A little geometry help please?

[mttt]

In a recent David Mark's episode - he makes a circular mirror, 24" in diameter.

starts with 8" wide cherry that's made into a square and sawn into a circle.

My first question is, what's the formula that takes the final diameter (and thickness?) of the circle and tells you how wide your stock must be?

My second question is: wouldn't other polygon shapes reduce the width of wood required? Seems to me a hexagon or octagon would mean thinner wood. Of course, I'd have to find someway to hide the extra joints.

[Simon]

> He starts with 8" wide cherry that's made into a square and sawn into a > circle.

Does this or does this not look just a little bit dangerous?

[Young Carpenter]

Do it all the time so what's the problem.

[Chris Merrill]

[JackD]

> He starts with 8" wide cherry that's made into a square and sawn into a > circle.

Sorry, I don't have a formula available off the top of my head, but you could make a scale drawing quite easily.

As for the number of sides reducing the width, you are correct. In fact with an infinite number of pieces you would have no wasted width. Use whatever you find pleasing. I think I'd rather go with a hexagon or even a septagon over a square.

-Jack

[Robert Bonomi]

for a square, the required width of the stock is "radius of outer circle" - 0.7071 * "radius of inner circle"

the minimum required length is: 1.414 * "radius of inner circle" plus '1 width' (as defined above)

this'll make pieces that go together like:

----| | | |----

if you want:

|---| | | |---|

the long pieces are 1.414 * "radius of outer circle", and the short ones are 1.414 * "radius of inner circle"

For hexagon, thickness is: "radius of outer circle" - 0.8660 * "radius of inner circle"

length is: "radius of inner circle" + "1 width" (per above)

[the_tool_man]

Hi:

For a wooden ring with outside radius of R and inside radius of r divided into N segments, each segment can be cut from a piece of wood that is x long and y wide, where:

x = 2*R*sin(180/N) y = R-r*cos(180/N)

Of course, this is strictly theoretical, and doesn't account for waste.

Regards, John.

[mark s.]

yes, other polygons will be a better fit to the circle, the more sides the closed the fit BUT every joint becomes a problem in getting a tight joint. I believe an octogon is the better shape for cutting a circle.

for working out the width of timber required you can use the formula to create a circle (x2+ y2 = r ) BUT i find it easier to draw it out full size (i keep a piece of the plain white masonite board used for walls in wet areas as a drawing board.)

[alexy]

Width = OutsideRadius - InsideRadius/sqrt(2).

Yes, and klogon is better and megagon better yet.

Yeah; there also comes a point where saw kerfs outweigh the gain due to narrower stock (but not at your more pragmatic hexagon or octogon suggestion).

[DJ Delorie]

I've got just the form:

in inner/outer radii and number of segments, and it tells you how wide and long each segment needs to be.

[mttt]

pick to describe marriage. But at times, it's probably a good fit.

[Simon]

I guess I am used to European laws about guards, in a professional shop it's considered illegal to not have the guard in place. I'm also a little bit prejudiced and wary, because 2 friends, in the last year, were doing the same thing and had their hands thrown in to tablesaw blades when the wood kicked on them, these days I will always use the mitre gauge with a clamp rather than holding it by hand. I like my hands too much.

[Andy Dingley]

You want to make it to "Old Carpenter" or "Stumpy" ?

I'm a hooligan - but that cut scares the crap out of me.

-- Die Gotterspammerung - Junkmail of the Gods