BUILDING BROCHS

For many years now, researchers have been thinking about brochs, wondering how these structures were erected. A process has been proposed, see - https://voussoirs.blogspot.com/2017/01/on-brochs-enigma-of-meaning-form.html This technique used the geometry of constructing a circle without knowing its centre. Here, with this method, the focii of an ellipse formed by two posts of the six that have been assumed to be at the centre of the broch, are used to draw the close-to-circular curve at various locations. It is not an exact strategy, but is one way to approximate a circle without knowing its centre or being able to easily access it.

A far more accurate system based on the use of simple pegs and string, seems to be possible as an alternative to this rough method. It adopts a similar strategy, almost being a variation of it; but it is a far more accurate and elegant method. It is discussed in this site: see - https://math.stackexchange.com/questions/862915/how-to-create-circles-and-or-sections-of-a-circle-when-the-centre-is-inaccessibl/862940 The chat starts with the question: how does one draw a circular arc without knowing or having access to the centre, for landscaping paths, garden edges, etc.? One idea uses the principle that says that the angle suspended by a chord of a circle is always the same for the same chord. So string and pegs can precisely manage a circular arc without knowing or using the centre; but what of a whole circle? How does one arrange the continuity of the arc, its coherence in circular rigour?

We know the length of the chord, so a piece of string kept at the same angle can easily define an identical arc from this same line length, giving the same portion of circle anywhere; but the orientation of this chord length is critical if one is to define a complete circle. The position of the new chord, (of equal length), must be aligned such that it is a chord of the same circle as that which the other chords relate to. The best, perhaps the simplest beginning for the definition of this circle is to use an equilateral triangle, or indeed, any geometrical shape that can be simply delineated and will fit within a circle. An arc can be structured off each of these chords, (three in the case of an equilateral triangle), which, being the same and related to the same circle, will describe a circle when the suspended angle is always 120 degrees. Various other alternatives of inscribed shapes are possible, all of which will have different suspended angles – e.g. 135 degrees for a square; 150 degrees for a hexagon. Without the exact angle appropriate to the shape, one will get, e.g. for an equilateral triangle, a trefoil form or a similar deformity; a quatrafoil form for a square; etc.

Typical broch plans

To set out a circle, one could start with a compact form, say a hexagon, (a circle with the radius marked out along the circumference as six equal chords), extend the alternate sides into an equilateral triangle, and use the sides of the triangle as the chords from which to suspended an angle of 120 degrees. One could ask: was the hexagon the start of the set out of the broch? The inner arrangement of posts could be easily defined and expanded to give the locations of the larger triangle for the larger circles by marking off points on the lines extended from the centroid of the triangle through each corner of the form. It may seem strange that one starts with the centre of the circle, (for the hexagon), and then does not use it for the setout. The complication comes with height. While it is simple enough to use pegs and a string to draw circles on the ground, and work up from these markings, matters become complex when things might get in the way, such as scaffolding. It is difficult to extend the centre line vertically as a line to a higher point in space without some fixed references. It is much easier to extend a structure up, say a braced set of six posts, to define the 3D location, but this complicates the access to the centre. So the idea of the circle being able to be drawn without access to its centre has to be contemplated. It is neither impossible, nor difficult.

The set out of the circle can be managed with pegs, a string, and a template with three pegs positioned at an angle of 120 degrees, (if one is starting with an equilateral triangle). By fixing the string at one peg, (one corner of the triangle), and having a second person pulling the string around another peg on a different corner of the triangle such that the string forms an angle of 120 degrees on the guiding template, the point of the template will be able to define a point on the circle. The template could be repeatedly manipulated into various positions such that the string touches all three pegs at 120 degrees as well as the second chord peg, with the apex peg on the template defining the various locations of the points on the circle in which the equilateral triangle sits. This process can be repeated for each side of the equilateral triangle to give one the complete circle. This accurate set out can be achieved with two people, pegs, a length of string, and a template with pegs set out to define the angle of 120 degrees, an angle that is easily set out by drawing a hexagon. This is a process requiring only one peg and one string. The angles between the sides of a hexagon are 120 degrees.

It is interesting to observe the plans of round houses and wheel houses. These illustrations show posts located in relation to the surrounding circular wall in the position required for this peg-string-template set out process. One can check this by extending the sides of the hexagon to make an equilateral triangle that touches the surrounding wall.

The set out from the hexagonal post arrangements using pegs, string and template

Typical round house

A set of twelve posts can give a hexagon, square, or an equilateral triangle to set out from.

What we do know is that dry stone builders do not do anything freehand – they use strings and profiles. Strings can draw arcs and manage profiles, even ellipses and circles, accurately, as has been described, so it all seems to be a reasonable beginning. The other controls required for construction relate to horizontals and verticals - to levels, and the vertical continuity of the whole. The solution to these issues are simpler than the drawing of the circle, but similarly require string, a timber template, and an additional weight. The plumb bob can be used to define the vertical projection, as well as the horizontal alignment. Shetland has an old, but simple and effective level. It is a forty-five degree triangular template made up as a timber frame, with a plumb bob hanging from the ninety degree intersection. The centre line of the hypotenuse is marked off as a base scale. The alignment of the plumb bob string with the centre line mark positions the hypotenuse on the true horizontal. It is an ingenious device that would have been easy for broch builders to both make and manage at all sizes for various types of tasks. Any isosceles triangle will do too, but the 45/90 set out is simple, and provides the mason with a square and the 45 degree angles. With any other triangle, the centre line of the base of the triangle will be the marker for the string suspended from the apex. The hypotenuse/base element can extend well beyond the scope of the triangle so as to provide a good length for the gauging of the horizontal level along or between elements.

As for broch verticality and continuity – a centre reference solves this. Even the modern laser scans of the broch use a vertical centre line as a primary reference. We could hypothesise that the six posts were the start of the set out, each being set up vertically, and became the vertical reference points that carried the walls up in their desired alignments. When dry stone walls are built today, profiles are used to control the planes. One can assume that broch builders used a similar technique. So while we can devise techniques to describe processes that could have been used in the set out of the broch, the question is: what holds the profiles for the upper levels? Might it be the scarcement? Was it the scaffold? Was the inner structure both the scaffold and the permanent fit-out?

A laser scan of the interior of Mousa broch.

Temporary scaffolding may have also been used internally along with the permanent framing.

Externally we can propose a system of scaffolding that leaned against the finished walls, being propped up and out from these as they progressed, providing a working platform that did not require scarcements. Projections could have been avoided externally so as to improve security; to not provide anyone with a ledge to use for climbing. In all of this speculation, one has to come to terms with the other question: how were the masses of stone managed? Even with a small dry stone structure, one is amazed at the quantity of stone that becomes the pile of rubble once the old walls have tumbled down. The quantity of stone needed for the broch would have been enormous. How was the stone lifted for the work to continue up to thirteen metres, (Mousa)? The mason must have had a plentiful supply of stone close by because the process of building the dry stone walls involves selecting and picking up what seems to be an appropriate stone and finding a place for it; and doing this time and time again. It is a different process to laying dressed stone. It would not make sense for stones to be transported from the ground one by one as the dry stone mason required. Reconstructions have taken brochs up to working heights manageable from the ground level. The challenge is to discover how the rubble was handled at the upper heights. One could perhaps guess that stones were stacked on the inner and outer scaffolds, and continually replenished to maintain the stockpile. This means that the scaffolds must have been fairly substantial structures, both in size and strength.

What we do know is that gravity has not changed, and neither have the juxtapositional forces of stone on stone, or of timber on stone. We should be able to re-imagine the process once we have some degree of certainty about the available processes that we can suppose involved the use of templates, profiles, string, pegs, and weights, because we still use these today, almost in spite of our clever technology: isn’t a laser merely a flash piece of string?

On the scarcement: this ledge looks like a change in construction strategy. It is such a self-conscious element that it must have a significant purpose. Was it there to hold the scaffold; maybe the upper profiles? Was it there to support the floor as well? How were the wall profiles managed? - see: https://voussoirs.blogspot.com/2017/01/on-brochs-enigma-of-meaning-form.html  Was the scarcement there to do all of these tasks? Multi-function appears to hold some logic in the interpretation of these times of efficient frugality with materials and energy. It is this latter feeling, an assumption, that gives one the idea that brochs had a definitive purpose beyond display and intimidation (Smith), qualities that maybe still played an inclusive, integral part of the dominance in appearance.#

It is not clear if the galleries actually have any floor space.

The void is bridged by separate stone ties.

Some researchers seem to support the idea that brochs were constructed from the void between the walls, without scaffolding. It is certainly an intriguing idea, but it has its complications: see - https://voussoirs.blogspot.com/2017/01/on-brochs-enigma-of-meaning-form.html  It is not too difficult to envisage the erection of the broch up to the scarcement height. Things to this level appear to be readily manageable from the ground, with traditional setout techniques and small scale scaffolding. It is above this level where things get tricky. The walls become twin dry stone walls that continue up to greater heights, to 13 metres in the case of Mousa. So how were these walls erected?

The 3D scan suggests a lower scarcement too - see *

One could just suggest that there were scaffolds that were erected for the work. Scaffolding can easily be pieced together for almost all circumstances: but might iron age man have been so generous with his materials and effort? It has previously been argued that it is not reasonable to suggest that the broch was built overhand from the space between the walls. One could simply suggest that planks were used to span the bridging stones to provide the work support, but the finish of the exposed surfaces of these walls seems too perfect to have been erected from the ‘away’ side. Supposing that the base of the broch was erected and completed up to scarcement height, then his mass would have provided a working surface for the masons to erect the walls spirally, working on the ends of the walls, and moving backwards in a spiral as the walls progressed, moving up to the next level once one circumference has been completed. At least there would be some continuity in work location.

The scarcement has frequently suggested a floor level.^^

Smith argues for it being there only for scaffolding.

This might seem reasonable, but there are issues to be answered: can a dry stone wall be built from the end and give the finish we see at Mousa? Even if this might be so, one has to answer the question: how were the massive quantities of stone supplied to the masons. Here one has to speculate that there were intermediate scaffolding platforms erected both inside and out for the piles of stone to be placed on. The question this raises is that, given that this scaffold for the stones exists, why would it not be used as a working platform for the masons to build the walls directly in front of them, maybe one team outside and one team inside?

It seems that the full sensing of the progression of the work is essential for the mason to contemplate, consider, and assess, as he picks up each stone and, as the rule seems to go, places it. A stone is never put back to be rejected for another; it is always used. The skills involved in this technique require a precise and comprehensive understanding of both the pile of stones and the walls in relation to the mason’s body and hands that makes demands that are not negotiable. The stance of the mason and his mental state, along with his coherence and well-being, is critical to a good outcome – both efficiently, visually and structurally. One is inclined to confirm the extensive use of scaffolding that, as with the idea of the spiral progress, could, perhaps, have been segmental and was moved around progressively to suit the programme. Internally, it seems that the idea of the vertical growth of the scaffold that could also be used for alignments and set outs, and left as permanent structure, seems the better option to promote.

There are always many competing issues for one’s consideration in these matters, but the peg, string, template and plumb bob concept along with the idea of permanent internal scaffolding and temporary external scaffolding, seems to hold more coherent logic than most suggestions. This inner and outer scaffold would be able to provide good support for the manipulation and set up of the walling profiles, and for the piles of stones that are required near the masons. Once the dry stone walls have been completed, parts of the external scaffolding could be used as the roof framing, with the upper perimeter walkway being the working platform for the roofers – for the framing and the thatching, whatever this arrangement might have been. The intramural stair is able to provide easy, permanent access to this upper level, but is unlikely to have been a main access point during construction. Lifting devices must have been used – simple ropes, baskets, pulleys and levers.

This model draws scarcements that do not exist.^^

There is little hope of any resolution when researchers invent possibilities.

One could ask why there is only one internal scarcement that seems to attract the attention of most researchers, prompting the popular view of there being a floor at this height. Smith has struggled with this matter and, along with his ‘no roof’ theory, has preferred to see the scarcement as a support for scaffolding. One has to realise that the scarcement is located at the top of the lower wall mass of the broch. Above this level the walls become thinner, twin elements tied with bridging stones.^ It is very likely that this ‘lightweight’ structure is unsuitable to provide the mass and stability required for the restraint of another scarcement for a higher floor level.+ The height of the void, (Mousa), has always been a concern for theorists trying to fit the broch out. Some solutions are just silly.* So it is that the idea of an inner frame supporting two timber-framed levels sitting on the scarcement seems to have good structural sense, as does the continuation of the inner posts to support the roofing purlins, and provide the continuous, vertical set out reference for the whole broch. The intramural stair is, of course, an access that would always have been available to reach the working level of the broch as the stair was raised with the walls.

Might the roof have been raised off the central purlin structure in order to provide light and ventilation?

Considering this overview of possibilities, one could summarise to suggest that the broch:

was set out from the hexagonal core;

used fixed internal scaffolding (and possibly some interim temporary supports too);

used temporary external scaffolding;

was roofed using portion of the external scaffolding on completion of the walls;

had two internal floor levels connected by stairs/ladders;

used only the voids formed in the base walls below the scarcement;

used the space between the walls for stairs to connect the lower level with the upper walkway;

did not generally use the gallery spaces.

The effort to fill the void creates some impossible situations.

One wonders how extra scarcements get to be illustrated (see upper level).^^

Just what the daily life in these volumes might have entailed is something that becomes more broadly speculative. The article, https://voussoirs.blogspot.com/2019/04/the-desert-broch-ksar-de-draa.html, does start to theorise on this. It seems clear that the broch was a defensive lookout; a place for the storage of food/supplies/special items; maybe a temporary refuge; perhaps a chapel, a spiritual centre; maybe a funereal location too. It seems clear that it was a community structure rather than a private, personal place.

It seems unlikely that the wall openings were used structurally

The inner openings

We can admire the stonework today, but might the habitable areas  have been lined?

Might it have been, like the Ksar de Draa, a store at high levels - the less accessible places – with the holes in the interior walls providing ventilation for the control of temperature, humidity and damp so as to overcome mould?^ The lower level might have been for fodder storage and for prized animals; the intermediate floor at the scarcement level could have been a temporary retreat, or a space for worship. It is a structure that would have isolated the damp base from the comforts of easy habitation/worship. The principle of the twin wall in construction is that the external wall can always be damp, with the inner one always kept dry. At the scarcement, the damp would collect and spread through the solid base below. One prefers to see the broch as multi-functional: a cosy, dry, warm retreat from the hub-bub of the village surrounds; a safe haven for tools, talismans, grains, oils, animals, body and spirit.

NOTES

#

Here one recalls Ralph Erskine, the English/Swedish architect. At a Brisbane convention some years ago, he presented his work and explained it rationally as being functionally formed by briefed requirements and climate. When asked privately about the self-conscious, ‘sculptural’ appearance of some of his projects, he commented that he never discussed this ‘art’ aspect of his work as it had become far too fashionable an excuse for forming, and only encouraged other, maybe younger architects to forget functional matters. He was saying that he was aware of both the functional and the artistic shaping in the one and the same form – both together. One can assume that broch builders were no different; that it is our limitation that seeks to place a singular purpose into our theories. In this regard we need to know much more about the spiritual life of the times too. Older eras were not like ours; the religious life was integrated into their very existence, their being. We should be wary of itemised explanations that rely only on unique, practical, functional interpretations other than when necessity might demand them, as in rational structural processes.

*

A close look at the 3D model of the Mousa broch interior suggests that Mousa has two scarcements, one at about three metres high, the other lower, maybe half a metre off the current inside ground level. One could easily propose that Mousa had a lower floor that was at the same level as the beginning of the intramural stair. Presently, one has to climb up to this start, an inconvenience that would have been overcome with the lower floor. That the intramural stair is still accessible today, suggests it played an important role in the daily goings on in the broch: see - 3D MODEL OF MOUSA

https://sketchfab.com/3d-models/broch-of-mousa-inside-d8bc9e5e74e64ead9cc7d7cb593e8ce4

+

BROCH FAILURES

This is an interesting article on the Safety of Iron Age Brochs, their failures:

https://safetyofironagebrochs.weebly.com/typical-broch-failure-modes.html

^

RESEARCH

See NOTES concerning broch twin wall structure and ventilation in:

https://voussoirs.blogspot.com/2019/04/the-desert-broch-ksar-de-draa.html

^^
On the graphic theories that have been drawn by researchers as cross sections, it is always alarming to see these drawings treated so casually; naively. Frequently structural elements are delineated completely inadequately, with significant structures being drawn as two thin parallel lines. While this approach distorts possible interpretations with fantastical impossibilities, it is far worse to see the existing fabric being invented. If we are unable to clearly determine and document what we have before our eyes, and use this information as a basis for careful, accurate interpretation; and are happy to liberally distort the record by adding bits and pieces to suit out theories, then we will get nowhere very quickly. Rigour and consistency are needed in every aspect of this research so that it can be tested. Personal inventions or simple carelessness does not get past the first assessment.

N.B.
For more on the building of brochs, see:
https://voussoirs.blogspot.com/2019/04/more-on-building-brochs-thinking-doodles.html

NOTE
25 February 2020
see: https://voussoirs.blogspot.com/2020/02/on-planning-meaning-mental-structures.html