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  1. #1
    Bike ≠ Car ≠ Ped. BarracksSi's Avatar
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    Are lumens cumulative?

    I haven't found a good answer to this anywhere --

    Coming from the music world, I've known that sound pressure levels from multiple sources do not add up in a linear fashion. That is, if one instrument can put out 100 dB and is joined by another, the result is not 200 dB (thank goodness!).

    I understand that lighting measurements are different, and that besides lumens, we've also got candela, foot-candles, lux, etc.

    So, do two 600-lumen lights really add up to 1200 lumens? Or do they still add up while measurements of luminance do not add up the same way?

    I'm having difficulty finding answers elsewhere because hardly anyone else seems to care about adding multiple light sources -- they usually just describe single sources. There was a similar question posted on a physics forum somewhere from a year ago that hasn't gotten any response, either.

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    Technically, in the audio world 3db is considered twice as loud...

    As for the lumens, I think that if you point them in different places then you definitely can add the lumens up. If you point them on top of each other I think it's pretty much a wash.

    I think the ideal setup for me would be one light as a flood and one as a spot. Then they'd be covering different areas and add up.

  3. #3
    DNPAIMFB pinkrobe's Avatar
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    There may be issues with constructive/destructive interference, but I was under the impression that the lumens were summed as long as they all focus on the same area. For example, 4 spotlights @ 200 lumen each will measure as 200 lumens if the beams don't overlap. However, if they are all pointed at one spot, measuring the lumens at that point should give ~800 lumen. This is just an educated guess, and I'm sure someone with more knowledge will chip in shortly.
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    Bike ≠ Car ≠ Ped. BarracksSi's Avatar
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    Quote Originally Posted by ovrrdrive View Post
    Technically, in the audio world 3db is considered twice as loud...
    Right, that's part of my questioning...

    Quote Originally Posted by ovrrdrive
    As for the lumens, I think that if you point them in different places then you definitely can add the lumens up. If you point them on top of each other I think it's pretty much a wash.
    Okay -- then:

    Quote Originally Posted by pinkrobe View Post
    For example, 4 spotlights @ 200 lumen each will measure as 200 lumens if the beams don't overlap. However, if they are all pointed at one spot, measuring the lumens at that point should give ~800 lumen.
    See what I mean? Directly conflicting thoughts.

    This is just an educated guess, and I'm sure someone with more knowledge will chip in shortly.
    +1 (especially about finding someone with more knowledge )

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    Lumens do add. Sound pressure adds as well, it's just reported on a logrithmic scale so the value doesn't add (dynes add and convert to dB). Two 600 lumen lights, on at the same time, make 1200 lumens worth of light.

    The problem with lumen measurements for bike lighting is it only tells half the story. The other half is where you put all those fancy lumens. Spray them out in all directions and 1200 lumens worth of light doesn't mean squat. The night will just be a little less black. Focus them on the road ahead and it's a ton of light. What needs to be considered is lumen output AND beam pattern as it's only the lumens that fall where you want to look that are important.

    Quote Originally Posted by pinkrobe View Post
    There may be issues with constructive/destructive interference, but I was under the impression that the lumens were summed as long as they all focus on the same area.
    This isn't too much of consideration with non-coherent (ex: stuff that isn't a laser) light.

  6. #6
    Bike ≠ Car ≠ Ped. BarracksSi's Avatar
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    Twice as many lumens doesn't help you see twice as far, though, right? Or does that get into a logarithmic-type scale, too?

    Say that one light can be useful for seeing objects out to 100 feet; would two lights work for 200 feet?

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    Mad bike riding scientist cyccommute's Avatar
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    Quote Originally Posted by pinkrobe View Post
    There may be issues with constructive/destructive interference, but I was under the impression that the lumens were summed as long as they all focus on the same area. For example, 4 spotlights @ 200 lumen each will measure as 200 lumens if the beams don't overlap. However, if they are all pointed at one spot, measuring the lumens at that point should give ~800 lumen. This is just an educated guess, and I'm sure someone with more knowledge will chip in shortly.
    I'd say you are pretty close. Lumens are a measure of the luminous flux or the perceived power of light output. If all the lights are focused on the same spot, it will look almost like one beam of 800 lumen. In practice, however, I've found that a single source putting out 800 lumen is brighter than 4 sources putting out 200 lumen each. I think it has more to do with beam placement...it's hard to focus 4 beams onto the same place...then total output.
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    Wikipedia to the rescue!

    http://en.wikipedia.org/wiki/Lumen_%28unit%29

    The lumen can be thought of casually as a measure of the total "amount" of visible light emitted.
    So, lumens add together regardless of whether they are projected into the same space or not. If you've got three emitters beaming out light from approximately the same place, you could add them together.

    Candlepower, OTOH, is a measure of luminous intensity based on the sensitivity of the human eye.

    All of these are not to be confused with luminance, which also takes the surface area into account.

    Note that the 60W halogen bulb used in those 15 million candlepower spotlights only outputs 1100 lumens!
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    Bike ≠ Car ≠ Ped. BarracksSi's Avatar
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    Quote Originally Posted by jeff-o View Post
    Yeah, I found that, and I read through all the other light-measuring-unit articles that Wiki has, too.

    I'm beginning to think that the lumen isn't exactly a useful unit of measuring light output, especially when running UFO-like clusters that we do. If four 200-lumen lights (or eight 100-lumen lights) don't shine as far as a single one putting out 800 lumens, then it's not really safe to assume that you'll see twice as far by merely doubling the number of lights.

  10. #10
    World's slowest cyclist.
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    Quote Originally Posted by BarracksSi View Post
    Twice as many lumens doesn't help you see twice as far, though, right? Or does that get into a logarithmic-type scale, too?
    Depends on the optics. If you have a bare lightbulb then it spreads its lumens out in a sphere. Let's say that sphere is 1 foot in diameter and the lightbulb puts out 100 lumens. The surface of the sphere is 3.14 (pi) times the diameter squared. 3.14x1x1. So 100 lumens gets spread out over 3.14 square feet. About 31.8 lumens per square foot.

    Now, double the size of the sphere. 3.14x2x2=12.56 square feet. The same 100 lumens makes for 7.9 lumens per square foot.

    Doubling the distance from 1 foot to 2 feet makes your lumens per square foot go from 31.8 to 7.9. That's a BIG differene. And that's why beam pattern is important. This example is one where there are no optics, there is no beam pattern. Concentrating the beam reduces how much area these lumens get spread over as the distance increases. There's no simple answer to the question "does doubling the lumens double the distance" since it's so dependant on beam pattern. I'd rather have a weak source and good optics than a good source and poor optics.

  11. #11
    Bike ≠ Car ≠ Ped. BarracksSi's Avatar
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    Say that the beam pattern is the same, then; that'll be another controlled variable.

    If so, then would a single 800-lumen lamp help the rider see farther than four 200-lumen lamps?

    Taken another way -- how many 200-L lamps would it take to equal the "reach" of a single 800?

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    Quote Originally Posted by BarracksSi View Post
    Say that the beam pattern is the same, then; that'll be another controlled variable.

    If so, then would a single 800-lumen lamp help the rider see farther than four 200-lumen lamps?

    Taken another way -- how many 200-L lamps would it take to equal the "reach" of a single 800?
    Well, four 200 lm lamps focused onto the same area as the 800 lm lamp would illuminate that area the same amount. A single 200 lm lamp focused onto that area would be one-quarter as bright. That brightness (or luminance, to be more accurate) may be washed out by other lights, or may be below the threshold of your eye's light-gathering capability.
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    Bike ≠ Car ≠ Ped. BarracksSi's Avatar
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    Let's eliminate the variable of where they're aimed, then.

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    Quote Originally Posted by BarracksSi View Post
    Let's eliminate the variable of where they're aimed, then.
    Given equal optics, four 200 lumen lamps pointed at the same point will be exactly as bright as one 800 lumen lamp.

    The problem is you can only point four 200 lumen lamps at exactly the same point as a single 800 at one fixed distance. Beyond that the beams are converging or diverging. So at twice the distance those four lamps are spread out over a wider field than the single 800. Still, that assumes equal optics which is a HUGE assumption (typically the optical needs for a 200 lumen source are very different from those of an 800 lumen source).

    In general though I'd rather have 4 200 lumen lamps than a single 800 lumen since the 4 lamps will allow me to select better beam placement. For a ride on a straight, fast downhill I can array them to light up the road in front of me AND down the road ahead. For a single track mountain bike ride I can array them around me in the near field so I get a wide picture of the close terrain.

  15. #15
    don't try this at home. rm -rf's Avatar
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    Many bike lights have full power and half power modes. Going from half to full power, you can see that the beam is noticeably brighter, but it doesn't appear to be twice as bright. Your eye senses brightness logarithmically, similar to hearing.

    It's good that it works this way, since daylight can be up to 100,000 lumens per square meter(lux), and moonlight is about .25 lumens per square meter. per Wikipedia.
    Last edited by rm -rf; 11-12-07 at 12:49 PM.

  16. #16
    Mad bike riding scientist cyccommute's Avatar
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    Quote Originally Posted by BarracksSi View Post
    Let's eliminate the variable of where they're aimed, then.
    I've been trying to come up with a way of explaining this and keep coming up short But, with a lot of hand waving and seat of my pants science, I'm going to try again.

    Let's start with 200 lamps of 1 lumen each with a suitable reflector for focusing them. Turn them on and shine them on a target a given distance away and you'll have 200 lumens (the intensity of the light that we perceive). But each lamp is going to be a different distance from the center of the light beam array where the light is generated. The distance from the target is going to vary for lamp to lamp. The intensity of the light on the target is going to be a certain value for a lamp at the middle of the array and different for a lamp a the outside of the array (assuming a flat target). Since intensity follow an inverse square, the distance from the target is going to have a significant effect on the amount of light reaching the target.

    Now take a source of light that puts out 200 lumen. The distance to the target is the same but the intensity of the light hitting the target is much greater because the light travels the same distance from a single source. Move the target and the amount of light still drops by the square of the distance but you only have one source of light rather than 200. The light from the array is going to be much, much dimmer.

    There are going to be other factors involved too. The light is traveling through air which scatters and diffracts it and absorbs little bits of it. The more individual sources you use the more the light is subjected to these factors. You can think of it as a single high intensity source will hold together longer than multiple low intensity sources.

    From the standpoint of how much light we perceive, lumens is a pretty good measure of light. Adding them together from multiple sources is probably correct for specific distances but once the distance changes...which happens all the time while moving...multiple sources aren't going to perform the same way as a single high intensity source.
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    Quote Originally Posted by Chris_F View Post
    Given equal optics, four 200 lumen lamps pointed at the same point will be exactly as bright as one 800 lumen lamp.

    The problem is you can only point four 200 lumen lamps at exactly the same point as a single 800 at one fixed distance. Beyond that the beams are converging or diverging. So at twice the distance those four lamps are spread out over a wider field than the single 800. Still, that assumes equal optics which is a HUGE assumption (typically the optical needs for a 200 lumen source are very different from those of an 800 lumen source).
    The ~3-4 inch separation of an array of four lamps will make little difference with regards to convergence, especially if you arranged the four lamps in a square pattern.
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    don't try this at home. rm -rf's Avatar
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    My Dinotte headlight has 50, 100 and 200 lumen settings with the same beam. I'm comfortable riding 8-10 mph at 50 lumens, 14-15 mph at 100, and 18-20 at 200 lumens. I can see details farther ahead with more light. So adding lumens really does help a lot. I guess this sortof contradicts my previous post. The higher setting doesn't look that much brighter, but it has a big effect on my riding speeds.

    I was riding with a rider that had a HID light. Those are usually in the 600-800 lumen range. It had an even, wide beam that really lit the road and the sides, too. But my 175 lumen Fenix spot beam could easily reach farther than the HID, in a much smaller area.

  19. #19
    Bike ≠ Car ≠ Ped. BarracksSi's Avatar
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    Quote Originally Posted by cyccommute View Post
    I've been trying to come up with a way of explaining this and keep coming up short But, with a lot of hand waving and seat of my pants science, I'm going to try again.
    Hey, I appreciate the effort; my original questions were about lumens, not optics, unequal distances, etc. If I could test them all in a lab, I'd still try to eliminate all those variables.

  20. #20
    Mad bike riding scientist cyccommute's Avatar
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    Quote Originally Posted by BarracksSi View Post
    Hey, I appreciate the effort; my original questions were about lumens, not optics, unequal distances, etc. If I could test them all in a lab, I'd still try to eliminate all those variables.
    I think we have to look at this as an optic problem. When you make the light, the source sits at the focal point of the mirror system. Light coming from the focal point is going to diverge as it travels away from the source. A stronger source is going to diverge less for a longer distance than a weaker source. If you take 200 lumen sources and shine them at the same thing you'll have two weak sources, each diverging as the inverse square of the distance. The amount of light hitting the target is going to be some fraction of a single 400 lumen source.

    I can't do the optics (it's been a long time since physics) nor can I back it up but I can tell you from experience that 2 weak sources don't equal a single strong one. You can gang a bunch of low intensity lights together (like lots of LEDs are doing now) and add the lumens to get the 'same' output but it's not going to have the same distance and intensity as a single source of the same output.
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  21. #21
    Mad bike riding scientist cyccommute's Avatar
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    Quote Originally Posted by rm -rf View Post
    My Dinotte headlight has 50, 100 and 200 lumen settings with the same beam. I'm comfortable riding 8-10 mph at 50 lumens, 14-15 mph at 100, and 18-20 at 200 lumens. I can see details farther ahead with more light. So adding lumens really does help a lot. I guess this sortof contradicts my previous post. The higher setting doesn't look that much brighter, but it has a big effect on my riding speeds.

    I was riding with a rider that had a HID light. Those are usually in the 600-800 lumen range. It had an even, wide beam that really lit the road and the sides, too. But my 175 lumen Fenix spot beam could easily reach farther than the HID, in a much smaller area.
    A question you can answer since you have variable light output settings (None of my lights do): I know you put out less light but does the distance that beam is thrown out in front of you vary by much? In other words, you should just get a less intense circle of light but the same distance from the bike at the different settings, correct?
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  22. #22
    don't try this at home. rm -rf's Avatar
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    Quote Originally Posted by cyccommute View Post
    A question you can answer since you have variable light output settings (None of my lights do): I know you put out less light but does the distance that beam is thrown out in front of you vary by much? In other words, you should just get a less intense circle of light but the same distance from the bike at the different settings, correct?
    Yes, the light pattern is the same.

    At dimmer settings, I would usually point it down, closer to the bike, since the beam spreads out more when it's far away.

    Unless I expect to need the longer run times that I get on medium or low, I always run the lights at high power.
    Last edited by rm -rf; 11-12-07 at 05:18 PM.

  23. #23
    Mad bike riding scientist cyccommute's Avatar
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    Quote Originally Posted by rm -rf View Post
    Yes, the light pattern is the same.

    At dimmer settings, I would usually point it down, closer to the bike, since the beam spreads out more when it's far away.

    Unless I expect to need the longer run times that I get on medium or low, I always run the lights at high power.
    That's why I suspect that adding lumens by using multiple sources is an optics problem. Your optics are the same and gives the same pattern and distance with just a lower intensity. Add another source of light and your brightness will go up but the distance and pattern won't change, BarracksSi.
    Last edited by cyccommute; 11-13-07 at 08:20 AM.
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  24. #24
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    IMHO, how much light you need depends on the ambient light level. On a sufficiently dark road, I can see perfectly fine a long distance ahead of me with a poor 3 W bulb. 20 mph would be no problem at all for me.

    However, on a road with lights nearby, or with a lot of oncoming traffic, your eyes will adapt to a different light level, and the light from your bulb is no longer enough to provide sufficient illumination.

    Remember that the light that reaches the ground from your lamp decreases exponentially with distance, but ALSO that the light reflected from the ground does so too on its way back to you and your eyes. Narrowing the beam or increasing the area intensity by increasing light output, will both increase the amount of light reaching the ground, and the intensity of the light reflected back to you.

    Another issue is how well you are seen by others. For an incandescent bulb in a parabolic reflector, bulb output divided by reflector cross-sectional area should give the apparent intensity to an observer.
    A regular car headlight uses a 55 W halogen bulb and a typical reflector diameter might be around 15 cm. My 3 W lamps are about 4 cm in diameter. The car's reflector then has an area 14 times that of my lamps.

    3 W * 14 = 42 (apparent watts)

    That means that the apparent intensity (brightness) of my bike lamp should be close to that of a car's headlight. This assumes that the light output of the bulbs are equal in terms of visible light photons/watt, which probably isn't the case. But I couldn't find any data on that through a quick search.

    My experience, though, is that a 3 W generator-powered bicycle lamp is nearly as bright to the eye as the headlight of a regular car.

  25. #25
    Bike ≠ Car ≠ Ped. BarracksSi's Avatar
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    Quote Originally Posted by cyccommute View Post
    That's why I suspect that adding lumens by using multiple sources is an optics problem. Your optics is the same and gives the same pattern and distance with just a lower intensity. Add another source of light and your brightness will go up but the distance and pattern won't change, BarracksSi.
    Higher intensity should give better distance, though, at least enough to be noticeable by the eye. I've also got a Dinotte headlight, and between its high & low settings, it's easier to see farther when it's set at its brightest.

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