Look at a hinge on the nearest door. Its halves slide smoothly around each other and around their centering pin. Then look at the ears of a cat or dog as it turns to face some rustle or squeak. Muscles pull on cartilage, twisting each structure around its pivot, and skin stretches to accommodate the motion. These ears are hinges, too, but they’re made from flexible materials that bend instead of solid parts that slide.
That distinction illustrates one great difference between our technology and the technology of the natural world. We prefer stiff materials--metals, ceramics, dry wood, and the like--that keep their shape. Nature, by contrast, commonly reserves stiff materials for special applications--bones, teeth, and so forth--where rigidity is crucial for the devices to work properly. Bones that bend lack standing, so to speak, and soft teeth have no bite to them. But such structures are rare, for nature doles out stiffness with a stingy hand. Her normal criterion is sufficient strength, a different matter altogether from stiffness. Strength means resistance not to bending or to other deformations but to actual breakage, however shape may have changed. In the unstiff, living world, putting pressure on a structure normally changes its shape. Push on an ear and it happily gives. Take your hand away, and it springs back.
It’s rather pointless to ask which criterion is better. The matter is far too subtle for some simple choice that pits human hubris against nature worship. We humans have millennia of accumulated knowledge about how to make things out of stiff materials, and only a really self- deceiving misanthrope would claim that we don’t use such materials well. Nonetheless, when we come to think about problems of mechanical design, we could benefit from taking a nonjudgmental and noncompetitive look at the world of the cat’s ear.
Stiffness, or resistance to deformation, and strength, or resistance to breakage, turn out to have a curious relationship. Things deform before they break, and a structure will often bend quite a bit on the way to snapping. Even if it’s in no danger of actually breaking under a given load, a structure might well need extra support to keep it from bending or buckling. Extra support, of course, means extra material, so it is more expensive to build stiff structures than it is to build merely strong ones. Perhaps a little less obviously, stiff materials tend to break easily--they’re all too apt to be brittle, succumbing with a sudden, catastrophic snap when the pressure’s on.
But as recent biomechanical investigations are showing, there’s more to the use of flexible materials than just circumventing a few cracks on the cheap. For nature, flexibility is a marvelously nuanced, versatile business--no simple softness, but a multidimensional world of opportunities for designing structures that change shape in highly useful ways.
The crash of surf presents a design challenge for many diverse organisms, from sailors to seaweed. Suppose you wanted to build a long, buoyant structure with a large surface area, one that can take a beating from water currents: the hull of a ship, say, or a strand of kelp. People generally opt for the stiff solution; hence metal hulls. However, stiff structures in the swim of things need a lot of bracing, may break suddenly, and are in real trouble if they hit other stiff structures. Marine algae, on the other hand, like the ones that live along the California coast, are in much less danger of splintering. These plants may grow as long as 130 feet, and because their business is photosynthesis, they need to keep wide expanses of surface area exposed to sunlight. But such algae are ordinarily attached to rocks at just one end, and their attachments seem remarkably weak for long structures subjected to the pull of storm-generated waves. Why don’t the waves tear them from the rocks?
It would seem that friction between the plant’s surface and the water it inhabits should drag on the plant, threatening to tear it to bits. But the alga takes advantage of the ocean’s regularity to reduce this drag dramatically. Here’s how: Waves produce flows that reverse direction every few seconds. As soon as an alga gets longer than the distance the local water travels between reversals, the additional length is swept back and forth with the water. Beyond the first segment, the plant literally goes with the flow. Since it’s traveling in the same direction as the water and at the same speed, there’s no friction to worry about. At a flow of three feet per second and a reversal every four seconds, only the first dozen feet of alga pull on the attachment. You can go to great lengths to avoid drag, but you’ll succeed only if, like the alga, you’re as flexible as a rope, so one part can extend in a different direction from another.
Flexibility isn’t an automatic advantage for structures being tugged about. For example, the flags and pennants we commonly fly on top of long poles have a distressing tendency to tatter in strong winds. Flags are notoriously draggy--their motion generates vortices that pull on them. A flag, for the same area, has around ten times as much drag as a rigid weather vane. Winds don’t help out by reversing direction like wave- generated currents. Nevertheless, nature flies flags on long poles; hers are called leaves. In high winds the drag they exert on trunks and roots can be so severe that storms may blow trees down.
Why, then, do trees stay up at all? While leaves may be flexible, they tend to experience something closer to the low drag of a rigid weather vane than to the high drag of Old Glory. They accomplish this feat by arranging their shape and flexibility with care. For instance, when the wind pulls on a maple leaf, it catches the lobes on either side of the leaf’s stem end. Those lobes bend upward, and the leaf blade curls into a witch’s hat, with the stem as its point. Because the leaf has exactly the right amount of flexibility in the right places, the cone rolls ever tighter as the wind increases. Even in highly turbulent and fluctuating winds, these cones are stable and the wind slides smoothly over them.
Leaves play communal as well as individual tricks. In a wind, adjacent leaves on a branch commonly cluster, forming large cones that diverge outward from the branch. Such a cluster usually has even less drag relative to its area than an individual leaf. Here the flexibility of each stem is as critical as that of the blade it holds--for the leaves to form a cooperatively working group, the stems have to twist readily. That requirement, though, presents a queer problem in design: after all, the primary function of a leaf is to absorb sunlight, and so the chief job of the stem is to hold the blade of the leaf outward, toward the sun--a task that demands that the stem resist bending. Thus the stem must be resistant to bending loads yet compliant to twisting loads.
In large part, stems depend on their geometry to make them twist more easily than they bend. You can see how they do it with a simple home demonstration. Take a cardboard tube or a plastic soda straw and try first to bend and then to twist it; then make a lengthwise slit in the cylinder and try again. The slit certainly makes it weaker, but the cylinder’s resistance to twisting is reduced far more than its resistance to bending. In fact, any lengthwise groove or line of weakness or even any deviation from a round cross section will have the same effect.
Many leaf stems have a lengthwise groove along the top. This alteration of the basic cylindrical shape (together with internal, material specialization) gives the stem an ease of twisting relative to bending between two and six times that of grooveless cylinders made from plastic or metal.
A look at one of the long feathers from a bird’s wing shows the same scheme at work. On one side, a lengthwise groove runs the length of the feather’s shaft. Here again, ease of twisting is important to proper functioning. Wings propel a bird in much the same way that a propeller moves an airplane--the main difference is that they beat up and down rather than spinning around and around. A propeller blade has to be twisted lengthwise in order to give a decent push to the air passing across it. If it were to spin in the other direction, the lengthwise twist of the blade would have to be reversed. But the feathers of a beating wing have to manage that change in direction and reversal of twist twice per stroke. At the same time, the feathers must resist bending--after all, wings are what lift a bird, so in flight its body truly hangs from its wings. Again, here’s a structure that must twist but not bend.
There’s an important difference, though, between leaf stem and wing feather--on the feather the groove is on the bottom, not the top. That, too, makes some sense, as you can demonstrate with your cardboard tube or soda straw. In bending, one side is stretched while the other is compressed, and the slit makes the least trouble for bending if it’s on the side that’s stretched. For the leaf stem, that’s the top, since the weight of the blade bends it downward. For the feather, it’s the bottom that’s stretched--its own lift makes the feather bend upward.
Like birds, flying insects twist their way aloft, as Roland Ennos of the University of Manchester in England has shown. An insect’s wing (which is too flat to have a groove) resembles a propeller blade even more closely than a bird’s does. The whole wing has to reverse its pitch (fore- and-aft inclination), its profile (fore-to-aft curvature), and its lengthwise twist at the top and bottom of every stroke--reversing up to several hundred times each second. It used to be thought that tiny muscles at the base of the wings did the job by adjusting the hinges and pulling on the wing veins. Before Ennos, no one seems to have seriously considered how muscles that cycled at such high rates would be coordinated. Ennos showed that the wings are designed with precisely the right flexibility so that as they beat, they are moved by the wind to the right alterations of pitch, profile, and twist. The muscles only modulate these changes as an insect adjusts its flying speed or engages in maneuvers.
From considering how protruding parts twist and bend, it’s not much of a stretch to see the importance of elasticity inside a body. Your entire circulatory system, for example, depends on the springiness of the heart and blood vessels. Every time your heart beats, its main pumping chamber, the left ventricle, contracts and generates a hearty pressure that forces the blood out into your arteries. Then that ventricle relaxes, allowing blood to flow in from another part of the heart to refill it.
Unlike a gas, a liquid can’t be compressed very much. We rely on this fact to help us measure blood pressure. Imagine a J-shaped tube, open at both ends and filled with mercury, a heavy, dense liquid. If you put your lips to the low end of the J and blow, you can make the mercury rise-- the harder you blow, the higher the liquid will go. We measure blood pressure in millimeters of mercury; one millimeter of mercury is the amount of pressure it takes to lift a column of mercury one millimeter.
When your left ventricle contracts, it pushes out your blood with a pressure of about 120 millimeters of mercury; when it relaxes, it’s not pushing any blood out at all, so the pressure at the ventricle’s exit, at that moment, is zero. Zero? Why then does the doctor measure a range of about 80 to 120 with a blood pressure cuff on your arm? Simply because by the time it reaches the arm, the blood has been traveling a fair distance through the arteries, and our arteries are stretchy enough to damp the pressure fluctuations of the heart. Blood pumped when the heart contracts stretches the arterial walls; when the heart relaxes, the arteries constrict and thus do a little passive pumping on their own. It’s a good thing, too. Blood entering the capillaries, the body’s smallest blood vessels, flows a lot more smoothly, which means the heart doesn’t have to work so hard to keep the blood moving. That’s why atherosclerosis-- stiffening of the arterial walls--means trouble.
Many ordinary pumps (piston pumps like the ones we use to inflate bicycle tires, for instance) are as pulsatile as any heart. We might smooth the flow with elastic pipes leading from such pumps, but in practice we ordinarily choose to use pumps in which several cylinders work together, each one producing its peak pressure at a slightly different time from the others. Same problem, different solution.
Our elastic arterial solution sounds simple until you play with an ordinary elastic. Inflate a cylindrical balloon and one part inevitably expands almost to the bursting point before the remainder does much at all. That’s because when it expands, a bit of balloon wall gets less sharply curved, and a given pressure is more effective in stretching a flatter wall. (The same principle allows the sharply curved walls of the tires of racing bicycles to withstand more pressure than those of large trucks.) So whatever spot on the balloon wall begins to expand first--and some spot inevitably will, since no balloon is perfectly regular--will just keep on expanding. The result of this stretchiness in an ordinary elastic artery would be a local bulge--an aneurysm, even worse trouble than atherosclerosis.
Fortunately, normal arteries expand uniformly. But as the balloon shows, uniformity in expansion isn’t the ordinary thing. To achieve uniformity, a cylinder has to be very flexible when stressed by low pressures but less and less flexible as pressure increases. The materials of the walls of our arteries are elegantly arranged so that it’s easy to start expansion but increasingly difficult to make them expand further. Again, flexibility is a subtle and multidimensional business.
Lest you think our remarkable arteries mark us as special, though, you should take a look at some creatures whose circulatory systems work much as ours do--creatures about as distantly related to us as animals can be. Recently, marine biologists have found almost precisely the same variable flexibility in the arteries of squid and octopuses. The main difference is that their flexibility is tuned to work at their lower blood pressures, just as it also does, they found, in toads and lizards, other low-pressure kin. What’s most startling is that octopuses and squid achieve their variable flexibility with a different elastic protein from the one we vertebrates use. Since genes make proteins, octopus and squid arterial flexibility must have a substantially different genetic basis and must represent an independent evolutionary innovation.
As if to emphasize the point, a third group of animals gets there by a third route. Crabs and lobsters have variably flexible arteries made of yet another protein, once again tuned to work at the appropriate blood pressures. And this tuning of flexibility permits powerful predictions. Given a sample of its arterial wall, one can make a good guess of an animal’s blood pressure. For instance, very large squid that haven’t been maintained in captivity apparently have blood pressures as high as our own.
How enviably supple and ingenious nature seems! But before we imitate the Tin Man, beating the breast of his stiff, man-made exoskeleton in longing for a biological heart, we should reconsider the central question of what this difference between the human and natural technologies means, and what it is based on. After all, no underlying bias toward stiffness or strength is required by either genetics or legislation. And these are only biases, not some inflexible prescription. Teeth are stiff and hard; hammocks are soft and flexible.
While no definitive answer is at hand, some components of an answer have emerged. Nature’s preference for flexibility may hinge on her cost accounting as much as it does on anything else. Energy and material not invested in structure can be put where they really count, in reproduction. Most of the loads creatures encounter can be borne by tensile elements, by pieces pulled upon, which is what ropy structures such as leaf stems and arterial walls do well. When compression is unavoidable, as when gravity presses down on a tree trunk or leg bone, stiff materials are unhesitatingly used.
Why don’t we make more use of flexible materials and structures? Well, as big, gravity-afflicted, terrestrial animals, we really do walk more easily on flat floors that don’t sag underfoot, and we can carry something across a bridge only when it’s rigid enough to let us balance on our legs, leaving our arms free. We use high temperatures in ovens and engines that only our stiff metals and ceramics can withstand; we want tools that cut and hammer and tall buildings that stand in all weather--and on and on.
Tradition certainly plays a role in how we make things, and our accustomed materials range from fairly stiff to extremely stiff; we have long experience and good supplies of such substances as dry wood, metal, stone, and masonry. But as we worry more about weight and material economy, and as we increase our use of softer plastics, we’re discovering the virtues of flexibility, developing devices such as hinges that truly bend and dentproof, impact-absorbing bumpers. Nonetheless, we’re still novices at nature’s game. She knows that virtue may flow from being bent out of shape, and we might well bend an ear and hear the message.
