Axial forces and normal distributed loads in twining stems of morning glory

Abstract

In analysing the mechanics of twining, we hypothesize that contact forces are important in maintaining the twining habit of viny stems. This hypothesis is formalized with a description of the force balance in the natural coordinate system associated with the Frenet vectors attached to the 'generative helix' of the vine. The force balance indicates that, if shear forces are neglected, an axial force within the stem is balanced by a normal load distributed along the line of contact between the supporting pole and the stem. Two kinds of empirical studies were conducted to verify the importance of the putative normal load. Firstly, vine geometry was measured on and off the supporting pole. When removed from the pole, the helical stem forms a coil of smaller radius, smaller wavelength and larger torsion. Next, forces were estimated from observations of the pressure exerted by a stem twining around a water-filled balloon. Twining around a dowel 0.95 cm in diameter, a typical stem of morning glory (Pharbitis nil) sustains a tension of 100 g balanced by a normal distributed load of -30 g cm-1. Thus the twining stem puts itself into tension and uses a helical geometry to generate contact forces which are large relative to the stem weight of 40 mg cm-1.