Heater Location

The location of the heater is important for optimal performance. For this project, I will make a band that wraps around the bicep near the armpit. There are big veins/arteries in your arm that will help distribute the externally warmed blood throughout your body. While sleeping in a mummy bag on my camping trips, my elbows tend to be at my sides. This also positions the heater physically closer to my core. There will be wires involved, but they won't have to run all the way up my legs or arms like they would for heated socks and gloves. Shorter wires will also be less likely to tangle and be uncomfortable.

Let's build the arm band heater first. Since it will be wrapping around the arm, a good starting point would be to use an exercise/sweat band. These are meant to fit around your wrists, so they might be a really tight fit around your bicep. It should fit a little tight so it won't slip, but not too tight that it reduces circulation. A better approach might be to use an adjustable version. After a quick search on eBay, I found a couple options:

Personally, I don't like the idea of having a bulky battery pack attached to my arm while I try to sleep. So I'll deal with the longer wires connecting to the battery pack.

Calculations

A comfortable length around my bicep is 14" (35.5cm). If that's the length of the filament, it will have a resistance of approximately 17Ω/m * 0.355m = 6Ω. When powered from 5V from my USB battery bank, it will draw a current of 5V / 6Ω = 833mA. My battery bank can deliver a maximum of 1A, so that still leaves some headroom as a safety margin. But how warm will this get?

Estimating Filament Temperature

Looking at the Temperature vs Length curves on http://www.carbonheater.us/, it is hard to tell what the temperature will be. I entered the same data into Excel and made my own graphs shown above. As you can see in the Temperature vs Length chart and the Temperature vs Power charts, the lines only match up with the corresponding voltages. But how hot will it get if I use a 5V supply instead? After all, it is very common nowadays with USB, phone/tablet chargers, and those rechargeable battery banks. In order to figure the temperature with a different voltage, I played with extra calculations in Excel. I eventually learned that I got a positive correlation between all supply voltages if I plotted Temperature vs Volts/cm. This technique allows one general equation to approximate the temperature for a given voltage and length. To figure out what that equation is, I again used Excel to plot the same chart with the best-fit-line. Keep in mind, however, that this equation is a rough approximation and is accurate only to about ±15%.

So, let's move on to estimate the filament temperature.

With a Volts/cm = 5V/35.5cm = 0.141, I calculated an approximate temperature of 57.5°C (135.6°F). That is a little too warm for me. So I'll increase the length to 61cm which drops the temperature to 37.9°C (100.2°F). Much better!

A filament that is 61cm long has a resistance of about 10.4Ω and will draw about 0.482A from a 5V supply. My battery bank claims to have a capacity of 12Ahr. At this load, my battery bank could theoretically power the heater for about 24.9 hours! In reality, though, I expect the battery life to be much less than this. The capacity of batteries is hard to define because it depends on the amount of current draw and the temperature and it also decreases with age. Performing your own battery life test will be a much better way check the capacity of your specific battery bank.