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gee, somebody actually read our paper...
24 oct 1996
>> consider a 1 m cubical solar closet (fig. 1a) sitting outdoors on an
>> average 0 c december day near philadelphia, pennsylvania, usa. the
>> south wall of the closet, i.e., the solar air heater, receives about 3
>> kwh/m^2/day of solar heat, i.e. ein = 3 kwh/day, more if there is snow
>> on the ground or a white surface or a shallow frozen reflecting pool
>> in front...
 
>this value is closer to 2.7 kwh/day and that is with a snow covered ground.

let's see. the nrel _solar radiation data manual for flat-plate and
concentrating collectors_ (printed with a renewable source ink on paper
containing at least 50% wastepaper :-) says the 24 hour average december air
temperature in philadelphia over the last 30 years has been 2.1 c, not 0 c,
with a daytime high of 6.3 c. the nice folks at nrel say the average amount
of sun that has fallen on south walls for the last 30 years in december in
phila has been 2.9 kwh/m^2/day, 1.8 min, 3.6 max, with an uncertainty of
+/-11%, and a standard deviation of 7.3%, given a 20% ground reflectivity,
using the perez model (perez, r.; ineichen, p.; seals, r.; michalsky, j.;
stewart, will. (1990), "modeling daylight availability and irradiance
components from direct and global irradiance." solar energy, 44(5),
pp. 271-289.)

ic = ib cos theta + id + ir, where
            theta is the incident angle of the sun's rays to the collector,
            and          ir is the radiation reflected from the surface
	                    in front of the collector
and the diffuse radiation 

id = idh [0.5(1-f1)(1+cos beta) + f1 a/b + f2 sin beta], where

     idh = diffuse solar horizontal radiation
     f1 = circumsolar anisotropy coefficient, function of sky condition
     f2 = horizon/zenith anisotropy coefficient, function of sky condition
     beta = tilt of the collector from horizontal
     a = the greater of 0 or the cosine of the incident angle
     b = the greater of 0.087 or the cosine of the solar zenith angle

they go on to say "the ground-reflected radiation received by a collector is
a function of the global horizontal radiation (ih) the tilt of the collector
from the horizontal (beta) and the surface reflectivity or albedo (rho):

     ir = 0.5 rho ih (1-cos beta).

they further illuminate: "surface albedo was adjusted depending on the presence
of snow cover, as indicated by the snow depth data in the nsrdb. if there was
snow on the ground the surface albedo was set to 0.6 (albedo for snow ranges
from about 0.35 for old snow to 0.95 for dry new snow.) if no snow was
indicated, the surface albedo was set to 0.2, a nominal value for green
vegetation and some soil types."

i live here. there is sometimes snow on the ground in december, but more often
not, i'd guess. i think it's a good idea to have a shallow reflecting pool in
front of a solar wall in this area, which will have a reflectance of about 0.6
when it's frozen (slightly higher at grazing angles), when it's cold outside,
when we need more sun, and 0.06 when unfrozen, eg in the summer, as i recall.

>besides which this is only the value of solar energy incident on
>the vertical surface, it is not the amount of radiation that is received
>on the other side of the glazing.

our single layer of 0.020" polycarbonate glazing with a nominal 92% solar
transmittance might have passed about 85% of this. the transmittance depends
on the angle. december sun rises in the se and sets in the sw here, a swing
of about 90 degrees, and most solar heating happens around noon. polyethylene
film has about the same solar transmission, but less greenhouse effect, ie
it is more transparent to longwave ir reradiation, which is bad. it also
costs 5 cents/ft^2, vs $1.50, and comes in rolls 40' wide, vs 4' wide. poly
film will last a long time if it's rolled up or has some shadecloth covering
it in the summer. "ir" poly film with more greenhouse effect costs more,
looks cloudier, and blocks part of the solar ir spectrum. prof david meer
of rutgers says the performance increase with ir poly should be small, at
interior temps of 70-100 f, altho it would lower the thermal loss at the
much higher temperature of an unvented greenhouse in the sun. 

>how about some tranmisssion-absorbance equations? 

you mean transmittance-absorptance equations? this isn't some academic
plaything. it's a way to stop bombing iraq and clean up the air on this
planet, but that won't happen unless we do it a lot more, and stop treating
solar heated houses as aesthetic toys or experiments or grant opportunities.

i'd like to keep all this very simple, so even architects can understand it.
a lot of solar houses are designed very badly in this country, or really not
designed at all, from a thermal point of view, or designed with very low
standards for performance, eg a 30% solar fraction, using the psic guidelines,
vs the 100% solar-heated houses which professional engineer norman saunders
has been building since 1944, which also make hot water, and don't have to
be absolutely airtight or superinsulated. most of the solar houses near me
(not many) look pretty, with "dramatic south-facing glass," but they are very
expensive custom houses, and they perform _miserably_, compared to what is
possible with better thermal design. improving their thermal design is like
shooting fish in a bucket, using a shotgun.

it seems to me that if architects used any basic physics at all in solar
house heating design, even with numbers that were off by 50%, and a few
"oversimplifications," they could do a much better job designing solar houses
than they do now, using cookbook approaches at best, with little insight
into the physics. we made a lot of approximations in this paper, but the
result seems reasonable and conservative and not too hard to understand.

it's conservative partly because of some facts we didn't talk about. for
instance, some sun shines in the house windows during the day, and the south
wall of the house is warm during an average day, because of the sunspace, and
the sunspace collects heat on days that are statistically warmer than average
days, with more sun, and days are warmer than nights: 43 f where i live, vs
the 36 f 24 hour average temperature. we ignored all this. tmy2 simulations
i've done seem to indicate that this simplified procedure results in slightly
overdesigned houses, from a thermal point of view. all this is capable of
infinite elaboration, to make ever more perfect models that are ever more
difficult to use and understand, if you want to spend your life that way, 
and if you don't want to build anything, or see others do so.
 
>> so if ein = eout, then tw = 0 + 3k/94.5 = 31.7 c. (2)
>
>ein doesn't equal eout,

i'd say that's a good approximation.

>this is only true if their is steady state conditions and no thermal storage.

i'd say the same about that, but i would use the words "there" and "are."

>your basic premises are flawed, thus invalidating the work.

thanks for your help :-)

our instruments will be living outdoors again this winter, in a larger box,
a 10'x 12' cabin at a youth hostel. the sunspace frame is now up and covered.
it's a quarter cylinder, about 8' tall and 8' deep and 12' wide, made with 4
curved spaced beams, each beam made with 2 12' 1x3s (costing $1.44 each :-)
with a 1x3 spacer block every 2' and some drywall screws.

there's a single layer of 0.006" greenhouse polyethylene film over that, held
in place underneath by 2 12' 1x3 cedar cap strips over the end bows, and held
down on top by a 12' piece of nylon twine stretched over the outside of the
poly between each bow, running from the peak to the ground, like a strapped
mediterranean-style poly greenhouse, vs an american air-inflated one with two
layers of poly. it looks nice to me, like a handmade boat or an airplane.
very light and strong. it's a bit cloudy to look through, like a translucent
shower curtain, which is also nice. another problem with direct gain houses
is lack of privacy. there will be a shower inside the sunspace, and perhaps
a hot tub, with hot water coming from 6 plastic 55 gallon drums above the
ceiling of the cabin, sitting on top of some strengthened collar beams. the
ceiling will likely be poly film, or perhaps nothing, since there are a couple
of single pane skylights above it (a pro-malo donation from a young architect,
who also installed 52 ft^2 of single pane windows on the north and west sides
of the cabin) in the gable roof, which will be insulated underneath with 6"
of fiberglass and a poly film vapor barrier. 

and we will add on another half-cylinder greenhouse section to the east,
12' wide x 18' deep x 8' high, with 4 $3 12' 1x3 beams to the south and 4
$5 16' 1x3 beams to the north. and a $100 24'x16' shallow reflecting pond
to the south, made from a 20' wide roll of epdm rubber roofing material,
with a shallow perimeter earth berm.

and, this morning clint buckwalter will start removing 2 fallen down apple
trees in front of my house and smoothing the ground for a 40' long x 16' high
x 8' deep curved lean-to poly film sunspace, and a 40' x 16' reflecting pond. 

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.edu

computer simulation and modeling. high performance, low cost, solar heating and
cogeneration system design. bsee, msee. senior member, ieee. registered us
patent agent. solar closet paper: http://leia.ursinus.edu/~physics/solar.html




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