Arch calculation: features, rules and examples. I don't know what it's called, but it's cute. Development in Gothic architecture

A pointed vault consisting of two segmental arches intersecting each other.

General description of Gothic architecture

The internal space, the ethereal air environment into which a person enters, acquired in the Gothic cathedral the power of artistic influence that heavy stone masses had in the East, and architectural forms carved from stone in Greece.

In terms of capacity and height, Gothic cathedrals are significantly superior to the largest Romanesque cathedrals.

Construction diagram of a Gothic cathedral

The most striking technical means used by Gothic are pointed arches and a frame system with a ribbed vault. They give the cathedral a special appearance and sustainability. Buttresses and flying buttresses are part of the outer frame structure of the cathedral, being not only decoration, but also a load-bearing element, taking a serious load from the outer walls.

The history of Gothic architecture

Gothic style originated in the 12th century in northern France. In subsequent centuries it spread to many European countries.

In the 11th and 12th centuries, the formation of the urban bourgeoisie became the impetus for the development of culture and economy. On this wave, in cities, widespread construction of buildings of a new archetype began, which, after a couple of centuries, began to be called Gothic. The name of this style belongs to the Italian architect, painter and writer Giorgio Vasari. Thus, he expressed his attitude towards the architectural style, which seemed to him rude and barbaric.

Gothic cathedrals were built not without taxes from the townspeople. Often, construction was interrupted for decades during wars and natural disasters. Many cathedrals remained unfinished. Some cathedrals began to be built in one style and ended in another. For example, Chartres Cathedral (1145-1260), decorated with two stylistically different towers.

The main preference was given to the construction of large cathedrals, churches and castles.

In the architecture of Western Europe, Gothic can be divided into 3 types, corresponding to different time periods:

Early Gothic or pointed (1140-1250). The transition from Romanesque to Gothic style. This has been happening since the middle of the 12th century in France, England and Germany. It is characterized by powerful building walls and high arches.
High (mature) Gothic. XIII-XIV centuries (1194-1400) Improvement of early Gothic and its recognition as the urban architectural style of Europe. Mature (high) Gothic is characterized by frame construction, rich architectural compositions, a large number of sculptures and stained glass.
Late Gothic (flaming). XIV century 1350-1550. The name comes from the flame-like patterns used in the design of buildings. This is the highest form of Gothic architecture, where the main focus is on decorative elements. Ornaments in the shape of a “fish bladder”. This period is characterized by the development of sculptural art. Sculptural compositions not only instilled religious feelings in people by depicting scenes from the Bible, but also reflected the life of ordinary people.

Unlike Germany and England, late Gothic in France, devastated by the Hundred Years' War, did not receive widespread development and did not create a large number of significant works. The most significant late Gothic buildings include: the Church of Saint-Maclou (Saint-Malo), Rouen, Moulins Cathedral, Milan Cathedral, Seville Cathedral, Nantes Cathedral.

In the homeland of Gothic, in France, the following stages of this style are distinguished:

— Lancet Gothic (early) (1140-1240)

- Radiant Gothic or Rayonnant - “shining style” (1240-1350)

The style of Gothic architecture that developed in France after the 20s of the 13th century is called “radiant” - in honor of the ornament in the form of sun rays typical of that period that adorned the graceful rose windows. Thanks to technical innovations, the forms of openwork stone window decoration have become richer and more refined; complex patterns were now made according to preliminary drawings made on parchment. But despite the increased complexity of the ornaments, the decorative structure still remained two-dimensional, devoid of volume.

— Flaming Gothic (late) (1350-1500)

In England and Germany, slightly different stages of the Gothic style in architecture are distinguished:

— Lanceolate Gothic. 13th century A characteristic element is the diverging bundles of ribs of the vaults, reminiscent of a lancet.

Cathedral in the city of Durham. Lanceolate Gothic

Interior of the Cathedral in Durham. "Blooming bunches" of ribs. Lanceolate Gothic

— Decorated Gothic. 14th century Decorativeness replaces the severity of early English Gothic. The vaults of Exeter Cathedral have additional ribs, and it seems as if a huge flower is growing above the capitals.

Exeter Cathedral. Decorated Gothic

Interior of Exeter Cathedral. Decorated Gothic

— Perpendicular Gothic. XV century. The predominance of vertical lines in the design of decorative elements. In Gloucester Cathedral, the ribs spread out from the capitals, creating the semblance of an open fan - this is called a fan vault. Perpendicular Gothic existed until the beginning of the 16th century.

— Tudor Gothic. First third of the 16th century. During this period, buildings were built that were completely Gothic in shape, but almost all, without exception, were secular. The most important distinguishing feature of Tudor buildings can be considered the use of brick, which rather suddenly spread throughout England. A typical Tudor manor (eg Knole or St James's Palace in London) is made of brick or stone, with a gate tower. The entrance to the courtyard is through a wide, low arch (Tudor arch), with octagonal towers often built on the sides. Often above the entrance there is a large family coat of arms, because many families had only recently acquired aristocratic status and wanted to emphasize it. The roof is often almost entirely covered with decorative turrets and chimneys. By that time, castles were no longer needed, so fortifications - towers, high walls, etc. - they were built purely for beauty.

Sondergothic (from German Sonder - “special”) is a late Gothic style of architecture that was in fashion in Austria, Bavaria and Bohemia in the 14th-16th centuries. The style is characterized by massive, majestic buildings and carefully carved wood details for interior and exterior decor.

Features of early Gothic. Main distinguishing features.

Tall lancet windows without masking (France), with masking and without crypt (Germany)
Facades of 2 towers with round windows (rosas). Rosas and the facade of Notre Dame in Paris become models for numerous cathedrals
Masverk, round Gothic window and wimpers of the highest sophistication
Important glass paintings
Wall division 4-zone
Round columns with 4 thin service columns
Rich ornamentation of capitals
Exceptionally pointed arches

Features of mature Gothic. Main distinguishing features.

Instead of walls, stained glass windows with paintings are installed. After replacing the shed roofs of the side naves with hipped and hip roofs, it is possible to provide rear windows and triforia (Cologne). round upper windows
Wall division 3-zone
Thin dividing walls
A striving upward that requires double (Chartres 36 m, Beauvais 48 m) and triple flying buttresses
Composite columns (beam-shaped)
Semicircular arches
4-part vault
The roofs of the towers are openwork

Features of late Gothic. Main distinguishing features.

Low upper window openings or reducing the size of windows, as well as round windows along with lancet windows with rich openwork ornaments
Higher arcades
More decoratively rich (Isabella style from 1475, Plateresque style - a combination of Eastern and Moorish influences)
Openwork ornament in the form of a fish bladder (Cathedral of Amiens 1366-1373)
The middle nave is higher than the side ones and there are fewer dividing elements between the naves. In Germany there is no transverse nave at all
The columns acquire a more simplified profile. round posts are installed far from one another
There is no capital on the service columns or there are on separate columns
Large arches - keeled (already Renaissance)
Star or reticulate vault and vault with interlocking ribs with pear-shaped profile
Triforium missing
Roofs with domes

Windows in Gothic architecture

The partition walls of the grass and choirs are filled with windows with colored glass, and the pediment walls of the main and side naves are filled with rosettes. The openwork Gothic ornament (masswerk) plays a particularly important role in architecture.

Massverk

Rose gothic cathedral understood as a pattern that fills round window, and like a celestial body. In the decoration of the rose, the speculative mindset of medieval thinking was clearly reflected: all lines are brought to a clear order (unlike the Muslim ornament), ornamental motifs are born one from the other, small circles along the edges are subordinated to the movement of the main rods.

Walls in Gothic architecture

The poetic fiction that is so striking inside the cathedral finds explanation outside. Openwork walls are held back by a complex exterior engineering design- buttresses. The contrast of strong bones with light infill became the cornerstone of Gothic architecture. It was reflected in the disappearance of the stone planes of the walls, replaced by openwork windows between the pillars, and in the rib vault, and in the triforium, and finally, in the supporting arches thrown from the bases of the vaults to the buttresses, the so-called flying buttresses, with their mass reduced to a minimum.

Doors (portals) in Gothic architecture

The lower tier of the façade is occupied by perspective portals. The doors are framed at the bottom with statues slightly larger than the height of a man. They greet him at the entrance with a friendly look, sometimes with a smile. The portals are framed by high pointed arches with a round rose in the middle. The proportions are brought to the extreme degree of harmony and delicacy. Sculptural decoration of portals, wimpers, consoles.

Conclusion

The development of Gothic art was brought to life by the rise of urban culture, the desire for free social life and mental activity. But many of these ideals, given the preservation of an unshakable feudal order throughout Europe, could not be realized. In the 13th century, a struggle between the petty and large bourgeoisie began in the communes, and royal power began to interfere more in the life of cities. Naturally, in the fragile organism of the new society, a desire to canonize what had been achieved could easily awaken. It replaced living creativity with theological accounting.

Material from Wikipedia - the free encyclopedia

Lancet or broken arch- a type of architectural arch, which is a figure of two semicircular arches intersecting at a certain angle. It is one of the characteristic construction techniques of Gothic architecture.

Origin and borrowing

The origin of the pointed arch dates back to the 6th century, when it gradually began to be used on the basis of special calculations in the architecture of Cairo. Since the 7th century, the pointed arch has been used by the architects of Alexandria. Calculations were originally made on the basis of a triangle drawn on the diagonal of a square-based pyramid, in which a vertical plane drawn from the apex parallel to the side of the base creates an equilateral triangle.

In architecture eastern countries and Byzantium, semi-circular and pointed arches were used simultaneously, with pointed arches being more often used in the architecture of Cairo and Persia. Sails and spheroidal tromps were erected here on broken arches. The Crusader states, which arose at the beginning of the 12th century on the territory of the Levant, began to use broken arches, common here, in the architecture of their buildings. At the same time, the borrowing of the pointed arch shape by European, primarily French, architects occurred, which was the result of the development of pilgrimage to eastern shrines and the implementation of the first crusades. It is believed that the architects of Cluny Abbey, who created their own architectural school, were the first to borrow and use the pointed arch.
The borrowing of the pointed arch occurred within the framework of Romanesque architecture that was dominant in Europe, so the form of broken arches appears here as part of buildings that were Romanesque in style. As Auguste Choisy wrote, “beginning in 1100, Romanesque architects made extensive use of the pointed arch, showing an amazing understanding of the advantages that could be derived from its weakened expansion”. In his opinion, Gothic architects adopted the broken arch from the Romanesque from imitation, initially without even fully realizing its static advantages. That is why in early Gothic architecture the pointed arch was initially used along with the semicircular arch. Similar combinations are clearly visible, for example, in the design of the choirs of the Noyon Cathedral (XII-XIII centuries) and the Church of the Abbey of Saint-Germain-des-Prés (XI-XII centuries).
In the triforium of the Church of Saint-Germain-des-Prés, the pointed arch is present solely for decorative purposes, and in the upper and lower main floors of the choir it is used only to align the height of the locks of the rounded arches with the locks of the straight part of the plan. It was the desire to install the cheek and diagonal arches of the vaults at one level that prompted Romanesque and then Gothic architects to introduce a broken arch shape into cross vaults, built on the basis of a semicircular diagonal arch. It can be said that until the 13th century, Gothic cross vaults, erected on ribs, had mainly a semicircular outline, rather than a pointed one. As Eugene Viollet-le-Duc wrote, “In all Cluny and Cistercian architectural monuments built in Palestine before the 13th century... using a pointed form in the construction of arches, the Romanesque system of construction is still preserved. But in none of these structures is the pointed arch used to modify the Roman cross vault... But as soon as it is introduced into French provinces north of the Loire, a pointed arch connects with the vault and modifies it" .

Development in Gothic architecture

Having borrowed the pointed form of the arch, French architects eventually completely replaced the semi-circular one in the construction of vaults and domes, one of the first examples of which is the vaults of the narthex of the Basilica of St. Mary Magdalene in Vézelay Abbey, built in 1135.

The pointed arch allowed Gothic architects to design vaults more freely on a rectangular base, while carefully observing the principle of proportionality.

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Notes

Literature

Viollet-le-Duc, Eugene Emmanuel. Encyclopedia of Gothic Architecture / trans. from fr. S. Batalina. - M.: EKSMO - Our Word, 2013. - P. 335-348. - 512 s. - (World Heritage). - ISBN 978-5-699-60674-0.
Choisy, Auguste. History of architecture / trans. from fr. E. G. Denisova. - M.: Publishing House of the All-Union Academy of Architecture, 1937. - T. II. - 694 s.

Excerpt characterizing the pointed arch

When it was announced to Napoleon with due caution that Moscow was empty, he looked angrily at the person who reported this and, turning away, continued to walk in silence.
“Bring the carriage,” he said. He got into the carriage next to the adjutant on duty and drove to the suburbs.
- “Moscow deserte. Quel evenemeDt invraisemblable!” [“Moscow is empty. What an incredible event!”] he said to himself.
He did not go to the city, but stopped at an inn in the Dorogomilovsky suburb.
Le coup de theater avait rate. [The end of the theatrical performance failed.]

Russian troops passed through Moscow from two o'clock in the morning until two o'clock in the afternoon, carrying with them the last residents and wounded who were leaving.
The biggest crush during the movement of troops occurred on the Kamenny, Moskvoretsky and Yauzsky bridges.
While, bifurcated around the Kremlin, the troops hid on the Moskvoretsky and Kamenny bridges, huge number The soldiers, taking advantage of the stop and the crowded conditions, returned back from the bridges and stealthily and silently snuck past St. Basil's and under the Borovitsky Gate back up the mountain, to Red Square, where, by some instinct, they felt that they could easily take someone else's property. The same crowd of people, as if for cheap goods, filled Gostiny Dvor in all its passages and passages. But there were no tenderly sugary, enticing voices of the hotel palace, there were no peddlers and a motley female crowd of buyers - only the uniforms and greatcoats of soldiers without guns, silently leaving with burdens and entering the ranks without burdens. Merchants and peasants (there were few of them), as if lost, walked among the soldiers, unlocked and locked their shops, and themselves and the fellows carried their goods somewhere. Drummers stood on the square near Gostiny Dvor and beat the collection. But the sound of the drum did not force the robber soldiers to run to the call, as before, but, on the contrary, forced them to run further away from the drum. Between the soldiers, along the benches and aisles, people in gray caftans and with shaved heads could be seen. Two officers, one in a scarf over his uniform, on a thin dark gray horse, the other in an overcoat, on foot, stood at the corner of Ilyinka and talked about something. The third officer galloped up to them.
“The general ordered everyone to be expelled now at any cost.” What the hell, it doesn't look like anything! Half the people fled.
“Where are you going?.. Where are you going?” he shouted at three infantry soldiers who, without guns, having picked up the skirts of their greatcoats, slipped past him into the ranks. - Stop, rascals!
- Yes, please collect them! - answered another officer. – You can’t collect them; we have to go quickly so that the last ones don’t leave, that’s all!
- How to go? they stood there, huddled on the bridge and didn’t move. Or put a chain so that the last ones don’t run away?
- Yes, go there! Get them out! – the senior officer shouted.
The officer in the scarf got off his horse, called the drummer and went with him under the arches. Several soldiers began to run in a crowd. The merchant, with red pimples on his cheeks near his nose, with a calmly unshakable expression of calculation on his well-fed face, hastily and dapperly, waving his arms, approached the officer.
“Your honor,” he said, “do me a favor and protect me.” It’s not a small matter for us, it’s our pleasure! Please, I’ll take out the cloth now, at least two pieces for a noble man, with our pleasure! Because we feel, well, this is just robbery! You're welcome! Perhaps they would have posted a guard, or at least given a lock...
Several merchants crowded around the officer.
- Eh! it's a waste of time to lie! - said one of them, thin, with a stern face. “When you take off your head, you don’t cry over your hair.” Take whatever you like! “And he waved his hand with an energetic gesture and turned sideways to the officer.
“It’s good for you, Ivan Sidorich, to speak,” the first merchant spoke angrily. - You are welcome, your honor.
- What should I say! – the thin man shouted. “I have a hundred thousand goods in three shops here.” Can you save it when the army has left? Eh, people, God’s power cannot be broken with one’s hands!
“Please, your honor,” said the first merchant, bowing. The officer stood in bewilderment, and indecision was visible on his face.
- What do I care! - he suddenly shouted and walked with quick steps forward along the row. In one open shop, blows and curses were heard, and while the officer was approaching it, a man in a gray overcoat and with a shaved head jumped out of the door.
This man, bending over, rushed past the merchants and the officer. The officer attacked the soldiers who were in the shop. But at that time, terrible screams of a huge crowd were heard on the Moskvoretsky Bridge, and the officer ran out onto the square.
- What's happened? What's happened? - he asked, but his comrade was already galloping towards the screams, past St. Basil the Blessed. The officer mounted and rode after him. When he arrived at the bridge, he saw two cannons removed from their limbers, infantry walking across the bridge, several fallen carts, several frightened faces and the laughing faces of soldiers. Near the cannons stood one cart drawn by a pair. Behind the cart, four greyhound dogs in collars huddled behind the wheels. There was a mountain of things on the cart, and at the very top, next to the children's chair, a woman was sitting with her legs turned upside down, screaming shrilly and desperately. The comrades told the officer that the scream of the crowd and the squeals of the woman occurred because General Ermolov, who drove into this crowd, having learned that the soldiers were scattering among the shops and crowds of residents were blocking the bridge, ordered the guns to be removed from the limbers and an example was made that he would shoot at the bridge . The crowd, knocking down the carts, crushing each other, screaming desperately, crowding in, cleared the bridge, and the troops moved forward.

Meanwhile, the city itself was empty. There was almost no one on the streets. The gates and shops were all locked; here and there near the taverns lonely screams or drunken singing could be heard. No one drove along the streets, and pedestrian footsteps were rarely heard. On Povarskaya it was completely quiet and deserted. In the huge courtyard of the Rostovs' house there were scraps of hay and droppings from a transport train, and not a single person was visible. In the Rostov house, which was left with all its good things, two people were in the large living room. These were the janitor Ignat and the Cossack Mishka, Vasilich’s grandson, who remained in Moscow with his grandfather. Mishka opened the clavichord and played it with one finger. The janitor, arms akimbo and smiling joyfully, stood in front of a large mirror.

An arch formed by two convex semi-arches intersecting at an angle at the apex and outlined from two or more centers by arcs with radii of more than half the span length

(Bulgarian language; Български) - arrow-shaped [island] arc

(Czech language; Čeština) - hrotity oblouk

(German; Deutsch) - Spitzbogen

(Hungarian; Magyar) - csúcsív boltív

(Mongolian) - suman guldan

(Polish language; Polska) - łuk strzelisty

(Romanian language; Român) - arc ogival

(Serbo-Croatian language; Srpski jezik; Hrvatski jezik) - gotski luk

(Spanish; Español) - arco ojival; arco ojivo

(English language; English) - equilateral pointed arch; Gothic arch

(French; Français) - arc brisé; arc en ogive

Source: Construction Terminology Dictionary in 12 languages

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