Mechanical solutions for the formula-challenged woodworker.

There was a time when I was fairly good at math – but that was back when “personal” and “computer” were two words you’d never expect to see together. A few decades later, I often find it difficult to multi-task long enough to add two numbers together, while also remembering why I added them in the first place.

So even though I am still capable of most shop mathematics – at least briefly, after my sixth cup of coffee – I tend to opt for mechanical and visual solutions when they’re viable.

Fortunately for us muddle-headed sorts, there are methods for laying out curves that will more than adequately approximate the lovely forms generated by (admittedly awesome) higher-dimensional parabolic equations, as demonstrated by Bruce Winterbon in his “Bow Shelves” article.

Here are three I have made use of in my shop.

Bow Method

This method (shown in the opening photo) is probably the most commonly used technique for laying out fair curves on furniture. It’s certainly the one I use most often. The basics are simple: First, find a sturdy form that bends elastically (that is, it springs back when released). Fortunately for woodworkers, thin strips of wood fill the bill nicely.

I most often use 1⁄8” x 3⁄4” strips of straight-grained hardwood, anywhere from 18 ” to 48″ in length. At either end, I cut a small slit to fit a piece of string or twine, and knot the ends of the string to hold the curve I want.

Mathematically, these curves (called an “elastica”) are not at all simple, but Mother Nature does all the calculation, and the resulting curves are quite visually pleasing.

Be aware that variations in the thickness of the wood will alter the shape, which can be quite useful for varying the curves. By selectively thinning the wooden bow it’s easy to vary the…

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