I would like to make a round waste basket that is 12" round at the
top and 8" at the bottom. I will be using 2"x1/4" hardwood slats. Is
there some simple formula that I can use to figure out how wide the
bottom part of the slats will be tapered, the angle to cut the edge
and how many slats will be needed?
If you approximate it as a circle, then
Circ = pi* Dia
Using 2" slats, this gives 12*pi/2.85 slats.
So plan on 19 slats.
You could use the circle approximation and be pretty close, but we may
as well get exact.
If you draw a triangle from the centre of a 19-sided polygon to the
centre of an edge and the outer point of an edge, the central angle will
be 360/(2*19) or 9.47 degrees. Remember this for later, as it's also
the bevel you'll need for the sides of the slats.
Trig says that
sin(theta) = opposite/hypotenuse
sin(theta) = s/2r
theta = central angle
s = length of the side
r = distance from outer vertex to centre
plugging in a slat width of 2", we get a max diameter of 12.15" which is
pretty close to what you asked for.
For the bottom, if we start with a desired max diameter of 8", this
gives a slat width of 1.317".
As mentioned above, you'll want to bevel the edges at 9.47 degrees from
Pi times 12 = 37.699. Pi times 8 = 25.133. Divide 37.699 by the actual
width of the slats to find how many slats you'll need. The bottom of
the slat will be 0.666 times the width of the top of the slat. Without
knowing the height of the basket, I can't give you the angle.
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