Sure, Brightnorm...
Part of it is "feel" for things electronic. However, most of it is looking at the actual graphs of the run time in the tech data sheets.
The simple way of doing it is taking the rated capacity of the cells (1300 mAh for the 123s and 2850 for the AAs) but then the AAs will give you erroneous results.
Taking the lithium case first, and using the 1300mAh and the average of 385mA you get 3.4 hours.
Backing up a step. Ohms law.
The spec I had was 2.1W
P=IE
Power=Current times Voltage
There is an internal impedance to the battery. That's why the lithiums (lower internal impedance) provide about 400cd more output). So I had to pick a voltage and a current. I took a midpoint for fresh cells.
Now that you have a current draw (385mA) you can grossly assume constant current (not true as voltage falls, but we're not going to let the voltage fall that much 'cause then the lights get too yellow.)
You take the basic battery capacity rating in milli-amp hours (mAh) and divide that by the current draw in milli-amps and that leaves you with an hours hanging out.
mAh/mA=h
1300/385 is 3.4...that's where my high estimate for the lithiums came from.
The lower estimate for the lithiums was based on using 1000mAh as the capacity and fudging a bit.
Sadly, the graphs at
http://data.energizer.com/datasheets/library/primary/lithium/el123ap.pdf were not much use.
The Alkaline graphs tell a different story. One of the challenges is that for AAs, 385mA is a relatively heavy load and the AAs won't deliver their full capacity at that level of constant drain.
The graphs at
http://data.energizer.com/datasheets/library/primary/alkaline/energizer/consumer_o em/e91.pdf are full of much more useful information.
Looking at the constant current discharge, I looked at the 1.1V cutoff curve and that gave me roughly 2.5 hours. The 1V cutoff curve gives about 3.5 hours. This is hard to read and that's why the numbers are to half hours. Remember, this is a logarithmic chart and the lines after 1 are 2 3 4 ... but the spacing is such that each decade takes up the same space.
An interesting thing to notice on that graph is that the 100mA draw will provide about 5 hours to 1.3V cutoff (easy to read) while the 10mA draw will run for 150 hours. That's a difference of 500mAh to 1500mAh!
This is where the graphs tell MUCH more of the story than the single mAh number!
One other part of Ohm's Law to remember is
E=IR or
Voltage=Current times Resistance
There is a good write up on Ohm's Law at (surprisingly)
http://ohmslaw.com/
Another thing to remember, the incandescent lamp acts a bit like a constant current load. As the voltage drops, the resistance of the lamp drops so the current draw will remain somewhat constant. That's one of the reasons that incandescents, once they start going, go quickly.
On the other hand, LEDs work quite differently.
LEDs have an (almost) constant voltage drop across them. Let's say the drop across the LED is 4V. You have a 6V source and a series resistor. The current is set by using 2V as the voltage in the resistance calculation, not 6V.
So, with a simple resistor in series with an LED, the current draw will go from max to zero as the battery voltage falls from initial to the voltage drop of the LED.
Well, the LED's voltage drop does reduce slightly as the current decreases, but LEDs are harder to predict to cutoff as their current drain DECREASES as the voltage falls. It's closer to the constant resistance (sort of) but not quite.
In practicality, however, I think that bright LED run times are similar to incandescent. As you may recall, I measured more drop in the Inova X5 (percentage wise) than in the E2e between a new pair and used pair of cells. It was at least a 10% greater drop in the X5.
As to LED life claims, the Aurora headlamp from PT is right up there! They claim 50 100 and 150 hours if I recall correctly. Those are probably overstated by a factor of 5, perhaps more.
See the other thread for some numbers in the LED section.
I hope this helps a bit.
Cheers,
Richard
