[Greenbuilding] The dynamic R-value scam...

[Nick Pine]

John Straube <jfstraub at civmail.uwaterloo.ca>

>... Thermal mass on the interior increases the fraction of solar energy that enters the building that can be used to offset heating.

Sure. That's different from "dynamic R-values."

>... For most people, who want to avoid the temperature exceeding 78 during sunny days and not drop below 65 at night, interior thermal mass is just the ticket.

But as you say, that requires lots of airtightness and insulation. And mass surface:

20 AW=48*8'single wall area (ft^2)
30 AC=48^2'ceiling area (ft^2)
40 FOR WS= 1 TO 5 STEP 4'wall area multiplier
50 FOR NW=1 TO 4'# 48'x8' mass walls
60 RV=40'house wall and ceiling Rv (ft^2-F-h/Btu)
70 GH=(4*AW+AC)/RV'house conductance (Btu/h-F)
80 CW=5*NW*AW'mass wall capacitance (Btu/F)
90 AM=NW*AW*WS'mass heat transfer area (ft^2)
100 GAF=1.5*AM'wall airfilm conductance
110 RC=CW/(GH+GAF)'air-wall time constant (hours)
120 THC=30+48/(1+GH/GAF)'Thevenin air temp (F)
130 TCMAX=THC+(65-THC)*EXP(-6/RC)'max wall temp at dusk (F)
140 ENEED=18*(71-30)*GH'overnight storage need (Btu)
150 ESTOR=(TCMAX-65)*CW'overnight heat stored (Btu)
160 IF ABS(ESTOR-ENEED)>100 THEN RV=ENEED/ESTOR*RV:GOTO 70
170 RVR=INT(10*RV+.5)/10'round
180 RCR=INT(10*RC+.5)/10
190 PRINT AM;RVR;RCR;TCMAX,ESTOR
200 NEXT NW
210 NEXT WS

#walls  holes     surface     R-value   time constant   mass temp    stored heat  

1       closed    384 ft^2    157.4     3.2 hours       74.35755 F   17966.5 Btu
2       closed    768         78.8      3.2             74.35908     35938.86
3       closed    1152        52.6      3.2             74.36158     53922.66
4       closed    1536        39.4      3.2             74.36038     71887.74
1       open      1920        118.7      .7             77.46236     23927.73
2       open      3840        59.2       .7             77.46373     47860.7
3       open      5760        39.5       .7             77.46388     71791.96
4       open      7680        29.6       .7             77.46442     95726.72

It looks like a 48'x48'x8' tall house with 4 block walls with the holes lined up for vertical indoor internal airflow would need R29.6 exterior insulation to allow storing overnight heat with a constant 6-hour 78 F air temp from a sunspace  and a 65 F air temp at dawn, on a 30 F day. Fewer block walls and less surface raise the required R-value. Insulation between the mass wall and house air would increase the required R-value dramatically. 

Nick