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Castel del Monte |
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Castel del Monte → Elevation Design → Room and Vault Heights – Study Findings |
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Note: Figures referenced in text are located in a separate file. Follow link to see figures as slides in a separate browser tab:  Elevation Slides
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1. Introduction |
The principal issue in the design of the elevated structures is the construction of the vaults. The technique of erecting cross vaults was established at the height of the middle ages. What remains in the design of the elevated structures is determining the height of the walls, the height of the vaults and consequently the height of the rooms, Fig. 12 .
[These are figure that accompany the study, file “cdm-152-130=elev-figs-en”.]A starting point in considering the dimensions of key elevation structures is the diagonal of the cross vault base square, Fig. 13. This is a fruit of the plant design algorithm, but is also related to the elevation of the vault. The relationship is the form of a semicircle given to the diagonal rib, which spans over this diagonal, in the medieval practice of ribbed cross vault construction. The study of key room elevation dimensions has brought to light some new geometric construction models as well as many interesting details about the columns and construction issues that the medieval builders ran into, and how they resolved them. [“Room and Vault Heights - Measurement Analysis”, “Tas-de-Charge and the Rib Support System - Analysis”.] |
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2. Measurements |
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Key room elevation dimensions needed for the study are summarized in Table 1.
W. Scirmer and H. Götze do provide some elevation data; however they are few and incidental. Their focus, like the work of many other scholars and this study as well, is on the plant layout. Therefore, special measurements were made at the castle in the fall of 2018 to collect required missing elevation measurement data. [Wulf Schirmer, Castel del monre, Forschungsergebnisse der Jahre 1990 bis 1996 (Verlag Philipp Von Zabern · Gegründet 1785 · Mainz).] [Heinz Götze, Castel del Monte, Geometric Marvel of the Middle Ages (New York, 1998).]A detailed analysis is outlined in an extensive narrative documented separately . It has been an eye-opening study for much that has been learned and the many interesting findings and amazing revelations. Following is an orderly and logical account of how the design unfolded, with detailed explanations. |
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3. The Room Design and Dimension |
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The structural design is the same for all 16 rooms at Castel del Monte. This is a ribbed square cross vault nested in the center of a trapezoidal-shaped room. Triangularly truncated gothic vaults form the side-vaults that cover the ceiling between the central square cross vault and the room dividing walls, Fig. 3.
The rib system includes two semi-circular diagonal ribs that intersect each other at the keystone, and four transverse ribs with ogival forms along the perimeter of the cross vault base square. All ribs merge in commons structures, the tas-de-charge, at the four corners of the cross vault square, Fig. 7. The static load of the ribs is discharged through the ta-de-charges onto column supports plastered to the wall and shaped as the vertical half-portion of a traditional round column, Fig. 5 and 6. Accordingly, the ceiling has different elevations: at the keystone where the diagonal ribs intersect, at the crest of the transverse ribs, and at the dividing walls. Other key elevation measures are the height of the vaults and the height of the vault spring line; the latter is marked by a horizontal molding around the room, Fig. 5, 6 and 8. All rooms have the same disposition and look, except of course for doors, windows, and incidentals such as fireplaces. The room dimensions outlined in Table 1 show that the rooms on the upper floor are larger and taller than the rooms on the ground floor. This is not too surprising as a visitor gets a feeling of rooms that are loftier and more luminous walking up to the upper floor. The rooms on each floor all have exactly the same dimensions, with amazingly very small variances in dimensions. Surprising is the fact that room 1 on the upper floor, often referred to as the throne room, is distinctively larger than the other seven rooms on that floor. [The rooms on each floor are numbered sequential counterclockwise, starting at the portal wing, room 1.]The dimensions indicate that the medieval builders followed the same basic room design, but with three separate sets of measures. The study therefore deals with three separate sets of room dimensions:
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4. The Geometric Design Approach |
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The geometric algorithm that defines the plant design in all forms and dimensions stands for the character and mystical purpose of Castel del Monte. It behooves then that the design of the elevated structures would follow a geometric model, likely as an extension of the plant design algorithm. The study has indeed brought to light two significant but simple geometric models that guide the definition of the elevation measures.
The form of the elevated structures is preordained by the established pattern of ribbed cross vault construction at the height of the Middle Ages. In fact, the erection of ribbed crosses vaults was in essence more of an established construction procedure. Accordingly, the design and construction of the elevated structures is based on three models:
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4.1 Ribbed Cross Vault Construction Procedure |
The construction of ribbed cross vaults is outlined in the “Cross Vault Construction Technology” section. It is an assembly procedure, much like the sheet instructions to assemble a crib. It requires no design, just the measure of a key parameter. In a simplistic description, the procedure is as follows:
[Ribs are made of a center section of free rib voussoirs and tas-de-charge where multiple ribs are sculptured in the same stone blocks. Aside the stone form, the construction process is also different. The tas-de-charge are erected simply by stacking tas-de-charge drums vertically while the free rib voussoirs span an open space and require the support of centering frames. Coordinating the design, positioning and erection of these components is a challenging operation; see the “Tas-de-Charge and the Rib Support System Analysis”.]This procedure invariably produces three characteristic features:
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4.2 Squared Octagon Figure |
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This geometric construct is the provenance for the measures given to the semi-octagonal form of the column bases and capitals, Fig. 23 and 24.
The figure is an octagon inscribed inside a square with which it shares four of its sides, Fig. 25. This squared-octagon figure includes four identical equilateral triangles, each tucked in one of the four corners of the square, Fig. 26. The hypotenuse of these triangles is a side of the octagon. If the equilateral sides of these triangles are given a measure of one unit, then its hypotenuse has the measure of 1.414 units and the width of the square and octagon both is 3.414 units (1.000 + 1.414 + 1.000 = 3.414). The relevance of this figure is that if the unit of measure is the unit of linear measurement used at Castel del Monte, a foot of 0.302 m, then the side of the octagon is 0.427 m, and the width of the octagon is 1.031 m. These are essentially the measures for the semi-octagon of the column base and capital. It is a geometric model used for assigning dimensions to the structural components of the column; it is totally separate and unrelated to the plant design algorithm. Indeed, the discovery of this geometric model came about from a fruitless search to tie the dimensions of the column base to a parameter in the plant design algorithm. The squared-octagon figure was certainly a fascinating geometrical construct for medieval builders, especially the stonemasons that found these dimensions symbolically suitable for sizing the column base. Built into this choice is the message of what is the unit of measurement used at Castel del Monte. |
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4.3 Standing Circle |
The geometric model for the design of the elevations is theorized to have been a standing circle in the vertical plane along one of the cross vault base square diagonals with a diameter that is the measure of the cross vault base square diagonal, Fig. 17. The standing circle sets the main features of the room elevations:
This model ties the height of the room to the plant design algorithm through the cross vault base square diagonal. This is specifically significant on the ground floor where the room size is an integral part of the plant design. Indeed, the fundamental elements in the construction of the vaults are the diagonal and transverse ribs located respectively along the diagonals and sides of the cross vault base square. The span of these ribs is established in the ground plan design, by the dimension given to the cross vault base square, Fig. 13. |
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5. Room Enlargement on the Upper Floor |
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Although similar in the main structural features, the rooms are wider on the upper floor, Fig. 20. The room widening is achieved by carving the additional space out of the walls, most significantly on the façade and courtyard sides respectively, Fig. 14. Accordingly, the rooms are taller on the upper floor in proportion to the width enlargement, per the standing circle model, Fig. 17. Therefore, determining the measures for the elevations on the upper floor entails first a consideration for the room enlargement, which translates into a determination of the enlargement of the cross vault base square, Fig. 14.
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5.1 Theorized Room Enlargement |
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As in most other case for key measures, it is presumable that the medieval designers may have sought some geometric rationale to arrive at a measure for the room enlargement on the upper floor.
In the initial design phase, when deciding the width of the façade wall on the ground floor, a starting geometric consideration was the space in between adjacent towers and bound by the two lines that join the corners of the tower octagon innermost sides, Fig. 15. This choice gives a result that emphasizes the octagonal form of the tower with a minimum attachment to the body of the castle. The width of this space is the 45° projection of the side of the tower octagon, 2.17 m, Fig. 15. This is the footprint of a deep and structurally sound wall for the support of the vaults on the ground floor. However, details of the actual construction show that the width of the tower footing, 0.383 m, was added on the inside of this space, Fig. 15; the width of the façade wall on the ground floor is indeed 2.55 m. The rational inference is that the builders were already thinking of a ledge in the wall that rises to the pavement of the upper floor. The ledge wide of the tower footing dimension, 0.383 m, would provide a solid masonry support straight down to the foundations for the columns supporting the ribs of the cross vaults on the upper floor , Fig. 34. This ledge sets back the interior side of the façade wall on the upper floor with respect to the ground floor. [On the ground floor, the bedding for similar columns is a buried detail because the foundation for the columns on the ground floor is the bedrock right in front of the wall, with no other visible clue.]This seems to be confirmed by the bench seat everywhere on the upper floor that runs around each room with columns mounted directly on top, Fig. 5 and 33. The width of the bench seat seems to be the width of the tower footing, thus seeming to confirm the idea that the room enlargement on the façade side on the upper floor is indeed by the width of the tower footing . [The tower footing is indeed the measure by which the tower octagonal basement is larger than the tower octagon itself.]The uniform extension of the bench seat around the room indicates that a similar room enlargement is made on the courtyard side of the room. Indeed, a similar enlargement on all sides of the cross vault base is inevitable for symmetry and in order to retain the square form for the cross vault. This means that the overall enlargement of the cross vault base square and the room width from façade to courtyard wall on the upper floor should be by two measures of the tower footing. At the level of the plant geometry, it is an elegant solution to the location of the indoor side of the façade wall: it is the plant octagon formed by the innermost corners of the tower octagons for the upper floor, and the plant octagon formed by the innermost corners of the tower octagonal basement for the ground floor, Fig. 15. The impression from the visual observations and the geometric considerations outlined so far strongly support the theory that the enlargement of the rooms on the upper floor is by the measure of the tower footing on all sides of the cross vault base square. This is the perception that the medieval builders seem to have wanted to convey with their design choices on the upper floor. Most of the published studies on Castel del Monte focus on the ground floor as the map for the plant design, accompanied by detailed measurements . The upper floor is addressed for its more refined decorations; there is little measurement information. Götze indicates (pg. 180) an alignment of the indoor side of the façade wall with the tower innermost corners, with a setback of 0.30 to 0.40 m. Götze also says that the width of the rooms on the upper floor is 7.00 m (pg. 180). [The publication by Götze and Schirmer are exceptional scholarly works on Castel del Monte. ]The theorized width for the rooms on the upper floor is 7.17 m (the width of the room on the ground floor, 6.40 m, plus twice the tower footing measure, 0.383 m). This is definitely larger than the measure reported by Götze. Detailed measurements taken on the upper floor for this study show that the width of the room is 6.94 m for rooms 2-8; this is in line with the measure indicated by Götze. An analysis of what can explain the shortcomings in the theorized dimensions for the room enlargement on the upper floor has unveiled a geometric constraint to the room enlargement that the medieval builders eventually came to realize as well, at some point during the design or construction of the castle. |
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5.2 Room Enlargement Constraint |
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The plant design of the castle is that of an octagon with the base area divided into eight equal triangular wings. A cross vault base square is wedged within each of the eight wings, near the base of the isosceles triangle formed by the wing. This maximizes the floor area of the room after allowing some space for the walls, Fig. 26.
The space to enlarge the rooms on the upper floor is gained by decreasing the width of the façade and courtyard walls on the interior side; but this is an operation with more stringent limits on the courtyard side. The enlargement of the cross vault base square cuts into the width of the dividing wall significantly on the courtyard side, Fig. 26. The width of the dividing wall is reduced to zero when the corners of the cross vault base squares between adjacent rooms come together, and the base squares cannot be enlarged any more without overlapping each other. This geometric constraint limits by how much the room can be enlarged on the upper floor. The constraint is further heightened by the realization that the room dividing wall must have a reasonable physical dimension and cannot be zero. Additionally, the corners of the cross vault base square are formed by columns that also take a physical space. Furthermore, the columns have to be distanced from the corners of the trapezoidal room on the courtyard side to avoid the architectural effect of columns wedged in the room corners, Fig. 33. The medieval builders quite surely ran into this consideration and chose a more compatible measure for the room enlargement on the upper floor. Indeed, a smaller and more fitting measure than the theorized enlargement of 0.766 m (twice the tower footing dimension) is the measure of the width of the bench seat, 0.54 m. This is a measure that came from the semi-octagonal form of the column base, which had already been established on the ground floor per the squared-octagon figure discussed above (dimension “z” in Fig. 24). It is half the width of the full octagon (dimension “d” in Fig. 24) that delineates the semi-octagonal perimeter of the column base. Interestingly, the free seating space of the bench seat is 0.40 m, essentially the width of the tower footing (0.383 m); the back of the bench seat is taken by a back splash topped by the lower molding for the wall finishing layer, Fig. 37. Measurements show that rooms 2-8 on the upper floor are 0.54 m larger than the rooms on the ground floor from façade to courtyard sides. This is overall only one (1) measure of the width of the bench seat; in contrast, the free seating space of the bench seat on each side of the room purports to indicate twice the measure of the tower footing for the enlargement. These appear much more than coincidences; it could very likely be an arrangement intended to give the impression that the room enlargement is twice the tower footing when in reality is by a smaller measure. |
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5.3 Column Support on the Upper Floor |
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The room enlargement on the upper floor creates bigger and more luminous rooms made possible by narrower walls and taller rooms. While this may have been the primary objective for the room enlargement, there is the question of the masonry foundation for the columns on the upper floor.
As interpreted in the “Theorized Room Enlargement” above, the enlargement of the rooms on the upper floor is likely to have been motivated structurally by the perceived notion by the medieval designers to create a solid masonry support for the columns on the upper floor, all the way down to the foundation. Rooms that duplicated the dimensions of the ground floor would result in columns on the upper floor that discharged their load on top of the overburden covering the vaults of the ground floor. Setting back the interior sides of the walls on the upper floor, as mentioned above, leaves a ledge on the wall masonry rising straight up from the ground floor. This ledge provides the needed solid masonry support for the columns on the upper floor, Fig. 34. The overall enlargement of rooms 2-8 on the upper floor, 0.54 m, is apportioned between the façade and the courtyard sides, 0.27 m on each side. A ledge of 0.27 m is half the depth of the column base, which is the full width of the bench seat. This means that half of the depth of the column bases and half the width of the bench seat extend over the overburden of the vault of the ground floor, Fig. 34. The material used for the overburden is typically an amalgam based on discarded stone debris, which does not yield the same compressive strength of stone. Realizing this, it is likely that the builders replaced the overburden sections directly under the columns with solid masonry, down to the masonry of the vault on the ground floor, which includes the tas-de-charge drums. |
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5.4 Throne Room Enlargement |
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Measurements indicate that the width of the throne room from façade to courtyard sides is 7.247 m, which implies an enlargement of 0.841 m compared to the rooms on the ground floor. Compared to the other rooms on the upper floor, the enlargement is 0.307 m, essentially one (1) CdM-ft. It is also greater than the theorized enlargement, 0.766 m. Aside its decorations and features, the throne room is clearly unique also because of its larger room dimensions.
` The further enlargement of the throne room is made possible by the fact that the corresponding cross vault base square on the ground floor was moved inward toward the center of the plant to accommodate the portal; see the “Portal Wing Design” for further details. This created the opportunity to enlarge the throne room an additional CdM-ft on the side of the façade wall. However, there are no measurements to assess the exact relative position of the throne room. The cross-sectional diagram provided by Schirmer of the castle in correspondence of the throne room, Fig. 39, does not provide a clear answer. |
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6. Room Width and the Cross Vault Base Square Diagonal |
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The room width is the distance between the façade and the courtyard wall; it is the side of the cross vault base square, Fig. 3. The measurement is made between the stone surfaces of the walls, because the finishing layer is missing. However, the design reference dimension is from the finished surfaces, so it is derived from the measurement taken between the stone surfaces.
The diagonal of the cross vault base square is the key measure for the analysis of the elevations per the standing circle model. It is not measurable directly; it is inferred by combining other related measurements or from the side of the base square through the Pythagorean relationship. Measurements were taken at Castel del Monte in the fall of 2018, focused principally on the dimensions of the cross vault base square and the heights of the rooms. The data shows a very small variance in the dimensions from room to room, less than 0.2% on the ground floor and less than 0.7% on the upper floor. This is an indication of the high precision that the medieval builders achieved in the construction, but also that there was a fixed design dimension that the medieval builders established and followed throughout; this is the nominal value. Table 1 shows the nominal value for the room width and the cross vault base square diagonal derived from measurements. The value of the cross vault base square diagonal is normalized to a whole number of CdM-ft, or fractions, with essentially no discrepancy from measurements. This is significant because it is thought that the medieval designers may have indeed chosen whole numbers and fractions for a dimension that impacts on many other processes. These vary, from defining derivatively other room dimensions to the preparation of masonry for the ribs and tas-de-charges, and the fabrication of structures such as the centering frames. The cross vault base square diagonal has a different value for each of the three room cases: 30 CdM-ft (9.06 m) on the ground floor, 32.50 CdM-ft (9.82 m) for rooms 2-8 on the upper floor, and 34 CdM-ft (10.27 m) for the throne room. |
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7. Room Height at the Keystone |
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The room elevation is highest at the top of the diagonal rib semicircle, in correspondence of the keystone. The height of the room at the keystone should therefore be the diagonal of the standing circle model, which is the length of the cross vault base square diagonal.
Table 2 shows a comparison between the dimensions theorized according to the standing circle model and those measured.
There is a clear shortage in the measured heights of the room from the theorized dimensions in all three cases. The shortage in the throne room is considerable and stands apart, requiring a special examination. Intriguingly however, the shortage in the height of all the other rooms is the same on both floors. Some difference would be expectable in the shortages of the room heights between the two floors, as it seen to be the case for the throne room, because of the overall different dimensions of the rooms between the floors. Instead, the shortage in the room height is exactly the same, 0.2275 m ±1.5 mm between the two floors; the throne room being the sole exception. It is an amazing detail; furthermore this is exactly ¾ of one (1) CdM‑ft, and essentially it is the height of the top molding on the ground floor, a molding that is missing at the column on the ground floor but is included in the column on the upper floor. These are tantalizing coincidences that merit further probing; but first there is a need to consider the other room elevation measurements, such as the height of the vault spring line. |
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8. Vault Spring Line, Columns and Top Molding |
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The interior walls throughout the castle, except for the towers, were designed to be covered by a finishing layer of thin stone panels, as outlined in the plant design. The panels are now missing, exposing the rough surface of the bearing wall, Fig. 8, 9 and 10. This covering rises up to the vault spring line where it is capped by a molding (“upper molding”), Fig. 5.
The vault spring line is thus marked visually by the top molding line around the room, Fig. 8 and 10. Physically, the elevation of the vault spring line is at the top surface of the column capital, where the tas-de-charge is mounted, Fig. 5. Therefore, the height of the vault spring line corresponds to the height of the columns. There is a difference in the top molding between the two floors, most significantly in the way the top molding is or is not incorporated into the column capital, the height of which sets the elevation of the vault spring line, Fig. 5. The top molding breaks open up in correspondence of the columns on the ground floor, thus interrupting the top molding line around the room. On the contrary, the top molding wraps around the column capital on the upper floor, thus presenting a continuous line for the top molding around the room, not interrupted at the columns, Fig. 5. This is a first, most visible, structural discordance between the two floors on this matter. A second discordance is the thickness of the top molding, 0.214 m on the ground floor and 0.141 m on the upper floor. These discordances are indication of a likely issue that medieval builders encountered during construction. Here too, it is thought that the medieval builders may have chosen measures for the thickness of the top molding that are whole fractions of a CdM-ft. Indeed, short of about a centimeter, the thickness of the top molding is ¾ of a CdM-ft on the ground floor and ½ CdM-ft on the upper floor. |
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8.1 Column Height |
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The top molding line around the room is made of straight voussoirs with a horizontally sculptured decoration. In correspondence of the columns on the upper floor, the top molding follows the semi-octagonal perimeter of the column capital. The top molding at the column is actually a stone drum (“molding drum”) on top of the capital with thickness, sculptured side face, and stone material that match the top molding on that floor. The tas-de-charge is mounted on top of the molding drum. As such, the molding drum is part of the column on the upper floor. On the contrary, there is no molding drum under the tas-de-charge, on top of the column capital on the ground floor that matches the top molding in thickness, profile and stone material.
The height of the columns on the ground floor is 4.350 m (Table 2). The height of the columns in all rooms on the upper floor is 4.335 m, including the molding drum. These are essentially the same heights. Being the same height is not a good point for the height of the columns between the two floors. Since the columns stand for the height of the vault spring line, the columns on the upper floor should be taller, because the vault spring line for the larger rooms on the upper floor is taller per the standing circle model (the height of the vault spring line is the radius of the standing circle). |
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8.2 Vault Spring Line |
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Based on the nominal dimensions for the cross vault base square diagonals identified above, which are the diagonals of the standing circle models, the height of the vault spring line should be 15 CdM-ft (4.530 m) on the ground floor, 16.25 CdM-ft (4.908 m) for rooms 2-8 on the upper floor, and 17 CdM ft (5.134 m) for the throne room.
Table 3 shows a comparison between the theorized and the measured dimensions for the height of the vault spring line, which are considered to be the height of the columns. The comparison shows a considerable shortage in the height measurement of the columns on the upper floor. The height of the vault spring line is a component that when added to the height of the vault gives the height of the room at the keystone. The shortage in the height of the column compared to the intended height for the vault spring line on the upper floor are much larger than the overall shortage in the room height, which is only ¾ CdM ft, as indicated above.
While the column is the only element that raises the vault spring line above the pavement on the ground floor, there is an additional element besides the column that raises the vault spring line on the upper floor that has not been considered. The columns on the upper floor are mounted on top of another pedestal that is extended around the room as a bench seat, Fig. 5, 8 and 10. Table 4 shows the adjusted comparison between the theorized height for the vault spring line and the measure of the column mounted on top of the bench seat.
The effect of the bench seat is to bring the shortage for the height of the vault spring line for room 2-8 on the upper floor to within the overall range noted above for the shortage in the room height, ¾ of a CdM-ft. Again, the shortage for the throne rooms stands apart and requires special examination. This shows that the presence of a bench seat on the upper floor serves a structural function, to raise the vault spring line. The height of the bench seat, besides being a reasonable and comfortable height for a seat, is also the measure of the depth of the semi-octagonal form of the column base, measure “z” in Fig. 24. Sourcing the measure for the height of the bench seat from the column base underlines the visualization likely in the mind of the medieval builders of the bench seat as a pedestal extension of the column base. This additional pedestal was then extended around the room to serve all four columns of the square cross vault, and to mitigate the unusual aspect of this additional pedestal. In other words, the bench seat serves to camouflage its structural function at the columns by giving the common impression of a seating function around the room. The latter seems indeed fitting for a living habitat of the upper floor in contrast to the support function of the ground floor that would not necessitate a seating structure in every room. The bench seat covers the space by which the rooms were enlarged on the upper floor, as indicated above, a correlation that merits further analysis. The more pressing question is why the medieval builders did not set the height of the columns on the upper floor to the theorized dimension, which is the height of the vault spring line per the standing circle model. |
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8.3 Questions About the Columns |
There are diverse questions that have come up about the columns of the cross vault between the two floors; specifically, differences in their dimensions and the composing elements. The stone material and sculptured forms are also different, but are not issues in the structural analysis. Aside for the throne room that remains a singular case, the puzzling considerations for all other rooms are as follows:
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8.4 The Short Column Blunder |
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The many construction details of the castle involved certainly many phases and many tasks. The construction is said to have likely spread over many years, which certainly is cause for some changes to occur in the design plans and construction commitments. For example, the columns and the jambs for the passage doors between rooms were all made of breccia rossa on the ground floor. For the similar construction on the upper floor, the column components including the bench seat are made of marble and other white stone. However, the jambs for the passage doors from room to room are still made of breccia rossa, likely the result of an earlier decision contemporaneous with the construction on the ground floor, an oversight or a early manufacturing of these parts, before the selections of the stone type were finalized for the construction on the upper floor.
The manufacturing of complex stone components such as the columns likely required rarer skills and long manufacturing times, especially considering that 64 columns are needed for the 16 square cross vaults of Castel del Monte. It is surely the case that the request for the manufacturing of the columns was made very early in the course of the construction so that the columns would be on hand when they were needed for the construction, as was likely the case for other pieces as well. This may have been especially the case for the columns on the upper floor where the column shaft requires a more elaborate and delicate sculpturing work. Adjusted for the ¾ CdM-ft shortage that will be explained next, the height of the columns on the ground floor have the measure of the theorized height per the standing circle model for the vault spring line, which is half the measure for the cross vault base square diagonal. So the height for the columns on the ground floor was set and given to the stonecutters based on the standing circle model of the ground floor. Per a snafu that we cannot obviously discern, the same column height dimension was given to the stonecutters manufacturing the columns on the upper floor, a blunder that was not acknowledged for some time or when it was too late to correct. When the shortness of the column was realized, certainly before construction started on the upper floor, it was too late or otherwise unworkable getting columns of the right height. So the builders came up with the bench seat concept to raise the column off the floor and coming close to the expected height for the vault spring line. |
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8.5 The Missing Molding Drum Blunder |
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It is presumed that the ¾ CdM-ft shortage of the columns on the ground floor was due to confusion and miscommunication among the various stonecutter groups regarding the upper molding at the columns.
An upper molding of the thickness of ¾ of a CdM-foot was likely intended to be added to the column capitals at an early time in the design and planning process. This would have served to provide a continuous top molding motif around the room, rising above windows when necessary (Fig. 10) and certainly not interrupted at the columns. The column height that sets the height of the vault spring line was reduced accordingly by ¾ of a CdM-ft. The stonecutters manufacturing the column stone pieces for the ground floor divided this height into five parts: the base, two semi-drums for the column shaft, a capital, and a top molding drum, all to be made of breccias rossa, Fig. 5 and 31. The blunder was including the top molding drum in this partitioning; a height allowance for the top molding had already been reserved for the stonecutters preparing the top molding stonework. The miss-coordination was aggravated further by the fact that the stonecutters making the top molding did no manufacture the top molding drum that was supposed to go on top of the column capital. Conjunctly, the stonecutters preparing the column parts did include such a piece within the shortened height of the column, but with a thickness of ½ a CdM-ft. It is likely that by the time construction started on the ground floor and the manufacturing of the special stonework for the columns and top molding was taking place, there was discordance not only on who was to manufacture the top molding drum, but also what the height of the top molding drum should be, ¾ or ½ of a CdM-ft, and the stone type, breccias rossa, white stone or marble. When the stonework came together during construction at the top of the column, the molding drum manufactured by the column stonecutters did not match, in thickness and stone type, the top molding manufactured by the other stonecutters. Furthermore, it was ¾ of a CdM-ft below the height that was to be the vault spring line. With the stonework parts already manufactured and likely partially assembled, it was too late and too onerous to correct the problem. The tas-de-charge was mounted on top of the column, which locked in the height of the vault spring line, short of the intended height. The top molding voussoirs were installed just above the vault spring line, on the sides of the tas-de-charge, making a break for the width of the column capitals, Fig 31. |
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8.6 The Structural Function of the banch Seat |
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The stonecutters manufacturing the column stone pieces for the upper floor followed a similar procedure and divided the prescribed height for the columns, which was the same as the columns on the ground floor, into four parts: the base, a shaft, a capital, and a top molding drum, all to be made of marble, Fig. 5 and 32. The molding drum this time matched the top molding voussoirs perfectly in marble, face decoration and thickness, Fig. 32. The molding thickness was reduced to ½ CdM-ft and matched the thickness of the molding drum manufactured by the stonecutters making the column pieces.
The builders were able to correctly coordinate the top molding stonework on the upper floor and avoid the gaffe on the ground floor. It seems however that it was too late to change the height of the columns, which were manufactured with the same exact height of the columns on the ground floor. It is construed that this was the principal motivation for the bench seat concept, which was to achieve the correct height for the vault spring line by mounting the columns on top of the bench seat. Extending the bench seat continuously around the room served a secondary but propitious purpose, which was of a structure that with its width conveyed a sense of room enlargement on the upper floor, as well as providing a useful function. The height for the bench seat was taken from the column semi-octagonal dimensions, as indicated above. It is a congruent choice within the concept of the bench seat being a pedestal extension of the column capital, and it is fortuitously a comfortable height for a seating function, as mentioned above. But it is still short to raise the columns to the required vault spring line on the upper floor for rooms 2-8. Coincidentally however, the resulting shortage is in the range of ¾ of a CdM-ft, similar to the shortage of the height of the vault spring line on the ground floor that could not be corrected, so there was no need for a further correction in the final height of the vault spring line on the upper floor. |
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8.7 The Height of the Room at the Keystone |
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The vault height is dictated by the semicircle form of the diagonal ribs. The height of the vault spring line is locked by the columns and is ¾ of a CdM-ft short on the ground floor. When later it was time to erect the rib system on the ground floor, the builders adjusted the centering frames of the diagonal ribs to ensure the height of the room at the keystone would be the correct one, which is the dimension of the diagonal of the cross vault base square on the ground floor reduced by ¾ of a CdM-ft for the molding drum that was missing on top of the column.
When later it was time to erect the ribs on the upper floor, the builders followed a similar procedure. The builders adjusted the centering frames for the diagonal ribs, just as was done on the ground floor. The goal was to ensure that the height of the room at the keystone was the expected height according to the standing circle model. This height is the size of the cross vault base square diagonal on the upper floor reduced by ¾ of a CdM-ft, which is the shortage in the height of the columns. This is therefore the rationale explanation for the uniform shortage of ¾ of a CdM-ft in the height of all rooms, on both floors of Castel del Monte, except for the throne room. This provides support to the standing circle model theorized to be the guide that the medieval builders likely followed in setting the room elevation dimensions. |
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9. The Shortages |
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The blunder in coordinating the stonework that incorporates the top molding in the columns resulted is a systemic shortage of ¾ of a CdM-ft in the height of the rooms at the keystone, as indicated above. This shortage should be reflected in a corresponding and identical shortage in the height of the vault spring line, since the vault along the diagonal ribs is expected to be a perfect semicircle.
However, measurements indicate that this is not quite the case. Table 5 outlines key measurement shortages from the theorized dimensions per the standing circle model. The shortage in the height of the room at the keystone is actually divided into a significant but smaller than expected shortage in the height of the vault spring line, and in a surprising but small shortage in the height of the vault at the keystone. It is unlikely that the small shortages in the height of the vault are the result of measurement errors, or due to variances in the measurements. The shortages are systemic and consistent in all three cases. There are, however, simple and very plausible explanations for why the shortage in the height of the vault spring line is less than expected and why there is a surprising shortage in the height of the vault.
The following are reasons for the portioning of the ¾ CdM-ft shortage between a minor deficiency in the height of the vault spring line and a small and unexpected deficiency in the height of the vault at the keystone. |
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9.1. Small Shortage in the Height of the Vault Spring Line |
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The shortage in the height of the vault spring line for all rooms but the throne room is expected to be ¾ of a CdM-ft, 0.227 m. This is what has been reasoned to cause the shortage measured in the room height at the keystone, specifically in the case of the ground floor.
The actual shortage in the height of the vault spring line is somewhat shorter, 4.7 cm on the ground floor and 7.5 cm for rooms 2-8 on the upper floor (Table 5). A likely explanation is that the stonecutters working on the column divided the height dimension of the column among the separate stone pieces that make up the column: base, shaft (made of two pieces on the ground floor), capital and molding drum, Fig. 5. This would yield a shortage of exactly ¾ of a CdM-ft in the height of the vault spring line. However, this does not account for the grout lines among the various pieces, which is what may have happened. There are five grout lines in the columns on the ground floor, which would easily amount to the 4.7 cm that the height of the vault spring line rises above the expected shortage of ¾ of a CdM-ft. On the upper floor, there are only four grout lines in the column assembly, because the shaft is made of a single piece. However, there is the bench seat that is part of the height for the vault spring line, which adds few more grout lines. Here too, these grout lines likely explain why the shortage in the height of the vault spring line is 7.5 cm less than the expected shortage of ¾ of a CdM-ft for rooms 2-8 on the upper floor. |
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9.2. Shortage in the Height of the Vault at the Keystone |
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The missing shortage in the height of the vault spring line shows up as a shortage in the height of the vault itself. It is a small shortage, from 4 to 8 cm for nearly all rooms (Table 5).
The presence of a shortage in the vault height at the keystone indicates that the radius of the semicircle is shortened at the top, corresponding to the keystone. The radius of the semicircle does not change in correspondence with the columns, because the span of the semicircle is the diagonal of the cross vault base square. The result is therefore a slight distortion in the shape of the semicircle. It is a small and imperceptible distortion that the builders likely introduced when they set the centering frames for the ribs among columns already in place, including the tas-de-charges. The centering frames were likely set and adjusted to yield the intended height of the room at the keystone, as indicated above. This is the diameter of the cross vault base square, which is also the diameter of the standing circle, reduced by the ¾ CdM-ft shortage in the height of the columns. As explained above the shortage in the height of the columns was caused originally by a missing molding drum on the ground floor. |
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10. Room and Vault Heights at the Tranverse Ribs and Dividing Walls |
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The ceiling is a cluster of vaults: four cusped webs that give form to the square cross vault with a triangular slice of a cusped-barrel vault on each side, Fig. 7. The keystone at the center of the cross vault has the highest elevation over the floor. The crest of the cross vault webs slopes down from the keystone to the top of the transverse ribs; the crest of the side vaults runs horizzontally from the top of the transverse ribs to the dividing walls.
The height of the room at the keystone is determined by the standing circle, as outlined above, with a correction per the missing molding drum on the ground floor. The remaining ceiling elevations of interest are the height of the room and the vault at the transverse ribs and the dividing walls. These heights just “happen” per the ribbed squared cross vault construction procedure outlined above. Part of this procedure is the formation of the ogive for the transverse ribs: two intersecting arcs with the radius of the standing circle. The height of the ogive, which is the height of the vault at the transverse ribs, is accordingly a dimension that is predictable and determined geometrically, Fig. 19. The height of the vault at the transverse ribs is theorized to be 4.331 m on the ground floor, 4.692 m for rooms 2-8 on the upper floor, and 4.909 m for the throne room. The drop of the vault from keystone to transverse ribs is also theorized to be 0.199 m on the ground floor, 0.215 m for rooms 2-8 on the upper floor, and 0.225 m for the throne room. The ribbed squared cross vault construction procedure starts with the height of the room at the keystone, and the vault forms drop down in a preordained measurable pattern. Accordingly, any issue in the height at the keystone, such as the ¾ CdM-ft shortage, will show up in the height at the transverse ribs. Measurements show that this is essentially the case. The shortage in the height measurement of the room at the transverse ribs from the theorized dimension is essentially the ¾ CdM-ft shortage of the room height at the keystone, Table 6.
The dimensions derived from measurements for the vault height at the transverse ribs and the drop of the vault from keystone to transverse ribs (Table 1) are indeed close to the theorized amounts. The differences are in the order of few centimeters, Table 6; well within the small variance in the measurements. The throne room presents a small exception as addressed next. The side vaults have the ogive profile of the transverse ribs that seems to be projected horizontally to the dividing walls. Accordingly, the crest of the side vaults runs horizontally at the same elevation. Measurements show that the height of the room at the dividing wall is taller of the height of the room at the transverse ribs by 3.5 cm on the ground floor, 5.3 cm for rooms 2-8 on the upper floor, and are essentially even for the throne room. These differences are in the range of the measurement variance. Therefore measurements support the conclusion that the builders intended to keep the height of the room at the dividing walls the same as the height of the room at the transverse ribs. |
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11. The Throne Room |
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The throne room is larger by a CdM-ft than the other rooms on the upper floor; the diagonal of the cross vault base square is accordingly 34 CdM-ft, as indicated above. Therefore, the height of the throne room at the keystone is theorized to be 34 CdM-ft, 10.268 m, per the standing circle model; this is substantially taller (0.453 m) than the theorized height of any other room on the upper floor (9.815 m).
The measurement for the height of the throne room at the keystone is 9.752 m (Table 2), 32.29 CdM-ft. The actual height is 0.516 m, 1.71 CdM-ft, shorter than the theorized dimension. This large shortage should be reflected in the height of the vault spring line, which theoretically should be 17 CdM-ft, 5.134 m, half the diagonal of the standing circle, that is half the diagonal of the cross vault base square. The throne room has a support system for the ribs that is identical to the other rooms on the upper floor: columns that include the upper molding and are mounted on a similar bench seat. Indeed the height of the bench seat-column combination, which determines the height of the vault spring line, is the same as in the other rooms on the upper floor, 4.756 m (Table 4). Therefore, the height of the vault spring line is 0.378 m short of the theorized dimension. Thirdly, the height of the vault at the keystone should be 17 CdM-ft, 5.134 m, which is the radius of the standing circle, which is half the diagonal of the cross vault base square. The measurement for the height of the vault is 4.996 m (Table 1), which is derived as the difference in the measurements between the height of the room at the keystone and the height of the vault spring line. The height of the vault at the keystone is 0.138 m short of the theorized dimension. Indeed, it is verified that the shortage in the room height at the keystone, 0.516 m, is divided between a shortage in the vault spring line, 0.378 m (Table 5), and a shortage in the vault height of the vault at the keystone, 0.138 m, as seen above for all the other rooms. The shortage in the height of the vault, 0.138 m, is significant in the throne room and implies that the arc formed by the diagonal ribs in the throne room is far from being a perfect semicircle; it is likely a flattened semicircle, more like an oval, or some other distorted form depending on the tas-de-charge curvatures. The theorized height of the vault at the transverse ribs is 4.909 m; measurements indicate however a height of 4.821 m. The shortage, 0.088 m, is slightly less than the shortage at the transverse ribs in the other rooms on the upper floor, 0.096 m (Table 6). On the other hand, the drop in the ceiling height from keystone to transverse ribs, 0.175 m, is a bit less than the drop in the other rooms, 0.234 m (Table 1). The height of the room at the dividing walls in the throne room is essentially the same as at the transverse ribs, one centimeter less. The significance of the measurements and discrepancies from the theorized dimensions is that the design of the elevations for the throne room deviates from the standing circle model for no rational explanation other that the construction was improvised. It was likely an afterthought, rather than an early, precise and predetermined design. The changes for the throne room may have been motivated by a consideration to give this room a royal feel in dimensions as well, taking advantage of the opportunity presented by the foundations from the ground floor where the corresponding room had been moved toward the center of the plant by one CdM-ft. The column support for the ribs, which had to be taller, was instead made of the same exact columns of the other rooms on the upper floor. This is a likely outcome if there were no plans yet for the enlargement of the throne room when the premature order for the columns was made. This is a planning shortcoming just like the other issue addressed above of columns of the same height as the columns on the ground floor while taller columns were needed on the upper floor. The rib centering frames for the throne room would need to be different from the centering frame used in the other rooms, because of the larger room dimension. Instead, it is likely that the builder used the same centering frame that had been used for the other rooms, adjusting the framing components to give a slightly taller vault, but still far short of half the diagonal of the cross vault base square to result in a perfect semicircle. It is also likely that the tas-de-charges installed in the throne room also had the wrong radial curvature, matching the other tas-de-charges on the upper floor. The erection of diagonal ribs, which are composed of free rib voussoirs mounted on centering frames between tas-de-charges, is a challenging construction as discussed in the “Tas-de-Charge and the Rib Support System Analysis” section. The precision in the stone work for the tas-de charges and the rib voussoirs, and the arrangement made in properly setting the centering frames are critical in the form that the diagonal ribs take at the end of the construction. The centering frame adjustments presumed above in the throne room that seem to have resulted in a significant distortion of the diagonal rib are likely to produce localized excessive shearing forces, especially in correspondence of the tas-de-charge. These shearing forces are one of the causes responsible for the defacing of the rib stonework. Notable in this respect is the defacing of all tas-de-charges in the throne room, Fig. 38. In conclusion, the vault in the throne room was built in line with the medieval practice of building ribbed cross vault. However, the builders used key elevation material, such as columns and likely centering frames, used for the other rooms. These were short to yield the room elevation at the keystone per the standing circle model and consequently shorter elevation at the transverse ribs and dividing walls as well. All indications are that the elevation of the throne room was an improvised construction. |
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12. Conclusions |
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The study of the room elevation has been very productive in many ways. It has brought to light two new geometric models that the designers followed: the squared octagon to define the dimensions of the columns bases, and the standing circle to set the dimension for the height of the room at the keystone and the height of the vault spring line. The medieval ribbed cross vault construction practice is also confirmed, especially in regard to the ogive form and heights at the transverse ribs, as well as the drop of the vault from keystone to transverse ribs.
While the rooms follow a similar design throughout the castle, the study has established three sets of measurements: one set for the ground floor, another for the larger rooms on the upper floor, and a third one for the throne room. Except for the throne room, the standing circle model does explain the key room elevations. The study has also brought to light interesting details: (1) a blunder that the medieval builders ran into in coordinating the integration of the top molding into the column; (2) a shortcoming in the height of the columns on the upper floor; (3) the structural reason (likely main reason) for the bench seat on the upper floor; and (4) the improvised nature in the erection of the throne room. |
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13. Documentation Notes |
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File: “cdm-152-130=elev-study-findings-en”
Castel del Monte — Study of the Elevations Room and Vault Heights: Data Analysis: “cdm-152-130=elev-measurement-analysis-en” Figures: “cdm-152-130=elev-figs-en” Findings: “cdm-152-130=elev-study-findings-en” Tas-de-Charge: Report: “cdm-152-230=tas-de-charge-study-en” Figures: “cdm-152-230=tas-de-charge-figs-en” Domenico Lanera domenico.lanera@gmail.com www.lanera.com January 2021 |
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