re: growing cubes SOLAR.KnowledgePublications.com

re: growing cubes
2 nov 2001
i wrote:

>...we could add a few windows around the perimeter to light the rooms
>within, say 16', and add a lightshaft down the middle with a reflective
>concentrating south sunscoop on top and automatically-controlled diffuse
>reflective "windows" with hinges beneath that open into the lightshaft
>for daylighting the inner 32' core... direct sun is about 200x brighter
>than a well-lit room, so lighting 8x32x32' of floorspace takes about
>41 ft^2 of solar aperture at 100% efficiency. we might use a 4'x8' shaft
>under a 4x linear parabolic concentrator with a 4' focal line at dawn. 

well, it looks like that 4'x8'x64' shaft would only transmit 0.56% of
the light to the bottom, with 90% diffuse reflective walls and low-angle
beam sun, eg 20 degrees elevation in december. it might work better with
mirrored walls (eg alumninized mylar) and a diffuse reflector at the
bottom, and reflective panels hinged at the top, with more of the sun
entering vertically, like shining a flashlight down a tube... 

10 rho=.9'lightwell wall reflectance
20 w=4'lightwell width (feet)
30 l=8'lightwell length (feet)
40 c=4'concentration factor
50 ec=.8'concentrator efficiency
60 tflux=8000*w*l*c*ec'total flux entering well (fc)
70 for f = 1 to 8'floor number
80 h=8*(8-f)'lightwell depth (feet)
90 r=5*h*(w+l)/(w*l)'well cavity ratio
100 e=exp(-.0443*r/rho)'transmission
105 print f,e
110 attn=attn+1/e'cumulative attenuation
120 next
130 ata=attn/8'average attenuation
140 print ata'average attenuation
150 area=32^2*8'floor area (ft^2)
160 er=.9'secondary reflector efficiency
170 print er*tflux/attn/area
180 er=.6'eg 2 wall bounces, and a bottom reflection...
190 print er*tflux/area

floor     lightwell
number    transmittance

  1       .0056940 
  2       .0119144 
  3       .0249304 
  4       .0521655 
  5       .1091535
  6       .2283978
  7       .4779098
  8       1

average diffuse well attenuation: 41.9

illumination from diffuse well: .268 footcandles

illumination from mirror well: 60.0 footcandles(?)

nick