# How do I calculate lumens?



## dlrflyer (May 3, 2007)

I'm getting the pieces together to make a fairly potent cheapo light but I have no idea what sort of lumens it's capable of. I using an Energizer Hard Case 4D lantern, using 4 3AA-D series adapters to overdrive an XPR12 which is a 12v 0.7a xenon bulb. Is there any way to calculate how many lumens this will generate? I don't have any specs other than volts and amps.


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## mdocod (May 3, 2007)

we might be able to come up with a rough estimate... but more specs on the bulb would be great...

are you going to run NIMH, alkaline? lithium?

from what I was able to gather, the bulb is rated 12V, 0.7A, 20 hour life... but another source was saying more like 50 hour life... so I really don't know...

problem is.. if the bulb is already at 20 hours life at 12V, then you don't have a lot of room to overdrive.

If it really is 20 hours life at 12V, then I would guesstimate that it makes about 200-275 bulb lumens. (I can't gives a definite number here, but this is conservative and reasonable)... If you were to drive it at 15V, the bulb life would rerate to about an hour, with an output around 500 bulb lumens, but with that kind of life rating, that the likelihood of instaflashing would be almost garanteed. 

try to find some more info about the bulb if you can...


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## dlrflyer (May 3, 2007)

Well my plan was to use 12 nimh AAs for a nominal 14.4v, hard to say since i'm expecting fairly high resistance given all the connections. But if bulb life is only about 1 hr, yuckk. I could use an XPR14, which is a 14.4v, 0.7a bulb, certainly longer life, but no overdrive. There's just very little info on these bulbs, Don's Bulbs has the most data. I'm surprised that bulb life is so low. I've used 4 nimh with KPR139 which is a 3.85v bulb rated at 10hrs, but I've gotten 10hrs overdriven.


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## mdocod (May 3, 2007)

buy both bulbs and give it a try... keep in mind that NIMH are more like 1.4V off the charger, and settle to about 1.3V after a few days. 12NIMH could deliver around 17V fresh off the charger... but like you said, with all the resistance in the connections, it may work just fine.

hey does that energizer hard case have a metal reflector?


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## DrifT3R (May 3, 2007)

The short answer is you can't calculate lumens very accurately.
You can measure lux with a light meter though.


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## abvidledUK (May 3, 2007)

I spreadsheet torch info, and it becomes obvious approx Lumens for various torches in between, using lux, CPF comparisons, etc.

(Not every torch, just ones I am interested in, or have owned)

In conjunction with my own EV measurements.


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## litho123 (May 3, 2007)

Some bulbs list Mean Spherical Candle Power (MSCP) others list BULB_Lumens
Take the MSCP * 12.57 to get an approximate BULB_Lumens (B-lu)

That gives you the approximate lumens @ spec.
Overdrive is another formula to factor in.

Rerated lumens = (Overdrive voltage / @spec voltage)^3.5*Bulb_lumens)

Over the year's it has been determined that it's best to take 65% of the B-lu figure to approximate a more real world lumens number - TORCH-lumens (T-lu)


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## dlrflyer (May 3, 2007)

Thanks everybody for your help. I'm not a scientist, so I don't feel the need for anything more than a ballpark number on the lumens. The Energizer Hard Case has a thick plastic reflector with about a 1" diameter metal "fitting" where the bulb rests. It's threaded and a plastic cap holding a spring secures the bulb. I'm sure this fitting provides the + and the cap has the - connection.


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## LED BriCK (May 3, 2007)

litho123 said:


> Rerated lumens = (Overdrive voltage / @spec voltage)^3.5*Bulb_lumens)


Can you help me read that formula? Is that (overdrive V/spec V) raised to the 3.5 power, then all that multiplied by bulb_lumens?


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## CM (May 3, 2007)

Too many have tried coming up with lumen figures, from poor man's integrating shoebox "spheres" to outright incorrect extrapolation from lux measurements. While the poor man's method is somewhat sound, there's no other way than to measure it with the proper instrument. For comparative output purposes, a light meter in conjunction with bouncing the light off the ceiling will give you acceptable ballpark figures. Don't overstimate the precision or repeatability of that test though. It's still subject to a lot of "noise"


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## mdocod (May 3, 2007)

> Can you help me read that formula? Is that (overdrive V/spec V) raised to the 3.5 power, then all that multiplied by bulb_lumens?



yep

so say the bulb is rated for 12V 200 lumen.
lets say you are gona hit it with 14.4V.

14.4/12=1.2

1.2^3.5=~1.9

1.9x200=380 lumen.


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## 2xTrinity (May 3, 2007)

> Over the year's it has been determined that it's best to take 65% of the B-lu figure to approximate a more real world lumens number - TORCH-lumens (T-lu)


This is what is throwing me off... are reflector surfaces really that inefficient that third of the light is being absorbed? Even if a glass lens isn't anti-reflective coated, most of the light that makes it through the first time should bounce back into the reflector, then back out of the light the second time (as spill). 65% losses would seem to suggest that reflector surfaces are only about 50% efficient, which makes no sense whatsoever. It seems like with the kind of money people are willing to putting flashlights on here, it should be possible to get higher-quality Aluminized surfaces (which can be well over 90% reflective), or even some sort of total-internal-reflecting optics like projector headlights.


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## LED BriCK (May 3, 2007)

Thanks, mdocod! Now I have a rerater spreadsheet on my Pocket PC! Does this formula apply to all incans, or only halogen?


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## mdocod (May 3, 2007)

> Does this formula apply to all incans, or only halogen?



It's kindof a general middle of the road for re-rating halogens... for rough estimates it works with most halogen and xenon bulbs reasonably well. Some manufactures will give their own re-rating formulas because different bulbs re-rate differently than this "standardized" formula. There are also more halogen formulas...

formula for halogen lumens re-rating:

Lr = (Va/Vd)^3.5*Ld, where Lr is re-rated lumens, and Ld is design lumens, and Vd is design voltage and Va is applied voltage.


formula for halogen lamp life re-rating:

Lr = (Vd/Va)^12*Ld, where Lr is re-rated life, and Ld is design life, and Vd is design voltage and Va is applied voltage.


formula for halogen current re-rating:

Ar = (Va/Vd)^0.55*Ad, where Ar is re-rated current, and Ad is design current, and Vd is design voltage and Va is applied voltage.


formula for halogen CCT re-rating:

CCTr = (Va/Vd)^0.317*CCTd, where CCTr is re-rated CCT, and CCTd is design CCT, and Vd is design voltage and Va is applied voltage.





> This is what is throwing me off... are reflector surfaces really that inefficient that third of the light is being absorbed? Even if a glass lens isn't anti-reflective coated, most of the light that makes it through the first time should bounce back into the reflector, then back out of the light the second time (as spill). 65% losses would seem to suggest that reflector surfaces are only about 50% efficient, which makes no sense whatsoever. It seems like with the kind of money people are willing to putting flashlights on here, it should be possible to get higher-quality Aluminized surfaces (which can be well over 90% reflective), or even some sort of total-internal-reflecting optics like projector headlights.



there was a long thread discussing that... I can't find it right now..

the jist is that, a filament emits light in all directions, the problem is, the bulb is shoved through a hole in the bottom of the reflector, so a "cone" of light emitted downward towards that hole is lost, that accounts for about 15-20% of the light loss in most reflector configurations. another 10-20% loss from the reflectivity not being "perfect" on the surface of the cone, and about 1-5% loss through the window..

when you load an LED into the base of a reflector, you loose a lot less, efficiency is more like 85-90% because LEDs emit light on a "half-plane" so to speak. so they don't loose light out the back of the hole.


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## [email protected] (May 3, 2007)

mdocod,

For gas-filled lamps, halogen lamps (gas-filled with halogen and some argon or xenon), the power for rerated voltage ratio to Lumen ratio should be 3.38 instead of 3.5. The 3.5 power is only for vacuum lamps.

Mark


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## mdocod (May 4, 2007)

hmmm, 3.5 is the number i've seen posted time and time again around here.. that's interesting.


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## litho123 (May 4, 2007)

the B-lu vs. T-lu discussion is in this thread here...
https://www.candlepowerforums.com/threads/106790

and thanks mdocod for the other formulas posted.


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## Lurveleven (May 4, 2007)

[email protected] said:


> mdocod,
> 
> For gas-filled lamps, halogen lamps (gas-filled with halogen and some argon or xenon), the power for rerated voltage ratio to Lumen ratio should be 3.38 instead of 3.5. The 3.5 power is only for vacuum lamps.
> 
> Mark



Welch Allyn is using 3.5 in their rerating formulas for gas-filled lamps. Does this mean their reratings are wrong?

Sigbjoern


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## [email protected] (May 4, 2007)

Sigbjoern,

The performance of a miniature tungsten filament lamp at different voltage is governed ROUGHLY by the following rules:

(1) Candlepower (Lumens) of a lamp is directly proportional to 3.5 power of voltage.

(2) Life of a lamp is inversely proportional to the 12th power of voltage.

(3) Current consumption is proportional to 0.55 power of voltage.

The above rules were developed several decades ago and are roughly for the estimation. This is quite true as at that time, most incandescent is vacuum. The 3.38 power was listed in another Electrical Dictionary for large gas-filled lamps basically for household operation.

It seems reasonable that the power should be less than that of 3.5 which is applied for vacuum lamp most of the time because the gas-filled lamp may dissipate more heat via the filled-gas.

It is understandable for WA to use the original formula to CALCULATE the rerated lumens for their halogen gas-filled lamp. I don't think the rerated lumens was detected under the photometric integrating sphere as the rerated lumens is actually a calculated result based on the original formula.

On the other hand, the rerated lumen is also related to the pressure the gas-filled in. The more gas filled in, the more inaccurate the rerated lumens.

I have used one of our high pressure xenon lamps (8 atm. pressure xenon at ambient temperature) to test the performance and found the rerated lumens have a 3.0 power relationship instead of 3.5 power. It is because the high pressure xenon lamp was developed in this decade and nobody has done a research on it. Nevertheless, the results using 3.0 power and 3.5 power are only a few lumens difference.


Therefore, don't bother too much on the lumens output, our naked eyes cannot distinguish the brightness in +/- 15%. This is quite a large number in a high lumen output lamp.

Mark


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## dlrflyer (May 9, 2007)

Hmm, I'm no math professor, but I'm not so sure I believe these rerating formulas are accurate. For example: I have a 2D Mag with 6 AA nimh in series for a nominal 7.2v and am using a SKPR823 bulb, which is a 4.8v 1.1a krypton bulb rated at 84 lumens. Using these formulas, it rerates to 425 lumens. Using a tLu value of .65, that comes out to 276 lumens. While it is quite bright, I can't believe it's that bright. Not to mention I'm wayyyy past the re-rated bulb life. Certainly, I'm not accounting for resistance, but then nimh come out hotter than 1.2v off the charger too. I'm not sure what to believe anymore.


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## mdocod (May 9, 2007)

[email protected]=5.28W>84 lumen. ~16 lm/w

at 4.8V, this bulb is really being driven VERY gently. only delivering 16lm/w is an indication that it would have about 1000-2000 hours life at that drive level.

I'm pretty sure krypton bulb re-rate formulas are different than halogen/xenon. Seems I recall reading somewhere that krypton lamps have less extreme responses to changes in voltage. (the exponents are lower in the formulas). 

but assuming the regular formulas. 
@7.2V it would be @1.375A. 9.9W. Assuming the original lamp life was around 1500 hours, the new lamp life is around 10 hours.
Lumens re-rate to 344,. So torch lumens would be about 223. ~35 Bulb lumen/watt, which is about right for a lamp driven pretty hard.. 

it could be less than that... I think Mark is on to something with the new gas-fill lamps probably dissipating heat differently than vacuum lamps. Something closer to 3-3.3 probably is more appropriate for the lumen re-rating. Life rerating may be a little less harsh than ^12,


[edit] I'm not sure how you came up with 425 lumens, must have made an error


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## dlrflyer (May 9, 2007)

I took 7.2v divided by 4.8v to come up with 1.5. Took 1.5 to the 3.5 power, comes out to a hair over 5. Took that number(5.0625) and multiplied by 84 lumens to get 425.25 lumens. Bulb life was rated at 15 hrs. My info came from Energizer and from Don's Bulbs website.(Both identical) This bulb came from my Energizer Hard Case 4D lantern that I'm wanting to hotwire as above, I just recycled the bulb into my 2D Mag. I think it's a neat bulb. Waste not want not


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## mdocod (May 10, 2007)

1.5^3.5=4.133


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## dlrflyer (May 10, 2007)

I don't have a scientific calculator so I used this website.

http://www.webwinder.com/wwhtmbin/jexpont.html

I tried a couple of easy ones like 2 to the 3rd power and it came out accurate.


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## mdocod (May 10, 2007)

after playing with that one a minute, I noticed why it's not working right, it is not capable of handling exponents with decimals, it rounds to the next whole number... try again with 1.5^4 and you'll get the same result and realize what I am talking about.

I'm pretty sure mac, pc, most linux, just about every operating system distribution comes with a calculator app, you sometimes have to set a preference to change it to scientific calc.


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## winny (May 10, 2007)

Peoples estimates of about 200 lumen at 12 V seems about right, but too high if any. If you look here: link, more than 20 lm/W is unrealistic at 8.4 W, assuming 100 hour bulb life. That is at 12 V. 
From there, you can use the overdrive formula the same people are suggesting to calculate it at 14.4 V.


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