Which is to say that I need to figure it out using math.

Somewhere a math teacher that I told “I’m never going to need this after I get out of school” is laughing uproariously.

It’s nice that I can continue to amuse them so many years later.

Step One: Ask an Engineer

I asked my wife how to figure out the correct angle for the sides of each stave of the tankard.  She looked me right in the eye and said “AutoCAD“. After a moment’s reflection, she changed her mind. “Actually, Solidworks is better for this kind of thing.”

Hmmm… Thanks, honey.

Okay, for the record, I studied technical drawing “the old fashioned way” in art school and can use CAD if I have to. I could also have my dearest darling draw it up for me. And she offered to do so.  It would certainly be easier for her since numbers aren’t really my favorite thing and tech drawing wasn’t my favorite class.

The problem with teaching anything, is convincing the student that the subject will be important enough for them to pay attention to. In my past experience, math teachers were especially bad at this. Mine certainly never really did a very good job of telling me why I needed to know this stuff.

To be honest, I didn’t do a very good job of listening either, so a plague on both our houses, I guess. Like almost everyone in the world, I use algebra and physics on a daily basis. Only as an adult did I come to really appreciate that fact and had to go back and teach myself (or humble beseech my wife to teach me) those subjects.

Pay attention in math class, kids.

There are several ways to do this without using a computer, or even using a calculator.

Step Two: Do It the Easy Way

Years ago when I started making wheelbarrows, I had to figure out how to cut felloes of the correct arc and length. (“Felloe” is the technical term for the wheel sections of a wooden wheel.) I made my template by cutting out a circle and folding it in half several times to make something that resembles a pie.

If your scale is 1:1, then each pie piece is the correct size and the edges are at the correct angle for a section of a wheel or the stave of a tankard. Cut the center out and the widest point of each pie piece is a template for every angle you’re going to need.

Step Three: Find a Method Closer to Period:

One of my favorite measuring devices is an ancient tool called dividers. They appear in museums (these supposedly belonged to Michelangelo) and paintings and drafting sets and the bookbags of school children.

Most of those children grow up to be adults who call them “compasses” and think that all they’re good for is drawing circles. And for most people, that’s enough.

About the only places I still run into them being used in their original capacity is in navigation where they’re used to mark out distances on charts and in woodworking. Woodworkers tend to use them to scribe circles and copy relief surfaces.

This is historical woodworker Peter Follansbee’s article on using dividers: http://pfollansbee.wordpress.com/tag/compasses/.

They can be very expensive and finely made or they can be cheap as chips, bought in the school supply section of your local Target.

If you stand your staves in a circle and set your dividers to the width of the farthest point, you can draw the line of the bevel as illustrated below.