Corrugation options for PUCK weaving

A length = 6, frequency = 1, PUCK weaver made from the wall of an aluminum soda can.

Every PUCK weaver has folds at 90 degrees to its sides that divide the weaver into squares. Optionally, there may be additional corrugations running at 45 degrees to the sides. PUCK weavers can be categorized by an integer, called the frequency, that gives the number of these 45-degree folds per square. (For example, the frequency is 0 when there are no 45-degree folds.)

If the folds can be assumed to be equally spaced and arrayed symmetrically about the parallel diagonal of the square, then the corrugation pattern is fully specified by its frequency.

Even frequencies (e.g., 0 or 2) require chess-colorable triangulations, which can be undesirable for smoothly curved surfaces because the smallest allowable deviations from a flat surface (6 triangles around a vertex) are 4 or 8 triangles around a vertex. With odd corrugation frequencies, 5 or 7 triangles around a vertex are also permissible.

Commercial corrugated steel sheets use a corrugation wavelength of 1.25" with 26-28-29 gauge steel and a wavelength of 2.5" with 18-20-22-24-26 gauge steel. Deeper corrugations are made in a wavelength of 2.67" with 18-20-22-24 gauge steel.

Steel sheet of these gauges are

#18 .048"
#20 .036"
#22 .030"
#24 .024"
#26 .018"
#28 .015"
#29 .014"

lambda/t ranges for different steel corrugation wavelengths

lambda   lambda/t    geometric mean
1.25"      69 to 89         78
2.50"      52 to 139       85
2.67"      56 to 111       79

Aluminum soda cans have about 100 micron (.004") thick walls. At lambda/t = 80, corrugation wavelength is 8mm = 0.315"

PUCK weavers with 0.6" squares (which can be cut as 6:1 weavers from can-height 3.75" strips) give

f      lambda     lambda/t
0          1.0"         250
1           0.5"        125
3           0.25"        63

At this scale, both f = 1 and f = 3 give acceptable corrugation wavelengths for aluminum can material.