GlosCathArch

If you walk into Gloucester from the River Severn at Over you can find the cathedral, which includes semicircular Romanesque arches built by the Normans between 1089 and 1100, and much later ones in the perpendicular style, with more or less pointed tops.

Although the empire Romans had collapsed hundreds of years earlier, some of their ideas were more robust, and the style brought to England by the Normans continued to use the massive piers and arches that the Romans had favoured. Many Roman buildings, bridges and aqueducts are still standing, and in good condition. Some would say that this proves that they over-engineered. Yes, but their bridges could withstand the loss of an arch or two from enemy action or from flooding. And it depends on your definition of good engineering. In modern times we would of course include the cost, not only financial, but also often human and environmental, in our deliberations. For the Romans, these constraints may not always have been felt so strongly.

When you see this porch outside Gloucester cathedral, you are not prepared for the sight of the massive Norman piers and arches that support the nave. Some of these are shown in the next two pictures. The Normans brought much else besides a style of architecture, in terms of organisation and culture. Inside this cathedral, you can find the tomb of Robert of Normandy, or more correctly, Robert de Normandie, as French was the official language for a long time after the Norman invasion. French was just one of the numerous linguistic influences on the language that came to be called "English".

Romanesque Style

Some of the piers in Gloucester cathedral are reddish at the bottom because the thatched roof caught fire and collapsed into the nave. The intense heat from the burning debris affected the surface of the limestone.

Unlike these 11th century piers in Gloucester cathedral, those in the cathedral of Durham, the oldest Norman building in England, are carved with decorative patterns. Durham cathedral is a magnificent edifice, on a commanding site. If you go there, don’t forget to see the ingenious Kingsgate foot-bridge over the river Wear. This bridge was built in two halves, each parallel to the river. The two parts were then rotated about a vertical axis and then joined to form a single beam. A splendid construction. Tewkesbury abbey is also well worth a visit.

The crossing of Gloucester cathedral has two of these flimsy looking east-west arches. What do they do? What is not apparent from these photographs is that they carry the springing of one part of the 14th century vault above the choir. Evidently the builders did not think that they could carry the forces from the vault into the existing walls and arches. From details like this we can see that this type of building was not created from a single plan, as would be done today. Cathedrals often grew over several centuries, and sometimes parts fell down, even, in some cases, soon after completion. The cathedral at Beauvais would have been one of the wonders of the world, if it had been completed, and if it had survived. In fact it is but a fragment of the intended structure.

The gothic cathedral gives the lie to the idea that design grows out of engineering, and that engineering grows out of science. These ancient people did not understand what they were doing, but almost a thousand years later in some cases, people still come to marvel at what they created.

Much later, the industrial revolution began long before anyone understood much about energy – even the law of conservation of energy was unknown when the first steam engines were built. Thermodynamics was far in the future. So the first steam engines were almost incredibly inefficient. What did it matter: trees and coal abounded in England.

That is not to denigrate science: the world has changed, and we now realise the immense benefits that come from knowing the science. People in France, Germany and USA made great contributions to thermodynamics and other branches of science during the nineteencth century, revealing that a perfectly efficient heat engine was a myth, but at the same time enabling engineers to approach closer to the limits of the possible. From that work sprang the internal combustion engine.

Later, the discovery of quantum mechanics made possible the discovery and design of semiconductor components upon which our communications, computing and entertainment technologies are based. The world has changed incalculably during the last hundred years: many of the changes would probably not have happened had people not been prepared to spend money on pure research. Perhaps that is too strong a statement – what do you think?

We got off the subject here. But then, there is no subject: everything is created from stuff, so everything has structure, and everything feels forces, so the subject has no boundaries.

Keystones

In engineering, the keystone has no structural significance, but it has developed into a decorative element in many buildings. Sometimes, looking at a small window or porch, there is an unworthy suspicion that the whole arch, including the "keystone", is cast as one piece of concrete. This building is a Unitarian chapel.

21st century tubular scaffolding on the south transept of Gloucester cathedral. Note the outward lean of the south wall at left. It is being pushed by buttresses that are connected to the tower. They are referred to later in this page. This is not the subject of the repair. These arches are more recent than the Norman ones.

Ruins in Gloucester, near the library. Well built arches are very resilient. These have been here for a very long time, but are in quite good condition. A modern building has been built on to these ruins, rather incongruously.

Part of the North side of Gloucester cathedral, with newer pointed arches at left close to older Norman ones at right. Many English cathedrals and churches contain a mixture of styles like this. Evidently people then were not prevented from adding new styles to old buildings by considerations of incompatibility.

Domes

One of the lovely features of architectures, for example, Islamic and Christian, is the way that the idea of the arch has been extended far beyond the basic spanning and supporting element. Rotating the arch about the centre produces the dome. The dome of the Taj Mahal is a well-known example.

Another is Brunelleschi’s dome in Firenze. The other dome below is in Isfahan. The picture was downloaded from Welcome to Isfahan, which offers an informative guide to Islamic Iranian architecture.

The dome idea can be extended to the cone and polygonal pyramid, as in church spires, and of course the igloo. The oast houses of Kent, and many pottery kilns in the Midlands, also used cones.

Domes are surfaces with positive curvature. Surfaces of negative curvature are seen in the cooling towers of power stations, in the form of hyperboloids of revolution. These surfaces have the theoretical advantage of being developable from straight lines, like the once fashionable hyperbolic paraboloidal roof.

Here are some views of the sky-line of a typical small English city. We see the elegantly simple domes and minaret of the modern mosque, the intricately constructed tower of the medieval cathedral, surrounded by 20th century rectangle-esque, or trabeate, offices, the modern but ageing hospital, and the rusting gas-holder – nearly 900 years of history in building.

Note that the gas-holder is cylindrical because the pressure is equal all around, and that the top is slightly domed for rigidity. The circular shape allows the use of helical guides for expansion. With vertical guides, each cylinder could wobble inside the one below. Each cylinder has a helical inspection stairway which is high enough to reach the next level when the gas-holder is full.

The three pictures below are very large JPEGs showing general views of parts of the same city, the last being a part of a typical English suburb, with its numerous variations on the themes of semi-detached houses, detached houses, and bungalows. Here and there are older buildings that preceded the development from a scattered village, based around the route of a Roman road, to a large suburb. From the third picture we see that the cathedral is almost at the far side of the city. The town was originally a small religious community near the river. Because the other side of the river is a low-lying flood plain, the town developed almost entirely on one side. Even so, the streets nearest are frequently flooded, to the despair of the inhabitants, and the foundations of the cathedral are said to be permanently waterlogged. What would happen if they dried out?

The Brunelleschi dome in Florence clearly demonstrates one big difference between domes and arches, the distribution of forces. This particular dome comprises eight pointed sectors (on a globe map of the earth they would be called gores). Actually, the inner dome is so thick that at all levels it contains a horizontal circle. An arch is generally made of parallel sections, with the same width throughout. So the distribution of forces and weights is subtly different, leading to the other big difference between a dome and an arch.

The second important difference is that a dome can in principle be erected without centring, as the Inuit do with igloos. An arch needs centring, unless the halves are treated as cantilevers and held back during construction. This was done in the cases of the Eads bridge and in the Sydney harbour bridge. The dome can be built with falsework supported on the built sections.

On the other hand, arches are generally built on the ground, which reacts against the thrust. Domes, except igloos, seldom spring from the ground. They often include chains or cables around the base to contain the outward forces. In this they resemble bow-string arches or tied arches, except that in the case of a dome, the constraint does not interfere with the space within. In that sense, a dome can include its own abutments.

A plan view of a dome shows that if we imagine it divided into sectors, the width of the sectors is proportional to the distance from the centre. For a simple cable or arch with a catenary shape, the mass per length along the curve is constant.

From this information can you guess what the ideal shape for a uniform shell would be as compared with a catenary for a uniform arch?

Salisbury Cathedral

Here are three diagrams, showing an arch, a dome, and a peculiar spidery object. To find out what it is, visit Salisbury cathedral and go to the beautiful chapter house. There you can forget about stresses, strains and bending moments, and just enjoy the view.

Salisbury’s chapter house is made by rotating an arch about one pier, producing a kind of arch with a narrow central pier and an octagonal wall around the outside. It dates from the middle of the 13th century. The central pillar at first looks amazingly slim, but it is only supporting about a quarter of the weight of the roof, and it feels virtually no lateral forces because of the symmetry. Its function is analogous to that of the neutral wire in the three phase electrical supply that would be invented hundreds of years later.

If the thrust of the ith arch of N is Ti, the total thrust is given by

which is zero in the symmetrical case where all the T_i are equal. For the case of an N-phase power supply, current in the neutral wire is

which is zero in the case where all the currents Ii are equal.

In the arch formula, the value N = 2 corresponds to a pair of arches in a normal multi-arch bridge.

This chapter house includes a medieval frieze of sculptures of early bible stories. You can also see there a Magna Carta from 1215. Only three other originals exist. A similar construction, but in a rectangular space, is found in Marienburg castle. These two links are about the roof of the Great Court of the British Museum and Great Court – B M.

In Salisbury cathedral you can see the four main piers, visibly bowed by the weight of the tower, surmounted by a spire for which the columns were not designed. The columns are stabilised by inverted arches.

The spire is visible for many miles around, even though Salisbury is in a valley. Salisbury cathedral without the spire is unthinkable, yet that is how it was designed. The transmission of the weight of the spire from the polygonal cone to the four great pillars must entail some interesting engineering, especially as the tower was not designed to receive these forces.

We are so used to this building that we sometimes do not see that the tower and the spire are quite different in style. In a more purist age, the original building might have been "listed", and the building of the spire might not have been allowed. In fact, some other English cathedrals lost their spires, either by collapse or by deliberate removal.

In Salisbury cathedral you can also see the oldest clock in England, dating from the late 14th century.

In any case, this is surely one of the most beautiful buildings in England. Painting by Constable

Wells Cathedral has a most peculiar construction which looks like an inverted arch above a normal one. This was built as an attempt to strengthen the structure after cracks appeared in the tower in 1338.

A picture taken in the cloister garden in Gloucester cathedral, showing the large windows, and the buttresses that take the thrust of the fan vaulting that forms the ceiling inside the cloisters.

Vaults

Here is a picture of the north aisle of Gloucester cathedral. Diagonal arches spring from the walls and the piers. Between these, vaults, parallel and perpendicular to the aisle, complete the roof. The transverse parts open the way for the pointed windows. This is a very simple vault. The later styles produced some very complicated designs, including the skewed lierne vaults in Lincoln cathedral. Here the apices of the bays of the north and south windows do not meet: they are offset by a fraction of a bay that looks, from a photograph, like about the golden ratio cubed, 0.236, but this could be purely coincidence. If you did not find the golden section elsewhere in this building, and preferably in other cathedrals of the time, you would not have evidence of deliberate use of this ratio.

Here in the west vaults of Gloucester cathedral we see the juxtaposition of two completely different styles, in the first two pictures. This would probably not be done today, though we cannot know what will happen to current buildings in a hundred years time. The plain vault dates from the 13th century, while the more complicated western part dates from the 15th century, having been built after the western towers fell down. The third picture shows a part of the south transept.

Looking up at these vaults we are reminded of the triangulation of a truss. The force of gravity acts in the plane of a truss, but here it is at right angles to the structure, which is why the arches are needed.

Fan Vaulting

Here are pictures of a part of the cloister of Gloucester cathedral. From the narrow piers in the walls, arches grow out like the branches of a tree, forming fan vaulting. At the top they support pieces of stone that are flat, apart from the carving. These are held in place by the inward thrust of the arches. Whereas a dome has positive curvature in both directions, these surfaces have negative curvature in one direction and positive in the other. In the second picture the architect has suggested the flow of the forces from the fan down into the arch. Is this realistic? Wouldn’t have been sufficient to have the three forces meeting at a point?

The fifth picture shows the external buttresses that make all this possible: in a sense the interior is a little fraudulent in that it looks as though the forces flow down into the wall. What does it matter – it looks good – one purpose of a religious building is to create an atmosphere inside that is conducive to worship. From this point of view, all else is subsidiary, including the outside. Question – Why does a tent need guy ropes while a church needs buttresses?

If you walk right round the cloisters, and look carefully at the vaults, you will spot some variations. On the south side, nearest the cathedral, the builders have made circular arcs that join along the centre line in a symmetrical manner. But on the west side of the cloister, the arcs on the west half of the vault are complete, while those on the east half are interrupted – in other words the west half was built first, and the east half was fitted to it. The effect is not obvious unless you are looking for it.

To the east of the cathedral, in Kings Walk, you can see a covered shopping area which echoes the fan vaulting. Unfortunately, this roof is a complicated array of steel tubes, which although easily understood and completely logical, looks a mess. The eye is given no guidance at all – it just does not know where to look. Better examples of modern design are shown later in this page.

Not far away, in Cirencester, you can see a nice example of fan vaulting in a side chapel of the splendid church. From the top of the tower, on a fine day, you can view the town and countryside.

Between Gloucester and Cirencester, if you leave the main road, you can view styles from pre-Norman onwards, in the villages of Brimpsfield, Syde, Winstone, Duntisbourne Abbots, Duntisbourne Rouse, Daglingworth, North Cerney, Bagendon, Rendcomb, Elkstone, Colesbourne and Coberley. Then there are the wool churches at Fairford, Lechlade and Northleach. Not one village lies on the A417, which follows the line of the Roman road, later called Ermin street, or at least it did, until recently built bypasses changed the route at several places, cutting fifteen to twenty minutes off journey times, and greatly benefitting the people of Cirencester and Latton. Another bypass takes the route around Brockworth, again with great improvement to life in the village.

Here are details from a church in Evesham. The builders make the stone seem to float like feathers in the air. Yet it is the same material that was used to build heavy looking medieval castles.

These two pictures were taken at Birmingham airport and Geneva airport. A similar style can be seen at Stansted airport and inside some parts of Heathrow airport. In a sense these supports represent fan vaulting simplified and taken to an extreme. The other extreme is the simple pillar and flat roof so often seen at petrol garages, such as the one in the next picture. The flat roof is usually made of I-beams.

Between the fan vaulting and the petrol garage we can place the mushroom headed columns of Maillart, which spread the load smoothly into the roof.

Here is a part of a footbridge between Balexert, a shopping centre, and Les Avanchets, a large apartment complex, in Geneva. The fanning out of the piers was more or less forced by the truss design, the alternative being four separate piers at each node of the bridge.

In this design the fan-out is taken to the extreme: there is no vertical part at all. Why do think this was done instead using a simple pier? Hint: look at the middle of the span.

Here are some example diagrams. Click here to skip. They show how a trabeate or beam building and a fan vaulted building are two extremes. In between are many variations, including Maillart’s mushroom pillars.

Buttresses

These buttresses outside the south aisle at Gloucester oppose the the thrust of the roof of the aisle. Though not as spectacular as the flying buttresses of Chartres or Notre Dame de Paris, they do the job. The little spires on the buttresses may be for decoration, or they be for extra weight to direct the thrust more steeply. Even if they are for decoration, they may have been copied from an example where they were functional in steering the thrust.

These sturdy buttresses are seen on the north side of the cloister garden in Gloucester cathedral.

Part of the cloister garden of Gloucester cathedral, showing the west and north sides. Note the small buttresses needed to take the thrust of the fan vaulting in the cloisters.

These buttresses are a part of the ruins of Bolton Abbey, which was built on a beautiful site near the River Wharfe. Bolton Abbey is one of many ecclesiastical ruins in Britain.

The tower of Gloucester cathedral is furnished with buttresses, one of which is visible here, going westward from the SW corner. Others are built into interior walls, like the one shown in the next picture.

Here are two views of the buttress that runs south from the SE corner of the tower. On the east side of the south transept you can see a similar buttress from the outside. Not surprisingly, the south wall of this transept leans outwards, having pushed by the buttress for several hundred years. You can find several other supporting features around the cathedral. Since the foundations are in ground that is below the water table, being near the river Severn, and not very elevated, problems are to be expected.

Note the great contrast between the upper and lower parts of the buttress. The upper part is a beam, supported by narrow pillars, both above and below, but the lower part spans the entrance to a small chapel, and requires an arch to support the beam which actually takes the thrust. Many details in such a building reveal existence of problems, and the thoughts that went into solving them.

The beautiful tower of Cirencester church has buttresses which go right down into the ground in the west wall. Because of difficulties with the ground, threatening the tower, this wall had to be taken down on the south side in order to add the buttresses. The NW and SW corners of the tower are also well buttressed. Should you climb the helical stairway to the top to see the splendid view of the town and country, you can be quite sure that the tower will stay upright.

There is actually something peculiar about these buttresses – they are straight. If you look at the page about the funicular you will see that the buttresses should logically curve towards the ground. In the case of Cirencester we can imagine that the builders wanted to anchor the buttresses as far from the tower as possible, in the hope of finding better ground.

Perhaps appearance entered into the design, since a window was required, and curving the buttress around the window would have looked rather strange. On the other hand, the builders might not have understood the flow of the forces at all, as everything seems to have been done empirically in the middle ages. In the first picture, we see that the buttress actually reaches the ground perilously near the corner of the building, but in fact there probably isn’t much thrust left in it by that point.

Here is a fine stone barn in the Cotswolds. The roof is heavy, being made of Cotswold limestone, which cannot be split into thin sheets. So the outward thrust of the roof, which behaves like a three pinned arch resting on the walls, is resisted by massive buttresses. Looking at the shape of the buttresses, you can see that the builders’ insights were sound, and that the outline imitates the funicular quite well. A nice piece of work.

These buttresses receive thrust from the south aisle of a church at Wotton in Gloucester, and indirectly from the nave as well. Note that a buttress cannot eliminate the horizontal component of thrust. All it can do is increase the vertical component, thus making the line of thrust steeper. This is why extra masonry or a statue was often added to the pier of a flying buttress, as well as above the outer half of the arch. The outward component of the thrust can only be resisted by an inward force, which is only counteracted finally when the buttress reaches the ground. The inward push of the ground on the buttress is cancelled by the diffuse tensile force in the ground under the building. In a sense, all forces in static objects comprise closed loops of tension and compression. This is not true of rockets and gas turbine engines, in which the momentum of the ejected gas creates a pressure on the engine.

Here we see two buttresses on the end of a building where there is no apparent thrust. What reasons can you think of for these additions?

The famous tower at Pisa never received the buttress treatment, whether for stylistic reasons or for structural reasons. It is one thing to buttress at a corner: another to push into a cylinder. In such a case there would probably have to be strong floors at the level of the buttress to spread the load. Digging to make foundations for a buttress would have weakened the ground on the side which could least afford it.

The exciting Wildwalk at Bristol includes a tropical area with a tented roof and trussed ends. Here we see at the bottom right how the support leans inwards, because the funicular can never become vertical. Next to Wildwalk is Explore At Bristol, which is a magnificent exploratory of engineering and science. Unfortunately, the road was too wide for the camera lens, and the camera was tilted, leading to converging verticals in the image.

Flying Buttresses

Here are some flying buttresses. These have sizable towers going well above the line of the flying buttresses, adding weight to the piers, changing the flow of the forces.

The flying buttresses at the lower left of this photograph are a part of the cathedral of Seville. Flying buttresses are not always outside the building; in the south aisle of Gloucester cathedral you can see examples cutting across the arches of the aisle.

Flying buttresses demonstrate clearly the difference between a buttress and a gravity dam. In a buttress the force is applied near the top: in a dam the force increases towards the bottom, and is purely horizontal. The vertical component on a buttress is the easy bit: it’s the sideways push that’s the problem.

This picture is of a part of Liverpool cathedral. The conical roof reaches almost to the ground, and the thrust is continued right to the foundations by the struts which hold up the roof. Exactly like the walls in a medieval cathedral, the walls of this cathedral play no part in taking the thrust of the roof. The structure is not a dome: the straight sloping beams are just that – beams. They experience bending moments, and are therefore quite thick. Unlike a horizontal beam, however, they experience thrust, and could in a sense also be called piers. They are giant roof rafters.

France has many beautiful Gothic cathedrals. These pictures of the cathedral at Chartres, from the south-east, show flying buttresses at the east end and on the south side. The first picture file is very large. Some of the buttresses are buttressed in their turn. The cathedral of Notre Dame in Paris has many buttresses also.

Here is a part of the beautiful city of Assisi, before the earthquake of 26th September 1997. The church at the right has some buttresses which are connected well below the roof-line. Why?

Here is another look at Assisi. Down in the plain, inside a huge basilica, you can find a little chapel that St Francis used. But he isn’t there, but his spirit can still be sensed in the town on the hillside.

More About Vaults

Here is one bay of the south aisle at Gloucester, showing the four intersecting vaults. The peculiar lighting comes from directional lamps that are spaced around the cathedral. As they are yellow, it is difficult to achieve a good coloured picture, especially on dull days when the incoming light is bluish.

Here are two of the vaults on the centre line of Gloucester cathedral. These could almost be regarded as stone trusses with all the parts held in compression by their weight. The third picture was downloaded with kind permission from Welcome to Isfahan, and shows a very different style of vaulting – much more symmetrical, and probably based on geometry rather than rule of thumb.

Perpendicular Style

The perpendicular work here at the choir end of the cathedral could hardly be more different from the Norman style. The material is the same – the feeling completely different.

The 14th century choir at Gloucester shows how much the technology had changed. In the "wool churches" of Gloucestershire, for example in Cirencester, Fairford, Lechlade and Northleach, you can see other fine examples of the lighter and more airy styles of building that replaced the Romanesque.

And of course in many Islamic buildings we see elegance and lightness of touch taken to great heights, in arches, vaults, piers and decoration. See Welcome to Isfahan.

A fundamental part of any mosque is the mihrab, which indicates the direction of Mecca. This sometimes has an arch shaped opening.

Some synagogues, too, have made great use of arches, as in Casale Monferrato. Southport new synagogue includes arched windows, likewise the Touro Synagogue. Park Synagogue has a dome.

In the Sikh Golden Temple also, we see domes and arches.

Almost 1000 years after the bringing of the Romanesque arch to England by the Normans, the magnificent Shri Swaminarayan Mandir at Neasden brought Hindu stone architecture with arches and domes.

The buildings are, of course, only the most visible manifestation of both the indigent and the incoming cultures. The English language has been enriched again and again by people from other lands – the Romans, the Vikings, the Normans being just three of the groups who came to England. And not just language – literature, mathematics, medicine, music, and science have all been given new life by imported ideas.

Some cultures, notably the nomadic ones, have left no legacy in stone, or even on paper, but their ability to create and express ideas in music and poetry has nevertheless influenced what we hear. (See Bartok and Kodaly, for example.) Technology enables us to hear music from all over the world without travelling, and even though we cannot understand its history and meaning, we can appreciate its structure and ornamentation, and enjoy the sound it makes.

No doubt, in future times, people will realise that the 20th century was another great period of enrichment of English culture by ideas and practices from overseas. At the same time, cultural memory can be long, and even today there are people who can say – "My ancestors came over with the Normans."

Buildings for religious worship often express most clearly what we see in many other buildings, namely that they are far more than just boxes to keep the weather out while people perform some activity. A building can be an expression of the ideas and ideals of the designers and builders, and of the users. In some trading estates you can actually see constructions which are indeed little more than large boxes.

But we can also find examples that are both elegant and functional. The medium is not the message: whether we build in brick, stone, wood, steel or concrete, we can create works ranging from the superb to the downright ugly.

Many pictures in this web-site are of houses and other small buildings, because these, as much as large and famous ones, express peoples’ tastes and aspirations. modified, of course, by the limitations set by their income. Like the larger buildings, even the smallest houses bear the imprint of their inhabitants’ personality.

One of the pleasures of architecture is the huge variety of solutions to the technical problems posed by the users’ requirements and the limitations of the laws of physics and the properties of materials. Many buildings appear to transcend these so well that we can easily forget that they weigh thousands of tons.

The great weakness of stone and brick as structural materials is their inability to take much tension, and their availability in only small pieces. The arch, the dome, and the vault, are the brilliant responses of people who were not willing to be imprisoned by these limitations. Not all cultures have made use of these structures. The "ancient Egyptians" and the "ancient Greeks", though possessing considerable mathematics, seem to have generally ignored the arch.

Looking at temples and shrines much further east, in Japan, one sees mainly beams and cantilevers. Many arched bridges there have intermediate supports which mean that these are beams and not arches. Some stone bridges were, however, built in gardens, often with steep gradients.

Given the preponderance of flat horizontal beams in the architecture, the number of arched beams is perhaps a little surprising, especially in garden bridges over little streams and ponds. But in a bridge which is a part of a carefully planned path around a garden, speed and economy were not the main determinants. By making an arch, especially a steep one, the designers gave the bridges a centre, encouraging people to stop and look at the view. The placement of the bridge was often chosen precisely for this reason.

In bridges that were actually built flat, corners or steps were often provided to slow people down, and hint at the places to stop and admire the view.

If you are not restricted to stone, you are freed from the tyranny of the arch, because you can employ tension. The chapel shown here has a roof based on wooden beams. From an engineering point of view, "tyranny" may be a suitable word, but from an aesthetic point of view, possibly not. Even in the few examples in this web-page, we can see a wide range of styles and techniques within the category of arches and domes.

Often it is the very restriction in possibilities which forces the creation of ideas and techniques. In music and poetry, the necessity of adhering to the logic of the piece, for example in key, metre, rhyme-scheme and so on, may cause problems which lead to innovative solutions. Without a structure, anything goes, and where do you even start? And how do you know when you’ve finished.

With the huge range of strong materials now available, designers on the smaller scales are freed from the coupling of form and function. Many kinds of domestic equipments, from radios to food mixers, and of course cars, are designed for appearance. And why not – people have to live with them. Few people would want to live with things looking like tiny Pompidou centres.

At the larger scales, however, it is hard to escape from the necessities of engineering. The original design for Sydney opera house used roof sections that looked rather like gothic arches. But the pointed shapes did not correspond with the distribution of forces, and considerable ingenuity was needed in order to create something that resembled the original design, and was reasonably practicable. "Ingenuity", of course, comes from the same root as "engineer". And "reasonably", of course, normally includes cost. The question of cost is not quite straightforward. Maillart won contracts on price: had his designs been rather more expensive, would they have been built? But if we always build the cheapest of everything, what would our world look like? What do you think about this question?

The problems in engineering are generally of a different kind, but they also can lead to innovation. And the result will very often have aesthetic quality. Art and technology are not necessarily as different as might be thought. C P Snow’s "Two Cultures" created a myth which was very persistent. Looking at some types of art, one might even think that some types of science and engineering have more beauty than those. But then, art does not have to be beautiful – it only has to express what is true for the artist.

To look at the details of large buildings, both internal and external, low-power binoculars are very useful.

These pages are entirely about the large and heavy artefacts that people have made to assist in living and travelling. But people who travel all the time, if they have dwellings at all, need ones that can be quickly built and taken down, and easily carried if re-used. Click A, B, C, and D for web-pages including a picture of a Kirghiz or Mongolian tent.

The walls of a Kirghiz tent are made using a large number of sloping strips of wood, with some horizontal hoops to help with rigidity. The roof is a dome, also braced with wood. The diagram below shows roughly how the walls are built. The diagram is made with straight lines for simplicity of programming, but the real thing uses smooth helices, with a few horizontal hoops to aid rigidity.

Such people do not leave grandiose ruins for future historians and tourists: their culture comes to us, if at all, in their influences on music and literature. We can hear this in music of eastern Europe, for example Bulgaria, Romania and Hungary, where the "east" has met the "west". These people may also express themselves in costumes, in the use of their animals, and of course in the type of social interactions they develop, which may be too subtle for the casual tourist to detect.

And even if, wherever we live, we have never seen a single foreign building, we have the benefit of ideas from all over the world. Even now, western scientists are re-discovering specialist medicinal techniques that have been used by many different cultures.