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Blog entry by stefang posted 1168 days ago 3682 reads 0 times favorited 32 comments Add to Favorites Watch

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.

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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?).

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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.

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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.

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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).

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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.

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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.

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Next we reposition our mock stave back in the same position and we easily draw our angle line on each side.

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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.

The angle
Lastly I checked the derived bevel with my bevel thingy and it was indeed 15 degrees. So another huge success. (applause).

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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, an American living in Norway.



32 comments so far

View swirt's profile

swirt

1912 posts in 1470 days


#1 posted 1167 days ago

Incredibly clever and simple approaches. Fun to read.

-- Galootish log blog, http://www.timberframe-tools.com

View daltxguy's profile

daltxguy

1373 posts in 2412 days


#2 posted 1167 days ago

Hi Mike. Excellent demonstration!

The last part of laying out the angle is exactly how i would imagine doing it but I still contend that staves of equal width is not important and was not likely the case. I think if you measured the staves of the Ikea bucket (from their annual 1050 catalogue), you would find the staves to be of uneven width.The last stave is sized to fit the space remaining and you can see that in the picture.

The exact centre of a circle can be found using a compass and a straightedge alone using simple geometry . If they could draw a circle, I assume they had something like a compass.

The laying of the stave on the circle as you have done will give you the precise angle to cut that piece. It is not even required to know what that angle is and it does not matter how many staves you have or how wide they are. No math required whatsoever

-- If you can't joint it, bead it!

View mafe's profile

mafe

9231 posts in 1587 days


#3 posted 1167 days ago

Hi Mike,
Interesting thoughts, and what a way you have walked, thank you.
I do not agree though.
I think it was more simple, so I think they made first the bottom, and then made one staf at the time, set it on the edge of the bottom and adjusting the angel to the previous, in this way they needed no math, and no angels, just sence, and practise. The circle could be made with a string or a rod and a knife. I do belive it’s why the last staf have a funny name.
I build my theory only on assumptions. I assume, most people would be able to make one, but not all had the ability or and the tools to make it mathematical or even a constructed angel. I also assume the wood would varie in thickness and with, du to the fact they would try and use all, and that it was made by hand, probably often only with drawknifes, and wooden spokshaves.
I have made a PDF that shows my thoughts download by click here.
Best thoughts,
Mads

Here some inspiration:
http://www.willadsenfamily.org/sca/danr_as/bucket/Viking_Bucket.pdf
http://www.buzabunch.com/bucket_making_at_tillers.htm

-- Mad F, the fanatical rhykenologist and vintage architect. Democraticwoodworking.

View daltxguy's profile

daltxguy

1373 posts in 2412 days


#4 posted 1167 days ago

Mads – you and I are saying the same thing but having a picture helps. We both agree that no math is required whatsoever.

Also, your conclusion that thinner or narrower is less wasteful is interesting, though thinner might have implications on strength and narrower means the number of staves is increased and therefore requires more of them to be fitted. Since staves were likely rived, both width and thickness probably varied to a point. I only considered variable width but both variable width and thickness can be handled with this method.

So, have we discovered the secrets of the vikings? How to build a bucket with only a length of twine, a piece of charcoal and an axe?

-- If you can't joint it, bead it!

View Dennisgrosen's profile

Dennisgrosen

10850 posts in 1613 days


#5 posted 1167 days ago

Daltxguy …...LOL

Mike thank´s

Dennis

View Dave's profile (online now)

Dave

10904 posts in 1338 days


#6 posted 1167 days ago

I believe all ancient structures or projects were built with water, twine, time and sweat. One tool makes another. You have to use what you have on hand. Take a mule vs a tractor. You only have two men and a mule working a field. One man is cutting timber in a bottom. He fells the tree, ties it to the mule and the mule drags it to another man on the other side of a hill hill. Try to get a tractor to do that.

-- Superdav "No matter where you go - there you are." http://chiselandforge.com

View mafe's profile

mafe

9231 posts in 1587 days


#7 posted 1167 days ago

One more important thing is to turn the stafs right way!

The wood you use are cut like the one on the left, so it will curve outwards in the ends.

This will secure that the movement in the wood don’t make the bucket loose the water…
My problem is that eighter way it will be a problem… So perhaps the clever thing will be to change front-back-fron-back… in this way the gaps will not grow.
Hmmmmmm, perhaps I just think tooo much!
Best thoughts,
Mads

-- Mad F, the fanatical rhykenologist and vintage architect. Democraticwoodworking.

View TopamaxSurvivor's profile

TopamaxSurvivor

14397 posts in 2174 days


#8 posted 1167 days ago

(Standing ovation!! ) Mads, the rived staves would be like the one on the bottom. That would be the most likely, IMO.

Mike, I don’t think they went to all that trouble. I doubt if they measured anything or marked much. A craftsman who works with tools all day everyday just does it. I serioulsly doubt if a “dovetailer” in a production shop in the middle ages used a markig gauge. If you look at the picture of the bucket laid flat in the book picture above, the staves lok random width, there looks to be 2 weeping staves and top edges seem to be evenly worn wiht very little breakage. I think that all supports a stave whipped out n a few minutes, set around the bucket’s bottom which was what it was, certainly not precise, and it was assembled.

At any rate, awesome blog as usual.

-- "some old things are lovely, warm still with life ... of the forgotten men who made them." - D.H. Lawrence

View mafe's profile

mafe

9231 posts in 1587 days


#9 posted 1167 days ago

We have to try and remember that they did not buy wood in those days at the local store. They would do things fast and easy, so they would split the wood with a axe or froe, and then shave the stafs in app. thickness. Next step would then be to get around that bucket bottom…
http://www.heartofthewood.com/riving2.htm
Smiles,
Mads

-- Mad F, the fanatical rhykenologist and vintage architect. Democraticwoodworking.

View stefang's profile

stefang

11812 posts in 1832 days


#10 posted 1167 days ago

Many good and valid thoughts here guys that I totally agree with. The methods you have described are in fact very well documented. And as Bob said, the craftsmen were surely so practiced that the could probably do these things without measuring anything at all, although I do think they might have used templates to some extent.

However, we have the problem that most of us are buying lumber in a uniform width or we are cutting it a uniform width for convenience. I did consider cutting different widths from wider stock, but I was worried about messing this up. Maybe I should have tried it anyway to be more authentic. I don’t want to do that now though because my new stock isn’t really wide enough to give a proper range of widths and it is too narrow to get the diameter I need if I make it even narrower. Some others might have the same problem.

Would it be valid to assume that the basic construction of these containers remained the same over a very long period, but that the methods used to do the work and the way of arriving at stave widths and edge angles perhaps evolved quite a bit and that craftsmen perhaps became more desirous of uniformity? If so, that leaves us with the dilemma of picking our methods. That is, how ancient?

Mads, thank you for reminding about the importance of the grain orientation. The best material would be quarter-cut for stability, but with the materials we can get today we just have to orient the pith to the buckets outside as you also point out in your illustration. Another way stave’s were often created in the past was to cut them out with a curved iron directly along the end grain of a log with the open side of the iron’s curve on the outside of the log. This open side which would naturally curve even more with drying would then be oriented toward the inside of the bucket. So the need for sawing/shaving/planing both sides of each stave were greatly reduced.

Please let me know your thoughts on how you think we should proceed. Do you intend to use different widths and angle them as you go?, or will you have uniform widths calculated with coopers math?, or should we use some primitive method similar to the one in my blog? We can of course all do this however we want to individually, but since we are all interested in authenticity It would be nice if could reach a consensus on how to proceed.

Thanks everyone for all this great input and the interesting discussion around it. I look forward to hearing more from you on this subject.

-- Mike, an American living in Norway.

View mafe's profile

mafe

9231 posts in 1587 days


#11 posted 1167 days ago

Hi Mike,
I would love to try and make the bottom forst, and then one staf at the time in different withs, but I can do a temporary bottom and set them arround, then cut the grooves after like you.
But I have not been in the shop today, so perhaps some hours tomorrow.
Best thoughts,
Mads

-- Mad F, the fanatical rhykenologist and vintage architect. Democraticwoodworking.

View mafe's profile

mafe

9231 posts in 1587 days


#12 posted 1167 days ago

Update:
http://lumberjocks.com/mafe/blog/21023

-- Mad F, the fanatical rhykenologist and vintage architect. Democraticwoodworking.

View TopamaxSurvivor's profile

TopamaxSurvivor

14397 posts in 2174 days


#13 posted 1166 days ago

Hi Mike, I won’t be pushing a plane. Other hand work depends on shoulder stress. Rotary cuff is a little upset with me. I over did it trimming trees at the Tree
Farm last summer. ;-(( Random widths and odd angles could get to be a bit of a pain if time is limited. If you really want to be authentic, fitting each as you go should be easily accomplished is time is not an issue.

-- "some old things are lovely, warm still with life ... of the forgotten men who made them." - D.H. Lawrence

View mafe's profile

mafe

9231 posts in 1587 days


#14 posted 1166 days ago

So!

This is status now. I will post my pictures of how I got there asap but it might be in a day or two.
Next week I will be off class, sorry Mr. teacher Mike (Hope I give you no grey hairs)!
Best thoughts,
Mads

-- Mad F, the fanatical rhykenologist and vintage architect. Democraticwoodworking.

View mafe's profile

mafe

9231 posts in 1587 days


#15 posted 1166 days ago

Is it allowed to use silicone?
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Laughs!

Best thoughts,
Mads

-- Mad F, the fanatical rhykenologist and vintage architect. Democraticwoodworking.

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