It looks like we might store overnight heat for an 8' R10 cube near Phila
with a 4'x8' air heater that keeps 70 F air near the glazing using 16' of
fin-tube under the ceiling and 8' under the floor. The ceiling tube might
heat 50 lb/h (0.1 gpm) of 53 F water to 96 during the day. The floor tube
might cool 15 lb/h of 96 F water back to 53 F at night, with a 36 gallon
unpressurized stratified heat storage tank under the floor. Eric Hawkins
of Powertech in the UK says has found that the fin-tubes can stay primed
for years if the ends of the supply and return pipes are underwater.

We might keep the room air 70 F over an average solar collection day with
varying sun and outdoor temp by pumping more or less water through the
ceiling tubes. A ceiling fan might do away with the floor tubes (or poly
film water duct under the floor) and heat the cube faster after a setback.

The tank must be larger for 5 cloudy days in a row. More insulation (R10
isn't much) or an 8'x8' vs 4'x8' air heater would raise the water temp and
reduce the tank size. It might make water for showers with a coil in the
unpressurized tank and a flat tank under the floor for a greywater-to-air
heat exchanger. The 8'x8' air heater might be 2 4'x8' pieces of 0.020 inch
polycarbonate film over a picture frame over a dark south wall, with 2
4'x8' pieces of dark window screen for the mesh absorber.

10 RV=10'wall and ceiling US R-value (ft^2-h-F/Btu)
20 GC=5*8*8/RV'cube to outdoor conductance (Btu/h-F)
30 TA=30'outdoor temp (F)
40 TS=50'setback temp (F)
50 EDS=2*(70-TA)*GC+16*(TS-TA)*GC'daily heat storage requirement (Btu)
60 EDSH=EDS/6'daily heat storage rate (Btu/h)
70 SSUN=1000'daily sun on south wall (Btu/ft^2)
80 AHA=4*8'air heater area (ft^2)
90 NAHG=.9*SSUN*AHA-6*(70-TA)*AHA/1'net air heater gain (Btu/day)
100 EDW=6*(70-TA)*(4*64-AHA)/RV'6-hour heat loss from walls (Btu)
110 TC=TA+(NAHG-EDS-EDW)/(6*64/RV)'average daytime air temp under ceiling (F)
120 LU=16'ceiling fin-tube length (feet)
130 GU=5*LU'ceiling fin-tube to air conductance (Btu/h-F)
140 QD=50'daytime water flow rate (Btu/h-F)
150 TIND=TC-EDSH/(QD*(1-EXP(-GU/QD)))'daytime input temp (F)
160 TOUD=TIND+EDSH/QD'daytime output and nighttime input temp (F)
170 DAWNHEAT=(TS-TA)*GC'heat requirement at dawn (Btu/h)
180 QN=DAWNHEAT/(TOUD-TIND)'nighttime water flow rate (Btu/h-F)
190 LL=-(LOG(1-((DAWNHEAT/QN)/(TOUD-TS)))*QN)/5'floor fin-tube length (feet)
200 PRINT TS,TIND,TOUD,TC'Ts,Tcold,Thot,Tc (F)
210 PRINT QD,QN'day and night water flow rates (lb/hour)
220 PRINT LU,LL,LU+LL'upper, lower, total fin tube length (feet)
230 CTANK=EDS/(TOUD-TIND)'stratified tank volume (pounds of water)
240 PRINT CTANK,CTANK/8.33,CTANK/(8.33*8)

Setback Tcold Thot Tceiling
50 53.2066 95.87326 106.6667 F

daytime nighttime
water flow water flow
50 15 lb/hour

ceiling floor total
fin-tube fin-tube fin-tube
16 7.982017 23.98202 feet

Stratified tank size
300 lb 36.01441 gal 4.501801 ft^3

Happy new year,

Nick