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a similar house, with no cows
29 sep 1998
a modern 1 story 32'x32' house might have 90ft^2/r3 = 30 btu/h-f of
us r3 windows plus (8'x128-100ft^2)/r20 = 46 btu/h-f of r20 walls plus
1,024ft^2/r40 = 26 btu/h-f of r40 ceiling plus 0.25achx1,024x8/55
= 37 btu/h-f of air infiltration at 0.5 house air changes (volumes)
per hour, for a total thermal conductance of about 140 btu/h-f.

january is the most difficult month for solar house heating in phila.
the national renewable energy laboratory (nrel) says the long term
average temperature in philadelphia in january is 30.4 f, with an
average daily max of 37.9. on an average january day, 1,000 btu of sun
falls on a square foot of south wall, and 620 falls on a square foot 
of horizontal surface, with a standard deviation of 42. (the answer 
is always 42.)

our house needs 24h(70f-30.4f)140btu/h-f = 133k btu to stay warm on an
average january day, using "ohm's law for heatflow." using 300 kwh/mo
of electrical energy might add 300x3412/30 = 33k btu/day (about 1/2 cow),
leaving 100k btu/day or 500k btu for 5 cloudy days in a row. that might
come from 500k/(130f-80f) = 10k pounds of 130 f solar hot water cooling
to 80 f, if 80 f water can keep the house at 70 f on a cold day, ie about
1,250 gallons in 24 3' tall x 2' diameter 55 gallon drums inside a solar
closet in a sunspace, if the house has lots of internal thermal mass,
eg masonry walls with external insulation. if the house has less thermal
mass, we might use 312 4 gallon hdpe plastic tubs with tight-fitting lids
in a solar closet with more glazing and airflow.
a solar closet is a small room full of sealed containers of water
completely surrounded by insulation, with a solar air heater that covers
its insulated south wall. the closet normally lives inside a sunspace.
sun shines in through the sunspace glazing and then through the separate
closet air heater glazing to heat air which circulates through the closet
during the day, heating the water containers. the air circulation stops
at night. the sun doesn't shine directly on the sealed water containers,
and sunspace and closet air don't mix. 

suppose our house has a low internal thermal mass equivalent to about
6,000 ft^2 of 1/2" drywall, ie 3,000 btu/f. if it's 70 f during the day
and 60 f at night, it can store about 3kbtu/f(70f-60f) = 30k btu overnight.
on an average day with an average amount of sun, nrel says the house
windows might about collect 300btu/ft^2x100ft^2 = 30k btu of sun,
offsetting the 100k btu/day the house needs to stay warm, including
electrical usage, so on an average day the house needs about 70k btu
of heat from some other source, eg a sunspace. 

one linear foot of 8' deep x 8' tall sunspace with a single layer of
r1 plastic south wall and roof glazing with a solar transmittance of
90% might collect 1'x8'x0.9(1000+620) = 12k btu of solar heat and lose
6h(80f-34f)16ft^2/r1 = 4k btu over a 6 hour solar collection day. if it
has little thermal mass, the sunspace temperature might be 80 f during
the day and about 30 f at night (with little heat lost through the
glazing at night), for a net gain of about 8k btu per day per linear
foot of sunspace. 

bare solar collectors with no glazing or insulation inside the sunspace
can supply hot water for the house with a normally pressurized warm-water
convection loop through a conventional water heater in the attic, with
no pumps or heat exchangers or antifreeze (this requires some heat tapes
on the collectors, or keeping the sunspace just above freezing at night,
as it also needs to be to grow a few plants.) each square foot of 110 f
bare collector might collect about 1,060 btu of sun per day and lose
6h(110f-80f)2ft^2/(r2/3) = 540 btu from both sides to the 80 f sunspace
air (which in turn heats the house) over 6 hours, for a net gain of 520
btu per square foot per day. say we need enough hot water for 4 10 minute
showers per day at 3 gallons per minute, heating water from 58 to 110 f,
ie 4x10mx3gpmx8lb/gal(110f-58f) = 50k btu/day. then we need 50k/520
= 96 ft^2 of bare water heating collectors inside the sunspace. they
could be something like zomeworks' big fins, which are dark-painted
aluminum extrusion strips with c-shapes on the back that snap hard on
to 3/4" bare copper pipes. some foil insulation under the collectors
might reduce the area needed to about 64 ft^2.

the sunspace might be vented and mostly shaded in summertime. the
collectors might provide overhead shade in their part of the sunspace.

to supply 70k btu of space heat and 50k btu of hot water on an average
day, the sunspace needs to be at least (70k+50k)/8k = 15 feet long. let's
make it 24 feet long. sunspace air needs to supply 6h/24hx70k = 18k btu
of space heat for the house during the day, and another 30k btu of heat
for the house thermal mass, a total of 48k btu of heatflow in, say, 6
hours, or 8k btu/h. since 1 cfm of airflow with a temperature difference
of 10 f moves about 10 btu/hour of heat, this requires about 800 cfm of
daytime airflow between the sunspace and the house, which might come from
a couple of $12 20" window box fans in series with a heating thermostat
in the house and a cooling thermostat in the sunspace.

if we allow the sunspace to become warmer than 80 f during the day,
it's less human-friendly, and the sunspace solar collection efficiency
drops a bit, but heating the house requires less airflow, which might
come from passive natural convection instead of fans. 

another box fan in the sunspace in series with a heating thermostat and
a humidistat might blow in dry outdoor air at dusk in the winter to keep
the sunspace relative humidity less than 100% to make condensation less
likely on the inside of the glazing.

if warm sunspace air supplies 48k btu/day of house heat on an average
day, the closet needs to supply an extra 70k - 48k = 22k btu of heat. 
a square foot of 130 f closet glazing might gain 1000x0.9^2 = 900 btu/day
and lose about 6h(130f-80f)1ft^2/r1 = 300 btu to the 80 f sunspace air
(which in turn heats the house), for a net gain of 600 btu, so we need
at least 22k/600 = 36 ft^2 of closet glazing. let's make it 64ft^2, eg
2 4'x8' strips of replex (800) 726-5151 clear polycarbonate plastic,
which has a 10 year guarantee and costs about $1.25/ft^2 ($13/m^2) in
rolls 49" wide by 0.020" thick by 50' long. rimol greenhouse systems
at (603) 425-6563 (nh) sells it for $250/roll plus $10 ups. it can
be cut with scissors.

for thermal efficiency, the closet needs a large ratio of thermal mass
surface to air heater glazing, say 10:1; 64 ft^2 of glazing needs 640
ft^2 of thermal mass surface. this means the water containers inside the
closet need to be smallish. we also need 1,250 gallons of water, and
larger water containers tend to be more convenient, if they need to be
topped up every few years. we might use a combination of 55 gallon drums
with a thermal capacitance of about 450 btu/f and a surface of about
25 ft^2, and some 9"x9"x13" tall 4 gallon 32 btu/f plastic tubs with a
surface of about 4.4 ft^2. (these nesting hard plastic tubs are made by
letica corp of rochester, mi, and used by the cherry central cooperative
in traverse city, mi 48684, for distribution of fruit products. they can
be stacked 22 feet high, full of water, if the stack doesn't tip over.
the pottstown, pa recycling center has about 1,000 of them, with lids,
free for the taking.) with d drums and t tubs, we need

   (1) 450d + 32t >  8,000 of thermal capacity and
   (2) 25d + 4.4t >    640 of thermal mass surface, or
   (3) 450d + 79t > 11,520 (multiplying (2) by 18), or
              47t >  3,520 (subtracting (1) from (3)), or 
                t >     75.

if we use 8 drums, we need 450x8 + 32t > 8,000, by (1), so we might use
150 tubs stacked 6-high in a 4x4x8' part of the closet, with the drums
stacked 2-high in another 4x4x8' section, making the closet 4x8x8' tall
with 8x8' of glazing. the closet needs to be fairly airtight. it might
have 3.5" of fiberglass insulation, with 1.5" of foamboard over that.

for "charging up" the thermal mass in the closet at 22k/6h = 3.7k btu/h
on an average day, we might use a $100 differential thermostat or a $6
130 f thermostat in a glazed box controlling 2 $60 36 watt 10" diameter
grainger 4c688 560 cfm cooling fans, which have a 149 f upper operating
temperature spec. this would make air that enters the closet about 3 f
warmer than air that leaves. the fans might consume about 0.4 kwh/day
or 13 kwh/month of electrical energy.

for closet discharging at 100k/24h = 4.2k btu/h on a cloudy day, we might
use another fan, or natural convection with a foamboard damper attached
to a honeywell 6161b1000 motor that uses 2 watts of electrical power when
moving, in series with a house heating thermostat. with a height h = 8'
and a temperature difference dt = 80-70 = 10 f, closet airflow might be
16.6 av sqrt(hxdt) = 148av cfm with 1480av of heatflow, so we need a
minimum damper area av = 4.2k/1480 = 2.8 ft^2 near the closet top and
bottom. or, the closet might be in the airflow path of a forced-air
heating system with an electric resistance element that rarely turns on.

the closet might be used for summer cooling. july is the warmest month
in phila, with a 24-hour average temp of 76.7 f and an average daily
min/max of 67.2/86.1. july air has about 1.33% of water by weight with
a dew point or shaded pond temperature of about 65 f. cooling an 8,000
btu/f closet and 3k btu/f house to 70 f at night with outdoor air and
closing the house up during the day while circulating air through the
closet makes about 16h(81-70)200 = 35k btu plus 40k of electrical heat
gain, raising their temperature 75kbtu/(8,000+3,000)btu/f = 7 f by the
end of the day. 


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.edyou

computer simulation and modeling. high performance, low cost, solar heating
and cogeneration system design. bsee, msee. senior member, ieee. registered
us patent agent. web site: 

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