Making a Cutting Bow
The basic idea here is a small diameter wire will heat up due to resistance and melt it's way through foam. It's really very easy to setup, but after some careful consideration I have decided not to provide exact plans on making a cutting bow. However, I will provide all the information one would need on how to assemble one and with a little math, and the old E=IR law (Voltage = Current x Resistance) you should find it to be no problem.
You will need a power supply capable of putting out no more then 1-3 Amps at no more then 24 Volts, either AC or DC. An automotive battery charger should fit this bill nicely, of course if you have an adjustable DC power supply that will work nicely as well. I have also heard of people using electric train transformers. Remember either AC or DC will work, and it should draw less then 3 amps.
You will also need about a yard (or meter) of single stranded stainless steel fishing leader wire of a diameter of about 0.010 inches. A little thicker wire will be fine, but it will draw more current as the resistance will be lower. For reference my setup uses 0.010 Dia wire and will draw no more than 2 amps tops at about one yard of wire.
Now I don't want to provide an exact way of putting this all together, as I don't want to be responsible for anyone getting a poke. But if you're following this so far, this setup will act as a light bulb, and it will only draw so much current so don't think of it as applying a direct short across your power supply. In case you are wondering a light bulb connected to a power supply will only draw what the bulb is rated for at it's given voltage. It does not matter how much current is available, it will only take so much. Now if you increase the voltage, the current will go up, and the bulb will get brighter. Too much voltage the bulb will burn out faster. Light bulbs also work on AC or DC circuits, so will your wire. I purchased my wire from Cabellas hunting and fishing store from the fishing department. Strung across my 3 foot bow it will draw 1.5 amps at about 20 volts and cuts pink foam like butter.
I have heard of people using braided, or wound, wire -and even coated stuff, but I would not recommend it. Try these two links if you can't find the stuff anywhere else:
Bass Pro Shops
Also buy yourself one of these: Multimeter (to get the resistance of your wire).
After you put this all together and plug it in, remember the wire will expand as it heats up. So you will need some method of taking up the slack. Some recommend springs. I do this manually with my setup by physically pulling my bow apart making it longer and friction holds it taunt. (My bow is made from two bent metal pieces of conduit, and a long piece of plastic conduit between them, it's impossible for the bow to short out as the center piece is too long for the elbows to ever touch, they fit nicely together and the plastic gives a slight flex when under tension).
If absolutely none of this makes any sense to you I highly recommend that you DO NOT attempt to build yourself a bow, honestly though, if you've come this far I think you can hack it. But always be careful, electricity can be very dangerous, and I would hate to see anyone get seriously hurt. I also recommend that you fuse all connections and operate on a GFIC outlet -just in case. Put safety first!
Some facts and stats:
E=IR, Volts = Current (in Amps) x Resistance (in Ohms)
Longer thinner wires will have higher resistance, thus requiring more voltage.
Shorter thicker wires will have lower resistance, thus drawing more amps.
Higher resistance will take less work to heat the wire a given amount.
That given amount may not be enough to melt your foam, so work from a reference.
My SS wire measures 13 ohms at three feet, it draws about 1.5 amps at about 20 volts. The entire circuit measures 13.5 ohms, leaving 1/2 an ohm of resistance to heat wire I'm not cutting with (wasted heat).
Nichrome wire may heat at a different rate, I do not know what that is.
E=IR, or I=E/R so check the math 1.5A = 20V / 13.5Ohms
And if you want to figure the power, it's as easy as P=IE, or 1.3A x 20V = 25 Watts
Only takes a rinky-dink power supply, if you ask me, for very cheap SS wire.
Hopefully this gives the essential information you need, good luck in building!