Alkalines and maximum power
HKJ said:
That might be the reason, but Alkaline can provide full power for some time, at least at the levels TK40 is using.
Is is bad regulation or just the inherent limitations of alkaline battery chemistry? There's a limit to how much power you can obtain from a battery. If the device has a very low resistance, battery power is maximized, but almost all of the power is wasted in the battery, causing it to heat up (this is true regardless of battery chemistry). With very high device resistance, less power is wasted, but the total power from the battery decreases, so again, the usable power will be low. There's an optimum somewhere in between, and according to my simple calculations, the unsurprising result is: This maximum usable power is obtained if the resistance of the device is equal to the battery's internal resistance. In this case, we can calculate the maximum device power as U^2 / 4Rb, where U is the unloaded voltage and Rb the battery's internal resistance.
I applied this formula to some
publicly available information from Duracell, in particular on the CopperTop AAs (MN1500). This is the result (discharge percentage, approximate maximum device power). Note that for a TK40 in turbo mode, about 1.3W per battery are required. A more accurate estimation could be obtained by taking the 2P4S setup into account.
0% - 7W
10% - 4W
20% - 3W
30% - 2.5W
40% - 1.8W
50% - 1.6W
60% - 1.4W
70% - 1.2W
80% - 1W
This indicates that CopperTops which have been discharged less than 35% should be easily capable of driving the TK40 in turbo mode at full lumens. If the batteries have been discharged 35% to at most 65%, it should still be possible though the efficiency will noticeably decrease, speeding up the discharge rate. Below 35% remaining charge (65%+ discharged), there's no way the TK40 could continue at full power even if the regulation were perfect, which of course it isn't. I also looked at the Procell and Ultra data, but didn't analyze it further because both battery types have better characteristics than the CopperTop, so you should see a performance increase over the CopperTops in any case.
The bottom line is: Duracell CopperTops should absolutely be able to power the TK40 turbo until they have somewhat less than 50% remaining charge. Being an NiMH advocate, I'm pleasantly surprised by this observation, however I do have to note that run-of-the-mill alkaline batteries from your local discount store probably will not keep up with these numbers. For instance, if you assume that a cheap battery may have twice the internal resistance (same voltage), this means they can also deliver only one half the power. In this case, even after only a 25% discharge, the power may be insufficient for turbo mode. In addition, they will discharge less efficiently, so it will take less time until the 25% mark is hit.