In general it's wattage in=wattage out of any regulator, less the losses of the regulator itself.
Exactly... I can't speak to any tests or results you've found with your (JeremyR) own device. If you are finding that drastic of a performance increase (if I'm understanding what you're stating correctly) then perhaps the regulator happens to be super efficient with an 8.4v input versus a 4.2v input. I don't know...
But, the above statement is exactly right... Though I think it may get confusing for some vapers because of what "wattage" denotes to them. Remember wattage is "power". What's being stated above is "power in = power out". The simple fact is, as you increase how much power you put out you MUST increase the power you put in... If not, you would have perpetual motion.
Voltage and Current can be thought of as "interchangeable". I'll use the water hose analogy. If I place my finger over the end of a water hose I can increase pressure (voltage), but at the expense of flow (current). Vice versa applies when I remove my finger.
Excluding any losses in the regulator (R) it looks like this...
4.2v 10a --> R --> 8.4v 5a
When I use the regulator to double the voltage, I'm also going to double the amount of current I draw from the source... So if I run a 5A load on 8.4v then I'm going to draw 10A off my 4.2v battery... E x I = P.... 4.2v x 10A = 42W and 8.4v x 5A = 42W If I'm producing 42W of power on the output I MUST be drawing 42W from the source....
So let's think about that for a minute.... Let's say we had a 1000mAh 4.2v battery.... and we wanted to run a 42W load... So we run a .42ohm coil... This as pointed out above pulls 10A at 42 watts...
4.2v @ 10A on our 1000mAh (1Ah) = 6 minutes of continuous run time (it's not that simple as voltage won't stay constant from just a battery source, etc, but for the sake of our demonstration let's assume it does).
Now what if used a 100% efficient (so we don't have to calculator loss) regulator to bump the voltage up to 8.4v but still wanted to generate 42W.... Now we need a 1.68ohm coil and we are only drawing 5A...
But remember in order to generate that voltage from a 4.2v source we have to TRADE current for voltage... ExI=P So we STILL draw 10A off our 4.2 volt battery... which means we STILL only get 6 minutes of continuous run time....
Now suppose.... instead of using a regulator we stacked batteries.... two 4.2v batteries stacked will give us the same 8.4v which means we can only draw 5A from them... WONDERFUL... So we calculate it...
8.4v @ 5A on a 1000mAh source (capacity isn't doubled by putting batteries in series, only voltage is so it's still only a 1000mAh battery source). So yes, we now get 12 minutes of run time! We've doubled our run time using the SAME power output!!!
But wait... Don't buy the party decorations just yet.... Because we've just went from 1 1000mAh battery to TWO 1000mAh batteries... So even though we haven't doubled the capacity when they are in series (i.e. a 10A load will still draw 1000mAh in 6 minutes) all we did was halve the current and add an extra battery...
To illustrate that... Let's make this fair.... So NOW we take those same two batteries and put them in parallel instead.... So we STILL get 4.2v output but we now have 2000mAh capacity instead of 1000mAh...
4.2v @ 10A on 2000mAh = 12 minutes of runtime... The exact same figure we had when running 8.4v @ 5A....
Does that hopefully help make things more clear?