# A Final Project

A project which uses multiple materials and techniques

While there are many guides for making coopered boxes, none of them discuss the underlying mathematics and algorithms. This project allows one to design a traditional chest made up of multiple boards, and straps of different materials. The project will use metal for the central flat straps, and leather for the edging and corner protectors way be fashioned of either material, or suitable hardware may be sourced commercially.

The first consideration is the necessary parameters. Rather than using absolute/specific dimensions, the height and length and width of the project will be defined in terms of the base width of the boards, so the first parameters would be to define:

BoardWidth

BoardThickness

BoardGap

In keeping things proportional, it will also be expedient to use that last value as the gap for the metal parts, but since metalwork is normally more precise we will use one-fourth that dimension.

The actual size of the base of the box will be calculated from:

BoxWidthinBoards

BoxDepthinBoards

BoxHeightinBoards

In addition we will provide the following options for styles of lid:

Flat — a plain flat lid

Faceted — a three-sided, Mansard-style lid

Arched — a traditional coopered (curved, multi-piece) lid

In order to facilitate the strapping (for simplicity's sake it is assumed the flat strapping is the same width and thickness as the angle profile) it will be necessary to specify the dimensions for it:

AngleWidth

AngleThickness

Lastly we will need to fasten things with some sort of hardware which requires that a hole is placed through the strapping — for simplicity a matching hole will not be machined during manufacture, instead it is expected that the holes will be drilled during assembly. Similarly, the actual hardware used is not specified, only the diameter of the necessary hole:

HardwareDiameter

This yields:

In addition, since we are cutting the boards in half lengthwise for the lid parts it will be necessary to know the width of the saw kerf (dimension of material lost to the cutting), so add:

SawKerf

Working in multiples of boards we need a module to create an array of boards. The inputs should be obvious, as are the calculations and looping. It will be expedient to calculate out the actual dimensions of the (lower portion of the) box:

boxwidth

boxdepth

boxheight

Next we erect the front and back and ends:

Next is the logic for the lid, a simple if-then construct based on the allowed lid types (which will become a drop-down menu in OpenSCAD). Since the skirt will vary, amongst designs, but the basic version will work for multiple designs it is made into a module (from which code will be copied for the 3-faceted version):

Placing the flat lid is simply a matter of positioning a duplicate of the bottom:

The faceted lid is a basic variation, starting with appropriate angles on the skirt pieces:

Adding the front/back facets is easily done:

The ends require a bit of trigonometry to calculate the offset of the angled boards and necessary gaps:

Add the boards at the top to finish this version of the box:

The arched form requires some additional variables:

Arching the lid so that it fits requires calculating two triangle angles:

Combining all the wooden parts and one arrives at:

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