Thank you for your suggestion. I used autocad to present the concept and
because I used it in the brute force method. Having the most recent openscad
code available means that the slice or segment to be rotated is entirely
openscad and eliminates the outside program. The other advantage is that
openscad is easier to use in parametric situations such as this one.
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nophead wrote
The center needs to be at the same height as your top point, i.e.
75mm, and equidistant from your top point and your bottom point.
The fact I haven't seen mentioned explicitly here is that the tangent is at
right-angles to the radius. This is a fundamental feature of the circle and
the above requirement flows from it -- you need the tangent to the top of
the arc to be vertical and therefore the radius must be horizontal at that
point.
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The math involved in the construction of the duct is based on the top point
having a tangent which is indeed a vertical line, which then follows that
the radius at that point is horizontal. The radius of the circle is
intersecting with the bottom-most point, creating an isosceles triangle.
As of late, my high school geometry has been failing me, so I brought the
end formula to our local makerspace meeting yesterday. A few of us had fun
with Pythagoras' theorem as we identified each component and simplified it
to match the provided formula.
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