re: not needed--pyjamas SOLAR.KnowledgePublications.com

re: not needed--pyjamas
16 dec 2001
a@here.com wrote:
 
>...we turn the furnace off every night, even if it is minus 40 outside.
>even the cat comes creeping under the covers. meanwhile, our neighbours
>are ranting and raving about their high heating costs.

we might improve that savings significantly. we can't make it colder than
32 f without freezing the pipes, and most houses have long time constants 
(at least 8 hours), so they don't cool off much overnight... 

an 8' r16 cube with 1/2" drywall inside has a natural time constant rc
= r16/(6x8'x8')x6x8'x8'(0.5btu/f-ft^2) = 8 hours. if it's 70 f at 8 pm and
40 f by 8 am, (40 = t +(70-t)exp(-12/8), so it was t = 31.4 f outdoors),
it loses dtc = (70-40)6x8'x8'(0.5) = 5760 btu overnight. quickly heating
the drywall back to 70 f at 8 am replaces that heat. 

keeping it 70 f for 12 hours takes 12(70-31.4)6x8x8/r16 = 11,117 btu, so
we use 11,117+5760 = 16,877 btu with the night shutoff. making it 70 f for
24 hours takes 22,234 btu, so we saved 100(1-16,877/22,234) = 24% of the
heating energy. 

now suppose the inside is covered with foamboard with very little thermal
mass, eg 1" of 2 lb/ft^3 polystyrene with 0.29 btu/f-lb, ie 0.58 btu/f-ft^3
or 0.048 btu/f-ft^2. c = 6x8x8(0.048) = 13.92 btu/f and rc = r16/(6x8x8)xc
= 0.77 hours, so the cube is 31.4+(70-31.4)exp(-12/0.77) = 31.400000658 f 
after 12 hours, very close to the outdoors after about 16 time constants.
it only loses (70-31.4)13.92 = 537 btu overnight, so it uses 11,117+537
= 11,654 btu over 24 hours, and we save 100(1-11,654/22,234) = 48% of the
heating energy. 

but wait! we might use foil-faced board, or a more durable shiny surface.
that reduces the human heat loss by radiation, so we can be equally comfy
with a lower room air temp during the day. say humings with 20ft^2 of 93 f
skin and r1 insulation lose 4se540^3(93-t) btu/h by radiation and 20(93-t)
btu/h by convection to a t f room with walls with emissivity e, where s is
the stefan-boltzman constant, 0.1714x10^-8. they would be equally comfy in 
a 70 f room with e = 1 (normal) walls or a t f room with e = 0.05 (shiny)
walls when 4s(1)540^3(93-70)+20(93-70) = 4s(0.05)540^3(93-t)+20(93-t), ie
t = 68.8 f, not a big difference, but an additional energy savings.

if it's -40 outdoors, we could save more by moving the sink and toilet
traps to the basement and using some sort of freeze-proof faucets...

nick