Models: The Red and Yellow Books

When in 1958 the engineers at Arup and Partners requested that Utzon define the curves of the roof, he took a plastic ruler and, holding it perpendicular to a table, made it bend. Tracing the curves, he sent them to London explaining these were the shapes he wanted.

The outcome of the first exchanges between architect and engineer produced an initial sketch of the roof in which every curvature is different, a structurally unsound form with difficult bending moments near its footings.

However, this first geometrical approach to the shells was also visually beautiful in a distinctly different way to the drawings Utzon had submitted for the competition.

The ridge profiles were much higher and pointed now, and the end shell form of his competition drawings no longer cantilevered like a cliff cave over the sea.

These higher profiles also allowed far more volume for the stage towers, auditoriums and acoustics.

Utzon’s architects redrew all of the elevations of the Sydney Opera House to the new forms, and these are shown in the 1958 design documentation, known as the Red Book.

Clearly the profile of the roof had changed considerably, but it was received by the client and the public as a transformation for the better, for both logistical and aesthetic reasons.

Thin shell structures were the form of his original sketches and much favoured by leading architects and engineers at the time. Eero Saarinen, Felix Candela and Pier Luigi Nervi had already used concrete shell membranes in world-renowned structures.

The Yellow Book presented the "Spherical Solution" - a final design rationale for the roof of the Sydney Opera House.

The form of the shells had changed again and again, as architect and engineers struggled to find a buildable structure that captured the spirit of the design and could house the complexity of a working building.

After many failures, Utzon had a now famous epiphany that would solve what had apparently become an intractable problem.

Utzon's breakthrough was to derive each of the shells from the constant and universal form of the sphere. This one decision solved a multitude of problems. It captured the essence of the original sketch, while allowing the building blocks to be prefabricated with comparative ease.

It also raised the finished building out of a style identified with the times and gave it an ageless form.

The spherical solution underpins the roof form that we see today and is explored in more detail in "The Masterful Solution" exhibit.

In these models, we can see the fusion of the ribbed approach with the spherical geometry through which Utzon famously arrived at a final approach to the roof, informed by a three-year period in which Arup engineers struggled – and ultimately failed – to find a workable solution through parabolic geometry.