solar attic water and space heating
20 may 1998
brian ferris wrote:
>is it possible for a do-it-yourselfer to make a new roof out of panels.
i think so. the roof might face the equator, with a slope that equals the
latitude, for optimal overall yearly gain, or it might be more vertical, for
more winter gain. it might be a single layer of corrugated polycarbonate,
like my 640 ft^2 roof, covered with "dynaglas" or replex (800 726-5151),
which costs about $1/ft^2 and comes in 4'x12' sheets with a 10 year light
transmission guarantee and an expected mechanical lifetime of 20 years.
with no plywood or shingles, this could be cheaper than other roofs,
including the labor to attach the 4x12' sheets to rafters with a screw gun
and hex-head screws.
>...have the panels serve as a roof also, just for hot water not pv?
you might think "transparent sheathing," with some way to collect solar
heat underneath, vs "panels." attach corrugated black aluminum sheets on
top of the rafters, under the polycarbonate, and trickle some water over
the sheets, as h. e. thomason did? will the rafters rot, if water vapor
escapes? this seems to require good sealing. other concerns are leaks,
freezing, corrosion, pumping power, and heat loss by condensation on
the inside of the glazing.
>...i just wondered if they were actually the roof of the house without
>any air flow underneath if they would get too hot.
an opening at the soffit and some sort of vent that opens near the ridge
peak, when the rafter cavity gets too hot? polycarbonate can withstand
130 f indefinitely, although it may last longer if cooler. being thin,
it would have a temperature close to the average of the air temperatures
on each side.
you might put some sort of air-water heat exchanger near the peak, eg some
fin-tube pipe, the kind used in baseboard radiators, with some dark window
screen inside the cavity to help absorb solar heat, and fiberglass insulation
or foil with dark paint on the south side under that. my rafter cavities are
about 27" wide x 20' long. each receives about 12k btu/h of peak sun. the
us r1 clear roof above each cavity has a thermal conductance to outdoors of
about 45 btu/h-f, so when outdoor air is 30 degrees f and the average air
temperature in the cavity is t degrees, the heat loss to outdoors is
(t-30)45 btu/h. if the average cavity air temperature were 130 f, 4,500
btu/h would go outdoors, leaving 7,500 btu/h of useful heat output, and the
collection efficiency would be 7.5k/12kx100 = 63%, with this linear model.
fin-tube pipe has a thermal conductance of about 5 btu/h-f-ft in still air,
and costs about $5/ft. how would that work as an air-water heat exchanger?
here's one equivalent thermal circuit, with cavity air temp t, water temp
tw, and air-water heat exchanger conductance u (btu/h-f):
|---| --> |-------*--x---www-----tw
----- | 1/u
12k btu/h |
temporarily disconnecting the air-water heat exchanger at point x
and using a (thevenin) equivalent circuit makes this simpler:
297 f----www------|------www-----tw = 130 f.
if tw = 130 f, t = 130 + (297-130)/(1/45+1/u)/u = 130 + 167/(1+u/45),
and the solar collection efficiency is (t-tw)u/12k = 167u/(1+u/45)/12k.
to make this 50% efficient, we need 167u/(1+u/45) = 0.5x12k, so u = 178,
like 35' of fin tube pipe between each rafter. ick. moving air would help,
ie venting the cavity to increase the air velocity and fin-tube pipe
conductance from 5 to about 5(2+v/2)/2 btu/h-f-ft, where v is in mph.
one might let some outdoor air flow from soffit to ridge continuously,
but that wastes heat...
if the warm air can be used to heat the house, it's thermally more
efficient to allow warm air to flow out of the top of the cavities
through a duct heat exchanger and blow it down to the house with a fan.
cooler house air could enter the cavities near the floor. in this case,
the peak solar current source (for the whole roof) becomes 600x0.9x311
= 168k btu/h, and the entire roof's thermal conductance is 600 btu/h,
so we have
|---| --> |-------*--x---www-----tw
----- | 1/u
168k btu/h |
and the thevenin equivalent temperature tt = 30 + 168k/600 = 310 f:
310 f----www------|------www-----tw = 130 f,
and the solar collection efficiency is (t-tw)u/168k = 180u/(1+u/600)/168k,
so 50% collection efficiency requires that 180u/(1+u/600) = 0.5x168k, and
u = 2,100 btu/h, something like 2 or 3 auto radiators with fans... hmmm.
with a single duct heat exchanger with a conductance of 800 btu/h-f, like
magicaire's $166 shw2347 made by united electric at (940) 767-8333, the
solar collection efficiency = 180(800)/(1+800/600)/168k = 37% (although the
"waste heat" heats the house), and the hydronic output power in peak sun
may be 0.37x168k = 62k btu/hour, which should be enough for showers, etc.
t = 130 + 62k/800 = 208 f, theoretically, with no air movement. with a
2,000 cfm fan and no water heating, the air temperature rise in peak sun
would be about 168k/2k = 84 f. this looks like the right ball park...
this might heat water and cool the attic with no fan power in the summer,
with warm air from a shaded lean-to sunspace flowing up through the soffit
into the rafter cavities, and hot air flowing past the heat exchanger,
through the unpowered fan, out of a seasonal movable damper and up out
of a roof vent near the ridge.
ps: i'll be speaking on "solar house heating arithmetic"
from 1-2 pm this saturday 5/23/98 at the hilton hotel
in allentown, pa. all are welcome.
10 aroof=640'solar roof area (ft^2)
20 pksun=aroof*311'peak solar power input (btu/h)
30 netsun=.9*pksun'sun transmitted into roof (btu/h)
40 rroof=1'r-value of roof (ft^2-f-h/btu)
50 uroof=aroof/rroof'thermal conductance from roof to outdoors (btu/h-f)
60 uaw=800'thermal conductance of air-water heat exchanger (btu/h-f)
70 tout=30'outdoor air temp (f)
80 tatt=70'air temp into collector (f)
90 c=1000'airflow (cfm)
100 print " temp (f) heat power (btu/h) efficiency (%)"
110 for tw=70 to 130 step 30'water temperature (f)
120 num=netsun+tout*uroof-tatt*uroof+tw*uaw+tatt*c'tcol numerator
130 den=uroof/2+uaw+c''tcol denominator
140 tcol=num/den'max collector air temp (f)
150 pw=(tcol-tw)*uaw'peak solar power collected by water (btu/h)
160 effw=100*pw/pksun'peak sun solar water collection efficiency (%)
170 print "water ";tw;" "pw;tab(41);effw
180 pa=(tcol-tatt)*c'peak solar power collected by air (btu/h)
190 effa=100*pa/pksun'peak sun solar air collection efficiency (%)
200 print "air ";int(tcol+.5);" ";pa;tab(41);effa
210 print "combined solar collection efficiency (%)";effw+effa
230 next tw
temp (f) heat power (btu/h) efficiency (%)
water 70 49485.28 24.86198
air 132 61856.6 31.07747
combined solar collection efficiency (%) 55.93945
water 100 34541.88 17.35424
air 143 73177.35 36.76515
combined solar collection efficiency (%) 54.11939
water 130 19598.49 9.846506
air 154 84498.11 42.45283
combined solar collection efficiency (%) 52.29933