an abilene roofpond house SOLAR.KnowledgePublications.com

an abilene roofpond house
19 may 1997
suppose we built a naturally heated and cooled 16x16x16' superinsulated den on
the back of our house in downtown abilene, texas (behind the garage, so only
a few neighboring fossil-fueled texans could complain of our sneaky renewable
ways), with 1,500 ft^2 of average r20 walls and ceilings, an inherent thermal
mass of 750 btu/f (1/2" drywall) and a thermal conductance of 1,500/20 = 75
btu/h-f. let's assume air leaks and internal energy use are negligible.

the 24-hour average july temperature in abilene is 84 f, with average daily
min and max of 72.7 and 95.2. keeping the den at 70 f all day requires
24h(84-70)75 = 25k btu, about 2.5 kwh of electrical energy worth 25 cents at
10 cents/kwh, using an ac with a cop of 3, ie one that moves 3 kwh of heat
per kwh of electrical energy input.

if every day were 95.2 f and every night 72.7, cooling the den to 70 f for 12
night hours would require 12h(72.7-70)75 = 2,340 btu or about 1/4 kwh/day of
ac energy, if the den had no thermal mass. but the den's inherent thermal mass
makes its rc time constant 750/75 = 10 hours, so if it were 70 f at dawn, it
would warm up to 95.2-(95.2-70)exp(-12/10) = 88 f at dusk. cooling it back to
70 f requires an additional (88-70)750 = 13k btu, making the total cooling
required about 16k btu/day, a total of 1.5 kwh of ac energy. 

now let's add more thermal mass to the den, say 112 55 gallon drums full of
water, eg 4 layers of 28 vertical drums, each 2' diam. x 3' tall, around the
inside perimeter, making interesting radiant "coolwalls" and holding up a 2nd
floor, as well as helping support some exterior strawbale or 6" fiberglass
walls with 2 horizontal perimeter 2x4 deadmen running under each layer of
drums, and some plastic film under the whole den to keep out moisture and bugs,
but no foundation. this adds 112x55x8 = 49k btu/f of heat capacity, raising rc
to 50k/75 = 667 h or 28 days, making the dusk temp 95.2-(95.2-70)exp(-12/1770)
= 70.4 f, so it's pointless to turn the ac off during the day in this case,
since the duck temp won't rise much at all, so there would be little energy
savings. this den requires almost the same ac energy as the den in the first
example, even though the ac only runs at night. (however, the ac may be more
efficient at night, being cooled by cooler outside air.)

if we open the windows at night and close them during the day, or use a whole
house fan, this den can be close to 72.7 f all day, which might be comfortable
in abilene, with an average relative humidity of 53% in july, average humidity
ratio of 0.0130 #water/#dry air, a dew point of about 64 f, average 10.3 mph
windspeed, elevation of 1112 feet and average air pressure of 13.8 psia, vs
14.7 psia at sea level.

instead of opening windows at night, we might move water down into the den
from a shallow roof pond to a water-air heat exchanger, something like an
auto radiator with a fan, or a shallow water tray above the top drums, or a
passive plumbing arrangement like a zomeworks cool cell. a 16x16 = 256ft^2
70 f pond with a still air film conductance of 1.5 btu/h-f-ft^2 might gain
12h(72.7f-70f)x256x1.5 = 12k btu of heat per night by convection, which 
doesn't help, but...

the ratio of evaporative to convective pond heatflow is 1000(pp-pa)/(tp-ta)),
independent of windspeed, where pp and pa are pond and air vapor pressures of
water in inches of mercury, and tp and ta are farenheit pond and air temps.
the vapor pressure of 70 f water is 0.74 "hg (ln(pw) = 17.863-9621/tabs), and
air with a 0.0130 humidity ratio, w, has pa = 29.92/(1+0.62198/w) = 0.61 "hg.

abilene's elevation increases the e/c ratio by a factor of 14.7/13.8, so the
pond might lose 1000(0.61-0.5)/(72.7-70)x14.7/13.81 = 44 times more heat by
evaporation than it gains by convection (assuming this works with opposite
heatflows), on an average july night. the net cooling would total about a half
million btu/day, equivalent to a dozen 5,000 btu/h window air conditioners
running 8 hours per day, and about 32 times more cooling than the den needs.
night sky radiation helps even more. cooling the den with 13k btu/day requires
evaporating about 13 pounds of water per night, just under 2 gallons, perhaps
with a very small, low-head, low-power, 0.002 gpm pump.

this might also make a good solar house. the 24-hour average jan temperature
in abilene is 42.8 f, with an average daily max of 54.8 and average 1,400
btu/ft^2/day of sun falling on south walls. keeping this den at 70 f over an
average jan day requires 24h(70-42.8)75 = 49k btu. a square foot of thin
low-thermal-mass sunspace at 80 f during the day with an r1 clear plastic
single glazing (facing south, peeking above the shallow-pitched white-painted
house roof, in this case) that transmits 90% of the sun would gain about
1260 btu and lose about 6h(80-54.8) = 150 btu over a 6 hour winter day, for
a net gain of about 1,100 btu, so this den might be 100% solar-heated with
49k/1,100 = 48 ft^2 of glazing, something like a 4x12' clear plastic picture
frame air heater over the upper part of the dark-colored, insulated, low-
thermal-mass den wall, with holes in the wall at top and bottom to let warm
air circulate through the den during the day, with the help of a ceiling fan. 

four of the upper drums might be plumbed together with a float switch to fill
them, making a 220 gallon gravity-feed solar water supply, in which case the
roof pond might have an inflated or quonset-shaped greenhouse polyethylene
cover. the minimum average sun that falls on a horizontal surface in abilene
is 900 btu/ft^2/day in december, when the average daily max temp is 57 f. if
90% of it enters the r1 poly film cover, ie 256ft^2x0.9x900 = 207k btu/day,
and 6h(120-57)256ft^2/r1 = 97k btu is lost through the cover, 110k is left to
heat 110k/(8x(120-60)) = 230 gallons of water per day from 60 to 120 f. 

having lots of insulation, few air leaks, and lots of thermal mass inside the
house makes for a large rc time constant, which makes it possible to use these
monthly weather averages, vs detailed daily or hourly temperatures.

nick