Hi there D6859,
many thanks for taking the time to explain these difficult concepts. I certainly learned a lot more than I knew before about lux/lumen formulas.
I see your point about the integration operation "destroying" information about the shape. And you are right, in general.
My non-mathematician understanding was based on a simpler approach where the integration operation is done over a simple geometry, resulting in the formula:
Lux = Lumen divided by beam cross-sectional area.
In layman's terms, each LED has a fixed beam angle. This is then fed into the geometry of the flashlight reflector, and perhaps further through an optic, giving the final lux measurement given a lumen input.
But, another way of thinking is this: once we fix the LED and flashlight geometry, if we are able to pump more lumen out of the flashlight (say, by increasing the current we feed to the LED), we also increase the lux.
That's why I came up with the Lux per Amp draw as a useful measure.
Maybe I am a bit influenced also by my strong focus on runtime in flashlights, which led me to be interested in a measure that combines the lux and the current draw.
Anyway, as you explained your measure more it does sound like it could be an interesting approach, I hope to find some time to input it into my database and maybe see how it correlates with the measure I propose, or how it classifies flashlights that I know about to see if I agree with its classification scheme.
To be continued!
So as indicated in my earlier post (quoted above), I went ahead and plugged in the alternative formula for throwiness:
"Throw distance squared over Lumen"
into my own database.
First conclusion: there is some significant correlation between this proposed measure and the one I proposed earlier (lux per Amp draw), at 0.61, but, indeed, the correlation is not perfect.
Next, the "distance squared over lumen" formula does capture flashlights that I consider more throwy:
--The Vihn thrower still comes out on top (measure about 360 ).
--the M30/M60 Malkoff drop-ins come in between 60-90 or so (a bit under-rated, I'd say).
--a Tekna 6 (which also has an XR-E LED) diving flashlight, which is a strong thrower, which I wasn't able to calculate using my own measure, can be calculated at 260.
--The Nailbender XPG-2 smooth reflector drop-in also comes in strong at 135.
--The MacGizmo classic, the Ti-PD-S continues to show strongly (despite its LED being so many generations behind by now), at 105.
Does it miss anything? (in my opinion, naturally!).
--For LEDs in the color red, it seems to over-state the throwiness, maybe because the color LED needs a higher current to produce its throw than the white LEDs, a factor which of course it ignores.
--Also for the same LED driven at different current, sometimes it looks to me to be producing insufficient variation; of course, LEDs have different efficiencies at different currents, and it is an advantage of the lux/amp draw measure that it can account for these.
Finally, for those who wish to focus on the distance squared/lumen measure, is there a kind of "natural" breakpoint" between throwiness and non-throwiness?
Eyeballing my database, perhaps at around 60 or so.
Though, mainly for the highest current at which the flashlight is driving the LED, as this number can vary quite a bit in some cases especially for very low current draws. (you see that the current draw matters!).