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re: advice sought on passive solar design
14 feb 2003
doug  wrote re a:

>...greenhouse made in two sections - the south glass section would have
>its own cement slab thermally broken from the main house slab and this
>small slab would have its own radiant floor zone to keep the plants from
>freezing at night.

this might work better if

a) the outer section has greater temp extremes than the inner one, and
b) the "slab" is vertical, since winter sun has a low elevation and the
   plants might like to grow in the soil floor), and
c) the mass wall contains water vs masonry, with 2-3x more specific
   heat by volume and a higher thermal conductance. 

>the northern section will have a lot of thermal mass especially in
>the back wall. a roll out insulated barrier would separate the two
>sections at night. during the day, both sections are quite open to
>the rest of the house.

sounds complicated. how about making a box on part of the back wall 
with an r1 cover with 90% solar transmission and a few vertical 55
gallon drums inside? it might have a passive thermofor temperature-
sensitive vent or $11 leslie-locke automatic foundation vent at the
top that opens when the air temp dips to 32 f (or slightly higher.)

on an average january day in phila, 1000 btu/ft^2 of sun falls on a
south wall. the 24-hour average temp is 30.4 f, with a 22.8 average
min and 37.9 average max temp, ie the daily temp is a sine wave with
an average value of 30.4 and a (37.9-22.8)/2 = 7.55 f peak amplitude:
t = 30.4+7.55sin(2pit/24) = 32 when t = sin^-1(32-30.4/7.55) = 0.82 h,
with the argument in radians. the number of "freezing degree hours" is
the integral (gasp) of 32-t from t1 = 12-0.82 = 11.18 to t2 = 24.82 h,
ie (32-30.4)(t2-t1) - 2x7.55x24/(2pi)cos(2pix11.18/24) = 78.16 fdd.

the difference between the 24-hour average temp and average daily min
is 7.6 f. we might want our box to keep the greenhouse at 32 f on a
colder night, say 22.8-7.6 = 15.2 f. with 16'x32' of r1 glazing and
a conductance of 16x32/r1 = 512 btu/h-f, we need to supply 78.16x512
= 40k btu on an average night. on a 15.2 f night, we need to supply
heat at a peak  rate  of (32-15.2)512 = 8602 btu/h.

if a 2' diameter x 3' tall vertical 55 gallon drum sits behind 6 ft^2
of glazing, it will collect 0.9x0.9x1000x6 = 4860 btu on an average
day. if the sunspace is 80 f (no more, because any excess heat goes to
heating the attached house) for 6 hours per day and 32 f for 13, the
average daytime greenhouse temp is about 56 f. drum water at temp t
would lose about 10h(t-56)6ft^2/r1 = 60(t-56) btu through the glazing
during the day. 4860n = 60n(t-56)+40k makes t = 137 - 667/n.

each drum has about 25 ft^2 of surface with a 1.5 btu/h-f conductance to
slow-moving air. with free airflow, 8602 = (t-32)25x1.5n makes n = 8.5.
we might stack 8 drums with t = 53.6 f and an average nightly temp swing
of 40k/(8x55x8) = 11 f 4-wide and 2-high behind an 8'x8' layer of glazing
with 2' of smaller water containers on top.


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