MAAS Magazine

Roof geometry model of the Sydney Opera House

Principal Curator Matthew Connell explores the ideas behind the creation of Sydney’s most famous building. This is an extract from the publication Icons, which can be purchased online

Sydney Opera House Model
Sydney Opera House model: Timber, illustrates the origin of the roof geometry of the Sydney Opera House, designed by Jørn Utzon, made by Ove Arup and Partners, England/Australia, 1961–65.

In 1957 Jørn Utzon’s daring design for the Sydney Opera House was retrieved from the reject pile by the competition jury and presented as the winning entry for a new opera house to be constructed on Bennelong Point, Sydney Harbour. It was a brave choice from among 222 entries. Utzon was a young and relatively unknown architect. His great concentric shells were striking and evocative, but the plans were unaccompanied by any obvious way to build them. Nevertheless, he was awarded the prize and contracted to deliver the iconic new building.1

There is an extensive selection of models in the Museum of Applied Arts and Sciences collection. They relate to many different collecting areas and categories of human endeavour. Some are direct scale replicas of built structures, many are abstractions of particular ideas. In this latter role, Jørn Utzon’s model for the Sydney Opera House is especially elegant and effective. Initially made by Utzon to explain his thinking to engineers at Ove Arup and Partners, including Ove Arup himself, it was later used to inform and engage other stakeholders, including the public. It has been such a successful communication tool that several models have been produced and are held in various institutions around the world, and there is a version on public display in the forecourt of the Opera House. A photo of the model in Yuzo Mikami’s 2001 book Utzon’s Sphere confirms that the Museum’s model is the original.2

The model represents an exchange between the two main players in the design and construction of Sydney’s most famous building. The Sydney Opera House is now recognised as the building that initiated the trend towards signature buildings ‘to create a focal point in a city’ and, remarkably, is almost universally viewed as both ‘great architecture and a mass-culture icon’.3

The modest timber model is comprised of a dome, part of a sphere, mounted on a square timber backing board. Meridian lines radiate out from the centre point at exactly 3.65-degree angles. Also from that centre point, four different-sized ‘triangular’ segments can be removed from the whole and arranged side by side to show the distinctive form of the Sydney Opera House. Through this feature the model demonstrates, with remarkable efficiency and clarity, the final geometric solution for the shape of the Opera House and how the protracted problem of the construction of the ribs required to support the great shells is resolved.

The four 'triangular' segments of the model
The four ‘triangular’ segments of the model can be arranged into the now iconic form of the Sydney Opera House. The meridian lines show the consistently repeated shape of the ribs, so essential to the building’s construction.

Utzon’s shells were not the first shell structures to be designed or built, but the engineering theory was in its infancy. Danish-British engineering firm Ove Arup and Partners was one of the only firms with an established reputation in the field. Ten years before the general availability of computers, one of Arup’s partners, Ronald Jenkins, had established and published new approaches for shell structure analysis. They used mathematical methods that would become the mainstay of computer-based structural analysis. Arup agreed to take on the job and, with Utzon, set about determining a suitable geometric discipline.4

Engineers need to calculate all the forces that will affect the structure of a building during its lifetime — the weight of materials, the occupants and contents, as well as wind, rain and natural disasters. Having a known geometry means they have mathematical formulae that allow them to calculate the forces at each point on the structure, under various load conditions, and therefore the internal stresses that have to be built into the structure to withstand those forces.

Between 1957 and 1961 12 different arrangements were tried. Variations on circular, paraboloid and ellipsoid arrangements were experimented with, and each delivered a new set of problems. There was a particular problem with the actual construction of the ribs required to support the shell. These were to be made from precast concrete, cast on-site. All of the proposed structures required each rib to be different, which meant manufacturing a special form — an enormously expensive prospect. The spherical geometry underpinning the Opera House meant only one form could be constructed and each rib terminated at the correct length, allowing the Opera House to be built.

While the Sydney Opera House was ultimately constrained by the dictates of its construction and bound by simple, well-established geometry, it was still a very complex structure and the calculations could not be completed by the traditional means of slide rules, log tables and mechanical calculators.

In the late 1950s the first digital computers became available for business and civilian use. The engineers behind the Opera House relied on computers in Britain and Australia to assist with their analysis. Indeed, the Opera House appears to be the first architectural work that would not have been possible without the development of computers.5 In the 21st century the biggest influence on architecture is computation. The freedom to design any shape was not available to Utzon in 1957, but his work foreshadowed the innovative architecture to come, including iconic buildings designed by Frank Gehry and Zaha Hadid. In fact, Gehry has commented that his commission to design the Guggenheim Museum in Bilbao, Spain, was modelled on the Opera House: ‘They picked me as the winner because they thought they had a chance of getting a Sydney Opera House out of it’.6

Jørn Utzon and Ove Arup embody an ideal. Both men were exceptionally creative and extremely adept mathematically and technically. Arup said, ‘Utzon was a genius, probably the best architect with whom I have ever worked.’7 Arup is renowned as one of the great creative engineers of the 20th century. While the success of the Opera House is largely attributed to these two men, and Utzon is viewed as the creative genius behind it, ‘his vision was enriched by the contribution of many other participants’, and the collaborative design environment established by Utzon and Arup ‘inspired exceptional feats from the project team’ and ‘an international array of contractors’.8

In addition, there is a long history of individual and collective genius embedded in the mathematical thinking that informed this model. That history includes Euclid and Apollonius, two ancient Greek mathematicians who established the mathematical principles that informed the model and building’s structure, and English mathematician Alan Turing, who conceived of the first digital computer.

This model not only captures Utzon’s genius and represents the process behind his thinking, it also signifies a conversation with Arup and, as demonstrable proof of a very elegant solution to a complex engineering problem, it embodies centuries of mathematical and scientific thought.



1 Anne Watson, ‘An opera house for Sydney: genesis and conclusion of the competition’, in Anne Watson (ed) Building a Masterpiece: the Sydney Opera House, Powerhouse Publishing, Sydney, 40th Anniversary Edition, 2013, p 46.

2 Yuzo Mikami, Utzon’s Sphere: Sydney Opera House – How it was designed and built, Shokokusha Publishing Co Ltd, Tokyo, 2001, p 66.

3 Bronwyn Hanna and Patricia Hale, ‘“A masterpiece of human creative genius”: recognition, reconciliation and heritage conservation’, in Watson (ed), Building a Masterpiece, p 170.

4 David Taffs, ‘Computers and the Opera House: pioneering a new technology’, in Watson (ed), Building a Masterpiece, p 91.

5 Taffs, pp 84–101.

6 Hanna and Hale, p 170.

7 Taffs, p 105.

8 Hanna and Hale, p 175.


Cover of Icons book publication.
Icons, published 2016.


Purchase Icons online or from MAAS Store and selected bookstores.