Leonardo Was Wise: Trees Conserve Cross-sectional Area Despite Vessel Structure
Abstract -- Beginning with Leonardo da Vinci's assertion that trees conserve total cross-sectional area across every branching point, I tested ten species of trees in the vicinity of Princeton, New Jersey, to see if they do indeed adhere to the rule of conservation as asserted by the Italian master and those who followed him. Based on my review of the literature, I expected to find that trees would either conserve area or not depending on the porosity of their wood to water. To my surprise, I found that all ten species conserve cross-sectional area in approximately the same way despite large differences in porosity. In particular, their twigs roughly doubled in cross-sectional area across each branching while their larger branches approximated area-preservation, as Leonardo had predicted. Rather than precisely preserving area, the trees actually tended to increase in area ever so slightly as I moved from trunk to twig tips. For this reason, I describe a conical model of tree form originated by Horn (1998, in press), which may estimate the volume of a tree more accurately than the traditional cylindrical model.
Journal of Young Investigators