New way to think about efficiency

I came up with a formula for measuring the overall efficiency of a flashlight--one that should be more useful than the more familiar numbers such as bulb lumens, lumens per watt, etc. The idea is to correlate the energy input in batteries (not watts) to the relevant output in beam lumens (not lamp or emitter lumens) over time.

The goal is to estimate how many lumen-hours per cell a flashlight can achieve. This metric accounts for the entire chain of possible inefficiencies--battery internal resistance, regulator losses, emitter losses, and optical losses. The metric also accounts for more cells providing more output or runtime. For now, I have limited myself to 123A lithium cells for the purpose of simple comparisons.

Most of the numbers are based on data from flashlightreviews.com. Lumens were taken as initial lumens, and the time is estimated according to how long the batteries would last if the initial brightness were maintained. I did this by eye from the output curves. More precisely, it would be in integrated lumen-hours over the battery life, divided by the initial lumens.

Here is my graph for some popular flashlights (Luxeon lights divided by one or two cells):



Here we can see that the Inova T1, Longbow Micra, and Nuwai Q3 have pretty poor efficiencies. The E1L and Amilite are a little better. A large segment of the flashlights on the graph lie along a horizontal line from the E2L to the L4. These lights have roughly the same efficiency despite a wide range of light output.

The Inova T2 and Surefire KL3 are particularly good among the 2x123A Luxeon flashlights. This efficiency likely comes from pulling a low current from a high voltage power source. The batteries and regulator are not being strained as they are in the more strongly driven flashlights.

The Dorcy 1x123A Luxeon is surprisingly good, and it will still be good even if you use a more conservative normalized runtime estimate of 2 hours rather than 2.5 like I used. Having a Q bin instead of R will knock the efficiency down even more.

There's not too much of a surprise that the HDS 60 gets a very high efficiency on its underdriven primary beam. The maximum beam looks better on the graph than it probably should, since it's running at full power for only about half of the normalized runtime.

The 2 cell incandescents aren't too bad, especially when compared to some of the more poorly-performing Luxeon lights such as the Nuwai Q3. However, the data for the E1e show why 1-cell incandescents aren't too popular.

Nice work! So the Dorcy kicked butt? That is surprising...I thought that my Dorcy Wal-Mart lights were second-rate.

Is that saying the HDS 60 runs at 12 lumens or so for 140 hours? I'm skeptical.

paulr said:

Is that saying the HDS 60 runs at 12 lumens or so for 140 hours? I'm skeptical.

Click to expand...

Nope ... It's saying that it gets 140 lumen-hours per cell, which in this case is the result of producing 12 lumens over 11.5 hours.

Looks right at 65ish or more for the HDS EDC (Well its ment to put out 60 lumens max right?)

Great idea. I am concerned about using initial lumens rather than an average or integral.

Going to the 50% brightness point: a light that linearly goes from 100% to 50% will look 25% better than one that is perfectly regulated and then drops suddently to 50%.
Even worse are lights that are really bright for the first 15 minutes then drop down and have a flatter curve to 50%.

I haven't looked at the curves for the lights on your chart (recently) so I don't know if the problem is as bad as I make it.

Greg

I suspect an L1P v2.5 running on low with a 2 stage mode would do pretty well using this.

With 5 ohms, mine is very, very close to an unmodified Dorcy 1AAA judging total output on ceiling bounce. flashlightreviews.com puts the Dorcy at 4 lumens. Based on current measurements, it should run about 30 hours with a 2500 mAH NiMH for a 120 score. With the 2.7 ohms I'm running, I think it's at least 6-7 lumens and should run 15-16 hours putting it in the 90-105 range as a conservative estimate.

On high, it's probably about < 65 based on ~2.5 hours @ 26 lumens (2500 mAH NiMH) based on the initial output. The R bin Lux 1 looks very efficient when underdriven considering about 30% of the power used is being consumed in the resistor on low.

Mike

greg_in_canada said:

Great idea. I am concerned about using initial lumens rather than an average or integral.

Going to the 50% brightness point: a light that linearly goes from 100% to 50% will look 25% better than one that is perfectly regulated and then drops suddently to 50%.
Even worse are lights that are really bright for the first 15 minutes then drop down and have a flatter curve to 50%.

Click to expand...

Here's how I derived my normalized run times from the graphs:



I picked a time so that the negative "red" area and positive "blue" area are nearly equal. So in this case, the Surefire E1L has a normalized runtime of about 1 hour and 25 minutes. This trick is equivalent to applying the integral average value theorem by eye. The resulting physical quantity--from multiplying the initial lumens by the normalized runtime--is equivalent to integrating the real lumen output over the entire battery lifetime. My method doesn't require you to do the integration explicitly.

Here is the complete data table that I used for the graph:

Very very interesting, excellent work!! :thumbsup:

Intresting, but there are limitations to it's usefullness in the graph's current form IMHO it is not really fair to compare a 20 lumen to a 60 lumen light. The lower amp draw gives it an advantage.

Allong these lines, the "efficiency king" would be a 3W luxeon connected in parallel to a large number of 123s (100?) which will be able to support the current draw for a really long time.

Suggestions for improvement
Seperate lights into categories:
All Lights--->Luxeon ---># of batteries --->0-10 lumen
--->10-20 lumen
--->20-30 lumen
--->30-40 lumen
--->40-50 lumen
--->50-60 lumen

--->Incan ---># of batteries --->0-10 lumen
--->10-20 lumen
--->20-30 lumen
--->30-40 lumen
--->40-50 lumen
--->50-60 lumen

lightmaster said:

Intresting, but there are limitations to it's usefullness in the graph's current form IMHO it is not really fair to compare a 20 lumen to a 60 lumen light. The lower amp draw gives it an advantage.

Click to expand...

Very true ... which is why I decided to not compensate for power draw. Lights like the Inova T2 have a efficiency advantage over lights that drive their batteries and emitter harder. That's a real design tradeoff that should be shown plainly and not normalized out.

The x-axis of the graph that I posted approximately corresponds to the power draw per cell. If I were to use straight lumens rather than lumens per cell, it would approximately correspond to the emitter power instead. Both graphs would be useful for different purposes.