The Masterful Solution

Sydney Opera House

Jørn Utzon's decision to derive the form of the shells of Sydney Opera House from the surface of a sphere marked a milestone in the architecture of the Twentieth Century.

Between 1958 and 1962, the roof design for the Sydney Opera House evolved through various iterations as Utzon and his team pursued parabolic, ellipsoid and finally spherical geometry to derive the final form of the shells.

By late 1961, three years had passed since Utzon had bent a plastic ruler on a table and traced the forms he wanted expressed in the roof of the Sydney Opera House. It was this action that had determined the early parabolic shape of the roof shells shown in the Red Book in 1958, but which proved, like the form expressed in his competition entry, unbuildable from an engineering perspective.

As the years and iterations continued without a satisfactory solution, resolution of the issue went from pressing to critical.

Utzon was even asked by his client, the New South Wales 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.

Architect Jørn Utzon describes the difficulties in designing the roof of Sydney Opera House.

Various myths surround the discovery of the so-called Spherical Solution, Utzon’s 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’s eureka moment came 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 at his Hellebæk, Denmark, office one evening, 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.

This simplicity and 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.

It also shifted the principle of the design away from the expression of a style, in this case shell architecture, to the more permanent idea, one inherent in the universal geometry of the sphere.

For Utzon, the realisation was an epiphany. His assistants were stunned when he explained the idea and set to providing drawings that would prove its validity.

By finding the parts of a sphere that best suited the existing shapes of the shells, each new form could be extracted. Furthermore, only one side of each profile was required as this would be mirrored to complete the arch.

The Spherical Solution would become the binding discovery that allowed for the distinctive characteristics of the Sydney Opera House to be realised finally.

The vaulted arches, the exceptionally beautiful finish of the tiles, and the timeless sail-like silhouette of the Sydney Opera House all derive from Utzon’s decision to create the form from a spherical geometry.

By any standard it was a beautiful solution to crucial problems: it elevated the architecture beyond a mere style into a timeless expression of the fusion between design and engineering.

An illustration of the Spherical Solution resolving into the cover of the Yellow Book which documented the final roof geometry of the building.

Utzon had the Helsingør Shipyards create a wooden model of the top of a sphere.

Note the derivation of each of the shell forms from the solid state of the wooden model.

Each of the vaulted shells that makes up the roof of the Sydney Opera House is derived from spherical geometry. Here you can see some of the intersecting perimeter lines that demark the extraction of the shells from the surfaces of spheres.

Utzon's note approving the form of the side shells.

Credits: Story

Created by Sam Doust and the
Sydney Opera House GCI Team

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Contributors:
Australian Broadcasting Corporation Library Sales
State Library of New South Wales
State Records NSW

Credits: All media
The story featured may in some cases have been created by an independent third party and may not always represent the views of the institutions, listed below, who have supplied the content.
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