Hydraulic Architecture of Woody Shoots

Abstract

As a painter and naturalist, Leonardo da Vinci was a keen observer of nature. He made the following entry in his notebook about the construction of trees:

“All the branches of a tree at every stage of its height when put together are equal in thickness to the trunk (below them). All the branches of a water [course] at every stage of its course, if they are of equal rapidity, are equal to the body of the main stream. Every year when the bows of a plant (or tree) have made an end of maturing their growth, they will have made, when put together, a thickness equal to that of the main stem; and at every stage of its ramification you will find the thickness of the said main stem; as i k, g h, e f, c d, a b, will always be equal to each other; unless the tree is pollard — if so the rule does not hold good.” (Fig. 5.1; Leonardo’s notes 394, 395, Richter 1970).

Although this is no evidence that Leonardo ever did any measurements to confirm this remarkable observation, botanists are well aware of the approximate correctness of this statement; measurements were made around 1900 to investigate the significance of stem dimensions in satisfying both mechanical and hydraulic demands (Metzger 1894, 1895; Jaccard 1913, 1919; Rübel 1919). This concept of even conductance throughout a tree has been called the “pipe model” by Japanese workers (Shinozaki et al. 1964), because a tree can be imagined as consisting of many thin, tall plants, bundled together. It must be emphasized, however, that these ‘rules’ provide only ‘order of magnitude’ approximations of the real situation.