Hey mrheosuper, here’s my input.
Of course P = (I^2)*R is applicable, but one can wonder how it is applicable. The total amp draw is 40A in 4P configuration - which is four times higher than in 4S configuration - resulting in a 16x higher electrical loss (=heat), but this fact itself does not display what is going on.
I’m going to do an efficiency calculation, but this is at first a ball park calculation, as I don’t have all the required exact data. But you should get a good idea. And of course, there may be mistakes in what I’m calculating and reasoning, so feel free to object and discuss!
From what is written, the DT70 seems to be putting out about 12000 OTF lumens or so. With an efficiency (estimate) of 85% from led lumens to OTF, this means the amount of led lumens is about 14100 lumens. A single emitter is then putting out about 3500 lumens. We do not know the output bin, but according to: https://farm8.staticflickr.com/7567/16071892179_7d89411e10_o.jpg the led produces 3500 lumens with 4.5A at 6.5V. This means the required power is about 30W (=4.5*6.5) per led. So for 12000 lumens OTF, the four leds require 120W.
The total amp draw as you stated (I believe it can be found somewhere on the internet) is 40A. What we don’t know is at voltage this amp draw occurs. Assuming it’s from fresh cells, and with some voltage sag, I’d say let’s take 4V, meaning the power input to the driver (from the 4P cells) is 160W (=40A*4V).
We just happen to have nice rounded figures; the leds need 120W, and power input is 160W, meaning efficiency is 120/160 = 0.75 = 75%.
Again, this is just a ball park calculation as we don’t have more accurate data. Nevertheless it show that a large part of the total power, 75, is going to the leds. Haven’t searched intensively, but about 30 of this power is turned into light, so the remaining 70% is turned into heat. This means that of the 120W for the four leds, 84W (=70%) is generating heat. This means that of the total 160W power input, about half of this (=84W) is heat generated by the four leds.
The driver on the other hand produces 40W of heat (=160W-120W). So with a total power input of 160W (=40A at 4V) from the four cells, only 36W (=30% of 120W) is turned into light, and the rest is heat. The total wasted power turned into heat is therefore 124W (=160W-36W), and 84W of this is from the leds, and the remaining 40W is from the driver.
Conclusion: roughly 2/3 of the heat is generated from the leds and 1/3 from the boost driver. Of course with a driver for a 4S cell configuration, you will not get an efficiency of 100%, and heat will be produced as well, but less than with a boost driver for 4P configuration. Therefore a large part of the heat is generated from the leds, and to a much lesser extent from the driver as a result of a 4P configuration.
One can then wonder where the equation P = (I^2)*R is applicable. The Vf of the four leds remain identical of course regardless of driver type, but the difference in power loss, 4P vs 4S due to electrical resistance is applicable on the driver input side that is operating at the given low voltage of 3-4.2V. There is a total effective R value resulting in a power loss P = (I^2)*R, however, this value as calculated above is much smaller than the total heat generated by the leds.
Cheers!
Edit: included in the 40W is also the electrical losses of the path between cells and driver.
