Subject: Cooling a house with ice

From: [email-masked] (Nick Pine)
Date: 15 Jul 1995 11:34:54 -0400

It's 85 F so far here today, and it's supposed to hit 100...
How much ice does it take to keep a house cool in the summer?

Suppose it's a completely shaded two-story house, 32' on a side, 16' tall,
with R20 walls and R40 ceiling, and 20% of the walls have R2 windows, and the
house leaks 1 air change per hour, and two people live in the house, and use
500 kWh/month of electricity, ie 500 kWh/30 days/month/24 h/day = 700 Watts,
all of which goes into heating the house, so the house itself is heated in
summertime by about (2 people x 100 W + 700 W) x 3.4 Btu/W = 3K Btu/hour. 

The thermal conductance of the house is the sum of each area divided by its
R-value. The walls contribute 4 x 0.8 x 512 ft^2/R20 = 82 Btu/hour/F, and
the windows 4 x 0.2 x 512/R2 = 205 (more than twice as much heat gain, even
with no sun...) The roof only adds 32' x 32'/R40 = 26 to that number, and
the volume of the house is 32' x 32' x 16' = 16384 ft^3, so air infiltration 
adds another 16384 ft^3/55 ft^3/Btu/F = 298 Btu/F, the biggest heat gainer
of all. The total above is about 600, so when it's 100 F outside and 80 F
inside, it takes (100-80) x 600 = 12K Btu/hr to keep the house cool, plus the
3K of internal heat gain in the house, ie 15K Btu/hr total, ignoring humidity.

It takes about 144 Btu/pound to melt ice, and warming the water from 32 F
to say, 72, requires another 40 Btu. Say 200 Btu/lb in round numbers. So
each hour of summer AC requires 75 pounds of ice to begin with, ignoring the
heat leaks to the ice battery itself. A month of AC requires 30 x 24 x 75
pounds of ice, 54K pounds or 27 tons, with a volume of 54K/62 = 870 ft^3,
a cube 9.5 feet on a side, not counting insulation, or a 32' x 32' basement
with 10" of ice in a perfectly insulated tank, under the floor, a tank in
the corner, 8' high x 10.43' square, not counting insulation.

I live near Philadelphia, which has average daily minimum temperatures of 
-5.1C, -4.0 and -2.2 in Jan, Feb and Dec of each year, according to NREL.
Say it's this cold, ie 25 F, average, for 4 hours a day for 90 days, ie
2,440 cooling degree hours, with a 32 F base temperature. How large would
our low-thermal mass, shallow anti-freeze pond have to be, ie how much shaded 
surface area do we need, with an R1 still-air film resistance, to somehow
collect 54,000 pounds of ice, or 7.8 million Btu in the winter? This looks
like Ohm's law for heatflow to me, ie Q = delta T x delta t x Area/R-value,
with Q = 7.8 million = 2,440 Area/R1, so Area = 7,800,000/2440 = 3200 ft^2,
eg a square pond, 56 feet on a side... This would work better on a night
with some wind, or on a clear night with no clouds and no wind. 

Or perhaps some snowmaking machines in a tent, over an insulated pit, with open
tent flaps in the winter, or... Let's see, if an auto radiator with a fan can
get rid of the heat from a gallon of gasoline in an hour, ie 100K Btu/hr, with
200 F water and 100 F air, that's 1000 Btu/hour/degree F, 1000 times better
than a square foot of pond surface, so we'd need 320 of them. 

Once again, some numbers on the back of an envelope seem helpful.

Nick

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From: [email-masked] (Nick Pine)
Date: 16 Jul 1995 11:30:01 -0400

Mike Allenbau <[email-masked]> wrote:

>Simpler solution - carefully cut the house into 150 pound pieces, number
>them, UPS them to Fort Yukon, Alaska, reassemble the house, and then it
>will be cool.

You gotta worry about your girth limits too, if you want to be practical
about this. I seem to recall UPS accepts a max of 108" length and perimeter
combined, with ovals and circles counted by the rectangles they inscribe.
Doesn't it get hot in Alaska sometimes?

Barrow looks coolish too, with a 1% dry bulb max summer temp of 57F, and
average temperatures of -13 F and -15 F in December and January, with an
average of 0.00 Btu/ft^2/day of sun. Perhaps there is a version of Murphy's
law that says, "If it's cool enough in the Winter to easily make enough ice
to cool your house in the Summer, you won't need to do that."

I keep picturing a shallow swimming pool, or perhaps a crawl space foundation
or a literal "floating slab" basement floor, insulated on the bottom--this
is the most expensive part to imagine--perhaps just some perimeter insulation
and a layer of plastic, on the ground, with a foot or so of dry soil on top
of that, then a little plastic pipe, then a layer of EPDM rubber, then a foot
or so of plain water, then a thermal cover of some sort, eg a building or
grass or a parking lot on top of some kind of low, thin, concrete roof mound
with a radiant barrier, over the water, and lots of those $10.83 Leslie-Locke
or $19.95 Solar Tex automatic foundation vents around the perimeter, with the
bimetallic springs reversed so the louvers  open  when the air gets below
freezing outside. Of course most people wouldn't want to live inside this
cold store...

Or perhaps we can change our metabolism... My grandmother used to tell me
about a local character in Kentucky: "Frozen Usher" used to come to town
in a horse-drawn wagon, once a year, on the hottest day of the year, all
wrapped up in layers of sweaters and coats and hats and gloves...

>I'm impressed by all that math, though - is any of it correct?

I think I done it right, within an order of magnitude, except for that there
last number. And I'm not sure how well that 0.2 radiator will work...
My grandmother also used to yell "Turn down the radiator!"
when we had the station up too loud.

Nick

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From: [email-masked] (Nick Pine)
Date: 16 Jul 1995 02:25:20 -0400

Nick Pine <[email-masked]> wrote:

>... Ohm's law for heatflow...  ie Q = delta T x delta t x Area/R-value,
 
>... Let's see, if an auto radiator with a fan can

Oops. Perhaps 3.2 of them...

Nick

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From: [email-masked] (Nick Pine)
Date: 19 Jul 1995 11:57:50 -0400

Jonathan M. Elson <[email-masked]> wrote:

>Big math is not needed here, because residential air conditioners are rated
>in TONS.  Tons of what?  ICE, of course!  If you have a 2 ton air conditioner
>which runs 50% of the time, you are getting 1 ton of air conditoning.  That
>means the equivalent of one ton of ice delivered per day! 

Hey, that's pretty simple :-)

24 hours x 12K Btu/hour /144 Btu/pound = 2000 pounds.

I knew a ton of ice was involved, but I didn't realize it was this simple.
How ignorant. I imagined there were a lot of other ad-hoc factors, somehow,
or that the ton of ice just sat there in the room somewhere, and one measured
the RATE of cooling at 12K Btu/hour, from some sort of standard surface area,
not that one measured the ice CONSUMPTION. That makes a lot more sense.
Thanks for explaining this...

>Practical?

Sure... :-)

>Remember that after melting, there will be one TON of cold water,

That's a lot.

>or if you melt it into brine, one ton of salty water to get rid of!

I've been thinking about plain water, in a shallow tank somewhere in the
ground. I wouldn't get rid of it. I would just let it sit there, liquid,
until the next year. Perhaps win some sort of major water recycling award
for thinking of this :-)

>That's 1250 gallons, every day! 

Let's see... 2000/8 = 250? Without the 1? About 32 ft^3, a cube 3' on a side,
or a layer of water 32' x 32' x 0.4" ? 4" for 10 days, 40" for 100 days...?

>What does a ton of ice, delivered daily cost?

I don't know. But if it is delivered by cold air... There is a tradeoff
between having a large surface area for good ice production by direct
exposure of a layer of water to cold air, and having a small surface to
volume ratio for efficient ice storage. Some sort of heat pipe might help,
a la permafrost freezers in Alaskan pipeline foundations, but cheaper.
Or some sort of insulated underground storage with a radiant barrier above, 
with doors that open or fans that turn on when it is cold. If it's fairly
large and flat, one could use the top for something else.

>I don't know, but it probably costs more than the equivalent electrical
>air conditioning.

Doubtless. About $2 for a 10 lb bag.

>besides, where will you put the "Ice Chute"?

In the basement, I guess.

>Sort of like the coal chute, only bigger - lots bigger!

I'm not sure that I made myself clear...

>One ton of coal will heat a reasonable house all winter, but the ice man
>will come DAILY!

Just like the play. We might need more than one ice man. Perhaps an army 
of Girl Scouts, all working on renewable energy merit badges, saving the
ice from their Diet Cokes all summer. ("Extra ice, please.")

>A whole new infrastructure to build!

Awesome. They could sing cheerful ice-delivery songs, as they marched along
in their white socks.

>No, how about a SOLAR-powered air conditioner?

Sounds good to me...

>A hotel in Minnesota (I think) built an ice house, which was to spray water
>in the air all night (and cold days) all winter, and build an ice block the
>size of a football field and 30 feet thick.  Then, in the spring, a prefab 
>building would be placed over the block, and the water spray would melt 
>the ice and cool the hotel.

This might have worked better if they had layed a few plastic pipes in the
basement or under a parking lot, so they could suck the cool out from below
the ice with some more plain water running through the plastic pipes, and
put a layer of EPDM rubber over that, and opened the basement windows or
turned on a fan when it was cold out, while adding water on top in 2" layers
every week or so. I have a paper somewhere with models and data for maximum
winter ice production in reed beds used for municipal sewage treatment,
as used in one of our local sewage treatment plants, where the ice helps
a lot in sludge dewatering. Ice forms faster if you add the water in layers.
Or spray it on in droplets. But that's more complicated, and then it might
end up snow, not ice. Heaped up in the middle. Less compact. More compact,
in surface to volume ratio, but not what I had in mind. 

Cooling and sludge dewatering might be a nice combination, on a smaller scale,
except that in that case, one relies on the reeds to evaporate the water from
the sludge. They get cut back in the early spring, and grow to 12' tall or so
by fall, when they are cut down and burned right in the reed bed.

I guess this requires more thought.

>What happened?  The warmest winter in recorded history!  Very little ice.

Bad luck.

>I never heard what happened the next winter.

Perhaps this was not a design problem. Perhaps the accountants acted in haste. 

Here's a quote from Steve Baer's nice little 1979 book, _Sunspots_ 
"An Explanation of Solar Energy Through Fact and Fiction." Some of the
numbers have changed since 1979, of course. He's talking about potable 
ice production, where the ice has to be physically moved, and sold
somewhere else, and the water must be replaced, vs. just forming and
reforming the ice in one place:

  One business that needlessly consumes millions of dollars of electrical 
  energy is the production of ice. It used to be common practice to harvest 
  ice from ponds and rivers, but with the advent of refrigeration and
  machinery this fell out of fashion. We should get back into the business,
  this time exploiting modern insulation and methods of moving materials.

  Over the entire country ice is made with mechanical refrigerators powered
  by electricity. Here in Albuquerque ice sells for 3 cents a pound in
  blocks and 7 cents a pound crushed. Firewood, hauled from miles away and
  cut into stove-sized pieces, sells for $0.015/pound; adobe bricks, cured
  and stacked, sell for $0.005/pound. It is strange that ice is so expensive.
  In Albuquerque at least six feet of ice can be harvested from shallow ponds
  of water-filled trays during a year. This is over 300 pounds per square
  foot of pond. If the value of ice were 1 cent/pound, each square foot would
  yield a harvest of $3, or $125,000 per acre. The production of ice with
  electrically powered refrigerators requires approximately $0.15 per 100
  pounds of ice, so an acre of ice ponds would save approximately $19,000 
  in electricity each year.

  What work must one do to make the ice? One method is to fill plastic trays
  with a hose during the afternoon and lift off the ice in the morning. During
  very cold weather two layers can be harvested each day. Some people would
  object at first to shards of ice from the top of a pond. "Why, this looks
  like it was pulled off the top of a puddle." Eventually users of such ice
  would realize that the texture of a bag of ice chunks is interesting itself;
  it can tell them of the severity of the previous winter, just as the variety
  of a bag of oranges is more interesting than a can of orange juice.

  The storage of such an ice harvest is the most difficult part. If the ice
  were stored in a huge insulated pit, the mass of ice might lose a rind two
  feet thick during a year as heat travelled through the walls and melted it.
  An efficient ice ranch would require considerable capital to make the
  insulated storage shed, and would also require an efficient way to handle
  the daily harvesting of the ice. Who wouldn't rather work at an ice ranch,
  with its own peculiar reversed harvesting weather, than in a refrigeration
  plant?

  There is a texture to reality, good and bad, a mixture of fortune and
  misfortune. If this texture is presented to people always through other
  people, machinery, or prices, then eventually we become bitter about our own
  species. If it appears as an unavoidable part of reality, a result of the
  weather, we do not have others to blame.

  An enterprise such as an ice ranch, especially if the activities are visible
  to passersby, is interesting. Cold weather is then useful to someone in a
  productive way.

Nick

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From: [email-masked] (Nick Pine)
Date: 19 Jul 1995 16:50:03 -0400

Paul Bixel <[email-masked]> wrote:
 
>  I picture a hocky rink.  It would be interesting to investigate the
>type of equipment used to run those things.  It would be much
>larger than you need of course in BTU/hour but the principle
>applies.  The phase change of water seems important in your
>calculations.  You must make ice for it to work.

It works a lot better that way, but I was thinking of natural ice, not
heat pump ice...

>  I know of such an installation as you descibe.  This guy had a heat 
>pump and a large in-ground vat lined with plastic topped with an 
>insulated shed.  The coils of his heat pump we supposed to freeze the ice 
>in winter and melt it in summer.

Sounds interesting. Now, could one do that in reverse, using winter ice and 
summer heat to power a Stirling engine, with a cycle time of one year? Or
a high thermal mass sunspace with a cycle time of one day?

Nick