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storing overnight solar heat from windows
15 mar 2004
dan chiras writes:

  when sizing mass in relation to solar glazing, remember that the first
  7% of the glazing [in proportion to square feet of floor space] in
  a passive solar home is accommodated by incidental thermal mass,
  such as gypsum wall board, framing, floors, and furniture. 

  when glazing exceeds the 7% value, additional mass is required.
  three glass-to-mass ratios are useful... 

  the first ratio relates solar glazing to floor mass in direct
  contact with sunlight... each square foot of solar glazing over
  the 7% mark requires 5.5 square feet of _uncovered_ and sunlit
  (directly illuminated) floor mass.

  the second ratio relates solar glazing to floor mass not in direct
  contact with incoming solar radiation, but in the same room...
  40 square feet of uncovered and "unlit" mass accommodate one square
  foot of solar glazing. (the efficiency of floor mass falls off
  dramatically when it is covered by carpeting.)

  the third ratio relates solar glazing to wall mass. in a room being
  warmed directly by sunlight, you'll need 8.3 square feet of wall mass
  for each square foot of solar glazing over the 7% limit. according to
  the sunstainable buildings industry council, it doesn't matter whether
  the wall mass is directly in contact with the sun or not. however,
  not all experts agree with this assessment, noting that wall mass in
  direct contact with sunlight absorbs more heat. 

  both floor mass and wall mass should be four to six inches thick.
  any thicker, notes the sbic, and the mass has little effect in
  absorbing more heat. once again, some designers disagree and call for
  much thicker mass to provide greater thermal stability and longer
  periods of solar heating between recharges [sic]... 

          from pages 102-104 of "the solar house," chelsea green, 2002.

some sbic (formerly psic) members really like bricks and concrete:

  although all the members of psic, especially the technical committee,
  contributed to the financial and technical support of the guidelines,
  several contributed far beyond the call of duty. stephen szoke, director
  of national accounts, national concrete masonry association, chairman of
  psic's board of directors during the development of the guildlines; and
  james tann, brick institute of america, region 4, chairman of psic's
  technical committee during the development of these guidelines... gave
  unstintingly of their time, their expertise, and their enthusiasm. 
         from the acknowledgements section of the 1995 edition of the
	 passive solar design guidelines for homebuilders for philadelphia,
	 by the passive solar industries council, national renewable energy
	 laboratory, and charles eley associates.
suppose we want to keep an 8' cube about 65 f over an average 30 f december
day in phila, when 1000 btu/ft^2 of sun falls on a south wall, using a 4'x8'
r2 window with 80% solar transmission. with 6 walls with us r-value r and 
0.8x4x8x1000 = 25.6k btu/day = 24h(65-30)(32ft^2/r2+(6x64-32)/r), r = 24.3
and g = 30.5 btu/h-f, more than half window loss...

with a 32 ft^2 window, vs 4.5 ft^2 (7% of the 64 ft^2 floorspace), sbic
guidelines prescribe (32-4.5)5.5 = 151 ft^2 of uncovered daylit concrete
floor, 6" thick, or (32-4.5)40 = 1100 ft^2 of carpeted concrete or brick
floor, 6" thick, ie 550 ft^3 of concrete inside the 512 ft^3 cube...
some engineers call this "a five-pound bag problem" :-) 

if sun arrives over 6 hours at a constant rate of 25.6k/6h = 4267 btu/h,
and the cube has no thermal mass, we have an equivalent circuit like this
(viewed in a fixed font): 

             ti = 30+4267/30.5 = 170 f for 6 hours, and
      ---    |
 |---|-->|---*---www--- 30 f      30 f for the rest of the day.  
      ---       1/30.5             
   4267 btu/h                     uncomfortable. 

with enough short-time-constant thermal capacitance c around the room in
the shade, we can limit the max temp to 70 f, if it's 60 f at dawn...

             ti = 70 max = 170+(60-170)e^(-6/(c/30.5))
      ---    |
 |---|-->|---*---www--- 30 f 
      ---    |  1/30.5                   
   4267 btu/h| 
            --- c = -183/ln((70-170)/(60-170)) = 1,920 btu/f. 
we might stack 1920x16/12 = 2560 12 oz beer cans (427 6-packs in 44 ft^3,
with 838 ft^2 of can surface) around the room. a 2.5" diameter x 4.75" tall
can with 0.327 ft^2 of surface and a still airfilm conductance of 0.327x1.5
= 0.49 btu/h-f would have rc = 12/16btu/f/(0.49btu/h-f) = 1.53 hours.

if the top edge of the window is 4' above the floor, direct sun will cover 
the 64 ft^2 floor at noon on 12/21. if the cube air is 70 f when the floor
temp t = 70 + (70-30)30.5/(1.5x64) = 82.7 f, after 6 hours...

                                                     close switch
             t = 82.7  70 f max                        at 9 am. 
      ---    |         |                                  .
 |---|-->|---*---www---*---www--- 30 f  -      ---www---.  ---*- t  
      ---    |  1/(1.5x64) 1/30.5       -     |  1/23.1       |
   4267 btu/h|                          -     |               |
            --- c  thevenin equivalent-->    --- 214 f       --- 64c
            ---                               -              ---
             |                                |               |
             -                                -               -

82.7 = 214+(60-214)e^(-6/cbtu/f-ft^2x64ft^2/23.1btu/h-f-ft^2) makes c
= -2.17/ln((82.7-214)/(60-214)) = 13.6 btu/f-ft^2, ie 6.5" of concrete
for a total slab capacitance of 870 btu/f, vs 1920 for the beer cans,
since the concrete stores more heat with a larger temp swing, charging
from about 60 to 82.7 vs 70 f. but concrete has thermal resistance. we
might do better with 5.1" thick fish tanks on all the windowsills with
darkened water inside. thermally similar to the slab, with half the
surface losing heat from both sides. 

as an alternative, the window might store heat in a 8'x2' tall "thermal
counter" with a transparent south wall along an east-west line 4' north of
the window. on 12/21 at noon, beam sun from the upper edge of the window
would touch the top of the counter. at the same time, a mirrored floor to
the south of the counter could reflect sun up from the lower edge of the
window to the countertop. this 2:1 solar concentration and insulation
over the north wall of the counter could make heat storage very efficient.

                                                     close switch
             t = 146   70 f max                        at 9 am. 
      ---    |         |                                  .
 |---|-->|---*---www---*---www--- 30 f  -      ---www---.  ---*- t  
      ---    |  r1/16ft^2 1/30.5        -     |  1/10.5       |
   4267 btu/h|                          -     |               |
            --- c  thevenin equivalent-->    --- 436 f       --- 16c
            ---                               -              ---
             |                                |               |
             -                                -               -

146 = 436+(60-436)e^(-3.94/c) makes c = -3.94/ln((146-436)/(60-436))
= 15.2 btu/f-ft^2, eg 2.8" of water, for a total counter capacitance
of 243 btu/f vs 870 for the lower-temp fish tanks. with more water depth,
eg about 10" for horizontal 2-liter bottles, the counter might store heat
for more than one day, with a thermostatically-controlled panel near the
top of the north wall that opens and closes to regulate room air temp. 

as another alternative, we might move the window up to the top of the cube
and add a 4'x8' external horizontal lightshelf to double the sun that enters
the window and reduce its size from 4'x8' to 2'x8' and lower the cube's
nighttime and cloudy-day thermal conductance and heat storage requirement.
in this case, the "thermal counter" would be only 8' wide x 1' tall, with
the base on an east-west line 2' north of the window and 6' above the floor
and two suns on its south wall, one from a 2'x8' lightshelf to its south.
it would intercept all the beam sun from the window on 12/21. an equal amount
from the external lightshelf would spread over the entire ceiling, which
might have some thermal mass of its own. for more on lightshelves, see 

warm thermal mass near the ceiling (vs cooler and lower mass) can allow
better room temp control and deeper night setbacks and reduce the need for
stored solar heat. a thermostat and slow ceiling fan or reflective louvers
("deep space coolers" in nasa terms) might control room air temp. a high-
performance cube might have a thermosyphoning air heater over the insulated
south wall and ceiling mass, with no window. with r-value r walls, it needs 
a min ceiling temp tmin (f) = 60+(60-30)6*64/r/(1.5/96) = 60+120/r at dawn.
on an average day, with tb air in the heater, 25.6k btu = 6h(tb-30)64ft^2/r2
+ 18h(65-30)64ft^2/r + 24h(65-30)5x64ft^2/r makes tb = 163.3-1610/r, where
tb = (tmax-tmin)/2, and keeping the cube 65 f on an average day requires 
309120/r btu, so we need (tmax-tmin)64ft^2c = 309120/r, ie a ceiling thermal
capacitance c = 23.4/(r-14.4) btu/f-ft^2, eg 3" of water, with r16 walls.

keeping the cube 65 f for 5 cloudy days in a row requires c = 244/(r-14.4)
btu/f-ft^2, eg 3" of water, with r30 walls, if i did that right, or less, if
there's any internal electrical usage. 

windows are bad news, thermally-speaking. they are poor insulators, compared
to walls, and they tend to ruin perfect thermal envelopes. they are expensive
and complicated to install. can we live without their architectural drama?

a house of the future might have no windows at all. it might have insulated
doors for fire egress and fans for ventilation and nice, efficient, electric
lighting and a closed circuit tv camera projecting a view of the outdoors on
a large interior wall, with web cam sources for other views. virtual reality
(touring the louvre or hiking in new zealand) would cost extra. 


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