another geometry question

[Jacob]

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

Also wrong.
35.6 would be the length of the arc of the circle of the outside face, if the staves are to be shaped to the circle, but the width of the staves would be the chord.
So calculation and SketchUp both get it wrong!
Stick with paper and pencil.

 

[Jacob]

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.

It's an ellipse on my screen.

 

[Brentingby]

Maybe you need to adjust your screen. It looks like a 30-sided polygon to me.

 

[MikeG.]

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.

Well you got something wrong then. Looks to me like your cutter isn't 12 degrees.

 

[Jacob]

Same tiny error on each face is multiplied x30 by the time you've put it together.

So you need either
mega precision beyond normal workshop capabilities
or
the usual joinery wheezes and wangles to make thing fit.

Full size drawing comes in handy here - for starters you can stand the staves on it and see if they fit the drawing, and if not why not.

 

[galleywood]

I think MikeG's post has set things right.
Sunnybob's originally said 30 staves and 12 degrees, then changed it to 15 staves.
Brentingby's original screenshot was an ellipse which has since been edited - it was based on 30 staves and 12 degrees and the 170 diameter was applied over the corners of the segmented as opposed to over the flats (as per MikeG).

 

[MikeG.]

.......Full size drawing comes in handy here - for starters you can stand the staves on it and see if they fit the drawing, and if not why not.

I'll happily supply my drawing as a PDF printable at full size so that the OP can do just that. I'll need his email address.

Alternatively, if supplied with micrometer measurements of the actual cutter angle I can work out an alternative arrangement.

Frankly, I'd have more fun sorting this out with a plane, but as I'm stuck here drawing anyway, that's not an option.

 

[sunnybob]

Wow, dont egg heads enjoy a good discussion!

The story so far... I thought I needed 30 staves because i have a 12 degree cutter (360 divided by 12 = 30)
(hey! after using computers since the commodore amiga, I've just found out there isnt a division sign on the keyboard!!!!) WTF?

Anyway, I digress.
30 staves.
Then I'm told only 15 because there are two x 12 degree angles on each stave. being thick in this department, I agree.

I had built in extra wood on my design so I was not too upset to find i have cut my staves at 31 mm, not 36.

Putting these together I come up with a circle that will NOT complete with 15, and is way over the original size required.

Now then (he says, as an old penny rolls creakily down the rusty slot.... )
what if that cutter is 12.5 degrees? I have nothing accurate enough to measure that. Would the half degree cause the chaos?

 

[MatthewRedStars]

You don't have to get it perfect!

If you get it close enough you can make two semi-circles, then shoot the joining edges of each semi-circle on the table saw so they are in plane.

Glue your two perfectish semi circles together with a strap to get a perfect circle.

 

[Jacob]

Yes thats it, but you have to go through all the options first! :lol:
Though i wouldn't quite do that - more likely to offer the two halves up and see how they fit and where to take off a bit with a hand plane

.... you need either
mega precision beyond normal workshop capabilities
or
the usual joinery wheezes and wangles to make thing fit........

 

[MikeG.]

.......what if that cutter is 12.5 degrees? I have nothing accurate enough to measure that. Would the half degree cause the chaos?

Yep, chaos:

 

[Brandlin]

You don't have to get it perfect!

If you get it close enough you can make two semi-circles, then shoot the joining edges of each semi-circle on the table saw so they are in plane.

Glue your two perfectish semi circles together with a strap to get a perfect circle.

NOT if you have an ODD number of staves!
see my earlier post

 

[Yojevol]

Or , you could do this way:-

Use 16 staves. Set a jig to hold each at 22.5deg. Use a straight cutter. Glue up in pairs, then quadrants, semi- circles then full circle. Trim off by what ever means you have.
By this means you can get the jig pretty accurate and you can true up at each glue stage.
Brian

 

[Yojevol]

Help Please!
How do I get my 48K image to show? I put in a Dropbox link between the 2 [img} s that come up when clicking on Insert Image.
Brian

 

[Jacob]

You don't have to get it perfect!

If you get it close enough you can make two semi-circles, then shoot the joining edges of each semi-circle on the table saw so they are in plane.

Glue your two perfectish semi circles together with a strap to get a perfect circle.

NOT if you have an ODD number of staves!
see my earlier post

3 x 5? Fit 3 five stave pieces together.

 

[CHJ]

Angle and dimensions are easy for any number of segments. Control of the cutting accuracy is another matter, I cut staves as close as possible and check with digital angle gauge on a flat surface, then dry assemble and plane the odd edge to adjust the fit.

 

[sunnybob]

I'll have another go today, but its looking like this will be another days firewood for the old boy that lives at the end of the lane (I save him a fortune in kindling).

 

[Jacob]

You don't have to get it perfect!

If you get it close enough you can make two semi-circles, then shoot the joining edges of each semi-circle on the table saw so they are in plane.

Glue your two perfectish semi circles together with a strap to get a perfect circle.

NOT if you have an ODD number of staves!
see my earlier post

3 sets of 5 staves. Perhaps put each set together in a cradle so you know they are not too far out

 

[dizjasta]

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

Also wrong.
35.6 would be the length of the arc of the circle of the outside face, if the staves are to be shaped to the circle, but the width of the staves would be the chord.
So calculation and SketchUp both get it wrong!
Stick with paper and pencil.

Jacob you are exact in what you have pointed out regarding stave width for 15 staves located by circumscribing circle of 170 mm diameter. The arc length for each stave is 35.6 mm as you mention. The stave width which represents the chord to the arc of 35.6 mm is 35.34 mm. This gives an error of 0.71%. Perhaps calculation is not all bad.

 

[Brandlin]

You don't have to get it perfect!

If you get it close enough you can make two semi-circles, then shoot the joining edges of each semi-circle on the table saw so they are in plane.

Glue your two perfectish semi circles together with a strap to get a perfect circle.

NOT if you have an ODD number of staves!
see my earlier post

3 x 5? Fit 3 five stave pieces together.

The point of glueing up in two semi circles is that the final 2 glue joints are on opposite sides and are co-planar. this means that fettling can be done simpy by putting sand paper down on a flat surface and sanding until the whole surface of both glue edges have been touched. Its far simpler than planing or sanding each edge individually.

However to get 2 semi cricles you need an even number of staves - half in each semecircle. If you glue up three lots of five staves you will have to adjust SIX edges by eye without any reference plane.