SWAGing PAR differences between bulbs with math.
 

So for all you uber-geeks out there here's the brain teaser of the day, and by no means do I have the answer which is why I bring it up. Anyways:

[url=http://www.greenwichaquaria.com/]Greenwich Aquaria[/URL] uses 400 watt Radiums set 12 inches above a 36 inch deep aquarium. I am trying 250 watt XM 20k bulbs set 8 inches above my tank which is 24 inches deep. Given the PAR readings from Sanjay's website, I'd like to estimate the ratio of PAR at 18 inches depth in the Greenwich tank (30 inches from the bulb) versus 8 inches depth in my tank (16 inches from the bulb). Intuitively I am assuming that PAR from a MH will drop off in proportion to the square of the radius, but when I try to convert that to a theoretical chart showing the expected percentage reduction in PAR for every 4 inches below the surface I get something like

surface = 1
4 inches below = - 50%
8 inches below = - 80%
16 inches below = - 90 %

and that doesn't make sense to me when I look at MH lighting charts showing PAR measurements for various depths. My estimate seems to drop off much faster than actual measurements.


I realize there are a myriad other factors that will get involved such as water clarity, bulb age, reflector, etc etc, but like the title says I'm just trying to SWAG this for fun as I intend to purchase an Apogee light meter soon and compare the light in my tank versus Greenwich Aquaria using raw data, and [b]I think it would be interesting to create a chart for estimating the PAR at various depths in a tank given a certain bulb/ballast configuration[/b]



So the question is: [I]Should PAR drop in proportion to the square of the radius and is that radius properly measured in meters and how do I convert that to a chart estimating the percentage reduction in PAR?[/I]




A hearty thanks to any that take the time to answer :eek1:



Joe


P.S. I have already changed to 4 x 250 watt XM 20k bulbs for reasons I plan on discussing in a future thread after trying this setup for 90 days, but just for grins I'll throw in the pictures of 4 corals I took for comparison 3 months from now. Wish me luck! :D



[IMG]http://www.bluefrags.com/images/gallery/pictures/20ktest1.jpg[/IMG] [IMG]http://www.bluefrags.com/images/gallery/pictures/20ktest2.jpg[/IMG] [IMG]http://www.bluefrags.com/images/gallery/pictures/20ktest3.jpg[/IMG] [IMG]http://www.bluefrags.com/images/gallery/pictures/20ktest4.jpg[/IMG]

I've been rereading the chapter on lighting in The Reef Aquarium Vol. 3 and they do talk and refer about experiments and the data from the exp. on depth to PAR ratios and A bunch of other stuff thats a little over my head. Wondering if your aware of this book and it's info? It may provide sum of the answers to your question.

The Reef Aquarium?
 

Thanks for the tip. I'm eager to find the reference. Who wrote [u]The Reef Aquarium[/u] vol. 3 to which you are refering. I have [U]The Modern Coral Reef Aquarium[/U] by Fossa and Nilsen as well as [U]The Reef Aquarium[/U] by Sprung and Delbeek, but the Fossa volume 3 doesn't mention lighting and the Sprung volume only has vol. 1 and 2 in my collection. Did they come out with a volume 3 that I don't yet own or is it another book?

Thanks for the input :)


Joe

Yes,The Reef Aquarium Vol 3 By Delbeek and Sprung is Science,Art and Technology and wow it really covers things the lighting section is very indepth 74pgs of indepth.The section on Total light received by the aquarium shows how to calculate and compare natural sunlight over a reef to our aquarium fixtures.I found the book one of the best in my 64 book collection

Without any real optics knowledge I think....

Light flux drops off in proportion distance squared for [B]point sources of light[/B]

Reflectors in large degree are supposed to make the light rays parallel rather than diverging as in a point source. So the choice of reflector will alter calculations. You might assume that a good reflector, Lumenarc or Lumen Bright, that the rays are parrallel.

Light is absorbed by seawater differentially according to wave length in accordance to Beer-Lambert law. This drop off is exponential. Longer wavelengths have a higher aborption coefficient than shorter (blue) wavelengths in general. Dissolved or suspended organic matter and phytoplankton will have some specific wavelengths absorbed preferentially.

Probable the attenuation of PAR in aquariums follows an exponential loss via Beer-Lambert.

[url]http://calmit.unl.edu/people/drundquist/pdf/2005/Mishra%202005%2060-1-48-64.pdf[/url]

For the scientifically inclined

[QUOTE][i]<a href=showthread.php?s=&postid=11503501#post11503501 target=_blank>Originally posted</a> by marsh [/i]
[B]Without any real optics knowledge I think....

Light flux drops off in proportion distance squared for [B]point sources of light[/B]

Reflectors in large degree are supposed to make the light rays parallel rather than diverging . . .
the attenuation of PAR in aquariums follows an exponential loss via Beer-Lambert. [/B][/QUOTE]


And that my dear Watson is stupendous! Thanks for the link and the lesson. I can safely say that the "light" went on in my tiny brain, and I have a whole new avenue of research to follow.

Thanks again, :)

Joe

Re: SWAGing PAR differences between bulbs with math.
 

I believe this would be true if you assume a point source in space with no attenuation or reflection. This is obviously very far from what we have!


Also, I was told that main display at Greenwich Aquaria uses HQI ballast to drive the snot out of the radiums. I am curious as to why they don't use better reflectors too...for a store in a high end market like Greenwich, you'd think they wouldnt cheap out there. Oh yeah, I also thought the tank was only 34" deep, haha.

Wish mine looked as good no matter what they do...



[QUOTE][i]<a href=showthread.php?s=&postid=11497361#post11497361 target=_blank>Originally posted</a> by JPMagyar [/i]
[B] Intuitively I am assuming that PAR from a MH will drop off in proportion to the square of the radius
So the question is: [I]Should PAR drop in proportion to the square of the radius and is that radius properly measured in meters and how do I convert that to a chart estimating the percentage reduction in PAR?[/I]



[/B][/QUOTE]