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[APD] lighting efficiency coefficient

We can define a dimensionless constant, call it the lighting efficiency coefficient, or LEC to coin a new acronym, which measures
the percentage of rated lamp lumens which reaches the bottom of an aquarium. This is a gross measure of reflector efficiency since
the reflector geometry & reflectivity are the dominant parameters. The constant will depend upon a number of factors including:

1) the geometry of the reflector, lamp, aquarium tank & water.
2) the transmissivity of the water (think turbidity)
3) the reflectivity of the interior walls
4) the reflectivity coefficient of the reflector
5) the diffusiveness of the reflector
6) the reflectivity & angle of refraction of light incident to the water surface

In general, the LEC will be quite similar for typical configurations.


  LEC = the dimensionless lighting efficiency coefficient
  I = the average light intensity at aquarium bottom
  L = the amount of light generated by the lamps
  A = the area of the aquarium bottom

then the formula

  I*A = LEC*L

lets you estimate the average luminous value on the surface of the plant leaves. The reason that I state it this way is that
experimentally, it is nearly impossible to conduct a growth experiment where the luminous value on the surface of the plant leaves
is controlled (but I'll bet that Tom knows a way to *approximate* it in a laboratory using tissue). We can however conduct growth
experiments using a measurable engineering value, the base level illumination. We should use this empirical measure because it takes
into consideration the experimental confounds caused by shading of lower leaves by upper growth. It is important that growth be
modelled in circumstances identical to aquarium conditions in order for it to be practical, in order for us to apply it in real

The upper bound for the LEC coefficient is 1, the lower bound (no reflector) is approximated by theta/2pi where theta is the angle
occluded by the base of the aquarium with apex at the lamp. Refraction & internal reflection tend to increase the lower bound, while
turbidity & surface reflection decrease it. For a lamp at 20" above a 1 foot wide aquarium base:

tan(theta/2) = 6/20 = 0.3
theta = 0.583
lower bound LEC = theta/2pi = 0.0928

If the reflector is able to increase lighting by a factor of 4, we get a LEC of about 0.4. We might get this with a diffuse white
reflector. With a high quality reflector, we might get an LEC approaching 0.75 or better. It has been said that a good reflector
increases illumination by a factor of 8 times over no reflector. Measurements by Ivo Busko
<http://www.thekrib.com/Lights/reflectors.html#18> indicate that a good quality reflector improves lighting intensity of his
configuration by a factor of about 3.05 to 3.5. I suspect that the black matte plastic material (no reflector case) was actually
reflecting some light or there may have been some ambient reflection or ambient light from the room. Ivo's reflectors were not
geometrically well designed to focus the light into a parallel beam such as might be achieved with parabolic reflectors or M shaped
parabolic reflectors.

Measurements by George <http://www.thekrib.com/Lights/power-compacts.html#22> show an average illumination level of 3364 lux with 1
yr old bulbs & tar ballast. For this he's using 4 40 watt NO T12 lamps. The surface area is 60" x 20" or 0.77 sq meters. If assume
65-75 lumens / watt for these lamps we get 10400 to 12000 lumens. The LEC would be 3364 / 0.77 / 10400 = .420 for George's
configuration. Using 75 lumens per watt, the LEC drops to 0.364 but I think this unlikely given 1 year old bulbs.

If we do the same calculations for the 4 55watt CF lamps we find an average illumination of 6228.5 lux. If we use 85 lumens/watt we
have 4*55*85=18700 lumens which correlates nicely with George's estimate of 80% more light. The LEC this time is 6228.5 / 0.77 /
18700 = 0.43 This agrees nicely with the previous calculation & should be identical since LEC is independent of lamp output & all
other configuration parameters are unchanged.

The measurements above were made in air so internal reflection should substantially increase the LEC. From
<http://fins.actwin.com/aquatic-plants/month.200007/msg00467.html> we can estimate that attenuation losses in water might be on the
order of 5%. Surface reflection might further reduce illumination since a significant portion of light strikes the water surface at
an oblique angle.

Let's suppose we have 2 32watt T8 lamps over a 4'Ln x 1'Wd x 18"Ht long 40 gallon tank. That's about 2 WPG. If the lumen output per
bulb is conservatively only 2500 lumens or 5000 lumens total and the bottom of the tank is 4 sq ft = 0.371 sq meters, with an LEC of
0.4, we have 5000*.4/.371 = 5391 lux!

If we now look at George's posting of the Allgayer and Teton table <http://www.thekrib.com/Plants/Tech/lighting.html#8> for Crypts
with an optimum lighting level of 800 lux we have 6.7 times more light than Crypts need for peak nutrient efficiency. In fact, we
have 3.3 times more light than Crypts could optimally use (1600 lux) if all nutrients were available in abundance (unlikely).
According to my calculations, with a LEC of 0.4, to grow Crypts at optimum nutrient efficiency, you should use 0.3 watts/gallon. I
don't know if Allgayer and Teton based their experiments upon equivalent base surface area lighting level or actual light intensity
at the leaf surface. If the latter, then we should revise the optimal Crypt WPG estimate higher since shading effects will decrease
actual illumination levels at the leaves.

I find that a tank populated primarily with Crypts & Anubias lit at 1.7 WPG of T8 lighting has systemic problems with BGA when
supplied with moderate levels of nitrate. An identical tank populated with A madagascariensis, Alternanthera, H poly, Lobelia,
Hemianthus micranthemoides, Anubias lanceolata, E horemanii, C pontederiifolia and C retrospiralis has no problems with BGA. The
tank with fast growing plants uses higher doses of N without any problems. Interestingly, this tank gets little or no fish food so
has a lower P load. There is a definite correlation between BGA and excessive lighting. Perhaps the P input is too high on the
problematic tank? I wonder if shortening the photo-period would be helpful?

I hope that this posting is clear & understandable.

Steve P

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