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.