We cannot imagine what Gaudi might design today if he had access to modern computer-aided design tools. But Gaudi didn’t even have a mechanical calculator. So graphical calculations were his workaday tool.

Almost all of Gaudi’s drawings and models were destroyed by mistreating and looting of the Spanish Civil War. What we know about his designs and methods has been reconstructed from the few remaining photos, notes and fragments of physical models. The Gaudi museums at the Sagrada Familia and the Casa Milá (La Pedrera) have assembled wonderful exhibitions that give us perspective on how Gaudi worked.

One outstanding example are Gaudi’s clever physical form-finding methods. For catenary arch designs, Gaudi developed the hanging-chain funicular model in depth for his Colònia Güell chapel project. The image below is an * inverted* photo of the detailed reconstruction of the Colònia Güell model. The actual model is, of course, hanging “upside down”. Inverting the photo makes it easier to visualize the catenary arches as built. Gaudi constructed these models over a mirror so he could visualize the actual building as he worked.

This method exploits the property of a catenary curve, which describes a chain in pure tension. When the catenary is inverted it becomes a curve in pure compression.

The remarkable website of the Sagrada Familia is rich with architectural information. One example is The Calculations of La Sagrada Família [PDF], excerpt:

Gaudí always chose the simplest path when it came to making the calculations for his projects. At that time, with no calculators or computers, a good graphic calculation was more efficient that a pile of papers of calculations with analytical operations. But that was the most trodden path. Gaudí distanced himself from his contemporaries’ way of doing things and went beyond that phase of the graphic calculation and on to empirical experiments with hanging models with weights and strings, a system which no other architect in the world had ever developed to the degree and on the scale which he did.

Another useful source is the MIT project paper: CatenaryCAD: An Architectural Design Tool. Here is an excerpt on Gaudi’s technique from their proposal:

Catenary systems have been used for construction in Catalan areas of Spain for a long time. For example, if a Catalan stair has to be constructed it is not detailedby the planners or architects. Instead, the masons on site hang a rope between the point of departure and the point to be reached, trace the shape and flip the curve over to use as the guide for constructing the masonry arch that carries the stairs. The rope is in pure tension, as it can not take any compression due to its flexibility. Therefore the form it finds contains the pure tensile force within the envelope of the string. If one inverts the parabola, one gets a pure compression arch which is necessary for brick construction, which cannot take any tensile forces.

Antonio Gaudi developed the system of catenary string statics into a spatial design system. He constructed scaled models of his design ideas by developing forms through a weighted string form-finding method. In his case, the models are spatial and are much more complex then the catenary staircase example. Gaudi achieved the desired forms through the control of three variables – anchor points of the strings, the length of the strings, and the weights attached to them. By designing his forms this way, Gaudi knew that the resulting geometry would act purely in compression when inverted. He also had a pretty precise estimate of the loads necessary on the different members of his construction. Beyond structural form finding, Gaudi also used this method for rendering the interior and exterior shapes of the buildings. He imagined them by painting and tracing over the “wire frame” models of lines in photos.

Axel Kilian and associates have continued to develop the project — now called CADenary. Some useful further resources:

A one minute video demonstration of CADenary (fun). A CADenary web applet — you can try out your own simple designs.

Axel Kilian “Linking Hanging Chain Models to Fabrication“, and

Axel Kilian and John Ochsendorf Particle-spring systems for structural form finding published in IASS VOL. 46 (2005) n. 147.

Axel Kilian’s website.

A virtual visit to Church of Colònia Güell .