Team:Cambridge/Tools/Lighting

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(Modelling)
(Modelling)
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To show that it may one day indeed be possible to have bioluminescent trees replacing street lamps we considered how efficicient the plants would have to be in order to match a low-intensity street lamp.
To show that it may one day indeed be possible to have bioluminescent trees replacing street lamps we considered how efficicient the plants would have to be in order to match a low-intensity street lamp.
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==Radiation In===
Figure 1 shows the radiation spectrum recieved from the sun at sea level. In total this gives about '''1,321 – 1,471 W/m<sup>2</sup>''' of radiant energy for regions in North America. (Data supplied by American Society for Testing and Materials ([http://www.wmo.int/pages/prog/www/IMOP/publications/CIMO-Guide/CIMO%20Guide%207th%20Edition,%202008/Part%20I/Chapter%208.pdf. ASTM]) Terrestrial Reference Spectra, a common standard used in photovoltaics).  
Figure 1 shows the radiation spectrum recieved from the sun at sea level. In total this gives about '''1,321 – 1,471 W/m<sup>2</sup>''' of radiant energy for regions in North America. (Data supplied by American Society for Testing and Materials ([http://www.wmo.int/pages/prog/www/IMOP/publications/CIMO-Guide/CIMO%20Guide%207th%20Edition,%202008/Part%20I/Chapter%208.pdf. ASTM]) Terrestrial Reference Spectra, a common standard used in photovoltaics).  
This is a lot of energy, but of course most of it is not accessible to plants. They can only absorb in the visible region (corresponding to roughy 45% of total solar energy), radiation known as PAR (photosynthetically active radiation). In addition, there are other constraints, such as reflectivity of leaves and the absorption spectrum of chlorophyll. The net result is that in general plants are only able to take between '''3''' and '''6%''' of total solar radiation, corresponding to roughly '''60 W/m<sup>2</sup>''' (Figures from Hall, D.O. and House, J.I., Biomass and Bioenergy, 6,11-30 (1994).)
This is a lot of energy, but of course most of it is not accessible to plants. They can only absorb in the visible region (corresponding to roughy 45% of total solar energy), radiation known as PAR (photosynthetically active radiation). In addition, there are other constraints, such as reflectivity of leaves and the absorption spectrum of chlorophyll. The net result is that in general plants are only able to take between '''3''' and '''6%''' of total solar radiation, corresponding to roughly '''60 W/m<sup>2</sup>''' (Figures from Hall, D.O. and House, J.I., Biomass and Bioenergy, 6,11-30 (1994).)
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==Radiation out==
Since that's the energy which plants have available to, we then considered what they need to be putting out in order to function as street lights.
Since that's the energy which plants have available to, we then considered what they need to be putting out in order to function as street lights.
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It should be noted that this is actually a really good conversion factor, only about 33% of the radiant energy is lost to the outer regions of human perception (at best 1lm = 683.002 W). This is due to the fact that (as you can see from the scotopic luminosity function in figure 3) the human eye is better at seeing blue light in the dark than red light, and our bacterial light is clearly blue.
It should be noted that this is actually a really good conversion factor, only about 33% of the radiant energy is lost to the outer regions of human perception (at best 1lm = 683.002 W). This is due to the fact that (as you can see from the scotopic luminosity function in figure 3) the human eye is better at seeing blue light in the dark than red light, and our bacterial light is clearly blue.
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==Bringing it all together==
Now we combined the above calculations. If we assume that the tree absorbs all light passing through its projected area '''A''' (not a bad approximation, since only a few percent is able to make it through the canopy) then the total radiant light energy falling on it during the day time per second is '''60*A''' W. If the total radiant energy outputted at night per second is '''E''', then the luminous flux is '''471.13E''' lm, which we desire to be as bright as a street lamp '''X''' lm, then combining these we find that the total efficiency of our plant has to be:
Now we combined the above calculations. If we assume that the tree absorbs all light passing through its projected area '''A''' (not a bad approximation, since only a few percent is able to make it through the canopy) then the total radiant light energy falling on it during the day time per second is '''60*A''' W. If the total radiant energy outputted at night per second is '''E''', then the luminous flux is '''471.13E''' lm, which we desire to be as bright as a street lamp '''X''' lm, then combining these we find that the total efficiency of our plant has to be:

Revision as of 18:55, 26 October 2010