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a 12' non-cube
9 mar 2001
looks like we can save even more by moving the heat storage tank back
outside on the ground... 

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 0.9x729x12'x12' = 94.5k btu/day with a 12'x12'x12'
tall open-sided box with a parabolic reflective north wall and roof.

the reflector would bounce dawn sun down onto a 3'x12' horizontal target
at the base of the north wall. the focus moves closer to the north wall
during the day until the upper edge of 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.) still lots of hot water in summertime. 

with a 3' strip near the north wall dedicated to solar collection and
9'x12' of clear floorspace, the structure could also serve as a run-in
shed for horses or cows or a place to park a car when it's snowing. 

the target might be a $7 12'x24" round uv polyethylene film greenhouse
air duct laid flat on the ground over black plastic film. it might heat
water for an 8' diameter x 4' tall 1,200 gallon polyethylene-film-lined
tank on the ground near the reflector and near the house.

to make the tank, we might put an 8'x8' piece of plastic film on the
ground, then make an 8' diameter x 4' tall cylinder of 2"x4" welded-wire
fencing (tractor supply sells 100' rolls for $39.99, with 0.081" diameter
wire) on top of the film. this tank could be made larger, say 24', with
32' poly film, but it would need more layers of fencing.) then pile dry
leaves, mulch, peat moss, sawdust, etc. about 2' thick on top of that,
then line the cylinder with a $13 16'x16' piece of 6 mil poly film, then
build a frame around that with 12 pieces of 1.5" pvc pipe or conduit.

the frame might be 10' square, seen from the top, with a 4-sided roof
with a peak in the middle about 6' above a 10' pipe square supported
4' above the ground by 4 5' vertical pipes driven a foot into the ground
over 4 30" rebar stakes to keep the frame from sliding. 

the top 4 pieces of pipe leading up to the peak would be 9.4' long,
joined with 4 6"x1 5/8" galvanized strapping tabs with a bolt to hold
each tab in the end of each pipe and a bolt for the middle to join
the 4 tabs. the other ends of the upper 4 pieces could be joined to the
10' pipe square and the vertical pipes in the same way. this requires 10
10' pieces of pipe ($30?) and 10' of tab material ($12 for the stiff
kind, with prepunched holes) and 25 nuts and bolts and washers ($5.)

now we make a 10' square welded-wire fence enclosure with the 4 posts as
corners and a couple of rebar stakes in the middle of each side to help
keep it square and fill the cylinder with water and fill the space between
the cylinder and the square pen with 200 ft^3 of dry leaves in bags for
sidewall insulation (it's illegal to burn leaves or put them in landfills
where i live, so some of my neighbors put out special leaf bags in the fall
for a special leaf collection at 75 cents per bag.)  

then we run a couple of diagonal pieces of galvanized wire across the
square pipe frame and the top of the cylinder and attach a horizontal $5
10'x10' piece of 6 mil poly to each of the 4 horizontal pipes with sheet
metal screws and another 10' pipe ripped in fourths. 

then we drill horizontal holes every foot in each of the 4 pipes that go
up to the peak (or do this before the pipes are installed), and thread
more galvanized wire through the holes to make about 7 horizontal wire
squares decreasing in size from 7' square near the bottom to 1' square
near the top, while placing more bags of leaves on top of the 10' square
to completely fill the pyramid above, and we cover the top with a $20
20'x20' square of uv polyethylene film, attached to the square pipe
frame with the same cap strips. (epdm would be more durable and costly.) 

assuming the leaves have about r2 per inch and compact to 1' under the
tank, its thermal conductance would be at most 175ft^2/r24 = u7.3, with
rc = 1200x8btu/f/7.3btu/h-f = 1316 hours, or 55 days.

so far, we have a $7 duct (griffin greenhouse and nursery supplies,
978-851-4346) plus 4'x65' ft^2 of tank fencing worth $26 plus about
$50 for the tank frame and $38 for poly film, subtotaling $121.

the reflector might have 4 white-painted 18' kerfed 2x4 bows with 12'
2x4s at the top and bottom edges ($24.) let's tie the bottom edge to
the ground with screw anchors or deadmen made from old tires (-$4) and
bolt 2 vertical 6' 2x4s to the sides of the reflector between the point
above the 3' focal line and the ground as compression struts and tie
the upper edge to ground anchors with 2 12' synthetic ropes with twitch
sticks near the top.

then glue or heat seal or foil-tape 216 ft^2 of mylar ($20, from
http://www.snomo.com/mylar.html) to an $11 sheet of uv greenhouse
polyethylene and stretch it over the upper side of the bows and
staple it to the reflector sides with 1" vinyl poly batten tape. 

the target has about 1.5x3'x12' = 54 btu/h-f of thermal conductance to
outdoor air. we might collect 31.5k btu/h of beam sun over 3 hours in
190 f water and lose (190-30)54 = 8.6k btu, for an average hot water
production of 65.6k btu/day. can we get rid of the pump? let's enclose
the poly target duct between 2 layers of welded-wire fence ($5) in an
$8 4'x12' 2x4 frame so it has a chance of withstanding a 4' water head. 
(would some www.solec.org selective paint help?)

with 180 f tank water and a 190 f max target temp and 22.9k btu/h of
target heat, we need a thermosyphoning water flow q ft^3/s, where
3600s/hx64btu/f-ft^3q(10f) = 22.9k, so q = 0.0099 ft^3/s, about 5 gpm.  

water weighs about 63.74 - 0.0158t lb/ft^3, so a 4' height difference
and 10 f temp difference makes a pressure difference of 0.632 lb/ft^2.

we might have about 30' of pipe with radius r in feet running mostly
under the target in a thermosyphoning loop, which makes q = 0.0099
= pir^4(0.632)/(8mu30') ft^3/s for laminar flow, where mu = 7.41x10^-6
lb-s/ft^2 for 180 f water, so r = 0.055' or 0.66", eg a 1.5" pipe
(or larger, with some fitting head losses), which makes the total
materials cost $198, or $198/(22.9k/3.41) = 2.9 cents per peak watt.

at t degrees f, the tank loses heat at a rate of (t-30)7.3btu/h. if 
hot water use removes heat at a constant 65.6k/24h = 2733 btu/h, so
dt/dt = -((t-30)7.3+2733)/9600 = -0.0007604t -0.2619 = -ct +d, and
d/c = -344 and t = -244+(180+344)exp(-0.0007604t) = 120 f when
t = 159 hours, after 6.6 cloudy 30 f days in january.

and we might lay 3'x16' of pvs on the target floor and collect 130 f
water at about 3 suns. 

nick




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