Here is a nice explanation. It's in German, so use Google Translate.
For throw only two things matter:
1. luminance of the light source (cd/mm^2)
2. Size (diameter) of the reflector or optic as seen from the hotspot (mm^2)
1. The luminance of a light source is what some people refer to as "surface brightness". It is the only unit of light that the human eye can directly perceive (how bright a light source looks when you look directly at it). Most LED manufacturers unfortunately don't list this in their datasheets (only Osram for some LEDs). It can be measured though, but a lot of careful work is needed. Luckily for us sma and Köf3 have measured some emitters and have compiled lists
here and
here (also in German).
Generally LEDs don't have a very high luminance compared to the best (short-arc) HID bulbs. Thats why no one has beaten the Maxabeam yet with an LED light of the same size. The LED with highest luminance (
Osram Oslon SYNIOS DMLN31.SG white) currently goes up to ~300cd/mm^2. This is much higher than most other LEDs, but comes with a lot of trade-offs (very small Die, very low lumens etc.). The next best one which seems much more reasonable for flashlights because it produces much more lumens is the
Osram Black Flat Gen2. It goes up to around 250cd/mm^2 and 900 Lumens.
So luminance is candela per square millimeter of the size of the light source. To measure this you need to measure the luminous intensity of the light source (candela, lux@1m) without any optic or reflector from head on and also precisely measure the size of the light source. You also need to be very careful to not let any stray light of the light source hit the sensor of your lux meter. Only direct light should hit it. After you have done this you just divide the luminous intensity by the size to get the luminance.
One thing to note: the luminance of a light source is constant. It doesn't change with the angle you look it at and optics don't increase it.
2. The other thing that matters is the size of your optic or reflector. Imagine that you are standing where the hotspot of the flashlight is. What do you see when you look into the light? You see a glowing circle. You need to determine the size of this circle. So for reflectors you just need the diameter of both openings and for lenses you just need the diameter. Area = radius^2 * pi. This is the reason why the depth of a reflector doesn't really matter for throw. It has almost no effect. Only the outer diameter really matters.
So how do you get throw with these two values?
You just multiply them.
Luminous_intensity [cd or "lux@1m"] = luminance[cd/mm^2] x area_of_optic_or_reflector[mm^2]
Of course to be more precise you need to account for optical losses. A glass lens only transmits 92% of the light, a coated one 96-99%. A standard aluminium reflector will only reflect 90% of the light etc. But in general this is how you get throw. You can calculate it without actually measuring the flashlight (as long as you know all the details).
Since LEDs are basically
lambertion emitters there is an approximating formula you can use to calculate the luminance based on the lumens and the size of the LED:
Luminance_of_LED = luminus_flux[lm] / (size_of_LED [mm^2] x pi)
This gets you a ballpark figure.
There are also some special things to consider:
- Many LEDs have silicon domes on them to increase lumens extraction (because the round silicone dome has a more suitable refraction index compared to bare phosphor). These domes unfotunately halve the luminance! This is why "de-doming" an LED increaes throw. Stray photons are reflected back into the phospor and re-exite it (photon recycling). A better, more in depth explanation can be found here.
- The Wavien collar is a way to increase the luminance of a LED by reflecting 75% of the light back onto the Die allowing it to be "recycled" and emitted in a different angle. sma studied the collars here. A maximum of 120% gain was observed, so with the best current LED 660cd/mm^2 would be possible. TSome downsides are that it can only be used with aspheric lenses (so no spill), the hotspot will always be very small and that they aren't available anymore without buying a 120$ flashlight.
Other light sources:
The light sources with the highest luminance are Xenon and mercury short-arc HID bulbs. They concentrate extreme amounts of power into a very small arc. They operate on the physical limits of what materials science has to offer (especially regarding maximum temperatures of the Wolfram elctrodes and the quarz glass envelopes). The highest achievable luminance is around 6000cd/mm^2 which is 20-times as much as the best LED. They also produce more lumens compared to LEDs with high luminance values.
So, to answer your question, you will only get more throw with 8000 Lumens compared to 2000 in your TN-42 if the brighter LED is of similar size. If it gets larger than the luminance stays the same or even goes down and thus you might actually get less throw.
Here I have built a flashlight with the precision reflector of a Maxabeam and the Osram Black Flat LED at maximum power. It's very extreme for an LED flashlight, but still falls well short of the the real Maxabeam with it's Xenon short-arc bulb.
Here Enderman built a light with Osram Black Flat, a Wavien collar and a large aspheric lens. He got 4.6Mcd which only some guys with much larger fresnel lenses have beaten. It shows what can be done if all you want is a farthest throwing LED flashlight.
Here I have compiled a list of the farthest throwing portable lights regardless of the used light sources. Lets just say - LEDs are still pretty dim compared to short-arcs!