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re: hot water idea
fri, 3 sep 1999
anthony matonak  hits and runs... :-)

> i'll go through this once and then i'm off to other things...
> um, lets see if i understand the math (i might not)...

choost a little high-school algebra...

> area of collection (front glass) 4'x8', aprox 2.9728 sq meters.
> (lets call it 3 sq meters for simplicity sake)
> assuming 1000 watts/sq meter of sunlight, that's about 3kw.
> 1 watt hour is about 3.4144 btu so 3000 watt-hours = 10243 btu.
> so for 28800 btu/day that assumes 2.8 hours of sun.

sounds like the right ball park, altho i also figure that each layer of
absorbs and reflects about 10% of the incoming sun power.

> > with no water flowing, the tank absorbs about 28.8k btu and
> > loses 24h(t-30)40 = 960(t-30) btu over an average day, so
> > t = 30+28.8k/960 = 60 f.

that stagnant water just keeps itself warm, at about the same temperature
for 24 hours a day,
with no night insulation, and it provides no useful hot water for showers,
etc. ohm's law for heatflow
says the heatflow in btu/h is the (f) temperature difference times the
thermal conductance (1/resistance.)
and we assumed that the solar energy that flowed into the box over an
average day was equal to
the heat energy that flowed out, ie ein = eout, ie 28.8k =
24h(t-30)40btu/h-f, ergo t = 30+...

> next, heat loss. to find t (final temp) the formula seems
> to be t = avgtempf + btuin / (btuout_hrs_f * 24hrs).

and btuout increases with increasing box temperature and decreases with more

> for r10 insulation and r1 glass with 40 btu/hr/f this then works
> out to a final temp of 60 f. this is obviously much above freezing
> so that at least is one concern taken care of as long as the tank
> size is large enough that it doesn't swing under 32 f at night.

but some of the pipes might freeze at night, unless they have insulation,
and a cold cloudy week might partially freeze the tank.

> lets see if beefing up the insulation helps matters...
> make it 4 inches of insulation instead of 2 for an r20 walls and
> double glass for an r3 front. 32ft^2/r3 = 10.6, 78ft^2/r20 = 3.9
> total about 15 btu/h-f. for t = 30+28.8k/(15*24) = 110 f.
> this is hot enough for most folks.

sure, if they climb in the tank to take a bath :-) the temperature will be
if we heat some incoming 50 f water... (btw, i figure r2 for two layers
of glass, and 80% solar transmission.)

> lets try those formulas out with 6 inches of insulation (r30) and
> three layer glass giving about r5

or maybe r3, with 0.9^3 = 73% solar transmission?

> 32ft^2/r5=6.4, 78ft^2/r30=2.6, total=9 btu/h-f.
> t=30+28.8k/(9*24) = 163 f.

> now that should be hot enough for anyone...

parboiled people, if they climb into the tank.

> but all that glass could get pretty expensive.

replex polycarbonate only costs $1.25/ft^2 in 49" wide rolls. it's 200x
stronger than glass against hail and children with baseball bats,  and
it can be cut with scissors and has a 10 year light transmission

> lets try another idea. put a mechanical shutter over the glass at
> night (aprox 12 hours) made out of 2 inches of that insulation stuff.
> the same thing as the walls are made out of.

styrofoam. lasts for years with latex paint on the outside. but the shutter
might not,
in wind and snow, and it is likely to have lots of air leaking around the
cracks at the edges,
and who wants to operate it twice a day? a bubblewall might help here... i
figure "night"
lasts 18 hours in phila in january, btw.

> heat loss at night would
> be 110ft^2/r10 = 11 btu/h-f in place of 40 btu/h-f during the day.
> i don't know the formula for calculating this but i'd think you're
> going to get more than 60 f out of it.

ein = 32ft^2x1000btu/ft^2/dayx0.73transmission = 23.4k btu.
eout = 6h(t-30)32ft^2/r3 (for the glass, during the day)
       + 18h(t-30)32ft^2/(r3+r10) (for the glass, at night)
       + 24h(t-30)78ft^2/r10 (for the rest of the box, all day.)

ein = eout ==> 23.4k = (64+44.3+187.2)(t-30), so t = 109.2 f.
i'd add more back and side insulation. and make the water move...

> how about instead putting up two 'wings' of reflectors like foil or
> mylar outside the glass, each the same size at x degrees so that
> they effectively double the energy collection during the day.

sounds better, but foil degrades in the weather. maybe white painted
more heat gain, less loss: 46.8k = 295.5(t-30), so t = 30+46.8k/295.5 =
theoretically-speaking, but reradiation begins to rear its ugly head, at
these higher
temperatures, vs the lower temps where glazing r-values are usually

> the temps will get higher in the afternoon it might be enough.

that's another little improvement. the 24 hour average temp in phila in
january is about 30 f,
but the average daily max is about 38, so we might figure the box is exposed
to an average of 34 f
during the day (when it is less well-insulated), and a bit less than 30 f at
night, when it is better insulated.
to be honest, we could pick the 18-hour night temp to make the 24-hour
average 30 f again.

> if we go with r30 walls and keep the r1 glass front and use the
> reflectors to (about) double the collecting then heat loss would
> be 78ft^2/r30=2.6, 32ft^2/r1 = 32, total 35, t = 98 f.
> not enough of a difference to really matter is it?
> ok, double paned glass with r3, and r10 sidewalls, with the above
> reflector.... 78ft^2/r10 = 7.8, 32ft^2/r3 = 10.6 = 19 btu/h-f.
> t = 30 + 57.6k/(19*24) = 156 f.  this sounds like it could
> work pretty well and still be inexpensive. might even get too
> hot in the summer but i guess you could always shade the reflectors.

some numerical fooling around helps get the proportions right...

> > say we preheat enough 50 f water for 6 110 f 3gpm 10 minute showers per
> > ie 180 gallons per day, so 28.8k = 960(t-30)+180x8(t-50), and t = 54

aha, moving waters! let's try this with 2:1 side mirrors (say se and sw so
don't block much of the winter sun), double-glazing, no night shutter, and
4" of foam
on the back. say we collect  48.6 btu/day of sun. the thermal conductance of
the box
is 32ft^2/r2 = 16 btu/h-f+ 78ft^2/r20 = 3.9, about r20 total. if ein = eout
heating 180 gallons of water from 50 to t degrees f),

46.8k = 24h(t-30)20btu/h-f + 180x8(t-50), so 1920t = 133200, and t = 69.4 f.
hooboy. cold showers, without a post-heater...

but better than before. the tank provides 180x8(69.4-50) = 27.9k btu/day of
useful heat,
32% of the water heating energy... at 70 f, it still might work better

> > this arrangement might work better in an attic, with a long "tank" (a
> > 30' long x 4" diameter black-painted pvc pipe, with a 3/4" copper
> > pressurized pipe inside?) along the ridge line, and a transparent
> > south roof, and a concentrating parabolic reflector below the tank, and
> > foil-faced foam above the tank, which extends down below
> > the tank bottom to make a secondary concentrating reflector...
> >
> > the tank might be suspended from ropes, and swung north and south to
> > the sun, with a high concentration ratio. nielson's
> > (253) 941-7281 aluminized mylar film costs about 15 cents/ft^2 in
> > rolls. it lasts for years indoors, and can be "glued" to curved masonite
> > scored foil-faced foamboard with a roller and axle grease, says duane
> > johnson, who reports it's sufficiently mirrorlike
> > for 100:1 concentration.
> i don't think we need to get that complicated (and dangerous) for
> just some hot water.

but we could heat a whole house that way, with a few large insulated poly

or make electricity (wow!) it only takes 6:1 to make steam... okokok. for
house heating, 3:1 seems fine, and maybe a 4' wide galvanized water trough
lined with epdm rubber as the target, vs a moving target, with a layer of
foamboard above it. let's see: a 24' wide house with a 1:1 pitched roof
and y^2 = 4 fx makes f = 1.33' if  y = 8' when x = 12'. that would still
collect lots of summer sun for hot water if the parabola were aimed at
the horizon for good winter collection... and houses need roofs anyhow,
and we could use the space under the parabola for storage... and skateboard
on the parabola.


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