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Making coopered conical forms

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Making coopered conical forms

Postby 9fingers » 24 Nov 2018, 21:22

On and off recently I've been making making conical forms out of multiple staves glued together. These are usually known as coopered from the technique used to make barrels.

Here are the first few.

Coopered Bin project 011.jpg
(624.74 KiB)


At first sight you might think the angles needed are varying from top to bottom but in fact they are constant as sections cut through the form will all be polygons with the same angle but only varying in the length of each side.
Each stave needs to be defined in terms of its width at the top and bottom and its length. All other details stem from these three definitions.

There needs to be a little arithmetic to convert from the overall dimensions of the final article in to stave sizes but it is not that onerous and then a couple of jigs can be made which greatly simplifies the production.

In the course of making these I had a few difficulties and have refined the method which I will describe in this and following posts.

I will rely on the dimensions of a polygon being approximate to a circle especially when the number of sides increases. A polygon with an infinite number of sides is in fact a circle.

Definitions:
Top diameter =TD
Stave width at top =T
Bottom diameter =BD
Stave width at bottom =B
Stave length =L
Number of staves = N

Pick some target parameters TD =250, BD =150, L=250 N =16

Calculating T
As above,
Treat the bin as circular so the circumference round the top = 250 * Pi. Divide this by the number of staves to find T

T =250* Pi/16 = 49.087 mm

Round that one way or other - I'm going to pick T=50mm

Repeat the excercise for the bottom diameter BD

B=150*Pi/16 = 29.452mm - I'll pick B= 30mm

So we have staves 50mm wide at the top tapering to 30mm at the bottom and 250mm long.

No we have a couple of angles to work out. I did think about try to do the project without working out the angles. It is possible but I think it is easier to use the angles especially with decent calculators built into phones. Note that if you have not tried it before both apple and android calculator turn into scientific calculators when you rotate the screen to landscape.

This is the diagram of a single stave.

angle calcs.jpg
(66.91 KiB)


Don't be frightened by ArcTangent, Arc Tangent(X) or Tan-1(X) simply the angle whose tangent is X

So for our chosen stave size we have an angle of 87.709 degrees - 87.7 degrees is more than accurate enough.

The other angle we need is the chamfer to be applied to the long edges of each stave.

polygon stave chamfer.jpg
(108.76 KiB)


The angle between each stave is 360/N and each chamfer is half of that. In our example 11.25 degrees.

This is critical to making tight joints. Just 1/2 a degree error on every stave will give a cumulative error of 32 x 1/2 degree = 16 degrees which works out to be nearly a whole stave.

Before you cut into your precious timber stock I really do suggest you make test pieces using MDF or ply. I found it really essential to get to grips with the jigs (coming up soon) and to check the setting of your saw blade angle. This is the reason you see a black painted bin in my first photo. Bare MDF is none too pretty and a quick coat of paint turned into an acceptable waste bin for the home office.


I'll give you a break now to reach for the aspirins and ask any questions if you are not following this far and I'll try and explain further before we get into making the jigs you will need.

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Re: Making coopered conical forms

Postby Mike G » 24 Nov 2018, 21:34

I'm just going to have a little guess that the old cooper's didn't know any maths. At all.
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Re: Making coopered conical forms

Postby 9fingers » 24 Nov 2018, 21:40

Mike G wrote:I'm just going to have a little guess that the old cooper's didn't know any maths. At all.

I'm sure you are correct Mike but instead they had several years apprenticeship and having to remake any barrels that leaked without pay!

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Re: Making coopered conical forms

Postby Robert » 24 Nov 2018, 23:35

Just wondering if the inside of a cyclone has to be smooth to work.

If you are bored one day....
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Re: Making coopered conical forms

Postby 9fingers » 25 Nov 2018, 12:05

Robert wrote:Just wondering if the inside of a cyclone has to be smooth to work.

If you are bored one day....


I'm sure being smooth would be better but if you used a lot of staves and maybe some epoxy filler where they meet it should work.
I have the original prototype of the IKEA cyclone that the late Barry Burgess built so not looking to make another.

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Re: Making coopered conical forms

Postby Malc2098 » 25 Nov 2018, 12:25

Aspirins?!! I had to go and have a lie down!

It brought back memories of log tables!

Nice post!
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Re: Making coopered conical forms

Postby Andyp » 25 Nov 2018, 12:35

Bob, I have been wonderng how you made them ever since you first posted. Thanks for sharing. I was fine up until
A polygon with an infinite number of sides is in fact a circle
. The missus understands but the girls are with me. :)
cheers

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Re: Making coopered conical forms - JIGS

Postby 9fingers » 25 Nov 2018, 12:59

A couple of jigs are needed to trim the staves. These will enable the staves to be tapered and chamfered in the same operation.

Coopered Bin project 015.jpg
(175.46 KiB)


I made mine from 12mm mdf and some scraps of birch ply for the guides. Make sure these strips are thicker than the thickest staves you plant to use.

Coopered Bin project 010.jpg
(193.12 KiB)


A slight aside for a tip I learned at school where our woodwork master got fed up with us boys breaking small drills. Simply cut the head off a wire nail or panel pin of the right size and use that.

Coopered Bin project 009.jpg
(111.33 KiB)


IMPORTANT.
The jigs I'm showing suit right tilt table saws like mine. The blade is tilted over away from the fence.
The jig rides along the fence with the workpiece on the right of the jig.
If your saw blade tilts left then you need jigs that are mirror image of mine.

These drawings show the dimension of the jig. Only the angles are important, the sizes are approximate.

Jig 1 dwg.jpg
(30.83 KiB)


Jig 2 dwg.jpg
(35.64 KiB)



This will be the last time you have to worry about angles for quite a while and instead get on with cutting wood.

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Re: Making coopered conical forms

Postby 9fingers » 25 Nov 2018, 13:36

Now prepare your blanks for the staves.

They need to be a smidgen wider than T, cut to length L and whatever thickness you want.

If you are re-sawing them from thicker boards, then plane, sand to final thickness and surface finish you need.

Don't forget to to make 1 set of staves from mdf or ply or other sacrificial wood and make some spares for this set at least. Trust me the f***-up fairy will visit you at some stage through the project.

Now apply any finish that you want on both sides and the ends allow to dry fully and de-nib.

Dont be concerned that this will compromise glue strength later as all surfaces to be glued will have a trim cut and expose raw, clean wood.

I found this to be an essential part of glue control during the final assembly. I did not do it for the first batch and cleaning up excess glue from the joints raised the grain (and fluffed up the mdf) and re-sanding the insides of the bins was quite difficult.

More and more on my projects I am doing surface preparation and applying early coats of finish at key stages during the assembly, masking off surfaces to be glued if needed and it really does make life easier.

Thicknessing on the drum sander.

Coopered Bin project 003.jpg
(196.02 KiB)


Some zebrano staves

Coopered Bin project 002.jpg
(285.54 KiB)


Note, I am not varnishing with horseradish sauce, simply a convenient jar for my special variant of Sam Maloof mixture.

One or two of my photos do show a deviation from my written method. These staves were tapered first, then varnished and then chamfered as I was being ultra mean with a small stock of zebrano. I do NOT advocate you work this way as it led to a few errors and subsequent bodges that I am not proud of.

Follow the written method please.

To be continued

Bob
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Re: Making coopered conical forms

Postby RogerS » 25 Nov 2018, 13:58

Andyp wrote:Bob, I have been wonderng how you made them ever since you first posted. Thanks for sharing. I was fine up until
A polygon with an infinite number of sides is in fact a circle
. The missus understands but the girls are with me. :)


Ah, but which 'infinite' ? For there are many...see George Cantor

Excellent thread, Bob. I feel the urge to get a drum sander again !
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Re: Making coopered conical forms

Postby Rod » 25 Nov 2018, 14:55

Very interesting Bob, can this be “stickered” for future use?

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Re: Making coopered conical forms

Postby 9fingers » 25 Nov 2018, 15:14

Now for a critical bit.
Fit your bestest(!) sharpest blade. Although technically you will be ripping. a 40 tooth plus crosscut blade should give you best results.

Setting the tablesaw blade to the correct angle. I use my trusty digital angle box.

Zero it on the table and then use its magnetic base to stick to the saw blade making double sure it is all on the saw body and not catching on the teeth.

Coopered Bin project 022.jpg
(284.46 KiB)


As you can see the gauge is reading 78.8 at the moment but picking a setting where it is flicking between 78.8 and 78.7 will be the closest you can get to 11.25 degrees off vertical.

With the fence set to face away from the blade tilt and the height only just enough to cut through. Cut N/2 scrap strips of parallel MDF/Ply about 50mm wide, 100 long between the fence and blade, flipping each one end for end, same face up to get a chamfer on each long edge.

Sweep away any dust from these and with widest face up and edges abutting, join these with masking tape stretching the crepe nice a tight as you go. A roller can be useful to press the tape into place. Sorry I forgot to take a photo of this but it is similar to this showing some of the taping. do every joint with tape.

Coopered Bin project 034.jpg
(173.63 KiB)


Now take the taped staves and roll into a part circle until all the joints are closed.

As you have N/2 staves, if the angles are correct you will have a semi circular (ish) half polygon that should sit nicely on a flat surface.

like this

Coopered Bin project 035.jpg
(131.56 KiB)


If the arc is less than a semi circle, then the chamfer is too little. If when it sits on flat surface any of the joints open up then the chamfer is too much.
As mentioned earlier in the thread this need to be accurate as gaps in the stave will look awful and if the chamfer is too small, your bin wont pull into a circle.

If needed, take it apart, adjust the blade by a gnats tadger, move the fence towards the blade by a mm or so and recut all the chamfers and retest until you get a perfect result.

By now your varnish etc should be dry on the mdf trial staves and you can get going with the jigs.

Put the first stave on jig number 1 so called because you use it first - ok!

Coopered Bin project 024.jpg
(314.33 KiB)


Make a mark on the bottom left corner of the stave for later (this will eventually be cut off)

move the fence way to the left an take the jig past the (stationary!! blade) with the stave pressed against the long guide of the jig and into the gap between the two guides - dont worry that it only contacts the short guide at one point.
Align the jig so that the blade tooth will just clear the end of the stave nearest you. Bring the fence in to touch the left hand edge of the jig. - easier to do that describe!
The idea is that when you make the cut, the absolute minimum is cut from the right hand corner of the stave nearest you.

Bring the jig and stave back to the starting position for a cut and make a trial cut. You are quite likely to cut into the jig for the first cut. That is just fine.

Examine the cut surface closely, there should be no visible flat from the original cut edge and there should be a nice sharp corner all the way along the chamfered edge.
If you need, move the fence a hairs breadth to the right and take another dust cut until the chamfer is perfect.

Set aside jig 1 and set the half cut stave rotated 180 (ish) degrees onto jig two so that your mark is now top right and still facing upwards.

like this
Coopered Bin project 018.jpg
(159.21 KiB)


Adjust the fence position until the upper face of the top end of the stave will be cut to your desired dimension T.

Coopered Bin project 019.jpg
(157.25 KiB)


Maybe set it over to just greater than T for your first cut on jig two, and take a second dust cut as before. Again you may well cut into your jig but this is not a problem.
The cut edge should again be sharp all the way along. If you find it is not, then you might have to reduce your target dimension T by a gnats. It is more important to get that sharp edge as without it, your joints will gap.

You should now have one stave looking like the drawing.

angle calcs.jpg
(66.91 KiB)



Mark that stave as a reference 2. Note that if you fit that onto jig 1, you will have lost the reference edge in the second cutting process so use Jig 1 to cut another reference stave and mark that as reference 1

Now you are all set to run N off on jig one is a series - remembering to add your mark! and then reset to jig 2 using reference 2 to set the fence and run all the second edges through.

You now have two reference pieces and N identical staves.

Next time: One more angle to work out and I have to draw some more diagrams so there will be a break in the posts for a while.

Bob
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Re: Making coopered conical forms

Postby 9fingers » 25 Nov 2018, 15:20

Rod wrote:Very interesting Bob, can this be “stickered” for future use?

Rod


Thanks Rod. I'm glad you are enjoying it.
We could sticker it but I'd want to avoid having too many stickered items clogging up the top of any board.
We might look at setting up some sort of reference area for threads that are deemed to be worthy of long term retention.

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Re: Making coopered conical forms

Postby Malc2098 » 25 Nov 2018, 16:13

Really good reading! Waiting for elect instalment.
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Re: Making coopered conical forms

Postby 9fingers » 25 Nov 2018, 17:04

Malc2098 wrote:Really good reading! Waiting for elect instalment.


Elect?
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Re: Making coopered conical forms

Postby 9fingers » 25 Nov 2018, 17:50

Well I promised you another angle and here it is but with a spooky coincidence.

We now need to cut a groove in each stave for the base of the bin and trim the top and bottom edges so they will be parallel to the base.

Here is a vertical section through a bin.

cross section.jpg
(125.96 KiB)


we need to trim the top to make it level

Top detail.jpg
(14.1 KiB)


and a similar cut on the base plus a groove to locate the bottom

base detail.jpg
(11.14 KiB)


Conveniently these cuts are all at the same angle.

This time we need Arc Cosine which just like its brother the Arc Tangent is the angle whose cosine we can read off the diagram as 50/L which in my example is 0.2 That angle is 78.5
The angle between the base and the sides is 180-78.5 = 101.5
Because of the way we cut these flat on the table, we need the blade at 101.5-90 =11.5

Hang on a minute we already have it set at 11.25 and we dont need to lose and sleep over a quarter of a degree for this job.

So dig out your reference 2 and place it on jig 1 with the outside face upper most (the same was as when you cut it) but on the otherside of the long guide so that the wide end hangs over the end of the jig and parallel to the blade. Use the mitre gauge to push the jig and stave into the blade to cut off the sliver we need to remove.
I found I needed to trim the bottom guide on the jig very slightly to get it to settle on the mitre gauge nicely

Coopered Bin project 028.jpg
(302.19 KiB)


Trim all the tops in this way.

With the fence on the right of the blade, place reference 2 stave on jig1 on the other side of the long guide outside face up as usual so the narrow end of the stave hangs over the end of the jig.

Using the mitre gauge in the left hand slot and with a piece of parallel scrap clamped to it, ride the jig along the fence and at the same time guided by the scrap mitre fence extension.
One hand on the mitre gauge and the other on the jig and workpiece.
When making a cut like this, it is important to keep lots of pressure on the jig pushing it hard against the fence.

Set the fence such that you trim off the sliver from the narrow end of the stave.

Coopered Bin project 030.jpg
(295.9 KiB)


Trim all the staves in this way.


Now to cut the groove for the base.
I use a 4mm flat top ground blade for this sort of job but you could just do two passes with a normal blade. No one will see the groove does not have a flat bottom but has a double M created by an ATB ground blade.

I cut my groove about 4mm deep and 4 mm in from the end of each stave.

The guide and jig set up is identical to the one just used to trim the short end of the stave but obviously with the blade set lower :D

The end of the stave should look like this now and you base material should be a loose fit. My bases are 3.5mm thick in a 4mm groove. The last thing we need on glue up is fighting to slot the base into each stave with our fifth hand :lol:

Coopered Bin project 027.jpg
(288.93 KiB)


Thats it for now as I have to go and finish cooking dinner. More this evening with luck or tomorrow.

Bob
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Re: Making coopered conical forms

Postby Malc2098 » 25 Nov 2018, 18:05

9fingers wrote:
Malc2098 wrote:Really good reading! Waiting for elect instalment.


Elect?



Next. Bloomin' autospill and fit fongers!
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Re: Making coopered conical forms

Postby 9fingers » 25 Nov 2018, 18:15

Malc2098 wrote:
9fingers wrote:
Malc2098 wrote:Really good reading! Waiting for elect instalment.


Elect?



Next. Bloomin' autospill and fit fongers!


Ok it was pretty close :lol:

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Re: Making coopered conical forms

Postby 9fingers » 25 Nov 2018, 22:18

Now we need to de-dust the staves ready to stick them together with lots of masking tape.

I did mine in groups of 4 aligning the ends and face up with strips of tape stretched across 4 staves top and bottom, then along each long join between staves.
Then with 4 set of 4, join those in the same manner to get all 16 linked together. Press down on all the tape with a J roller. Now roll them into a cone and close the gap with a couple of bits of tape top and bottom. Hope fully every thing fits. I you have the odd joint that is gapping there might be the odd little bit of sawdust or a splinter keeping it open.

Turn it bottom up and measure for the base disc.

Coopered Bin project 032.jpg
(153.31 KiB)


Mark out your disc with a compass and cut out. Do a trial fit and adjust if needed remembering not to make it too tight. sand the edges and faces of the base and apply finish.

Open up your set of staves and check none of the tape is coming adrift, repairing as needed.

Roll done the tape one more time and place tape down on a flat surface. use something like a piece of dowel to roll under the surface of the taped side, you can open up each joint in turn to brush some glue in to each joint and onto the open edges. Add more glue into the groove that retains the base.

Tear off a few lengths of tape about 6" long and one a bit longer than the height of the bin. stick these hanging off the edge of the bench where you can get to them. Start the base off in one of the staves and roll up the bin tucking in the base as you go. Grab the tape and stick across the join in several places and then run the long piece of tape along the joint.

Coopered Bin project 033.jpg
(117.35 KiB)


Before the glue starts to go off, examine and adjust any joints that have slipped out of line.

Clean up up any squeeze out glue with a damp cloth or sponge and be thankful that due to all the parts being pre-finished that it comes off nicely.

That is your prototype built so you should be able to produce as many as you want now.

Here are the two Zebrano ones complete.

Coopered Bin project 031.jpg
(228.54 KiB)


Thanks for reading and good luck if you decide to have a go yourself.

Bob
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Re: Making coopered conical forms

Postby Malc2098 » 25 Nov 2018, 22:23

:text-goodpost:

Thanks, bob!
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Re: Making coopered conical forms

Postby oddsocks » 25 Nov 2018, 22:51

thanks for the great post Bob, that's another project to attempt to add to the ever increasing list!

I'm also still trying to get my 8 year old granddaughter to accept that a circle has an infinite number of sides, not zero!

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Re: Making coopered conical forms

Postby 9fingers » 25 Nov 2018, 23:02

oddsocks wrote:thanks for the great post Bob, that's another project to attempt to add to the ever increasing list!

I'm also still trying to get my 8 year old granddaughter to accept that a circle has an infinite number of sides, not zero!

Dave


You could always make her one of those boards of nails where you stretch straight lines of wool out and make a curve out of straight lines.
A bit like this but with equally spaced panel pins on X and Y axes
https://www.wikihow.com/Draw-a-Paraboli ... t-Lines%29
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Re: Making coopered conical forms

Postby oddsocks » 25 Nov 2018, 23:58

9fingers wrote:You could always make her one of those boards of nails where you stretch straight lines of wool out and make a curve out of straight lines.
A bit like this but with equally spaced panel pins on X and Y axes
https://www.wikihow.com/Draw-a-Paraboli ... t-Lines%29
Bob

Thanks for the link, I'll try and do that with her (either nails&board or graphpaper)
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Re: Making coopered conical forms

Postby RogerS » 26 Nov 2018, 07:44

oddsocks wrote:thanks for the great post Bob, that's another project to attempt to add to the ever increasing list!

I'm also still trying to get my 8 year old granddaughter to accept that a circle has an infinite number of sides, not zero!

Dave


Keep drawing circles using SketchUp as it treats circles as polygons and you can specify the number of sides. So gradually increasing the number of sides will show the polygon turn into a circle.
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Re: Making coopered conical forms

Postby RogerS » 26 Nov 2018, 07:44

Bob, I'm guessing that a disc sander or linisher would be ideal for finessing the sides in the base ?
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