NREL says 1000 Btu/ft^2 falls on a south wall on an average 30.4 F January day with a 37.9 max in Phila, so a $320 8'x40' Dynaglas wall would collect 900x8x40 = 288K Btu on an average day, or more, with a reflective deck to the south and/ or a reflective overhang (which could also prevent overheating in summertime.)
With 120 F water in an 800 Btu/h-F auto radiator and fan near the peak and insulation under the roof, it might look like this, viewed in a fixed font:
--- 1/320 |---|-->|-------www--- 34 F --- | 288K/6h x = 48K Btu/h | w w 1/800 w | | |
Opening the circuit at x makes the solar (Thevenin) equivalent temperature 34+48K/320 = 184 F, like this:
1/320 184 F ---www--- | x | w w 1/800 w | | |
... which might collect (184-120)/(1/320+1/800) = 14.6K Btu/h or 87.8K Btu/day, enough to make lots of hot water for showers (with a $60 300'x1" PE pressurized pipe coil in the heat storage tank) and provide some space heat. The attic temp might be 120+14.6K/800 = 138 F. We might also circulate some attic air through a filter and the 2nd floor of the house.
This seems efficient, even if the upstairs needs little heat. A dark mesh near the glazing (eg black aluminum window screen) with 70 F house air flowing through it could greatly lower the heat loss by convection through the glazing, as in a Scandinavian "breathing wall." With 70 F air near the glazing, we might capture up to 288K-6h(70-34)320ft^2/R1 = 218.9K Btu on an average January day. Polycarbonate blocks longwave IR, but there would still be radiation loss from the mesh to the glazing.
http://www.cibse.org/pdfs/8cimbabi.pdf has an equation for the dynamic metric U-value of a breathing wall, as corrected:
Ud = VRhoaCa/(e^(VRhoaCaRs)-1) W/m^2K, where
V is the air velocity in meters per second, Rhoa is air density, 1.2 kg/m^3, Ca is the air's specific heat, 1000 J/(kg-K), and Rs is the wall's static thermal resistance in m^2-K/W.
Using V = 1/3600 (1 meter per HOUR :-), and Rs = 5.7 m^2K/W (a US R32 wall), Ud = 0.058 W/m^2, like a US R98 wall. A more typical V = 10 meters per hour makes Ud = 1.7x10^-8 W/m^2K, like a US wall with an R-value of 334 million :-)
If 1 meter per hour (0.0055 fpm) flows through 320 ft^2 of mesh, the total is 17.5 cfm... 100 lfm up into a 1' wide x 2x4 cavity 8' tall with a 0.29 ft^2 cross section (29 cfm per linear foot of wall) would not increase the glazing loss much over still air. In that case, the total airflow would be 320x29 = 9300 cfm. So it looks like a wide range of airflow is possible, depending on how much heat the house needs.
With no mesh and 2 glazing layers, eg sliding glass doors, we might have this:
2/320 Tsun ---www--- Tsun = 34+259K/6/(2/320) = 304 F. | x | w w 1/800 w | | |
.... which might collect (304-120)/(2/320+1/800) = 24.5K Btu/h or 147.2K Btu/day with a 120+24.5K/800 = 151 F attic temp. (We datalogged 157 F in December of 1995 in the sunspace of our phone-booth-size experiment at Ursinus college.)
We might start by drilling holes from the inside of the attic with a long bit near the ridge next to the present rafters, then Sawzall a rafter-size piece of roof from the outside and slip a 12' 2x6 into each hole parallel to the rafter and bolt the bottom foot to the rafter, then build the new roof, then remove the old one (or not) and build the wall...
I bought a used 1984 Dodge Omni automobile radiator for $35. We might attach a $50 Lasko 2470 cfm 90 watt window fan to it... 800/5 = 160' of fin-tube pipe with no fan would cost about $320. I like that better, since it is simpler and uses less electrical energy and the fan may not last very long over 100 F. (My 640 ft^2 Dynaglas solar attic has a $433 2764 cfm 275 W Swedish Multifan with special ball bearings and lubricant rated for 311 F.)