Lumens per square foot to adequate coverage question...

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NYC_Diesel x Jack_Herer

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Ok guys so here is my thought process...
I have calculated that the floor of my grow partner's flowering chamber is exactly 16.7 square feet... Figuring a desired amount of 5,000 lumens per square foot, this gives me a desired total of 83,500 lumens...
Ok, so at first glance this would lead me to believe that my friend needs to purchase one 600watt HPS that puts out roughly 95,000 lumens...
However, after further reading and consideration I began to realize this was NOT adequate lighting coverage after reading up on HID lighting. One 600HPS in the middle of this space would be putting off 95,000 lumens. But plants on the outer regions of the grow room would be too far from the light to receive the desired 5000 lumens and this got me thinking about light dispersion....
...Here is where my math is shaky, this may be completely innacurate, any input is appreciated.
Ok, so a 600watt HPS puts off roughly 95,000 lumens in all directions. Now let's figure out how many of these lumens are hitting a one square foot canopy one foot below the light. I assume the light output of 95,000 lumens is the lumens output 12 inches from the bulb. So this means if you were to encompass your bulb with a sphere that had a one foot radius, this inside surface of that sphere would be receiving 95,000 lumens of light. Now this sphere, with a one foot radius, has a surface area of exactly 12.56637 square feet. So if your light is putting out 95,000 lumens in all directions and none of the light is being reflected, your one square foot area one foot below the light is only receiving 1 square foot of the 12.56637 square foot output rated at 95,000 lumens, this equals 7.96% of the bulbs lumens, therefore roughly 7562 lumens are hitting your one square foot space. That is great...more than the desired 5,000 lumens per square foot. However, lumens decrese by a factor of 4 by a doubling in distance...
Ok, so picture my 16.7 square foot room mentioned above. This 4x4 room with one 600 wattHPS in the center of the room (reference the schematic below). Each plant in the grow room in a sea of green takes up one square foot of space and therefore a total of 16 plants are used. The plants furthest from the light (the 4 in the corners), are exactly 28.14 inches from the light source (distance to center of sqaure foot in corner of 4x4 room with light 12 inches above canopy). Plants two feet from the light source are only receiving 1,890 lumens since light decreses by a factor of 4 as distance doubles. At 28.14 inches from the light source, your 4 corner plants are now receiving roughly 1,500 lumens each at canopy level...not exactly what we need.


This leads me to two questions...
1) What kind of light HPS array would you use to ensure that each square foot receives a minimum of 5,000 lumens in a 4x4 area? Be it 4x400, 2x600, 1x1,000, etc...
2) Why are all hoods designed to reflect light directly down when the plants growing directly under any HPS are already receiving the necessary lumens and it is the plants on the fringe that need the extra light?. How about a reflector that looks like a flattened pyramid or one that is bent in the opposite direction of a normal reflector? (see attachment #2 for description). Reflectors like these seem like they would more evenly disperse light over a plant canopy. The reflective panels would be angled towards the fringe of the garden instead of straight down helping those on the exterior receive enough light....whadda ya think.




View attachment hypothetical.bmp

View attachment diagram #2.bmp
 
Wow Im glad somone on here thought about size of the area instead of pure lumens per foot... Im on here preaching about this all the time... Anyways for your area I would use 2 600 watt lights or 2 1000 watt lights. With the 600's you may need to hang some cfls on the edges of the area, a 600 watt lights is good for 3x3 area, but 2 1000 watters will cover it nicley... If you use the 1000 watters make sure you dont skimp on a fan to cool those puppies....
 

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