This blog will be about showing you a plausible way that ancient man might have calculated the width of the stave’s needed to make a bucket with the diameter he had in mind. First our logo photo of the bucket we are making and then a Swedish bucket made like ours from 1050 AD. I think this was the very first product sold by Ikea. And lastly a logo photo of the shop-made tools to make our bucket with.
CALCULATING THE WIDTH OF THE STAVE’S
Step 1. The bottom as a starting point
First we draw a circle representing the inside diameter of the bucket. Then we draw an outer circle. The difference between the two circles represents the the thickness of the materials we intent to use. I have used 15mm thickness in the photo below (I am just showing this metric to show the method). In this photo you see several things of interest. They are:
1. The inner and outer circles drawn on the bottom piece
2. A straight line intersecting the circle creating to equal halves.
3. A thin stick which has been bent around the outer circle and marked at each end with a black line denoting the beginning and ending of exactly 1/2 of the circle’s circumference.
The clamping was done so I could photograph the set-up. In reality this could be handheld with a little assistance and then marked. The stick could also be a thin pliable twig and the markings could be with a knife in the bark (the ancient way?).
Step 2. String theory
Now we have a stick that has the length of 1/2 the circumference of the circle as a starting point. Now we need a way to divide that stick into 6 equal lengths, or 1/2 the number of stave’s we wish to use. !/6 of that length will of course be equal to the width of one stave.
But, it seems to complicated to try to equally divide that stick since we ancients have no rulers and we don’t know how to divide.
The easy way is replace the stick with a piece of string that is flexible and can be folded. So in photo 1 you see that we place a piece of string on our stick and mark the string to be cut at the same length.
Now we can fold the string in two and cut it in half. That half will now represent 1/4 of our circles circumference as shown in photo 2 below.
Next we take one of the halves of the string and fold that into 3 as shown in photo 3 below. and cut the 3 lengths as shown in photo 4. We don’t really have to do the cutting, but it looked a little messy just folded. If you haven’t fallen asleep by now you will probably notice that the 3 string pieces aren’t exactly the same length. Sloppy folding! Anyway I picked out the longest one to use as my stave width. It was 7cm. So at last I had my Stave width! (fanfare).
Determining the edge angle
As I’ve said more times than you want to hear, with 12 stave’s the edge angles will have to be 15 degrees for us to get the stave’s tight against each other and in a circle. Here’s how our ancient bucket maker might have done it.
Step 1. prepare a mock stave
My mock stave is shown in photo 1 below. It is the same thickness as my real staves will be. I have cut it to a width equal to that remaining piece of string. Modern man would call it 6.6cm in width. Only the height is not the same as a real stave. Who cares? The mock stave has been positioned with the right back corner just touching the radius line where it intersects the outer circle. The left corner is just is also sitting on the outer circle. We mark that point on the left onto the outer circle where it intersects with the left corner.
Now we draw a new line from the center of the circle and straight through the dot we just marked as shown in photo 2 below. That radius line is shown in photo 3.
Next we reposition our mock stave back in the same position and we easily draw our angle line on each side.
PROVING THE ACCURACY OF THE METHODS
I hope that if you weren’t impressed that you were at least a little amused at my convoluted way of doing this. But now we want to prove if these methods are viable.
The stave width
I didn’t think I would get 100% accuracy with my method, but I wanted to get close. The result will be used only for the first 11 stave’s. The last stave aka the ‘weeping stave’ will be a different size, smaller in this case, which is always better that wider in my opinion.
I checked the results of my method with coopering math and based on the outer ring diameter, which told me that the circumference was 82.3cm resulting in a uniform stave width of 6.86m.
That compared to a circumference of 84cm using the width based on the length of the little piece of string. which indicated a width of 7cm.
However I won’t know about the discrepancy until I get to the last stave and see that the opening is 1.7cm too narrow to fit a stave with a 7cm width. So the last stave will have to cut down to 5.3cm to fit.
Lastly I checked the derived bevel with my bevel thingy and it was indeed 15 degrees. So another huge success. (applause).
Well that’s it for now. Tomorrow I will be starting over on a new bucket. I’m not sure how far I will get. I hope this blog will make things easier for the purist who want to do as much of the work as practical in the old way.
Here again is the link for the enlightened ones to learn cove cutting on the tablesaw. A really great link it is too. http://woodgears.ca/cove/index.html
Thanks for reading and I hope you find it helpful.
-- Mike, American in Norway