Biomechanical Advantages and Disadvantages of Elliptic Plant Stems and Petioles Relative to Cylindrical Ones
Gábor Horváth, Géza Kolovratnik, Loránd HorváthABSTRACT
Although plant stems are mostly cylindrical, the cross‐sections of the stems of some plant species are oval or lens‐shaped, closely approximating an ellipse. The aim of this work is to determine under which geometric parameter configurations an elliptic stem cross‐section is more resistant to mechanical strains than a circular one. Our study is based on the premise that the greater the second inertia moment I of the stem cross‐section, the more resistant the stem is to mechanical strains exerted by wind and gravity. Therefore, we calculate and compare I circle and I ellipse of plant stems with circular and elliptic cross‐sections of equal surface areas. Beyond plant stems with elliptic and circular cross‐sections, our results are generally applicable to other types of natural and artificial elliptic and circular tubular structures, such as petioles, hairs, quill shafts of bird feathers, bones, swords, daggers, and blades, as well as technical rods and tubes used in engineering practice. On the basis of the results, we analyze how the vertical and horizontal angular deflections of the oscillation of wind‐blown leaves depend on the degree and direction of petiole flattening. Finally, we discuss the relationship between the loudness of rustling sound of wind‐blown foliage and the length and flattening direction of fluttering leaves.
Key Point
Biological aspect: Plant stems and petioles with elliptic and circular cross‐sections. Physical aspect: Mechanics. Second moment of inertia of tubular structuress.