Building a foam wing cutter
This page will describe my hot wire foam cutter.
Foam cutter considerations and options
Before I describe my foam cutter it's important to understand how the foam is cut.  You might think that a sharp blade would do the job, and it would, but it would be very difficult to cut an accurate wing profile with a 24 inch long blade.  Most foam cutters rely on an interesting property of foams used in wing making:  When heated, the foam does not melt, it "gasses-off", which is to say it turns directly from a solid to a gas.  Using this property, we can design a cutter that uses as it's cutting edge a hot length of thin wire.  As the wire is brought into contact with the foam, the foam gasses off, and the wire passes smoothly through the foam leaving a surprisingly smooth surface. 
Construction Details
Here's a picture of the foam cutter.  At the top of the picture is the cutting bow, which is a length of picture wire stretched between two fiberglass rods which have been drilled into a piece of oak. The bow is dragged across the surface of the table by the black and red wires.  The black and red wires are routed over a series of pulleys to a weighted bar, which applys the force that drags the bow.  The weighted bar is suspended at one end and is allowed to pivot downward. The black and red wires serve double duty, as they also carry the current that is used to heat the wire stretched across the bow. 
Here's another shot from a different angle.  In this picture you can see part of the power supply used to heat the wire on the bow.  It's a 12v car battery charger that has a manual 2amp setting.  The battery clips are clamped to the red and black wires by 'capturing' the wires against a small bit of wood. 
This is the other half of the power supply.  It's a common household light dimmer who's output powers the electrical socket to the right of the dimmer.  The 12v battery charger is plugged into the electrical socket, and the dimmer is used to vary the amount of power applied to the battery charger.  This in turn varies the amount of power applied to the wire on the bow.  In this way the cutting temperature can be carefully regulated via a safe low-voltage DC power source.
This is a detailed shot of the pulley system used.  Notice that the pulley on the front edge of the table (top pictures) extends above the surface of the table.  This is to allow the pulling cables to feed smoothly into the pulley on the top of the table.  The bottom pictures shows how the pulley on the top of the table extends over the edge also, so that the pulling cable feeds smoothly into the pulley on the front of the table.