Growth Patterns of Plants That Maximize Vertical Growth and Minimize Internal Stresses

The geometry of plant axis flexure is analyzed as the result of orthotropic growth and the stresses caused by a vertical weight distribution along the axis. Distal responses to light and gravity and proximal sagging flexure result in a curvilinear axial geometry. The stresses associated with this geometry are analyzed by means of the flexure theory for curved beams. A flexed plant axis is shown to conform to some portion of a logarithmic spiral, r = r0ekθ, of which a special case is circular flexure, k 0. Calculations of the maximum bending moment, Mmax and the maximum tensile stress, max, acting parallel to the axis indicate that the optimal mode of flexure (one that minimizes Mmax and max) is some arc of a circle. Examination of 11 plant taxa indicates that this mode of curvature is statistically the most prevalent condition in plants lacking or having limited secondary growth. Indeterminate apical growth of orthotropic axes is shown to result in a type of failure where portions of vertical axes are reapportioned into a horizontal or supported position.