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a solar cave
sun, 30 oct 1994
rex roberts talked about caves dug into south-facing hills... 

suppose cavepersons had had glass:

                    .         ^
                     .        | up
                      .        
     r10 earth at      .        south ==>
         55 degrees f   .
                         .
                        / g    if the enterprising caveperson had insulated
            rc         /   g       the inside of the cavern with leaves and
    ------------------g  w  g       mud, until, say, rc = 10, and the daytime
   |                  .----- .       temp of the cavern had been 65 degrees f
   |  20 x 20' cavern |       .       and the nighttime temp had been 55, and
   |     10' tall     |        .       he or she had desired to warm the cave 
   |                  |         .       for, say, 5 days without sun, with an
    --------rf--------           .       average sunnytime steady-state floor
   |vaulted -- stone  |           .       temp of, say 90 f, and mammoth skins
   |   -----  -----   | t          .       piled on top of the floor to make
   |---   floor    ---|             .       a sunny day r-value of rf (which
        .                .           .       skins could be moved aside to 
             .             rc .   .   .       decrease the r-value of the floor
                 .                     g       during sunless times), how much 
note that since      .rc                g       glass area, ag, would have been
the upper edge of the    .               g  ag   needed, and what would rf and 
glass is lower than the      .            g       the average floor thickness t
bottom of the floor, the floor   .aa       g        have had to have been, 
stays warm during sunless times,     .      g        ignoring the clerestory
because of this igloo-like heat trap.    .   g        cave window, w?
(how did the caveperson insulate around     . g   
the edge of the floor?)                        g        south ==> 
                                                .
the daily heatloss of the cavern would have been . 
                                                  . 
    lday = (8 hours)(1200 ft^2/r20)(65-55) ~ 5k btu.       32 f outside temp
                                                    .
during sunny times, the sun would shine onto the     .
absorbing surface aa, assumed equal to ag, and some   .
heat would be lost thru rc to the earth underneath...  .
                                                        .
the daily net heat resulting from each square foot of    .
glass might have been on the order of                     .
                                                           .
    eg = 1000 - 8(90-32)/r1 - 8(90-55)/r20                  .
         sun    glass loss    absorber back loss             .
       = 500 btu/ft^2/day                                     .
                                                               .
so keeping the cavern warm might have required only about       .
10 ft^2 of glass... a 3.16 x 3.16' single-glazed window, or      .
an early sliding-glass door...                                    .
                                                                   . 
the mammoth-skin floor resistance would want to have been about     .
                                                                     .
    rf = (90-65)(400 ft^2)/(5000/8) = r-16.                           .
                                                                       .
    during sunless days, the skins would be moved around or a trapdoor  .
    in the floor would have been opened to reduce this, to get more heat .
    out of the floor...                                                   .
                                                                           .
assuming the floor would have had a minimum r-value of 1, per square foot   .
(both sides), the required heat transfer rate would have been about 5000/8   .
btu/hour, from 800 ft^2 of floor, which leads to a minimum temperature        .
differential, after 5 days, of about 1 degree f.

so if the masonry had held about 22 btu/ft^3/degree f, the floor thickness
might have wanted to be about 

    t = (5 days)(5000 btu/day)/((90-66)(22)(400 ft^2)) = .12'

    hmmm. ferro-cement...

other improvements might include making the whole thing above ground, including
some throwaway diet-pepsi bottles filled with water in the floor, making the
absorbing surface a parabolic reflector, and making the floor a wall.

nick pine (nick@ece.vill.edu)




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