another 12' non-cube SOLAR.KnowledgePublications.com

another 12' non-cube
15 mar 2001
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 90%
absorptive target, we might collect 0.9x0.9x729x12'x12' = 85k btu/day with
a 12'x12'x16' tall open-sided box with a parabolic reflective north wall and
roof (y^2=12x, with y=0 on top of a 4' tall tank, with the upper reflector
edge 12' above that. the focus moves closer to the north wall as the sun
rises until the upper reflector edge shades the target north edge at
atn(14/12) = 49.4 degree elevation. still lots of summertime hot water...

we might reflect dawn sun down into a 3' wide x 12' long x 2' deep trench
with 48 ft^2 of reflective mylar sides. grafix plastics at (800) 447-2349
http://www.graphixplastics.com sells 54"x50'x0.002" rolls of one-surface
metalized mylar for $48.31, about 22 cents/ft^2, with a $100 minimum order.
(anyone want to split an order?) it has a 740k psi modulus of elasticity
up to 5% in the 54" direction and a tensile strength of 34k psi. dupont
says it loses less than 10% of its strength at 100 c and only begins to
soften at 250 c. 

the target might be a mylar film sandwich stretched over a slightly curved
3'x12' piece of osb, 2' off the ground and 1' below the tank water surface,
with some welded-wire fence over the top of the mylar to resist the head.
tractor supply sells $39.99 4'x100' rolls of this fence with 2"x4" 0.081"
diameter galvanized steel mesh. with 50k psi strength, each wire can hold 
50kxpi0.081^2/4 = 258 pounds, so 1' of fencing with 6 wires on 2" centers
can support 1546 pounds.

a linear foot of 3'-wide collector containing 64 psf water (a 1' head)
needs to contain 1'x3'x64psf = 192 lb in the vertical direction, so each
side of the upper surface needs to support 96 pounds. if the middle bulges
d inches above the edges with tension t (in pounds), td/18 = 96, roughly,
so t = 1728/d < 1546 when d > 1.1".

we might screw 3'x12' of 1/2" osb to a 12' vertical 2x4 down the middle,
then screw a couple of 12' 1x3s flat to the edges of the other side of the
osb, then stretch 2 3'x12' layers of mylar over that (with some silicone
caulk near the edges) and around the back and screw them to the back with
2 more 1x3s, then wrap the fence over the mylar and around the back of the
osb and screw it on with 2 more 1x3s, then add some 1x3 tension straps
over the 2x4 to make the osb bulge up 2" in the middle. we might paint
the upper aluminized mylar flat black or selectively (anyone know if solec
paint dissolves mylar? they have no idea, but say it can make e = 0.24 and
alpha = 0.9 on aluminum, and want to sell it for $80 per gallon, including
hazardous shipping. anyone care to split a gallon?)

to make a 7' diameter x 3' tall 924 gallon polyethylene-film-lined tank
under the reflector, we might put a 7'x7' piece of plastic film on the
ground, then make a 7' diameter x 4' tall wire fence cylinder on top of
the film (3' of water makes about 1.3 psi near the bottom, with a 4"
vertical wire spacing, making the wire tension 7x12x4x1.3/2 = 223 pounds,
so it looks like a single layer of fencing will do.) then we pile about
1' of dry leaves, mulch, sawdust, etc. inside, then line the tank with
an $11 15'x15' piece of 6 mil poly film.

then make a 9' wire cylinder around it and fill the tank to 3.5' with
water (and keep it full with a hose and an $8 stock tank float valve,
and empty it with a 12v rv pump with a built-in pressure switch) and
fill the 1' space between the cylinders with 100 ft^3 of dry leaves
in bags for insulation, with another 20 ft^3 of leaves or sawdust in
plastic film drum liners floating on top of the water.

r2 per inch for the leaves, compacting to 6" under the tank, make its
thermal conductance 143ft^2/r24 = u6, with rc = 7389btu/f/6btu/h-f
= 1240 hours, or 52 days.

the reflector needs sqrt(4x^2+y^2)+y^2/(2x)ln((2x+sqrt(4x^2+y^2))/y)/2
= 17.75' long curved rafters, plus 2' more at the bottom. they might be
4 white-painted kerfed 2x4 bows with 12' 2x4s at the top and bottom edges.
we could tie these edges to a pressure-treated 10' 2x4 deadman under the
tank with a pair of 2' ropes at the bottom and a pair of 16' ropes at
the top, with twitch sticks near the top, and bolt 2 pressure-treated
vertical 10' 2x4s to the sides of the reflector between the point above
the 3' focal line and the ground as compression struts.

then we'd attach 216 ft^2 of mylar ($46) to an $11 sheet of uv greenhouse
polyethylene with axle grease (to make smoothing and replacement easier)
and stretch the poly it over the upper side of the bows and staple it to
the reflector sides with 1" vinyl batten tape. 

the target has about 1.5x3'x12' = 54 btu/h-f of thermal conductance to
still outdoor air. we might collect 28.3k btu/h of beam sun over 3 hours
in 190 f water and lose (190-30)54 = 8.6k btu/h, for an average hot water
production of 59.2k btu/day.

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) = 19.7k, so q = 0.0086 ft^3/s, about 4 gpm.  

water weighs about 63.74 - 0.0158t lb/ft^3, so a 1' height difference
and 10 f temp difference makes a pressure difference of 0.158 lb/ft^2.

we might have about 20' of pipe with radius r in feet running mostly
under the target in a thermosyphoning loop, which makes q = 0.00856
= pir^4(0.158)/(8mu20') ft^3/s for laminar flow, using a formula from
one of william shurcliff's books, where mu = 7.41x10^-6 lb-s/ft^2 for
180 f water, so r = 0.067' or 0.81", eg a 2" pipe (or larger, with
some fitting head losses), which makes the total materials cost $198,
or $198/(19.7k/3.41) = 3.4 cents per peak watt.

at t degrees f, the tank loses heat at (t-30)6btu/h to the outdoors.
if hot water use removes heat at a constant 59.2k/24h = 2467 btu/h,
dt/dt = -((t-30)6+2467)/(924x8) = -0.0008063t -0.3096 = -ct +d, and
d/c = -384 and t = -384+(180+384)exp(-0.0008063t) = 120 f when
t = 139 hours, after 5.8 cloudy 30 f days in january.

nick