How do I determine these angles?

[Wade Lippman]

My wife volunteered me to make 4 small chests for a friend.
334499

The side piece is 7.5" across, and the offset is 0.84". I found an online calculator that says the radius is 8.75". That seems about right.

The pieces that form the top have to be cut at a bevel, but what angle? Is there anyway to calculate it? The one I am copying doesn't have any two pieces the same, but I hoping to do better.

Of course, if anyone has plans for a small chest (8" deep, 12" long, 8.5" high) they could share, I could build that instead of trying to duplicate this one. I think the friend will be fine with anything similar.

[Rick Whitehead]

The angles would depend on the size of the piece and the number of pieces that make up the top.
One way to figure out the angles would be to draw the side view in CAD and then divide the arc of the top radially. Or, you could cut an approximate angle and fit each piece to the previous one,which is what it looks like that the original maker did.
If you don't have CAD, send me the dimensions and I'll do it for you.
Rick

[Matt Day]

I agree with Rick. I'd put it in Sketchup and determine the angles.

Very nice of him to offer his help.

[lowell holmes]

How about lofting the piece full size on a piece of plywood?

When I make a chair, a full size loft is made and angles measured from it.

[Bradley Gray]

I would avoid math entirely - set the sample on a piece of drawing paper and draw around it, plot the center of the curve, use a sliding bevel to pick up the angles.

Sorry, Lowell i wrote this before I saw your post - this is a +1

[Robert Hazelwood]

I happen to have CAD open in front of me and I love geometry problems so...

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Assuming a width of 7.5" and a sagitta of 0.84, the arc of the top of the chest subtends an angle of 50.5033 degrees with a radius of 8.7905". Assuming the chest tops are made of seven equal-width planks, each plank will subtend an arc of 7.2146 degrees. That is the angle from one edge to the other - you would set your saw blade to half that angle (3.4090).

I would still recommend lofting the piece, but these numbers can serve as a cross reference. Good luck.

[Wade Lippman]

I happen to have CAD open in front of me and I love geometry problems so...

334502

Assuming a width of 7.5" and a sagitta of 0.84, the arc of the top of the chest subtends an angle of 50.5033 degrees with a radius of 8.7905". Assuming the chest tops are made of seven equal-width planks, each plank will subtend an arc of 7.2146 degrees. That is the angle from one edge to the other - you would set your saw blade to half that angle (3.4090).

I would still recommend lofting the piece, but these numbers can serve as a cross reference. Good luck.


That looks good to me. Thank you so much.
40 years ago I actually passed a course in partial differential equations; now I find these angles bewildering.
I also worked for several years as a computer programmer, but now can't handle sketchup.

I already made up this drawing, so I might as well post it.334505

[lowell holmes]

I would avoid math entirely - set the sample on a piece of drawing paper and draw around it, plot the center of the curve, use a sliding bevel to pick up the angles.

Sorry, Lowell i wrote this before I saw your post - this is a +1
It doesn't make any difference whether you draw it on paper or plywood, you and I were on the same approach.

I took some rocking chair classes from Paul Sellers a long time ago. We always had a full size lofted drawing on plywood. By the time you lay it out on paper or plywood, you've built it in your head. After that, the actual making is much easier because you'v probably have thought about the details.

[Wade Lippman]

I finally got around to cutting these slats. I tried 3.5* and it was a bit thin. 4.0* fit nicely.

[Tom Ewell]

Bead and cove canoe/coopered barrel bits