# Bulb Re-rating & Torch Lumens Questions

#### TBrogden

##### Newly Enlightened
All,

Are there any formulae or rules of thumb for "re-rating" of incandescent bulbs? I'm finding that Welch Allyn's website doesn't offer re-rating for all its bulbs and, even when it does provide that info, it doesn't extend to voltages in which interested.

Also, I often see here in the forums that torch lumens have been calculated at 65% of bulb lumens. If not too much trouble, I would very much like to know how that number was derived and the weighted contributions of those things making up the 35% "loss".

Many thanks,

Tony

#### Lurveleven

##### Flashlight Enthusiast
See my signature for WA re-rating.

For bulbs from other manufacturers you can use the following formulas for re-rating:

The formula for halogen lumens re-rating is as follows:

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.

The formula for halogen lamp life re-rating is as follows:

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.

The formula for halogen current re-rating is as follows:

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.

The formula for halogen CCT re-rating is as follows:

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.

To find voltage sag:
Va = (Aa/Ad)^1.818*Vd, where Aa is applied current, and Ad is design current, and Vd is design voltage and Va is applied voltage.

To find applied voltage from lamp life:
Va = Vd/((Lr/Ld)^(1/12)), where Lr is re-rated life, and Ld is design life, and Vd is design voltage and Va is applied voltage.

To find applied voltage from lumens:
Va = (Lr/Ld)^(1/3.5)*Vd, where Lr is re-rated lumens, and Ld is design lumens, and Vd is design voltage and Va is applied voltage.

I'll let JS chime in on how they arrived at 65% for the torch lumens.

Sigbjoern

#### bwaites

##### Flashlight Enthusiast
Sig,

Thanks for those formulas again!

I lost them with my computer crash and hoped someone would post so I wouldn't have to go looking!!!

Bill

#### TBrogden

##### Newly Enlightened
Sig,

This is great!

Thanks very much,

Tony

#### Phaserburn

##### Flashlight Enthusiast
dummy question: what does ^ mean?

:duh2:

#### Haesslich

##### Flashlight Enthusiast
That's the Exponent sign: So in other words, the equation 'Lr = (Vd/Va)^12*Ld' can be rewritten as so:

Lamp Rating is equal to the product of the design voltage divided by the applied voltage of a lamp, to the power of 12 times the design life of a lamp.

#### Phaserburn

##### Flashlight Enthusiast
Thanks, Haesslich!

:thanks:

#### JimH

##### Flashlight Enthusiast
Sig,

Thanks for the formulas, but, unless I missed it, you forgot one. Carley lists the output of their lamps in Mean Spherical Candlepower, which is directly convertable to lumens.

MSCP (mean spherical candle power)

lumens = MSCP X 4 Pi = MSCP X 12.566

If you don't mind, I'd like to copy those formulas over to the CPF Wiki where it's easy to find them.

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#### Lurveleven

##### Flashlight Enthusiast
Thanks Jim.

Btw, it should be: Lumens = MSCP x 12.566
I guess you don't have Pi on your calculator so you must have miss-entered 3.1715 instead of 3.1415 when using your calculator.

Sigbjoern

#### JimH

##### Flashlight Enthusiast
Lurveleven said:
Thanks Jim.

Btw, it should be: Lumens = MSCP x 12.566
I guess you don't have Pi on your calculator so you must have miss-entered 3.1715 instead of 3.1415 when using your calculator.

Sigbjoern

I did enter it from memory but made a typo
- damned fat fingers
.

Good catch, I'll correct it.

#### PaulW

##### Flashlight Enthusiast
Tony,

TBrogden said:
. . . Also, I often see here in the forums that torch lumens have been calculated at 65% of bulb lumens. If not too much trouble, I would very much like to know how that number was derived and the weighted contributions of those things making up the 35% "loss". . . .
As far as I know, the 65% figure came from empirical tests. That is, when measuring the light from a torch using a WA bulb, it seemed generally to be about 65% as bright as a Surefire torch with the same designated lumens. This led to folks making "total light output" tests designed to comare two torches.

Such tests are designed to get a measure of total light rather than direct light in the beam center. The light reflected from a wall or corner is measured for each torch. Some folks have even constructed little chambers, such as milk bottles to collect the light.

No one knows exactly where the other 35% of the light goes. It has been guessed by some of our smarter CPFers that it is probably lost within the torch's head -- in reflection at the lens surfaces, absorption by the reflector surface, and capture in the hole in the reflector near the bulb's base.

Paul

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#### bwaites

##### Flashlight Enthusiast
Actually, that 65% figure was arrived at with a little more objectivity and research than just comparisons. It took into account aluminum coating reflectivity, window loss, etc.

I suspect that Ginseng (and probably js!) has it logged away where we came up with that figure, but it is pretty widely aknowledged on the board that it is close to correct.

Another interesting factoid:

Surefire rates their lights with a very conservative "torch lumens", or actual lumens out the front, while most companies rate their lights with "bulb lumens" or lumens produced by the bulb, before reflection.
Bill

#### PaulW

##### Flashlight Enthusiast
bwaites said:
Actually, that 65% figure was arrived at with a little more objectivity and research than just comparisons. It took into account aluminum coating reflectivity, window loss, etc.

I suspect that Ginseng (and probably js!) has it logged away where we came up with that figure, but it is pretty widely aknowledged on the board that it is close to correct.

Bill
Thanks, Bill. It's always a good day when I learn something new. I had no idea you guys had been working on that.

Paul

#### bwaites

##### Flashlight Enthusiast
No credit on my part!! When I say "we", I mean those of us who quote it, not that I had anything to do with the number!!

Someone on CPF, and I don't remember who it was, but I'm sure js or ginseng or both will, came up with that number and it has proven pretty reliable when we compare it with the "known" numbers from Surefire.

Bill

#### Size15's

##### Flashaholic
bwaites said:
Another interesting factoid:

Surefire rates their lights with a very conservative "torch lumens", or actual lumens out the front, while most companies rate their lights with "bulb lumens" or lumens produced by the bulb, before reflection.
Bill

To follow what Bill has written, SureFire's rating is not the peak output over the course of the unregulated runtime but a value more representative of the light output over the course of the runtime of the batteries.

For example, SureFire rates it's E2e at 60 lumens. Independant rate put the output in the order of 80 lumens I believe.

Comparing lumen ratings between manufacturers is almost as pointless as comparing candlepower ratings. At least that's my opinion.

Al :shrug:

#### andrewwynn

##### Flashlight Enthusiast
manoman thanks so much for the formulas.. my 'master database' of WA lamps running from every possible battery combination just took a huge step up in performance.. it automatically recalculates everything you just put in the switch (circuit) resistance and blamo.. i even figured out how to have it resolve circular references so that it recalculates the ending current after considering voltage drop.

I think i'll makes a quick n dirty re-rater spreadsheet that i can post.

the WA re-rater will let you use any bulb you just have to put it in manually.. i've been told and it makes sense that re-rating can only bet trusted maybe 20% +/- but the formula is what you have to go with, and i'm sure that certain bulbs can be pushed a lot harder than 20% overdrive..

One thing i've adeed to my re-rating spreadsheet: the ability to track how close to the melting point the filament is.. i'm finding that 4-5% away from the melting point is a really nice place to run WA bulbs.. you end up with low 30s for lumen/watt and the color is spot-on gorgeous.

I think i'm going to go make a simplified version of my spreadsheet now i'm betting it'd be very helpful to hotwire folk.

-awr

#### andrewwynn

##### Flashlight Enthusiast
OK.. here it is:

That is a screen shot of the re-rater spreadsheet..

(right click and save target).

the key is right inside the file just scroll down to read it.

I have a couple bulbs in there...my 'master spreadsheet' has a different theme to it... it's broken down by host light.. i.e. has all the bulbs that work well from a 7.2V source and also has all the battery combinations that work in that voltage.. it would take an hour just to explain how to use it, but it is awesome.

This is a much more simple design.. has spots for two bulbs.. and will let you either put in the bulb voltage you desire and it will show you the input voltage required.. or you can put in input (battery) voltage and it will show you the bulb voltage you will get based on a resistance value you put in (there is a chart included for all the basis possibilities).

As you can see from the sample. .the 1111 is a kick butt bulb.. in a 7.2V source you can expect 834 bulb lumen nominal with the KIU socket!

If you put the 1274 in a 2D-3bore with 9 CR123 primaries.. regulate to 8V and get 800 lumens.. the Vbulb and Vbat are entered as well as the 'blue' values for the design values of the bulb.

My favorite part is now everything is calculated including current.. it actually is a circular reference since the current is based on the voltage but the bulb voltage depends on the current.. it just 'finds the answer' automatically.. gotta love computers sometimes.

This spreadsheet takes into account the voltage losses on the switch.. put in your favorite bulb and change the resistance value from 30 (KIU socket) to stock pr bulb (177) and watch the dastardly effect it has on the lumen output!

Hope people find it useful, please post if you grabbed it and it helpd you out.

-awr

#### Nereus

##### Enlightened
Thanks, Lurveleven, for _very_ useful bulb re-rating formulas! I noticed that they produce very similar results with WA's site when re-rating 01185 and 01166 bulbs. I would not be surprised if WA used them directly. Now I have two questions for you (or for anyone who knows the answer):

Where did you get those formulas?

Sometimes people say that bulb is running xxx% from the (tungsten?) melting point. How do you calculate that percentage?

WBR, Nereus

#### Lurveleven

##### Flashlight Enthusiast
The two first formulas have previously been posted on CPF, but the rest I had to create myself. To do that I collected a few data points from the output from the WA rerater and used those to reverse engineer the formulas.

Sigbjoern

#### andrewwynn

##### Flashlight Enthusiast
Kelvin temperature is an abolute scale.. 0K is absolute zero it's a direct fraction. W melts at 3695K. the formula is: (1-bulbtemp-3695) (and x100 if you want to read %).

the formulas Lurveleven posted are what WA's re-rater uses.. the results from the formula that i included from lurve into my spreadsheet match to the decimal point exactly what the results show from the WA re-rater... they might go more than 3 sig. digits but it's a moot point.. they are perfect.. i love that the current calculations even though 'circular' i was able to let the spreadsheet iteratively calculate 'til it finds the solution that is my favorite part... you have no idea how many times i used a calculator to estimate the current at a different voltage! (which of course.. changes as soon as you change the current. aaaaah)

-awr