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Design spreadsheet for a solar pergola?

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Posted by WoolPark on October 30, 2005, 7:50 am
 
Hi

Does anyone have a design program for a solar pergola, one of those
pergolas with fixed but angled slats that allow the sun to penetrate
in winter but block the light in summer?

Thanks
Robin

Posted by nicksanspam on October 30, 2005, 2:32 pm
 
WoolPark  <> wrote:


Are you talking about a shading structure that extends horizontally towards
the sun from the top of a window? It might have 2' slats parallel to the rays
of low winter sun with a max elevation of 90-lat-23.5 = 26.5 degrees on 12/21
at noon where I live at 40 N lat. To block summer sun at a 73.5 elevation at
noon on 6/21, the slats might overlap so sun passing the upper edge of one
is blocked by the lower edge of another, like this, viewed in a fixed font:

                b            .  ---
            .            .
      2' .            .           y = 2 sin(26.5) = 0.89'
    .            .
.            a                  ---


|      p     |
|       x       |<-- 2 cos(26.5) = 1.79'

If the a-b elevation is 73.5 degrees, tan(73.5)=0.89/(x-p) makes p = 1.53',
so the slats would be on 1.52' centers with a 1.79-1.53 = 0.26' overlap,
seen from above.

A sunspace roof might have larger and steeper slats that are reflective
beneath, or some sort of solar staircase (tm), maybe like this...

        4'
.   .   .   .   .   p        
.   .   .   .   .   .   o
                .2'     .   l
      polycarb->.           .   y  
                .   .   .   .   .   c
                foil-faced foam .   .   a    
                                .       .   r
                                .           .   b
                                .   .   .   .   .
                                .   .   .   .   .

Where I live, a 1'x2' strip of inner glazing would transmit 0.9x0.9x1000x2
= 1620 Btu/day of direct south sun + 0.9x0.9x0.9x1000x2 = 1458 of reflected
sun, for a 1.5:1 solar concentration. The lower foil layer could help avoid
overheating the sunspace by ceiling radiation during the day.

Nick


Posted by nicksanspam on October 30, 2005, 7:29 pm
 
Then again, this would have more summer shading and winter concentration:

.   .   .   p        
.   .   .       o
    . 2'            l
    .<- polycarb        y  
    .   .   .   .   .   .   c
    .  foil-faced foam  .       a    
                    .               r
                    .                   b
                    .   .   .   .   .   .   o
                    .   .   .   .   .   .       n
                                    .               a
                    | D |           .                   t
                                    .   .   .   .   .   .   e
                                    .   .   .   .   .   .  
                                        |       L       |

Tan(73.5) = 2/(D/2) makes D = 1.18', and tan(26.5) = 2/L makes L = 4.01'.

It looks like a 1' wide x 2' tall strip of inner glazing would collect most
of the sun falling on the outer glazing, about 0.9x0.9(0.9x4x620+2x1000)
= 3266 Btu on an average January day. At 120 F near the ceiling, it might
lose about 6h(120-34)2ft^2/R1 = 1032 Btu, for a net gain of 2234, so a 32'
wide x 12' deep 6:12 sunspace roof would gain about 3x32x2234 = 215K Btu
on an average day, the heat equivalent of about 2 gallons of oil... 8'x32'
of south glazing might gain 0.9x8x32x1000 = 230K and lose 6h(70-34)8x32/R1
= 55K, for a further net gain of 175K Btu. Total: 390K Btu.

Nick


Posted by nicksanspam on October 31, 2005, 1:37 pm
 
Scaling so D+L = 4' makes D = 0.91' with a 1.54' vs 2' tall inner glazing.

The foamboard might screw onto notched flats in parallel rafters above
and below it, with an aluminum cap strip above and 1x3s below and
clear flat 0.020" polycarbonate screwed to the 1x3 edges.

Nick


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