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Roof Perforation Optimization using Grasshopper and DIVA

I would like to share my experience with the design of the competition winning entry for the TGV Station in Montpellier, France by Marc Mimram Architects. Together with my team at ELIOTH , my job was focused on the design of the perforations for the concrete vaulted roof system. The tools used were Rhino, Grasshopper and DIVA.

The primary challenge was designing a perforation pattern that targeted light onto specific zones on the platform while at the same time making sure that the space remained cool by minimizing the amount of direct light passing through the roof. This is a common scenario for most projects; we want to have as many apertures as possible to maximize the natural light in our spaces, however, the price we pay is the energy required to cool these spaces due to the large amount of solar radiation passing through the apertures. In all cases, design parameters need to be adjusted to find a balance where the apertures are large enough to allow enough natural light but small enough (and oriented correctly) to minimize the amount of solar irradiation. The amount of natural light that falls on a surface inside the space is measured by the Daylight Factor value.

What is a Daylight Factor?
In general, building regulations quantify the amount of natural light in a space as a value called the Daylight Factor. In general, we can find the daylight factor on any surface by assuming that it is enclosed in a giant glowing sphere. The inside of this sphere is evenly lit and light is incident on all surfaces from all directions This makes Daylight Factor independent of solar orientation; the floor of a north facing room with a small window will have the exact same Daylight Factor value of an identical room that is facing South. Because of this, Daylight Factor values cannot be used to assess how much heat a space will gain but is excellent for other purposes such as if an office table near a window will need artificial lighting or not. Maximizing the Daylight Factor will earn you a thumbs up from a sustainability perspective but care should always be taken with regards to the solar irradiation entering these spaces.

Project Goals
For the train station at Montpellier, we had two Daylight Factor requirements:
1. The office spaces/ticketing counters should achieve a daylight factor of at least 1.0 (in blue)
2. The platform should achieve a daylight factor value of 0.5 (in red)


Solar Heat Gain
Since the station spaces are non-conditioned, another requirement was that the internal temperature could not be too high for the comfort of the occupants. This meant that we needed to keep the station as cool as possible. Even though we had a natural ventilation system in place, we also needed to make sure that the least amount of light penetrated the roof.

We were told that the station geometry is fixed and not editable. This meant that we could not relocate nor orient the roof or office spaces to suit our needs. The only way that we could regulate the light was by designing an appropriate roof perforation pattern. At first we applied constant perforation across the entire roof. We were easily able to achieve a Daylight Factor of 0.5 but, the offices spaces were still severely under-lit. Also, with a constant pattern the roof was not responding to its solar orientation and was allowing a large amount of direct light into the space.

Thus our design had to resolve two challenges
1. Design the perforations large enough to achieve the daylight factor of 1.0 at the offices
2. Respond to the solar orientation of the roof and minimize the solar heat gain.

Office Spaces
What proved most challenging was the office spaces as they were shaped like boxes and had only one surface open to light, the windows that faced the platform, all the other surfaces were opaque walls. In order to get light into these areas, we needed to strategically place fairly large perforations in the roof. The location of these large perforations was largely unknown and we would have experiment to find the best location. The image below shows two of the possible configurations for the large perforation panel locations.


Solar Orientation
In addition, we needed to adjust the size of the perforations according to the solar orientation.To resolve all these issues we created a parametric model of the entire roof where we changed the perforations of individual surfaces based on their solar orientation.


Parametric Model
The geometry of the roof is symmetric along two axes and consists of 5 longitudinal bays that form an arc. Each bay consists of a row of 4-sided concrete panels. Although all concrete panels were identical in geometry, each had a unique orientation with respect to the sun.

We could simulate the amount of solar irradiation falling on each of these panels using DIVA. The irradiation values were then used to size the perforations for that panel. For example, the side of the panel with the highest irradiation had the smallest perforations (thus blocking most of the light) and the side with the least irradiation had the largest perforations (letting most of the light pass though).

We can use our Grasshopper script to size the perforations automatically according to the simulation results. The script was set up so that we could assign a minimum and maximum perforation value as a percentage. For example we could apply perforations that fell within a range of 8-25% as shown above.


The next step was to run this perforated roof model though a simulation to calculate the daylight factor on the platform. Depending on the results we changed the range of the roof perforations. For example, if we needed more light we could change the range from 8-25% to 15-30%. Since the model is parametric the geometry is updated automatically and we are ready to run successive simulation quickly.

Daylight for Office Spaces
We designed the script so that we could choose specific areas of the roof that follow a different perforation range, much larger than the rest of the roof. These areas targeted the office zones and we ran several tests to make sure that we could achieve the Daylight Factor of 1.0 with the minimum number of the larger perforated panels. The images below are Grasshopper screenshots displaying the areas with the nominal perforation range (gray) and the areas where the perforation is higher to allow light into the office spaces (blue).

At this point the script is setup so that all the concrete panel perforations are responsive to their solar orientation. Also, we are able to select the range of perforation (as a percentage) and the zones that allow for a higher percentage perforation.

These parameters, the perforation range and the zones, are tweaked after each simulation until we reach our Daylight Factor goals. There was a discussion regarding the use of a genetic algorithm such as Galapagos, to solve for the optimized solution however there were some drawbacks to this method.

Given the intensity of the model it took approximately 40 minutes to run a single Daylight Factor simulation. If we were to use Galapagos it would take several days to have enough iterations from which we could evaluate an optimized result. For this specific case it was easier to establish an initial condition through intuition and then proceed to adjust the parameters from there.

The resulting roof is perforated such that it minimizes direct light entering the primary station volume, especially for the summer months when it is critical that we maintain a low, comfortable temperature within the space. At the same time the perforations are such that they allow plenty of ambient light to enter the station to illuminate the volume. The zones for larger perforations are situated to maximize the amount of ambient light into the office spaces.




Azhar Khan is a computational designer at Hugh Dutton Associates in Paris, France. Azhar studied aerospace engineering at Embry-Riddle Aeronautical University and then received his masters in aerospace engineering and architecture from the University of Florida. He is passionate about the role technology plays in the design process, sustainability and engineering. He currently develops digital tools that strengthen the firm’s multidisciplinary approach to architecture.