Biomechanics of Trees
Let me show you actually what biomechanics can do. Here are five different kinds of plant tissues and here are their stiffness and density. You recall we talked about stiffness and density. You want stiff material but you don't want heavy material. You can quantify this relationship by dividing stiffness by density. So, we take this stiffness, we divide by this density, and look, we see that tissue called parenchyma is not very stiff compared to its density. This tissue called wood is extraordinarily stiff compared to its density. So if you're building a big structure that has to support its own weight, and that has to be strong as well, you see that wood is by far much better than this kind of tissue called parenchyma.
By the way, you all know what parenchyma is. Every time you've cooked a potato, you've cooked parenchyma. The basic building block, the filler material of most vascular plants is called parenchyma. You also know what collenchyma is. Every time you've eaten a stalk of celery, you've gotten those strands caught in your teeth. There's a little bit of primary xylem in each of those strands but, most of the stretchy stuff is collenchyma. It's a very visco-elastic fibrous material. You can almost use it like a rubber band until it dries out.
The bottom line is that you remember that
equation. It's the last equation I want to show you. It tells me that if I know the stiffness and I know the density of these different tissues, and if I know the diameter of a stem, then I can tell you how high the stem can get before it will fall over under its own weight. This equation is very important for building ship masts and skyscrapers by the way. But, it's also extremely important for building trees.
All we need to do is to take a stem diameter and plug in these values for different tissues. Here are the same data I showed you before, but now you see a jagged line. That jagged line shows how tall stems can get, given each of these particular ranges in stem diameter, if you built these stems up mostly or exclusively of parenchyma or collenchyma or tracheids or sclerenclyma or wood. Now the curious thing is you now see that these are the limits to plant height. You can't get any taller stems. Everything I've plotted falls basically to the one side of this jagged line except for that pesky data right there.
That by the way, is a palm tree. I found out why that palm tree is falling on the wrong side. It did not violate the rules of physics. The people that reported the data for that palm tree reported the length of the palm tree not the height. It's longer than it's high. It simply began to buckle under its own weight. Trees can be very large things. There's a tree, there is a human being. Notice how small we look in comparison. Let's take a look at the marvel of wood. The curious thing about wood is that it actually changes its mechanical properties as it's weighted down by the growth of a tree.
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