Some Notes On The Thermal Calculations
======================================

Simplifications Made And Their Winter Effects
---------------------------------------------

There are a few factors--some trivial and some not--that 
might affect the validity of the calculations; those effects
might be favorable or unfavorable.  Here they are.

One possible negative is the foam insulation, which was
assumed to have a long-term-aged R value of 6.9 the inch.
It used to be specified at 7.14 but has been downrated
recently, for reasons unknown to me.  The 6.9 value was
quoted by an experienced installer; a sales rep mentioned
6.8 or 6.75, so the 6.9 might be a little optimistic.

Another small negative is the heat that will be lost when
the HRV is running.  The HRV has an effective recovery of
about 60% of the heat that would be lost if the flow were
simple infiltration.  The flow when the HRV runs is perhaps
150 or 160 cfm, or about 9,300 cubic feet an hour.  Its net
loss is thus about 2,700 BTUs an hour.  It is unlikely that
the HRV would run more than an hour or, at very most, two
hours a day (shower and cooking time), so the likely loss is
5,000 BTUs or so a day, not a large factor (and controllable
in especially cold snaps).

Yet another small negative is that there is no allowance for
the loss of insulating value owing to any in-wall plumbing
or wiring runs in outside walls.  Well, first, there is NO
plumbing running in any outside wall.  Second, there is but
the minimum electrical wiring needed to supply outlets
numerous enough to meet the insane "Vacuum Cleaner"
requirements of the Electrical Code (which, with the 
built-ins, means none in the west wall).  So this is a 
pretty small negative.

A big favorable factor not considered is that nearly half of
the house west wall is not actually exposed to outdoor air 
at the average outdoor temperature but instead to the tank 
room, at an average temperature about 20 degrees warmer. 
Moreover, the entire exterior west house wall (including the
entrance door) is sheltered from direct outdoor air and so 
might be a degree or a few degrees warmer, plus will have at
least a trivially higher R value (owing to the zero 
windspeed at the wall surface).

Also, no account was taken of the fact that the "attic" 
space (it's not really an attic, but that's where it's 
located) will almost surely be warmer than the raw outdoor 
temperature, and is also wind-protected.  Considering the 
ceiling area, a few degrees difference could mean a bit:
every degree the attic is warmer than the raw outside is 
1,150 BTUs less heat loss.

Another ignored minor possible source of heat gain is the 
east window, which might be unshaded for a couple of hours a
day of sun (10 am - noon, when east sun disappears)--maybe a
1,000 or so extra BTUs if anyone bothers to pull the shades.

A final probable plus is the floor heat loss.  Simply
assigning an R value of 9.2 to bare earth is very
conservative.  The deep-earth (well-water) temperature
should be 50 degrees (it is usually the average annual
temperature--about 48 degrees for Ritzville--plus 2
degrees).  Thus, assuming for simplicity that the slab
itself is essentially transparent to heat, the underslab
temperature is the house temperature, an average of 64
degrees.  That means that if the slab were infinite in
extent, the deltaT across the XPS insulation would be 14
degrees at all points, which implies a 24-hour heat loss
through a house-sized section of slab of 40,873 BTUs,
compared with the calculated 73,640 BTUs for the average
coldest day and 147,281 BTUs for the very coldest day
possible.  Now the slab is, obviously, NOT infinite in
extent and, as everyone knows, the majority of heat loss
occurs at or near the perimeter of a slab; that is because
the ground adjacent to the slab is not at deep-earth
temperature until a depth of 6 to 20 feet.  The true physics
of heat flow through a slab on grade are immensely complex.
Nonetheless, with thick perimeter insulation as is found on
this house, the true loss is almost certainly less--and
probably materially less--than the calculations show.

All in all, one may mentally write the attic off against the
HRV, ignore the east window, and write the floor off against
the possibility of a lower foam R--leaving the warmer west
wall as a substantial error reserve against the rest of the 
negatives.

And, in the tank room, no account has been taken of the fact
that plant lighting would be running about two hours a day
in the winter, generating perhaps up to a couple of thousand
BTUs a day.



Tank-Room Freeze Risk
---------------------

As the calculations show, the 24-hour average temperature in
the tank room on the average coldest day of the year will be
43 to 44 degrees.  With over 3,400 gallons of water in the
room (the 3,000-gallon tank plus eight 55-gallon drums of
water), it requires well over 28,000 BTUs of heat flow to
change the temperature even 1 degree, so the daily highs and
lows will not be far from the daily average.

As the numbers also show, the worst-case 24-hour BTU outflow
from the tank room on the very coldest possible day day will
be about 70,000 BTU.  In reality it would be rather less
since, as heat flows out and the temperature drops, the heat
outflow would slow; but for simplicity, the calculations
show the heat outflow assuming a constant inside temperature
equal to the average-coldest-day value.

Now, as noted above, with over 3,400 gallons of water in the
room, it requires well over 28,000 BTUs of heat flow to
change the temperature even 1 degree.  With the average
coldest-day temperature over 43 degrees, a drop of more than
10 degrees inside would be required to just approach a
freezing temperature.  Thus, the tank room could easily
withstand four consecutive days of the coldest temperatures
ever recorded in Ritzville before getting close to freezing.

And, in the fantastically unlikely event of such a bizarre
cold snap, a mere 1000-watt space heater--a toy--running
constantly could produce about 81,400 BTUs a day, far more
than offsetting the entire daily loss.



House Cooling Notes
-------------------

On the average hottest day of the year, assuming for 
discussion that the sun is 100% blocked by the sunshades, 
the cooling need to offset internal gains (the average 
inside can equal the comfortable 72ø outdoor average) is 
about 86,800 BTUs.  If we assume that air is allowed to flow
into the house throughout the 16-hour shades-up ("night") 
period, and that that air is at an average temperature of 10
degrees below the house temperature, the average flow rate 
needed is about 500 cfm.

We can justify guesstimating that average air-temperature
differential by assuming that the outdoor temperature varies
linearly between the daily high and the daily low and that
the outside is down to the house average (72ø) by the time
the shades are rolled up, about 6 pm., and that it is back
up to the house average by the time they are closed again,
about 10 am.  Under those assumptions, the average outdoor
temperature--the low being 54ø--swings from 72 to 54 and
back to 72, and its average is 61 degrees, which is 11
degrees below the presumed house average.  The assumptions
are pretty loose, but obviously we are at least in the
correct order of magnitude using that guesstimated 10-degree
cooling potential.

To put the values in perspective: 1.0 mph is 88 feet a
second; a doorway is 20 square feet; and so a movement of 
500 cubic feet a minute through an open door signifies an 
average breeze through that door of 0.284 mph, which is very
certainly not much, hardly over a quarter of a mile an hour 
average.  It would appear that with the entry door opened 
fully and a good-quality window fan mounted in the TV Room 
window as an exhaust to pull air into and through the house,
summer cooling should be . . . a breeze.

Even on the worst-case day, only about 1,300 cfm would need
to be moved--a breeze of about three-quarters of a mph.  Of
course, that assumes the same 10-degree cooling potential,
which would not be the case if we still assume an indoor
temperature of 72ø; but at worst the house average rises 
tolerable a few degrees during such a rare heat onslaught.



Tank-Room Cooling Notes
-----------------------

Left to itself, the tank room has no way to void its slow
heat gain in warm months, so it cannot be left to itself. 
By opening the door at night and placing a small vent fan in
the roof of the storage area, we can draw a decent amount of
cooling air through the tank room (which is also beneficial 
to any plants grown there).  That requires an intake vent, 
probably on the south wall somewhere--or an openable window. 
The cooling need is only for a few cfm (10? 15?), so 
changing one of the windows to a casement would suffice; the
extra infiltration loss in winter should not be material.




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