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re: ...geodesic dome questions
8 nov 2003
alec chiasson  wrote re:

>...a geodesic dome home.  has the solar closet been modified for such a
>structure? i am assuming the structure will consist of a dome about 28 ft
>in diameter, supported on a riser wall of 3 ft.

a 28' hemisphere with 2pi14^2 = 1232 ft^2 of surface on top of a 3' cylinder
with 28pi3 = 264 ft^2, totaling 1496 ft^2? or floating on a 28'x4' deep
swimming pool, tracking the sun with a system of ropes and pulleys attached
to sunflowers in a sunspace :-)

>...after visiting this site
>http://www.ibiblio.org/ecolandtech/links/start-392001/msg00413.html ( the
>thermal cistern and the solar closet ) i am wondering about the
>effectiveness of a solar closet in canada (say, 43-45n lat ), and the
>comparative feasibility of a thermal cistern.

"thermal cisterns" seem like poor performers, with too much thermal resistance
in the sand, which stores less heat than water by volume and is spread out and
hard to insulate, compared to a box with a lower surface-to-volume ratio, and
it's harder to get solar heat into water than air. they would work better with 
water flowing through the sand itself rather than water in pipes. this needs 
a waterproof "tank," but the sand could support a wood floor over a vapor
barrier, if the water isn't too deep. how would we heat and insulate it and
distribute the heat as needed? john paul jones of seco (the great^n grandson
of the john paul jones) suggested something like this 30 years ago, with 70 f
water circulating among large sand planters and heat pumps made from water-
cooler compressors in every room. 

the solarium workbook (nrc, 1981) has long-term average weather data for 

                           dec               jan   
		      temp sdd  sun     temp sdd  sun

fredericton, nb      -6 c  82   2127   -9 c  97   2811 wh/m^2-day
moncton, nb          -5         1895   -8    67   1888
halifax, ns          -1    79   1650   -3   102   2341
charlottetown, pei   -4    77   1838   -7   108   2914

>i'd like to be able to figure out the "thermal mathematics" of a structure,
>just like nick pine does.

he often starts by finding the "worst-case month" for solar house heating,
with the least "sun per degree-day," a metric from norman saunders, pe, who
divides the amount of solar energy that falls on a south wall on an average
day of the month by the indoor-outdoor temp diff, eg sdd = 1888/(20-(-8))
= 67 for moncton in january, the worst-case combination above. december in
moncton is clearly easier, with more sun and a higher outdoor temperature.

then we convert to quaint us units, from -8 c to 18 f and 1888 wh/m^2-day
to 598 btu/ft^2-day, and realize this is very cold and cloudy, not a nice
climate for solar house heating. 

then we imagine the dome has two floors and an attic and 96 ft^2 of r4
windows with 50% solar transmission, with 48 ft^2 facing south and 24 east
and 12 north and west. if the dome itself has r30ish insulation, eg 2"
styrofoam outside 6" fiberglass, or 8" sips, or plywood panels made from
9.5" i-joists with cellulose fill, so its thermal conductance is 96ft^2/r4
= 24 btu/h-f (24 buhfs) for the windows plus 1400/30 = 47 for the "walls"
plus 30 buhfs for 30 cfm of air leaks (with 30cfmx60/7594ft^3 = 0.24 air
changes per hour, a very tight structure), totaling about 100, so it needs
about 24h(65-18)100 = 113k btu on an average january day. a frugal 600 kwh/mo
of indoor electrical use could provide 20 kwh/day (68.2k btu/day) of this.
it needs 5(113k-68.2k) = 224k btu for 5 18 f cloudy days. 

the solarium workbook says a horizontal surface receives 1164 wh/m^2-day
(369 btu/ft^2-day) of sun, and east and west windows get 908 wh (288 btu) in
january in moncton, so the windows collect about 0.5x12(4x598+3x288) = 19.5k
btu on an average day. subtracting this and the electric heat from the daily
heat requirement, we need an additional 113k-68.2k-19.5k = 25k btu/day of
solar heat. this might come from thermosyphoning air heating panels, eg dome
triangles with polycarbonate glazing over an air gap and dark window screen
as a mesh collector with 70 f air near the glazing and r30 insulation behind
the screen, or a transparent skirt over the southern part of the 3' cylinder.

a square foot of r2 air heater glazing with 80% solar transmission might gain
478 btu over 6 hours on an average day. with 70 f air near the glazing, it
might lose about 6h(70-18)1ft^2/r2 = 156 btu, for a net gain of 332 btu (not
much), so the extra heat might come from 25k/332 = 78 ft^2 of air heaters, eg
a 4'x25' skirt around a 4' stemwall, if the floor is 4' above the ground.
higher heaters might avoid reverse thermosyphoning at night with automatic
foundation vents, or thermostats and motorized dampers. 

on an average day, the dome needs to store about 18h/24h(113k-19.5k) = 70k
btu of overnight heat. with a 70-60 = 10 f day/night temp swing, we might
store this heat in a 7k btu/f thermal capacitor with a low series resistance,
eg 1400 hollow 5 btu/f concrete blocks in an 8'x8'x16' column or a 4'x4'x16'
column with 4" thinwall pvc water pipes threaded through holes in 561 blocks.

as an alternative, we might let 100 f air-heater air pool under the first
floor ceiling, with something like a 100-80 = 20 f temp swing and 3500 btu/f
(55 ft^3) of water in poly film ducts in the ceiling. if the ceiling has
pi(14^2-5^2) = 527 ft^2 of surface, the water would be 1.2" deep. 

we might store cloudy-day heat in an 224k/(130-80) = 4480 btu/f (70 ft^3)
well-insulated water tank that cools from 130-80 f over 5 cloudy days and
provides hot water, with the help of a 97% greywater heat exchanger. with a
4' stemwall, the attic floor could have pi(14^2-12^2) = 163 ft^2 of surface. 
a draindown floor under an r2 roof with 80% solar transmission might gather
0.8x163x369 = 48k btu/day of sun and lose 6h(t-18)163ft^2/r2, which makes
t = 116 f, or more, since daytime average temps are warmer than 24-hour temps,
and in cloudy climates, most of the btus arrive in a few hours per week of
beam sun, "gift-wrapped" for minimum heat loss and possible concentration,
according to pe howard reichmuth.

you can find more thermal math in the 2000-page archive at
http://www.ece.vill.edu/~nick, which also has a pdf of the
nov/dec 2003 solar today story "soldier's grove soldiers on."

nick

   it's a snap to save energy in this country. as soon as more people
   become involved in the basic math of heat transfer and get a gut-level,
   as well as intellectual, grasp on how a house works, solution after
   solution will appear.
                                     tom smith, 1980




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