sciencecenter:

Leonardo da Vinci, back from the grave, to explain why trees don’t splinter

The graceful taper of a tree trunk into branches, boughs, and twigs is so familiar that few people notice what Leonardo da Vinci observed: A tree almost always grows so that the total thickness of the branches at a particular height is equal to the thickness of the trunk. Until now, no one has been able to explain why trees obey this rule. But a new study may have the answer.

Leonardo’s rule holds true for almost all species of trees, and graphic artists routinely use it to create realistic computer-generated trees. The rule says that when a tree’s trunk splits into two branches, the total cross section of those secondary branches will equal the cross section of the trunk. If those two branches in turn each split into two branches, the area of the cross sections of the four additional branches together will equal the area of the cross section of the trunk. And so on. […]

Botanists have hypothesized that Leonardo’s observation has something to do with how a tree pumps water from its roots to leaves. The idea being that the tree needs the same total vein diameter from top to bottom to properly irrigate the leaves.

But this didn’t sound right to Christophe Eloy, a visiting physicist at the University of California (UC), San Diego, who is also affiliated with University of Provence in France. Eloy, a specialist in fluid mechanics, agreed that the equation had something to do with a tree’s leaves, not in how they took up water, and the force of the wind caught by the leaves as it blew.

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