Shape cheap, Materials Expensive
by Julian Vincent, 09 March 2012
It's always interesting how abstract ideas interact with reality. Physics went through a very productive time about 100 years ago, when Einstein wondered whether he could see his reflection in a mirror if he, and the mirror, were travelling at the speed of light. Could the light catch up with the mirror? It's thoughts like these which, developed along practical lines, can open up whole areas of understanding. Einstein dreamt up his theories of relativity. I can't claim anything so general, but I still have my dreams . . .
Some years ago I got interested in the idea that there are very few structures in the animal world that act like the trunk of a tree - taking loads along their length - but many which take side loads like a horizontal branch. This would be the difference between taking a load on the backbone as we stand upright, compared with the load on an arm outstretched holding a weight in the hand. I decided that the prickly spines of hedgehogs would be good examples of a column and began to look at their structure and mechanical properties. Amazingly nobody had looked at them in detail. The spines are hollow tubes (they are modified hairs, which can also be hollow). I made the assumption that the spines took their loads end-on. How it can the spine be structured to resist collapse?
image showing section of the hedgehog spine with nearly all the septa/bulheads removed, showing the stringers which run longitudinally. The Diameter of the tube is about 1 mm
Fig 1 - diagram of a short section of hedgehog spine, cut open to reveal the internal structures. The internal ridges running straight up and down ("stringers") support the wall from buckling locally. The horizontal plates ("bulkheads") resist the change in shape of the tube when it collapses (shown in Fig 2)
We found that hedgehog spines have internal stringers along the length (Fig 1) that stabilise the wall against local failure (the legs of North Sea oil platforms have a similar structure, as do flight feathers on a bird), and membranes extending across the tube that stabilise it as it bends (Fig 1, 2). If the spine needed only to resist bending and collapsing, it would make more sense to have a thicker wall, which is what you find in the spines of the marsupial, Echidna. But the shape is so complex . . . I realised that with the way biological structures are formed, shape is relatively easy to generate. But getting material (as food) from the surroundings and converting it into the keratin of the spine probably required more energy. For a hedgehog, shape is cheap but material is expensive.
Fig 2 - This is what happens when you load a strut on the ends. Try it with a straw and see how it collapses suddenly and the section changes shape at the bend. This is called "ovalisation"
More recently I was asked to generate some rules which would help engineers to design in a more 'biological' way - what is known as biomimetics or biomimicry. With two Russians (Olga and Nikolay Bogatyrev) we generated lots of ideas and data, much of which can be summarised in the two graphs (Fig 3 below) showing the main variables that are used to solve problems in technology and living organisms. We divided the controlling variables into substance, structure, energy, space, time and information. One or more of these can be changed (increased, decreased, simplified, made more complex, etc) to solve the problem. The vertical axis represents all problems.
The 'technology' graph (Fig 3a) summarises the solutions to about 5000 problems from the molecular (nm) to environmental (km) scale; the 'biology' graph (Fig 3b) is from about 2,500 problems. The most remarkable difference is the reliance of technology on energy: 70% of technical problems at the µm size (loosely, materials processing) are solved by changing energy. The second most important factor is material resource. In engineering, material is cheap and shape (resulting from energy-intensive processing) is expensive.
Fig 3a. Technology - the main variables used to solve problems or control difficult situations. The vertical scale is "all problems" and the horizontal scale is size, from molecule to international airport or ecosystem
Fig 3b. Biology - the main variables used to solve problems or control difficult situations. The identical vertical scale is "all problems" and the same horizontal scale is size, from molecule to international airport or ecosystem.
In biology it's the other way around. Energy is the least important factor. It's replaced by information (derived from the DNA in each cell which defines the sequence of atoms on molecules and how those molecules then interact) and the shapes and structures that result from these interactions (most biological materials are composites of several components and many are cellular, like the hedgehog spine). In other words, to progress from traditional engineering (with its attendant environmental problems) to a more benign way of doing things (biology has done well for billions of years) we should concentrate on structure and intrinsic (molecular) information. This general message is being repeated in my more detailed analyses. Even so, not all energy is bad.
Biology uses energy, for instance in the immune response, to counteract environmental threats such as disease. That's partly why you feel tired when you are ill. In terms of structure, the most important characteristic is the quality of the design at the level of detail that improves durability by suppressing breakage. It does this by avoiding notches and sharp angles that can focus forces and start a crack. Another aspect of structure is that organisms are divided into many small units (cells) that can be independent and so isolate any problems. This approach allows detailed local adaptations to changing requirements - information can be exchanged and responded to by individual cells.
By the way - we later realised that hedgehog spines are shock absorbers, because they can bend without breaking. So when a hedgehog climbs a tree it descends by rolling into a ball and dropping to the ground. Later work at Harvard University showed the hedgehog spine to be the most efficient shock absorber known. The information in DNA produces a lightweight structure which, by virtue of its shape, is remarkably efficient.