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a 16' non-cube
8 mar 2001
looks like we can save some serious bucks by removing the glazing and 
putting the heat storage tank in the basement. less "roof" required,
10% more sun, the unpressurized target can be a lot simpler, the tank
can have less insulation, and the heat loss from the tank warms the
house, but... we need a pump. 

nrel says a 1-axis ew concentrator can collect 729 btu/ft^2 over 3 hours
in phila on an average 30.4 f january day. with a 90% reflector and a
layer of r1 clear polycarbonate glazing with 90% solar transmission,
we might collect 0.9x0.9x729x16'x16' = 151k btu/day with a 16'x16'x16'
tall open-sided box with a parabolic reflective north wall and roof.

the reflector would bounce dawn sun down onto a 4'x16' horizontal target
at the base of the north wall. the focus moves closer to the north wall
during the day until the reflector begins to shade the base of the wall
at a 45 degree sun elevation (at noon on april 4 and september 28, at
40 n latitude.) we would still have lots of hot water in summertime. 

with a 4' strip near the north wall dedicated to solar collection and
12'x16' = 192 ft^2 of clear floorspace, the structure could also be 
something else, eg a run-in shed for horses or cows or a place to park
a car temporarily when it's snowing. 

the target might be a $10 16'x30" round uv polyethylene film greenhouse
air duct laid flat on the ground over black plastic film. it might heat
water for a 4'x12'x4' tall 1,024 gallon epdm-lined tank in a basement
corner, with 9 inboard 4' studs on 2' centers and 1" of r7.2 foamboard
underneath inside 4' and 12' 2x4s attached flat on the floor. we might
put 3.5" fiberglass r11 insulation between the studs with a 1" layer of
foamboard over that and a 1" layer of foamboard between the tank and the
basement walls and another 2 layers over the tank. its thermal conductance
would be 48ft^2/r17.2 = 2.79 for the floor plus 48ft^2/r14.4 = 3.33 for
the cover plus 64ft^2/r7.2 = 8.89 for the outside walls plus 64ft^2/r18.2
= 3.52 for the inside walls. g = 18.53 and rc = 8192btu/f/18.53btu/h-f
= 442 hours, or 18.4 days.

so far, we have a $10 duct (griffin greenhouse and nursery supplies,
978-851-4346) plus 64 ft^2 of tank osb, $12 at $6/4x8 sheet. we've
also used a $72 20'x12' piece of epdm for the tank liner, 64 ft^2 of
fiberglass worth $16, 272 ft^2 of foamboard at $85 and 52 ft of 2x4s
at $13. these materials subtotal $196. 

the reflector needs 384 ft^2 of osb and another 384 ft^2 of epdm for its
roof ($187), and 9x24' = 216 ft of 2x4s on 2' centers with a dozen (11 :-)
kerfs in each bow. the lower and upper edges could use 32 ft of 2x4s. we
might support the open south wall with 3 16' posts with 2 2x4s attached at
right angles with deck screws, with some upper diagonal bracing. that's
344 ft of 2x4s worth $86. the bottom part of each post could be pressure-
treated wood bolted between the sidewalls of 2 vertical underground tires
filled with stone.

gluing 384 ft^2 of mylar ($0.09/ft^2 from
under the parabola adds $35. grainger's 4pc89 120v 0.7a pump adds $135 and
$7/year at 10 cents/kwh, making the total materials cost $639.

the target has about 1.5x4'x16' = 96 btu/h-f of thermal conductance to
outdoor air. we might collect 151k btu/day of beam sun over 3 hours at
200 f and lose 3h(200-30)96 = 49k btu, for an average daily hot water
production of 102k btu at $639/(102k/3.41) = 2.1 cents per peak watt.

at t degrees f, the tank loses heat at a rate of (t-70)18.53btu/h, and
hot water use removes heat at a constant 102k/24h = 4250 btu/h, so dt/dt
= -((t-70)18.53+4250)/8192 = -0.002262t -0.3605 = -ct +d, so d/c = -159
and t = -159+(200+159)exp(-0.002262t) = 120 f when t = 111 hours, after
4.6 cloudy 30 f days in january.

now how can we make it frugaler?


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