Subject: A solar greenhouse

From: [email-masked] (Nick Pine)
Date: 6 Apr 1996 08:16:01 -0500

There has a plan to create a new wetland as well as restore an old greenhouse,
perhaps, at 121 Wartman Road owned by the Perkiomen Valley School District
in SE Pennsylvania, that looks approximately like this:

                                              N
                                      |       16'     |
The greenhouse sits on a cinder       ................. ---
block foundation that rises 2-3'      .       .       .
above the ground. The greenhouse      .       .       .
itself is made of metal angles and    .       .       .
glazing bars to fit overlapping       .       .       .
single panes of glass approximately   .       .       .
2' x 1.5' each. Above the block wall  .       .       .
is about 2' of vertical glass, then   .       .       .
another 4' or so of glass sloped at  W.       .       . 32' E
slightly less than a 1:1 pitch.       .       .       .
More than half of the panes of glass  .       .       .
are broken. There are no ventilation  .       .       . (These ASCII
fans, but the top sashes can be       .       .       .  pictures make
cranked open. The greenhouse has no   .       .       .  more sense in
insulation. Inside the walls there    .       .       .  a non-kerning
are two block troughs about 4' wide   .       .       .  font like courier.)
and 3' deep with some fin-tube pipe   ................. ___
beneath bench supports. To the 
north of the greenhouse is a small            S
equipment shed which used to contain
an oil burner (?) to heat the fin-tube pipes, with an expansion tank
in the ceiling. A tree is growing up through the broken glass of the
greenhouse at the north end. The top of the tree is about 6' above the
9' peak of the greenhouse. 
                                              .         ---
                                          .       .     ~4'
How might we solar heat this          .               . ---
greenhouse? This is a                 .               .
challenging project because the       .               . ~5'
greenhouse faces the wrong way        B   B       B   B
for that. Solar greenhouses usually   B   B       B   B 
run east and west, ideally with   ...............................
a reflective and insulating 
north wall, in the northern hemisphere.

It seems to me that the way to start this project is to remove all the
glass from the roof of the greenhouse and replace the broken glass on the
sides and endwalls with some of the unbroken panes. Then stretch two layers
of polyethylene film over the greenhouse itself, using one large 32' long
roll, and inflate a poly duct tube running north and south near the peak
of the roof to stretch the two films on cold or windy days with a small
(50 watt) blower, more or less following standard commercial plastic film
greenhouse practice. On warm calm sunny days the poly duct would be flat,
letting the two poly films form one surface, which would decrease the
R-value and increase the solar transmission, and save electricity. (The
cost of running a 50 watt blower 24 hours per day is about $50 per year.)

Next it seems like a good idea to remove the two tilting interior block walls
of the troughs and replace them with OSB or plywood walls with pressure
treated 2 x 4 bracing, to make a box that will be lined with some foamboard
and single pieces of EPDM rubber to make two water troughs about 32' long
x 4' wide x 2' deep, below the benches, to add about 512 ft^3 x 64 = 33K Btu/F
of thermal mass to the greenhouse. 

We might add another layer of plastic film inside the vertical glazing along
the walls, and a diagonal transparent roll-up R2 cover over the benches as
shown below from the south. This might be made from a 4' wide roll of bubble
pack insulation or some aluminized greenhouse fabric. 

    36 F   .         ---
       .       .     ~4'
   .               . ---        c is the transparent roll-up cover 
   . c           c .            p is the new plywood wall
   . T c       c   . ~5'        i is insulation under the plant benches
   B i p       p i B            w is water 
   B w p       p w B            T is the temperature of the plant benches
..............................

Suppose we keep the plants at T=66 F, 24 hours a day, when the roll-up
covers are closed. How much energy will that take, on an average winter day?

The plants will lose heat to the outside through the side glazing and plastic
films, which altogether have an R-value of about two. Let's be conservative
and assume the greenhouse itself is also 36 F inside, like the outdoors on
an average December day in Philadelphia. Then the amount of heat that leaks
out from the plant benches on an average day, Eout, will be about

Eout = 24 hr (66F-36F) 6'x 32'/R2 x 2 benches = 138K Btu/day.

Since a south wall in Philadelphia receives an average of about 1000 Btu/ft^2
of solar heat on an average day in December, of which 600 might be captured,
this means we need a solar collection area of about 138/0.6 = 230 ft^2, eg
a south wall 8' tall and 29' long. Adding a shallow frozen reflecting pool
(skating rink?) along the wall with a pond liner draped over a perimeter earth
berm would reduce the required size of the wall by about 50%, and prevent
vegetation from blocking the sun.

How warm must the water in the troughs be to provide stored heat for, say,
5 days without sun? About 66 F + 5 days x 138K/day/33K = 87 F.

The solar collecting wall could have a foundation made from the cinder blocks
recycled from the inner trough walls. It might look like this in cross section,
seen from the west:

          |  1 to 4'  |
      --- ............g     S -->
        iii        f  g
        iii    --> f  g     f might be the 4 sections of 32' fin-tube pipe
        iii--fan?--f  g       removed from the troughs
        iii   ^    f  g
        iii   |   s   g     s might be two layers of greenhouse shadecloth
        iii       s   g
        iii      s    g     g might be a single layer of flat Replex
      8'~~~           ~       polycarbonate glazing, or perhaps polyethylene
        iii   s       g
        iii   s       g     i might be fiberglass insulation in a stud wall
	iii  s <--    g       or a more interesting wall made of strawbales 
	iii  s        g       and mortar. Ray Lehman on 8th Avenue, Trappe,
	iii           g       sells 16" x 16" x 36" R30 rye strawbales for 
	iii s         g       $1.75 each. Rodents do not like rye straw.
 .......iii...........g.....  Ray also has some interesting strawbales that 
        cbcbcbcbcbcbcbcb      are 4' wide x 4' tall x 8' long...
     3' cbcbcbcbcbcbcbcb
    --- cbcbcbcbcbcbcbcb

The sun would shine in through the glazing and heat up the greenhouse
shadecloth here, which would heat up the air in the wall as it moves from
south to north, and the warm air would rise up north of the shadecloth and
flow through the fin tubes at the top, heating some antifreeze solution
that circulates through the fin tubes with a tiny pump when the sun is
shining and the trough water needs heat. How well would this work?

Each foot of fin-tube passes about 5 Btu/hr for each degree F of air-water
temperature difference in still air, so the overall thermal conductance of
128 linear feet of fin-tube is about 640 Btu/degree F. Or higher, if a
photovoltaic fan is used to whirl some air around through this large fin-tube
radiator at the top of the wall. The overall thermal conductance of 8' x 32'
of wall glazing is about 256 Btu/F, which seems promising, since heat tends
to take the path of least resistance, ie greater conductance. So the solar
heat that enters the wall will be happier going into the fin-tubes than back
out the glazing. What would the water and air temperatures Tw and Ta be on
an average 43 F (daytime) day in December using this system, with no fan? 

Here's the equivalent electrical circuit:   (sun current source)
                                                  ---------
                                                 | 256K Btu|       |
                      Tw -------wwww---------<---| over 6  |-------| |
                                 Rf      |       | hours   |       |
                                         |        ---------
                                         |
                                         |---------wwww---------- 43 F
                                         Ta         Rg

Rf is 1/640 and Rg is 1/256, and the sun power in is about 43K Btu/hour.

This is equivalent to the following (Thevenin) circuit:
 
                                                  ---------
                                                 | 43K Btu |       |
                      Tt -------wwww---------<---|   per   |-------| |
                                 Rt      |       |   hour  |       |
                                         Ta       ---------
                                          
in which Rt = 1/(640+256) = 1/896  and Tt = 0.714 Tw + 12.3, so

Ta = Tt + 43K/896 = Tt + 48 = 0.714 Tw + 12.3 + 48 = 0.714 Tw + 60.3 F.

So if Tw = 87 F, the sunspace air temperature will be about 122 F. Not bad.

If the energy that flows into the greenhouse during a day, Ein, is equal
to the energy that flow out of the greenhouse during a day, Eout, then
we have this approximate equation: 

Ein = 1000 (256) = 256K Btu/day sun energy 
    = 6hr (Ta-43) 256 solar wall loss (day)
    +18hr (28-28) 256 solar wall loss (ie no loss at night)
    +138K             greenhouse loss (24 hr) = Eout.

Solving this equation, we find Ta = 43 + 118K/1536 = 119.8 F, which is
pretty close to 122 F. This means the water will be almost 87 F. Good.
But it looks like we will need the frozen reflecting pond here, or a bigger
wall, or more fin tubes, or a fan or two, or two layers of glazing, or
a bench curtain with a higher R-value.

With the skating rink, we might have Ein = 1000 (256) 1.5 = 384K/day, so
the sunspace air temperature would be Ta = 43 + 246K/1536 = 160 F during
the day, and the water temperature would be Tw = (160 - 60)/.714 = 140 F.
Now we're cookin':-) There is lots of extra solar heat this way, so
the greenhouse interior can be a lot warmer than 43 F during the day.
This is all done with mirrors, of course :-)

So, here is one possible solution: 
                                              N
                                      |       16'     |
                                      ................. ---
 .....................                .       .       .
 .                   .                .       .       .
 .   chicken coop    .                .       .       .
 .                   .                .       .       .
 .                   .                .       .       .
 .                   .                .       .       .
 .....................                .       .       .
                                    W .       .       . 32' E
                                      .       .       .
                                      .       .       .
                                      .       .       .
                                      .       .       .
                                      .       .       .
                     ..................       .       . 
                     .    straw wall  .       .       .  
                     .......................glass...... ___
                  4' .         solar wall             .
            .....................................................
            .        |               32'              |         .
            .                                                   .
            .                   reflecting pool                 .
         16'.          made from a single roll of 20' wide      .
            .              EPDM rubber roofing material         .
            .                                                   .
            .                      <--  50' -->                 .
            .....................................................

                                     S

                                       36 F   .         ---
                     .....................        ..... ~4'
                     .                .               . ---     
                     .                . c           c .        
                  8' .   solar wall   . T c       c   . ~5'   
                     .                B i p       p i B      
            .        .                B w p       p w B         .
.........................................................................

Happy Easter, everyone.

Nick

    My favorite structure on this property is a 12' x 20' dilapidated chicken
    coop, with the long dimension running EW, the right way to orient a solar
    structure. It has a roof that slopes up 2' from the north to the south
    along the 12' dimension. Part of the building was probably used for plant
    propagation, since there is a bench on the south side behind some windows,
    with an old green 4" x 6" box on the wall marked "Mist-a-Matic," made by
    E C Geiger of North Wales, PA. More about that chicken coop later...