michael writes re:
NREL says 540 Btu/ft^2 of sun falls on the ground and 990 falls on a south
wall on an average 24.4 F in Omaha in December. The deep ground is 50.1 F.
Then again, plants need headroom. A 10'x10'x13'-tall greenhouse with
a 12/12 roof and 2 layers of R1 south glazing with 80% solar transmission
would collect 0.8x10'(13'x990+5'x540) = 124.6K Btu/day. With insulated
non-south surfaces and a thermal conductance G = 10'(8+5/cos(45))/R2
= 75.4 Btu/h-F, 124.6K = 24h(T-24.4)G would allow an average indoor temp
T = 93.3 F on an average December day.
So the pipe has holes? And mold isn't a problem? If most of the water
condenses in the pipe vs on the inner glazing, it must be cooler than
the glazing. If greenhouse air is (say) 80 F and it's 24.4 outdoors and
(80-24.4)/1ft^2/R2 = 27.8 Btu//h flows through 2 layers of R1 glazing,
an R2/3 indoor air film makes the inner glazing 80-27.8x2/3 = 61.5 F. If
the pipe is (say) 60 F at dusk and it keeps the house 50 F for 16 hours
at night and 16h(50-24.4)G = 31K Btu = C(60-50), C = 3100, eg 3100/30
= 103 ft^3 of damp soil, eg 2 4'x10'xi15" deep beds on each side of
a 3'x10' walkway, with lots of pipe.
But tomato plants want to be warmer at night. Benton Jones says (on page
18 of "Tomato Plant Culture," CRC Press, 1999) they like to be 80 F max
during the day and 65 at night. If the pipe is more than 61.5 F at dusk,
there will be condensation on the inner glazing film with more heat loss
to the outdoors (how much?), but we can keep the house warmer at night...
65 F for 16 hours takes 49K Btu.
It's probably "critical" to move enough air to store enough heat to keep
the house warm at night. If Q cfm of 80 F air moves through a large mass
with a large conductance for 8 hours and 8h(80-65)Q = 49K, Q = 408 cfm.
C = 5000 Btu/F (2 4'x10'x2.1' beds) and 5000(T-65) = 49K makes T 74.8 F,
which makes RC = -8/ln(74.8-80)/(65-80)) = 7.6 hours and R = 7.6/5000
= 0.00151 = 1/cfm + 1/(1.5A), approximately. With a 1000 cfm fan, we need
A = 1307 ft^2 of pipe surface, eg 131 10'x4" pipes :-)
A 1000 Btu/h-F (R = 0.001) $5 20-watt car radiator seems more practical:
If a C Btu/F tank reaches T (F) after 8 hours and T = 80+(65-80)e^(-8/RC)
and C(T-65) = 49K Btu, C = 3267/(1-e^(-8000/C)). Plugging in C = 3267 on
the right makes C = 3576 on the left. Repeating, C = 3657, 3679, 3686, and
3687, eg 59 ft^3 of water in a 2'x4'x7' tank in the trench. The radiator
could also go in the trench, for freeze protection and minimal pump power,
with a downflow duct from the top of the greenhouse. During a long string
of cloudy days, we might keep the greenhouse about 40 F with the radiator
and (40-24.4)G/(50.1-40))/8.33/60 = 0.23 gpm of wellwater.
We could wear stilts to pick indeterminate tomatoes :-)
The trench could warm the greenhouse. With 2x3x3+3x10+2x3x10 = 108 ft^2 of
50.1 F soil surface (at best) and (T-24.4)G = (50.1-T)108x1.5, T = 42 F.
Lots of wet rocks in the trench could help. Warm air rises. Humid air rises.
Freeze-tolerant plants could help, as in Eliot Coleman's unheated houses.
The drums are absorbing water?
Freeze-tolerant fins could help. Warm water stops rising at 39 F.
Bubblewalls could help...
My 100' tomato greenhouses are about 12' tall, with 4' rollup sides.