[Greenbuilding] A solar garage

[nick pine]

Inflatables have more promise for air than water heating, IMO, altho
"solar siding" seems better for that purpose. Polyethylene film has
high IR transmittance, ie not much heat-trapping greenhouse effect,
compared to glass or polycarbonate, so a 140 F water heater would be 
inefficient, but an air heater could double as an attached garage:  

                          f                      ---
                        fsf f  
                      fsf     f  \
    S<--            fsf         f 8'    
                  fsf             f \
              / fsf                 f  
           16'fsf              45 deg f
          / fsf.........................f        ~14'
          fsf .           9'            f
        fsf   .                         f |
      fsf     .                         f 8'
    fsf       .                         f |     
  fsfoamboard .                         f 
fsf 60 deg    .                         f 
gggggggggggggggggggggggggggggggggggggggggggggggground 

|                     ~14'              | 

With 28' in the east-west direction, it needs 2x28'x16' = 896 ft^2
of film for the walls plus 265 for endwalls, totaling 1161 ft^2, eg
a $136 16'x75' 4-year roll from http://www.greenhousemegastore.com

The south wall would receive 580sin60+430cos60 = 717 Btu/ft^2 on
an average December day with a 32 F daytime temp in South Bend, IN,
ie 0.9x717x16'x28' = 289.1K Btu. With 70 F air inside for 6 hours,
it would lose 6h(70-32)16'x28'/R1 = 102.1K Btu to the outdoors, for
a net gain of (289.1K-102.1K)/6h = 31.2K Btu/h (140 F air inside 
real R1 film for 6 hours would lose 6h(140-32)16'x28'/R1 = 290.1K
Btu/day, more than the solar gain.)   

With a dark mesh screen ("s" above) and polyiso foamboard behind it,
the film might be the main south wall heat loss, with a net gain of
187K Btu/day. (A less expensive and less efficient version could 
have film vs polyiso foamboard behind the mesh.) 

With a few layers of gauzy mesh or felt to keep the surface near
the film cooler and increase its thermal resistance (a wall can't 
lose much heat by convection to an airstream approaching the wall,
see equation 1 on page 4 of http://www.cibse.org/pdfs/8cimbabi.pdf),
we might collect and store higher temperature heat in water as well,
using a car radiator, despite the high IR loss of the polyethylene
film, ie keep a cloudy day heat store warm as well as solar heat 
air for the house. The film's high IR loss can help prevent melting
the mesh or felt under stagnation conditions.

If 100 ft^3 of 140 F water in a 30" diameter x 25' polyethylene film
duct inside a 2'x2'x25' bench with 108 ft^2 of R20 surface (bags of
dry leaves?) loses 24h(140-29)108/20 = 14.4K Btu on an average day,
we can keep it warm with 14.4K/6h = 2400 Btu/h for 6 hours with 1000
cfm of air at T = 140+2400/1000 = 142 F with a 1000 Btu/h-F car 
radiator. With C cfm of airflow and (T-140)C = 2400 Btu/h,
C = 2400/(T-140). 

Heating C cfm from 70 to T (F) requires (T-70)C Btu/h. If the same
air flows into the mesh at 70 F and into the radiator at T (F) and
through the house and back into the mesh, and 31.2K Btu/h = (T-70)C
= (T-70)2400/(T-140), then T = 145.8 F and C = 411 cfm. (Or more,
since the radiator will be more efficient with less than 1000 cfm
of airflow.)   

A 1000 Btu/h-F car radiator inside a house with a G Btu/h-F thermal
conductance can keep it 65 F on a 29 F day with a minimum water temp
Tm = 70+(65-29)G/1000. If 100 ft^3 of 140 F water cools to Tm over
5 cloudy days and 5x24h(65-29)G = (140-Tm)100x62.33, G = 96 Btu/h-F,
or more, with some help from indoor electrical use.

The garage might also supply 289.1K-102.1K-14.4K = 173K Btu of warm
air for the house on an average day, enough to warm a 200 Btu/h-F
house with no windows or electrical use, which would require another
100 ft^3 of water in the garage to stay warm for 5 cloudy days with
a solar heating fraction close to 100%.

Nick
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