My quilt

[GrizzlyAdams]

The following method has worked well for me (warning: some math talk follows). For a baffled quilt, you take the loft L as the height of your baffle (and then overstuff), so you have a down area per unit length of L * W, where W is the width of each down chamber. I figured with a differentially cut quilt, you want to have the same area per unit length for insulation. So, I computed the parabola with zero crossings at -W/2 and W/2 that would give me an area under the curve of L * W. Then I took the arc length of that parabola as the chamber width for the outside. Since catenary curves are so popular around here, you could go through the same exercise with a catenary curve. It would be interesting to see how much of a difference it makes.

This approximation has worked well for me, but I split the down volume between baffle and differential cut. On a sewn through quilt, the approximation may not be as good (or it might be better), but it's a starting point. YMMV.

Among all two-dimensional closed curves, the circle maximizes the ratio of area enclosed to length of the enclosing curve. In nature, when shapes take form under uniform force they tend towards such maximal configurations. If you blow up a long ballon, the cross-section tends to a circle for this reason.

So on the sew-through thing I've been thinking circular arcs. Given a base
(diameter) b the cross-sectional area is b*pi . Depending on b (the width of a baffle chamber) b*pi may be too small for the area you need for the amount of down you'll stuff into the chamber. For this then I approximate the chamber cross-section as a rectangle with base b and height h, such that the cross-sectional area b*h + b*pi is equal to what I've computed I need for the baffle chamber. That's for small b of course (narrow chambers). For larger ones I figure the base b is a chord on a circle and work from there. Like you, when I have the shape of the curve of the outside fabric, I compute the arc length.

Well that's theory anyway. I'm heading out to the lab right now....

Grizz