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solar heating the s.a.v.e. house
17 jan 1997
the 300-odd members of the environmental club students against violating the
earth (s.a.v.e) of souderton area high school (southeast pa) are looking into
ways to solar heat the new environmental building they have constructed. it
was not designed to be 100% solar-heated, with the long axis north-south and
lots of windows with no thermal shutters inside them, and insulation inside
vs. outside the masonry walls. it might have been easier to solar heat if the
north masonry walls had exterior foam insulation like dri-vit with a stucco
finish, vs brick, with some plastic 55 gallon drums above the greenhouse.
the building will be used 24 hours a day, vs a daytime classroom. 

they have now installed electric resistance baseboard heating, a fine solar
backup system with low initial cost, if rarely used, as in the new england
houses of norman saunders, pe, or dr. bill freeborn's harleysville, pa house 
with an electric heating bill of about $58 per year.

here's an approximate diagram from memory:

                                            south-southwest
                                                 ~ 12'
the building has about                       ------------
                                            |tile floored| ~6'
  50x16' of r3.3 windows,                   | greenhouse |
  90x16' of r20 walls, and             --------|......|--------
  22x42' of r20 ceiling,              |                        |
                                   ~8'| r3.3   all glass  r3.3 |~8'
so the thermal conductance            |                        |
  might be approximately              |                        | 
  240 for the windows,             -- |    cathedral ceiling   | --
   72 for the walls, and              |                        |
   46 for the ceiling, ie             |                        |
  358 btu/hr-f total.                 |                        |
                                      |                        |
air infiltration might add another    |                        |
  22x42x16/55x0.5ach = 134 to this,   |                        |
  making the total heat loss          |                        |
  coefficient 492 btu/hr-f.           |                        |
                                      | r20          balcony   |~34'
over an average 30 f january day,     |...........   ..........|
  the building might need about       |          .....         |
  24hours(68-30)492 = 449k btu        |  bedroom   ^   kitchen |
  to stay warm, about 132 kwh or      |  below     |   below   |
  3 gallons of oil. or 560 ft^2       |            |           |
  of south glazing...                 |            |           |
                                      | fireman's pole         |
                                       ------------------------
  an average 1000 btu/ft^2/day of sun            ~22'
  falling on 22'x16' = 352 ft^2 of 80% solar-transmitting south windows
  could keep this house reasonably warm during an average january day, if
  the heat could be stored. a pv-powered ceiling fan will help distribute
  the heat. circulating warm air from the ceiling under an insulated floor
  slab might have helped here. 

the building might have 3 heating zones, with the big space cooler at night,
and a cool bedroom and a cold kitchen, so the refrigerator does not have to
work hard. (my kitchen is 35 f this morning.) it has a concrete floor slab
which may tend to keep temperatures from changing quickly inside. 

if the glass doors to the greenhouse were closed on a cloudy day, the thermal
conductance of the glass area would decrease from 240 to about 185 btu/hr-f,
reducing the total thermal conductance from 492 to 437 btu/hr-f. covering 50%
of the remaining windows with r10 foamboard shutters in december and january
would reduce the glass loss to about 93+400ft^2/13.3=123 btu/hr-f, reducing
that total thermal conductance to 374, while leaving 400 ft^2 of windows for
an average indoor solar intensity of about 10,000x80%x350ft^2/880ft^2 = 3100
footcandles at noon, 62 times more than a well-lit 50 fc classroom. some
reflective light shelves under high windows might bounce the sun off the white
ceiling and diffuse it around the main area. compact fluorescent lights with
individual switches or occupancy sensors could fill in lower-intensity areas.
this might be a nice project for a student with a light meter.

the south window shutters might be dark green on the outside, with an air gap
between window and shutter and an opening near the top to make those windows
seasonal air heaters, with something like half the former solar gain, since
they would have warmer air next to the window, but little loss at night or
on a cloudy day. (more efficient window shutter collectors might have a layer
of dark mesh dividing the air gap, and passively persuade room air to flow
down the cold side between the mesh and the window, and back up into the room
via the warmer side of the gap to the north of the mesh.)

these seasonal interior shutters with simple solar collection would reduce
the average net heat requirement to about 24x(68-30)374 - (350)0.8x1000/2
- 0.5(350)0.8x1000/2 = 341k - 140k - 70k = 131k btu per day, with direct gain
from half the south windows and solar collection at 50% efficiency from the
other half. limiting air infiltration to 0.5 ach may not be easy, even though
about 15% of the walls are below ground. a blower door test on a cold night
with an army of students with scaffolds and smoke sticks and caulking guns
might accomplish this :-) some of the daily heat might come from students,
at about 300 btu/hour/student, eg 30x3x300 = 27k btu/day from a 3 hour class
with 30 students, and some of that 201k btu might come from electrical energy
consumption, eg 500kwhx3410/30=57k btu/day, but the building may be empty at
times, and the students intend to be frugal with electrical power, so it looks
like this building, as modified, needs at least 131k/1000btu/ft^2/day = 131
ft^2 of additional south glazing to stay warm on an average january day, if
it only uses the sun for heat, vs. wood, a heat pump, etc. what works for
january should work for the rest of the year. 

over 5 cloudy days, the modified building would need about 5x341k = 1.7
million btu to stay warm, which might come from 1.7m/(120-80) = 43,000
pounds or about 700 cubic feet of warm water cooling from 120 f to 80 f
in some insulated plywood or ferrocement tanks lined with 10' wide epdm
rubber roofing material, supporting 2 benches inside a nearby 30' wide by
32' long greenhouse to the west of the save house with an equivalent winter
south glazing area of about 400 ft^2, using $2,000 worth of materials.
a 4' wide x 3' tall x 32' long tank would hold 384 cubic feet of water,
a total of 768 ft^3 for 2 of them. 

this leaves 22' x 32' of floorspace in the middle of a half-cylindrical
greenhouse which might be used as a classroom, which could be fairly cold
at night, except for special occasions. the north tank might have a
transparent cover, and the north wall/roof of the greenhouse might be
reflective, to gather some concentrated sun, like this:  

       .                                        ---
               .
                    .
                        .
 <- s                      .                   12-15'
                              .   y
         (32' long)             . |     z
       /                    ......|   /  
     /                      .tank . /
x <............................f............. ---

about 640 ft^2 of 1" foil-faced foamboard might be slotted and bent and
screwed to the bottom of curved galvanized pipes on 4' centers to make a
reticulated 4.5:1 concentrating parabolic shape, with the reflective surface
inside the greenhouse, with a focus f at about x=2.68' (y^2 = 4fx). the same
sheathing might be used for the endwalls, reflective side in, or they might
be 1 or 2 layers of polycarbonate or polyethylene film.

the north tank might have a shallow drain-down pool made from a 4' wide piece
of epdm rubber draped over vertical 2 x 4 edges with 5 3/16" x 46" x 76"
single-pane tempered sliding glass door replacement panels laid on top. a
low-power pump (e.g. grainger's 100 watt 2p079 pump) might circulate about
12 gpm at about 1' head between the tank and the shallow pool when the sun
is shining. a lower power and possibly simpler alternative might have an
insulating cover under the glass that sinks a bit during the day. 

here's an approximate energy balance for the north tank:

energy in = 12 x 32' x 1100 btu/ft^2/day x .9 trans. x .8 reflectance
          = 300 k btu/day

energy out = (t-32)(4'x32')/r1*6 hours/day, in january.

energy in = energy out ==> 768 t - 25k = 300k, ==> t = 428 degrees f :-)

the water might heat up 10 degrees f per day if it starts cold. with r20
insulation and 472 ft^2 of surface, ie a thermal resistance of r = 0.042
f-hr/btu and c = 384x62 = 23808 btu/f, the north tank would have a natural
time constant rc = 1000 hours or 42 days. if it were 130 f initially, with
no additional heat loss, it would cool to about 30+(130-30)exp(-24/1000)
= 127.6 f on a cloudy day. the tanks might supply space heating to a fan-coil
unit in the save house using magicaire's $150(?) all-copper 2'x2' shw 2347
duct heat exchanger, which transfers 45k btu/hour between 125 f water and
68 f air at 1400 cfm, ie about 800 btu/hr-f, with a 0.1" h20 fan pressure
drop. the low pressure water might move between greenhouse and house via
two insulated hot water hoses laid in a short trench.

the tanks might serve as foundation, perhaps making this structure temporary
for building permit purposes, one that might sit on flat ground or a strong
flat roof of a city building, with no roof penetrations. the lower perimeter
edges should lie in a plane, especially if the greenhouse is covered with
clear flat polycarbonate glazing. the $35 galvanized pipe half-bows might be
bolted to vertical 2x4s that form one wall of the tank, instead of being
slipped into $10 ground stake pipes, which is the way these greenhouses are
usually constructed. 

an alternative to this concentrating system might have a large dark vertical 
mesh absorber running down the length of a half-cylindrical greenhouse, say
an $80 32' long x 12' tall piece of 60% solar-absorbing dark green shadecloth
with a $60 piece of 80% black shadecloth north of it and $20 worth of uv 
polyethylene film on both sides 6" away from the absorber. the shadecloth
would absorb 92% of the sun, creating a light side and an 800 fc "dark side"
for the greenhouse. a fan-coil or two might push air east or west through a
polyethylene duct with holes near the top of this sandwich, making the air
flow horizontally from south to north through the mesh absorber and back, in
a closed loop. some posts might keep the sandwich from ballooning and help 
support a snow load while the greenhouse melts snow using stored solar heat. 

a shallow reflecting pool to the south of the greenhouse might serve as a
skating rink and help keep weeds and lawnmowers away from the glazing and
increase the solar intensity by about 30% when frozen, in this non-parabolic
geometry. (engineer rudy behrens of aurora farms at 1547 north trooper road,
norristown, pa 19403 is building more magical cassagrainian greenhouses for
year-round vegetable crops with arrays of fixed 8'x8' mylar film/plywood
reflectors to concentrate winter sun into $5k canvas/steel 30' geodesic
pacific domes with their large vinyl bay windows facing north :-)

the air-heater sandwich might be built into the south wall/roof using an
extra layer of polyethylene film, if this were not a working greenhouse full
of plants needing full sun. hanging the sandwich in the middle keeps it and
the greenhouse warmer than if it were built into the south wall and losing
heat directly from the higher sandwich temperature to the outside world.

as another alternative, the sandwich might have fin-tube pipe near the top
instead of fan-coil units, which would cost more but use less electrical
power. that would also be quieter, and might help support the roof. 

so, what happens here? the sun shines into the greenhouse and gets absorbed
by 2 layers of poly film, with a solar transmittance of 0.92 each and a
combined r-value of 1.2. the sun keeps on shining into the sandwich, and
its single layer of poly film (or perhaps polycarbonate) transmits 92% of
the sun and absorbs or scatters 8%, which heats the greenhouse to an air 
temperature tg, and the greenhouse loses heat to the outdoors through the
south glazing, as well as the r5 north and endwalls. meanwhile, the air
inside the sandwich has a warmer temperature ts, and the sandwich loses
heat to the greenhouse through both us r0.8 poly sides, ie the waste heat
from the water heating process is heating the greenhouse air in a kind of
thermal cogeneration.

two 800 btu/hr-f heat fan-coil units (or 2 automobile radiators with efficient
12 volt fans) might be modeled with an analogous electrical dc steady-state
circuit that looks something like this:

          glazing resistance   end wall resistance
        --------www--<-----------------www---------------->---- 30 f
       | rg = r1.2/750 ft^2  | re = r5/700ft^2
       |                     | north wall resistance
       |  small solar        |---------www---------------->---- 30 f
       |  current source     | rn = r5/750ft^2
       |    ------           |                   ts  fan-coil 
       |   |      |          |   sandwich res.  |    resistance
30 f ------| ---> |-------------------www---<------->-www------ tw 
           |      |         |  rs = r0.8/768ft^2  |  1/1600 |
            ------           tg                   |         |--> 131k
    14'x32'x1000x1.3x0.08/6hr                     |         |    btu/day
      = 7.8k btu/hr (2.6 kw)                      |         |
                                                  |      ------- tanks
          large solar                             |              for the
          current source                          |      ------- memories
            ------                                |         | 
           |      |                               |         |
30 f ------| ---> |--------------------------------        ---
           |      |                                         - 
            ------                                          
    14'x32'x1000x1.3x0.92^3/6hr                             
      = 75.6k btu/hr (22.1 kw)                               
                                                         
which simplifies to 
                       ts                               tw
              rt      |       fan-coil resistance      |    131k/6hr =
tt ----------www----------------------www----------------------> 21.8k
                          rf = 1/1600 = 0.000625 f-hr/btu    |   btu/hr
                                                           -----
    tt = 161 f is the (thevenin) equivalent temperature,   -----
         which is ts above with the tanks disconnected.      |
    rt = 0.00053 f-hr/btu is the resistance from ts to      ---
         ground with tanks disconnected, current sources     - 
         opened up and voltage sources shorted, ie
	 rg, re, rn and rs in parallel.

thus we can easily see (i hate these words :-), tw = 161-21.8k(rt+rf) = 136 f.
it looks like we may be able to make the water at least 120 f this way. if it
turns out we can't, and the sandwich has studs on 4' centers, we can insulate
some of the dark side with foamboard or replace the 5 cent/ft^2 poly film on
the front with $1.25/ft^2 polycarbonate plastic, which comes in rolls 49" wide
x 50' long from replex at (800) 726-5151 or commercial greenhouse suppliers
like rimol greenhouse systems at (603) 425-6563, who sell this plastic film
for $250 per roll + $10 for ups shipping.

ts = tw + 21.8krf = 150 f, using this model, and tg comes from another 
thevenin equivalent circuit:

                       tg                               ts
              rt      |       sandwich resistance      |  
tt ----------www----------------------www----------------------> 150 f
                        rs = r0.8/768ft^2 = 0.0010417
                                                           
    tt = 38.5 f is tg with the tanks disconnected, and 
    rt = 0.001093 f-hr/btu is the resistance from tg to ground
         with tanks disconnected and current sources opened up.

so the greenhouse temperature tg = 38.5+(150-38.5)rs/(rt+rs) = 92.9 f, so we
may want to vent the greenhouse during the winter to keep it cooler or waste
less solar heat by adding some insulation to the north side of the sandwich
and allowing some warm air to flow out of the sandwich as needed to keep the
greenhouse at 68 f on a sunny day.

domestic hot water for save showers, hot tubs, etc, could be supplied via a
heat exchanger attached to the existing water heater in the house, in the
same circulation loop as the fan coil unit. 

the fan-coil unit or baseboard radiators inside the save house need to supply
about 131k/24 = 5500 btu/hour on an average day, with a water temperature
difference of about 7 f, and a water flow rate of about 800 pounds per hour
or 2 gallons per minute. the building needs about (68-10)374 = 22k btu/hr on
a very cold night, at the ashrae-recommended philadelphia 99%-tile outdoor
dry bulb winter heating design temperature of 10 f. this might come from an
additional fan-coil unit and pump, with a water temperature difference of
14 f and a total water flow of about 4 gpm.   

nick

nicholson l. pine                      system design and consulting
pine associates, ltd.                                (610) 489-0545 
821 collegeville road                           fax: (610) 489-7057
collegeville, pa 19426                     email: nick@ece.vill.edu

computer simulation and modeling. high performance, low cost, solar heating and
cogeneration system design. bsee, msee. senior member, ieee. registered us
patent agent. solar closet paper: http://leia.ursinus.edu/~physics/solar.html
web site: http://www.ece.vill.edu/~nick 



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