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Re: R-value conversions (was: Solar Heating, Empirical Measu(r)ements & Experience)

David Hoadley <s840157@minyos.its.rmit.EDU.AU> wrote:
>nick@vu-vlsi.ee.vill.edu (Nick Pine) writes:

  Here's another litmus test for an energy expert: what will the average water
  temperature be inside a 4' cube full of water surrounded by 5 R20 foam walls,
  sitting outside in December, when the air has an average 24 hour temperature
  of 36 F and the sun puts 1,000 Btu/ft^2/day of heat into the R1 glazed side
  of the box? And how will that change over time if we shade the sunny wall?
  Anyone care to answer that question? I'll offer a $10 reward to the first
  person who answers it correctly.

Still no numerical answers, 16 hours after this posting. Perhaps $10 is
insufficient bait to catch an energy consultant, or they are out of season? 

Or perhaps it should be rephrased in international units:
 
Here's another litmus test for an energy expert: what will the average water
temperature be inside a 1 m cube full of water surrounded by 5 R5 foam walls,
sitting outside in December, when the air has an average 24 hour temperature
of 2 C and the sun puts 3 kWh/m^2 per day of heat into the R0.175 glazed side
of the box? And how will that change over time if we shade the sunny wall?
Anyone care to answer that question? I'll offer a $10 reward to the first
person who answers it correctly.

>This brings me to another point (thus the change of topic title). When I
>first started reading these groups I was rather taken aback by the high
>R-values people mention. Here in Australia, they are generally in the
>range R-1.5 to R-3 or 4 for (say) fibreglass insulation.

R30 house walls are pretty good walls in the US. Perhaps a good new
Australian or French or British house has R5 walls, made with
straw bales and mortar, 40 cm thick? A 1 bale wall?

>The units are, naturally, degC.m^2/W.

Of course Mother Nature thinks in meters and C, not feet and F :-) The
natural thing about a Btu (the amount of energy in a kitchen match) is that
it takes eggsactly 1 to raise 1 pound of water or 55 ft^3 of air 1 degree F.
It takes about 100 Btus to make a cup of coffee. Chickens make about
5 Btu/hr/lb of sensible heat. A typical 5.41 lb bunny makes 40. 1 cfm of
air flowing with a temperature difference of 1 F moves about 1 Btu/hour,
a single pane window is about R1, and 2 layers are R2. A pound of water
takes 144 (1 gross) Btus to freeze at 32 F, which is close to the average
air temperature in December where I live, and it takes about 1000 Btu to
boil away a pound of water at 212 F. A south wall in December receives
about 1,000 Btu/ft^2/day of sun where I live, 300 Btu/hour/ft^2 peak. The
thermal conductance of an airfilm with air moving at V mph is about
2 + V/2 Btu/hr-ft^2-F for rough surfaces. A black body at T degrees F
radiates 0.174x 10^-8(460+T)^4 Btu/hr-ft^2. US hardware stores sell rolls
of 6" fiberglass insulation stamped R19 in big letters (R10 with 2%
moisture, R0 in a good wind) for 25 cents/ft^2, and R10 foamboard 2"
thick costs about 50 cents/ft^2.   

What is natural in metric? Water freezes at 0 C and boils at 100 C, and
it takes about 1 kWh to heat 1 m^3 of water or 3,000 m^3 of air 1 C. A cup
of coffee takes about 30 Watt-hours. People make about 100 Watts, rabbits
5 W/kg. 1 m^3/sec of air flowing with a temperature difference of 1 C
moves about 1 kW of heat. It's a little harder to remember that 1 layer
of glass with an airspace has metric R0.175, and 2 layers have R0.35.
It takes about 100 kWh to freeze a cubic meter of water and 663 kWh to
evaporate one. The ratio of evaporative to convective power loss at a
wet surface with temperature Tp in Ta air is about (Tp-Ta)/(Pwp-Pa)/2,
independent of windspeed, where Pwp and Pa are vapor pressures in mm Hg.
A south facing wall in December receives about 3 kWh/m^2/day of sun where
I live, with a peak of 1 kW/m^2, and the thermal conductance of an airfilm 
with air moving at V m/s is about 10 + 2V W/m^2-C for rough surfaces, eg 
100 W/m^2 in a 5 m/s wind for a 25 C surface on a 20 C night. How much
more if the surface is wet, and the air has 50% RH? How much more if the
sky is clear? Do French hardware stores sell R2 foamboard 5 cm thick for
about about 30 FF/m^2? Why does the Lord permit such Suffering on Earth,
if He is Omnipotent?

>I was surprised to find that American ones are expressed in British Thermal
>Units (which I had thought went out with the ark)...

Now that Britain and Australia use Watts and meters, we are thinking of
calling these American thermal units, or perhaps Bunny thermal units.

>So I tried to work out a conversion factor. Can someone confirm it for me? 
>
>  Is it true that 1 watt = 3.412 BTU/hr?  If so, have I got it right that
>  R-1 (International) degC.m^2/W = R-5.678 (US) degF.hr.ft^2/BTU?

I think so.

Or would those be degrees K, in that particular alphabetical procession? 

Nick

   When we play tennis or walk downstairs we are actually solving whole
   pages of differential equations, quickly, easily and without thinking
   about it, using the analogue computer which we keep in our minds. What
   we find difficult about mathematics is the formal, symbolic presentation
   of the subject by pedagogues with a taste for dogma, sadism and
   incomprehensible squiggles.

          From _Structures: Why Things Don't Fall Down_, by J. E. Gordon
References: