The inverse square law, light penetration, and max ppfd
Posted: Tue Nov 27, 2018 2:01 am
So in my efforts to better understand lighting for horticultural purposes, I've been reading up on the inverse square law. This image on wikipedia really helped me understand things better. (thanks and credit to wikipedia user Borb for this awesome illustration)
The source is spitting out a bunch of photons in every direction, and the density of the photons for a given area is going to be greater near the source and less the farther away you go. At first when I heard this I thought it meant that I had to get my lights as close to the plants as possible, because that would make the most sense from an efficiency standpoint, right? But then I thought about what the implications of moving the light source closer to the canopy was for the lower parts of the plant and realized that it wasn't that simple.
Imagine that you have a plant that fills up the space between R and 3R here, then imagine on another scale(plants are actually same size), you have a plant that fills up the space between 2R and 3R.
The former would be a situation where the light source is close to the canopy and the latter it would be farther away. In the first situation, with the light source close to the top of the plant, the bottom of the plant is only getting 1/9th (1/3^2) of the PPFD that the top of the plants is getting. When the light is further away, however, we see that the difference between the PPFD at the top and the bottom of the plant is less comparatively than before as the top is getting 1/4 the PPFD at R and the bottom is getting 1/9th the PPFD at R. ((1/9)/(1/4))=.44444.... while 1/9=.11111... So you can see the bottom of the plant with the light closer to the canopy is only getting 11.11% of the light that the top of the plant is getting while the bottom of the plant with the light farther away is getting 44.44% of the light that the top of the plant is getting. The trend continues as you continue to increase the distance of your light which is why the brightness of the sun from 10 feet off the surface of the ground isn't that much different from the brightness at the ground even though 10 feet makes a big difference with say a floodlight that can appear just as bright as the sun at the right distance.
Now if both those lights were the same brightness, it would obviously make sense to move the lights closer, but if you were to boost the output of the more distant light so that the PPFD at the top of the canopy matched the PPFD that the other light put out there, you would get the same intensity of light at the top, but greater intensity of light throughout the rest of the plant. I finally understood what people were talking about when they mentioned light "penetration". Higher intensity lights placed farther away like HIDs would "penetrate" better lower down into the plant than LEDs with low wattage individual diodes.
Assuming you take advantage of canopy management techniques like mainlining and defoliating so that the lower plant is not entirely shaded, it would make sense that you would need more powerful lights farther away to take advantage of this and fill out the lower parts of your colas. The question is, though, just how much?
I have gathered that cannabis can only take a certain level of light intensity before issues arise. What exactly is that PPFD level? It seems that ideally you would want the tops of the plant to experience the maximum PPFD while the rest of the plant would experience adequate levels. Assuming your plant is going to be around 2 feet tall, what is the best tradeoff between efficiency and penetration?
Another factor I'm still not clear about is how reflective surfaces in the grow space affect all this. So far I've been treating this like all the light is being emitted equally in every direction from the source and that any light not going where we want is lost. Normally that would be true because the light would hit something and absorb, but with reflective surfaces, some of it would bounce off. Also, shading has to be taken into account. A single source will shade anything directly beneath it while multiple sources can illuminate more angles.
Can anyone provide some more guidance on what the optimal tradeoff between light intensity, distance, penetration, and efficiency would be? Looking for wattage of individual diodes and distance from the top of the canopy specifically. Many thanks to anyone who stuck with me through this lengthy post!
The source is spitting out a bunch of photons in every direction, and the density of the photons for a given area is going to be greater near the source and less the farther away you go. At first when I heard this I thought it meant that I had to get my lights as close to the plants as possible, because that would make the most sense from an efficiency standpoint, right? But then I thought about what the implications of moving the light source closer to the canopy was for the lower parts of the plant and realized that it wasn't that simple.
Imagine that you have a plant that fills up the space between R and 3R here, then imagine on another scale(plants are actually same size), you have a plant that fills up the space between 2R and 3R.
The former would be a situation where the light source is close to the canopy and the latter it would be farther away. In the first situation, with the light source close to the top of the plant, the bottom of the plant is only getting 1/9th (1/3^2) of the PPFD that the top of the plants is getting. When the light is further away, however, we see that the difference between the PPFD at the top and the bottom of the plant is less comparatively than before as the top is getting 1/4 the PPFD at R and the bottom is getting 1/9th the PPFD at R. ((1/9)/(1/4))=.44444.... while 1/9=.11111... So you can see the bottom of the plant with the light closer to the canopy is only getting 11.11% of the light that the top of the plant is getting while the bottom of the plant with the light farther away is getting 44.44% of the light that the top of the plant is getting. The trend continues as you continue to increase the distance of your light which is why the brightness of the sun from 10 feet off the surface of the ground isn't that much different from the brightness at the ground even though 10 feet makes a big difference with say a floodlight that can appear just as bright as the sun at the right distance.
Now if both those lights were the same brightness, it would obviously make sense to move the lights closer, but if you were to boost the output of the more distant light so that the PPFD at the top of the canopy matched the PPFD that the other light put out there, you would get the same intensity of light at the top, but greater intensity of light throughout the rest of the plant. I finally understood what people were talking about when they mentioned light "penetration". Higher intensity lights placed farther away like HIDs would "penetrate" better lower down into the plant than LEDs with low wattage individual diodes.
Assuming you take advantage of canopy management techniques like mainlining and defoliating so that the lower plant is not entirely shaded, it would make sense that you would need more powerful lights farther away to take advantage of this and fill out the lower parts of your colas. The question is, though, just how much?
I have gathered that cannabis can only take a certain level of light intensity before issues arise. What exactly is that PPFD level? It seems that ideally you would want the tops of the plant to experience the maximum PPFD while the rest of the plant would experience adequate levels. Assuming your plant is going to be around 2 feet tall, what is the best tradeoff between efficiency and penetration?
Another factor I'm still not clear about is how reflective surfaces in the grow space affect all this. So far I've been treating this like all the light is being emitted equally in every direction from the source and that any light not going where we want is lost. Normally that would be true because the light would hit something and absorb, but with reflective surfaces, some of it would bounce off. Also, shading has to be taken into account. A single source will shade anything directly beneath it while multiple sources can illuminate more angles.
Can anyone provide some more guidance on what the optimal tradeoff between light intensity, distance, penetration, and efficiency would be? Looking for wattage of individual diodes and distance from the top of the canopy specifically. Many thanks to anyone who stuck with me through this lengthy post!