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I am trying to a make a miniature groin vault (right angle intersection of two semicircular arches. I’be made matched keystone-shaped slats to line the arch: they run perpendicular to the face of the arch with the bottom of each keystone running flush and tangent to the arc of the arch.
The arch radius is 3.5 inches and uses 13 “keystone-shaped” slats .844 inches wide at the base with sides at 7 degrees form the base. I placed a keystone at the top of the arch then lay the others around in succession to fill it in. Resulting angles from the top keystone to each succeeding keystone face were 14, 28, 42, 56, 70 and 84 degrees.
The miter calculation was straightforward: So miters were
Slat Miter Miter
Face Angle Angle
Angle Calc Used
14 44.3 44.5
28 41.6 41.5
42 36.8 37
56 29.3 29.5
70 19 19
84 6 6
Miter anlgle calc = arctan ((cos (slatface angle)*.844)/.844)
But how do I calculate the compound angle?
Replies
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I don't think you do. From my reading of your description, I think nearly all your joints are compound curve mitres, and the requisite curved cuts were/are generally ascertained by developed drawings of the lines of intersection of the relevant shaped parts, preferably full size to see where the mouldings must intersect. (The other way is to just fudge it, and some of it fits where it touches, or not,....as the case may be!)
Check in your copy of Ernest Joyce, The Technique (US Dictionary, I think) of Furniture Making, or George Ellis, Modern Practical Joinery. These guys have pretty well got all these problems licked between them, even though both books are at least 50 years old. In the case of Ellis, nearly 100 years old.
If you were making a simple polyhedran, then I would be able to tell you what the requisite dihedral angle and 'true' angle that the side describes to the baseline are, but I think this does not apply in your construction, as I've understood it. I'd need to see it graphically illustrated to be sure that I've got the picture right though, so I might be wrong here. Sliante.
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