3.4 Barrel vaults

Masonry barrel vaults are the most commonly used type of bombproof vaults. The gunpowder magazines are the direct result of military architecture treatises. Because it is such a common construction technique, most of the engineers do not even mention the material used for the vault of the magazine. This is what happened in the projects for Ceuta (1724) [MPD, 39, 083], Longone (1725) [MPD, 12, 222], A Coruña (1738) [MPD, 17, 058], San Sebastián (1738) [MPD, 27, 092], Peñíscola (1739) [MPD, 18, 262 and MPD, 18, 263], Játiva (1748) [MPD, 54, 012], Palma (1748) [MPD, 65, 048], San Sebastián (1750) [MPD, 27, 093], Viveiro (1778) [MPD, 19, 241], and Santa Cruz de Tenerife (1792) [MPD, 05, 033]. With regard to the projects which do specify the material used for the construction of the barrel vault, a distinction must be made between those which use stone for the first layer of the vault and those which use ceramic bricks.

The main projects which use stone masonry include those for Barcelona (1715) [MPD, 18, 097] and Dénia (1748) [MPD, 65, 085]. There is a variant which uses an ashlar arch with wooden beams on top, such as the project for Santa Cruz de Tenerife (1758) [MPD, 18, 050] (this variant was already used by Fernández de Medrano in the previous century). In other cases, ashlar masonry is substituted by

Figure 10. Gibralfaro Castle in Málaga (1724).

Scientific Knowledge of Spanish Military Engineers in the Seventeenth Century DOI: http://dx.doi.org/10.5772/intechopen.87060

brick masonry with a lime and pebble covering, as in the case of San Sebastián (1722) [MPD, 28, 034] (Figure 9).

As for the projects which use ceramic bricks, a distinction must be made between four different types: firstly, those which feature a single-layer ceramic vault, like the ones for Zamora (1738) [MPD, 13, 113] or Ciudad Rodrigo (1739) [MPD, 12, 154]; secondly, those which feature a bottom layer of ceramic bricks, an intermediate layer of stone, and a top layer of lime and pebble, like the gunpowder magazine in Cardona (1718) [MPD, 18, 028]; thirdly, vaults designed with a double layer of ceramic bricks and a top fill of lime and pebble, like in the projects for Pamplona (1718) [MPD, 31, 032; MPD, 31, 033; MPD, 31, 034; MPD, 31, 035; MPD, 31, 036]; and lastly, projects which feature three layers of ceramic bricks, for instance, in Longone, Italy (1728) [MPD, 12, 221], or even four layers, like in Badajoz (1749) [MPD, 65, 045].

#### 3.5 Pointed vaults

and El Ferrol (1738) [MPD, 47, 094]. Other projects feature scissors trusses, i.e., in Monzón (1740) [MPD, 54, 049], Palma (1748) [MPD, 65, 047], and Valencia (1754) [MPD, 06, 170]. The project for Barcelona (1796) [MPD, 46, 035] features a double-framed roof but with two horizontal rafters as tie beams. In other cases, such as the project for Málaga (1721) [MPD, 64, 022] (Figure 8), there is a mansard truss with two horizontal rafters (this structure is more similar to the models used

Masonry barrel vaults are the most commonly used type of bombproof vaults. The gunpowder magazines are the direct result of military architecture treatises. Because it is such a common construction technique, most of the engineers do not even mention the material used for the vault of the magazine. This is what happened in the projects for Ceuta (1724) [MPD, 39, 083], Longone (1725)

[MPD, 12, 222], A Coruña (1738) [MPD, 17, 058], San Sebastián (1738) [MPD, 27, 092], Peñíscola (1739) [MPD, 18, 262 and MPD, 18, 263], Játiva (1748) [MPD, 54, 012], Palma (1748) [MPD, 65, 048], San Sebastián (1750) [MPD, 27, 093], Viveiro (1778) [MPD, 19, 241], and Santa Cruz de Tenerife (1792) [MPD, 05, 033]. With regard to the projects which do specify the material used for the construction of the barrel vault, a distinction must be made between those which use stone for the first layer

The main projects which use stone masonry include those for Barcelona (1715) [MPD, 18, 097] and Dénia (1748) [MPD, 65, 085]. There is a variant which uses an ashlar arch with wooden beams on top, such as the project for Santa Cruz de Tenerife (1758) [MPD, 18, 050] (this variant was already used by Fernández de Medrano in the previous century). In other cases, ashlar masonry is substituted by

in the upper body of military barracks).

of the vault and those which use ceramic bricks.

3.4 Barrel vaults

Military Engineering

Figure 10.

38

Gibralfaro Castle in Málaga (1724).

Pointed vault structures were described by Bélidor (1729), and Müller (1769) said they are less resistant to bomb impacts than barrel vaults. They belong to the Gothic building tradition, and they need a smaller abutment than barrel vaults, even though magazine walls in military treatises are dimensioned depending on the impact of pyroballistic weapons (those employing gunpowder) and not on the basis of masonry mechanic criteria. This is the case of the gunpowder magazines in Zaragoza (1729) [MPD, 39, 041] and San Fernando de Cádiz (1749) [MPD, 56, 029], which have only one enclosure. It is the same construction type as the projects for Gerona (1738) [MPD, 01, 018] and San Sebastián (1749) [MPD, 27, 094], but these two magazines are protected by an encircling wall, and therefore they have two enclosures. The gunpowder magazine projects for Gibralfaro Castle in Málaga (1724) [MPD, 59, 046 and MPD, 59, 047] (Figure 10) and Ceuta (1737) [MPD, 07, 180] feature two parallel vaulted vans which are separated by square pillars supporting round arches, thus forming the central valley of the roof.

### 4. The curve of equilibrium and the Spanish military engineers

In the construction of gunpowder warehouses, barrel and pointed vaults are generally used, although there are some examples with elliptical vaults, such as that one built in 1694 by Hércules Torelli in Pamplona. This construction was remodelled by Francisco Larrando de Mauleón (1718) [MPD, 31,031] (Figure 11) [43]. Mauleón was professor at the Mathematics School of Barcelona and Zaragoza and authored the Estoque de la Guerra y Arte Militar, published in Barcelona (1699). The viceroy had ordered the repair of the fortifications and the gunpowder warehouses to make them bombproof. The elliptical vault was replaced by a barrel vault to make it less visible and vulnerable to enemy artillery. It was reinforced and reduced in height according to the concept introduced in the military treatises by General Ambroise (d. 1587) in Le Timon du Capitaine (1587) [44].

The simple vault of the warehouse of Montjuïc mountain in Barcelona (1731) [MPD, 07, 057], a project attributed to Miguel Marín (Figure 12), is not generated through an arch of circumference. The geometric study reveals that the vault has a length of 16 feet in toise, a rise of 11.5 feet, a width of 3 feet, and a buttress of 7 feet. A geometric element having the shape of a catenary can be drawn running through

the springing points and the key of the vault (Figure 13). The shape of this element, which has the same span and rise as the vault, is very similar to the shape drawn in the project.

Other projects, such as the project from Miguel Marín for Tortosa (1733) [MPD, 13, 035] (Figure 12), have a span of 21 feet in toise, a rise of 14 feet, a width of 3.5 feet, and a buttress of 7 feet (Figure 13). Another similar project is the simple warehouse layout by Juan de la Feriére y Valentín in A Coruña (1736) [MPD, 17, 057] (Figure 12), which contains a span of 22 feet in toise, a rise of 14 feet, a width of 3 feet, and a buttress of 7 feet (Figure 13).

The design of the pointed vault is initially compared with the catenary, as obtained with a chain over a reproduction of the plans on a larger scale (Figure 14). Thus, the arch described by the chain is very similar but not coincidental to the profile of the vault because there are small deviations near the springline of the vault. This deviation is because it is not possible to lay out the catenary with traditional drawing tools, such as rulers and compasses.

The assessment of the original section drawing of the warehouse reveals three compass marks. One point is made over the vertical axis of symmetry of the figure, while the other two are made over the perpendicular axis, slightly below the springline of the vault. An oval was drawn on each project using these compass marks, and the obtained curves were coincident with the curves of the projects. Thus, to draw the projects of the warehouses, both Miguel Marín and Juan de Feriére y Valentín used the geometrical solution of an oval. Therefore, the curves drawn in the three projects are oval, but the major axes of the oval are higher than

the springline of the arch. As a consequence, the curves are not tangential at the springing. So, the military engineers drawn the curve of the vault as an arch apaynelado, carpanel of Tosca (1712), or anse de panier of Bélidor (1729) (Figure 15). The geometric layout of these vaults, based on ovals, was well known by the eighteenth-century military engineers. They began from the essential feature that oval vaults are tangential to the springline of these building elements. When

Gunpowder warehouses: Marín (1731), Marín (1733), and Feriére y Valentín (1736).

Scientific Knowledge of Spanish Military Engineers in the Seventeenth Century

DOI: http://dx.doi.org/10.5772/intechopen.87060

Figure 12.

41

Scientific Knowledge of Spanish Military Engineers in the Seventeenth Century DOI: http://dx.doi.org/10.5772/intechopen.87060

Figure 12. Gunpowder warehouses: Marín (1731), Marín (1733), and Feriére y Valentín (1736).

the springline of the arch. As a consequence, the curves are not tangential at the springing. So, the military engineers drawn the curve of the vault as an arch apaynelado, carpanel of Tosca (1712), or anse de panier of Bélidor (1729) (Figure 15).

The geometric layout of these vaults, based on ovals, was well known by the eighteenth-century military engineers. They began from the essential feature that oval vaults are tangential to the springline of these building elements. When

the springing points and the key of the vault (Figure 13). The shape of this element, which has the same span and rise as the vault, is very similar to the shape drawn in

Other projects, such as the project from Miguel Marín for Tortosa (1733) [MPD, 13, 035] (Figure 12), have a span of 21 feet in toise, a rise of 14 feet, a width of 3.5 feet, and a buttress of 7 feet (Figure 13). Another similar project is the simple warehouse layout by Juan de la Feriére y Valentín in A Coruña (1736) [MPD, 17, 057] (Figure 12), which contains a span of 22 feet in toise, a rise of

The design of the pointed vault is initially compared with the catenary, as obtained with a chain over a reproduction of the plans on a larger scale (Figure 14). Thus, the arch described by the chain is very similar but not coincidental to the profile of the vault because there are small deviations near the springline of the vault. This deviation is because it is not possible to lay out the catenary with

The assessment of the original section drawing of the warehouse reveals three compass marks. One point is made over the vertical axis of symmetry of the figure, while the other two are made over the perpendicular axis, slightly below the springline of the vault. An oval was drawn on each project using these compass marks, and the obtained curves were coincident with the curves of the projects. Thus, to draw the projects of the warehouses, both Miguel Marín and Juan de Feriére y Valentín used the geometrical solution of an oval. Therefore, the curves drawn in the three projects are oval, but the major axes of the oval are higher than

14 feet, a width of 3 feet, and a buttress of 7 feet (Figure 13).

Warehouse of Pamplona, Francisco Larrando de Mauleón (1718) [MPD, 31,031].

traditional drawing tools, such as rulers and compasses.

the project.

40

Figure 11.

Military Engineering

#### Figure 13.

Metrology of the projects for the gunpowder magazines.

the springline is higher than the axis, a non-tangential curve is obtained, which is a feature of the catenary definitions given by Frézier (1738). Concurrently, Bélidor (1729) specifies the method to lay out the true shape of the catenary vault. By knowing the rise and the span of the vault, the architectonic shape is determined with a hanging chain. Thus, a scale model can be built and can easily be taken to the construction site. By contrast, the layout of the catenary in military engineers' projects is more complex, because it needs the use of an approximation of the catenary through the geometrical shape of a lowered oval.

The ovals are derived from the centres of the circumferences (the compass center points on the paper). They are referred to (O1) for Barcelona (1731) [MPD, 07, 057], (O2) for Tortosa (1733) [MPD, 13, 035], and (O3) for A Coruña (1736) [MPD, 17, 057]. They are consistent with three different types of ovals, and they all share the common feature that the origin of the vertical tangent to the minor axis of the oval is located 1 foot below the impost line (Figure 16).

• a2 describes the distance between the centre of the minor arc and the

distance from the semiminor axis to the springline (feet).

Scientific Knowledge of Spanish Military Engineers in the Seventeenth Century

DOI: http://dx.doi.org/10.5772/intechopen.87060

Chaînette method applied to the projects for the gunpowder magazines.

• d1 describes the ratio between the length of the semimajor axis and the vertical

• d2 describes the ratio between the length of the minor axis and the distance from the center of the major arc to the point of tangency between the major arc

minor axis.

Figure 14.

43

and the minor axis.

The main ovals' geometric data are shown in Table 1, where:


Scientific Knowledge of Spanish Military Engineers in the Seventeenth Century DOI: http://dx.doi.org/10.5772/intechopen.87060

Figure 14. Chaînette method applied to the projects for the gunpowder magazines.


the springline is higher than the axis, a non-tangential curve is obtained, which is a feature of the catenary definitions given by Frézier (1738). Concurrently, Bélidor (1729) specifies the method to lay out the true shape of the catenary vault. By knowing the rise and the span of the vault, the architectonic shape is determined with a hanging chain. Thus, a scale model can be built and can easily be taken to the construction site. By contrast, the layout of the catenary in military engineers' projects is more complex, because it needs the use of an approximation of the catenary through the geometrical shape of a

The ovals are derived from the centres of the circumferences (the compass center points on the paper). They are referred to (O1) for Barcelona (1731) [MPD, 07, 057], (O2) for Tortosa (1733) [MPD, 13, 035], and (O3) for A Coruña (1736) [MPD, 17, 057]. They are consistent with three different types of ovals, and they all share the common feature that the origin of the vertical tangent to the minor axis of the oval is located 1 foot below the impost line (Figure 16). The main ovals' geometric data are shown in Table 1, where:

• a1 describes the distance between centres of the minor axis.

lowered oval.

42

Figure 13.

Military Engineering

• e1 describes the clear span.

Metrology of the projects for the gunpowder magazines.

• e2 describes the rise.

Figure 15. Oval method applied to the projects for the gunpowder magazines.


The ovals used in the layout of the gunpowder magazines are thus used as a reference for purposes of comparison with the cellar's layout. The layout of [O1, O2, O3] is based on a ratio between d3 and e2 of [0.39:0.36:0.50].

5. The curve of equilibrium and the civil constructions of the eighteenth

Geometrical analysis of the vaults of the projects for the gunpowder magazines.

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DOI: http://dx.doi.org/10.5772/intechopen.87060

After the Bourbon dynasty's ascendancy to the Spanish throne (1700), Catholic diplomatic and military families of Irish and Scottish origin emigrated under royal protection, preserving their status. O'Connor family was installed in Benicarló in the eighteenth century, and they associated with the McDonnells in the wine export

The Bourbon dynasty, which established itself in Spain in 1700 with King Philip V (1683–1746), created the Army Corps of Engineers by the Royal Decree of 17 April 1711. Several Irish families moved to eastern Spain in the mid-seventeenth century. Patrick White Limerick, a trader in agricultural products and wine, and the

century

Figure 16.

business.

45

In addition, the layout of each oval is compared with a catenary that has the same rise and span, which is drawn using InnerSoft software. According to the results, the inner surface defined between the corresponding geometric shape and the springline is different (1.33 m<sup>2</sup> vs. 0.98 m<sup>2</sup> ). Furthermore, the ratio between the maximum distance between geometric shapes and the arch's span ranges from 2.14 to 3.44%. From these data, we can conclude that the approximation made by the engineers by drawing ovals in the three projects considered is sufficiently precise for the drawing scale used, between E: 1:90 and E: 1:70. Finally, the curves are compared with an elipse with the same rise and span. The obtained shape is clearly not coincident with the curves of the projects.

### Scientific Knowledge of Spanish Military Engineers in the Seventeenth Century DOI: http://dx.doi.org/10.5772/intechopen.87060

Figure 16. Geometrical analysis of the vaults of the projects for the gunpowder magazines.
