Like most modellers, you have already cut wing cores from polystyren foam. The airfoil templates for root and tip sections are made with plywood, aluminium or formica. They are used to guide the hot wire. In the case of a trapezoidal wing, as both root and tip chords differ, you will be obliged to get different cutting speeds on each template. The speed may be adjusted manually or automatically using some tools. The system operates very well but requires to prepare templates for each type of wing. In fact, you physically copy the airfoil sections.
 

With a computer controlled machine, the outline of the airfoil section is digitallized and described by a finite list of points. Each point is represented by it cartesiennes coordinates (x, y). The computer drives the cutting tool (a hot wire in our case) in order to join all points of the section. So the wire movement is a succession of straight lines or vectors described by a couple of points, for instance :{(x1,y1),(x2,y2)} (see figure) 
 

In other terms, the principle is to start from the O origin, then draw a line up to next point Pt. The equation describing of the straight line is y = b/a * x. The coordinates x and y will be incremented so that whatever the point the wire is (between points O and Pt) the equation y = b/a * x is verified. Once arrived at Pt location, we just change the reference mark: Pt become the new origin and the next point is extracted from the coordinate list, and so on.
If a wooden leading edge is expected, then the first point of the section is not the origin. Therefore it is necessary to displace the wire to reach the first point and then one can proceed as before.

In order to cut a wing section, it is necessary to drive X and Y axis on both sides (right and left) of the wing. This simultaneous displacement requires to face many challenges:
 

Challenges for computer controlled cut:

• Airfoil section definition: The definition depends on the number of points used to describe the airfoil. The more points, the better the approximation and therfore the better the cut precision. On the following drawing, the same section is described with different numbers of points (profil 1, 2 , 3). The improvement is obvious !

Most airfoil section descriptions (selig, Naca, MH) are described with a hundred coordinates. In order to improve this definition, it is possible to add intermediate points between two original points. This interpolation may be linear (the line segment is divided in two) or polynomial (a spline curve is build between the two original points). Both technics increase the number of points describing the airfoil section.  The problem is to define enough coordinates to reached the desired quality level for the cut, and to be able to handle the corresponding volume of data during the cut process. The CNCnet software actually provide support for linear interpolation.

• Axis displacements: The second problem is to schedule and synchronize the X and Y axis at both right and left hand. In fact, in a trapezoidal wing, both chords values differs. This induce undesired secundary effects which requires correction or compensation. The lower the cutting speed, the thicker the foam melting due to glow of the wire. These effects increase whith the differences between the two chords. The nastiest geometry is a delta wing with a nearly null tip chord and a large root chord value. All the diffculties are then melted:
• Cut speed at tip is nealy null. As a consequence, the foam melting (glow effect) is very important.
• The root speed should be maximum in order to keep the cut period short and limit the tip glow. Unfortunately, stepper motors will remind  you of their speed limits.
• Last, the wing span will imply to adjust the distance between the right/left drivers and/or extrapolate the tip chord.
• Loosing steps: As you allready understood, the quality of the cut depends on speed, wire temperature, number of points and foam type. The faster the speed, the higher the risk to loose some steps at the motors. As any displacement always refer to preceeding position, you can easily imagine the disaster if this ever arise. 

It is necessary to adjust with a great care all the parameters with the foam type.

The main benefits of computer controlled foam cutter (CNC) are:

• Versatility, due to the easy defintion of airfoil section (or  section of any other  shape, as long as it remains continuous)
• A very good reproductibility, thanks to automation
• Precision of the cut, as long as enough points are provided