Descriptive Geometry and Computer Modelling in Support of Planning the Restoration of the Roof Covering of the “Dormition of the Mother of God” Cathedral in Varna ^†

Abstract

Preserving and restoring architectural monuments of symbolic national significance stand as an unequivocal priority for both local and state authorities. Indeed, with advancements in the technology, materials, and methods of work, there are some specific stages involved in the process of restoring historical buildings; however, maintaining their authentic form and impact poses a serious challenge, necessitating the development of innovative, non-standard technologies and the adaptation of a multifunctional methodology to achieve the desired outcome. The present study focuses on the restoration of the roof covering of the historical building of the “Dormition of the Mother of God” Cathedral in Varna, in terms of technological feasibility and cost-effectiveness. Proposed in this paper is a solution that strives to restore the magnificent roof in adherence to the heritage conservation principles by applying a genuine gold coating instead of retaining the previous dull goldish coating made from alkyd paint, yellow pigment, and gold dust. Through the implementation of descriptive geometry techniques and AutoCAD, followed by verification using Inventor, the study presents a feasible solution for accurately determining the surface area of the domes to be gilded.

1. Introduction

The restoration initiative initiated in 2019 for the iconic “Dormition of the Mother of God” Cathedral in Varna, which is the first grandiose church in Bulgaria following the country’s liberation in 1878, reaffirms Bulgarians’ sense of national pride and self-worth. The construction of the cathedral was made possible through contributions from both the people and the state. Positioned within the city’s central park area, this majestic building invariably dominates the landscape with its substantial proportions, five domes above the main structure and a dome-crowned belfry tower. The cathedral also boasts intricate stone façade carvings, vibrant stained-glass windows, and a spacious interior central space adorned with elaborate frescoes. Its imposing presence has become an integral part of the city’s skyline, serving as its emblematic feature and a true emblem of distinction [1].

A crucial aspect of its current refurbishment involves the restoration of the roof slopes and domes, which have not been repaired for over twenty-five years.

The project entails removing the existing sheet metal roof coverings from the domes and roof slopes and replacing them with new copper sheeting. The undertaking extends further to include the gilding of the domes.

The purpose of the present paper is to establish the exact quantity of the copper sheets required for the restoration of the cathedral’s roof structure, with an exclusive focus on the cubes, which, in principle, are non-developable surfaces, necessitating a meticulous calculation to ensure optimal estimation of the necessary amount of gold required for gilding.

2. Exposition

Gilding the domes of Orthodox churches is an ancient and revered tradition that holds great significance. The domes serve as the church’s main symbol of pride, evoking a sense of celestial transcendence in those who behold them. Found across different cultures, beliefs, canons, and geographical locations of the churches is a great variety of dome shapes—pear-shaped, helmet-shaped, bulbous, or hemispherical—constructed over round or polygonal (multi-angular) bases. These domes possess exceptional structural strength, enabling them to span vast open spaces without the need for internal support [2].

Bulgarian traditions in the construction of churches’ domes closely mirror those of Orthodox Russian churches, with a prevalent preference for bulbous shapes. This can be observed in the dome of the bell tower and the four small cubes of the Cathedral in Varna. An exception, however, is made for the central dome, which takes on a graceful hemisphere shape.

Throughout the years, the church has undergone numerous renovations, each adding distinct architectural elements, but it was during the third stage of renovation, carried out from 1941 to 1943, when the bell tower was extended and enhanced by an additional 13 m, and the existing four small side cubes were replaced with the new ones, boasting improved proportions and dimensions. The central dome also underwent a process of renewal. Despite the passage of time, the modifications made to the roof’s dimensions and construction have remained unchanged.

During the restoration’s fifth stage in 1994, running repairs were completed on the Cathedral’s roof slopes and domes, and a golden coating was achieved via a special technology involving a mixture of alkyd paint, yellow pigment, and gold dust (Figure 1) [3].

Despite the improved general appearance, subsequent observations revealed that this technique proved ineffective as a substitute for traditional gilding.

Accordingly, in the current sixth restoration of the Cathedral, the primary focus has been given to the renovation of the compromised roof structure, and as for the refurbishment of the domes, which will be gilded, envisaged is the application of a new copper sheet with a thickness of 0.55 mm. The under-dome wreath (base) of the four smaller domes will also be renewed using sheet metal of the same thickness. Gilding will be further applied to the crosses that sit atop the domes.

The roof slopes will be renewed and covered with factory-treated copper sheeting with a thickness of 0.55 mm and a permanent colour that will not change over time. Such a method of treatment effectively prevents the occurrence of uncontrolled variations in the crude copper sheet’s colour [4].

Accomplished, in line with the study’s objectives, will be an expanded (development) view of the highest dome of the Cathedral, specifically that of the bell tower.

The bell tower’s dome has a distinctive bulb shape, which falls under the group of non-developable surfaces. These surfaces are characterized by generators that are not straight lines, parallel or intersecting at a single point like cylinders or cones. The unfolding of non-developable surfaces cannot be accurately determined as the starting material undergoes plastic deformation in two directions during the process of manufacture. From this perspective, the expansions can only be approximated. However, if the unfolded surface is divided into as many parts as is reasonable and permissible, the approximation will be as close to the actual cylindrical shape as possible. In the case hereto discussed, the bulb-shaped bell tower is divided into 60 equal parts, and its elements are not subjected to plastic deformation, which allows for a more accurate calculation of the required copper sheet and gold warak.

Undoubtedly, the most sensible approach for preparing the unfolding is to utilize meridian sections, as this aligns with the dome’s construction (Figure 2).

In order to retrace the unfolding, it is necessary to have both projections of the surface to be unfolded. By constructing 30 meridian planes that form equal angles to each other through the dome’s axis of symmetry, or by employing a geometric method involving a bundle of planes intersecting at the axis of symmetry, the surface can be divided into 60 equal parts (Figure 2 and Figure 3). In reality, the dome is composed of 60 elements that form its surface collectively. Built, in addition, are the parallels that divide the dome’s surface into approximately equal parts and created, through the points of division, are the planes parallel to the equator of the dome (Figure 3).

To illustrate the unfolding, a straight line is initially drawn, which is taken as the base. Utilized herein is the equator of the dome (Figure 4) or its most prominent section. The length of this line should match the perimeter of the dome’s equator. It is then divided into 2n equal parts which, in our case, amounts to 60 pcs (Figure 5). Drawn from the midpoint of the resulting divisions is a perpendicular line plotted onto which the length of each of the segments is obtained at the final generator that shapes the dome (Figure 6). The advantage of employing an automated design software, such as Auto CAD, is that it enables ready measurement of the actual length of every arc.

The width of each parallel is measured from the horizontal projection, while its length is symmetrically distributed and applied to the vertical line, which serves as the axis of symmetry for the unfolded 1/60 part of the dome. In the provided representation, these measurements are colour-coded (Figure 7).

Displayed in Figure 8 is the unfolding of 1 sector out of the 60 and noticed in the Properties panel of the AutoCAD drawing program is the enclosed section’s face and its calculated surface area − Area = 12,642.1 cm².

Thus, the surface area of the bulb-shaped cube can be easily calculated as 75.85 m².

Individual elements of the cube are connected using flange joints (Figure 9). The proper length is necessary for these joints to enable the flanges to be folded in accordance with their design. The method adopted for the execution of the flange seam involves a technique that requires double folding the sheet metal (Figure 9) [5].

A total area of 131.0526 m² was necessary for the copper sheet used in the construction of the bell tower dome.

When determining the amount of gold needed to cover the dome’s surface, no allowance is made for gilding in the fold of the flange seam, since the gold coating is applied after the final fabrication of the copper sheet cube and all seam connections already made (Figure 10). It can be stated subsequent to the calculation of the dome’s face that the surface area intended for gilding is 101.05 m², including the unavoidable and permissible over-expenditure of gold which is normally within 15% due to the necessary overlap of the applied gold leaf (warak).

Upon completion of the necessary calculations, it was concluded that approximately 308 g of gold would be required for the gilding of the bell tower.

The gold warak used for this project was sourced from a reputable German company and was 23.75 carats. The gold leaf dimensions are 80 × 80 mm and are organized into booklets containing 25 sheets of tissue paper. A total of 12 booklets are combined to form a 300 sheet booklet.

Once the gilding process is finalized, a careful examination of the surface is conducted under oblique lighting to guarantee that no areas have been left without being gilded.

Gilding requires the initial construction of a scaffolding equipped with shrink-wrapping frames to ensure that workers can effortlessly reach any spot on the dome. It is also essential to construct a protective enclosure, referred to as chapiteau, to cloak the scaffolding, which, in turn, will isolate the dome from its surroundings, providing a protected environment that is void of winds, dust, rain and direct sunlight. To facilitate the gold adhesion process, the temperature within the chapiteau must be carefully controlled. To achieve this, air conditioners are installed beneath the protective cover, while moisture absorbers help maintain appropriate humidity levels.

To enhance the adhesion strength, the copper sheet is carefully treated with fine sandpaper prior to use. The chips are removed from the surface, and then it is de-greased before a primer is applied. These steps thus prepare the surface for the subsequent application of a varnish coating, followed by the gold warak itself [6,7].

Once the gilding process is complete, the protective coating encasing the dome is removed following a period of at least three weeks.

When dealing with non-folding surfaces that require identification of the surface face, various software products, such as SolidWorks and Inventor can be effectively utilized [8,9,10]. The methodology involves drawing a plane curve, representing the dome’s profile, and obtaining its exact shape through the frontal projection in the architectural drawing (Figure 2). This shape is then rotated around an axis to obtain the dome’s spatial form. Measured thereupon is the face of the resultant surface (Figure 11).

Employed for the purposes of the present study was Inventor, a product of Autodesk. By simulating the required surface, the surface face of the dome was obtained, resulting in a measurement of 76.415 m².

The surface area of the dome, as determined through descriptive geometry methods, measures 75.85 m². Despite the slight divergence, less than 1%, it is still perceptible. The discrepancy emerges from the utilization of the classical method to ascertain the surface’s face, leading to an unfolding of a polyhedron comprised of 60 identical segments. In practical scenarios, the geometric method proves more applicable, primarily due to the use of copper sheet metal to cover the domes, as it does not undergo plastic deformation, while the model simulated in Inventor represents a surface (mesh model) and is not composed of a finite number of equal segments.

3. Conclusions

The restoration of historically significant buildings is a process of utmost importance, both in terms of its relevance and complexity, involving specialized knowledge and skills. The renovation of historical buildings and monuments plays a pivotal role in safeguarding our ancestral heritage. It is imperative, therefore, that such a process should address problem areas while also prolonging the operational lifespan of the structures, without compromising their technical characteristics or aesthetic appeal.

Restoration becomes mandatory for those landmark buildings that have lost their unique appearance and inherent merits.

Advanced in the present paper is a method for unfolding (development) the dome surface and accurately calculating the required amount of copper sheet needed for its creation along with a precise estimation of the quantity of gold warak necessary for gliding the dome of the bell tower at the Cathedral in Varna.

Conducted to that effect was a comparative analysis of two methods for determining the face of the dome surface. Through a meticulous examination, the applicability of these methods was evaluated, ensuring that the chosen approach is both effective and efficient.