I am making a hutch for my wife. She wants the two sections at the ends of the hutch to have arches on them. I am thinking of gluing together one or two inch wide strips of 3/4 inch red oak with the edges cut at an angle to form the arch. Is there a formula for finding the angle that the strips of wood should be cut at? Does the angle change if I alter the width of the wood? The arch will be 180 degrees (a semi-circle) and 12.75 inches wide inside edge to inside edge. If I changed the arch such that it covered only 120 degrees rather than 180 degrees, how would the angle change?
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Replies
I am going to need a sketch of what you propose to do as I am not picturing it. A simple sketch on paper and scanned will do.
With best regards,
Ernie Conover
In thinking about your problem overnight I suspect that you want to curve the ends like a barrel. That is your are going to cooper the ends from 2" wide staves running the height of the hutch. If this is the case I think I can make you a drawing that will help you.
With best regards,
Ernie Conover
You're right, except I decided that 1/2" wide slats would work better. I also eventually figured out from trigonometry that my question has a simple answer. Calculate the number of slats you need by calculating the circumference of the circle (assuming you plan to span the distance with an arch of 180 degrees, a half-circle) and cutting the circumference in half (since it's a half-circle). Then, divide the resulting half-circumference by the width of the slat you plan to use. Then, you divide the number of slats into 180 degrees, and the result will be the degrees of bevel you need. You can then bevel one side of each slat by that number of degrees or both sides of the slat by half the number of degrees. For instance, say you are spanning a distance of 14.25 inches. The circumference of the half circle will be about 22.4 inches (pi times 14.25 divided by 2). Say next that your slats will be 1/2 inch wide. Dividing 22.4 by 0.5 yields about 45 slats. Dividing 180 degrees by 45 slats will give you a cut of 4 degrees per slat, which you can achieve by beveling one side of the slat 4 degrees, or both sides of the slat by 2 degrees. If you choose the former cut of 4 degrees, be sure to glue the beveled side of the slat to the unbeveled side of the next slat; if you don't, you will not get a smooth curve.
I expect coopers figured this out years ago.
You have it right. Yes it is standard coopering. They did most of their trig with dividers.With best regards,
Ernie Conover
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