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re: hey nick!
3 aug 1999
 wrote:
 
>hello nick,

hello paul,

>i have been interested in building a solar heated house for some time...

good idea.

>we live in the sw corner of nc and presently heat with wood
>about 7 months of the year.

more work than solar. ("work!" --maynard g. krebs.)

january's the worst-case month for solar house heating in asheville (lat.
35.43 degrees north, with a sun elevation of about 90-35.4-23.5 = 31 degrees 
on 12/21.) the average temperature is 35.7 f, with an average daily high
of 46.5. a lot of sun falls on a south wall, an average of 1180 btu/ft^2
per day, and an average of 790 falls on a horizontal surface. that average
number has a standard deviation of 62, with a min and max of 630 and 900. 

>metal roofs... i have been thinking about a design where the ridge vent
>would be a duct inside the attic and the vents usually installed under
>the eves would also tie into ducts. the roof would consist of 4" - 6"
>of insulation placed on the decking, a reflective coating, an air space
>perhaps with baffles or deflectors to increase surface area, and
>finally the metal roof with a selective coating.
 
bad idea? (i can't quite picture this. where's the "decking" and the
reflective coating?) have you looked into selective coatings lately?
they seem expensive, and may not last a long time in the weather. 

>the ducts in the attic would be headers where cool air
>would be forced in at the bottom of the roof and be
>collected in the duct that ran inside the roof at the ridge...

you also need to store heat somewhere, probably downstairs. i guess that
means significant fan power, if you collect warm air from the attic. have
you considered a sunspace on the south side of the house instead? you have
enough sun and mild enough temperatures that your heating system might be
powered by natural convection that way. 

>it would be nice if sufficient thermal gain could be achieved with no glazing.
 
yes, it would.

>...would you have the time to show me how to do the analysis?

well, the amount of sun you can collect that way depends on wind, inter alia,
eg collection temperature. (have you considered a clear dynaglas corrugated
polycarbonate roof like mine, with some dark shadecloth underneath to act
as a mesh absorber? dynaglas costs about $1/ft^2 in standard 4'x12' sheets,
goes on quickly with hex head screws, and has a 10-year light transmission
guarantee and an expected mechanical lifetime of 20 years.) 

you might consider the thermal conductance from metal to air as 2+v/2
btu/h-f-ft^2 where v is the windspeed in mph, as measured at 20 c in
fig. 1 on page 22.1 of the 1993 ashrae handbook of fundamentals. this
might apply with higher temperatures and a selective surface. the average
jan windspeed in asheville (it varies a lot with location) is 9.7 mph.
say the roof has a thermal conductance to air of about 7 btu/h-f, so a
square foot of roof at temperature t (f) collects about 790 btu/day of
sun and loses 6h(t-41f)7btu/h-f in january, making t = 59.8 f at the
breakeven temp where there's no leftover heat for the house. the good news
is you don't need a selective surface at that temperature. the bad news
is you can't store any useful house heat at that temperature.

for an r1 transparent roof, 0.9x790 = 6h(t-41)1ft^2/r1, so t = 159.5 f,
which seems more promising...

one basic solar house formula is "ohm's law for heatflow," with btu/h
replacing amps, temp (f) vs. voltage difference, and thermal resistance
in f-h/btu (a us r-value divided by a wall area in ft^2) vs. ohms.

there's another heat loss from air infiltration. a very tight house has
0.1 air volume changes per hour (ach), which adds about 0.1xv/55 btu/h-f
to its effective thermal conductance... one cfm of airflow with a temp
difference of 1 f moves about 1 btu/h of heat.

here's a 36'x36' square 2-story house (to minimize cost and heat loss)
on a concrete slab with an 8' deep sunspace and solar collector:

          |   8'  |                36'                 |
                           perimeter insulation
       -   -------------------------------------------- p  -
          |   s   |       |         .                  |e
          |   u   | tank  | 8'      .                  |r
          |   n   |       |         .                  |i
          |   s   |--r25--          .                  |m
      16' |   p   |                 .                  |e
          |   a   r                 .                  |t
          |   c   2                 .                  |e
          |   e   5 . . . . . . . .....                |r
          |       |      duct     .....                |  36'
       -   -------| . . . . . . . ..... 4'x4' column   |i
                  |                 .                  |n
                  |                 .                  |s
                  r                 .                  |u
                  2                 .    concrete      |l
                  5                 .        slab      |a
                  |                 .                  |t
                  |                 .                  |i
                  |                 .                  |o
                   ------------------------------------ n  -
                           perimeter insulation
   (use courier font)
                               . 
                  clerestory-->     .                     - 21'
       skylight under shutter->.  .....  .
                          .duct ==> s  ==>vent . 
south                .            b e b   opener   .      - 16'
                  |d              b w b                |
                  |u              b e b                r
                  |c              b r b                2
                  |t              b   b                5
               .  |-----------------p------------------|  -  8'
      6' - .  big |             . b i b                |
           .fins  | stairway? .   b p b=concrete blocks|
           .     b|         .     b e b                |
           .     f|   duct.    <==h s h<==             |
         ----refl-----------------h   h------------------ -  0'
           |              slab                         |
            --------under-slab-insulation--------------

a large polyethylene tank might store long term heat. tractor supply corp
sells 2100 gallon cylindrical tanks about 7' in diameter x 7' tall for $899.
the tank might also store rainwater and provide hot water for showers, a
hot tub, etc, with grainger's $64 flojet 2p366 12v 7a 3.9 pound 2 gpm 30 psi
pump attached to the outlet. it has a built-in pressure switch and a 2 year
guarantee.

the tank might be in the house, in a two-story sunspace, or in a basement.
the water might be heated with something like big fins (bare water heating
panels) in a sunspace, or with a fan-coil unit (like an auto radiator) in
an air heater inside the sunspace, or with a linear parabolic concentrating
reflector in a sunspace or solar attic with a shallow drain-down 4' trough
along the north wall. on a cloudy day, we could circulate tank water through
a hydronic slab or another fan-coil unit to warm the house. 

suppose 8% of its 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.)
in january, an average of 530 btu/ft^2 per day of sun falls on a west wall,
with 510 on an east wall and 220 on the north. so the daily sunlight that
enters the house through windows is 0.5(0.5(1180)+0.2(530)+0.2(510)+0.1(220))
= 410 btu/ft^2.

let's say the whole house is built with 6" $3/ft^2 r25 structural insulated
panels (sips--plywood/foamboard sandwiches), except for the column, made
from hollow concrete blocks for greater strength. suppose the house only
leaks 0.1 air changes per hour (a local sip manufacturer guarantees this
with a blower door test) and it uses 150 kwh/month of electrical energy
(~1/4 of the national average.)

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 it needs
24h(70f-35.7f)224btu/h-f = 184k btu to stay warm on an average january day
in asheville and 18(70-35.7)224 = 138k to stay warm over an 18 hour "night."
the windows gain 200ft^2x410btu/ft^2 = 82k/day of sun, and electrical 
energy adds another 17k btu, so the sunspace needs to provide 99k btu on
an average day. 

the sunspace heats the house on an average january day, and the tank heats
it for 5 cloudy days in a row after that, at the average jan temp. the house
stores daily overnight heat in 35 $8 20' vertical sealed thinwall pvc sewer
pipes full of water in a 4'x4' central column which might also contain a
fluepipe for a woodstove or electrical generator. the woodstove might be
located near the column, with a hood that collects warm air from the stove.
the pipes are solar heated by air from the sunspace during the day and
warm the house overnight.

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 pipes, and out the bottom through hollow concrete blocks with
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 slab might contain some
4" thinwall pvc pipes or through/utility-ducts to return air to the sunspace
and the north side of the house.)

the sunspace roof might be clear corrugated polycarbonate r1 dynaglas/
replex/ge plastic in standard sheets 12' long that overlap on 4' centers.
this 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. the south wall of the
sunspace might be flat replex polycarbonate, which comes in 49" rolls and
costs about $1.25/ft^2. it's clear as a window, with a 10-year guarantee.

a 1' slice of a 6' south wall gains 0.9x1180x6 = 6.4k btu/ft^2 per day,
and a 1' slice of an 8' ceiling gains 0.9x790x8 = 5.7k. the combination
loses about 6h(80f-41f)14ft^2/r1 = 3.3k, for a net gain of 8.8k btu, so
the sunspace needs to be at least 99k/8.8k = 11' long to keep the house
warm on an average day.

let's make it 16' long to collect some extra sun for domestic hot water.
the north wall might be covered with dark porous mesh with an air gap
behind it to increase solar collection efficiency by a) keeping solar-
warmed air away from the cold glazing and b) partially blocking reradiation
and c) reducing absorber surface temperatures by increasing the absorber
area and absorber-to-air conductance. 

storing 138k of heat overnight with a 20 f temperature swing requires about
7k btu/f of thermal mass with a short charging time constant. the house
walls and ceilings and furnishings might add 2k btu/f to its capacitance,
(an open ceiling fan can help distribute air in the house and store more
heat in the slab), leaving 5k btu/f for the column, eg 300 hollow concrete
blocks with about 1500 btu/f and 35 20' 4" sewer pipes each holding about
100 pounds of water. the combination has about 2200 ft^2 of surface, about
10x the sunspace glazing area. each pipe has a 3.3 hour time constant in
slowly moving air with a surface film thermal conductance of about 1.5
btu/h-f-ft^2, so bathing them in 100 f air for 6 hours warms them to about
100-(100-70)exp(-6/3.3) = 95 f, if they are 70 f at dawn. the column can 
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 = 138k,
so q = 1,150 cfm. this might come from grainger's $109 86 watt 21k cfm 315
rpm 48" diameter 4c853 ceiling fan turning at 1150/21kx315 = 17 rpm, with a
theoretical power consumption of (1150/21k)^3x86 = 0.014 watts, moving
138k/3.41/6h = 6.7 kw of heat with a cop of 477,531.

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 1150 cfm requires a
minimum free airflow cross section av = 3.6 ft^2 in the column; 35 4"
pipes occupy 3.1 ft^2 of solid cross section, which makes the minimum
column cross section 6.7 ft^2, less than the 7.1 ft^2 cross section of
the 32" core of the column.

the house needs 5x(184k-17k) = 835k btu of heat for 5 cloudy days in a row.
with 2100x8 = 16.8k pounds of water cooling from 130 to 80 f, the tank
stores 16.8k(130-80) = 840k btu of heat.

in a 70 f house, the tank in an 8' r25 cube needs 24h(130f-70f)6x64ft^2/r25
= 22k btu/day of heat. heating water from 60 to 110 f for say, 4 10 minute
3 gpm showers a day requires 4x10x3x8(110-60) = 48k btu, so we need to
collect about 70k btu/day of sun in water. we might do this with an array
of 6 6"x16' vertical big fins under the roof on 16" centers with 12" light
shelves in front of them to roughly double their output and raise their
efficiency. (we might gather even more sun by tilting the array back and
squooshing it closer together.) the big fins might be 6" pieces of 1" foil-
faced foamboard with a layer or two of 0.010" copper foil over that, with
1/2" copper pipe soldered to that. (we might gather additional winter solar
heat with another 2' high layer of big fins (or water-cooled pvs :-) along
the north wall, with a ground reflector in front of that.) 

on a 10 f night (ashrae's 99th percentile minimum ashville temperature),
the house needs (70-10))224 = 13.4k btu/h of heat from the closet, so
the thermostatic discharge vent damper needs 16.6xavxsqrt(8')x10f^1.5
= 13.4k, ie av = 9 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'x4' foamboard
dampers attached to passive greenhouse vent openers, or a thermostat and
a couple of 20" 1000 cfm window fans with 13.4k = 10cfm, on a cold day.
with 21' of height, the column only needs 5.6 ft^2 of discharge area, eg a
4'x2' vent at the top and an 8 ft^2 hole below.

nick

a foil-faced foamboard+copper foil big fin efficiency calculation

10 ts=30'sunspace temp (c)
20 tw=55'water temp (c)
30 i=2*800*.9'peak insolation (w/m^2)  [2 suns]
40 fw=.152'fin width (m)
50 fl=1'fin length (m)
60 ein=fw*fl*i/2'peak sun power into half-fin (watts)
70 sigfa=8.5'still air film thermal conductivity (w/c-m^2)
80 ga=sigfa*fw*fl/2'half-fin-->air conductance (w/c)
90 tt=ts+ein/ga'thevenin equivalent temperature (c)
100 sig1=385'copper thermal conductivity (w/mc)
110 thkse=.01'metal1 thickness (in)
120 thks=.0254*thkse'metal1 thickness (m)
130 g1=fl*thks/(fw/2)*sig1'half-fin metal1 thermal conductance (w/c)
140 sig2=211'aluminum thermal conductivity (w/mc)
150 thkse=.005'metal2 thickness (in)
160 thks=.0254*thkse'metal2 thickness (m)
170 g2=fl*thks/(fw/2)*sig2'half-fin metal2 thermal conductance (w/c)
180 gs=g1+g2'half-fin->pipe conductance (w/c)
190 u=(tt-tw)/(1/gs+1/ga)'useful heat into water (w)
200 eff=100*u/ein'solar collection efficiency (%)
210 print "sunspace temperature (c):", ts
220 print "water temperature (c):",, tw
230 print "half-fin peak sun power (w):", ein
240 print "thevenin temperature (c):", tt
250 print "half-fin --> air conductance (w/c):", ga
260 print "half-fin --> pipe conductance (w/c):", gs
270 print "solar collection efficiency (%)", eff

run

sunspace temperature (c):              30
water temperature (c):                 55
half-fin peak sun power (w):           109.44
thevenin temperature (c):              199.4118
half-fin --> air conductance (w/c):    .646
half-fin --> pipe conductance (w/c):   1.639303
solar collection efficiency (%)        61.14689




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