Flattening Cones

Update:  I just updated this frustum calculator with javascript versions that will run from the browser.  One will calculate the flattened frustum from the radii, the other uses the circumferences of the frustum shape.

Have you ever wanted to lay out the frustum of a cone on a flat surface?”
“A what?”
“A frustum, the part of a cone that is left when you lop off the top.”
Oh, yeah. If I had a nickel… sadly, I’m still poor.

It can be a little intimidating if you’re not familiar with the concept of how to go about it. Our draper came to me wondering how she could accurately lay out a dress based on an actor’s measurements. (Apparently the traditional layout method wastes fabric.) So I came up with this simple excel sheet that does the calculations based on the following measurements: waist (small circumference), hem (large circumference) & inseam (height of the frustum.) It gives back the details needed to lay the cone frustum out on a flat surface. The diagram below gives the general gist of what’s what. There is a larger version of the image in the excel document.

Frustum.xls
From fabric to sheet goods, I hope this calculator finds some use.

frustum-model
Update: There is a great description of how to flatten a frustum in AutoCAD over at Woodweb.