Why does not these 6 sides fit together.

[ornulv]

Hello folks.
Wondered if anyone would have an answer to this mystery.
Earlier I have made 2 skewed, 6 sided boxes, or bowls.
The skewed angle I have used was 6 degrees, and they have fitted perfectly together.
Then I would try 22.5 degrees, still 6 sides, 60 degree angles.

But now there are 2 large gaps, opposite each other inside the box, or rather, the bowl.
Strangely, when one side is removed, and there are 5 left, the fit is almost perfect.
All measurements and angles are double checked, everything is equal.
Is the misfit due to the larger angle of 22.5 in relation to only 6 degrees?
And what is the largest ,skewed angle possible , were the 6 sides will still fit?

 

[RobinBHM]

The compound angles are wrong.

 

[sunnybob]

when you make a taper joint, the angle changes as it gets to the narrower end. You will never get those pieces to fit together seamlessly.

This video explains very carefully what is happening
https://www.youtube.com/watch?v=8CPSj1Qx41w&t=452s

 

[deema]

There is a calculation to determine the angle you have to cut at that enables the pieces to cone together properly. The angle is the same for the entire length and doesn’t change at the narrow end. I came across this online calculator whilst I was looking for the formulae which I can’t remember any more!

http://www.pdxtex.com/canoe/compound.htm

 

[OscarG]

There is a calculation to determine the angle you have to cut at that enables the pieces to cone together properly. The angle is the same for the entire length and doesn’t change at the narrow end. I came across this online calculator whilst I was looking for the formulae which I can’t remember any more!

http://www.pdxtex.com/canoe/compound.htm

Great site! I've bookmarked that.

 

[Rorschach]

If you are having trouble getting the angles perfect, glue up in two halves and then sand the faces flat before joining the two.

 

[Hornbeam]

THere are 2 extremes to a 6 sided object
A flat hexagon made up of 6 equal sided triangles with the cuts all done at 90 degrees
A hexagonal tube where all of the cuts are done at 30 degrees (limit case)
In all cases the plan/projected view of each triangle cut will be and equilateral triangle
Rather than doing more complex maths to work out the angle of the saw blade and the angle of each edge, I would make a jig to go on the table saw where each piece to be cut is securely held with what will be the outermost edge at th height you want it to be in the finished bowl.
You then set the saw blade to cut at 90 degrees and cut one side. Rotate the jig through 60 degrees and cut the other side.
When you remove the piece from the jig, the edges will actually be bevelled and the angles of what will be an isosceles triangle will be correct for the rim height
Ian