How many lumens from a light bulb do I need for 200-400 foot-candles of light, 18-24 inches from the source?
I am growing some algae. The required light level is 200 to 400 ft candles of fluorescent light, 18 to 24″ from the culture. At the store, fluorescent light output for a light bulb is given in lumens. How many lumens of output should my light bulb have in order to have 200 to 400 ft-candles of fluorescent light when the light source is 18 to 24 inches from the algae culture?
The algae will be in a 3 inch x 3 inch x 3 inch container. Say the light source is 21 inches from the center of the container. Very roughly how many lumens must the light source have to give around 200-400 foot-candles of light?
One foot-candle is equal to 1 lumen per square foot. A candela is a measure of flux. So first what we need to know is the solid angle which will be covering the algae in light, call it Omega and the solid angle over which the light is emmited (if that is in every direction that will just be 4*pi). We devide the lumens by the solid-angle overwhich the light is emited and then we have the candela produced by the bulb. We now multiply that by Omega and we have the total lumens hitting our algae. If we then devide that by the square footage of your algae, and you have your “average foot candles”. This is only an average because the actual candela accross the surface will vary as the distance from the source varies and so will our ft-candles. A more exact measurement of ft-candles on a point by point basis would require more information on the setup, a more rigorous approach to mathmatics, and a little bit of fudging 
.
Now to help you figure out the solid angle you’ll need. If your algae is in a nice square, and your lightsource is positioned directly above the center of your square a distance 1/2 the length of the side of your square, then youd have a nice solid angle of 2/3 pi. I really don’t know how to help you out with this without more information except by pointing to websites http://mathworld.wolfram.com/SolidAngle.html .
For a nice little example, lets have a 20 lumen sources emmiting in every direction 6 inches perpandicularly centered above a square foot of algae. Whats the average foot-candle? 20 lumens / 4 pi = 5 / pi lumens. 5 / pi lumens * 2/3 pi = 10/ 3 lumens. 10/3 lumens / 1 sq ft = 10/3 ft-candels or 3.33.. ft-candles.
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