Math to estimate what your PAR is from DIY LEDs (Bulbs, downlights, home made)

[Tower258]

Hey all, 

So I'm a total nerd and went down a 2 day rabbit hole when I decided to do DIY lights for my 60 Hex project. My big thing is that I had no idea how bright "low", "medium" or "high" light actually was. When I looked it up, I always found vague lumens/gallon or just PAR values. Because I don't want to spend the money on anything that gives a PAR values, I had to figure them out.

Most common white LEDs are phosphor-converted type LEDs and they all have a similar spectrum assuming the color temp is the same. This is why this can be done without knowing the specific spectrum of the LEDs you are using.

The equation is as follows: PPDF=Fa(lumens/(H(Tan[Φ/2]))

(PPFD is what we think of as PAR)

 

Lux*Fa=PPFD      Fa-factor from reference link   

Lux=lumens/area

Area= Pi(B/2)^2

B=2H(tan(Φ))         H-Hight of light from substrate.   Φ- angle of LED reflector (total angle from side to side)

 Phosphor LED factors based on color temp;

• Less than ~ 3000K = 0.017
• Between ~ 3000K to 4000K = 0.015
• Greater than ~ 4000K = 0.014

Because this is an estimate, I plan to also estimate the angle of the LED reflector, thought down lights will sometimes give them. A source of error in this method is that it assumes 100% of the photons emitted from the LED will hit within the designated area (This also assumes the reflector will absorb no light), Therefore this estimate will likely be on the high side. 

The equation is best used for a single light, however, if you have a few that are close together it could still be an alright estimate given that the distance between the lights is relatively small compared to the area they are shinning on (most LEDs use this idea). If they are far apart, you can add the values where they overlap (like a Venn diagram). 

 This equation could be changed to estimate a light bar by using B to find Area with a different equation. I'm tired now but will show this if anyone has interest

Hope this helps someone save a few bucks! Who says you'll never use trig after high school?

[Keeg]

Can I save this onto a document for personal use? I feel like it would be such a great resource to have on hand for the future as well as the present. 

[Tower258]

Of course! Granted I have no idea how accurate it is... maybe someone with a PAR meter will test it for me😃. I also forgot units, The height is measured in Meters and make sure you are using the trig functions of degrees and not radians.

 I have a google sheet that I used for my current project, if I think about it and have some time I'll clean it up and put it on here as well

[CT_]

I use this webpage to do the conversion for well characterized light sources using my phone as a lux meter (they all have ambient light meters for the screen dimming feature and to tell if its pressed against your ear or not).

As a side note PPFD which is quantity people usually use when they say PAR isn't weighted by color while YPFD is, though it turns out the weighting is fairly flat anyway, which surprised me.

[Tower258]

On 8/25/2021 at 5:43 PM, CT_ said:

I use this webpage to do the conversion for well characterized light sources using my phone as a lux meter (they all have ambient light meters for the screen dimming feature and to tell if its pressed against your ear or not).

As a side note PPFD which is quantity people usually use when they say PAR isn't weighted by color while YPFD is, though it turns out the weighting is fairly flat anyway, which surprised me.

what website is that? I'd love to see how the math for lux compares to an actual sensor! And that's interesting, I hadn't come across YPFD so ill have to look into it

 

also here is the little excel sheet: https://docs.google.com/spreadsheets/d/1WMN5YVej_MwAP72kPZ4-lF3MrTvBFo3nUJpyJ3FOZqk/edit?usp=sharing