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a cool casa for killer
2 may 2001
suppose our doggie friend killer lives in phoenix, where it's 93.5 f in
august, on average, with an average daily min and max of 81 and 105.9. 

let's build him a 2'x4'x4' tall r32 doghouse from something like 3 layers
of atlas energy shield 1" polyisocyanurate "r7.2" double-foil foamboards
(killer is not a green dog) with 3/4" air spaces between them. the heat
conductance of walls and roof is then 64ft^2/r32 = 2 btu/h-f. suppose the
doghouse is airtight and killer makes no heat of his own. (with extra
credit for fixing those details.)

let's keep the house at 85 f max and 83 min on an average day and assume
the outdoors is 81 f for 6 hours and 93.5 for 12 h and 105.9 for 6 h on
that day (like a modified square wave inverter.) so the average indoor
temp is about 84 f and the house gathers 18h(97.6-84)2 = 491 btu of heat
from the outdoors over 18 hours, with an average 97.6 outdoor temp. 

let's cool some thermal mass in the house with outdoor air for 6 hours
at night and let it warm by 2 f when the house is closed up for 18 h...
2c = 491, so c = 245 btu/f, like 31 gallons of water or 10 ft^3 of rocks.
exposed to 81 f air, it needs to cool from 85 to 83 f in 6 hours, ie
83 = 81 + (85-81)exp(-6/rc), so rc = -6/ln(2/4) = 8.7 h max, with min
conductance 245/8.7 = 28.3 btu/h-f and surface 28.3/1.5btu/h-f-ft^2
= 18.9 ft^2 in still air and 18.9/245 = 0.077 ft^2-f/btu s/v ratio,
like a 10" water pipe or a 3.3' diameter boulder (with 25 btu/f-ft^3
and no internal thermal resistance.) let's stack 32 6"x6"x10" tall
1 gallon plastic milk jugs on 2x8 shelves along one of the 4'x4' walls.

with an average 84-81 = 3 f temp difference over 6 hours, we need an
h foot chimney and a ft^2 vent area, where 491 = 6hx16.6asqrt(h)3^1.5,
according to one empirical formula, ie asqrt(h) = 0.95. h = 4' makes
a = 0.47 ft^2, eg a 2"x4' slot at the base of the jug wall with another
slot at the top of the opposite wall. the upper slot might have a
lightweight one-way plastic film damper over the outside, or we might
install a couple of $12 8"x16" automatic foundation vents with opposed
springs or a pv panel and a battery and a differential thermostat and
a 16.6(0.47)sqrt(4'x3f) = 27 cfm fan.


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