The building’s shape slowly shifted away from Utzon’s competition drawings. His new curves were detailed in the Red Book, a complete set of plans, sections and elevations sent to the NSW government in March 1958, which expanded on the schematic drawings from his competition entry. The roof’s ridge profiles had become higher and more pointed; the end shell form no longer cantilevered like a cliff over the sea. These higher profiles also allowed for more volume for the stage towers and auditoriums.
Yet the drawings contained in the Red Book were structurally unsound, with difficult bends near the roof’s footings. Each shell was different. The lack of a defining geometry would make it impossible for the builders to reuse formwork and would add to the building’s costs.
As the years and iterations continued without a satisfactory solution, resolution of the issue went from pressing to critical. By late 1961, three years had passed since Utzon had bent his plastic ruler on a table and a solution to building the shells had still not been found.
Utzon was even asked by the NSW government whether he should consider another engineering firm – but the architect refused to look elsewhere, convinced his collaboration with Arup would yield the solution. In the end the solution would come from Utzon himself.
Various myths surround the discovery of the so-called Spherical Solution, the unified answer to the problems of buildable shells. The iconic sculptural form of the Sydney Opera House essentially relies on the form of these shells, so the importance of finding the best solution to the roof cannot be underestimated.
As one of the more popular myths has it, Utzon had a eureka moment while peeling an orange. While it’s true that the solution can be demonstrated in this way, it had in fact been architect Eero Saarinen who, over breakfast one morning years earlier, cut into a grapefruit to describe the thin shell structure of the roof of his TWA Building, and later used an orange to explain the shape of the shells to others.
By his own account, Utzon was alone one evening in his Hellebæk office with a number of the most intractable Sydney Opera House problems weighing heavily on his mind.
Utzon was stacking the shells of the large model to make space when he noticed how similar the shapes appeared to be. Previously, each shell had seemed distinct from the others. But now it struck him that as they were so similar, each could perhaps be derived from a single, constant form, such as the plane of a sphere.
The simplicity and ease of repetition was immediately appealing.
It would mean that the building's form could be prefabricated from a repetitive geometry. Not only that, but a uniform pattern could also be achieved for tiling the exterior surface. It would become the single, unifying discovery that allowed for the distinctive characteristics of Sydney Opera House to be finally realised, from the vaulted arches and timeless, sail-like silhouette of the Opera House to the exceptionally beautiful finish of the tiles.