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solar heating a mobile home on stilts
25 feb 1999
there's a newish single wide mobile home by a creek near me sitting
about 11' off the ground on top of 14 concrete block pillars on 10'
centers, 7 under each of the twin i-beams. it was lifted there with
a crane to satisfy a flood plain requirement, which also requires
allowing the creek to flow under the house when flooded. they might
have used 4 fork lifts instead, i guess, or hauled it up into some 
trees with winches. 

it's not very hurricane proof, but the location is very unwindy. it
has a wide set of open wooden stairs going up to the door. the only
thing underneath is a doghouse and a couple of big propane tanks.

this home might be more simply solar heated than one on the ground.
the long way runs east-west, but the neighbor's home shades the area 
where the pillars are...

suppose we made the pillars just 8' high, with wire fencing on both
sides, and filled the 2' gap with bags of leaves to make an r36(?) skirt.
some foamboard over the pillars might avoid thermal short circuits. we
might make an inexpensive quarter-cylindrical plastic film housewarmer 
along the south side, 8' tall x 8' wide x 72' long. the floor could be
playground mulch over black plastic film on the ground.

a 14x72x8' tall us r11 home with 100ft^2 of r2 windows that leaks 0.5
air changes per hour has a heat conductance of 14'x72'/r11 = 92 btu/h-f
for the ceiling, 50 for the windows, 125 for the walls, and 0.5x14x72x8/55 
= 73 btu/h-f for the leaks, a total of 340 btu/h-f, so keeping it warm
on a 30 f day takes 24h(70f-30f)340btu/h-f = 327k btu.

we might collect solar-warmed air from the housewarmer and store 1635k
btu in sealed containers of water inside the skirt to keep the home warm
for 5 cloudy days in a row. with water cooling from say, 120 to 80 f,
we need a thermal capacitance c = 1635k/(120-80) = 40,875 btu/f, ie
40,875 pounds of water, eg 91 55 gallon water drums with some wrapped
in stone gabions to increase the surface, or about 360 linear feet of
8' high x 3" thick solviva-type waterwalls. 

january is the most difficult month for solar house heating near
philadelphia. the average temperature is 30.4 f according to the
national renewable energy laboratory (nrel.) on an average day,
1,000 btu of sun falls on a square foot of south wall and 620 falls
on a horizontal surface, with a standard deviation of 42.

the south wall of the housewarmer might collect about 8'x72'x1000x0.9
= 518k btu of sun on an average january day (more if it has a frozen
pond to the south.) the south half of the roof might collect another
322k, a total of 840k btu per day, 513k btu more than the home needs.
the housewarmer might be made with 12' wide plastic film with a solar
transmission of 90% and a us r-value of 0.8.

on an average 6 hour solar collection day in january, we'd have

513k btu = 6h(t-30f)12'x72'/r0.8      for the south wall during the day
        + 18h(t-30f)12'x72'/r36.8     for the south wall at night
        + 24h(t-30f)800ft^2/r36       for the other skirt walls
	 = 7436(t-30), 
so     t = 30+513k/7436 = 99 f. 

not very warm. let's add another layer of r1 polycarbonate glazing over
an air gap over the south side of the skirt. then we have two temperature
zones, a housewarmer temperature tg during the day and a temperature tc
inside the skirt, which doesn't change much over an average day. the skirt
gains 518kx0.9 = 467k btu of sun that shines in through the housewarmer
glazing, then in through the skirt glazing, and the thermal store loses
245k btu of heat to the house at night, leaving 221k, so 

221k = 6h(tc-tg)8'x72'/r1            south skirt, daytime 
    + 18h(tc-30)8'x72'/r37           south skirt, nighttime 
    + 24h(tc-30)800ft^2/r36          other skirt walls, and 

245k = 4269tc - 3456tg (1).

the housewarmer gains 322k btu during an average day, and 82k of that
keeps the house warm for 6 hours, leaving 240k, so

240k = 6h(tg-30)12'x72'/r0.8         heat loss to the outdoors
     - 6h(tc-tg)8'x72'/r1            heat gain from skirt glazing, and

434k = 9936tg - 3456tc, so tg = 43.7 + 0.348tc (2).

substituting (2) into (1) gives

245k = 4269tc - 151k - 1202tc, so tc = 129 f. tg = 88.6 f, from (2).

collecting 245k btu of heat over 6 hours, ie 41k btu per hour from warm
air with a 10 f temperature difference means moving about 4100 cfm,
which might come from a couple of $26 grainger 4ch71 20" box fans used
to exhaust air from the south side of the skirt, with some return holes
at the top with one way plastic film dampers to prevent reverse airflow
at night. the fans can each move 2100 cfm at 87 watts on low speed, so
they would consume 2x87x6 = 1 kwh of electrical energy per day. the
system cop might be 327k/3.41/1000 = 92, vs 3 for a typical heat pump.

with an uninsulated floor, 327k/24h = 13.6k btu/h of heat might flow
with a skirt/room air temperature difference of 13.6k/(14'x72')/r1
= 13.5 f. a few holes in the floor with small fans or $11 automatic
foundation vent registers with bimetallic springs could reduce this
temperature difference and better regulate the home air temperature.

the housewarmer might also be used to grow plants, and it might have
an in-ground pond on the north side to store rainwater (an average of
about 80 gallons a day in pennsylvania.) part of the space under the
home might be a sawdust "compost furnace" that provides more backup
heat and recycles water and takes care of sewage treatment. the top of
the home might have an insulated water tank connected with a warm water
convection loop to something like zomeworks big fins or some pvs with
hydronic heat sinks near the housewarmer ceiling for solar hot water.

it still seems to me that heating bills matter more to people who live
in mobile homes than people who live in million dollar homes, and they
might better appreciate having more floorspace, and they might have
fewer rigid ideas about what houses ought to look like. 

nick




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