Crease surfaces in leaves Pt1

In this post we’ll look at three different leaves and the strategies they have developed to build large stiff(ish) cantilever surfaces for the purpose of solar energy capture.

A nettle leaf. The leaf is ‘flat’ at large scale, but the areas between veins are larger in area than the pure plan, causing doming between the relatively stiff veins. It’s a very common pattern in soft leaves that rely on cell pressure for structural support. Linden and Horse Chestnut tree leaves are other good examples. In architecture, an example using this exact technique is the PTFE cushions of the Eden Project or Heathrow Bus Station.

A thistle. The leaf in the bottom half of the picture makes the sequential up/down warping of the spikes very clear. Holly leaves follow the same pattern. If you brush against it, contact with one line of spikes causes the leaf to rotate and press the next line of spikes into you.
The geometry ‘engine’ seems to be the circumference of the leaf grows faster then the interior, and the veins of the leaf are stiff enough in compression, to force this alternating buckling into a stable saddle shape. The continued circumference growth has folded over the edge of the spikes, giving it further structural rigidity as a perimeter rolled seam develops.

In architectural terms, if you define the perimeter spikes, the rest of the leaf is the minimum surface created between them. If you have have the simplest shape possible, you get the classic saddle roof, seen here at the entrance to Warszawa Ochota railway station. If you have a series of spikes, like the thistle, the minimal surface gets more complicated and can’t be directly constructed from straight lines. It might look a little like the first pier connection on Muscemi Bridge.

Sections through a South African Crocosmia leaf. Crocosmia produces long blade shaped leaves that cantilever up and out 300-600mm from the plant. That is a span to depth ratio of ~60-120, when a bridge truss is normally lucky to exceed 20. This performance is helped by materials being effectively stiffer at small scales, and the fact that bridge trusses tear themselves apart less often.

The origami style pleating is complemented by local stiffening at the creases. The leaf is thicker there to fit veins carrying sap for the leaf. In structural terms, these are big service tubes (pale blue in the cartoon) going down into the leaf along those pleats, and then additional tubules running transversely around them (pale green), smoothing the sharp inner corners. As the leaf dries these transverse tubes empty and shrink, pulling the leaf into a narrower form to reduce solar exposure.