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Kerf bending is a relatively easy and straightforward method that is used to produce a curved shape out of plywood. It consists of making successive parallel cuts, or kerfs, on the surface of the stock that will later become the inside surface of the curve. The kerfs remove sufficient material to allow a curve to be formed.
An article in The Family Handyman magazine (Radtke 1996, p. 104) describes a method of forming circular arches from strips of plywood by making a series of kerf cuts. Radtke wrote, "Kerf bending... is not the only method of curving wood, but it's the simplest and most direct," and gave the following algorithm:
1. Find the middle of your wood, and make a slice in the wood, leaving approximately 1/32" uncut. This slice is known as a kerf; hence, the name of the method.
2. Bend the wood inward at the cut, and measure along the wood the desired inner radius (r) of the arch. From this point, measure the vertical distance (w)to the flat surface below. (See fig. 1.) The distance is the length between cuts.
3. Make repeated cuts a distance of w from one another on either side of the initial cut until sufficient cuts have been made. Alternate sides of the initial cut as you make these cuts to ensure symmetry.
Radtke "does the math" to determine the necessary number of cuts: C = 3.14 * (r + 3/4") gives the circumference of the arch, where 3/4" is the thickness of the plywood and 3.14 is an approximation of pi. The value C divided by w gives an approximation to n, the number of cuts necessary.
Fortunately for a pair of inquisitive undergraduate students, a mathematics teacher, and a professor, Radtke did not justify his algorithm. Why does Radtke's kerf-cut method yield a circular arch?
PRELIMINARY INVESTIGATIONS
In an experimental phase of the investigation, we created several samples of kerf-cut arches. However, instead of semicircles, we obtained polygonal arches, as shown in figure 2, that looked like semicircles from a distance. Our conviction that we...