[APD] Dreaded Lumens/PAR/PPFD/Watt per Gallon Topic

[Jerry Baker <jerry at bakerweb_biz>]

Just a quick question for the group: I have heard it said that the old 
"watts per gallon" rule was formulated based on standard output T12 
fluorescent lights. Old T12's output about 50 lumens per watt or so. 
Would it be a fair extrapolation to say that 3W per gallon (for 
high-light plants) is really just a synonym for 150 lumens per gallon?

Watts per gallon is an extremely poor generalization even as 
generalizations go. Lumens are terrible in the context of plants, but 
what else are bulb manufacturers going to supply us with? If there is 
someone who thinks watts per gallon can even give you a remote idea of 
how much light you need, compare 4 T12 bulbs at 2000 lumens to a 
color-corrected 150W high-pressure sodium bulb at 16,000 lumens. Same 
wattages roughly, but the difference in brightness is a factor of two. 
Which watts per gallon is correct to get 4W per gallon in a 40-gallon tank?

Anyway, back to my original question. If I assume that high-light plants 
need around 150 - 200 lumens per gallon (I know about PAR and PPFD, but 
have no data for most bulbs), that means my 135G will need about 3 AH 
Supply 96W kits, 6 55W kits, or 3 175W MH fixtures. Somehow this doesn't 
seem right to me. I am still teetering back and forth between 2x175W MH 
fixtures or 4x96W PCs. The tank is 24" deep, but with substrate and 
everything, we'll be looking at 22" - 20" more likely. I want to be able 
to grow chain swords well at the bottom of the tank.

Forgive all this fussing. I assure you it's not "measure-bating" as some 
call it. Electricity is very expensive here in CA, and my apartment has 
a very low capacity per circuit (10A), so I need to maximize my 
efficiency as much as possible.

Thanks.

PS - Why hasn't someone come up with a metric that takes tank depth into 
account? It's not hard. Instead of saying "X watts per gallon" we could 
say something like "X lumens per size/depth factor."

After reading some stuff about the attenuation of PAR in fresh water, it 
seems to me like using an approximation of 0.46% of attenuation per inch 
of depth in an aquarium is reasonable (ignoring reflectivity of 
glass/acrylic walls). This is based upon interpolating a linear falloff 
from the equation % transmittance/m = 100(e^k) where k is the extinction 
coefficient (I used an extinction coefficient of 0.2 because aquaria 
tend to be very clear).

OK, so now we've got a rough estimate of how much light is lost due to 
depth. Now we need to know how much light is needed by low-light, 
medium-light, and high-light plants in those terms. I will assume that 
the rule of thumb (watts per gallon) was developed for tanks with a 
depth like a 55G (20"). Using those figures, and a lot of math I will be 
happy to show anyone who cares, it seems like the original rule of thumb 
gives us a net of 4 lumens per square inch for each watt per gallon. In 
other words, one watt per gallon in a standard 55G tank using 40W 2000 
lumen tubes gives us about 4 lumens per square inch at the tank bottom. 
The following equation should be a good approximation of light needed:

Total Gross Lumens = Total Net Lumens/1-(0.0046 * depth in inches)

So, let's make a real-world example. Say I am preparing to get a 
240-gallon tank. The dimensions are 96x24x24. I want to have a tank on 
the brighter end of medium-light plant levels ... say 3W per gallon by 
the rule of thumb. Using that as a reference, that would mean I wanted 
about 28,000 net lumens on the tank's bottom (4 lumens/square inch per 
watt). Plug that into my equation:

28,000/1-(0.0046*24) -> 28,000/0.8895 -> 31,478 gross lumens

Now I just need to spread about 32,000 lumens out over my tank and the 
light levels at the bottom of this tank will be the same as 165W of 
light from standard fluorescents over a 55G.

It's not perfect, but hey, right now we're working with watts per gallon 
which do not take depth into account.

-----
REFERENCES
http://www.cquest.utoronto.ca/env/env234y/bht/FACTS-234-04.pdf
http://www.aquabotanic.com/litg.htm

-- 
Jerry Baker
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