy ice-dam-preventing-we-promise cold air swirling over them . . . Occupational hazard of my occupation not being around (sorry Bubba)
Dick, how would the Mooney wall fit into this?
Minimal conduction area, 1 1/2" by 1 1/2" every 16" must make a huge difference, but how would it be calculated?
Joe H
As I was mowing the lawn last evening, I thought "someone's going to ask about the Mooney wall." Darn, more work. OK, first to repeat the comment that the effect of direct conduction through a stud can't be eliminated, only reduced, because it is still there conducting some heat more easily than the same volume of insulation it displaces. Next, for a section of wall consisting of side by side wood plus insulation, both contacting inside and outside and thus having the same terminal temperatures, the temperature profiles through both materials will be linear, there will be no lateral temperature differences, and therefore there will be no heat transfer laterally (we're talking hypothetical walls here, the kind everyone builds). Now, if you have an insulation layer continuous from inside to outside, but a stud that goes only part way through, then the temperature profiles will not be the same and there will be some lateral heat conduction in the vicinity of the wood. Trying to calculate that would take some computer work, integrating the partial differential equations involved. The answer still wouldn't be any better than the uncertainty in the R values of the wood and insulation.
As long as we're using wood and not solid aluminum studs, a good approximation of the answer to the original question can be found by calculating the effective R values of the two layers and adding them. Assuming this is a renovation and the outer wall is 2x4, then adding a layer of 2x inside the studs gives a 5" cavity for insulation. I've seen various R values for cellulose; typically from 3.4 to 3.6/inch. If Mike Smith figured an R18 wall, that would be for 3.6 if no stud conduction were figured in. So I'll report for both 3.4 and 3.6. All numbers below for R are rounded to 0.1, then added, so a spreadsheet calc of totals might be around a tenth of an R unit off (but we don't know the R of either material that well).
From the table, the 2x4 outer wall, 16" oc gives effective total R of 9.7 or 10.1. For the inner layer of horizontal 2x material, assume (as described by Mike) that they are 2x4 ripped lengthwise. Allowing 1/8 inch for saw cut, that gives 1.5 thick by 1.6875 tall pieces. The inner wall is then basically studs 1.5" deep and 1.6875" thick next to an insulation layer that deep and (16-1.6875)=14.3125" wide, turned sideways 90 degrees. Then for each foot of wall width, the same sort of calc is done:
R(eff.) = 16/[ 14.3125/(3.4 * 1.5) + 1.6875/(1.0 * 1.5) ] = 4.1 (rounded up)
Repeating for cells at 3.6/inch gives 4.2 (slightly rounded down)
The whole R for the Mooney wall, throwing in another R1 for drywall, sheathing, and siding, is then 9.7 + 4.1 +1 = 14.8 or 10.1 + 4.2 +1 = 15.3
If everything is repeated using R 1.25/inch for the wood, the totals come to 15.5 and 16.2, respectively. If the outer wall is 2x6 @16"oc, the totals for cells @3.4/inch would be 20.4 and 21.1. But these are real R values that work when it's zero outside, when you need it.
Edited 5/30/2007 9:09 am ET by DickRussell
Hypothetically it's one thing, reality is something else.
Still, the Mooney wall is probably closer to the hypothetical wall than the straight stud wall?
The real insulating value is better than the theoretical?
Don't need no stinkin' science, we're warm anyway.
Joe H
"Still, the Mooney wall is probably closer to the hypothetical wall than the straight stud wall?"
Sure. You've covered the inner edges of the outer studs with about R4.5 worth of insulation, roughly doubling the R of the stud (and adding that much R to the outer wall insulation as well). It's interesting to note that about the same total R can be obtained by replacing the (presumably FG filter) in the 2x4 stud with closed cell foam, without 2x2 fastened on the inside. No air infiltration, no VR needed, and upwards of $3.50-4.00/sq.ft. for the foam. The Mooney wall with cellulose, good air sealing, and VR should be much cheaper, and perhaps somewhat quieter inside, too. I'm not advocating either solution. Either is a giant leap in progress over the FG batt.
"The real insulating value is better than the theoretical?"
Well, now, what's "theoretical" anyway? If the latter is what you would get for R with no wood taking up space, then the "calculated" degradation in whole wall R due to the wood should be fairly close to real. But an interesting question comes to mind. Is the claimed 3.6/inch for cellulose derived from measured heat loss across just the insulation (in a lab), or is it measured across an insulated wall assembly consisting of insulation and studs, and presented as expected R for the whole wall? I suspect it is measured for just an insulation layer without studs, but I can't say for sure. If it is measured for whole wall, then the table I presented is based on an incorrect assumption. But if the insulation's reported R does include studs, then it would have to say at what stud spacing, because wider spacing reduces the heat loss.
Edit: OK, I found two references that help clarify what R includes, and both suggest the standard testing methods report R for just the insulation, without any accounting for stud conduction.
http://www.sprayfoam.org/R-values%20of%20SPF.pdfhttp://www.cellulose.org/pdf/cellulose_benefits/cons-report-1.pdf
Edited 5/30/2007 11:54 am ET by DickRussell
Here is the table, modified for R of the wood studs at 1.25/inch:
Dick Russell,
Extremely interesting! Thank you for your work!
I wonder what numbers would be arrived at if real world insulational values were used instead of the fixed 70 degrees lab conditions that R values are calculated at.. I'm thinking of thermo-cycling in particular as it pertains to fiberglas insulation.
Unfortunately, the table is of limited use when FG batts are used or when windows are left open, except when the outside air temperature is 70 F and no heat moves through the wall anyway. Just how much R degradation occurs by conduction through studs vs. the density-induced effect of low temperatures on FG batts would seem to be uncertain. I imagine the lab tests cover just just the whole wall or ceiling R, although that now famous ORNL piece in the early 90s did report the drop in R as a function of outside temperature. That change in R was due to the induced air movement, which got worse as the dT increased and thus the density was more pronounced (about a 15% difference at 70 F temp difference). Anyway, I imagine anyone who really finds the table useful already knows about the folly of FG batts.
Dick Russell,
Thank you for that answer.. now to spread the word!
your data really supports the SIP's agruement. I'd imagine it would also provide some support for ICF's as well although the endless debate about thermal mass etc.. will could that issue endlessly.
".. now to spread the word!"
But posting on Breaktime is like preaching to the choir.
Dick Russell,
I'm afraid that's really not the case.. Too many here are tradional stick builders and resent anything other than stick building.. Nationwide about 2% of homes are built other than stick framing so we have an extremely long way to go..
At least those on this site tend to be interested in learning, so we have a chance to inform some of the future decision informers.
As for spreading the word, I'll do my 2 cents worth. I sell to the construction industry and contact builders all the time.. In addition I'm building my own home so I have frequent contact with the building inspector.. I'll show him your chart. right now my city allows an 80% rating of R value, it would be helpful if that was increased to the 67% your chart indicates . (my Community is the wealthiest one in Minnesota so it should be reasonable to expect them to be among the most effective in building code requirements..
hi
i'm new here and i'm not a builder, yet... but i'm very interested in your discussions here and long time reader of Fine HomeBuilding [Dwell, etc.].
i've been researching ICF's and SIP's for several years, and after talking to several ICF's builders... between costs, concrete costs, and the seasoned pro's frustrations, it doesn't appear to be a very good solution for me, which brings me to SIP's
the thermal bridging of conventional SIP's using what [imho] is today's less than wonderful quality 2x6's, seems to be self defeating. coupled with something i really don't care for in my walls [today's quality 2x6's] and the thermal bridging they represent not only to gain their connection joints [as some do], but also their load bearing... [and please, i'm not knocking anybody that manufacturers or uses today's 2x material, it's just that it has changed drastically from 100 years ago [even 50 years ago]]
i was wondering your opinion and valuable knowledge on two fronts:
although not for the typical McMansion buyer, the thought of the 'timber frame' appearance of the 'red iron' on the interior [or exterior] would IMHO, well, i would just find pleasing for the small garage / studio i would like to build for my self [24x36 2-story somewhere just above snow-line in Northern California]
thank you in advance for your time and considerations!