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st. louis solar house musings
10 jul 1998
st. louis, mo, has an average air temperature of 33.9 f in december,
the worst-case month for solar heating, with an average daily max of
41.7, an average 580 btu/ft^2 per day of solar heat that falls on a
horizontal surface (with a standard deviation of the monthly average of
57, and a daily clearness index kt = 0.44, ie the sun shines during 44%
of the daylight hours), 940 btu/ft^2 falls on a south wall, and 390
btu/ft^2 falls on east and west walls, according to nrel's weather
data for 1961-1990. 

a 24x32' 1 story house with r20 walls and an r40 ceiling and 4% of the
floorspace as r3 windows has a thermal conductance of about 900ft^2/r20
= 45 btu/h-f for walls, 768/40 = 20 for ceiling, 30/3 = 10 for windows,
and 24x32x8x0.25/60 = 25 for air leaks at 0.25 ach, totaling 100 btu/h-f,
so it needs about 24h(70f-33.9f)100 btu/h-f = 87k btu/day of heat in
december. suppose none of this comes from the 100 w occupants or their
50 w pets or their 500 kwh/month = 57k btu/day of electrical usage.

a square foot of r1 single-pane vertical south sunspace glazing might
gain 0.9x940 = 850 btu and lose 6h(80f-38f)1ft^2/r1 = 250 btu over a
6 hour collection day, a net gain of 600 btu/day, so a shallow 87k/0.6k
= 144 ft^2 plastic film lean-to sunspace might heat our house, or a 12'
wide x 8' deep x 8' tall covered patio on the south side with a clear
roof that gains about 0.9x8x12x580+0.9x8x12x940+0.9x8x8x390+0.9x8x8x390
= 176k btu per day, and loses about 6h(80f-38f)(8x12+8(12+8+8))ft^2/r1
=  81k btu, for a net gain of about 95k btu. (the east and west endwalls
might have interior curtains to keep the sun from shining in through the 
roof or south wall and  back outdoors  through the endwalls.)

bayer's ((412) 777-3837) dureflex urethane film could be a nice patio cover.
it costs about 35 cents/ft^2. it's about as clear as plastic food wrap and
comes in 15' wide rolls with a 10 year guarantee. it might be stretched
over standard curved greenhouse galvanized steel pipe bows, with more pipes
as ground stakes and a pressure-treated perimeter board for the foundation.
the film is quite strong: some test greenhouses were completely destroyed
when very high winds buckled the pipes, but the film was removed intact
and reused.

or, we might make $5 bows on 4' centers from 2 12' 1x3s bent to an 8'
radius with 1x3 spacer blocks and deck screws every 2' to hold them
together. sandwich the bow bottoms around a horizontal 1x3 near the
ground, and bolt that through the treads of some used tires filled
with soil to make planters inside the patio. (my local garage pays me
$1.25 each to take away tires. my zoning board defines a building as
"any structure permanently attached to the ground.") a $10 12x16' piece
of 4 year cloudy (and private) greenhouse polyethylene film could be
held to the bottom 1x3 with a cedar or poly-film-covered 1x3 cap strip
and deck screws, with the excess draped onto the ground and covered
with gravel to make a walkway and air seal, and keep the ground
near the sunspace warmer and drier. 

or, the "sunspace" might be part of a monopitch shed roof with an 8'
high vertical glazed wall above the south side of the house, or the
clear south half of a high-pitched gable roof, with a solar water heater
under the roof, or 20'x8' of $1.25/ft^2 corrugated polycarbonate
"solar siding" on the south side of the house instead of normal siding. 

suppose the house were very massy, with 900 ft^2 of 1' thick stone walls
and a heat capacity of 900ft^3x25btu/f-ft^3 = 22,500 btu/f, and the wall
temperature varied by 87k/22.5k = 3.9 f on an average day. if the main
resistance to heatflow between the walls and the house air were a slowly-
moving interior airfilm with a us r-value of 2/3, then the maximum house
temperature might occur in the afternoon, when 87k/6h = 14.5k btu/h is
flowing into the warm walls, raising the house air temperature to, say,
63+3.9+14.5kxr2/3/900ft^2 = 77.6 f. the minimum might occur at night,
when 87k/24h = 3.6k btu/h is flowing out of the walls, making the air 
63-3.6kxr2/3/900ft^2 = 60.3 f, for a daily house air temperature swing
of 17.3 f.

that may be an overestimate, since the maximum heatflow doesn't occur
at the same time as the maximum wall temp, and most of the house heat
loss is through the insulation between the walls and the outdoors, which
doesn't directly change the house air temperature. on the other hand,
stone walls might have an effective thermal resistance of about r0.1 per
inch. reducing mass or insulation increases the daily house temperature
swing, if there is no additional overnight heat from a thermal store
on an average day. 

a "solar closet" is one form of thermal store. it's a room containing
some sealed containers of water completely surrounded by insulation,
with a solar air heater attached to its insulated south side. the water
containers are heated by solar warmed-air from its air heater. the sun
does not shine directly on the water containers. a solar closet may be
in a sunspace, but it has its own glazing and air circulation system.
sunspace air never mixes with air inside the closet. making a house with
massy walls and floor can simplify a closet by removing its burden of
helping to keep the house warm overnight after an average winter day.

a 3' tall x 2' diameter 55 gallon water drum cooling from 130-80f gives
up about 55x8x(130-80) = 22k btu of heat, and our house needs 5x87k
= 435k btu of heat for 5 cloudy days in a row, ie 435k/22k = 20 drum's
worth. these might be in a solar closet that's about 8' wide x 6' deep
x 8' tall. the sunspace and closet could be smaller if the house had
more insulation. the closet glazing and thermal mass surface and airflow
need to be larger if the house needs overnight heat from the closet
on an average december day.

an 8x6x8' tall closet with r20 insulation and no requirement to provide
overnight heat for a house on an average day, and a south side facing a
sunspace which is 80 f during the day and 30 f at night, and the other 5
sides inside a house that is 70 f 24 hours a day, would receive about
760x8x8' = 49k btu/day of solar heat through its own glazing. an average
closet air temp t means the south face loses about 6h(t-80f)64ft^2/r1 btu
over an 6 hour solar collection day, and another  18h(t-30f)64ft^2/r20 at
night, and the rest of the exterior surfaces lose 24h(t-70f)256ft^2/r20,
making t = 138 f, if the energy that flows into the closet on an average
day equals the energy that flows out.

if the closet glazing loses 6h(130f-80f)64ft^2/r1 = 22k btu/day of heat
to the sunspace, the net heatflow into the closet is (49k-22k)/6h = 4.5k
btu/h, so the closet needs about 450 cfm of airflow with a 10 f dt to
transfer heat to the water containers inside. the airfilm resistance
at the water container surface makes an air-water temp difference of
about 4.5k/(20x25x1.5) = 6 f, making the average water temp about 132 f.

now suppose the house only has 1,800 ft^2 of 1/2" drywall with 900
btu/f of heat capacity, and the furniture, floors, etc, double that, 
and we decide to have a day/night temperature swing of, say, 10 f, so
the inherent thermal mass of the house can store 1,800x10 = 18k btu
of its daily heat need. if the sunspace warms the house for 6 hours on
an average december day, the house needs 18/24x87k = 65k btu for the
rest of the day, of which 18k can come from its thermal mass, leaving
the closet to provide 47k of overnight heat on an average day. this
determines the size of the closet glazing and the amount of airflow
and internal thermal mass surface... 

a square foot of closet glazing collects about 760 btu on an average
december day. if the closet air is 130 f, with its glazing in an 80 f
sunspace, and the glazing loses about 6h(130-80)1ft^2/r1 = 300 btu,
the net gain is 460 btu/day, so this closet needs 47k/460 = 100 ft^2
of glazing, more than the 8x8' glazing that would work for the stone
house. it might be 12' wide x 8' tall, a glazed north wall for the
12' wide x 8' tall sunspace.

there are 3 air loops in this heating system: the first circulates
sunspace air through the house at 40k/6 = 6.7k btu/h, the second
circulates air between the closet and its air heater during the day 
at 47k/6h = 7.8k btu/h, and the third circulates air between the
house and the closet on a cloudy day at 87k/24 = 3.6k btu/h.

the sunspace airflow loop might use a $12 20" 800 cfm window box fan in
series with a cooling thermostat in the sunspace and a heating thermostat
in the house, or it might use natural convection, if there were large
enough air passages or a high enough sunspace temperature.

the closet charging loop might have a 10 f airflow dt with about 800 cfm
of airflow, using a $100 differential thermostat controlling 2 $60 36 watt
10" diameter grainger 4c688 560 cfm cooling fans, which have a 149 f upper
operating temperature spec.

closet discharging might use natural convection with a foamboard damper 
attached to a honeywell 6161b1000 damper actuator motor that uses 2 watts
of electrical power when moving and 0 watts otherwise (for a cop of over
10,000, with a 5% duty cycle) in series with a heating thermostat. with
cfm = 16.6 av sqrt(hxdt) = 148 av of airflow (using one chimney formula,
with h = 8' and dt = 10 f), we need a damper area av = 3.6k/(148x10)
= 2.4 ft^2 near the closet top and bottom. or, the closet might be part
of the airflow path of a forced air electric resistance heating system
with a heating element that very rarely turns on.

each 55 gallon drum has about 25 ft^2 of surface, so 20 of them have
500 ft^2 of surface, not much compared to 96 ft^2 of closet glazing. 
having 10x or more thermal mass surface than glazing surface allows
heat to flow from the solar-warmed air into the water containers with
a low air-water delta-t: each square foot of glazing collects 460 btu
over 6 hours, ie 77 btu/h. if this flows into 10 ft^2 of mass surface
with a slowly moving air film conductance of 1.5 btu/h-f, dt = 5 f.

we could increase thermal mass surface by using more drums, or putting
hollow cement blocks under the drums (each 8x16" block adds about
6 ft^2 and 5 btu/f.) in that case, it seems advantageous to draw air
through the blocks with the fans, since moving air at v mph past a
rough surface increases thermal conductance to 2 + v/2 btu/h-f, which
lowers the needed amount of surface.

each block might contain 4 bricks with holes in the cavities. some local
bricks weigh 4 pounds each, and have 97 in^2 of exterior surface and 53
in^2 of interior hole surface; 4 such bricks would add about 4 ft^2 of
surface and 2.5 btu/f of capacity per block. a 10'x4" pvc drain pipe
threaded through block holes adds about 10 ft^2 and 50 btu/f, at a cost
of about $6, including 2 end caps and a #3 rubber stopper.

other ways of increasing surface include using cement blocks for the
closet walls, with the holes lined up vertically and holes at the top
and bottom to allow closet air to circulate inside the wall, adding
some 1 gallon milk jugs on shelves, or adding some stone statuary, eg
gargoyles, and casks of amontillado. plastic soda bottles might lose 10%
of their contents each year by moisture vapor transmission. milk jugs
are easier to support and hold more water per cubic foot, and their
cross-linked polyethylene walls have about half the vapor transmission
of pet soda bottles. recycled 5 gallon plastic pails (about 1'tall x
1'diam.) with tight-fitting lids are easy to transport, since they nest. 
a local wiremaking factory buys teflon powder in 19 gallon plastic tubs
with good o-ring seals and tight-fitting lids with circular clamps.

now what can we do with a house that has very little thermal mass, or
one with the same house temperature 24 hours a day? store all the heat
inside the closet, with just enough extra sunspace glazing to keep the
house warm for 6 hours per day. we might move the closet out into the
sunspace, and add extra glazing and thermal mass surface and airflow. 
collecting 18h/24hx87k = 65k of heat over 6 hours at 10.9k btu/h requires
65k/460 = 141 ft^2 of closet glazing, eg a 20x8' closet containing about
1,600 ft^2 of mass surface and 8,800 btu/f of heat capacity and 1,100
cfm of airflow, with a 10 f airflow dt.

we might use d 55 gallon drums and j 1 gallon plastic milk jugs (about
15 cents each, if new, with screw tops) on shelves. if each jug is 6"
square x 10" tall, with about 2 ft^2 of surface, the total surface
requirement is 25d + 2j > 1600, and 55x8d + 8j > 8800 for thermal mass.
combining these constraints, 55x8d - 100d > 8800-6400. we might use 8
drums and 700 jugs, with 1x3 shelves screwed to 2 4' 2x4s on 4' centers,
which in turn rest on cement blocks. or, the shelves might be supported
with 2x4 posts on 4' centers.

if 2 flat 4' 1x3s support 7 jugs, each 1x3 supports 28 pounds, with
bending moment m = 28l/8 = 168 in-lb, modulus s = m/f = 0.168 in^4,
and minimum beam depth d = sqrt(6s/2.5") = 0.26", vs 0.75" for a 1x3.
each jug occupies 8x8x12" = 0.44 ft^3, so we need 311 ft^3 for 700 jugs
and another 8x2x2x3'= 96 ft^3 for 8 drums. we might have a 20' wide
x 8' tall x 4' deep 640 ft^3 closet, including insulation, with a
4x4' area for drums, a 4x8' area for 7 jug shelves made with 84 $1
8' 1x3s on 4" centers screwed to 21 4' 2x4s, and an empty 4x8' section
that might be used for a clothesline or sauna with woodstove and
firewood storage. another 8x8' of closet glazing with 10' of fin-tube
pipe near the ceiling might heat water for showers via a thermosyphoning
water loop through a conventional water heater above, with a heating
element that rarely turns on.

raising the sunspace temperature reduces the closet glazing requirement.
(making the whole sunspace 130 f would eliminate the need for a separate
closet glazing, but that would require about 300 ft^2 of sunspace glazing,
and it would make the sunspace less usable for other purposes.) with 16x8'
of closet glazing, eg 2 8x8' single pane sliding glass doors, and a 130 f
average closet temp, we need 65k = 760x16x8-6h(130-ts)16x8/r1, so the
sunspace temperature ts needs to be 88 f, and 850as=87k+6h(88-38)as/r1,
making the sunspace glazing area as = 158 ft^2. we might use a shallow
20x8' sunspace or a larger more interesting 24'x8'x8' sunspace that gains
about 0.9x8x24x(580+940)+0.9x8x8x390x2 = 263k btu per day, and loses
6h(88-38)(8x24+8x40)ft^2/r1 = 154k btu, for a net gain of about 109k btu
with 22k btu/day of leftover heat for water heating or clothes drying.

july is the warmest month in st. louis, with a 24 hour average temp of
79.8 and an average daily min and max of 70.4 and 89.3 and a humidity
ratio of 0.0145, corresponding to a dew point or shaded pond temp of about
68 f. cooling a 20 drum closet to 72 f at night with outdoor air and
buttoning up the house during the day while circulating house air through
the closet means the house would gain about 16h(85-72)100 = 20.8k btu,
raising the closet temp 20.8k/(20x55x8) = 2.4 f by the end of the day. 

again, more thermal mass in the house means a solar closet needs less
glazing and airflow and internal thermal mass surface...

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.edyou

computer simulation and modeling. high performance, low cost, solar heating and
cogeneration system design. bsee, msee. senior member, ieee. registered us
patent agent. hi/dvc board member. web site: http://www.ece.vill.edu/~nick 




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