In a recent David Mark's episode - he makes a circular mirror, 24" in
He starts with 8" wide cherry that's made into a square and sawn into a
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.
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.
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.
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"
"radius of outer circle" - 0.8660 * "radius of inner circle"
"radius of inner circle" + "1 width" (per above)
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
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
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.)
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