Are Vauban’s Geometrical Principles Applied in the Petrovaradin Fortress?
There is a widespread opinion in different sources, ranging from popular to scientific, that the project of the Petrovaradin Fortress was conceived under the influence of the most important European military engineer and innovator of the time, Sebastien de Vauban. By examining the historical context as well as by comparing Vauban’s geometrical methods for determination of the fortification master line (la ligne magistrale) with Austrian plans and the actual state of the Petrovaradin fortress, especially its Wasserstadt part, we have examined how well-founded this claim is.
KeywordsFortress design Star-fortress Vauban Geometrical construction Regular polygons Geometrical analysis Master line Petrovaradin Fortress
L’art de fortifier ne consiste pas dans les règles et les systèmes, mais uniquement dans le bon sens et l’expérience (The art of fortifying does not consists in rules and systems, but only in common sense and experience)
Sebastien le Prestre de Vauban (1633–1707)
Controversial data regarding the origin of the Petrovaradin Fortress design and its authorship have surrounded this aspect of the fortress history for many years, ranging from scientific, popular, unofficial and colloquial accounts to legends and myths retold persistently enough to enter even the official sources. There are numerous copies of the plans of the Petrovaradin fortress (over 200 in the Austrian State Archive) based on the built state of works, or done for a particular stage in the reconstruction, but the original conceptual blueprint is unknown. The story of the Petrovaradin Fortress invariably brings up the name of Sebastien le Prestre de Vauban (1633–1707) who gained fame by improving fortification systems and contributed significantly to the development of fortress construction techniques, which remained dominant and admired until the twentieth century.
Vauban’s stamp on design of the Petrovaradin Fortress is given varying importance in different sources—from bold claims that the project was his own (Lukić 1992) (a frequent and persistent datum that can be found in most brochures on Petrovaradin and Novi Sad), via official historical sources that his design was developed into detailed plans by several military engineers during Austrian reign (Marković 1984; Gajić 2003) to unfounded, though exciting and compelling accounts in which Austrian engineers (or Prince Eugene of Savoy himself) ‘stole’ the design from Vauban (Milković 2003). However, whether and to which extent Vauban’s doctrine was known and respected can be determined by means of comparative analysis of the design of the fortress and Vauban’s geometrical principles. It was our aim to apply these analyses to confirm or reject the claim that Vauban is the actual or conceptual author of this piece of military architecture.
The Petrovaradin Fortress: Position, Function, Significance
‘Gibraltar on the Danube’, as the Petrovaradin Fortress is often called, is the largest and best preserved building out of 284 fortifications in Serbia (comprising some forty fortresses and preserved fortified towers and monasteries) (Deroko 1964). Ever since the thirteenth century, it was a strategically important military fortress, which purpose it will serve for the next six centuries. It is situated on the banks of the Danube, on the rock of Petrovaradin (Novi Sad, Serbia) from which it radiates down towards the Pannonian basin. In its current state it is an impressive example of the traditional European style of fortification planning and construction that was dominant in seventeenth and eighteenth centuries and was developed under a resounding influence of the French, Italian and Flemish schools of military architecture. Due to gradual, evolutionary building interventions over a long period of time, the fortress acquired its actual form in the year 1780, which coincides with the end of the reign of Maria Theresa when the last phase of the construction of the complex of buildings on the right bank of the Danube was completed. It was placed under state protection in 1948, and declared a Spatial Cultural-Historical Unit of Great Importance in 1991.
In the second half of the nineteenth century, with the Austro-Hungarian Compromise (1867) and the weakening of the Turkish Empire, the importance of this fortification declined, so that its purpose ceased to be strictly military. In the twentieth century, many military buildings within the fortress became purely civilian, housing the Museum of Novi Sad, the Historical Archive, the Academy of Arts with accompanying studios, the Magistrate building, the Planetarium, as well as numerous bars and restaurants. The larger half of the northern complex still serves its military purpose. The Petrovaradin Fortress has recently become popular as the venue of the world-famous EXIT music festival (since 2000), and it is large enough to accommodate eleven separate stages and 200,000 people from all over the world during the four-day event.
The Petrovaradin Fortress Complex
the star-fortress, the last part of the fortress to be completed, also known as the Lower Fortress, or Wasserstadt (Water Town). Wasserstadt comprises one-third of the complex and is the least familiar to the public, since it has been used by the Serbian Army for decades;
the body (the oldest part of the fortification, the Upper Fortress);
the tail, which has been altered in the meantime—the two-pointed bastion called Hornwerk (Hornwork).
Inzelschanze, the Isle Fortress, which was submerged due to the change of flow of the Danube and construction of the Danube-Tisa-Danube canal;
Brückuckschanze, the Bridgehead, on the opposite bank of the Danube;
All parts of the complex are united by the single outer line of defense (envelope) consisting of interconnected fortification-defense system buildings: counterguards, ravelins, lunets and caponiers.
Due to its regular geometrical matrix and clearly identifiable principles of military fortification construction, the Wasserstadt in the north is the most interesting part for the purposes of this paper in terms of geometrical analysis, which is why we will focus on this part of the fortress. Hornwerk, the south-stretching tail of the fortification, was the part adapted to the terrain so that it aggressively encroaches upon the plain, thus defending the Upper Fortress on the Rock of Petrovaradin and giving the entire fortress a stable position.
The Early History of the Petrovaradin Fortress
Continuity of human settlements on the site of the Petrovaradin Fortress stretches from the Middle Palaeolithic era (Mihailović 2009) to the present. In the course of history, up to the seventeenth century, when the current shape of the Fortress started to emerge, different cultures occupied the Petrovaradin area, ranging from the Celts (circa 100 B.C.), through the Romans, who built a fortification named Cusum, the Huns (fifth century), Byzantium (when Petrovaradin, or Petrikon, as it was named at the time, grew further in military and strategic importance), Hungary under Bela IV (eighth century), who allowed Cistercians monks to manage the fortress, to Turkey (late fourteenth through the fifteenth century), after which the Turkish and Hungarian rulers alternated. In one of these periods, Hungarian archbishop Petar Varadi, after whom both the fortress and the locality were named, invested a lot of effort and in 1501 restored the remains of the former fortification, which was recaptured in 1526 by the Turkish army under the command of Suleiman the Magnificent. Petrovaradin remained under Turkish rule until 1688, when the army of the Austrian Empire seized the fort. This was followed by deconstruction of the old medieval (Hungarian and Turkish) fortress, while 1692 marked the beginning of the construction of a large, new fortress, designed according to the most modern fortification building system of the time. The foundation stone of the modern Petrovaradin Fortress was laid by the Austrian Duke Croy (Charles Eugen de Croy) in 1692 (Gavanski 1988). It is, therefore, evident that the construction started in Vauban’s lifetime, which was most likely enough for certain texts2 to identify him as the author of the plans.
Construction of the Petrovaradin Fortress 1692–1780
After the Karlovac peace treaty in 1699, the Turks finally left the area, but the Petrovaradin Fortress still kept its strategic importance. In the same year, engineer colonel Count Mathias Keyserfeld made the first blueprint for the fortress, while the next was done by the engineer colonel Count Luigi Ferdinando Marsigli (1659–1730). Engineer colonel Michael Wamberg was in charge of execution and when he died in 1793, engineer colonel Gisenbir succeeded him and remained in charge till 1728 (Marković 1984).
At the end of the eighteenth century, battles for this fortification, as well as for the others in the north of the Balkan Peninsula, ceased. When underground corridors and some smaller buildings were finished in 1780, the Fortress acquired its final appearance, which has been preserved till today.
The Principle of Military Fortification Building in Seventeenth and Eighteenth Century
The need to switch to new form of fortification construction and new geometrical patterns emerged when it became evident that the previous design was deficient in relation to new warfare techniques that used gunpowder. The circular shape of medieval forts proved to be vulnerable to damage caused by cannon fire aimed at vertical walls. Furthermore, if troops managed to reach the ramparts, they threatened the fort from the safety of the ‘dead ground’, as the defenders could not aim from the surrounding parapets due to blind spots (Bevilacqua 2007).
Defense of these fortifications gravitates towards the ‘bastion’, a four-sided addition to the fortress protruding from the ramparts. On two of its sides, cannons could fire over the glacis onto specially shaped open zones between the fortress and the surrounding area, so that cannons from the sides of the bastion could neutralize the frontal attack by enfilade. The bastions were placed at the angles of the fort in such a way that the defenders could cover all the fortification walls stretching to the next bastion, including the bastion itself. The number and design of the bastions varies depending on the shape and size of the fortification. The most common shape of smaller fortifications and separated citadels is that of a pentagram. In larger fortified towns the military engineer planned the position and shape of each bastion by using geometrical calculations (De Ville De Ville 1641; Du Fay 1691; Marolois 1627; Pagan 1668).
Between the bastions stretched the curtain, the main fortress wall. Just like the bastion, it had a thoughtfully designed profile that prevented the attacker from damaging the material it was built from. From the attacker’s point of view, only the ramparts above the glacis were visible. The glacis side facing the fortress ended in a palisade which protected the covered road, along which the defenders could move, and then fell steeply into a deep wide entrenchment which could, for purposes of additional defense, be filled with water (Holmes et al. 2004).
Star Fortresses: An Example of Regular Polygonal Construction Pattern
The radial distribution of the bastions according to a regular geometrical pattern resulted in the star-shaped fortification, star fortress or trace italienne, which emerged in the middle of the fifteenth century in Italy with the transition to angular fortification forms, as mentioned. The model of a regular polygon was ancestral from the Renaissance period and Utopian ‘ideal city’, the project of urban settlement that was based upon the abstract principles and regular geometrical schemes. The idea of utopian cities had existed almost as long as cities themselves, and many of them reflected the aspirations for political reforms and social reorganization, suggesting by its perfect geometrical form the values they pursued. Similar concepts can be identified in various epochs, from Plato and his Republic, whose ideal city “was one which mirrored the cosmos, on the one hand, and the individual on the other” (London 2013), to St Augustine, Sir Thomas More, Francis Bacon, Tomasso Campanella, Charles Fourier, James Buckingham, Étienne Cabet and others (Jones 1960). These ideas were raised to the level of principles by the famous Renaissance architect and polymath Leon Battista Alberti, who in his treatise De re aedificatoria developed, starting from Vitruvius’s theories, the rules of planning and construction of an ideal city based on proportion, firmitas (solidity), utilitas (functionality) and venustas (beauty).
Using this concept of ideal geometry, the designers of star fortresses developed a regular polygonal urban matrix of an ‘ideal city’, adding to it the ‘halo’ in the shape of single (or multiple) star-shaped polygons (most frequently identical, scaled and rotated). The newly obtained star was not the result of the stellation of the initial polygons, but rather a complex polygon created by adding equilateral triangles onto the sides of the basic polygon, which was accompanied by radial distribution of outworks, appropriate number of counterguards, ravelins, redoubts, etc., designed in accordance with the rules of defense and needs of such a fortification. The angular geometry of the bastion fits perfectly into the star-shaped form that enveloped the central polygonal core of the fortification.
Star fortresses were a lasting model, widely used all over Europe in the sixteenth, seventeenth and eighteenth centuries. The largest contributions to improved construction of these fortresses were made in the seventeenth century by Menno van Coehoorn, Blaise François Pagan and especially Sebastien le Prestre de Vauban, one of Louis XIV’s military engineers. The star fortress model was predominant until well into the nineteenth century, when the development of the explosive grenade changed the nature of fortification defense. However, in contrast to regular patterns of star fortresses, fortresses whose plans were irregularly shaped were also built, as the plans had to be adjusted to the conditions of a specific terrain. Furthermore, most fortresses were not ‘lucky enough’ to be built on ideal, flat ground, so that even those which contained a star-shaped citadel within the complex had to be combined with a chain of free-form walls.
The Petrovaradin Fortress, with one part on the rock of Petrovaradin and the other in the plain, in accordance with le bon sens et l’expérience as in the quote from Vauban that opened this paper, is designed and built using a combined system that unites the regular geometry of the star-shaped polygon of the Wasserstadt with the free-form plans of the Upper Fortress and the Hornwerk.
The Principles of Vauban’s Military Architecture
Historically speaking, Sebastien Le Prestre de Vauban (1633–1707) is primarily famous not only as the inventor of skilful and carefully designed siege systems (Ostwals 2006),4 but also as one of the most prominent fortification designers, who, thanks to his innovations and the doctrine of construction of effectively defended fortifications, excelled as one of the most significant military engineers of the period (Langinis 2003; Lepage 2009). Apart from introducing some new ideas and variations of the established manner of fortress building, Vauban is considered the first military engineer to have designed a fortress adjusted to the terrain. Respecting the symmetry inspired by classical principles of the aesthetics that governed the fortress design of the time, in the words of Christoper Duffy, “Vauban’s fortress stretches over a wavy terrain, encompassing it as though ‘embracing it” (Duffy 1985: 82–84).
By skilful application of geometrical principles and geometrical constructions, Vauban achieved not only the capacity for effective defense in the fortresses he designed, but a certain artistic quality as well, which most likely was not even deliberate, so that many historians and biographers of today consider him not only an architect, but an artist as well. Thus, the famous architect Jean Nouvel noticed that ‘Vauban’s fortresses were the early form of land-art and morphing’, without (Vauban) being aware of it (Nouvel 2007).
application of the star-fortress form, whenever the conditions of the terrain allowed it;
adjustment of the geometry of the fortress to the terrain;
a geometrical approach to positioning and shaping of bastions, which introduced certain changes in the scheme and construction of distances between the primary points of the master line;
remodelling the outworks: placing tenailles in front of the curtain, with ravelins and redoubts in front of them;
principles of construction and positioning of military facilities within the fortification, among other things suggesting that special purpose facilities (powder magazines, mills, stockrooms) be placed in the heart of the bastion.
Geometrical Principle of Master Line Modelling According to Vauban’s System
The radius of the circumcircle drawn around the inner polygon is called the inner radius (R1, segment OP in Fig. 9b), while the radius of the circumcircle of the outer polygon is called outer radius (R2, segment OQ in Fig. 9b). The inner radius is part of the outer radius starting from the centre of the polygon O and ending in the bastion gorge (P). The capital line (la ligne capitale) is the other portion of the outer radius, i.e., the extension of the inner radius starting from the bastion gorge (P) and ending in the vertex of bastion’s interior angle (Q).
Vauban’s system of tracing the master line is based on thoroughly calculated geometrical construction whose procedure is shown in Fig. 10.
Vauban divides the AB side of the circumscribed polygon of the master line into eight segments for a square, seven segments for the pentagon and six segments for the hexagon and larger polygons (Du Fay 1691). Thus divided, one segment of the side is transferred onto the perpendicular from the center of the polygon side, thus obtaining segments AC and BC, which present directions of the lines of defense. The length of the bastion face (AE = BF) is always 2/7 of the side AB. The intersection of the arc (r = AF = BF) and defense lines gives Vauban in this construction the end points of bastion sides (EM = FN) and the length of the curtain MN.
Lengths of the master line fragments according to Pagan's method
1t. = 6p. = 1.949 m
n = 4
5 ≤ n ≤ 12
AE = BF
CM = CN
73t. and 2p.
63t. and 4p.
63t. and 5p.
70t. and 5p.
60t. and 4p.
50t. and 4p.
EM = FN
19t. and 1p.
18t. and 3p.
24t. and 2p.
23t. and 2p.
AN = BM
141t. and 4p.
126t. and 1p.
115t. and 5p.
141t. and 2p.
126t. and 5p.
112t. and 3p.
The beginning of the construction procedure is the same as Vauban’s, the segment DC is a perpendicular from the midpoint of the side AB of the circumscribed polygon of the fortification base. All the other values are obtained by applying pre-defined values for individual sections of the master line. We should emphasize that in Les fortifications (1668), Pagan suggested the given values for fortifications with pentagonal to dodecagonal bases, paying special attention to square-based fortifications. The suggested values of master line segments are shown in Table 1.
Does Wasserstadt Geometry Reflect Vauban’s Principles?
In the light of the five geometrical principles mentioned above, which can be regarded as the stamp of Vauban’s influence, we will analyse one part of the Petrovaradin fortress, Wasserstadt, to determine whether it incorporates or violates these rules.
Analysis of the Geometrical Calculation of the Fragments of Wasserstadt’s Master Line
When Vauban’s construction is applied, some overlapping between the constructed and the existing bastion faces are observable, but there is also a significant deviation in the position of the curtain line. The surface that demonstrates aberration between the ideal master line according to Vauban and the actual line in Wasserstadt is shown in blue in Fig. 20.
Lengths of the Wasserstadt's master line fragments according to Pagan's method
n = 5
AE = BF
CM = CN
EM = FN
AN = BM
It was observed that the aberrations (blue surfaces in Fig. 21) of the actual master line of the Wasserstadt, from the line obtained by construction, are in this case significantly smaller, which suggests that military engineers who designed the plan respected the older method of Pagan, or at the very least, that in this segment of the design of Wasserstadt’s ground plan Vauban’s influence was inessential.
When it comes to the organization of the outworks, Pagan’s influence is observable once again, especially considering the fact that counterguards, which are not characteristic of Vauban’s method, are present, while characteristic teneilles and redoubts are absent. However, in terms of positioning of military facilities within the master line, echoes of Vauban’s doctrine are noticeable, particularly in placement of powder magazines within the bastions.
The presence of Vauban's system characteristics in the Petrovaradin Fortress
Characteristics of Vauban’s system
Coincidences of star-patterns
Adjustment to the terrain
Geometry of master line
Geometry of Ravelins
Works within the master line
Analysing the available sources and comparing the geometry of the Wasserstadt of Petrovaradin Fortress to the schemes and principles of Vauban’s method, we have concluded that there is not enough evidence to prove that the great French military architect was the author the project of the Petrovaradin fortress, in facts or in concept, although some influences of his doctrine are noticeable. The design of the fortress, created by the military engineers Keyserfeld, Marsigli, Wamberg, and Gisenbir—all of whom, unfortunately, are less famous than Vauban—is a compilation of various influences, which were modern at the end of the seventeenth into eighteenth and throughout the eighteenth century, having proven effective in the military engineering of Middle Europe. We can say that, as the research has shown, Blaise Pagan, for example, had an equal or even greater influence on the shape and organization of the Petrovaradin Fortress, since the Wasserstadt bastions are constructed in a manner much closer to his principles. Apart from that, the influence of the Renaissance ideal city and the need to adjust to the actual terrain, largely contributed to the form of the ground plan and the overall appearance of the fortress. Although the fact remains that these two characteristics also figure in Vauban’s designs, and allowing for the partial influence, it is remarkable that the outworks so characteristic of his work, are absent. To summarize, it cannot be claimed that the project was done by, or even modelled upon Marquis Vauban, since congruencies with his principles and construction doctrine do not prevail. We hope that this paper has shattered some of the persistent myths and brought one of the most freely interpreted chapters in the chronicles of the Petrovaradin Fortress closer to scientific truth.
The maps are used thanks to the kind permission of the Historical Archive of the City of Novi Sad, which keeps the digital record of the plans, transferred from the Archives of Vienna (Österreichisches Staatsarchiv) in cooperation with the City of Novi Sad, in November 2010.
The part of Petrovaradin which used to be the core of the fortress complex. As an architectural unit, it has preserved its authentic form and the characteristics of the particular ambience and the spirit of the time in which it was built.
These systems introduced circumvallation and contravallation lines, as well as a systematic approach to deployment of parallel trenches in order to capture the enemy’s fortress.
One toise was exactly 6 pieds (feet) (about 1.949 m) in France until 1812.
The bastions by number are: I—Bastion Benedicti; II—Bastion Francisci; III—Bastion Maria Theresa; IV—Bastion Joseph; V—Bastion Caroli.
Note: In geometrical drawings certain simplification and idealization of the actual state was made by ignoring and disregarding lesser imprecisions, to obtain a scheme suitable for analysis and observation.
The research is supported by Ministry of Science and Education, Republic of Serbia, under the project No. III 44006, “The development of new information-communication technologies, using advanced mathematical methods with applications in medicine, energy, e-governance and the protection of national heritage.”
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