Today I have been revising how to calculate the radius of an arc. I’m working on a design for a printable widget that I can use to damp the strings of the various instruments hanging on my wall. I’ve had some foam jammed between the strings and the fretboard, which has worked well, but the foam is beginning to tear apart on the ones I use more often.

One thing I spotted after my first version was that instruments typically have a radiused fingerboard. Rather than being completely flat, the fretboard is like a small section (or arc) of a much larger circle. That is good for playability but makes for another factor to consider in the design. Given the width of the fretboard and height of the centre compared to the edges, it can be calculated with the formula h/2 + w^2 / (h*8) (as it is written in OpenSCAD). The revision was to remind myself of how that is derived – easy to look up online but worth spending a little while to understand.

Mind you, having printed a second test piece, I still haven’t nailed the fretboard radius of the electroacoustic bass in question. It isn’t entirely straightforward to measure the height element, even with vernier calipers. As another step, I’ve downloaded some radius gauges which I’m partway through printing. Of course, if they work, I won’t need to go the measure and calculate route directly although the maths will still come in useful. Even if I can gauge the radius by feel, I’ll still need to work out the height of the arc for the fretboard width in order to position things properly on my model.