# beam angle calculator? Width at 6ft 23 degrees XR-E



## VegasF6 (Dec 28, 2009)

Hello, some help with math here. How do I figure approx how wide a beam of light I will get from and LED with a certain optic at a specific length? 

I used this calculator and came up with 2.5' from 6' which seems about right, but it isn't really designed for this I don't think?

So, what factors even matter? For instance, the XR-E data sheet says viewing angle is 90 degrees typical, (from primary optics only)
(I wonder why this page on Cutter says 75 degree primary lens with a viewing angle of 75 degrees??)

The secondary optic I am using is a Carclo frosted 20mm 23 degree. Is the size of the optic, or the frosted part a factor? 

Die size a factor? 

Power?

I don't expect a perfect solution, there are a lot of factors, the relative humidity and altitude I am at would probably have an effect! But, simple math?


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## rmteo (Dec 28, 2009)

For an optic with a FWHM divergence of 23 degrees, the beam width at 6 feet will be 2.44 - close to what you got.


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## VegasF6 (Dec 28, 2009)

Thank you. Apparently that is full width half maximum which I found on this wiki but, alas they don't have it in English, and I don't read Greek. 

As our teachers used to say, please show your work.


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## rmteo (Dec 28, 2009)

OK, I see you have done your homework so here is an explanation. Secondary optics are characterised by how wide a beam they produce. The beam width is quoted as an angular width rather than a physical beam size at a given distance. The angular width the optics produce is specified by measuring the angular separation between the directions (x1 and x2) at which the intensity has fallen to half its peak value (fmax). This value is called the Full Width Half Maximum (FWHM) divergence.


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## LukeA (Dec 28, 2009)

tan(FWHM˚) = (beam width)/(distance from source)

tan(23˚) = w/6 ft

6tan(23˚) = w = 2.54 ft


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## rmteo (Dec 28, 2009)

Technically it is:

tan(FWHM˚/2) = (beam width/2)/(distance from source)

6*tan(11.5˚)*2 = w = 2.441 ft


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## VegasF6 (Dec 29, 2009)

Awesome. I did find this page which explained FWHM in, to me at least, easier to understand terms. 

As well as another calculator that was more what I wanted. (mainly you can enter any 2 parameters and get an answer)

But, I really wanted to see the math, which both you (rmteo) and LukeA provided. So thanks for that!

I never even heard the term TAN (tangent?) before, had to google that as well, hah. 
Apparently that is Trig? I have a Las Vegas public education, derr. 

As a side note, Google truly amazes me. I did a further search for some of this stuff, (out on the web, not just here) and Google is already linking to this post!


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## rmteo (Dec 29, 2009)

I did not address the second part of your question regarding the secondary optic. It is impossible to produce a perfect beam of light that does not spread. The finite size of the emitting region of the LED source means that the light will diverge. How much the light spreads out depends on the emitting area of the LED chip and the type of secondary optics that are used. For this reason, the beam widths that the secondary optic produces, have been _*measured with each LED type*_ that it can be used with.

You are using the Carclo 10201 frosted 20mm. optic. Note that the FWHM divergence angle of this optic with an _*XR-E is 20 degrees*_ (not 23 degrees as you indicated which is for a Cree XR LED). Notice that the angles are different for each LED type. Your actual beam width will be 2.116ft. instead of 2.441ft.


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## Justin Case (Dec 29, 2009)

VegasF6 said:


> I never even heard the term TAN (tangent?) before, had to google that as well, hah.
> Apparently that is Trig? I have a Las Vegas public education, derr.



You've seen tangents every day and just didn't realize it. The tangent of a straight line is just the slope of that line. Slope is rise divided by run (Δy/Δx). If you put a 2x4 on a staircase, the tangent of the angle that the board makes to the floor gives you the slope of that board. The steeper the angle, the greater the slope. For example, at a 45 degree angle, the slope = 1, meaning that for every step forward (Δx), you go up by the same distance (Δy). Another example is a roof. Roof pitch is just the tangent (slope) of the roof angle to the horizontal. For a gradual slope, such as for a wheelchair ramp or a "flat" roof, you might have a rise over run of 1:12 (i.e., one foot up, 12 feet forward). Numerically, 1:12 equals 0.083. The angle that corresponds to that slope is given by the inverse tangent (also called the arc tangent). Using a calculator, Excel, Google, or other tool gives arctan(0.083) = 4.8 degrees.


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## rmteo (Dec 29, 2009)

I've long felt that education is the best investment that we can make. Pity that it is not given the resources and/or attention that it deserves.


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## VegasF6 (Dec 30, 2009)

rmteo said:


> I did not address the second part of your question regarding the secondary optic. It is impossible to produce a perfect beam of light that does not spread. The finite size of the emitting region of the LED source means that the light will diverge. How much the light spreads out depends on the emitting area of the LED chip and the type of secondary optics that are used. For this reason, the beam widths that the secondary optic produces, have been _*measured with each LED type*_ that it can be used with.
> 
> That's from page 4 of the data sheet  VegasF6
> 
> You are using the Carclo 10201 frosted 20mm. optic. Note that the FWHM divergence angle of this optic with an _*XR-E is 20 degrees*_ (not 23 degrees as you indicated which is for a Cree XR LED). Notice that the angles are different for each LED type. Your actual beam width will be 2.116ft. instead of 2.441ft.


 
Carclo of course mentions 
"It is important to note that it is​​​​*not *possible to calculate
from the FWHM beam width how big the beam will look​
to the human eye." (also from page 4 of the data sheet)
But, despite that, from experimenting I have decided to place the lights no more than 2 feet apart. Corresponds to the math pretty well. 

Also, I did completely miss that the FWHM for the XR-E is 20 degrees! I looked only at the first LED listed, the White XR. I have seen reports that the XR-E has had a die change? From the EZ1000 die to the EZ900? ( https://www.candlepowerforums.com/posts/2992875 )
How does that change things? I can see if you start with a slightly smaller point of light to begin with that your final beam of light would be slightly smaller, probably not very much at all. But it shouldn't change the angles used to figure the solution, should it?


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## VegasF6 (Dec 30, 2009)

Justin Case said:


> You've seen tangents every day and just didn't realize it. ~snip~ Another example is a roof. Roof pitch is just the tangent (slope) of the roof angle to the horizontal.


 
Ah, but what I said was I hadn't seen the term, as in I didn't understand it in the formulae. But, I do appreciate the explanation.



rmteo said:


> I've long felt that education is the best investment that we can make. Pity that it is not given the resources and/or attention that it deserves.


 
Yes, since I have become a father I realize that more. But, on the other hand, there are hundreds of roofs in the valley (to you Justin Case's example) that wouldn't have been sheeted if I hadn't done so. (Back when I was young and sheeting roofs)

*edit* upon re-reading this I may have appeared ungrateful, that wasn't my intent, thanks!


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## rmteo (Dec 30, 2009)

VegasF6 said:


> Carclo of course mentions
> "It is important to note that it is​*not *possible to calculate
> from the FWHM beam width how big the beam will look​
> to the human eye." (also from page 4 of the data sheet)
> ...



Here is the rest of that paragraph:


> It is important to note that it is not possible to calculate from the FWHM beam width *how big the beam will look to the human eye.* The visible size will depend on other factors such as ambient lighting conditions and the color LED that is being used. In very low ambient lighting conditions the beam will look far larger than the FHWM size because the observer looking at the spot of light can see clearly the very faint edges of the distribution. Against a bright background the beam will look much more like the spot size that would be calculated form the FHWM angular width.


That is why we cannot depend on visual observation, some type of measuring device is needed. A lux meter (common called a light meter) is indispensable when doing this type of stuff. It allows you to measure the brightness (luminous intensity in lux) of the beam - note that we are not talking about lumens (output) here, which a completely different thing altogether, and is no indication of brightness. Here is an example of a lux meter ($24):





To answer your second question, if there is a size change in the LED, it will affect the size (diversion) of the beam as you have correctly surmised. The only way to know for sure is to either check with the manufacturer of the optic if they have tested the new die OR you can measure the FWHM beam width yourself using the abovementioned lux meter.


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## vestureofblood (Jan 29, 2010)

Hey guys,

I have question about this.

When an optic or reflector says that it provides a 20* or 40* beam angle is this a measurement from the center? Example: 6* would be a tight throw type beam and 35* would be very wide?

Like this?


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## VegasF6 (Jan 29, 2010)

vestureofblood said:


> Hey guys,
> 
> I have question about this.
> 
> ...


 
What you are saying sounds correct, but the drawing isn't really accurate. The way I would understand it, the flat plane you drew would be 180 degrees. It is 90 degrees from straight on, but you would add both sides I guess. So, a 45 degree beam is only 22.5 from straight on. Probably not a very technical description, but hopefully it is accurate.


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## Al Combs (Jan 29, 2010)

I had a Trig teacher in high school that had a mnemonic I still remember 40 years later. If you pronounce it phonetically, SOHCAHTOA is everyday trigonometry. Sounds like an Indian princess. It stands for sine=opposite/hypotenuse, cosine=adjacent/hypotenuse and tangent=opposite/adjacent. In a scientific calculator if you have the angle, pressing tan (or whatever) will give you the ratio. If you have the ratio, pressing inv(tan) will give the angle.

As rmteo said, 23° is a reference to an isosceles triangle, so you have to bisect it first and then multiply by two. Trig only works with right angle triangles. The ratio of 23°= 2(Tan of (23°/2)) or 0.4069045988. Then 6 feet * 0.4069045988= 2.4414275928 feet. If you had the ratio and wanted to know the angle, just press inverse whatever two sides you know.


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