Cantilevers Two - Buildings and Nature
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Arch Beam Box Girder Cable Stayed Pre-Stressed Suspension Truss
Railway stations often have cantilevered roofs. Here we see an early 20th century style on the right, and a late 20th century style on the left. Pillars are certainly undesirable near the edge of a platform, because anyone opening the door of a moving train so as to get off more quickly would risk a collision between door and pillar, or worse still, a nasty injury.
Many modern buildings have cantilevered balconies, or even whole sides of the buildings. Frank Lloyd Wright built a house projecting over a river near a waterfall; this building is now famous. The balconies in the pictures at left project less beyond the supports than might be imagined. In multi-storey dwellings, the balcony is especially important, to provide an outdoor area for the inhabitants and their plants and animals.
In older times, as now, the balcony has had both personal and cultural significance. It is the perfect place for rulers to be seen, and sometimes heard, by their subjects, while remaining above and aloof - the antithesis of "the walkabout", "working a room", and "pressing the flesh". For other people, the balcony is a grand place to view the surroundings and take the air, inferior only to the roof, which is often enjoyed only by those who occupy the top floor. The plays "Romeo and Juliet", and "West Side Story", gave the balcony special significance. The significance of the top floor and the penthouse apartment is modern, however: in many buildings similar to these the roof space was taken up by small apartments where the servants lived.
Roofs and Eaves
Roofs are often supported by trusses, and where they overhang they become cantilevers. The Golden Pavilion at Kinkakuji is not very old, being the replacement for the original, which was burned to the ground in 1950. A fictional account of this event was written in 1956 by Yukio Mishima.
In principle, well overhanging eaves can counter-balance some of the weight of the roof, at the expense of greater weight on the walls or pillars. The roofs of many Chinese and Japanese temples are supported on series of cantilevered brackets which spread the load from the narrow pillars.
This picture shows a tall tower carrying antennas. When the wind blows, it acts as a vertical cantilever. Such towers are sometimes built in concrete. Another solution is a much narrower tower with guys.
Aircraft wings, fins and tailplanes are cantilevers. So are the front and rear of the fuselage. To obtain a very clean wing, some designers have placed the engines at the rear of the aircraft, as in this picture. But there are disadvantages. The air supports the wings throughout their length, though with a mean position much nearer to the fuselage than the tips. The load, apart from the weight of the wings, is of course carried at the roots, making for large bending moments. By putting much of the fuel in the wings, and hanging the engines from them, the bending moment is significantly reduced, though on the ground the situation is reversed, and the airframe must be structured to take that into account. To obtain lift, a clean upper surface of the wing is more important than what happens to the lower surface.
Most large modern turbojet aircraft, right up to the huge Antonov 225, have the engines under the wings, which makes them easily accessible for servicing, but even now, numerous smaller aircraft have rear mounted engines. Some aircraft with rear mounted engines are Trident, Caravelle, 727, VC10, HS125, 111, CL-600, Citation, DC-9, MD-80 etc, MD-91 etc, Fokker 28, Fokker 100 Gulfstream III, Il-62, Jetstar, TU-134, Tu-154, Yak-40, Yak-42. Most of these designs are either old or fairly small.
From time to time, people try out the idea of an aircraft which is all wing, a "flying wing". Examples are a very old Northrop aircraft and the recently introduced B-2. If you try to ignore the experience of generations, you may produce a stroke of genius, or you may find out why everyone does it the same way. Putting everything in the wing would certainly help with bending moment, but where do you put the stabilizing tailplane and fin? Well, you can use a high-speed swept-back wing, and put fins at the tips, but you won't get much moment. And you can use washout at the tips instead of a tailplane. Active control of stability by computer can help.
But for an airliner, passive stability is very desirable in case things go wrong. Aircraft have occasionally been flown using only the engines for control, after the hydraulic system has been wrecked. In 1985, as a result of a faulty repair to the rear pressure bulkhead, a Japanese 747 lost all hydraulic control, and the tail fin, when the rear pressure bulkhead failed. The pilots managed to fly it for about half an hour, using only the engines, but it then hit a mountain. Only four people survived. In another case, caused by the failure of an engine fan, causing a DC-10 to lose all hydraulics, a combination of air traffic control and skilled flying, again using control by the remaining engines, got the plane to an airport near Sioux City, and 184 of 296 people survived. Only with an intrinsically stable aircraft could this feat have been possible.
There is another disadvantage of a flying wing. Putting a pressurized cabin in a wing presents great structural problems, since it ought to be cylindrical for strength with lightness. Windows would not be possible, and emergency exits would be difficult to provide.
A turbo-jet aircraft contains many cantilevers - not only the wings and tail, surfaces, but the hundreds of smaller aerofoils that are found in the engines. Some are used in the compressors, to compress and accelerate incoming air, others are used in the the turbines at the back, where they extract some of the outgoing energy and feed it to the compressors to keep them turning. In a bypass engine there are also large fans that add greatly to the thrust. In addition to these blades, there are rings of stator blades interleaved with the rotating ones, each set of stators directing the flow on to the next rotor disc.
The rotating blades are subjected to enormous forces that accelerate them towards the axis, and should something break, a blade flies off on a tangent. An uncontained blade can wreak havoc, and the unbalanced disc will probably cause trouble if the engine is not shut down. In addition to the forces, the turbine blades have to withstand very high temperatures, and are made of special alloys, and of course, like every cantilever, each blade is capable of oscillating. You might argue that some of these blades are not cantilevers, because they are quite loosely fitted, and can be rattled when the engine is idle. But when the engine is in use, they are subject to transverse forces from the air flow, so they are indeed acting as cantilevers.
Can you think of any natural flier, reptile, bird or mammal, that has not separated the functions of lift, stability, control and payload? Well, gliding snakes have not yet evolved very far down this path, but then, their glides are very steep. Nature, of course, cannot produce "strokes of genius", jumping from one design to a completely different one, because evolution can only move in the direction of immediate greater survivability in the hugely multi-dimensional space of variables. Crossing to another "valley" is impossible. Another solution, however much better it is, cannot be reached if it would involve even the smallest temporary decrease in fitness for reproducibility.
Designers, however, can "go back to the drawing board" and start again, though attempts to be different have not always been successful. Sometimes the reason is commercial or practical: sometimes it is technical. In the 19th century there were two main railway gauges in Britain - 7 feet/2.13 m, and 4.71 feet/1.44 m. The broad gauge had to be abandoned, because it was introduced when the "standard" gauge already covered thousands of miles of track. It was technically good, but commercially bad. Had it been used from the start, things might have been different. Actually, the broad gauge did have the disadvantage that it could not contain curves as acute as those obtainable with the smaller gauge. Mountain railways often use a narrow gauge.
"Received wisdom" is not always a poor guide: often it is the result of long experience. But occasionally a completely new idea, such as the Dyson vacuum cleaner, really does take off and make inroads into a market. This usually requires immense effort and perseverance, technically because the existing products are made using years of past experience, while the new one requires all the research to be done quickly, and commercially because of the existing marketing and sales structures, and the conservatism of many customers.
One of the two inventors of the turbo-jet engine, Sir Frank Whittle, experienced immense difficulty in convincing officials that his idea was worth pursuing, in spite of the fact that the promised gain in speed would have been decisive in both military and civil flight. With hindsight, to have started research into a turbojet airliner instead of building the Princess flying boat and the Brabazon might have been a better choice.
The wings of this airliner are large cantilevers, supported by the undercarriage on the ground, and at the roots when in the air. The underside of the wing is subtly curved. All aircraft wings are subject to the requirement of being able to support the aircraft over a fairly wide range of speed, in order to land at a safe speed. The wings are rather larger than they need to be at high speed, though the use of high lift devices has enabled designers to make wings much smaller than they would have been forty years ago.
The first cruise missile, the V-1, had small wings, because they could be launched at high speed ,as can modern ones. As the lift of a wing increases as the square of the speed, the problem of low speed flight would appear to be great. Luckily, by increasing the angle of incidence, and by the use of flaps and slots, the lift can be increased, at the expense of increased drag. In fact, at the slowest possible flying speed, the power needed can be much higher than at the most economical cruising speed. Glider pilots know well that there is an efficient range of speed, because they have to get power from outside. There are two optimum gliding speeds, one that gives maximum time in the air, and one that gives maximum range. Why are they different, and which is the higher?