by J E Gordon
Of course, one does not have to use air. The sandbag is really another way of doing the same sort of thing, and so are ‘Dracone’ barges, which are simply large elongated floating sacks, filled with oil or water. They are used on the upper Amazon for transporting oil and are returned, deflated (but not on donkeys), in much the same way as the skin boats of the Euphrates. They are also used to bring fresh water to hotels in the Greek islands for the baths of the tourists.
Blown-up structures probably deserve to be developed much further than they have been for technological uses. However, the great exploiters of this form of construction are plants and animals. Both plants and animals are in business as chemical factories and are, in consequence, full of complicated and messy fluids. Nothing could be more ‘natural* and economical, for instance, than to make a worm in the form of an elongated bag stuffed, so to speak, with the worm’s squidgy insides.
Clearly, this works very well, and in fact it seems so natural and so economical that one wonders why animals ever bothered to acquire skeletons made from brittle, heavy bones. Would it not be much more convenient, for instance, if men were made like octopuses or squids or elephants* trunks? One view of the question, which was put to me by Professor Simkiss, is that animals never really meant to have skeletons at all; what may have happened was that the earliest bones were simply safe dumping-grounds for unwanted metal atoms in the body. Once animals had produced solid mineral lumps inside their bodies, then they might as well make use of them as attachments for muscles.
Wire wheels
It won’t be a stylish marriage,
I can’t afford a carriage,
But you’ll look sweet upon the seat
Of a bicycle made for two!
Harry Dacre, Daisy Bell
In the traditional wooden carriage wheel the weight of the vehicle is taken in compression by each of the spokes in turn. A carriage is therefore rather like a centipede with a great many long legs which, taken together, are heavy and inefficient. This fact seems first to have dawned upon that remarkable and eccentric man, Sir George Cayley (1773-1857). Cayley was one of the earliest and most brilliant of the aircraft pioneers and he was interested in making better and lighter landing wheels for his aircraft. As early as 180 8 it occurred to him that a great deal of weight could be saved by designing wheels in which the spokes were in tension rather than in compression. This thinking led, eventually, to the development of the modern bicycle wheel, in which the wire spokes are in tension while the compressive forces are taken by the rim, which can be quite light and thin, since it is well stabilized against buckling.
In conjunction with the pneumatic tyre, the wire wheel made bicycling practicable for ordinary people – with considerable social consequences, from Daisy Bell onwards. The saving in weight is, however, mostly confined to large lightly loaded wheels, such as bicycle wheels. When the wheel becomes smaller and the loads larger there is generally not much advantage to be gained from using tension spokes. In modern sports cars pressed-steel wheels are very little heavier than wire wheels, which are usually not worth the bother and expense.
On choosing a better material – and what is a ‘better’ material anyway?
Nature may be supposed to know her business when she chooses between the various possibilities in the way of biological tissues; but mere men, even very great men, seem to have the strangest ideas about materials. According to Homer, the bow of Apollo was made of silver* – a metal whose strain energy storage is negligible. In a rather later age we were told that the floors of Heaven were made of gold, or alternatively of glass: both very unsuitable substances. Poets are always quite hopeless about materials; but most of the rest of us are not much better. In fact very few people ever think rationally about the subject at all.
Quirks of fashion and prestige seem to play a large part in the matter. Gold is not really a very good material for watches, nor is steel for office furniture. The Victorians insisted on making all sorts of improbable articles, such as umbrella stands, out of cast iron, and there is the story of the African chief who had his palace made out of the same substance.
Although the choice of materials is sometimes irrational and eccentric, more often it is highly traditional and conservative. Of course there is sound reason behind a good deal of traditional materials selection, but it is so mixed up with unreason that it is difficult to separate the two. Artists from Lewis Carroll to Dali have discovered that it is possible to impart a considerable psychological shock merely by implying that some familiar object might be made from an apparently unsuitable material, such as rubber or bread and butter. Engineers are very susceptible to these effects; they would be a good deal shocked nowadays at the idea of a large wooden ship. Our ancestors were much more shocked at the idea of an iron one.
The acceptability of various materials changes with time in curious and interesting ways. Thatch is a case in poiftt. Thatch was once the cheapest and least regarded of roofing materials, but in the poorer country districts it often had to suffice even for the roofs of churches. During the eighteenth century, when these parishes became richer, subscriptions were raised to replace the thatch by slates or tiles. Sometimes the money was inadequate to do the whole job, and in these cases the thatch had perforce to be left on those areas of the church roof which were not likely to be seen by passers-by; only the side which faced the main road was tiled. Nowadays the balance of prestige is reversed, and in the Home Counties thatched roofs are the pride and joy of the wealthier of the business fraternity.
Materials, fuel and energy
The twentieth century may be known to posterity as the ‘age of steel and concrete’. It may also be known as the ‘age of ugliness’, and perhaps by other unpleasant names as well, such as the ‘age of waste’. It is not only engineers who are obsessed by steel and concrete (and quite indifferent to appearances); politicians and the man in the street seem to have caught the same infection. The disease seems to have originated two hundred years ago with the Industrial Revolution and cheap coal – which led to cheap iron -which led to iron steam engines fitted to turn that coal into cheap mechanical energy: and so on round and round in ever more energy-intensive circles. Thus coal and oil store a great deal of energy packed into a small volume. Engines process a great deal of this energy very quickly and within a small space. They then deliver the energy as electricity or mechanical work in concentrated forms. On this concentration of energy our whole contemporary technology rests. The materials of this technology, steel, aluminium and concrete, themselves require a great deal of energy to manufacture them; how much energy is indicated in Table 6. Because they need so much energy to make them these materials can only be employed with profit within an energy-intensive economy. We are not only investing money capital in a technical device; we are also investing energy capital, and in both cases it is necessary to secure a fair return on the investment.
TABLE 6
Approximate energies required to produce various materials
Material n = energy to manufacture Joules × 109 per ton Oil equivalent tons
Steel (mild) 60 1·5
Titanium 800 20
Aluminium 250 6
Glass 24 0·6
Brick 6 0·15
Concrete 4·0 0·1
Carbon-fibre composite 4,000 100
Wood (spruce) 1·0 0·025
Polyethylene 45 1·1
Note. All these values are very rough and no doubt controversial; but I think that they are in the right region. The value given for carbon-fibre composites is admittedly a guess; but it is a guess founded upon many years of experience in developing similar fibres.
In spite of the high cost and increasing scarcity of energy the trend in the energy-intensive direction is increasing rather than diminishing. Advanced engines, such as gas turbines, process more and more energy, more and more hectically, within less and less space. Advanced devices require advanced materials, and the newer materials, such as high-temperature alloys and carbon-f
ibre plastics, consume more and more energy in their manufacture.
Most probably this kind of thing cannot go on for very much longer, for the whole system is entirely dependent upon cheap and concentrated sources of energy, such as oil. Living Nature may be regarded as an enormous system for extracting energy, not from concentrated but from diffuse sources, and then using that energy with the uttermost economy. Many attempts are on foot at present to collect energy for technology from diffuse sources, such as the sun, the wind or the sea. Many of these are likely to fail because the energy investment which will be needed, using conventional collecting structures built of steel or concrete, cannot yield an economic return. A quite different approach to the whole concept of ‘efficiency’ will be needed. Nature seems to look at these problems in terms of her ‘metabolic investment’, and we may have to do something of the same kind.
It is not only that metals and concrete require a great deal of energy, per ton, to manufacture (Table 6), but also that, for the diffuse or lightly loaded structures which are usually needed for systems of low energy intensity, the actual weight of devices made from steel and concrete is likely to be very many times higher than it would be if we used more sensible and more civilized materials.
As we shall shortly see, timber can be one of the most ‘efficient’ of all materials in a strictly structural sense. For large dimensions and light loads, a wooden structure is many times lighter than one made from steel or concrete. One of the difficulties with timber, in the past, has always been that trees take a long time to grow and wood is slow and expensive to season.
Probably the most important development in materials during the last few years has been that made by the plant geneticists who have been breeding fast-growing varieties of commercial timbers. Thus varieties of Pinus radiata (Weymouth pine) are now being planted which, in favourable conditions, will increase in diameter by up to 12 centimetres per year and may be fit for felling, as mature timber, in six years. So there is a good prospect of timber becoming a crop which can be grown on a short time-cycle. Nearly all the energy which is needed to make it grow is provided, free, by the sun. Presumably, when one has finished with a timber structure, it could be burnt to yield up most of the energy which it has collected while it was growing. This is, of course, in no way true of steel or concrete.
Again, timber used to need lengthy and expensive seasoning in heated kilns, which used up a good deal of energy. As a result of recent research it is now possible to season sizeable soft-wood scantlings in twenty-four hours, at a very low cost. These are very important developments in relation to structures and to the world energy situation, and it behoves us to take account of them.
Some algebraical analysis of the structural efficiencies in various roles arid in terms of weight, of different materials, is given in Appendix 4. The design of a number of high-technology structures, such as aircraft, is largely controlled by the criterion E/ρ: that is to say, by the ‘specific Young’s modulus’ which governs the weight-cost of the overall deflections. It happens that, for the majority of traditional structural materials, molybdenum, steel, titanium, aluminium, magnesium and wood, the value of E/ρ is sensibly constant. It is for this reason that, over the last fifteen or twenty years, governments have spent such large sums of money in developing new materials based on exotic fibres such as boron, carbon and silicon carbide.
Fibres of this sort may or may not be effective in aerospace; but what seems to be certain is that not only are they expensive but they also need large amounts of energy to make them. For this reason their future use is likely to be rather limited, arjd, in my own view, they are not likely to become the ‘people’s materials’ of the foreseeable future.
TABLE 7
The efficiency of various materials in different roles
Young’s modulus, Specific gravity,
Material E MN/m2 ρ grams/c.c. E/ρ
Steel 210,000 7·8 25,000 190 7·5
Titanium 120,000 4·5 25,000 240 11·0
Aluminium 73,000 2·4 25,000 310 15·0
Magnesium 42,000 1·7 24,000 380 20·5
Glass 73,000 2·4 25,000 360 17·5
Brick 21,000 3·0 7,000 150 9·0
Concrete 15,000 2·5 6,000 160 10·0
Carbon-fibre composite 200,000 2·0 100,000 700 29·0
Wood (spruce) 14,000 0·5 25,000 750 48·0
The requirement for a strict and expensive control of overall deflections is likely to be a very limited one; however, as we have seen, the weight-cost – and often the money cost – of carrying compressive loads is frequently very high. The weight-cost of carrying a compressive load in a column is governed, not by E/ρ, but by . The weight-cost of a panel is controlled by (Appendix 4). These requirements are summarized in Table 7. It will be seen that there is a large premium on low density; thus steel comes out rather badly, even compared with bricks and concrete. Furthermore, for many light-weight applications – such as airships or artificial limbs – wood is even better than carbon-fibre materials, besides being much cheaper.
In Table 8 these virtues are expressed in terms of energy-cost.
TABLE 8
The structural efficiency of various materials in terms of the energy needed to make them
Material Energy needed to ensure a given stiffness in the structure as a whole Energy needed to produce a panel of given compressive strength
Steel 1 1
Titanium 13 9
Aluminium 4 2
Brick 0·4 0·1
Concrete 0·3 0·05
Wood 0·02 0·002
Carbon-fibre composite 17 17·0
Here the advantage of the traditional materials – wood, brick and concrete – is overwhelming. This table makes one wonder whether the pursuit of materials based on exotic fibres is really justified. What really pays off for most of the common purposes of life is not carbon fibres, but holes. Nature tumbled to this a long time ago when she invented wood; and so did the Romans when they started to build churches from empty wine bottles. Holes are enormously cheaper, both in money and in energy, than any conceivable form of high-stiffness material. It would probably be better to spend more time and money on developing cellular or porous materials and less on boron or carbon fibres.
* * *
* For instance, A. G. M. Michell, ‘The limits of economy of material in frame structures’, Phil. Mag. Series 6, 8, 589 (1904).
* Because the cross-section of a tension bar is proportional to the load, whereas the volume of the end fittings increases as the power of 3/2 of the load.
* Thinking algebraically, we can put the problem of carrying a load, P, over a length, JL, in n parallel tension bars in the form:
where Z = total weight of all the tension members, per unit length
P = total load carried
s = safe working stress
k = a coefficient connected with the cunning of the designer
W = work of fracture of the material
n = number of tension members employed
p = density of material.
The proof of this is to be found in Cox’s The Design of Structures of Least Weight. I have modified Cox’s formula slightly.
* i.e. for a given cross-sectional area of torsion-box.
* Neque semper arcum tendit Apollo ! (’ Neither is Apollo perpetually drawing his bow’, Horace, Odes II, x, 19). Horace perhaps knew that silver creeps nearly as badly as lead.
Chapter 15 A chapter of accidents
-a study in sin, error and metal fatigue
Have you heard of the wonderful one-hoss shay
That was built in such a logical way,
It ran a hundred years to a day,
And then, of a sudden, it -
Oliver Wendell Holmes, The One-Hoss Shay
The entire physical world is most properly regarded as a great energy system: an enormous market-place in which one form of energy is for ever being traded for another form according to set rules and values. That which is energetically a
dvantageous is that which will sooner or later happen. In one sense a structure is a device which exists in order to delay some event which is energetically favoured. It is energetically advantageous, for instance, for a weight to fall to the ground, for strain energy to be released -and so on. Sooner or later the weight will fall to the ground and the strain energy will be released; but it is the business of a structure to delay such events for a season, for a lifetime or for thousands of years. All structures will be broken or destroyed in the end -just as all people will die in the end. It is the purpose of medicine and engineering to postpone these occurrences for a decent interval.
The question is: what is to be regarded as a ‘decent interval’? Every structure must be built so as to be ‘safe’ for what may reasonably be considered an appropriate working life. For a rocket case this might be a few minutes, for a car or an aircraft, ten or twenty years, for a cathedral perhaps a thousand years. Oliver Wendell Holmes’s ‘one-hoss shay’ was constructed to last for a hundred years – neither more nor less – and it disintegrated, exactly as planned, on 1 November 1855, just as tjhe parson had reached ‘fifthly’ in the composition of his sermon. But, of course, this was nonsense. Again, the egregious but heroic Mr Honey in Nevil Shute’s No Highway predicts the failure of the tail of the Reindeer airliner from ‘metal fatigue’ after exactly 1,440 flying hours – plus or minus a day or so. This again was nonsense, as Nevil Shiite must have known, being an experienced aircraft designer.