Thread: Coopering angles

Keith,

The angles are a very simple calculation, provided you are creating a true arc.

Unfortunately describing it at this time of the morning is not!!

Sooooo....http://www.woodworkforums.ubeaut.com...ead.php?t=1127

Originally Posted by jacko

To calculate the length of the arc, first calculate the radius, you would need to do this anyway to be able to draw it.
This can be done using Pythagarus.
Radius is 750 mm
From this the angle subtended can be calculated using trig. Result is 108 deg, or 0.3 of the total 360 deg.
The circumference is 2 Pi r or 4713 mm, therefore the arc length is 4713*0.3 or 1413 mm

In the above example, say you wanted 20 staves on the curve, and you have decided that the curve calculated is the OUTSIDE dimension, each stave would be 1413mm / 20 or 70.65mm wide.

The angle of cut can now be calculated by by dividing the angle subtended (108°) by the number of pieces (20) = 5.5°, then subtracting the result from 180° and dividing by two. (in this case the angle of cut would be 87.5°)

Cheers,

P(who failed maths at every attempt, but can get by, by drawing stuff and nutting it out)

It's a lot simpler if you just know the angle of the arc. If you draw it out to scale then you can measure it with a protractor. But then if you are going to do that, you can just mark off two staves, scribe back to the centre point, and measure the angle straight off the drawing, which is what I do.

Thanks Peter, I should be able to nut it out from here...


K

There is an article on making a coopered cabinet in FW #163. The author describes making a coopering jig with arc-shaped ribs, from which it is possible to directly measure the bevel angle of the staves using a sliding bevel tool and a protractor. It seemed to me that the method is rather prone to error, so I used TurboCad to draw the staves and accurately determine the bevel angle. My version of the cabinet is here:

http://www.woodworkforums.ubeaut.com...ead.php?t=5667
Rocker

Even simpler - well in fact it is the mathematical formula for the length of an arc

The length of the arc is:

Length = radius * angle (but angle must be in radian which is the angle unit in trigonometry)

To convert in radian: angle in rad = (pi * angle in degree)/180

Originally Posted by silentC

It's a lot simpler if you just know the angle of the arc. If you draw it out to scale then you can measure it with a protractor. But then if you are going to do that, you can just mark off two staves, scribe back to the centre point, and measure the angle straight off the drawing, which is what I do.

That's what I do too!

But it didn't answer the question!

P

Originally Posted by Rocker

My version of the cabinet is here:
http://www.woodworkforums.ubeaut.com...earchid=301302

Rocker

Rocker,

I got "no matches" for your link. :confused:

Thanks for asking keith!
-Ryan

Originally Posted by ryanarcher

Rocker,

I got "no matches" for your link. :confused:

-Ryan

Oops; I have corrected it now.

Rocker

A tip when coopering.
Cut one test stave the width and angles that you reckon are correct, then cut it into the number of pieces that you are going to use in the final piece. These only need to be short. Join them up and check that they give the shape that you want. If so, cut the real pieces, if not, adjust the angles and/or width.

My maths has never been that great and I have always relied on the kindness of strangers to work out anything complicated.

However, it strikes me that for someone who does know maths it wouldn't be too hard to make up a small spreadsheet wherein a few dimensions could be entered to give the angles needed to properly cooper a drawer front etc.

Given:
The length of the drawer, say 462mm
The depth from the front of the bow to the back, say 95mm
Material thickness,say 19mm
Number of pieces required to be coopered together, say 5

Given all that, surely it is possible to work out the angles required?

Somebody??? Somebody???

I have attached to this a zip file that contains my excel spread sheet I use to calculate the information you want.

You need to enter the number of staves, the chord of the arc, the height above the arc above the chord and the rest is calculated for you. If these terms are not clear you can see the illustrations in the sheet that graphically depicts them for you.

You will also note that I have also provided a way to construct the exact angle using measurements. You need to enter the base of the triangle to use and the height is calculated. I used metric measurements but cubits or imperial measurements would work too. I used a dial caliper to get to the nearest hundredth of a millimetre as I was working to precise measurements. You may not need that precision.

If you have any questions I would be happy to assist you.

That is great Mark Well done.

Now, just to make sure that I understand it properly.

c= chord. I entered 540 here
The number of staved I put at 10 and this made the data at E2 change to 56.7 which I assumed was the width of the staves that I needed to cut.
h=height which I had entered as 75mm
This gave me the number 6.2 at E6 which I believe is the angle that I need to cut on the side of the stave. Do I need to divide this by 2 to get the individual angles for each stave?
Why is the radius r smaller than the chord c?
What do I do with the theta and the alpha?
As I said before, my maths is just VERY basic stuff indeed. I c'n spell good but.

Originally Posted by Bob Willson

That is great Mark Well done.

Now, just to make sure that I understand it properly.

c= chord. I entered 540 here
The number of staved I put at 10 and this made the data at E2 change to 56.7 which I assumed was the width of the staves that I needed to cut.

The width of the staves is the width at the outer edge or outside of the arc.

Originally Posted by Bob Willson

h=height which I had entered as 75mm
This gave me the number 6.2 at E6 which I believe is the angle that I need to cut on the side of the stave. Do I need to divide this by 2 to get the individual angles for each stave?

No. The angle is the angle. No further calculation is required. In other words, each side that is roughly "perpendicular" from the outer edge will slope 6.2 degrees inwards from the outer edge.

Originally Posted by Bob Willson

Why is the radius r smaller than the chord c?

I can't think of a way to say this without sounding like a smart **** but trust me I had to stop and think about it too when you asked the question: The Radius is half the diameter so the result is correct. The diameter is the maximum chord and that is 1047.

Originally Posted by Bob Willson

What do I do with the theta and the alpha?
As I said before, my maths is just VERY basic stuff indeed. I c'n spell good but.

Theta is the angle in Radians and Alpha is the angle in degrees, which is what we deal with. Theta is what mathematicians deal in because there are 2*Pi Radians in a circle and this makes for some neat mathematical statements. I put this in there for some double checking of results for myself. This spreadsheet wasn't written with publication in mind.

Some tips on coopering.

1. Construct the coopered panel first and build around it.
2. When assembling coopered panel, ensure that grain direction is running the same way. It is very painful if you don't! DAMHIKT...
3. More staves give you a smoother look, assuming that is what you are after and it's not actually that much harder.
4. To glue up a coopered panel first construct a jig. Make two semi-circle cutouts with the correct radius from your calculation and assemble the panel. I used epoxy glue and only light pressure to glue up hence avoiding a moderately complicated clamping solution.

Originally Posted by markharrison

I can't think of a way to say this without sounding like a smart **** but trust me I had to stop and think about it too when you asked the question: The Radius is half the diameter so the result is correct. The diameter is the maximum chord and that is 1047.

I just had another look at the drawing you did and I see where I went wrong. I was thinking of the radius as the diameter. Triple Duh.

Anyway, thanks again Mark. I will use this formula next time I make a coopered panel, which should be within the next month.