Rampant Arch and Its Optimum Geometrical Generation

Cristina Velilla,Ignacio Zavala,Carlos San-Antonio-Gómez,Francisco Manzano-Agugliaro,Francisco G Montoya,Alfredo Alcayde

doi:10.3390/sym11050627

Cristina Velilla, Ignacio Zavala + Show 4 more

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https://doi.org/10.3390/sym11050627

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Abstract

Gothic art was developed in western Europe from the second half of the 12th century to the end of the 15th century. The most characteristic Gothic building is the cathedral. Gothic architecture uses well-carved stone ashlars, and its essential elements include the arch. The thrust is transferred by means of external arches (flying buttresses) to external buttresses that end in pinnacles, which accentuates the verticality. The evolution of the flying buttresses should not only be considered as an aesthetic consideration, but also from a constructive point of view as an element of transmission of forces or loads. Thus, one evolves from a beam-type buttress to a simple arch, and finally to a rampant arch. In this work, we study the geometry of the rampant arch to determine which is the optimum from the constructive point of view. The optimum rampant arch obtained is the one with the common tangent to the two arches parallel to the slope line. A computer program was created to determine this optimal rampant arch by means of a numerical or graphical input. It was applied to several well-known and representative cases of Gothic art in France (church of Saint Urbain de Troyes) and Spain (Cathedral of Palma de Mallorca), establishing if they were designs of optimal rampant arches or not.

Highlights

The rampant arch is an arch whose starts, in walls or buttresses, are located at different levels, often with a considerable difference in height [1]
The most common rampant arch used in the flying buttresses of most well-known Gothic cathedrals is the one formed by a single circumferential arch [4]
According to Viollet-le-Duc (1854) [5] there are two types: flying buttresses in which the center of the circumference is in the wall (Figure 1A), and flying buttresses in which its center is displaced toward the interior of the building (Figure 1B)

Summary

Introduction

The rampant arch is an arch whose starts, in walls or buttresses, are located at different levels, often with a considerable difference in height [1] It was used extensively in Gothic architecture to shape the buttress, and its function was to transmit the thrust of the vaults to the buttresses and these to the foundations [2]. The most common rampant arch used in the flying buttresses of most well-known Gothic cathedrals is the one formed by a single circumferential arch [4]. The first are the oldest flying buttresses, while the second are the most used because, from a mechanical point of view, they perform better than the first [6]

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