Sunday, March 17, 2013

The Case

The design for the case has a steeply curved bentside due to the strict Pythagorean scaling.  The choice of method for bending depends on the radius of the curve needed and the thickness of the piece.  If unconstrained, a bend will cause the outer fibers to be pulled apart (tensile strain) and the inner fibers to be squeezed together (compressive strain).  Poplar in a dry climate can withstand a tensile strain of about 1.5%.  For the small Iberian case the value of the strain, approximately equal to the thickness of the lumber divided by the radius of curvature,  is about 1 cm (0.5 in) divided by 45 cm (18 in) = 0.022 (or 2.2%).  A special fixture that keeps the length of the outer part of the curve fixed, such as a steel band clamped at the ends, can avoid any tensile stress by subjecting the lumber through the whole thickness to compression.  Wood can tolerate a much greater strain in compression, such as up to 30%.  However, a machine to apply the necessary compressive force would require significant time and expense to construct.

A practical alternative is to build the side from a number of thinner layers laminated together.  Using three layers, each layer would be subjected to a strain one-third that of the full thickness piece, or about 0.7%.  Each layer can be bent more easily and with much less chance of failing.  Closely spaced wood bars that are clamped across the laminations apply the bending force needed to follow the required curve.  The hitch pin rail that is glued to the inside of the benstside is constructed in the same way.

The image below shows the jig holding the bent hitch-pin rail.  The benside itself, already constructed, rests on top of the jig.


The next image shows a view of the same from above.


The next steps are to trim the bentside and hitch-pin rail to the proper width and length.