EXAMPLE 7 How Tall Can a Tree Be?

Galileo suggested that no tree could grow taller than 300 ft. The world’s tallest trees are giant sequoias (Figure 18.8), which grow only on the West Coast of the United States and hence were unknown to Galileo. The tallest known sequoia today is 380 ft in Redwood National Park in Northern California. (To protect it, the National Park Service does not disclose its exact location.)

What limits the height of a tree? If the roots do not adequately anchor it, a tall tree can blow over. (This happened in 1990 to the world’s then-tallest tree, the Dyerville Giant in Humboldt Redwoods State Park in California.) The tree could buckle or snap under its own weight and the force of a strong wind. The wood at the bottom can be crushed if there is too much weight pressing upon it. Finally, there is a limit to how far the tree can lift water and minerals from the roots to the leaves.

Could a tree be a mile high? To make a rough estimate of the pressure at the base of the tree due to gravity, let’s model the tree as a perfectly vertical cylinder. Over each square foot at the bottom, there are of cells of wood, which weighs about half as much as water. A convenient scientific fact to know involving the metric system is that water weighs just about 1 gram (g) per cubic centimeter. So, to calculate the weight, we first translate into metric measurement:

So, of water weighs about

Consequently, of water weighs about . The weight of the same volume of wood is about half as much, or about 165,000 lb. Therefore, the pressure at the bottom of the tree would be about .

This is an overestimate because we assumed that the tree does not taper. A tree that tapers steadily looks like an elongated cone; using a more realistic cone model (as we did in the last section for a mountain), you would find that the pressure at the bottom of the tree would be one-third of , or about . A biological organism needs a safety factor of at least 2 to 4 times the absolute minimum physical limits, so a mile-high tree would need from 110,000 to of upward pressure for water and minerals. Tension in the string of water molecules from root to leaf ranges from 80,000 to 3.2 million , for different kinds and heights of trees, so this consideration does not rule out mile-high trees.

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At more than about , though, the bottom of the tree would begin to crush under this weight. On this basis, a mile-high tree is barely feasible, with little margin of safety. However, researchers who hauled themselves up to the top of the tallest trees in 2004 found a much lower limit, at least for giant sequoias. With increasing height, leaves are smaller, dryer, and less efficient at photosynthesis. The researchers estimated that trees can’t top out higher than 400 to 427 ft. The tallest reliably measured tree was a North American Douglas fir, measured in 1902 at 413 ft.

There are other considerations. The taller the tree, the greater the area from which it must draw water and minerals, for which nearby trees also compete. Moreover, for a tree to grow very tall, it would have to live for a very long time. Evolution and time may select against extremely tall trees, or maybe, for no reason at all, they have just never evolved.