Are squares the best shape to use for a karo step? What about triangles?
To answer this question, let's begin by identifying the performance aspects we design for.
Loft is probably the most important. This is a function of cell size: the larger the cell, the bigger (thicker) the bubble it will form when stuffed with down and hence the greater the loft. But what exactly do we mean by 'cell size'? At first glance we might say it's area. But consider the 'cell' of a continuous baffle. In that case loft is determined by width, the distance between the seams, rather than the total area. So I propose that the relevant dimension when considering loft is minimum cell radius; the shortest straight line that can be drawn from the geometric center of the cell to any point on one of its sides.
The next aspect is down mobility. One factor of this is again cell size, and again, I propose this is really minimum diameter. If a down bubble is too big, the down is too free to slosh around resulting in uneven distribution. Another factor is the mouth length of the cell. Shorter mouths (smaller holes in the corners of the cells) reduce down mobility.
So I propose that by holding minimum cell radius and mouth size constant, we can compare various cell geometries.
Here are the relevant values for the popular 12/6 square.
Side length = 12
Seam length = 6
Area = 144
Total seam length = 24
Total seam length / area = .166
Total mouth length = 16.97
Total mouth length / area = .118
Seam count / area = .0139
Here are the relevant values for two equilateral triangles with the same minimum radius as the square (6). Both of them have a seam count / area ratio 42% lower than the square. That's a definite win in assembly effort. They also both have a higher minimum radius on the 'interstitial cell' defined by the mouth lines. This means the cold(-ish) spots where cell corners meet will be warmer.
This design comes very close to having the same total mouth length / area ratio as the square.
Side length = 20.78
Seam length = 6.93
Area = 187
Total seam length = 20.79
Total seam length / area = .111
Total mouth length = 20.79
Total mouth length / area = .111
Seam count / area = .0080
This has 33% less seam length / area. That bodes well for warmth in a sewn-thru design, and saves weight in a baffled design. However, when drawn on paper it looks way too open for good down stabilization. In practical terms, the weight savings on a 1.5" finished baffle made from .7 oz / sq.yd. bug net is about 3 grams. The warmth improvement for sewn-through designs is probably a little more substantial than that, but still probably not huge and difficult to quantify.
This design has the same mouth size as the square and some friendlier dimensions to work with (no crazy decimal values).
Side length = 21
Seam length = 12.5
Area = 191
Total seam length = 37.5
Total seam length / area = .196
Total mouth length = 12.75
Total mouth length / area = .067
Seam count / area = .0080
This has an 18% higher seam length / area ratio than the square, but the drawing looks like it will have down mobility much closer to the square.
Clearly some experimentation is in order to calibrate design dimensions against down mobility, and in sewn-through designs, warmth impact. However, the greatly reduced seam count is a clear win.
Below are sketches of the square design and both triangular, or 'delta' designs. Sure enough, the delta pattern has 29 seams to the square's 49 – 41% less.
Curious to hear your thoughts and critiques.
(Note – I have yet to make a quilt or bag.)
12/6 square karo step:

21/7 delta karo step:

21/12.5 delta karo step:


