by J E Gordon
Another consequence of the algebra we have just done is that to contain a given volume of fluid at a given pressure will require a greater weight of material if we use a cylindrical vessel than if we use a spherical one. Where weight is very important – as it is with the oxygen-bottles which climbers use at high altitudes and also with aircraft starter bottles – then spherical vessels are usual. For most other purposes, where weight is not so serious a matter, cylindrical bottles are cheaper and more convenient. The ‘gas-cylinders ‘ used in hospitals and garages are a case in point.
Chinese engineering – or better bulge than bust
There is an interesting problem which has to be solved by the designer of every sailing vessel It is: What is the best method of preventing the ship from flinging her spars overboard? Opinion on this point is divided. There are two schools of thought: the Eastern and the Western schools. In the West we think the best way of keeping the masts in the ship is to fasten them rigidly in position with a complicated system of shrouds and stays. The disciples of the Eastern school hold that this is all nonsense – besides being very expensive. They stand a tall and rickety mast on end, set upon it vast areas of gunny mats, bamboo matting or anything else that comes to hand and then keep the whole business erect by the power of faith. At least, I have never been able to discover any other power interesting itself in the miracle.
Weston Martyr, The Southseaman
The theory of pressure vessels, which we have just derived, also applies, with minor modifications, to things other than closed containers: that is, to ‘open’ membranes and fabrics which have to sustain pressure from the free movement of wind or water. Of such a nature are tents and kites and awnings and fabric-covered aircraft and parachutes and the sails of ships and windmills and eardrums and fishes’ fins and the wings of bats and pterodactyls and the sails of the jellyfish called Portuguese men-of-war.
For all such purposes it is expedient and economical (as we shall see in Chapter 14) not to use a ‘rigid’ panel or shell or monocoque but to cover a stiff open framework of rods or spars or bones with some kind of flexible fabric or skin or membrane. Such a structure cannot be quite rigid, and it will be realized that, as soon as any lateral force comes upon the membrane by reason of the pressure of wind or water, it must deflect or bow into a curved shape which, to a first approximation, may be treated as a part or segment of a sphere or cylinder, and so the stresses in the membrane will obey much the same laws as those in the shell of a pressure vessel.
From this it is very easy to show that the force or tension in the membrane, per unit width, is pr, the product of the wind pressure (p) and the radius of curvature (r) of the membrane. Thus the more sharply the membrane is curved the less the force in it will be, and so the load which it puts upon the supporting framework will also be diminished.
When the wind blows, the pressure caused by the wind increases as the square of the wind velocity. In a strong wind the pressure becomes very high indeed and so do the loads upon the supporting structure. According to our Western, engineering-school, way of thinking there is very little we can do about this, for we would rather be seen dead than allow the membrane – whether it be a sail or part of an aeroplane or whatever – to bulge appreciably between its supports. Of course, we can never manage to keep the fabric perfectly flat, but we do everything we can to keep it as taut as possible. What we actually do is to make the supporting framework strong and heavy and expensive and hope that it won’t break – which of course it often does.
For instance, the rig which has been developed for modern racing yachts generally consists of tubular metal spars and almost inextensible Terylene sails. This aerodynamic mechanism is kept up to its job by many ropes and wires which, in turn, are tautened to a frightening degree by means of screws and winches and hydraulic jacks, all of which are needed to cope with the enormous loads set up in the sails when the vessel is sailing fast in a breeze of wind. The whole thing is a miracle of engineering ‘efficiency’ but it is also horribly expensive. Ships of this sort convey to their occupants a feeling of tenseness which is anything but restful.
A simpler and cheaper way of doing the job is to arrange for the sail to bulge between its supports so that, as the wind pressure increases, the radius of curvature diminishes, and so the tension force in the canvas remains roughly constant however hard the winds may blow. Naturally, one has to ensure that the distortions which help to ease the structural problem do not create aerodynamic ones.
Figure 7. Chinese junk rig.
One elegant and satisfactory way of doing this has been devised by the Chinese, who, after all, have been sailing about the seas in moderate comfort and safety for a good many centuries. The rig of the traditional Chinese junk varies according to local custom but is generally very much like Figure 7. The battens which cross the sails are attached to the masts and, since the whole rig is constructed from flexible materials, as the wind increases, the sail bows out between the battens after the fashion of Figure 8 without much loss of aerodynamic efficiency. If it doesn’t bulge enough it is quite simple to ease the halyard until it does. Lately, Colonel ‘Blondie’ Hasler (of Bordeaux Raid fame) has taken up the Chinese lug sail with very satisfactory results. Several yachts with Colonel Hasler’s rig have made long ocean voyages with success and in a comparatively relaxed manner. The ‘hang-gliders’ which are now so popular are designed on much the same principles, and, although they may shock the traditionalists, they are cheap and strong and they do seem to work.
Figure 8. Edge-on view of a junk sail with halyard eased.
Bats and pterodactyls
Take from the goblin his crinkly face,
His pointed ears from the gnome;
Borrow the nose of a leprechaun
And smuggle it carefully home;
Sew bawkie fingers to banshee wrist;
Stitch gossamer vellum between;
Fit legs to straddle with knees atwist
From a body of velveteen.
Douglas English (Punchy 11 July 1923)
The resemblance between a bat and a Chinese junk is immediately obvious (Figure 9). In all bats the wings are constructed by stretching a membrane of very flexible skin over a framework of long, thin bones which are, in essence, the fingers of a hand, Fruit-bats, for instance, are quite large animals with a wing-span of four feet or something over a metre. In their native India, where they are a pest, they think nothing of flying thirty or forty miles in a night in order to rob an orchard. Since they can do this without becoming unduly exhausted they must therefore be efficient flying machines. Furthermore, to save weight, as well as what is called ‘metabolic cost’, they have gone a long way in the matter of cutting down the thickness of their wing-bones.
Figure 9. The fruit-bat.
When a fruit-bat is photographed in flight it can be seen that, on the down-stroke of the wing, the skin membrane bulges upwards into a form which is roughly semi-circular, thereby minimizing the mechanical load upon its bones. It is clear that there can in practice be little or no aerodynamic loss as a consequence of this change of shape.
About 30,000,000 years ago the place of birds was largely filled by a wide range of flying creatures called Pterodactyls (finger-wings). Many of these much resembled bats, except that only one finger, the little finger, played any structural part. So the membrane wing of pterodactyls was rather like a Bermuda mainsail without any battens.
Figure 10. Pteranodon.
Some of these animals were very large. Fossil remains of Pteranodon, for instance, have been recovered which show that this beast reached a wing-span of 8 metres (27 feet) and possibly more. It stood about 3 metres high (10 feet), and it seems that its total weight was probably only about 20 kilograms (44 lb.). There was therefore little weight available either for bony structure or for flying muscles. Recently, the discovery of even larger pterodactyls, about twice the span of Pteranodon, has been reported from America.
Pteranodon was probably pelagic: that is
to say, it filled, roughly speaking, the ecological niche which is now occupied by the albatross. Like the albatross, it seems to have lived mostly in the air, soaring close above the deep-sea waves and fishing on the wing. Even more than the fruit-bat, the wing bones of Ptetanodon appear, from the fossils, to have been almost unbelievably thin and fragile. Of course, we know nothing experimentally about the elasticity of the skin which covered these vast wings, but it seems fair to infer that this skin must have behaved very much like that of a bat. The aerodynamic efficiency of the whole system must have been high and comparable to that of the modern albatross.
Why do birds have feathers?
Although bats flourish and survive very well today, pterodactyls were superseded by birds, which have feathers, a great many years ago. It is possible, of course, that the extinction of pterodactyls had nothing to do with structural considerations, but it is also possible that there is something special about feathers which gives birds an edge over other flying creatures. When I worked at the Royal Aircraft Establishment I used to ask my superiors, from time to time, whether it would not perhaps be better if aeroplanes had feathers; but I seldom succeeded in extracting a rational or even a patient answer to this question.
But, after all, why do birds have feathers? Given the job of designing a flying animal, a modern engineer would perhaps produce something like a bat, or possibly some sort of flying insect. I do not think that it would occur to him to invent feathers. Yet presumably there are very good reasons for their existence. One imagines that both bats and pterodactyls tend to lose a good deal of energy in the form of heat from the skin of their wings; but then reasonable heat insulation could be provided by fur.
Perhaps this is what did happen at an early stage in the evolution of birds, because feathers, like horns and claws, developed from hair. However, hair is presumably better when it is soft, and so the keratin from which hair is made has quite a low Young’s modulus. In feathers the keratin molecule has been made stiffer by cross-linking the molecular chains with sulphur atoms (which accounts for the smell of burnt feathers).
There are, no doubt, aerodynamic advantages in using feathers, since their employment extends the choice of outside shapes which the animal can make use of. For one thing, ‘thick’ wing-sections have often better aerodynamic efficiencies than the thin ones which result from membranes. It is easy to get an efficient ‘thick’ section by padding out the wing profile with feathers at the cost of very little weight increase. Furthermore, feathers are better adapted than skin and bone for providing anti-stalling devices such as’ slots’ and’ flaps’.
However, I am inclined to think that the main advantage of feathers to an animal may be structural. Anybody who has flown model aeroplanes knows, to their cost, how vulnerable any small flying machine must be to accidental damage from things like trees and bushes, or even from careless handling. Many birds fly constantly in and out of trees and hedges and other obstacles. Indeed they use such cover as a refuge from their enemies. For most birds the loss of a reasonable number of feathers is not a very serious matter. Besides, it is better to leave the cat with a mouthful of feathers than to be eaten.
Feathers not only enable birds to get away with more local scrapes and abrasions than other animals, but the body of the bird is protected from more serious damage by its thick resilient armour. The Japanese feather armour which one sees in museums was not, as one might suppose, the picturesque nonsense of a primitive people who did not know any better. It was an effective protection against weapons like swords. In the same kind of way, during the Russo-Finnish war, Finnish armoured trains were protected by bales of paper; and modern fighter-pilots’ splinter-proof boots are made from many layers of Cellophane. When a hawk kills a bird in the air it does not usually do so by wounding it with its beak or talons – which would probably not penetrate the feathers. It kills by striking the bird in the back with its outstretched feet so as to impart a violent acceleration to the bird as a whole which has the effect of breaking its neck – very much as happens in judicial hanging.
The whole constitution and design of feathers seem to be extremely cunning. Feathers probably do not need to be especially strong, but they do need to be stiff and at the same time resilient and to have a high work of fracture. The work of fracture mechanism of feathers is something of a mystery; at the time of writing I do not think anybody knows how it works. Like so many work of fracture mechanisms, that of feathers is sensitive to what appear to be small changes. Everybody who has kept and flown hawks knows that these intelligent, exacting and maddening birds lpse condition very easily. Even when they are properly fed and exercised in captivity, hawks’ feathers are very apt to become brittle and break off with undue frequency. The cure or palliative for this is to join the broken parts of the feather together again by ‘imping*. This is done by inserting a double-ended ‘imping-needle’, with a little glue, inside the hollow of the shaft at the break. The details of this process are described in the sixteenth-century books on hawking.
When one considers the appalling and expensive frequency with which motor cars nowadays incur bumps, bashes and abrasions, one sometimes wonders whether they have not a lesson to learn from the birds. Incidentally, I am told that, since the American army practically lives on chicken, there exist somewhere in the United States enormous quantities of unwanted chicken feathers. It would be rather nice to find a use for them.
* * *
*The muscular mechanism has recently been understood. It works by feeding energy into edge dislocations which operate, as it were, in reverse. For edge dislocations see The New Science of Strong Materials, Chapter 4.
*The number of vibrations per second (i.e. the frequency), n, of a stretched string can be written:
where l = length of string
p = density of material from which string is made (kg/m3)
s = tensile stress in string (N/m2).
* But then, during the same period, eighty-three steamboats were destroyed by fire, eighty-eight by running into sunken trees, and seventy from ‘other causes’. It seems that Life on the Mississippi, in the showboat days, was not uneventful.
† A partial solution was provided by Mariotte around 1680, but of course he was unable to make use of the concept of stress.
Chapter 7 Joints, fastenings and people
-also about creep and chariot wheels
And here I want to tell you a story about a ship that was madeduring the war. She wasa steamer, and she was built of wood – good wood; and the men who designed her were good and able craftsmen too...
She went along like a man who carries too heavy a burden, and presently she tripped and stumbled (it was only a little ground-swell) – and she opened out and fell apart like a flimsy old crate that someone had stepped on. In five minutes there was nothing there at all except a floating scum of coal dust, with some timbers and an odd man or two bobbing about in the middle of it.
This is a true story; but the point I want you to notice is that this ship was made by carpenters: house carpenters – shore carpenters; and she was not built by shipwrights at all.
Weston Martyr, The Southseaman
The steamer in Weston Martyr’s story sank, rather suddenly, because the joints which were supposed to hold her timbers together were much too weak, although the house carpenters who built her – who were honest men in their own way – were presumably satisfied with them. In fact, when a shore carpenter is building a house or putting together traditional furniture he is in the habit of making joints which a naval architect or an engineer would regard as weak and highly inefficient. Weak these joints certainly are; whether they are ‘inefficient’ depends upon what one is trying to do. The purposes of a builder of houses may not be at all the same as those of a builder of ships or aeroplanes.
It is perhaps too often assumed by engineers that an ‘efficient’ structure is always one in which each component and each joint is exactly strong enough for the loads which it has to bear, so that, for a
given strength, the smallest amount of material is used and the weight is minimized. Such a structure would, ideally, be equally likely to break anywhere. Or indeed, like the ‘one-hoss shay’, it might break everywhere at once. To work towards this kind of efficiency calls for great vigilance on the part of the engineer, since the least fault in design or manufacture must introduce a dangerous weakness.
Approximations to this kind of structure do, of course, exist, especially in ships and aeroplanes and in some kinds of machinery where weight-saving is very important. However, this represents an unduly specialized way of looking at the problem of efficiency, and it takes no account of the need for rigidity, let alone of the need for economy. Structures of the one-hoss shay type are sometimes necessary, but they are always expensive both to build and to maintain. Weight-saving by means of structural perfectionism is one of the factors which make space travel such an extravagant luxury. Even at a mundane level we may reflect that the cost of usable space, per cubic metre, is about twenty times as high in a small ship as it is in an ordinary house; the cost of space in aircraft is a great deal higher still.
Builders and joiners have more sense than to go in for fancy structures of this kind; houses are quite expensive enough as it is, and these people know very well that in the great majority of the common or stationary affairs of life the design of a structure is influenced much more by its stiffness than by its strength.