# LED visibility calculation

I want to select LEDs for a specific application. My requirement is as stated -

1. I have a beacon. this should be visible to a person at a distance of say 50feet.
2. Smallest form factor as weight is a criteria.
3. Visibility is the only criteria. I am not trying to illuminate a surface.

I want to know how can I go about selecting the LEDs for this particular application ? I understand that Lumens is the unit. Say, I select an LED of 500Lumens, how can I calculate the distance at which its visible ? Also, if it is visible, is it enough to be perceived as a legitimate source ? Probably this might require some field tests.

Also, are LED lumens additive ? Say, my requirement is 2000lumens, can I use 4 LEDs of 500LUmens to get the same effect ?

• Other than the LED specifications, this seems arbitrary on your part, so you are right to buy ones that have the high lumens, then buy lower cost LED's and test and compare them. We cannot do this testing for you as it is your judgement call. – user105652 Jun 14 '20 at 2:14
• Sorry, I haven't asked anyone to test on my behalf please. I was hoping for some guidance on the visibility of, say a 500Lumens LED, at 50 feet. At a distance of 50feet what would be the Lumens after dispersion ? And if its reduced by a factor of say "x", would it be sufficient for standard human perception ? – Board-Man Jun 14 '20 at 2:33
• Does it need to be visible from all directions? Low power but highly directional sources can be seen from orbit. – user1850479 Jun 14 '20 at 2:55
• The Talbot-Plateau law specifies that once the flicker rate exceeds the critical flicker fusion frequency (CFF), the brightness of point source will appear to be the same as if the light source were steadily operated at the time-averaged luminance. However, below the CFF the Bruecke-Bartley effect says that as the frequency is gradually lowered below the CFF, the effective brightness rises, reaching a value equal to that of continuous light (or transcending it) when the flash rate is 8-10 Hz. (The Broca-Sulzer effect from 1903, "La Sensation Luminense en Function du temps.") – jonk Jun 14 '20 at 5:13
• The human eye can see a single candle over a mile away under ideal circumstances (very, very dark). Contrast is a big factor. You need to consider the ambient light level. – Mattman944 Jun 14 '20 at 7:55

LED brightness is normally in lumens at one meter/one yard, so that is your baseline for intensity vs. distance.

Normally for radiant light, the intensity drops to 1/4 of original value every time you double the distance. For a given intensity at 50 feet, it will be 1/4 that value at 100 feet. It will be 1/16 that value at 200 feet. To see an LED 500 feet away you may need 50,000 lumens. Our eyes see green and yellow light the best. We do not see blue, red or violet very well.

I hope this helps in some way.

• All light follows the 1/r^2 rule. It's based on the premise that intensity is dependent on the fraction of the source you see, which is a fraction of the surface area of the the bounding sphere. Lasers and other ~collimated sources still follow this rule as all light must diverge because of the uncertainty principal. – SillyInventor Jun 14 '20 at 3:00
• @SillyInventor I agree with all you wrote. I did not want an elongated answer filled with equations as the OP may not be that skilled enough to understand. Maybe the OP will accept the average of several answers as a good answer. – user105652 Jun 14 '20 at 3:05
• You're right to keep it simple. I should have written that you should just exclude that last paragraph - since they don't seem to need it, and it's not quite right. – SillyInventor Jun 14 '20 at 3:37
• I removed the last paragraph as being too simple, thus not correct. – user105652 Jun 14 '20 at 4:16
• @user105652 the end of your paragraph isn't completely correct. In low light conditions (scotopic conditions), the human eye is most sensible to cyan, and in normal light conditions (photopic conditions) it's most sensible to yellow. Some manufacturers propose cyan LEDs with the standard 3,3V voltage drop. – Harnex Dec 15 '20 at 7:09

Many factors beyond just the light output of an LED can affect the ability of a light to be seen and recognized. Yes, more lumens is better, but other factors, such as color and eye sensitivity to the color, background/ambient illumination, and directionality/focus play roles in how visible a beacon is. Another factor that could draw attention to your beacon would be to have a flashing LED. There are integrated circuits (ICs) that are designed for this purpose. Some LEDs have the flashing function designed into the LED.

You might also get some ideas from looking at bicycle-mounted rear lights. Certain flashing frequencies are good for being noticed. Some use a chasing lights approach to increase visibility.

There is a very thorough treatment of factors affecting apparent brightness from pulsing LEDs that you might find helpful here.

I hope this helps.

• By measuring luminous flux (lumens) instead of radiant flux (watts), we are accounting for the color of the light and the eye's response to it. – The Photon Jun 14 '20 at 5:08
• You are correct. I was attempting to make the point that constant brightness with ambient background could cause perception to suffer from interference. – BalooRM Jun 14 '20 at 5:40

Lumen

LED lumen is only a part of the equation. Lumen is the luminuous flux ie the amount of light emitted per unit of time. You have a direct relation between electrical power and lumen: XML white LEDs produce about 100-120lm/Welec for example.

Candela

Then you have to consider the angle of emission of you LED. This leads to the luminuous intensity in Candela. That is the luminuous power per unit solid angle (lumen/steradians). Candela is what hurt your eyes if light is too intense. The more you concentrate equivalent lumen the more intense it will be. Small 5mm highly directional LEDs could provide thousands of mcd with less than 100mW within a very small emission angle (10degrees).

Lux

Finally there is the illuminance in lux (lumen/m2) but not relevant for your problem. It describes how illuminated a surface will be by a light source.

That's theory. Of course day light, distortion due to distance or atmospheric conditions are parameters to take into account. You will definitely have to do some tests. But I could tell you this: this kind of LED can easily been seen at 15m in normal ambiant light condition if you stand within the emission angle.

Hope it helps.