Now there are too many other variables such as the material the mPCB is bonded too, the type of the junction, the bond between the mPCB and the heatsinking, the amount of heatsinking material, etc, etc, etc.
Which add up into this thing called thermal resistance, for which the semiconductor die -> solder point value is specified in the datasheet.
There are methods to measure thermal resistance for other parts in the path from semiconductor die -> hand + flashlight-surrounding air.
One thing of note is that with multiple emitters & the same total heat flow, each emitter's thermal resistance is effectively parallel-ed with the other emitters. Or in other words: all emitter's thermal
conductivity gets put in parallel (= added up). Example:
An XP-G2 die dissipating 5W would sit at 20
oC higher (4
oC/W) than its solder point temperature. An XP-L die dissipating 5W would sit at 12.5
oC higher (2.5
oC/W) than its solder point temperature. Here the XP-L has the edge due to its lower die -> case thermal resistance.
But if that same 5W is distributed over 3 pcs. XP-G2's, each will take 1.67W. Putting each die at 6.7
oC higher than its solder point temperature. Effectively behaving like a (theoretical!) single XP-G2 with 4/3 = 1.33
oC/W die -> case thermal resistance. Which gives 3x XP-G2 the edge over an XP-L, due to the lower
overall thermal resistance.
Then there's efficiency: even if electric power is known, it's not known exactly what % of that power is radiated out as light, and what % dissipated as heat. So even with a higher die -> case thermal resistance, a higher lm/W LED may still come out on top, simply because of each W put in, a smaller % is dissipated as heat. Possibly up to the point where heat flow * thermal resistance gives a smaller number.
It doesn't end there, though: :hairpull: even though a multi-emitter setup
appears preferable, that heat still flows to another part of the flashlight. Which
in turn may become the bottleneck in the heat flow's path. 6.7
oC vs. 12.5
oC temperature rise makes little difference, if pill -> flashlight body thermal contact is so poor, that the entire pill sits 30
oC above the flashlight's body temperature. Likewise: if you're dissipating 5W
total, that will cause the same temperature rise for each element that's next in the path, since the same heat flow is going through it. Regardless of whether that 5W is dissipated by 1, or 3 emitters. Only exception here is if the heat flow is distributed such across flashlight parts, that a 3-emitter setup actually causes a lower thermal resistance from pill -> flashlight body.
Adding thermal mass (eg. a heavier pill) in itself doesn't make
any difference whatsoever for what final temperatures are reached (!). It does change this though: 1) how fast temperatures rise/fall with the same heat flow, and 2) more thermal mass often means better thermal conductivity (lower thermal resistance). But this depends a lot on the light's construction & the route along which most of the heat flows.
For those who think this is all very complicated: thermal resistance, and the related math, very much behaves like voltages, currents, series & parallel resistors in electronic circuits. Thermal mass could be compared to a capacitor in such circuits. So although complicated at first sight, it's
very possible to measure, calculate & predict things when the necessary lab work is done. Coming up with a good measurement setup isn't easy, though...
One final note: usually the bottlenecks are closest to where the heat is produced. So in the case of a LED, that's primarily die -> LED case. Next in line is pcb the LED sits on (copper or aluminium for example, and how thick). Followed by the question whether a heat-conducting paste is used between LED pcb and flashlight pill. From there on, things are likely to be less critical. Read: alu or brass pill likely makes a smaller difference for LED temps than the difference between alu or copper LED star.
