# Light per Square Inch and Depth



## Walking_Target (Jul 16, 2008)

So, Watts per Gallon and so forth are rather innacurate measures of aquarium light requirements. 

Square inches alone does not really express lighting requirements, nor is depth really a good measure either. 

If my math is correct (and so are the formulae on Wikipedia and other sites), Light attenuation in the PAR range is fairly insignificant if using 'clear' water with moderate hardness, with the most attenuation occuring at a rate of about 20% in the 600nm-800nm bandwidth over aproximately 16". From what I can tell, this is not a geometric curve, and for tanks over 16" in depth, are not going to see a significant drop in lighting levels, assuming water conditions as above. 

In fact, from aproximately 400nm-600nm wavelengths, under 5% of light is lost to attenuation in clear water at a depth of 16", getting into the sub 400nm wavelengths, attenuation drops off steeply and you see more actinic light making it farther down, but this is far, far beyond the reach of what we really need to consider in the average planted aquarium. 

So, really, the formula for figuring out appropriate light levels should probably be calculated out for

LightLevel=PAR Lumens/Square Inches/Attenuation at Depth

Attenuation is a complex formula, but for most aquariums, you are looking at a 1%-5% drop between the top area and bottom area of a tank. 

For instance, my aquarium has aproximately 403.5 square inches of substrate at a depth of aproximately 16.5 inches. Assuming the majority of my light falls within the PAR Range (10000k and 6700k flourescent T5NO Tubes) and that the light output of T5 NO is aproximately 100 Lumens per Watt, it would be safe to assume of that light energy aproximately 90 lumens is going to fall within the PAR range. My fixture holds 2x21W bulbs. 

http://www.lrc.rpi.edu/programs/nlpip/lightingAnswers/lat5/pc1a.asp (for info on how i got Lumens per Watt)


Light Level = ((90*42)/403.5)/1.05 
= (3780/403.5)/1.05
= 9.368/1.05
=8.92 PAR Lumens/Square Inch

This equasion should give me the approximate light level at the substrate.

Even going by a highly conservative estimate of 60 Lumens/Watt for T5 NO lighting, giving aproximately 50 Lumens per Watt at PAR.

Light Level = ((50*42)/403.5)/1.05 
= (2100/403.5)/1.05
= 5.204/1.05
=4.96PAR Lumens/Square Inch

Now, I know this is a greatly simplified way of looking at the problem, yes there looks to be alot of math, but most of it is estimative values, especially for Lumens within the Photosynthetic Active Range. Without a PAR meter and a Lumens meter for each individual type of bulb/tube encountered, this math can only give a very rough estimate. 

However, the basic idea behind this math is to break down *how* much light you are getting in a square inch, *how* much of that light is usable by plants for photosynthesis and how much of that light is lost to the water column. 

As with other methods of determining light levels, this has no bearing on what kind of obstructions occur with cloudy or tannin laden water, nor how the plants themselves affect the light levels. 

Now, i have a feeling that i've probably left out some key variable or other figure which will render all this pretty much useless (I'm looking at you Tom B.! Prove me wrong! :thumbsup

Hopefully though, i'm at least barking up the right tree.


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## Hoppy (Dec 24, 2005)

If we used perfect parabolic reflectors that fit the top of our tanks perfectly, and our bulbs were either a line source or a point source of light, your idea would work fine. But, we don't have bulbs and reflectors like that. So, we lose intensity as we move away from the bulb, roughly as the square of the distance for short bulbs, and roughly directly proportional to distance with long tubular bulbs. That is why tank depth is important. The light reflected off the inside of the glass sides of the tank helps reduce the loss of light with distance, but it doesn't come close to eliminating it.

Also, none of our light fixtures spreads out the light evenly across the entire footprint of the tank. So, the intensity at the center of the tank is always higher than at the sides and end, and that can be a pretty big difference.


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