By the way, discard my gauge sizing, I'm not good with that imperial system's part, so I'd rather check what I have exactly on the spool when I get home tonight. But here is the guidance table to follow:



To ignite paper you need as Ray Bradbury has suggested once 451F temperature or more (less for the fine tinder). A typical alkaline AA/AAA battery can give you bursts of current up to 1 Amp easily without any harm to its chemistry, so, anything thinner than 30 ga. should work well, according to the table. The thinner is better as that will allow to use less current for ignition or achieve higher temps for less favorable tinder, and also that's better for sawing as it will create a higher cutting pressure.

For the resistance, you need to chose the one which will allow the current from the table on the length of approximately 2.5" It also depends on the wire diameter, but also on the composition of the wire. The Ohms law should help in selection. R = V/I Where V=1.5Volt, I- from the table e.g. 0.3A and keep in mind that the wire is labeled per foot, so the stated resistance must be approx. no more than 5 times higher than what you have calculated for ignition.

However you must be especially careful with thinner wire, as it can get extremely hot even from an AA battery, so you should be able to stop heating any moment and reliably, so your skin and equipment are not damaged by extreme heat. To reliably ignite the tinder without overheating the device you must assure a good contact between tinder and the wire. I'm making a loose spiral out of mine (it's stored in that shape actually, as you can see on my LM Wave image in the Belt thread), and using only part of it to boost the current. Keep in mind though, that even a soft kink will almost certainly break the nichrome wire.