This is from some of the folks who make Kanthal wire.
It goes into some detail about designing things with Kanthal heating wires and elements.
At no point does it tell you how to calculate temperature from voltage and current or voltage and current from temperature because you can't do that.
- You have to have the ambient temperature.
- You have to have values for the heat conductivity from the Kanthal to the surroundings.
- You have to have the contact area where the wire touches whatever your wire is touching.
- You have to have the temperature of the stuff you are cutting.
- You have to know the heat conductivity of the stuff you are cutting.
It does tell you how to calculate the power consumed by the wire from the wire diameter and length.
It also tells you how to calculate the resistance of the wire from the applied voltage and the resulting current.
From the resistance of the wire, you can estimate its temperature - there are equations in there that tell you how.
From the estimated temperature of the wire, you can adjust the current or voltage to make the wire heat up to your desired temperature.
With appropriate controls (a proportional, integral, derivate (PID) controller and a dimmer type circuit to control the current and voltage,) you could make a regulated "hot knife" that will maintain a particular temperature.
Alternatively, you can do what most folks do who make this kind of thing:
Hook your wire to a variable output transformer (variac or a regular tranformer with a dimmer) and adjust it until it seems hot enough to cut without burning.
Then, cuss when it cools off and gets stuck halfway through or cuss because you turned it up to get it unstuck and now it is too hot and burns your material instead of cutting.
These folks built one, and added a third reason to cuss: The wire got too hot and parted (broke) under the tension needed to use it as a knife.
