Replacing 6 series AA alkaline batteries with NiMH batteries – how do I compare possible arrangements to optimise usable capacity?

I want to replace a battery pack of 6 AA 1.5V alkaline batteries arranged in series, with rechargeable NiMH batteries in an old transistor megaphone in such a way as to optimise the capacity. The existing battery pack is a typical 2×3 arrangement and it is connected with a PP3/PP6 snap connector. I want to use rechargeable batteries to reduce electronic waste.

I'm aware that usable capacity is subject to the device's cut-off voltage, the discharge curve, and the efficiency of the batteries given the temperature and load characteristics. Given that this is an old device and probably not designed with a low cut-off having rechargeable 1.2V batteries in mind, I'm concerned that 6 cells isn't enough and want to include a 7^th.

Although I'm aware that rated capacity is a generally misleading figure, I don't understand why my naïve calculations seem to be several times out from what I'd expect judging roughly by the mass/volume of the batteries. Are PP3s really that bad?

In the battery compartment there is space for 4 of the following 5 arrangements (see note 2 below) for which I'm demonstrating these naïve, seemingly false calculations. (In the case of arrangement #4, there is also space for a small adaptor I made using 3 snap connectors required to connect the batteries in parallel.) This is roughly related to how ‘big’ the batteries are and relates loosely to their volume, so these arrangements are likely to be applicable to other devices as well.

(#)  Arrangement                    Combined       Charge    Total energy
                                    rated voltage  capacity  capacity[1]
(1)  6 AA 1.5V alkaline in series   9V             2100mAh   15.12Wh = 54.432kJ
(2)  6 AA 1.2V NiMH in series       7.2V           2400mAh   17.28Wh = 62.208kJ
(3)  7 AAA 1.2V NiMH in series      8.4V           950mAh    7.98Wh = 28.728kJ
(4)  2 PP3 8.4V NiMH in parallel    8.4V           200mAh    3.36Wh = 12.096kJ

(5)  14 AAA 1.2V NiMH; 2 series[2]  8.4V           950mAh    15.96Wh = 57.456kJ

• Note 1: The ‘Total energy capacity’ is a naïve estimation based on the charge capacity and 1.2V per cell mean voltage.


• Note 2: 14 AAA batteries in a (1+√3)×5 arrangement (i.e. rows of 5, 4, 5) can occupy approximately the same cuboidal space as 2×3 AA batteries. I've included this for the general case; however, in this instance the battery compartment has rounded corners so the arrangement wouldn't quite fit.

That is not what I'd expect at all – not even close; PP3s look to be about 2 and a bit times the volume of a AA, so I'd expect the total energy capacity of arrangement #4 to be about 70% that of #2, but this rough estimation suggests 19%! I'm guessing that the rated charge capacity is rated in respect to a ‘typical’ load, so the efficiency of each rating is probably vastly different, and therefore can't be used to reliably determine the actual energy storage capacity which would be underestimated by a different amount in each case. In the case of arrangement #4, the combined internal resistance is halved (i.e. ‘internal conductance’ added), so it would be more efficient and would deliver more energy per battery given the same load, as compared to just a single PP3. In arrangements 1–3 the IRs are added. Arrangement #5 has half the combined IR as #3.

For what it's worth, the megaphone is a pulsing load rated 5W maximum power draw, and it's operated outdoors in the UK so the batteries probably generally operate with a temperature between 5°C and 25°C depending on the time of year. I'm trying to find datasheets for the NiMH batteries I use (Maplin L32BJ, L29BJ, and L31BJ for AA, AAA, and PP3 resp.) to actually see for myself the true data of what's going on with these figures, but I haven't yet obtained any. However, specifics aside, these figures seem to be so far out that a better general understanding of how to compare rechargeable replacements for battery packs of 6 AA alkaline batteries would be generally useful because I've seen such battery packs on other types of devices as well.