. ----
. .
. . 30 F
. .
. .
. pond .
.-----------. ----
12' . s 4' . 12' 10.4'
. s .
--S . s T .
. s . 6.92'
. s .
. s .
. s .
.duct duct.
----------------------------------------------------------------------
12'

We might build a 12'x16' equilateral A-frame with a 4'x12' shallow pond
at the top (view above, in a fixed font) and 2 poly film water ducts
along the north and south edges to avoid wind sliding and overturning...
20 psf makes 208 lb and 1082 ft-lb on each 1' EW slice of the greenhouse,
so we need 12W = 1082 ie W = 90 pounds of water in each foot of duct, eg
1.44 ft^3 of water in a 16" duct.

We could make each of the 10 slightly curved "half-bows" on 4' centers
with 2 12' 1x3s with 1x3 spacer blocks every 2' and a hinge at the top,
and use 3 horizontal 1x3 purlins.

The south side could have 80% shadecloth to make hot air rise under the
pond (which could be poly film over EPDM over foil over welded-wire fence.)

If we can somehow arrange that most of the greenhouse stays cooler while
the airpath between the shadecloth and glazing and under the pond is temp
T during the day, and the space above the pond is also temp T, we might
figure 0.9xsqrt(1000^2+620^2)12' = 12,712 Btu enters a 4' slice of south
glazing on an average 30 F Jan day in Phila, and 0.81^2x4x1177 = 3813 of
that enters the pond. At 130 F, it might also gain 6h(T-130)4ft^2x1.5
= 36T-4680 Btu/day from the bottom, and more, if the ground to the south
is reflective.

If the glazing loses 6h(T-30)12ft^2/R0.8 = 90T-2700 Btu/day and the daily
energy that flows into the slice equals the energy that flows out, 12712
= 3813+(36T-4680) + 90T-2700, so T = 129 F, and the pond slice gains about
3813 Btu, and 50K/3813 = 13.1', so a 16' greenhouse might provide most of
the heat in January. With about 3813x16'/6h = 10.2K Btu/h during solar
collection, 5 gpm (2400 Btu/h-F) would rise 4 F, and 400'x1/2" PE pipe
with 75 ft^2 of U30 surface would rise 10.2K/(75x30) = 5 F.

A row house with a flat roof might have a $98 12' diameter x 3' tall
EZ-Set pool in the basement with a $60 300'x1" fresh water pressurized
PE pipe heat exchanger near the top of the pool under floating Styrofoam
and a low-head pump with a $40 400'x1/2" PE pipe heat exchanger in the
pool bottom. With lots of insulation and 0.8xPi(11/2)^2x3x62.33 = 14216
pounds of water at 110 F after 5 cloudy days, after supplying 5x50K Btu,
it needs to be 110+250K/14216 = 128 F on an average day. Then again, it
might melt :-) It might need reinforcing, eg a tarp tied up around it.
Or maybe we need a different kind of pool.

This might also be a standalone structure in a yard, with the filter pump
that comes with the pool.

Nick