This being the part where we turn math into a drinking vessel…
n = the number of staves you want in your vessel.
And it doesn’t change no matter how big or small your vessel gets.
There seems to be a lot of confusion about that out in the Interwebs. The angle is the same whether you have a diameter of ten feet or ten inches or two inches. For an octogon (or an eight-piece circle) the angle for the cut is 67.5 degrees.
Geometry is awesome like that.
The mystery of the bevel solved, it only falls to us to decide how to cut that angle accurately. As I said in the lead-in to this project, every source I have just says “the cooper eyeballed it.” And the tool they used for that eyeballed angle was a big jointer plane mounted upside down on the floor of their shop.
You can see one being used in this engraving from my muse and tormentor Jost Amman. That’s one seriously large piece of equipment. I checked around and those things are expensive even if you make your own (mostly the cost of getting the blade made).
|Image source: Wikimedia Commons
Cleaned-up digitally by yours truly.
You can see it in use in this video I posted the other day of Ramona Vogel, journeyman cooper at the Colonial Williamsburg living history village: http://vimeo.com/11313428 I think that beyond some basic geometry, the real “art and mystery” here is how to finagle the right tools to make it all work.
Thankfully, the woodworking blog I got that video from (The Village Carpenter) came to my rescue once again with this post about a friend of hers who makes buckets.
He doesn’t use a huge floor-mounted jointer; he uses a hand plane mounted upside down and it seems to work just fine. He also uses a jig, but I wanted to try my hand at this “eyeballing” thing that everyone seems so impressed by, so I grabbed my largest bench plane and a handful of clamps and my eyeballs this is what I ended up with…
|I’ve already leveled the sole of the plane, now I’m making some fussy adjustments on the blade.|
|Taking the first few swipes across the blade.|
Thankfully, the upside down plane worked a treat and I didn’t so much as trim a fingernail on that razor-sharp blade that made such short work of that dense oak stave.
The tool I’m using to check the angle in the photos below is called a sliding bevel. I pre-set it to the correct angle and locked it off. I’ve only to hold the piece up to the light and slide the blade of the tool along the wood, watching for gaps.