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Plate arching has an important bearing on the structural integrity of a violin. Robert Zuger (and I assume others) has developed geometric formula to achieve a semblance of optimum arching. The math is not difficult, but the carving is tedious.
Since my objective is the making of a mould for an instrument, I think I have found a short cut. Injecting a fluid between a membrane and an underlying form should provide a structurally valid 3 dimensional arch based on elastic deformation. Thickness topography of the fluid should equate to iso-stress regions of the membrane.
I intend to use Mylar space blanket material for the membrane, plaster of paris paste as the fluid, and thin plywood shaped into the outline of a violin as the underlying form.
The iso-stress membrane method should be particularly useful in determining the arch of an instrument with asymmetrical bouts.
Without deviation from the norm, progress is not possible. —Frank Zappa
The future is already here—it’s just not very evenly distributed. —William Gibson