tapered tube curvature

[BillB]

If the intent is to have a set of leather cuffs similar to the gauntlet on a set of gauntlet gloves, and you want to make the edge closest to the elbow a curve, then the line that is drawn on the flat template can be anything some a simple arc to a parabolic to a hyperbolic curve depending on the amount of curve one wants to have one the final project. Some of the old Western Gloves used in shows had an extreme curve on them. In some cases I have simply started with some heavy drawing board, and started making prototypes. A lot easier to cut and a lot cheaper than leather.

[mikeymoto]

I'm pretty sure the page mentioned previously (http://mathcentral.uregina.ca/QQ/database/QQ.02.06/phil1.html) does answer your question.

In your case you know the diameter of the upper and lower "rings" of your "cuff" (or whatever your mysterious project is. You also need to choose the length of your project, which I don't think you mentioned. This is arbitrary and can be whatever you want it to be.

So let's say for the sake of example that you are making a cuff. The smaller hole (the wrist end of the cuff) is 7" in circumference, the larger hole (where the forearm enters the cuff) is 10" in circumference, and the length of the cuff is 8".

What you need to know is where to put the center of your compass to draw the two arcs on your flattened pattern which, when folded, will produce circular openings of sizes 7" and 10". Right? So what you need to determine is the radius of the two entire circles on the pattern, parts of which will be the arcs that when folded make the circular openings.

Doing the math on that web page, you find the from a center point, the diameter of the small circle is 18.699" and the diameter of the large circle is 26.713" and your project patterm uses 21.45 degrees of the circles you just drew.