another geometry question

[sunnybob]

I know you guys love these kind of questions....
I want to make a tube of staves.

The outside diameter of the tube is 170mm.
I want 30 pieces, so that I can use the router table to cut the 12 degree edges.
looking at the circle end, how wide do the staves have to be?

 

[dzj]

Wouldn't you need only 15 pieces if the edges of the staves are beveled at 12 degrees?

 

[sunnybob]

There, right there, is why I ask questions.
My first thoughts were 12 goes into 360 thirty times.
But as soon as you queried me I realised i have two angles per piece.

So yes, youre right (I think), how wide will the FIFTEEN staves be?
Please?

 

[petermillard]

So yes, youre right (I think), how wide will the FIFTEEN staves be?
Please?

Can you not just draw it out full size and measure it?

 

[dizjasta]

outer circumference of tub is 534.0 mm. Outside width of each stave is 35.6 mm.

 

[dzj]

Draw a 170mm circle with a compass, use a protractor to mark out 24 degree slices and depending
on your router bit height, you should be able to figure out/ measure the necessary width and thickness of each stave.
There probably is a way to calculate this, maybe one of those SketchUp type programs would work also.

 

[sunnybob]

My "geometry" equipment would be laughed at by a primary school child. No way could I use what I have and get anything accurate enough to cut to. Desperately trying not to buy more stuff that will only get used once, and even if I bought it I wouldnt know how to use it.

Disjasta; thanks, thats a starting point for me. I'm happy to cut slightly larger and trim to get the diameter i want.

 

[MikeG.]

outer circumference of tub is 534.0 mm. Outside width of each stave is 35.6 mm.

I make it 36.1mm. The perimeter is 542mm. This is the minimum size for the polygon which can then be turned down to a circle of 170 diameter.

 

[sunnybob]

I'll aim for a finished piece 36 mm. A decimal point isnt too important for this build as long as the joints are close fitting.
The inner diameter will be the most critical but I can sand that on the bobbin sander.
Thanks all.

 

[MikeG.]

The inner diameter obviously depends on the thickness of the timber you use.

 

[Phil Pascoe]

I'm sure you'll find something on https://www.blocklayer.com/woodturning-segmentseng.aspx
(this just happened to be the last page I looked at)

 

[Jacob]

My "geometry" equipment would be laughed at by a primary school child. No way could I use what I have and get anything accurate enough to cut to. Desperately trying not to buy more stuff that will only get used once, and even if I bought it I wouldnt know how to use it.......

If you can't afford a pair of compasses (£5 or less) then drill 2 holes in a lath 85mm apart. Pencil in one, pin in the other. Clutch pencil best with neat tube for the lead and hole to fit, but not essential. Actually very handy if you are likely to want to repeat it.
School geometry set costs 70p and you could pencil in the 24º angles easily, starting from a radius. You'd go 24,48,72 etc to avoid moving the protractor too many times.

 

[sunnybob]

jacob... affording is not the same as operating. I have a compass, working out how to divide the circumference into sections and marking same to 1 degree accuracy.......uh uh.

I'm commited now (I know you all think I should have a long time ago, but hey),
the pieces are cut to width, just need to do the rest now. If i get it halfway usable I shall post the pics.
ta muchly.

 

[Jacob]

Right! The secret is; you'd go 24,48,72,96,120,144,168º to avoid positioning the protractor too many times, with associated error. Just twice in fact.
That is - if you want to draw it all out, but you only need to draw one stave section to get the measurements.
I could be wrong but your next prob will be that your 12º angles won't be precise enough to complete the tube perfectly. 14 staves will fit perfectly but the last one will too big, too small, or show a bit of a gap at the joint.
Best of luck!

PS I'm a fan of simple graphical processes - often accurate enoug, quicker and easier than digging out a calculator, revising your trigonometry, or worst of all - using Sketchup - a sledgehammer to crack a nut!

 

[Brandlin]

I could be wrong but your next prob will be that your 12º angles won't be precise enough to complete the tube perfectly. 14 staves will fit perfectly but the last one will too big, too small, or show a bit of a gap at the joint.

Its usually easier to make an even number of staves. That way you can assemble as normal with band clamps or such like, but omit glue on two joins opposite each other. When the glue is dry you can fettle the last joint with sandpaper taped down to a flat surface.
Yes it means you have two joints that are ever so slightly different to the others, but unless you are doing something highly accurate/decorative you really cant tell.

 

[Brentingby]

Simple, graphical, accurate solution in seconds with sledgehammer.

 

[Jacob]

'Sledgehammer' in the sense of £500 or more worth of electronic device, steep learning curve, not necessarily available in your workshop, etc etc.
As compared to £3 worth of simple kit and a junior school level of maths.

 

[sunnybob]

well, its a good thing we werent building a space probe.

Using the supplied measurements I ended up with a circle that was half as wide again as I wanted, and it used 16 staves.

Luckily I have enough spare wood to try again tomorrow with a much narrower stave width.

 

[Jacob]

The thing about a drawing on paper is that you can see immediately if it's wrong.
Not so with a calculation, or easily with Sketchup; the SU drawing above shows the wrong angle, should be 24º, and an ellipse - could be confusing?
Keep it simple.
I'd expect paper and pencil to be far quicker than Sketchup, for such a simple calculation.

PS and of course the Sketchup answer above, in spite of being incredibly precise; 17.769639mm :shock: is also hopelessly wrong! :lol:

 

[Brentingby]

the SU drawing above shows the wrong angle, should be 24º

No. It doesn't show the wrong angle and it doesn't show an ellipse.

The polygon has 30 sides as Sunnybob initially said he'd use.