Silk W K, Hubbard M
Department of Land, Air, and Water Resources, University of California, Davis 95616.
J Biomech. 1991;24(7):599-606. doi: 10.1016/0021-9290(91)90292-u.
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.
在分析缠绕机制时，我们假设接触力对于维持藤蔓茎的缠绕习性很重要。这一假设通过描述与附着在藤蔓“生成螺旋线”上的弗雷内向量相关的自然坐标系中的力平衡来形式化。力平衡表明，如果忽略剪切力，茎内的轴向力由沿着支撑柱与茎之间接触线分布的法向载荷平衡。进行了两种实证研究来验证假定法向载荷的重要性。首先，测量了支撑柱上和支撑柱外的藤蔓几何形状。当从柱子上移除时，螺旋状的茎形成半径更小、波长更小且扭转更大的线圈。其次，通过观察缠绕在充满水的气球上的茎所施加的压力来估计力。缠绕在直径为0.95厘米的销子上，牵牛花（裂叶牵牛）的典型茎承受100克的张力，由-30克/厘米的法向分布载荷平衡。因此，缠绕的茎使自身处于张力状态，并利用螺旋几何形状产生相对于40毫克/厘米茎重量而言较大的接触力。
