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re: tent roofs?
28 jul 1997
robert segelke  wrote:
>rbean@earth.execpc.com (ron bean) wrote:
>>pg82@mindspring.com (steven m) writes:
 
>>>window awnings and many other outdoor exposed fabric last several season.

uv polyethylene film has a 4 year guarantee, and costs about 5 cents/ft^2 and
comes in rolls up to 40' wide and 150' long. it's cloudyish, affording some
privacy for a solar house. it can last a lot longer if mostly vertical and
covered with shadecloth in summertime. bayer chemical (the aspirin people)
have a new slightly clearer, stronger, more expensive urethane film
("dureflex") with a 10 year guarantee.

>>i've heard of people making temporary shelters by building a frame and
>>covering it with a couple layers of clear polyethlene. if it wears out
>>before you're done with it, just throw on another layer.

commercial growers do this every 4 years, removing the poly film and sending
it back for recycling, and easily installing new film in a few hours using
aluminum extrusion clamps around the perimeters of their greenhouses. 

>nick pine is always ranting about greenhouses that are built this way.

ranting? perhaps you have me confused with aesthetic tyrants :-)

greenhouses differ from solar houses by having lots of glazing, no insulation,
only one heating zone, not many air leaks (maybe), a requirement that plants
be in sunlight during the day and warm at night, a need for more hours of
daylight in the middle of winter, if the plants are to actually grow then, vs
just staying alive, lots of plant humidity, and not much inherent thermal mass.
commercial plastic film greenhouses are also extremely inexpensive. 

the very nice $35 nraes-33 "greenhouse engineering," book, 5th edition (?), 
available from the northeast regional agricultural engineering service at 152
riley-robb hall, cooperative extension, ithaca, ny 14853-5701 (607) 255-7654,
mentions that a greenhouse full of potted plants can evaporate about 1 pound
of water per square foot of floorspace per day, which requires about 1000 btu,
about the same as the amount of sun that enters a square foot of vertical solar
glazing on an average winter day where i live. that heat might be retained if
the water vapor were somehow condensed, but if it's blown out the greenhouse
as warm humid air, it's lost.

it seems that anything we can do to save daytime solar heat for nightime and
cloudy days would help. for instance, we might blow down warm air from the
peak of the greenhouse through tubes in the ground, using damp earth or sand
as a thermal store, piled over a waterproof liner to keep the water from
disappearing. normal practice in this country is to turn on ventilation fans
just after dawn on a winter morning to blow all the solar heat and plant
humidity out of the greenhouse, and turn on propane heaters at night, storing
little heat from the day. greenhouses have lots of glazing, of course, which
has a very low thermal resistance, about 20 times less than an insulated house
wall. it's difficult to keep a greenhouse warm on a sunny winter day and night,
and much harder to keep it warm for a cloudy week. 

for instance, two layers of polyethylene film have a metric r-value of about
0.2 m^2-k/w. a 9 m wide x 30 m "polytunnel" has about 420 m^2 of cylindrical
surface and 60 m^2 of endwalls, say 500 m^2 in round numbers. if the long
direction is ew, it has about 4.5x30 = 135 m^2 of projected vertical solar
aperture. keeping it 20 c inside when it's 0 c outside requires about
24h(20-0)500m^2/r0.2 = 1200 kwh/day. where i live, the average winter sun on a
south wall is about 3 kwh/m^2-day, and the solar transmittance of 2 layers of
poly is about 0.8, so if daytime solar heat could be perfectly stored for the
night with no extra losses, about 1200/3/0.8 = 500 m^2 of projected vertical
glazing solar aperture would be required to keep the greenhouse warm on an
average winter day, about 4 times more than the 135 m^2 that is normally
available. vot to do?

make the greenhouse 4 times longer? :-) keep the center part warm and add on
more "solar collecting" greenhouses with no plants to the east and west ends,
and use that extra space to collect solar heat during the day, and let it get
cold at night? use the space for daytime potting, transplanting, storing old
cars, tractors, materials, heat-generating compost, etc? put in some insulated
thermal storage for multiple cloudy days in a row, eg some drums full of water
surrounded by strawbales? commercial greenhouses only cost about $1/ft^2...

dutch greenhouses built hundreds of years ago had insulated reflecting north
walls, as does howard reichmuth's lovely ecotope concentrating greenhouse in
seattle, which has a parabolic reflective north wall, with a water trench in
the ground along the north edge... with no insulation in the north wall, a
9x30 m greenhouse might collect about 135x3x0.8 = 325 kwh/day of sun on an
average winter day, (assuming most of the low-angle winter sun doesn't shine
in one wall and out the other) and lose about 24(t-0)500/0.2 = 60,000t wh per
day of heat, where t is the average indoor temperature. so if the solar energy
flowing into the greenhouse equals the heat energy flowing out, and there's
lots of thermal storage, t = 324,000/60,000 = 5 c...

permanently filling the north wall with 4" of white polystyrene beads might
lower the thermal conductance of the entire greenhouse to about 210 m^2/r0.2
+ 210 m^2/r3 + 60 m^2/r0.2 = 1050 + 70 + 300 = 1420 w/m^2-k, so it would lose
24(t-0)1420 = 34,080t wh/day, making t = 324,000/34,080 = 9.5 c. better.

adding a 30m long x 9 m wide shallow reflecting pond to the south might raise
winter sun input by 30% to 324x1.3 = 421 kwh/day, making t = 421,000/34,080
= 12.4 c. better. the pond could also be a water supply, and keep plants from
growing up and blocking the sun along the solar greenhouse wall. greenhouse
water runoff with fertilizer sometimes causes groundwater pollution in the us,
and government regulations are coming. the pond might collect and treat and
reuse water after it runs off the plants, and it might contain fish...

merely doubling the length of this greenhouse by flanking it with greenhouses
that get cold at night might provide enough sun to keep the center part warm
over an average 24 hour winter day. keeping it warm for say, 5 cloudy days in
a row requires 5x34080x20 = 3400 kwh, which might come from about 600 :-) 55
gallon drums full of water cooling from 50 to 25 c, inside an insulated box
warmed by sun-warmed air during the day, with no airflow at night. with night
ventilation, these drums might also cool the greenhouse in summertime.

as an alternative, a 3m (16') cube full of water might store solar heat
collected with a large dark vertical mesh absorber running down the length
of the 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 poly film on both sides, 6" away
from the absorber. shadecloth layers absorbing 92% of the sun would create
a light side and an 800 fc "dark side" (vs a 50 fc well-lit office) for the
greenhouse. a fan-coil or two might push air east or west through a poly film 
duct with holes near the top of this sandwich, making 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 away the snow using stored solar heat. 

this 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 lost 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, costing more but using less electrical power.
that would also be quieter, and might help support the roof. 

sun shines into the greenhouse here and gets absorbed by 2 layers of poly film,
with a solar transmittance of 0.92 each and a combined us r-value of 1.2. sun
keeps on shining into the sandwich, and its single layer of poly film (or maybe
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 (usr5?) north roof and 
endwalls. meanwhile, the air inside the sandwich is warmer, with 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 heats 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 tw = 161-21.8k(rt+rf) = 136 f. we may be able to make
the water 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 some of the south poly film with $1.25/ft^2 polycarbonate which has more
"greenhouse effect," and comes in rolls 49" wide x 50' long from replex (800)
726-5151, or commercial greenhouse suppliers like rimol at (603) 425-6563, who
sell it for $250 per roll + $10 for ups shipping.

ts = tw + 21.8k rf = 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.

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

the fan-coil unit or baseboard radiators inside the nearby house might need to
supply about 131k/24 = 5500 btu/hour on an average winter 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. where i live, the house might need 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 flow of about 4 gpm.   

nick




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