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re: lowered thermostat - was: cheap ways to save heat this winter???
1 oct 1998
kevin wrote:
>is there a way to measure (2)? or perhaps a rule of thumb?
one might measure the setback savings by looking at average outdoor
temperatures and monthly electric and fuel bills...
one might predict the savings with various rules of thumb
with various levels of detail:
1. the simplest is to assume that when one turns down the thermostat,
the house instantly cools to the lower temperature, and the energy
needed to keep it warm during the setback period is proportional to
the lower indoor-outdoor temperature difference. this overestimates
the savings a lot.
2. next, one might assume the house has a typical thermal mass of
10k btu/f and a typical thermal conductance of 500 btu/h-f and a linear
temperature decrease during the setback period: i delta t = c delta v,
in electrical terms, so the house temp decreases after h hours by about
500btu/h-f(ti-to)h/10,000btu/f degrees f towards the limiting lower
setback temperature, where ti is the initial indoor temp and to is the
constant outdoor temp (say the long term local monthly average temp.)
for instance, if one turns down the thermostat in this typical house
from 70 to 50 f for 8 hours when it's 30 f outdoors, it cools about
500btu/h-f(70f-50f)8h/10,000btu/f = 8 f to 62 f. the average temperature
over that period is about 66 f. with no setback, the fuel consumption
is about 8h(70f-30f)500btu/h-f = 160k btu (1.6 gas therms, burned 100%
efficiently.) with the setback, it uses 8h(66f-30f)500btu/h-f = 144k btu,
a 10% savings, vs the 50% savings predicted with rule of thumb 1.
3. one might measure or calculate the thermal conductance and thermal
mass of the house, and use that in rule of thumb 2, vs using values
for typical houses. to measure thermal conductance, look at past fuel
bills and degree days or outdoor temperatures. to estimate thermal mass,
measure how fast the house cools on a cold day with the furnace off.
if the house thermal conductance is g btu/h-f and it cools dc degrees f
in h hours with an initial indoor-outdoor temperature difference of
dt degrees f, the thermal mass is roughly dtgh/dc btu/f. calculating
thermal conductance is mostly a matter of dividing each exterior surface
in square feet by its r-value and adding up the quotients. calculating
thermal mass is mostly a matter of adding up the thermal mass of the
house furnishings and all the house interior surfaces. for instance,
a 32x32x8' tall house might contain 2,000 ft^2 of 1/2 drywall with a
thermal mass of 1,000 btu/f.
this is all getting around to the natural rc "time constant" of a house,
the product of its thermal resistance and capacitance, rc or c/g, which
is the amount of time it takes a house to cool from some initial indoor-
outdoor temperature difference to 63% of that value. houses with long
time constants change temperature slowly, so short term setbacks don't
save much energy. charles wing likens the time constant to the amount
of time it takes for water to leak out of a bucket with a hole in it.
the size of the bucket corresponds to the thermal mass. the size of the
hole corresponds to the thermal conductance, the inverse of the thermal
resistance. a well-insulated masonry house has a long time constant.
a poorly-insulated wood frame house has a short one.
nick
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