I'm building a table which will have hollow, octagonal legs. (I'm making a copy of a table at the church. We have three and require another.). They're straight legs -- no taper.
The octagonal legs are four inches across. There must be a formula for determining how wide each of the eight boards must be on its outside face.
Can anyone supply the formula? I'm trying to figure this out by drawing it full-scale on graph paper but it's not going well
If you already have two other tables, why not just measure those?
I think I would find it LOT EASIER to make the legs solid than gluing up 8 staves to make them hollow.
You don't mention how much taper, but that could be taken care of after glue-up on the jointer. After coming out of the clamps, I'd square up the blank, then cut off the corners at 45º on the TS. Then I'd set a stop block on the infeed table to set the bottom / small end against, so the top starts out just on the edge of the outfeed bed of the jointer. If you set the depth at 1/8", then you would get 1/4" of taper once you've run down all sides.
All you really need is some basic principals of geometry and one number, the square root of 2, which is approximately 1.4142135623730950488…
For woodworking, 4 significant figures (1.414) is more than sufficient, especially for surface shaping and decoration. I usually just use the ratios 5:7:5 (the C:B:C dimensions in Dick's link) when I lay out a spar gauge for shaping octagonal furniture legs or spars.