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overnight heat storage
27 jun 2002
storing house heat overnight can be more difficult than storing heat for
a rare cloudy week, with a higher charging rate and a lower temp swing.

what's the min r-value for a 32x32x16' house with 8% of the floorspace
as r4 windows with 50% solar transmission and 0.2 ach and 300 kwh/month
of internal heat gain, based on overnight heat storage?

say it has 96 ft^2 of south windows, with 32 ft^2 on the east and west,
and 16 ft^2 on the north. with a 1024 ft^2 ceiling and 848 ft^2 of walls
with r-value r, its thermal conductance g is 1872/r plus 176ft^2/r4 = 44
btu/h-f for windows plus roughly 32x32x16x0.2/60 = 55 for 55 cfm of air
leakage, ie g = 99+1872/r. 

on an average jan day in phila, the sun gives 0.5(96x1000+64x420+190x16)
= 63k btu of heat, with 34.1k more from electrical use. if 24h(65f-30f)g
< 97.1k, 99+1872/r < 115.6, so we can heat the house with windows alone,
and 1872/(115.6-99) = r113 insulation :-) more south windows would help,
but that would raise the house conductance and the size of the cloudy-day
heat store.

let's add enough sunspace to keep the house 70 f for 6 hours per day.
with 3840 ft^2 of 1/2" drywall, c = 1920 btu/f, and rc = c/(3840x1.5)
= 0.33 hours, the drywall will be 70 f at dusk, after 18 time constants.  
to make 60 f at dawn, with constant electrical use, we need 18h(65-30)g 
< 10c+25.6k, ie r = -67 :-) looks like we need more thermal mass or
a higher temp swing.

let's try adding more mass. with r48 walls and ceiling, g = 138. we need 
86940 < 10c+25.6k, eg c = 6134 pounds of water, eg 1394 2 liter bottles
in a 2' wide x 32" high x 27' long room divider. rather large...

how about a higher temp swing? we might make the sunspace or air heater
large enough to supply 120 f air for 6 hours on an average jan day, with
ducts to a heat store inside the house. if c btu/f in the store charges to
120 f and discharges to 70 f every day, we need 18(65-30)g = 50c+44.8k,
counting the drywall and internal gain, so c = 352+23587/r.

a 16'x4" pipe holds about 90 pounds of water. we might use p = 3.92+263/r
16' vertical pipes inside a 4'x4' airshaft made with 3 4"x4'x16' vertical
sips, with doors on one side for a platform elevator with an overhead
winch. p = 10 with r48 house walls (eg 12" sips), 13 for r32, and 21 for
r16 (4" sips.) the 12' perimeter inside the airshaft can hold about 36
vertical pipes, so we might have r16 house walls. 

the top of the airshaft might contain a slow ceiling fan to circulate
air through the sunspace during the day. this might work naturally, with
a passive plastic film damper to prevent reverse airflow at night. with
r16 walls, g = 216 btu/h-f, so we need to store 18h(65-30)216-5.1k = 131k
btu over 6 hours. with a 90 f pipe temp, 6h(16.6)asqrt(16')(120-90)^1.5
= 131k makes the duct cross-sectional area a = 2 ft^2. 

will the pipes charge up to 120 f and discharge to 70? the house needs
(60-30)216-283 = 6.2k btu/h at dawn. each pipe has 16.7 ft^2 of surface,
so 28 pipes (a guess) have a conductance of 28x16.7x1.5 = 701 btu/h-f
to still air, approximately, so they have to be 60+6.2k/701 = 68.8 f
to keep the house 60 f at dawn. they have a 3.6 h time constant, so
they will only charge to 120-(120-68.8)exp(-6/3.6) = 110.3 after 6 hours
in 120 f air. so the real temp swing is closer to 110.3-68.8 = 41.5 vs
50 f, and we need something like 50/41.5x21 = 25 pipes. 

how big a sunspace? the house needs 24h(65-30)216 = 181.2k btu on
an average day, of which 34.1k comes from electrical use and 63k comes 
from windows, leaving 84.1k at 120 f. a square foot of sunspace with
r1 south glazing with 90% solar tranmission gains 900 btu/day and loses
about 6h(120-30)/r1 = 540, for a net gain of 360 (with a 36% collection
efficiency), so we need 84k/360 = 234 ft^2. doable, but that's almost
the entire south wall...

let's try 6" r24 sip walls instead. then we need a nominal 3.92+263/24
= 15 pipes, with 377 btu/f of still air conductance. g = 99+1872/24 = 177,
so the house needs (65-30)g-283 = 5912 btu/h at dawn, when the pipe temp
needs to be 60+5912/377 = 75.7 at dawn, rising to 120-(120-75.7)exp(-6/3.6)
= 111.6 at dusk. with a 111.6-75.7 = 35.9 f temp swing, we need closer
to 50/35.9x15 = 21 pipes.

we need to collect 24h(65-30)177 = 148.7k btu on an average day, 51.6k
more than the total from electrical useage and windows, so we need
51.6k/360 = 143 ft^2 of south glazing. that's better. 


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