Twining Plants: How Thick Should their Supports Be?

When twining plants grow they revolve around a support on which they exert a force in order to achieve vertical growth. In 1865 Charles Darwin realized that twining plants cannot grow on supports that are too wide. Here, mechanical aspects of this problem are investigated by modeling the stem close to the apex as a growing planar elastic rod with intrinsic curvature. The shape and forces as a function of the pole size are obtained and a critical radius limiting growth is identified.