The Arte & Misterie of Coopering: A method to the mathness…

This is going to be a longish post and it’s going to involve some basic math. If you’ve a fear of either, I feel for you because though I’m not skittish about reading novel-length posts as long as I’m learning something, math isn’t my bestest friend in the whole wide world.  I may be a nerd, but when I was a kid there were math nerds and there were art nerds and there were comic book nerds and band nerds.

The venn diagram of my life intersects all of those, but didn’t cross the border of math nerddom until I married one.

And if I want to make it as a cooper in even so small a way as this, I’m going to have to shake hands with a math book. This is what we’re going for with the coopering portion of the project.

Image Source: Wikimedia Commons
Image Source: Wikimedia Commons
It’s a tankard that was brought up from the wreck of the Mary Rose.  It is one of the many tankards of a similar sort that are knocking around museums in Europe. Several were brought up from the Vasa. They seem especially common in seafaring contexts (shipwrecks and port cities) and are hooped with wood or cane, which is easier to fabricate without a smithy (mine isn’t built yet) than iron or copper.
One of the key “mysteries” of the cooper is judging the correct angle for the staves to meet in order to make a perfect circle. The resources online and in the books I have available to me aren’t a lot of help on this one. Like the cooper in that video I posted, most sources simply say that a cooper learned to ‘eyeball’ it over the years.

Obviously, I don’t have years to devote to this. I’ve achieved a measure of acceptance for the idea that I’m never going to get past the apprentice level for most of these trades. The eternal apprentice am I.

The inner and outer curves are easy enough to make up as I go along; the bevel is another story all together. If the bevel’s wrong, this thing isn’t going to fit together or it’s going to leak like a sieve.

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.

If you run on a smaller scale, this method is almost infinitely scalable. Just use a sliding bevel to translate the angles from the template to the wood and you should get it done with a minimum of futzing around.

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:

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.

I own several pairs of varied vintage and before the project’s finished, I suspect you’ll see all of them. The ones in the photo below were purchased for a couple bucks at a Harbor Freight in Tacoma. 

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.

This gives you your bevel as well as letting you “eyeball” how much material you’re going to need to remove in order to get the walls to their desired thickness for your bucket, tankard, barrel, or butter churn. All of those things were made by coopers, and all demand slightly different wall dimensions as dictated by their end use.
I admit it. I needed geometry and math and all the things my high school math teachers had to put up with me complaining I’d never use. I not only needed them, I also needed to know how to apply them when the time came. My apologies to math teachers everywhere.
~ Scott

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