Algorithms & Simulations: Modelling the Mathematical Façade

    Designing a unique, Mathematical Façade at the New Auckland Engineering School Building.

    The 11 storey new school of Engineering at Auckland University (corner of Symonds and Grafton) is not yet built, but design for the façade of the building is already reflecting the innovation and science that’s housed within. We spoke with Krishna Duddumpudi about the algorithims he's himself written to simulate the design and orientation of the facade to see how it performs in different conditions.

    "The building is home to post graduate research, high spec laboratories and experimental areas for a range of engineering disciplines.

    The façade includes louvres that have been designed in a special way. My role in the project has been the development of the Engineering Schools façade from its inception.

    The whole Eastern façade, where the louvres are, covers areas which house post graduate research - so essentially office space where students will be sitting down. The point of the louvres is to mitigate solar gain during the morning and also control glare; in other words, to lessen the heating up of the building by the sun.

    Right from the beginning we really wanted people to have some sense of the kind of work that goes on inside the building by looking at the facade, and also to have a reaction to the façade. We wanted them to be thinking about maths, or geology, or ocean currents, vector fields. Capturing some of the language of engineering, maths or physics on the exterior of the building was really important - especially on the Eastern face, which looks over links to State Highway One, Auckland’s Domain and is highly visible to thousands of people.

    Capturing the dynamic nature of the discipline of engineering was important too, as were considerations of the different vantage points. As you look at this façade from the Owen Glenn Building (which is basically going to form one of the main entry points), you will see a very different aspect of the façade from elsewhere.

    There is a kinetic element to it.

    Writing New Software for the Façade

    When we wrote the first custom implementation of our software for this project, in java, the louver arrangement was initially driven using the Perlin noise algorithm developed by Ken Perlin in 1983 for computer graphics applications. This provided us a proof of concept for the Eastern Façade.

    We developed our own programme right from scratch to generate the aesthetic we were seeking.

    Later iterations of the software were designed to be very user friendly. Anyone can jump on it. You can move dots around, which are like magnets. You choose whether it’s a positive or negative field or experience by moving the dots. You can thin out the louvres.

    A member of our team recently asked: “Can you simulate rain on the louvres, and look at how the rain behaves?” I thought that was an interesting idea. I went away and integrated a physics library into the script (software) that simulates how rain will behave. We have inverted the louvres to avoid valleys that capture and funnel water to the ground. The new rain programme advocated localised canopy cover at the bottom level.

    As the design and our custom software progressed, we had a good conversation with the mechanical engineers at BECA. They basically said that this looks fantastic but the effect of the louvres needed tuning to achieve the necessary thermal performance. We had to relook at it them.

    We considered what would be optimum. The optimum turned out to be louvres at 45 degrees to the way the building was orientated. The fin of each louvre had to be at 45 degrees to the building.

    We then looked at what was in the building. We had office space, and in the central area it was toilet and lift areas where thermal control wasn’t as critical. At the lower end of the façade there were lecture theatres (towards the South), which completely blocked out the sun, so we could afford to get some articulation of the fins in that area.

    We ended up with this positive, negative, positive field across the façade, which informs the dynamic of the fin pattern.

    The building is extremely pragmatic. You’ve got an Eastern façade with a porous, light element, overlooking Auckland’s Domain, making the most of the views. The Western side which faces Symonds Street is the hotter side and is blasted with sun. That’s where there are all the lab spaces. These need a high degree of thermal control. So we decided to go for our solid cladding with punched windows.

    And then you’ve got a ribbon element below on the Eastern façade, informed by the rake of the lecture theatre, so there are views out of the theatre, and it splays open to the front. It opens up the lab spaces on the front (North-Eastern) side for views to Grafton Road and it allows views into the space itself.

    The end result is: there are 687 unique fins in the louvres, and double that for fixing points. The right hand fixing point is always the same; the left hand side is variable. Now we are in the process of coordinating this with Thermosash, who are our façade manufacturer. They’ll be fabricating all of these louvres as part of the unitised curtain wall system. I was able to give them the fixing points for each of these unique fins as an excel file. The look of the facade will be very dynamic in life, once you get the shadows falling on it."

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