Herringbone pleating

Herringbone pleating - first order

Unlike the more common parallel pleating the first order herringbone pattern offers resistance to bending in all directions - and might therefore find applications in the construction of corrugated materials.

Herringbone pleating - second order

Here's a herringbone pleating pattern that uses more vertices to more closely approximate the curves in the curved pattern shown above.

These patterns can be viewed as linear approximations of the basic pleating pattern with curved folds:

Curved pleats - the basis of herringbone pleating

Other similar patterns can be created by approximating the above curve by straight lines in various different ways.

Herringbone pleating appears to be understudied - though there has been some related work on "herringbone buckling patterns".

Applications

There is a folding technique known as the Miura-Ori map which employs the pattern.

Miura-Ori map folding

The pattern has been used to deploy solar panels in space.

Implementing herringbone pleating

However there may sometimes be a case to be made for it on aesthetic grounds.

For example, if one were constructing the roof of a swimming pool or an aquarium, then a "wavy" pattern on roof may be desirable.

Ridge cables can typically be made to adopt a zig-zag pattern by using a supporting structural framework that has that pattern.

However valley cables cannot be so easily manipulated.

If the underlying curved pattern is not too pronounced, it may still be possible to use roughly straight valley cables - with the membrane pushing the cables into a slightly curved path.

If that is not possible, implementors are faced with a rather unpleasant choice between replacing valley cables with pull-down cables, having the cables penetrate the fabric, or covering the "outside" of the structure with a framework to support the cables.

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