What do you mean by putting R5 on stud wall?
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if the walk-out basement wall is wood framed that portion..."
...you'd want R5 of sheet-goods insulation beween either the studs & gypsum or studs & siding, was what I meant. (Coulda been poured concrete, cement block or wattle & daub for all I knew. This sounds like fairly recent construction, not an antique, using 17th century materials, eh?
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Weathermate comes in different thicknesses with different R-values from R1.5 (3/8"), R3 (1/2") and R4 (3/4") . Whatever you have is probably "good 'nuff" with 2x6 studs, but for the sake of analysis, do you happen to know which it is?
From the Oak Ridge calculator, it looks like they were specifying that R5 goes on the exterior if the siding was removed and there is an "empty wall". My walk-out basement wall is (from outside) brick, Dow Weathermate Plus Styrofoam Housewrap, 1/2" OSB and 2X6 stud wall. So in this case should I just use unfaced fiberglass since with faced insulation moisture would not be able to escape inward through the facing or outward through the OSB? This is the area where the approach to unfaced vs. faced fiberglass has changed over the years.
Unfaced fiberglass (or better, dry blown cellulose) would be the right way to go. The OSB is somewhat vapor retardent, and in mixed heating/cooling climates you can set it up to dry in either direction (in this case, drying toward the interior. It's when you stack it with highly retardent matierials on both side that you'd run into issues in a mixed climate. OSB is not very strong vapor retarder, but keeping the other materials vapor-permeable (but not necessarily air-permeable) guarantees it won't stay wet if it happens to GET wet.
Blown cellulose will fill the gaps for a perfect fit, and will experience lower convection & air movement within the material, and provide significant hygric buffering, protecting wood from water damage/mold from occaisional wetting events. If you can, use "borate only" aka "sulfate-free" cellulose. The borate content of the fire retardent is somewhat protective against ants, termites & mold, and unlike the sufate fire retardent it's fairly innocuous stuff. The sulfates can erode metals if wetted, and if you don't catch the leak in time you experience some other damage- it's primarily an issue with copper, but not exclusively. (The borate only versions aren't usually available through home-center box stores, but some contractor supply houses would have it. Greenfiber Cocoon2 Stabilized Borate Formula is probably the most widely distributed/available, but there are others.)
I'd still prefer even sulfated cellulose over fiberglass, if that were all that was available. In a 2x6" stud wall blown cellulose will perform to a true R20+, whereas real-world installations of even high density R21 batts are actually more like R16-R18 (due to imperfect fit, compressions and voids.) Using insulation blowers isn't rocket science, and the stuff is pretty cheap. Box store home centers that carry cellulose usually have cheap daily rental rates, and will often throw a day's rental in free if you buy over some minimum amount.
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2.5" XPS, or 3" unfaced EPS beadboard glued in place with blobs of foamboard construction adhesive, with horizontal furring strips (through-screwed to the foundation with long masonry screws) for holding up the code-required thermal barrier (half-inch sheet rock) for fire control is probably the most cost-effective method.
I don't know what climate zone the BSC RR-202 Figures 13, 14 and 15 are targeting, but 2" seems excessive for NC. The total insulation from the ORNI calculator is only R11 (the combination of rigid foam and fiberglass).
Several below ground block wall sections already have a 2X4 stud wall with a small gap to the block. I won't be able to fish anything more than about 1/2" rigid foam behind most of that area. Where there isn't a stud wall yet, I will add rigid foam directly to the wall before putting up the stud wall.
The tests were done in MN, but the target is the entire lower-48- it's the groundwater vapor-drive issues that were of greatest interest.
If you can insert even 3/8" XPS sheet in there it's worth it (but half inch is better). XPS is preferable to EPS here, since it provides some vapor-retardency. Once the stud bays are insulated the wood facing the wall will be cold, making it's relative humidity higher, with more mold risk. By putting even R3 (1/2" XPS) between the stud and the wall you're keeping it warmer, which lowers the relative humidity. Then R11 or R13 unfaced friction-fit batts for maximum inward-drying capacity would bring it well over the Oak Ridge recommended minimums with low risk of mold.
For stud walls between finished and unfinished (unconditioned) rooms should the fiberglass insulation be faced or unfaced? However I do plan to have a vent in the unfinished space that will allow a small amount of conditioned air to circulate.
If you're running conditioned air into the space there may be no point to insulating the partition walls other than sound-proofing. What sort of temperature differences do you anticipate between the conditioned/semi-conditioned spaces? If it's less than 10F difference (and I suspect that's the case) forget about it! I'm assuming the non-built-out portion is minimal-daylight back portion or something, which would be thermally coupled to the subsoil earth temp which is probably in the high 50s or low 60s F in non-highland NC.) But if you want to insulate it anyway, unfaced friction-fit batts (or blown cellulose like the exterior wall) would work, or even an inch or two of unfaced EPS (R4-R8) under the gypsum. Vapor retarders might work against you there, but kraft-facing probably won't make or break it with conditioned air being circulated on both sides- whatever is most convenient is fine.
At the very least, insulating the upper half of the foundation in the non built-out areas to R10 with EPS sheet goods will have reasonable payback on heating (but not so much on cooling). Unless you have R15 or something in the joists between the basement & first floor the wintertime heat lost out of the foundation is significant. The cooling season heat GAIN through the foundation won't be much, unless you have a significant amount of above-grade portion of the foundation on an unshaded south or west wall (which could be remediated with some shrubbery.) If you later wanted to build it out you either could fill in the lower portion with the same and use furring for the finish wall, do the lower portion in R5 XPS and use 2x3 studs & R8 batts for the finish wall, or other variations on the theme.