Well Noitoen, different foam materials and densities, different cutting speeds, travel stops and reverses, cutting directions (horiz, vert) different wire materials, diameters, power supply ratings, etc all play into it.
Variable supplies are best, and in CNC the wire heat is controlled by direction and speed. For instance, cutting vertically upwards widens a kerf from excess heat. And at a trailing edge of a wing, the wire reverses direction near a thin section -- often creating too much heat locally. Regulation of a power supply, either constant current or voltage isn't a big requirement. Getting gear into the ballbark is. And being able to vary by cut position and direction is.
Actually the program I wrote assumed the closest thing to a constant you can approach is watts per unit length of wire. No matter what wire size or material, or power supply type, bow length, etc. Watts per inch (or cm) is a relatively constant number for cutting a similar set of materials. This programe was aimed at determining what to buy or make, given the gear you already have on hand, and what length bow you can accommodate with it.
As an example, a person has some .020" steel mig wire and a 12 volt car battery to supply a hand held bow -- he/she wants to know how long a bow is required to get them in the proper heat range for cutting foam. That's what my program was designed to answer -- given some variable set, what is needed to get them in the ballbark for cutting foam.
In that example, if the bow length required was too long or unwieldy, the length could be artificially created by using a wire coil air resistor -- in fact that could be made as a variable resistor with an alligator clip. Let's say someone else wanted to do it with with .012 stainless fishing leader, or a guitar string -- what would the length be for that. etc.