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a convective power tower house
27 jul 1999
the average outdoor temperature in december in sheridan, wy, is 21 f, with
an average daily high of 33. over an average day, 1,060 btu per square foot
of sun (enough to make 14 cups of tea, or lift them all up to the top of the
golden gate bridge tower) falls on a south wall (vs. 1,000 in philadelphia
and 460 in eugene, or) and 570 falls on a horizontal surface...

here's a 36'x36' square 2-story house (to minimize cost and heat loss)
on a concrete slab with a 12x24' sunspace and solar closet:

      |     12'   |                36'                 |
                           perimeter insulation
   -   ------------------------------------------------ p  -
      |   |       |                 .                  |e
      |   | s  c  |                 .                  |r
      | s | o  l  |                 .                  |i
      | u | l  o  |                 .                  |m
      | n | a  s  |16'              .                  |e
   24'| s | r  e  |                 .                  |t
      | p |    t  |                 .                  |e
      | a  -------| -               .                  |r
      | c         | . . . . . . . .....                |  36'
      | e <== owd |8'  stairs?    ..... 4' column      |i
      |           | . . . . . . . .....                |n
   -   -----------| -               4'                 |s
                  |                 .                  |u
                  |                 .    concrete      |l
                  |                 .        slab      |a
                  |                 .                  |t
                  |                 .                  |i
                  |                 .                  |o
                   ------------------------------------ n  -
                           perimeter insulation
   (use courier font)
                  clerestory-->     .                     - 21'
       skylight under shutter->.  .....  .
                          .duct ==> s .==>vent . 
south                .            . e .   opener   .      - 16'
                . |==>one way     . w .                |
           . fins |   damper (owd). e .                |
~13' - . s big    |               . r .                |
       . u   deck |               .   .                |
       . n  ------|-----------------p------------------|  -  8'
       . s |      |             . b i b                |
       . p | solar| stairway? .   b p b=concrete blocks|
       . a |closet|         .     b e b                |
       . c |     owd  duct.    <==h s h<==             |
     ----e------------------------h   h------------------ -  0'
       |      slab with optional 4" thinwall pipes     |

suppose 8% of the floorspace (~2,600 ft^2) is r4 windows with 50% solar
transmission, with 50% of the windows on the south side, 20% on the east
and west, and 10% on the north (mainly on the ground floor, with the north
second floor well-lit by skylights with movable insulating shutters above.)

let's say the whole house is built with 6" $3/ft^2 r25 structural insulated
panels (sips--plywood/foamboard sandwiches), except for the lower part of
the column, made from hollow concrete blocks for greater strength. the slab
might extend under the sunspace (with insulation above, eg foamboard under
dark green indoor-outdoor carpet), or it might end at the south wall of the
house proper, with the sunspace sitting on carpet on top of plastic film
on the ground.

this heating system resembles one tested and described in "solar heating-
ventilating system using a solar chimney," by e. bilgen and m. chaaban, 
genie mechanique, ecole polytechnique, montreal, quebec, canada h3t 1p8,
published in solar energy vol. 28, no. 3, pp 227-233, 1982, except that
the mass wall is an insulated column, most of the mass is water, and
a solar closet provides the long-term thermal storage.

the sunspace is sized to provide the heat the house needs on an average
december day, and the solar closet is sized to provide heat for 5 cloudy 
days in a row after that, at the average december temperature. the house
stores daily overnight heat in 100 $8 20' vertical sealed thinwall pvc
sewer pipes full of water in a 4' square central column (which might also
contain a fluepipe for a woodstove or electrical generator.) the pipes are
heated by air from the sunspace during the day, and they warm the house
overnight. the solar closet stores heat in 56 sealed 55 gallon water drums.

during the day, sunspace-warmed air flows up through a one-way passive
plastic film damper and then through a duct along the underside of the
south roof into the top of the column. then it flows down the column,
heating the sewer pipes, and out the bottom through hollow concrete blocks
with the horizontal holes. the air continues to flow from north to south
through a duct on the ground floor (which might be under some stairs)
and back into the sunspace via another plastic film damper. 

the column might have a passive adjustable thermostatic vent opener at
the top of the north side to release warm air into the room when the indoor
temperature drops below 70 f. (as an option, the floorslab might contain
some 4" thinwall pvc pipes or a trough-duct to return air to the sunspace
and the north wall of the house. this would increase the effective thermal
mass of the house and provide a warmer floor, and eliminate the need for
the duct below the stairway.)

suppose the house only leaks 0.1 air changes per hour (a local sip
manufacturer guarantees this with a blower door test) and the house uses
150 kwh/month of electrical energy (~1/4 of the national average.)

then its thermal conductance is 200ft^2/r4 = 50 btu/h-f for the windows,
plus 2104ft^2/r25 = 84 for the walls, 1296ft^2/r25 = 52 for the ceiling,
and 0.1x16'x1296ft^2/55 = 38 for air leaks, a total of 224 btu/h-f, so
the house needs 24h(70f-21f)224btu/h-f = 263k btu to stay warm on a
average december day in sheridan, and 18(70-21)224 = 198k to stay warm
over a average 18 hour december "night." on an average day, the windows
gain 200ft^2x0.5x715btu/ft^2 = 71.5k of solar heat, and electrical energy
adds another 17k btu, which means the sunspace needs to provide 174.5k btu
on an average day. 

the sunspace might be made from clear r1 dynaglas/replex/ge corrugated
polycarbonate, which comes in standard sheets 12' long that overlap on
4' centers. this r1 greenhouse roofing material has 90% solar transmission
and costs about $1/ft^2, with a 10 year guarantee against loss of light
transmission and an expected mechanical lifetime of 20 years...

a 1' slice of a 12' dynaglas south wall gains 0.9x1060x12 = 11.4k btu/ft^2
per day, a 1' slice of a 12' ceiling gains 0.9x570x12 = 6k, and the combo
loses about 6h(80f-27f)24ft^2/r1 = 7.6k, for a net gain of 9.9k btu, so
the sunspace needs to be at least 174.5k/9.9k = 18' long to keep the house
warm on an average day.

we might make it 24' long to collect some extra sun for water heating with
overhead big fins (bare solar water heating collectors in the sunspace.)
the north wall of the sunspace might be covered with dark porous mesh with
an air gap behind that to increase solar collection efficiency by keeping
solar-warmed air away from the cold sunspace glazing and partially blocking
reradiation loss and reducing absorber surface temperatures by increasing
absorber area. 

storing 198k of heat overnight with a 20 f temperature swing requires
about 10k btu/f of thermal mass with a fairly short time constant for
charging. each 20' sewer pipe holds about 100 pounds of water, so we
could use 100 of them in a 10x10 square array with a 40x40" cross section.
the pipes might have more space between them for better airflow by
natural convection. each pipe has a 3.3 hour time constant, so bathing
the pipes in 100 f air for 6 hours raises their temperature to about
100-(100-70)exp(-6/3.3) = 95 f, if they are 70 f at dawn. the column
could also store nighttime coolth in the summer.

let's assume warm sunspace air from behind the dark mesh enters the column
at 100 f on an average day, and the average water temperature in the pipes
is 80 f, and the sunspace air exits the column at the water temperature.
a q cfm airstream with a temperature difference dt transfers about qdt btu/h
of heat power, so with a 20 f temperature difference and at least q cfm of
air flowing down the column for 6 hours on an average day, 6hx20q = 198k,
so q = 1,650 cfm. this might come from grainger's $109 86 watt 21k cfm 315
rpm 48" diameter 4c853 ceiling fan turning at 1650/21kx315 = 25 rpm, with a
theoretical power consumption of (1650/21k)^3x86 = 0.04 watts, moving
198k/3.41/6h = 10 kw of heat, for a cop of 242,000.

or the air might flow by natural thermosyphoning, with an infinite cop :-)
one empirical chimney formula says cfm = 16.6 av sqrt(hdt) = 332 av with
a 20' chimney and 20 f temperature difference, so 6hxcfmx20f = 198k means
the 4x4' column needs a minimum airflow cross section av = 5 ft^2; 100
4" pipes occupy 8.7 ft^2 of cross section, which leaves 7.3 ft^2 for airflow
inside the column.

the drywall and slab and furnishings add more thermal mass to the house.
an open ceiling fan might also help distribute air in the house... 

the solar closet needs to store 5x(263k-17k) = 1230k btu of heat for
5 cloudy days in a row. this might come from c pounds of water cooling
from 130 to 80 f, so c = 1230k/(130-80) = 24,600 pounds or 3075 gallons
of water in about 56 55 gallon drums, eg a 7 drum-wide x 4 drum-deep
x 2 drum-high array.

if 1060x0.9^2x128ft^2 = 110k btu/day of suns enter the air heater glazing
over the insulated south wall of the solar closet (this might be enhanced
with a horizontal reflective surface to the south), and the steady-state
temperature inside the closet is 130 f, and the solar energy that flows 
into the closet equals the heat energy that flows out, over a 6 hour average
december day, when the air heater temperature is 130+dt,  

110k = 6h(130+dt-100)128ft^2/r1   south wall loss, daytime
    + 18h(130-21)128ft^2/r26      south wall loss, nighttime
    +  6h(130-100)192ft^2/r25     e wall and top, daytime
    + 18h(130-21)192ft^2/r25      e wall and top, nighttime
    + 24h(130-100)128ft^2/r25     w wall, 24 hours
    + 24h(130-70)128ft^2/r25      n wall, 24 hours

    = 768(30+dt) + 40.2k, so dt = (110k-40.2k)/768 - 30 = 60.9 f. 

the closet needs to collect 40.2k btu on an average day to stay 130 f. if
40.2k = 6hxcfmxdt = 6hx16.6avxsqrt(8')xdt^1.5, av = 0.3 ft^2. let's use
larger openings to make dt smaller, with less heat loss by radiation and
a faster recovery time, and greater solar collection efficiency. a couple
of 2 ft^2 inward-opening plastic film dampers at the top and a 3" slot at
the bottom of the air heater makes 40.2k = 6hx16.6x4ft^2xsqrt(8)xdt^1.5,
so dt = 10.8 f. on a cloudy day, the closet loses about 24h(130-21)4ft^2/r1
= 10k btu through the dampers, less than 1% of the useful stored heat. 

on a -14 f night (ashrae's 99th percentile minimum sheridan temperature),
the house needs (70-(-14))224 = 18.8k btu/h of heat from the closet, so
the thermostatic discharge vent damper needs 16.6xavxsqrt(8')x10f^1.5, ie
av = 12.7 ft^2 at a min 80 f closet temperature, after 5 cloudy days. the
upper edge of the closet's north wall might have 2 2'x8' foamboard dampers
attached to passive greenhouse vent openers, or we might use a thermostat
and a couple of 20" 1000 cfm window fans with 18.8k = 10cfm, on a cold day.
with 21' of height, the column only needs 8 ft^2 of discharge area, eg a
4'x2' vent at the top and an 8 ft^2 hole below.


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