Electronic – Nichrome wire not heating up with a 9v battery

You don't say what chemistry your battery is using. Different chemistries, lead, LiPo, NimH, have different behaviours in detail, but in general, the answer is, you cannot get an accurate SOC from the terminal voltage alone.

People are still doing PhDs on how to estimate SOC. I did some research into NimH for a commercial company recently and found that the history of the last hour charge/discharge affected the terminal voltage only SOC estimate at above the 20% level.

Your problem is not how to display the SOC, it's whether to 'fess up to the large uncertainties. The SOC will be essentially identical from one second to the next, even if you have switched from charge to discharge in that time, from pure physics reasoning alone. Your problem is the estimate you are getting from the IC changes under those conditions.

You have several choices.

1) Do more and better research on how to model SOC, and then implement the results of that. 'make it right'

2) Apply a low pass filter of several minutes to the results from your IC estimate, to disguise the step. 'hide it'

3) Figure out what the uncertainty in the estimate is, and then display your SOC as x% +/- y%. 'say what is'

1. At a given ambient temperature, it takes a set amount of energy to heat the nichrome wire to fusion temperature, and then another amount of energy to melt it. Calculate the power required across your nichrome wire depending on the power losses and the required time-to-melt.
2. Deduce what the required voltage and the corresponding current across the nichrome wire are
3. Rule of thumb: choose a battery technology that has a capacity (in Ah) equal to or greater than the required current (in A) (10x greater for sustained use) if possible (otherwise step 4 is mandatory). Stack as many cells in series as required to make up the required voltage

AA batteries are usually quite good in terms of resistance (~0.2Ohm for alkaline) and current capability (up to 1 or 2A, not for long though). They wildly vary in specs depending on the manufacturer though, therefore if yours didn't work, you should try with a better quality one before trying the C and finally D type batteries.

4. If the best stack you can afford (in terms of space, mass or whatever) can't provide the current or gets too hot, here is a potential solution: insert a Schottky diode that can handle the voltage and current in series with the stack (note that the stack voltage will be reduced by 0.2 to 0.5V), and duplicate that assembly in parallel as many times as required to reduce the current each stack has to provide. The diodes will prevent batteries fighting for the net voltage.

Note that this technique (step 4) is normally used to switch between power supplies, not increase the current capability. Only one diode will conduct at any time*, meaning that here the entire current will be supplied by one source before its voltage droops sufficiently to make another one conduct, and so on. This could work okay for this application though.

*: considering an ideal diode