Origin of Unusually High Rigidity in Selected Helical Coil Structures

Using continuum elasticity theory, we describe the elastic behavior of helical coils with an asymmetric double-helix structure and identify conditions under which they become very rigid. Theoretical insight gained for macrostructures including a stretched telephone cord and an unsupported helical staircase is universal and of interest for the elastic behavior of helical structures on the micrometer and nanometer scale.

Figure 1

(a) Photograph of a coiled telephone cord with the same topology as an unsupported spiral staircase. (b) Retouched photograph of the unsupported spiral staircase at the Loretto Chapel as constructed. (c) Trace of the helical inner or outer stringers of the staircase on the surface of a cylinder, which can be unwrapped into a rectangle.

Figure 2

Retouched photographs, with the background digitally removed, of the spiral staircase in the Loretto Chapel, Santa Fe, New Mexico. (a) Current view of the staircase including the railing, which had been added long after construction. (b) Likely view of the staircase as constructed, with no railing.